increased power flow guidebook

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Increased Power Flow GuidebookIncreasing Power Flow in Transmission and Substation Circuits

Effective December 6, 2006, this report has been made publicly available in accordance with Section 734.3(b)(3) and published in accordance with Section 734.7 of the U.S. Export Administration Regulations. As a result of this publication, this report is subject to only copyright protection and does not require any license agreement from EPRI. This notice supersedes the export control restrictions and any proprietary licensed material notices embedded in the document prior to publication.

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EPRI Project Manager R. Adapa

ELECTRIC POWER RESEARCH INSTITUTE 3420 Hillview Avenue, Palo Alto, California 94304-1395 ▪ PO Box 10412, Palo Alto, California 94303-0813 ▪ USA

800.313.3774 ▪ 650.855.2121 ▪ [email protected] ▪ www.epri.com

Increased Power Flow Guidebook: Increasing Power Flow in Transmission and Substation Circuits

1010627

Final Report, November 2005

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES

THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM:

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NOTE

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Electric Power Research Institute and EPRI are registered service marks of the Electric Power Research Institute, Inc.

Copyright © 2005 Electric Power Research Institute, Inc. All rights reserved.

iii

CITATIONS

This report was prepared by

EPRI 115 East New Lenox Road Lenox, MA 01240

Principal Investigator B. Clairmont

Power Delivery Consultants Inc. 28 Lundy Lane, Suite 102 Ballston Lake, NY 12019

Principal Investigators D. A. Douglass E. C. Bascom, III T. C. Raymond

J. Stewart 59 St. Stephens Lane N Scotia, NY 12302

This report describes research sponsored by the Electric Power Research Institute (EPRI).

The report is a corporate document that should be cited in the literature in the following manner:

Increased Power Flow Guidebook: Increasing Power Flow on Transmission and Substation Circuits. EPRI, Palo Alto, CA: 2005. 1010627.

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PRODUCT DESCRIPTION

The Increased Power Flow (IPF) Guidebook is a state-of-the-art and “best practices” guidebook on increasing power flow capacities of existing overhead transmission lines, underground cables, power transformers, and substation equipment without compromising safety and reliability. The Guidebook discusses power system concerns and limiting conditions to increasing capacity, reviews available technology options and methods, illustrates alternatives with case studies, and analyzes costs and benefits of different approaches.

Results & Findings The IPF Guidebook clearly identifies those cases where increasing power flow might be an alternative to upgrading the grid with major investment. The document reviews both established technologies and new developments in technologies with the potential to increase power flow—and addresses how to apply them for lines, cables, and substations. Because the guide compares the economic benefits of each available technology, it will assist utilities in making informed decisions in terms of what options for IPF are available and which options are most economical for application at their utility sites. By implementing one or more of the IPF technologies, utilities can obtain increased asset utilization with minimal cost. For example, if a utility decides to implement one of the IPF technologies, such as Dynamic Thermal Circuit Rating (DTCR) technology, that implementation will allow increased power flows on the order of 15-20% over the existing static ratings and, thus, increase utility revenue.

Challenges & Objective(s) Motivations for increasing power flow limits on existing transmission facilities (rather than constructing new facilities) are economic, environmental, and practical. Due to limited incentives for new construction and time delays that may result from public opposition to new power facilities, utilities around the world are being forced to find new ways of relieving modest constraints or increasing power flow through existing transmission corridors with minimal investment. This Guidebook will be an excellent reference document for transmission and substation engineers since it provides all possible IPF options in one place for ease of use.

Applications, Values & Use Training materials will be developed with the IPF Guidebook, including hands-on workshops at EPRI's full-scale laboratories. In addition, it is anticipated that, in the coming years, technical reports will be produced annually on new and updated aspects of IPF as well as new material on costing, economics, power storage, voltage upgrading, and case studies. This information will be incorporated into the Guidebook during subsequent work.

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EPRI Perspective Due to limited incentives for new construction, utilities around the world are undergoing a major transformation that is redefining the use of existing power equipment in the electric transmission network. Under these circumstances, utilities are forced to find new ways of increasing power flow through the existing transmission corridors with minimal investments. EPRI’s Increased Transmission Capacity Program directly responds to the needs of owners and operators of the transmission grid to get the most out of existing equipment in today’s competitive electricity business while increasing the availability and reliability of transmission and substation equipment. This Program helps customers accomplish these goals strategically, without jeopardizing reliability and driving up costs. A number of projects have been undertaken by EPRI in this Program under the Project Set 38A—Increase Power Flow Capability in the Transmission Systems. One major effort under Project Set 38A is the IPF Guidebook, the only available utility compendium of “best practices” for increasing power flow in transmission circuits. Other major EPRI developments include DTCR (Dynamic Thermal Circuit Ratings) software to calculate dynamic ratings of transmission circuits and Video Sagometer to measure sag of transmission lines.

Approach The Guidebook was developed by industry experts and draws on a combination of technology, documented case studies, and associated engineering and safety guidelines.

Keywords Overhead transmission Substations Transmission capacity Underground transmission

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ABSTRACT

The Increased Power Flow (IPF) Guidebook documents the state-of-science for increasing power flow capacities of existing overhead transmission lines, cables, and substation equipment. The Guidebook provides an overview of the electrical, mechanical, thermal, and system concerns that are important to increased power flow, presents all possible IPF options, uses case studies to illustrate the options, and compares their potential economic benefits. The Guidebook also provides an overview of dynamic thermal rating methods and summarizes other developments in hardware and software that are instrumental for IPF.

The IPF Guidebook provides utilities with the only available compendium of “best practices” for increasing power flow. The Guidebook will assist utilities in making informed decisions in terms of what options for IPF are available and which options are most economical for application at their utility sites.

Increased Power Flow Guidebook

Contents

Chapter 1 Increased Power Flow Fundamentals and Principles

1.1 INTRODUCTION 1-1

1.2 POWER SYSTEM ISSUES 1-2

1.3 LIMITING CONDITIONS 1-3

Circuit Power Flow Limits 1-3Surge Impedance Loading of Lines 1-4Voltage Drop Limitations 1-5Thermal Limits 1-6Environmental Limits 1-7Examples – Overhead Lines 1-8

1.4 CHAPTER PREVIEW 1-9

Overhead Lines (Chapter 2) 1-9Underground Cables (Chapter 3) 1-10Power Transformers (Chapter 4) 1-10Substation Terminal Equipment

(Chapter 5) 1-10Dynamic Rating and Monitoring

(Chapter 6) 1-10

REFERENCES 1-11

Chapter 2 Overhead Transmission Lines


Surge Impedance Loading 2-2Voltage Drop 2-2Thermal Limits 2-2Environmental Limits 2-2

2.2 UPRATING CONSTRAINTS 2-3

Introduction 2-3Sag-tension Calculations 2-3Limiting High Temperature Sag 2-5Uprating Constraints Related to Wind-Induced

Conductor Motion 2-8Electrical Clearance 2-10Loss of Conductor Strength 2-12Constraints on Structural Loads 2-13Environmental Effects 2-15

2.3 LINE THERMAL RATINGS 2-15

Introduction 2-15Maximum Conductor Temperature 2-16Weather Conditions for Rating Calculation 2-16How Line Design Temperature Affects Line Ratings 2-17Heat Balance Methods 2-17Thermal Ratings—

Dependence on Weather Conditions 2-21Transient Thermal Ratings 2-22

2.4 EFFECTS OF HIGH-TEMPERATURE OPERATIONS 2-23

Introduction 2-23Annealing of Aluminum and Copper 2-23Sag Tension Models for ACSR Conductors 2-27Axial Compressive Stresses 2-28Built–In Stresses 2-29Sag Tension Calculations 2-29Sag and Tension of Inclined Spans 2-31Calculation of Conductor High-Temperature Sag

and Tension 2-32Results of High-Temperature Sag Tension

Calculations 2-34Effects of Wind Speed on Thermal Ratings 2-40Thermal Elongation 2-41Creep Elongation 2-42Connectors at High Temperature 2-46Conductor Hardware 2-49

2.5 UPRATING WITHOUT RECONDUCTORING 2-51

Introduction 2-51Deterministic Methods 2-51Probabilistic Methods 2-56Development of a “Measure of Safety” as a Basis

for Line Rating 2-60Comparison of Probabilistic Rating Methods 2-62Device for Mitigating Line Sag - SLiM 2-62

2.6 RECONDUCTORING WITHOUT STRUCTURAL MODIFICATIONS 2-65

Introduction 2-65TW Aluminum Wires – ACSR/TW or AAC/TW 2-66ACSS and ACSS/TW 2-67High-Temperature Aluminum Alloy Conductors 2-70Special Invar Steel Core 2-70Gapped Construction 2-71ACCR Conductor 2-74Conductors with Exotic Cores 2-74Comparing ACSS and High-Temperature Alloy

Conductors 2-74

2.7 DYNAMIC MONITORING AND LINE RATING 2-75

Introduction 2-75Dynamic Ratings Versus Static Ratings 2-75Advantages of Dynamic Rating 2-76Disadvantages of Dynamic Rating 2-76Real-time Monitors 2-77Dynamic Rating Calculations 2-79Field Test Results 2-82Summary 2-84

2.8 CASE STUDIES 2-84

Introduction 2-84Selecting a Line Uprating Method 2-84Preliminary Selection of Uprating Methods 2-85Uprating Test Cases—Preliminary Uprating Study 2-87Economic Comparison of Line Uprating Alternatives 2-95

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Contents Increased Power Flow Guidebook

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Detailed Comparison of Uprating Alternatives—An Example 2-99

Conclusions 2-103

2.9 REFERENCES 2-104

Chapter 3 Underground Cables


3.2 CABLE SYSTEM TYPES 3-2

High-Pressure Pipe-Type (Fluid- and Gas-Filled) 3-2Extruded Dielectric 3-5Self-Contained Liquid-Filled (SCLF) 3-8Other Cable Types 3-10

3.3 POWER FLOW LIMITS AND SYSTEM CONSIDERATIONS 3-11

Thermal, Stability, and Surge Impedance Loading Limits 3-11

Load Flow Considerations 3-14Uprating Hybrid (Underground and Overhead)

Circuits 3-14

3.4 UNDERGROUND CABLE RATINGS 3-15

Introduction 3-15Concept of Ampacity 3-15Losses 3-16Equivalent Thermal Circuit and Thermal

Resistances 3-19Calculating Ampacity 3-23Effect of Various Parameters on Ampacity 3-24Emergency Ratings 3-25Inferring Conductor Temperatures from Measured

Temperatures 3-26

3.5 UPRATING AND UPGRADING CONSTRAINTS 3-26

Direct Buried Cable Systems 3-26Fluid-Filled Cable Systems 3-26Duct Bank Installations 3-27Trenchless Installations 3-27Other Installation Locations 3-27Hot Spot Identification 3-28Accessories 3-28Hydraulic Circuit 3-28

3.6 INCREASING THE AMPACITY OF UNDERGROUND CABLES 3-28

Route Thermal Survey 3-28Review Circuit Plan and Profile 3-36Evaluate Daily, Seasonal, or Other Periodic Load

Patterns 3-36Temperature Monitoring 3-38Ampacity Audit 3-40Remediation of “Hot Spots” 3-40Active Uprating 3-40Shield/Sheath Bonding Scheme 3-43

3.7 RECONDUCTORING (UPGRADING) 3-43

Introduction 3-43Larger Conductor Sizes 3-44

Cupric Oxide Strand Coating 3-44Voltage Upgrading 3-45Superconducting Cables 3-45

3.8 DYNAMIC RATINGS OF UNDERGROUND CABLE SYSTEMS 3-46

Background 3-46EPRI Dynamic Ratings on Cables 3-46Benefit of Dynamic Ratings 3-49Required Monitoring 3-51Quasi-Dynamic (Real-Time) Ratings 3-51

3.9 CASE STUDIES FOR UNDERGROUND CABLE CIRCUITS 3-51

CenterPoint Energy 3-51United Illuminating Company 3-53

3.10 SUMMARY OF UPRATING AND UPGRADING APPROACHES AND ECONOMIC FACTORS 3-55

REFERENCES 3-56

Appendix 3.1 Pipe-Type Ampacity Example 3-58

Appendix 3.2 Extruded Ampacity Example 3-65

Chapter 4 Power Transformers


4.2 TRANSFORMER DESIGN 4-2

General Construction 4-2Types of Cooling 4-5Losses 4-5Factory Testing 4-6

4.3 RISKS OF INCREASED LOADING 4-9

Short-Term Risks 4-9Long-Term Risks 4-11Additional Risks 4-18

4.4 THERMAL MODELING 4-21

Mechanisms of Heat Transfer 4-21Top Oil Model (IEEE C57.91-1995, Clause 7) 4-24Bottom Oil Model (IEEE C57.91-1995, Annex G) 4-26IEC Model (IEC 354-1991) 4-30Proposed IEC Model 4-32

4.5 THERMAL RATINGS 4-33

Ambient Air Temperature 4-34Load 4-34Rating Type and Duration 4-35Rating Procedure 4-35Condition-Based Loading 4-36Maintenance Considerations 4-37

4.6 WINDING TEMPERATURE MEASUREMENT 4-38

4.7 MODEST INCREASES IN CAPACITY FROM EXISTING TRANSFORMERS 4-39

4.8 EXAMPLES 4-39

REFERENCES 4-43

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Contents Increased Power Flow Guidebook

Chapter 5 Substation Terminal Equipment


5.2 SUMMARY—EQUIPMENT TYPES AND IPF OPPORTUNITIES 5-2

Equipment Rating Parameters 5-2Thermal Rating Parameter Comparison 5-4

5.3 THERMAL MODELS FOR TERMINAL EQUIPMENT 5-4

Bus Conductors 5-4Switch (Air Disconnect) 5-6Air-core Reactor 5-8Oil Circuit Breaker 5-9SF6 Circuit Breaker 5-10Bushings (Oil-immersed Equipment Only) 5-10Current Transformers 5-11Line Traps 5-11Other Types of Terminal Equipment 5-12

5.4 UPRATING OF SUBSTATION TERMINAL EQUIPMENT 5-12

Monitoring and Communications 5-13Maintenance and Inspection Procedures 5-13Reliability and Consequences of Failure 5-13

5.5 THERMAL PARAMETERS FOR TERMINAL EQUIPMENT 5-14

Manufacturer Test Report Data 5-14

5.6 CONCLUSIONS AND SUMMARY 5-14

REFERENCES 5-15

Chapter 6 Dynamic Thermal Ratings Monitors and Calculation Methods


6.2 ISSUES RELATED TO DYNAMIC THERMAL RATING METHODS 6-2

Where Should Dynamic Thermal Circuit Rating Calculations Be Performed? 6-2

Costs—Capital and Otherwise 6-3Why Dynamic Ratings Go With Increased Utilization 6-4

6.3 POWER EQUIPMENT CONDITION ASSESSMENT AND REAL-TIME MONITORS 6-4

6.4 DYNAMIC THERMAL RATING MODELS FOR POWER EQUIPMENT 6-5

Accounting for Heat Storage (Pre-load Monitoring) 6-5Overhead Lines 6-6Power Transformers 6-7Underground Cables 6-10Substation Terminal Equipment 6-11

6.5 EPRI'S DTCR TECHNOLOGY 6-13

Power Circuit Modeling 6-13DTCR Output 6-13DTCR is a Calculation Engine for SCADA 6-14Modeling Complex Interfaces—California “Path 15” 6-14Conclusions about the Dynamic Rating of Complex

Interfaces 6-16

6.6 OPERATING WITH DYNAMIC THERMAL RATINGS 6-16

Traditional Rating Definitions 6-16Traditional Operating Rules 6-17Operating with Dynamic Ratings 6-17

6.7 FIELD STUDIES OF DYNAMIC RATINGS 6-19

Overhead Lines 6-19Power Transformers 6-20Underground Cables 6-20Substation Terminal Equipment 6-20Power Circuits 6-20Communications and Monitoring 6-21

6.8 CONCLUSIONS 6-21

REFERENCES 6-22

Glossary G-1

Index I-1


CHAPTER 1 Increased Power Flow Fundamentals and Principles

1.1 INTRODUCTION

The purpose of this guidebook is to provide technical information and explain conceptsthat may aid power transmission company technical personnel in finding economic, tech-nically sound ways to increase the power flow capacity of existing circuits without com-promising safety or reliability.

The motivations for increasing the power flow limits on existing transmission facilities(rather than constructing new facilities) are economic, environmental, and practical. Themethods discussed are generally modest in cost—ranging from virtually free to about30% of the cost of equipment replacement. The corresponding increase in equipment rat-ing is similarly modest, usually between 5% and 30% (with the exception of overheadlines where reconductoring may yield an increase of over 100%). The methods are practi-cal since the environmental and/or visual impact is normally low, regulatory approval andpublic hearings may not be needed, and extended power outages are often avoided.

Given the extended time delays that may result from public opposition to the construc-tion of new power transmission facilities or even to any visible, physical modification ofexisting facilities, the use of increased power flow (IPF) methods may offer the only prac-tical solution to relieving modest constraints on power flow.

Determining the degree to which maximum power flow constraints can be eased on existingpower equipment (overhead lines, power transformers, etc.), power circuits (multiple powerequipment elements in series), and power system interfaces (multiple “parallel” power cir-cuits connecting power system regions) can be quite complex. For example, consider the fol-lowing:

• For an overhead line, any increase in power flow capacity is dependent on its length, theoriginal design assumptions, present-day environmental concerns, the condition of itsexisting structures, and the type of conductors originally selected. Depending on thesemultiple factors and which of the IPF methods suggested in Chapter 2 is applied, theresulting increase in the line’s thermal rating could be as little as 5% or as much as 100%.

• But overhead lines are only part of the transmission path (circuit). The lines are termi-nated at substations by air disconnects, circuit breakers, line traps, etc. The power flowthrough all of the circuit elements must be limited to avoid damaging the line or the termi-nating equipment, and the maximum allowable power flow over this circuit may be limitedby any one of the circuit elements.

• Finally, when seen as part of a power system interface, any increase in maximum allow-able power flow through any component circuit or circuit element does not necessarilyyield a higher rating for the complex interface.

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Chapter 1: Increased Power Flow Fundamentals and Principles Increased Power Flow Guidebook

In general, it may be stated that maximum power flow onthe transmission system is a function of the overall systemtopology (transmission lines, transformers, generation,series and shunt compensation, and load), and that manynon-thermal system considerations can also limit themaximum power flow on a specific transmission circuit.Therefore, transmission circuit ratings are often developedon a system basis, rather than on an individual line basis.The overall limit may be between operating areas irre-spective of ownership or individual lines, and may changeduring a day based on system conditions.

Chapter 1 provides an overview of the electrical,mechanical, thermal, and system concerns that areimportant to increased power flow. The chapter includesthree sections:

• Section 1.2, Power System Issues, presents a simplepower flow example to illustrate several principlesabout increasing power flow.

• Section 1.3, Limiting Conditions, describes limits onpower flow imposed by circuit power flow, surgeimpedance loading, voltage drop, thermal factors,and environmental constraints.

• Section 1.4, Chapter Previews, presents brief descrip-tions of the chapters in this guidebook.

1.2 POWER SYSTEM ISSUES

The power transmission system, in any region, is a com-plex combination of lines (including underground cable)and substations. With the exception of relatively short“radial” lines connecting generating stations to the sys-tem, power flow reaching any load point in the systemflows over multiple “parallel” paths (circuits). In anypath (circuit), the power flow moves through multipleseries elements.

This can be illustrated by the following simple powersystem (NERC 1995) shown in Figure 1.2-1. There arethree load areas (A, B, and C). Each load area has suffi-cient generation to supply the local load. With the sys-tem operating “normally,” there is no net power transferbetween load areas. Nonetheless, as a result of the avail-able electrical paths connecting the load areas, the dia-gram shows a “loop” flow of 200 MW. This loop flowoccurs even though there is no net power transfer to anyof the areas.

Consider the situation where power generated in loadarea A is considerably less expensive than local genera-tion in load area B. It would then be advantageous forpower customers in load area B to buy power from thegenerators in load area A. In doing this, the powertransmission system operator sets a transfer limit of

2834 MW from A to B. Given this level of transfer, thepower flows would be as shown in Figure 1.2-2.

Notice in Figure 1.2-2 that, even though load area C isnot importing power, the lines connecting load area C tothe other areas are carrying almost half of the totalpower transferred.

Now let us assume that the customers in load area Bwould like to buy even more than 2834 MW from thelow-cost generator in load area A. Consequently, theycontest the limit of 2834 MW set by the system opera-tor, noting that the emergency rating of the lines is 1000MW. The power system operator explains that the limi-tation on power import to load area B is not due to nor-

Figure 1.2-1 Base system operating "normally" with local generation being similar in cost and able to supply all local load.

Figure 1.2-2 Base system operating "normally" with local generation at A being much cheaper than at B, causing a net power transfer of 2834 MW.

1-2

Increased Power Flow Guidebook Chapter 1: Increased Power Flow Fundamentals and Principles

mal power flows but rather to the emergency power flowthrough one of the lines (#2) between A and C, asshown in Figure 1.2-3! With line #1 out of service, theredistributed power flow through line #2 reaches theemergency thermal limit of 1000 MW. Thus the imposedpower transfer limit of 2834 MW from A to B.

As shown in Figure 1.2-3, if the net power transfer fromA to B with all lines in service had exceeded the transferlimit of 2834 MW then, under this single contingencyloss of line #1 between A and C, the power flow in line#2 from A to C would have exceeded the line’s emer-gency thermal limit.

One can reach a number of conclusions regarding powerflow limits from this simple example:

• Economic power transfers can be limited by circuitsthat do not directly connect the low-cost generationsource and the customer.

• A 5% increase (50 MW) in the emergency rating oflines #1 and #2 connecting A and C from 1000 MWto 1050 MW might allow a similar 5% increase(141 MW) in the power transfer limit from 2834 to2975 MW.

• A 5% increase in the emergency rating of either line#1 or #2 between A and B would not allow anyincrease in power transfer from A to B.

• The long-term value of projects to increase thepower flow in any particular circuit is dependent onchanges in the cost of generation and the power flow

limits and electrical impedance of interconnectedpower circuits.

• Note that these observations do not depend on thereason for the power flow limit in any of the circuits.They would be equally valid whether the limitationon power flow is due to equipment temperature lim-its, limits on voltage drop, or electrical phase shiftstability issues.

1.3 LIMITING CONDITIONS

1.3.1 Circuit Power Flow Limits

Power circuits consist of series and parallel combina-tions of electrical equipment (each subjected to mechan-ical, electrical, and thermal stresses) whose collectivepurpose is to transmit power safely and reliably underwidely varying operational situations. Each element ofsuch circuits is typically specified to have certain powerflow limits that allow their safe, reliable operation for anextended period of time (e.g., 40 years).

Increased power flow inevitably means increased electri-cal current flow or increased circuit voltage since poweris the product of these quantities. In general, for substa-tion equipment and underground cables, increasing theoperating voltage is difficult or impossible, whereasincreasing the maximum electrical current is both possi-ble and economic. Overhead lines are often capable ofeither higher voltage or higher current levels if certainmodifications are undertaken.

Power transmission circuits are typically bimodal interms of power flow. Under normal operation, it is notunusual for power transformers and lines to operate atmuch less than half of their power flow capacity, onlyapproaching their operational limits under relativelyrare emergency events.

There are basically three methods of increasing powerflow: load control, improved modeling and monitoring,and physical modification of existing circuits.

Improved models may allow operation of equipmentwith reduced safety factors without reducing safety andreliability. Examples are the “bottom oil” model inAnnex G of the IEEE loading guide and the improvedmodels for high-temperature sag of ACSR conductor.

Similarly, monitoring of environmental factors (air tem-perature, wind speed, humidity, etc.) may allow the useof less conservative assumptions, again without reduc-ing safety and reliability.

Figure 1.2-3 Base system operating in response to a “single contingency” outage of line #1 between A and C while there is a power transfer of 2834 MW from A to B.

1-3


With monitors communicating data in real-time, it maybe possible to run equipment at higher power levels mostof the time by avoiding the use of “worst case” assump-tions. This approach is called dynamic thermal ratings. Itis unlikely that such real-time monitoring would allowany increase in non-thermal operating limits.

Overhead transmission lines are the primary means ofpower transfer over long distances. They have thermalratings just as power transformers, substation terminalequipment, and underground cables but, for long lines,power flow limits may also be necessary to avoid exces-sive voltage drop or system stability problems. In addi-tion, since the public has access to the area under lines,there may also be limits on voltage and current relatedto environmental effects. This section concerns the rela-tionship between the various types of power flow limitsfor overhead lines.

1.3.2 Surge Impedance Loading of Lines

Sometimes a power transmission line possesses a defi-nite power flow limit based on the design parameters forthe specific line, but at other times, the line as a compo-nent of the overall transmission system determines thelimit. System limits can result from factors such as volt-age drop, possibility of voltage collapse, and system sta-bility, both steady state and transient.

System limits are functions of transmission line reac-tances in relation to the overall power system. Seriesreactance, shunt admittance, and their combination,surge impedance, are relevant to system transfer limits.System planners have long recognized this relationship,particularly where there are prospects of changing theline surge impedance, either by adding equipment (e.g.,series capacitors) or by modifying the line itself (e.g.,reconductoring, voltage uprating, etc.).

Transmission line series inductive reactance is deter-mined by conductor size, phase spacing, number of con-ductors, relative phasing (double-circuit lines), and lineconfiguration. In transmission lines the series reactanceis significantly larger than the series resistance, and isthe dominant factor in a first-order explanation of sys-tem behavior. For this reason, simple reconductoring ofa transmission line results in only minor changes in sys-tem power flows.

Power flow on a transmission line, neglecting resistanceof the line, is given by Equation 1.3-1, which can bederived from a simple circuit consisting of sending andreceiving end voltage sources connected by a series reac-tance.

1.3-1Where:P = Real power transfer on the transmission line.V1 = Magnitude of sending end bus voltage.V2 = Magnitude of receiving end bus voltage.X = Line series inductive reactance between V1 and

V2.δ = Phase angle difference between V1 and V2.

Increasing voltage magnitude for the same line voltageand same phase difference between ends increases thepower flow. By increasing the voltages V1 and V2together, the power transmitted increases by the squareof the voltage for the same phase angle. Power flowincreases for the same end voltage magnitudes areaccommodated by an increase in the phase angle differ-ence between the voltages at the two line ends.

Equation 1.3-1 imposes a fundamental limit on theamount of power that can be carried by a transmissionline corresponding to a phase difference between lineends of 90° . Further increases in angle result indecreases in power flow. This is an unstable situationthat can be realized in practice in two ways. If thesteady-state power flow were to slowly increase to thepoint that the angle reached 90°, an attempt to furtherincrease power flow would actually decrease the powerflow. An increase in the power angle δ when δ is in therange from 90° to 180° results in a decrease in sin(δ) anda consequent decrease in power flow. The condition try-ing to increase the flow on the line actually results in adecreased flow, and system instability.

Secondly, a system disturbance—for example, trippingof a line—causes a redistribution of power flow amongthe remaining lines, and consequent changes in the busvoltage angles. It is insufficient that the new angle differ-ences on all the lines are less than 90°, because the angledifferences must remain lower than 90° during all thetransient system swinging from the time of the distur-bance until the system settles in its new operating state.If a line were to experience its angle difference momen-tarily passing 90°, it would try to accommodate thepower requirement by opening up the angle beyond 90°,decreasing the power flow. This is an unstable situation,and would cause the line to pass through the electricalpoint where its relay protection would sense a fault(even though none exists on the line), and result in a linetrip and probable system separation.

Surge impedance loading (SIL), defined in Equation1.3-2) provides a useful rule of thumb measure of trans-

1 2 sin( )V VP

X

δ• •=

1-4


mission line loading limitation as a result of the effectsof series reactance.

1.3-2

Where V is the line voltage, and ZS is the surge impedanceof the transmission line given by:

1.3-3

Surge impedance ZS is a resistance in ohms. L and C inEquation 1.3-3 are positive sequence inductance andcapacitance in henries per mile and farads per mile,respectively. Surge impedance loading is that loading ona three-phase power transmission line that it would haveif it were loaded by a Y-connected set of resistances ofZS ohms per phase. This is the same physical conditionas a radio frequency transmission line impedancematched to its termination (72 ohm coaxial cable termi-nated in 72 ohms in television cable). In electromagnetictheory, it corresponds to a pure TEM wave. The reactivepower (vars) generated in the line capacitance is exactlycanceled by the vars absorbed in the line inductance in apower transmission line at surge impedance loading(neglecting line resistance and real power losses). Surgeimpedance loading thus is a loading value based onphysical principles related to the line design itself.

Surge impedance loading is a handy tool for estimatingthe relative loading capabilities of lines of different volt-ages, constructions, and lengths from a system stand-point (St. Clair 1953). SIL is oversimplified for use inspecifying actual line ratings on an operating system.However, it is a useful guide both for assessing actualloading limits and for understanding the different fac-tors that limit line loading. Figure 1.3-1 gives a curve ofline loadability in per unit of SIL as a function of linelength for heavy loading conditions. Slightly differentversions of Figure 1.3-1 have been published, but theyare all very similar (Dunlop et al. 1979, Gutman 1988).The fundamental observation from Figure 1.3-1 is thattransmission line loadability decreases as length of theline increases. Three different regions come into play inderivation of Figure 1.3-1. Short lines tend to be ther-mally limited, irrespective of system conditions. As linelength increases, voltage drop considerations frequentlycome into play. At longer line lengths, stability factorsmay dominate. Short lines are often loaded at 2 or 2.5times SIL and thus need reactive power (var) support tomaintain the voltage. Long lines may be limited to 1.0times SIL or less.

An important observation from Equation 1.3-2 is thatsurge impedance loading is a function of the square ofline voltage. This has been a driving force in increasedtransmission voltages over the years, especially forlonger lines.

For an overhead transmission line, typical surge imped-ance is on the order of 300 ohms, while for a cable itmay be 50 ohms or less. At 345 kV, SIL of an overheadline is on the order of 400 MW. Short lines may be ableto carry 800 MW or more, while long lines of exactly thesame construction may be limited to less than 400 MWby system considerations. Because of limitations on heatdissipation, underground transmission cables alwaysoperate very far below SIL. A consequence is thatunderground transmission cables are a net source ofvars to the system, a condition that must be consideredin system design.

1.3.3 Voltage Drop Limitations

Voltage control on the power system is of concern assystem loadings increase. The system voltage distribu-tion is affected by the series inductance and shuntcapacitance of the transmission lines, and is related tothe flow of reactive power in the system. Depending onthe relative real and reactive power flow on a giventransmission line, the voltage may increase or decreasefrom one end to the other. It is not desirable for voltageto vary more than 5%, or at most 10%, from one end to

2

S

VSIL

Z=

S

LZ

C=

Figure 1.3-1 Line loadability in terms of surge impedance loading (Dunlop et al. 1979).

1-5


the other. In some cases, a voltage drop limit is placedon power flow corresponding to the maximum allowabledecrease in voltage magnitude. The longer the line orcable, generally the lower the power flow required toreach a voltage drop limit. Voltage control is a systemproblem, and is not generally solved by modifications toany one transmission circuit.

Methods to improve voltage control on transmissioncircuits may take a variety of forms:

1. In some cases, bundled conductors have been in over-head lines used for short lower voltage lines to reduceseries reactance, where the use of bundled conductorsis required neither for thermal or corona reasons.

2. Supply of vars at various points on the system can beused to control voltage. The supply can be fixed,switched, or adjustable. In former years synchronouscondensers were used to supply vars in a continu-ously adjustable basis. Capacitor banks are com-monly used, and may be switched on or offdepending on the local voltage. Static var compensa-tors (SVCs) are also used to control voltage on thebulk power system.

3. Shunt reactors may be used for long EHV lines wherethe var supply from the line capacitance is greaterthan the system can absorb.

Because voltage drop is primarily a function of linereactance rather than resistance, simple reconductoringdoes very little to decrease the voltage drop per unitlength. Reconductoring an existing 230-kV line byreplacing the original 636 kcmil Hawk ACSR with a 954kcmil Rail ACSR only increases the voltage drop limitby 5%. For an overhead line, adding a second conductorper phase to form two conductor bundles results in amore significant reduction in series reactance, and agreater improvement in voltage drop power limit.

Shunt reactors may be applied for reasons other thanvoltage control—for example, to control transient over-voltages during line switching. Series capacitors may beused to partially compensate for the line series reac-tance, but this is usually reserved for the longest lines inrelation to system stability. Whenever capacitors areinstalled in series with the transmission line inductance,the possibility of a series resonant condition exists. Sub-synchronous resonance has been the cause of genera-tor/turbine shaft failure and is a serious considerationfor a series capacitor installation.

Other problems present themselves with series capaci-tors—for example, provision for passage of fault currentwithout causing failure of the capacitors. The overalleffect of the concern with system voltage is that a partic-

ular transmission line may be limited in its power-han-dling capacity by system voltages and var f lowsirrespective of the thermal capacity of the line conduc-tors. In some cases, it is possible to increase the lineflows by addition of capacitors or similar measures.Flexible AC Transmission (FACTS) is a scheme wherethyristor-controlled devices are arranged to provide real-time control of transmission line flows in excess of thosethat would normally be allowed by system voltage andstability considerations.

While voltage drop has long been known as a transmis-sion limitation, attention has also been focused in morerecent years on voltage collapse, which is a system insta-bility that can occur under heavy loading conditions.Figure 1.3-2 shows a voltage collapse condition follow-ing a system disturbance, where the 115-kV voltagedrops to 50% of the nominal operating voltage (0.5 p.u.).Voltage collapse can occur for several reasons on aheavily loaded system where there is insufficient var sup-port. An example is the geomagnetic storm of March 13,1989, with its resulting voltage collapse and blackout.The March 1989 storm increased attention to systemproblems that result from solar activity. Utilities in areassubject to geomagnetic disturbances monitor solar activ-ity (Lesher et al. 1994), and can re-dispatch generationto reduce loading on affected lines during times of highgeomagnetic activity. However, geomagnetic distur-bances are not the only cause of voltage collapse.

1.3.4 Thermal Limits

Thermal limits are discussed in considerable detail laterin this guidebook (see, for example, Section 2.3). Inbrief, the current-carrying capacity (thermal rating) ofan overhead transmission circuit is determined by theassumed “worst-case” weather conditions, assumed

Figure 1.3-2 Voltage collapse condition following a system disturbance.

1-6


conductor parameters, and the maximum allowableconductor temperature. Some of the specific thermalrating parameters are:

• Conductor construction: outside diameter, conductorstrand diameter, core strand diameter, number ofconductor strands, and number of core strands.

• Conductor AC resistance, which itself is a function ofthe conductor temperature.

• Conductor surface condition: solar absorptivity andemissivity.

• Line location: latitude, longitude, conductor inclina-tion, conductor azimuth, and elevation above sealevel.

• Weather: incident solar flux, air temperature, windspeed, and wind direction.

The temperatures experienced by terminal equipmentmust also be limited. In certain circuits, the thermal rat-ing of substation equipment, in series with an overheadline, may determine the “circuit” rating. Disconnectswitches, wave traps, current transformers, and othersubstation equipment all have current ratings that canbe lower than those of the line. An example of terminalequipment limitations on older lines is 600 A disconnectswitches. At EHV, bundled conductors are employed toreduce the conductor surface electric field and conse-quent corona phenomena of radio, television, and audi-ble noise. Bundled conductors were original lyintroduced to lower line reactance and increase the lineloadability, and their use for noise reduction was recog-nized later. Especially at the higher transmission volt-ages of 500 and 765 kV, the thermal current-handlingcapacity of a bundled conductor may be far in excess ofthe ratings of the circuit breakers. In such cases, thethermal limit of the circuit is entirely dominated by theterminal equipment. A survey of utility 345-kV circuitthermal limits in New York State gave the following lim-itations:

• 41% of the circuits were limited by the line or cable.

• 18% of the circuits were limited by current transform-ers.

• 4% of the circuits were limited by wave traps.

• 4% of the circuits were limited by the bus-work.

• 3% of the circuits were limited by disconnectswitches.

• 4% of the circuits were limited by the circuit breakers.

Lines and substation equipment may have differentthermal ratings for normal and for emergency systemconditions. Emergency ratings typically apply for a lim-ited period of time, not exceeding 24 hours and as short

as 5 minutes. Emergency ratings are typically calculatedfor higher temperatures, and allow for some equipmentdeterioration in order to avoid load interruptions underunusual operating conditions.

Broader voltage tolerances may also be appropriateunder contingency conditions compared to normaloperation. Lower voltage may be acceptable for a shorttime. Likewise, conductor resistive power losses areinconsequential during emergencies.

1.3.5 Environmental Limits

The electric field produced by overhead power transmis-sion lines is influenced by the following factors:

• Line voltage.

• Height of conductors above ground.

• Configuration of conductors (line “geometry,” con-ductor spacing, relative phasing of multi-circuit lines,and use of bundled conductors).

• Lateral distance from the center line of the transmis-sion line.

• Height above ground at the point of field measure-ment.

• Proximity of conducting objects (trees, fences, build-ings) and local terrain.

The electric field near ground level produced by an over-head transmission line induces voltages and currents innearby conducting objects. These objects are typicallythe size of people, animals, motor vehicles, sheds, andsimilar-sized bodies. Electric field coupling is capacitivecoupling, and can be represented by a current source inparallel with a high source impedance (Norton equiva-lent circuit).

The allowable electric field is limited by the maximumallowed induced current and voltage. For example, theNational Electrical Safety Code specifies a maximum of5 mA short-circuit current induced into the largest vehi-cle that could be stopped under the line, based onhuman susceptibility to loss of muscular control (let-go). Thus, if an existing line induces 4.9 mA on a largetractor-trailer, it would not be possible to increase thevoltage without taking other measures to limit the elec-tric field.

Electric field levels are limited by law in some jurisdic-tions. Some regulations are specified at the edge of theright-of-way for public exposure. Other regulations aremaximum levels on the right-of-way based on inductionto an assumed size object. These regulations may restrict

1-7


voltage increases on presently existing transmission lineswithout taking electric field reduction measures.

Magnetic field is affected by the same variables as elec-tric field, except line current replaces line voltage, andnearby objects generally have minimal impact on themagnetic field. Magnetic field coupling is generally ofsignificance for objects that parallel the transmissionline for a long distance. Such objects include pipelines,telephone and railway signal circuits, and metal fences.Because magnetic field is a function of line current, andcurrent increases during fault conditions, it may be nec-essary to evaluate magnetic field effects under both nor-mal operation and faults. Magnetic field coupling isinductive coupling, and generally produces low voltageswith low source impedances.

Increasing current on a transmission line increases themagnetic field, and thus increases magnetically inducedvoltages and currents. This may be significant in casessuch as when a transmission line parallels a railroadright-of-way. This is the inductive coordination problemthat has been around since the dawn of the power indus-try with respect to telephone and railroad signal facili-ties. Increasing current flow on existing lines mayrequire coordination with parallel infrastructure. Insome jurisdictions, maximum magnetic field levels arespecified by regulation. If an existing transmission line isoperating near the magnetic field limit set by regulation,the ability to increase line current may be impaired,unless measures are taken to reduce the magnetic fieldlevels.

Electric fields can be shielded by conducting objects.Vegetation is sufficiently conductive to reduce electricfield levels. Grounded wires can be strung under thephase conductors at road crossings to reduce electricfield levels. Grounding measures can be taken for fixedobjects to eliminate induced voltages. On the otherhand, magnetic field shielding is significantly more diffi-cult than electric field shielding. Shielding a transmis-sion line by magnetic materials is impractical. Fluxcanceling loops have been developed, but incur powerloss and complexity in actively driven loops. Shielding isless practical as a mitigation measure for magnetic fieldsthan it is for electric fields.

1.3.6 Examples – Overhead Lines

Figure 1.3-3, adapted from (Gutman 1988), repeats thegeneralized SIL curve of Figure 1.3-1 with the additionof a curve for thermal limitation. Superimposed on theSIL curve are curves for:

• Thermal limit for a single 1414 kcmil conductor perphase.

• Voltage drop limitation of 5%.

• Steady-state stability margin of 35%.

The thermal and voltage drop limitation curves cross ata line length of approximately 110 miles. The voltagedrop and stability limitation curves cross at a line lengthof approximately 190 miles. Based on the thermal, volt-age, and stability curves, three regions are identified inFigure 1.3-3.

Figure 1.3-3 Three line loading limits: thermal limit, voltage drop, and steady-state stability.

1-8


• Less than approximately 110 miles line length, theline is thermally limited.

• Between approximately 110 and 190 miles line length,the line is limited by voltage drop.

• Beyond approximately 190 miles, the line is stabilitylimited.

Figure 1.3-3 thus illustrates the three regimes of line-loading limits. Figure 1.3-3 further illustrates that, for aspecific transmission line example, the data points forthe line fall near, but not on, the generalized SIL curve.The fact that the values are similar, but not identical,illustrates the point that the SIL curve is a handy refer-ence for sanity checking and rule of thumb analysis, butis not to be considered exact for any specific line.

Sample surge impedance and thermal loading values fortransmission lines of different voltages are given inTable 1.3-1.

For comparison with the 345-kV example in Figure 1.3-3, the 230-kV example in Table 1.3-1 has a thermal rat-ing of 440 MW and surge impedance loading of 145MW. Stability and voltage control limits for this linedepend on the system to which it is connected. As anexample of voltage drop, assume the 230-kV line is 100miles long. Further assume that the sending end bus hasa voltage of 1.0 per unit, and the receiving end bus has avoltage of 0.95 per unit, a 5% difference. Also assumethe 230-kV line is at 1.0 power factor at the receivingend, neither taking nor supplying vars to the bus. In thiscase, the 230-kV line flow would be 220 MW, about 1.5times SIL, but half the thermal rating. This result is inline with the 345-kV example given in Figure 1.3-3.

Because SIL is primarily related to transmission lineseries reactance rather than resistance, simple reconduc-toring would produce only a minor effect on SIL limitssuch as voltage drop. In this 230-kV example of 5% volt-age drop, reconductoring from Cardinal to FalconACSR would increase the loading from 220 MW to 230

MW, a minor difference. Adding a second Cardinal con-ductor per phase to make two conductor bundles wouldincrease the loading to 310 MW. Adding a second con-ductor per phase has a greater impact on surge imped-ance, and thus on SIL and line loading. Full use of the230-kV line’s thermal rating would require systemchanges to provide var support at the receiving end ofthe line.

The thermal limit is determined by line current and linevoltage. Equation 1.3-2 shows that surge impedanceloading is proportional to the square of the line voltage.Doubling line voltage doubles the thermal rating of theline, but multiplies SIL by a factor of 4. This has beenthe driving force during the history of the electric powerindustry for increasing voltage levels, and sometimes amotivation for voltage upgrades of existing lines.

1.4 CHAPTER PREVIEW

1.4.1 Overhead Lines (Chapter 2)

Overhead transmission lines are the predominantmethod of transporting power in any but the mosturbanized power systems such as the New York Cityarea. Of all the types of power equipment, overheadlines offer the largest opportunities for increased powerflow at modest cost. Limits are placed on power flowthrough overhead lines in order to limit electrical phaseshift, avoid excessive voltage drop, and limit the temper-ature of the current-carrying conductors. The emphasisin this book is on the latter of these limits.

Chapter 2 discusses the reasons for limiting the temper-ature of overhead lines and the consequences of exceed-ing such limits. The chapter also covers the techniquesfor modifying the clearance of existing lines, reconduc-toring them without rebuilding structures, and real-timemonitoring of weather and line sag-tensions.

A number of interesting case studies are included at theend of the chapter.

Table 1.3-1 Power Flow Limits on Lines and Cables

System XL XCSurge

Impedance SILThermal Rating

kV (Ω/mi) (Ω/km) (MΩ-mi) (MΩ-km) (Ω) (MW) (MW)

Transmission Line Characteristics

230 0.75 0.47 0.18 0.29 367 145 440

345 0.60 0.37 0.15 0.24 300 400 1500

500 0.58 0.36 0.14 0.26 285 880 3000

765 0.56 0.35 0.14 0.26 280 2090 8000

Transmission Cable Characteristics

345 .25 .16 .0060 .0097 39 3050 2100

1-9


1-10

1.4.2 Underground Cables (Chapter 3)

Chapter 3 provides an overview on underground cablesystems and a very brief background on each of themajor transmission cable types. As with overhead lines,the discussion on underground cable considers aspectsexternal to a specific cable circuit that may limit powerflow regardless of the cable circuit’s rating. The chapteralso includes an overview on cable system ampacity,including worked examples.

The major barriers to increased underground cable rat-ing are inherent to each cable system type or installationlocation. Methods for increasing the rating of under-ground cable—such as surveying the soil thermal resis-tivity along the route and removing thermal bottlenecksdue to other cable circuits or external heat sources—arediscussed in some detail.

Given the relatively long thermal time constant ofunderground cables, dynamic rating methods are veryattractive ways of increasing the rating. The chapter dis-cusses monitoring methods and the necessary real-timedata required for dynamic rating calculations withunderground cable.

Case studies are included for actual cable upratingprojects, and the chapter provides a summary compari-son of uprating methods.

1.4.3 Power Transformers (Chapter 4)

Power transformers represent a significant portion ofcapital investment costs. Under existing conditions inthe industry, utility budgets are reduced and networksare being forced to support greater power transfer overexisting transmission circuits than ever before. As such,there is increased interest in safely utilizing all availablecapacity of power transformers.

In general, transformer load capacity is limited by equip-ment (winding and oil) temperatures. Industry standards(IEEE C57.12.00 in the U.S.) specify a maximum averagewinding rise that defines the rated load. In other words,when operating at rated nameplate current, the averagewinding rise shall not exceed the given value.

Chapter 4 describes the general construction of powertransformers, outlines short- and long-term risks relatedto the loading of transformers, provides an overview ofheat transfer mechanisms and describes the four mostprevalent thermal models, and discusses factors behindthermal ratings, including ambient air temperature,load, and maintenance considerations.

1.4.4 Substation Terminal Equipment (Chapter 5)

Substation terminal equipment consists of many differ-ent types and designs of power equipment. Included inthis classification are line traps, oil circuit breakers, SF6

circuit breakers, rigid tubular bus, line disconnects, cur-rent transformers, bolted connectors, and insulatorbushings. The increase in circuit rating, resulting fromapplying the various methods of increasing power flowin overhead transmission lines, underground cable, andpower transformers is often limited by terminal equip-ment. In some cases, a large increase in circuit ratingmay be obtained for a very modest expenditure on ter-minal equipment rather than a relatively large invest-ment in lines, cables, or transformers.

Chapter 5 describes practical, rather simple methods ofincreasing the power flow through less capital-intensiveequipment such as switches, bus, line traps, breakers,and power transformer auxiliary equipment. The chap-ter includes a summary of terminal equipment types,specific thermal models for each type of equipment,dynamic thermal rating of terminal equipment, andmethods of determining specific thermal parametersfrom field test, laboratory test, and manufacturer heat-run tests.

1.4.5 Dynamic Rating and Monitoring (Chapter 6)

Since the mid-1980s, considerable attention has beenpaid to increasing the power flow of overhead lines,power transformers, underground cables, and substationterminal equipment by means of monitoring weatherand the equipment thermal state and by developingmore accurate thermal models. The resulting dynamicthermal rating techniques typically yield increases of 5to 15% in capacity.

Chapter 6 provides an overview of dynamic thermal rat-ing methods. The chapter aims to present a balancedoverall view of when dynamic rating methods are appro-priate, how they are best implemented in a practicaloperational application, and how such methods can beapplied to complex interconnections consisting of multi-ple circuits and many circuit elements.

The chapter discusses concerns related to dynamic rat-ings; outlines the need for inspections and/or real-timemonitors and the problems that may arise without them;provides an overview on models for overhead lines, trans-formers, underground cables, and substation terminalequipment; describes the use of DTCR software; identi-fies operating issues related to dynamic thermal ratings;and describes field studies of dynamic ratings used foroverhead lines, transformers, underground cables, substa-tion terminal equipment, and power circuits.


REFERENCES

Boteler, D. H. 1994. “Geomagnetically Induced Cur-rents: Present Knowledge and Future Research.” IEEE Transactions on Power Delivery. Volume 9. Number 1. January. pp. 50-58.

Dunlop, R. D., R. Gutman, and P. P. Marchenko. 1979. “Analytical Development of Loadability Characteristics for EHV and UHV Transmission Lines.” IEEE Transac-tions on Power Apparatus and Systems. Volume 98. Num-ber 1. March/April. pp. 606-617. correction May/June. page 699.

Federal Power Commission. 1964. National Power Sur-vey. Part II-Advisory Reports. U. S. Government Print-ing Office. Washington, D. C. October.

Gutman, R. 1988. “Application of Line Loadability Concepts to Operating Studies.” IEEE Transactions on Power Systems. Vol. 3. Number 4. November. pages 1426-1433.

Koessler, R. J. and J. W. Feltes. 1993. “Voltage Collapse Investigations with Time-Domain Simulation.” IEEE/NTUA Joint International Power Conference. Athens Power Tech Proceedings. Athens, Greece. Sep-tember 5-8.

Lesher, R. L., J. W. Porter, and R. T. Byerly. 1994. “Sun-burst—A Network of GIC Monitoring Systems.” IEEE Transactions on Power Delivery. Volume 9. Number 1. January. pp. 128-137.

North American Electric Reliability Council (NERC). 1995. “Transmission Transfer Capability.”

St. Clair, H. P. 1953. “Practical Concepts in Capability and Performance of Transmission Lines.” AIEE Trans-actions on Power Apparatus and Systems. Volume 72. Part III. December. pages 1152-1157.

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CHAPTER 2 Overhead Transmission Lines

2.1 INTRODUCTION

The degree to which the maximum power flow can be increased on an existing overheadline depends on its length, the original design margins, environmental concerns, andmany other issues. Because power flow on the transmission system is a function of theoverall system topology (transmission lines, transformers, generation, series and shuntcompensation, and load), system considerations can also limit the maximum power flowon a specific transmission line. Transmission line ratings are sometimes developed on asystem basis rather than on an individual line basis. The overall limit may be betweenoperating areas, irrespective of ownership or individual lines, and may change during aday based on system conditions.

Sometimes a power transmission line possesses a definite power flow limit based on thedesign parameters for the specific line; at other times the line as a component of the over-all transmission system determines the limit. System limits can result from factors such asvoltage drop, possibility of voltage collapse, and system stability, both steady state andtransient.

Power system limits, on the power flow through individual overhead lines, are describedin more detail in Chapter 1, which discusses power system limits on increased power flow.

System limits are functions of transmission line reactances in relation to the overallpower system. Series reactance, shunt admittance, and their combination, as well as surgeimpedance are relevant to system transfer limits. Transmission line series inductive reac-tance is determined by conductor size, phase spacing, number of conductors, relativephasing (double circuit lines), and line configuration. In transmission lines, the seriesreactance is significantly larger than the series resistance, and is the dominant factor in afirst-order explanation of system behavior. For this reason, simple reconductoring of atransmission line results in only minor changes in system power flows.

Critical factors related to power flow limits for overhead lines include:

• Surge impedance loading

• Voltage drop

• Thermal limits

• Environmental limits

2-1

Chapter 2: Overhead Transmission Lines Increased Power Flow Guidebook

2.1.1 Surge Impedance Loading

Surge impedance loading (SIL, defined in Equation 2.1-1) provides a useful rule-of-thumb measure of transmis-sion line loading limitation as a result of the effects ofseries reactance.

2.1-1

For an overhead transmission line, typical surge imped-ance is on the order of 300 ohms, while for a cable itmay be 50 ohms or less. At 345 kV, SIL of an overheadline is on the order of 400 MW. Short lines may be ableto carry 800 MW or more, while long lines of exactly thesame construction may be limited to less than 400 MWby system considerations.

2.1.2 Voltage Drop

Voltage control on the power system is of concern assystem loadings increase. The system voltage distribu-tion is affected by the series inductance and shuntcapacitance of the transmission lines. It is not desirablefor voltage to vary more than 5%, or at most 10%, fromone end to the other. In some cases, a voltage drop limitis placed on power flow corresponding to the maximumallowable decrease in voltage magnitude. The longer theline, generally the lower the power flow required toreach a voltage drop limit. Voltage control is a systemproblem, and is not generally solved by modifications toany one transmission line.

Because voltage drop is primarily a function of linereactance rather than resistance, simple reconductoringdoes very little to decrease the voltage drop per unitlength. Reconductoring an existing 230-kV line byreplacing the original 636 kcmil (324 mm2) Hawk ACSRwith a 954 kcmil (487mm2 ) Rail ACSR only increasesthe voltage drop limit by 5%. Adding a second conduc-tor per phase, to form two conductor bundles, results ina significant reduction in series reactance, and yields anincrease in the voltage drop power limit.

2.1.3 Thermal Limits

Thermal limits are discussed in considerable detail inthis chapter. In brief, the current carrying capacity(thermal rating) of an overhead transmission circuit isdetermined by the assumed “worst case” weather condi-tions, assumed conductor parameters, and the maxi-mum allowable conductor temperature. Some of thespecific thermal rating parameters are:

• Conductor construction: outside diameter, conductorstrand diameter, core strand diameter, number ofconductor strands, and number of core strands.

• Conductor AC resistance, which itself is a function ofthe conductor temperature.

• Conductor surface condition: solar absorptivity andemissivity.

• Line location: latitude, longitude, conductor inclina-tion, conductor azimuth, and elevation above sealevel.

• Weather: incident solar flux, air temperature, windspeed, and wind direction.

2.1.4 Environmental Limits

The electric field produced by overhead power transmis-sion lines is influenced by the following factors:

• Line voltage

• Height of conductors above ground

• Configuration of conductors (line “geometry,” con-ductor spacing, relative phasing of multi-circuit lines,use of bundled conductors)

• Lateral distance from the center line of the transmis-sion line

• Height above ground at the point of field measure-ment

• Proximity of conducting objects (trees, fences, build-ings) and local terrain

The electric field near ground level produced by an over-head transmission line induces voltages and currents innearby conducting objects (St. Clair 1953, FederalPower Commission 1964, Dunlop et al. 1979, Koesslerand Feltes 1993, Boteler 1994, Lesher et al. 1994, EPRI2005). These objects are typically the size of people, ani-mals, motor vehicles, sheds, and similar-sized bodies.Electric field coupling is capacitive coupling, and can berepresented by a current source in parallel with a highsource impedance (Norton equivalent circuit).

Electric field levels are limited by law in some jurisdic-tions. Some regulations are specified at the edge of theright-of-way (ROW) for public exposure. Other regula-tions are maximum levels on the ROW based on induc-tion to an assumed size object. These regulations mayrestrict voltage increases on presently existing transmis-sion lines without taking electric field reduction mea-sures.

Magnetic field is affected by the same variables as elec-tric field, except line current replaces line voltage, andnearby objects generally have minimal impact on themagnetic field. Magnetic field coupling is generally ofsignificance for objects that parallel the transmissionline for a long distance. Such objects include pipelines,

SZ

VSIL

2

=

2-2

Increased Power Flow Guidebook Chapter 2: Overhead Transmission Lines

telephone and railway signal circuits, and metal fences.Because magnetic field is a function of line current, andcurrent increases during fault conditions, it may be nec-essary to evaluate magnetic field effects under both nor-mal operation and faults. Magnetic field coupling isinductive coupling, and generally produces low voltageswith low source impedances (St. Clair 1953, FederalPower Commission 1964, Dunlop et al. 1979, Koesslerand Feltes 1993, Boteler 1994, Lesher et al. 1994, EPRI2005).

Increasing current on a transmission line increases themagnetic field, and thus increases magnetically inducedvoltages and currents. This may be significant in casessuch as when a transmission line parallels a railroadROW. This is the inductive coordination problem thathas been around since the dawn of the power industrywith respect to telephone and railroad signal facilities.Increasing current flow on existing lines may requirecoordination with parallel infrastructure. In some juris-dictions maximum magnetic field levels are specified byregulation. If an existing transmission line is operatingnear the magnetic field limit set by regulation, the abilityto increase line current may be limited, unless measuresare taken to reduce the magnetic field levels.

Electric fields can be shielded by conducting objects.Vegetation is sufficiently conductive to reduce electricfield levels. Grounded wires can be strung under thephase conductors at road crossings to reduce electricfield levels. Grounding measures can be taken for fixedobjects to eliminate induced voltages. On the otherhand, magnetic field shielding is significantly more diffi-cult than electric field shielding. Shielding a transmis-sion line by magnetic materials is impractical. Fluxcanceling loops have been developed, but incur powerloss and complexity in actively driven loops. Shielding isless practical as a mitigation measure for magnetic fieldsthan it is for electric fields (St. Clair 1953, Federal PowerCommission 1964, Dunlop et al. 1979, Koessler andFeltes 1993, Boteler 1994, Lesher et al. 1994, EPRI1994, EPRI 2005).

Chapter 2 includes seven sections:

• Section 2.2, Uprating Constraints, discusses con-straints on electrical and mechanical safety, withinformation on sag-tension calculations, limitinghigh-temperature sag, constraints related to wind-induced conductor motion, electrical clearance, lossof conductor strength, constraints on structuralloads, and environmental effects.

• Section 2.3, Line Thermal Ratings, explores the calcu-lation of line thermal ratings, and describes commonheat balance methods.

• Section 2.4, Effects of High-Temperature Operations,describes annealing, calculation of sag and tension,thermal and creep elongation, and connectors andconductor hardware at high temperature.

• Section 2.5, Uprating without Reconductoring, dis-cusses deterministic and probabilistic methods ofuprating without reconductoring.

• Section 2.6, Reconductoring without Structural Modi-fications, reviews the various reconductoring choicesusing new commercially available conductors.

• Section 2.7, Dynamic Monitoring and Line Rating,introduces the principles of dynamic rating methods.

• Section 2.8, Case Studies, includes a number of uprat-ing test cases and an economic comparison of lineuprating alternatives.

2.2 UPRATING CONSTRAINTS

2.2.1 Introduction

Increasing the thermal rating of an existing line requiresdealing with constraints on electrical and mechanicalsafety. The uprated line must remain safe under all elec-trical power flows up to its maximum without compro-mising the mechanical safety under severe ice and windloads.

This section discusses issues related to constraints onuprating, including determining what constitutes a con-straint in various areas of design, operation, and theenvironment.

2.2.2 Sag-tension Calculations

Normally, “sag-tension” calculations are performedusing numerical programs in order to determine the sagand the tension of a conductor catenary as a function ofice and wind loads, conductor temperature, and time.Calculation examples from a program like SAG10 areshown below to illustrate how tension limits are appliedand how maximum conductor tension and maximumfinal high temperature sag are taken for the purposes ofstrain structure design and tower placement. Details ofsag-tension calculation methods are not included, butexamples and key references are cited.

In the design, uprating, or simple maintenance of powertransmission lines, the concern of primary importance ispublic safety. It is more important that a line be safethan it carry power. Other than designing the support-ing structures such that they remain standing undereven the most severe weather conditions, the safety of aline is essentially determined by the position of its ener-gized conductors relative to nearby people, buildings,and vehicles. Maintaining minimum distances to nearby

2-3


objects and people is primarily a matter of limiting thesag of the energized conductors under high mechanicalloads and high temperature conditions.

In addition to making lines safe, other important con-straints are the level of electric and magnetic fields pro-duced (e.g., electric fields increase as the conductor getscloser to the ground), the maximum structure loads dur-ing occasional high wind and ice loads, and the maxi-mum temperature at which the energized conductors areallowed to operate. Given standard “worst-case”weather conditions, the thermal rating of an existing lineis determined by the maximum allowable conductortemperature. Thus, uprating such lines without recon-ductoring normally requires finding ways to maintainelectrical clearances while operating at a higher conduc-tor temperature.

Figure 2.2-1 is a basic sag-clearance diagram, whichillustrates how minimum ground clearance must bemaintained under both heavy loading and high temper-ature events over the life of both new and re-rated trans-mission lines. The figure shows ground clearance andline sags under normal conditions, high ice/wind load,and high temperature conditions for a ruling (or “equiv-alent”) span. Note that the sum of the minimum groundclearance, the buffer, and the sag at maximum tempera-

ture is the minimum attachment height, which deter-mines structure height and spacing. In a detailed linedesign that has many different spans, this sort of sag-clearance calculation must be developed for all spans(Ehrenburg 1935, Winkleman 1959).

Definitions of the labels in Figure 2.2-1 are as follows:

• “Init” is the initial installed unloaded (with no ice orwind) sag of the conductor. It is typically at a con-ductor temperature of 10°C to 25°C (50°F to 80°F).This is also typically referred to as the line “rulingspan stringing sag.”

• “Final–STC” is the final sag of the conductor at 15oC(60oF) after an ice/wind-loading event has occurredfor a short time—typically an hour. STC stands for“short-time creep.”

• “Final–LTC” is the final sag of the conductor at 15oC(60oF) after an extended period—typically 10 years—where the conductor simply persists at a conductortemperature on the order of 15°C (59°F) without iceor wind. “LTC” stands for “long-time creep,” whichoccurs even if heavy ice and wind loads never occur.

• “Max Load” is the sag of the conductor during thespecified maximum ice and wind loading at a reducedtemperature—typically 18°C to 0°C (0°F to 32°F).Note that the sag prior to this event is normallyassumed to be the Init sag and the sag after this eventis the Final–STC sag.

• “TCmax” is the sag of the conductor when its tem-perature is the maximum for which the line isdesigned—typically 50°C to 150°C. The final sag at15oC (60oF), prior to this high temperature event, isassumed to be the larger of the Final–STC and theFinal–LTC sags.

Figure 2.2-1 shows typical behavior of transmissionconductors where the sag under maximum ice and windload conditions is less than that at the maximum tem-perature. For small or weak conductors experiencingheavy ice loads, this may not be true.

Note that the diagram illustrates the “snapshot” natureof traditional sag-tension calculations. The actual con-ductor sag position at any time in the life of the linedepends on the actual mechanical and electrical loadhistory of the line. If the high load event is more severeor persists for a longer time than assumed in determin-ing the Max Load condition, then the corresponding sagat Max Load and the sag increase will be greater. Theuse of buffers is required because of such uncertainties.

For transmission conductors made up primarily of alu-minum strands under tension, sag never stops increasing

Figure 2.2-1 Sag diagram showing sags for various times and loading conditions.

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with both time and high loading events throughout thelife of the line (Aluminum Association 1974, Harvey andLarson 1972, Harvey 1979). That is, the sag at a givenconductor temperature (e.g., 15.5°C, or 60oF) increasessteadily over the years after construction. However, withmoderate unloaded and loaded conductor tensions (typ-ically 15% and 50% of rated strength), the rate of changein sag with each such event decreases over the life of theline. Thus, if a heavy ice load event occurs 10 years afterinstallation, the permanent increase in sag is muchsmaller than if it occurred in the first 6 months afterconstruction. Similarly, under everyday unloaded condi-tions, the rate of change in sag will decrease with time,over the life of the line.

Tension-Elongation Diagram (Normal)The “tension-elongation” diagram shown in Figure2.2-2 shows how the conductor tension changes corre-sponding to the changes in sag position with load, time,and temperature shown in the preceding sag diagram.

The initial unloaded (“Init”) sag corresponds to the ini-tial unloaded (Init) tension. In the design of a new over-head line, increasing this initial tension decreasesmaximum temperature (Tcmax) sag and can allow theuse of fewer and shorter structures. However, increasedeveryday tension levels also increase the maximum(“Max”) tension loads (and thus the cost) on angle anddead-end structures, and decrease the mechanical self-damping of the conductor, which can lead to Aeolianvibration-induced fatigue damage unless dampers areapplied.

With an older existing line that has reached its final sag,increasing the conductor tension reinitiates creep(though at a reduced rate). It also increases angle anddead-end structure loads (though perhaps not higherthan they were upon initial installation) and is likely toincrease Aeolian vibration activity.

When reconductoring an existing line, an increase in themaximum tension load may lead to the need for rein-forcement or replacement of angle and dead-end struc-tures and may be a critical factor in determining whetherreconductoring is an economic uprating solution.

The modulus (actually the spring constant) of the con-ductor determines the increase in tension betweenunloaded and loaded states. Figure 2.2-2 shows typicalbehavior for a transmission conductor where the differ-ence in tension between unloaded and loaded states mayresult in a tension increase by a factor of two or more.Specification of a realistic, nonlinear conductor modu-lus (stress-strain behavior) under high tension loads is

important to the correct calculation of maximum ten-sion. Use of a linear modulus will result in an overesti-mate of the maximum tension.

As the temperature of the conductor increases, its lengthand the resulting sag increase while the line tensiondecreases. Errors in modeling the conductor modulus athigh temperatures have little or no effect on the calcu-lated sag, but the thermal elongation behavior of con-ductors at high temperatures is very important. As isnoted in Section 2.4, the thermal elongation of ACSRcan be particularly complex.

2.2.3 Limiting High Temperature Sag

The thermal elongation of stranded conductors is essen-tially the same as that of its component strands. There-fore, for an all aluminum or copper conductor, once thesag at “final” everyday conditions is established, the sagat high temperatures can be calculated and limited withrelatively small uncertainty.

High Temperature Sag with All Aluminum ConductorsFor example, consider a line section of an all-aluminum,37 strand (Arbutus) conductor having a ruling span of600 ft (183 m) installed to meet the following con-straints: maximum tension of 50%, 33% initial unloadedat 15°F and 25% final unloaded at 15°F (-9.4 °C). Anequally typical SAG10 program line design sag-tensionrun is shown in Table 2.2-1.

Figure 2.2-2 Tension diagram showing conductor tension for various times and loading conditions.

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High Temperature Sag with ACSRBecause steel elongates thermally at half the rate of alu-minum, the thermal elongation rate of ACSR conductoris less than that of all aluminum conductor. Therefore,older lines (which often have relatively small conductorswith high steel content) sag less than all aluminum con-ductors for the same change in temperature.

The degree to which an ACSR conductor’s thermalexpansion is less than that of an all aluminum conduc-tor (AAC) is dependent on the ratio of the steel to alu-minum area. This ratio, expressed as a percentage, isusually referred to as the ACSR “Type” number. Table2.2-2 lists the composite thermal elongation of ACSRconductors with different type numbers. Typical valuesfor the coefficient of thermal expansion (α) of an ACSRare shown in Table 2.2-2.

Although we have listed composite thermal elongationcoefficients for ACSR, in reality the aluminum strandselongate at twice the rate of the steel strands. Thereduced thermal elongation coefficient of the composite

is actually the result of both this difference in expansionwith temperature and the change in component tensionsthat it produces.

Ignoring Aluminum Compression in ACSR at High TemperatureOver the past 40 years, the Varney graphical method(Aluminum Company of America 1961) has been thebasis of most sag-tension programs. The Alcoa SAG10program is widely used. The sag-tension Table 2.2-3,taken from the SAG10 program, shows the sag and ten-sion (total, aluminum, and steel component tensions)for initial and final conditions for 30/19, 795 kcmil (405mm2) ACSR (Mallard) initially sagged so as not toexceed a final unloaded tension of 25% of Mallard’sRated Breaking Strength at 60oF (15.5oC). NESCMedium Loading conditions and conductor tempera-tures up to 302oF (150oC) are included.

Notice that the knee point temperature, where the alu-minum tension goes to zero, under final conditions,occurs at only 90oF (32oC).

Figure 2.2-3 shows final sag versus conductor tempera-ture for ACSR (Mallard) in four different ruling spanlengths. Note the change in slope of the curves below50oC where the knee point is predicted to occur.

Many older lines that are typical candidates for upratingwere designed with high steel ACSR such as 30/19, 30/7,and 26/7. The low thermal elongation beyond the kneepoint temperature, illustrated in the preceding calcula-tions, makes these older lines attractive candidates foroperation at higher temperatures. In such design situa-tions, the difference in predicted sag at high temperaturecan be very important.

Table 2.2-1 Sag-Tension Calculations for 37 AAC (Arbutus)

ALUMINUM COMPANY OF AMERICAN SAG AND TENSION DATA

Conductor Arbutus 795.0 kcmil 37 Strands AAC Area = 0.6234 sq in. Dia + 1.026 in.

Wt = 0.746 lb/°F RTS= 13900 lb Span + 600.0 ft Creep is a Factor NESC Medium Load Zone

Design Points Final Initial

Temp(°F)

Ice(in.)

Wind (psf)

K(lb/°F)

Weight(lb/°F)

Sag(ft)

Tension(lb)

Sag(ft)

Tension(lb)

15. .25 4.00 .20 1.451 12.02 5446. 10.65 6140

32. .25 .00 .00 1.143 12.00 4294. 10.06 5118

0. .00 .00 .00 .746 8.77 3833. 6.63 5067.

15. .00 .00 .00 .746 9.67 3475.a

a. Design condition.

7.27 4621.

30. .00 .00 .00 .746 10.58 3179. 7.98 4212.

60. .00 .00 .00 .746 12.34 2727. 9.54 3524.

90. .00 .00 .00 .746 13.99 2406. 11.19 3006.

120. .00 .00 .00 .746 15.54 2167. 12.82 2624.

167. .00 .00 .00 .746 17.78 1897. 15.24 2210.

212. .00 .00 .00 .746 19.73 1711. 17.37 1941.

Table 2.2-2 Coefficients of Thermal Expansion for Bare Stranded Conductors

Conductor Type Number α (per degree C)

AAC 0 23.0 x 10-6

36/1 ACSR 3 22.0 x 10-6

18/1 ACSR 5 21.1 x 10-6

45/7 ACSR 7 20.7 x 10-6

54/7 ACSR 13 19.5 x 10-6

26/7 ACSR 16 18.9 x 10-6

30/7 or 30/19 ACSR 23 17.5 x 10-6

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Table 2.2-3 Sag-Tension Calculations for 30/19, 795 kcmil ACSR (Mallard)


Conductor Mallard 795.0 kcmil 30/19 ACSR Area = .7669 sq. in. Dia + 1.140 in.

Wt = 1.235 lb/°F RTS = 38400 lb Span + 600.0 ft Creep is a Factor NESC Medium Load Zone


Temp(°F)

Ice(in.)

Wind (psf)

K(lb/°F)

Weight(lb/°F)

Sag(ft)

Tension(lb)

Sag(ft)

Tension(lb)

15. .25 4.00 .20 1.955 7.8011283.3423.A7859.S

6.8312880.4986.A7894.S

32. .25 .00 .00 1.667 7.689773.2377.A7395.S

6.3611804.4462.A7342.S

0. .00 .00 .00 1.235 5.3010495.3193.A7302.S

4.4512499.4972.A7527.S

15. .00 .00 .00 1.235 5.799600.a2508.A7092.S


4.6911864.4623.A7242.S

30. .00 .00 .00 1.235 6.348775.

1860.A6914.S

4.9511241.4277.A6963.S

60. .00 .00 .00 1.235 7.567357.693.A

6664.S5.54

10039.3605.A6435.S

90. .00 .00 .00 1.235 8.656432.0.A

6432.S6.23

8921.2966.A5955.S

120. .00 .00 .00 1.235 9.266010.0.A

6010.S7.03

7910.2373.A5537.S

167. .00 .00 .00 1.235 10.275422.S

0.A5422.S

8.456580.

1553.A5027.S

212. .00 .00 .00 1.235 11.274939.0.A

4939.S9.94

5600.894.A

4706.S

257. .00 .00 .00 1.235 12.304528.0.A

4528.S11.45

4864.343.A

4522.S

302. .00 .00 .00 1.235 13.344178.0.A

4178.S12.80

4352.0.A

4352.S

Figure 2.2-3 Sag for a “strong” 30/19 ACSR conductor (calculated ignoring aluminum strand compression) as a function of conductor temperature and ruling span length.

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Considering Aluminum Compression in ACSR at High TemperatureStarting with the studies of Barrett at Ontario Hydro(Barrett et al. 1982), the assumption of zero compressivestress in ACSR beyond the knee point temperature hascome into question. The question centers not on thecorrect calculation of the knee point temperature but onwhether the aluminum strands can support compressivestresses above it.

The Canadian Electrical Association’s STESS softwareprogram incorporated Barrett’s research. Inclusion ofthe compressive effects of the aluminum strands of highsteel content conductors such as 26/7 ACSR (Drake)can add as much as 3 ft (0.91 m) to the sag at 150oC in a1200 ft (366 m) span. The effect is less with smaller rul-ing spans and with lower conductor temperatures.

Recent studies by Rawlins (Rawlins 1998) seem to con-firm the existence of compressive effects as well as resid-ual stresses (due to manufacturing) in aluminum strandsat high temperatures. The effect on sag at high tempera-tures appears to be much smaller than those predictedby Barrett. The widely used SAG10 program has incor-porated Rawlins’s studies as an optional calculation. Ina 1200 ft (366 m) span, Rawlins’s method would addabout 1 ft (30 cm) to the sag of a high steel conductorsuch as Drake at 150oC.

Figure 2.2-4 shows a comparison of sag as a function ofconductor temperature calculated with the followingassumptions:

• The SAG10 computer program with an assumptionof zero compressive stress in the aluminum strands.

• The SAG10 computer program with the defaultassumption of 2500 psi (17.2MPa) residual stress andallowance for aluminum compression.

• The STESS computer program with the defaultassumption of 10 MPa (1450 psi) for maximum com-pressive stress and no residual stress.

Figure 2.2-5 is a similar plot that shows the somewhatlarger sag differences that occur in a 1200 ft (366 m) rul-ing span.

At this point, there is no clear way to determine whichof these methods is correct. Indeed, there is no way tobe certain that the stress assumptions for any of the cal-culations is correct for all ACSR conductors installed inold and new lines. However, there is a distinct possibilitythat the original line design sag-tension calculations,assuming no compressive stress in the multiple alumi-num layers, yielded sags above the kneepoint that weretoo small. The uncertainty centers on how much the sagshould be increased to be certain that electrical clear-ances will be maintained at an increased maximum con-ductor temperature.

2.2.4 Uprating Constraints Related to Wind-Induced Conductor Motion

Transmission lines must be designed not only to provideadequate vertical clearance for electrical and safety con-siderations, but also to allow for adequate horizontalclearance to tall objects and buildings at the edge of theROW under high wind conditions. This conductor dis-placement is termed conductor blowout and is normallyat its maximum midway between conductor supportpoints, as shown in Figure 2.2-6. Note that the horizon-tal displacement at midspan (XH) is determined in partby the conductor sag (D).

The maximum displacement of the outermost conduc-tors from the center of the ROW under high wind condi-tions can be one of the most important variables in

Figure 2.2-4 Sag at high temperatures calculated with and without aluminum compression.

Figure 2.2-5 Final sags for Mallard ACSR in a 1200-ft span.

2-8


determining ROW width or for a given ROW width,determining the maximum structure spacing.

In addition to blowout in strong cross-winds, wind cancause certain oscillatory conductor motions. See Table2.2-4. By far the most common oscillatory wind-induced motion is aeolian vibration since it occursunder low-speed everyday wind conditions. Unless it iscontrolled, aeolian vibration can accumulate millions ofcycles, which cause fatigue failure of copper, aluminum,or steel strands. A less common, but more dramatic,form of wind-induced conductor motion is ice gallop-ing. It occurs for strong winds in combination with iceon the conductors and can yield high amplitude, oscilla-tory conductor motions that result in repeated flash-overs between the phase conductors or between a phaseconductor and a shield wire.

The amplitude of wind-induced conductor aeolianvibration is generally less than the conductor diameter.It can be measured with special monitors, but the calcu-

lation methods are complex. Two simple methods ofcontrol are widely used: (1) the tension of the line con-ductors under everyday conditions is limited and;(2) vibration dampers are clamped to the line conduc-tors. In regions where aeolian vibration is a problem,transmission line conductor tensions are typically lim-ited to between 15% and 20% of RBS during the coldestmonth of the year, and vibration dampers are routinelyinstalled in every span.

Ice galloping motions can be predicted in a crude waythrough the use of ice galloping ellipses. By comparingsuch ellipses to the spacing between the line conductors,the likelihood of flashovers from galloping can be mini-mized by providing sufficient phase spacing and by off-setting any vertical phases. Also, since the major axis ofthe galloping ellipse is proportional to the line conduc-tor sag with ice and wind loading, the amplitude of icegalloping motions can be reduced by minimizing the sagof conductors in the typical span.

Wind-induced subconductor oscillation only occurs forbundled phase conductors when wind speeds exceed acertain critical velocity. If uncontrolled, it can result infatigue damage to spacers and suspension hardware.Oscillations are controlled by keeping bundled conduc-tors at a spacing-to-diameter ratio of about 20 or moreand by avoiding uniform spacer spacing.

With regard to increasing maximum allowable powerflow through existing lines, wind-induced conductormotions are a primary constraint on increasing the lineoperating voltage, on retensioning the existing conduc-tors to allow operation at higher maximum conductortemperatures, on reconductoring the line with high–temperature, low-sag conductor, and on bundling (add-ing a second conductor per phase).

Figure 2.2-6 Illustration of midspan conductor blowout due to wind.

Table 2.2-4 Cyclic, Wind-induced Conductor Motions

Aeolian Vibration Ice Galloping Subconductor Oscillation

Types of Overhead Lines Affected All All in regions with iceLines with bundled con-

ductors

Approx. Frequency Range, Hz 3 to 150 0.08 to 3 0.15 to 10

Approx. Range of Vibration Amplitudes (Peak-to-peak, Expressed in conductor diameters) 0.01 to 1.0 5 to 300 0.5 to 80

Weather Conditions Favoring Conductor MotionWind Character:Wind Velocity:

Conductor Surface:

Steady1 to 7 m/sec (2 to 15 mph)

Bare or uniformly iced


Asymmetrical, thin ice deposits


Bare, Dry

Damage Characteristics:

Direct Causes of Damage:

3 months to 20 years for damage to occur

Conductor fatigue due to cyclic bending

1 to 48 hours per occurrenceRepeated Flashovers, High

dynamic loads on structures, premature wear of hardware

1 month to 8+ years for dam-age to occur

Conductor clashing, acceler-ated wear of hardware

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HTLS conductors such as ACSS are particularly advan-tageous in reconductoring if they are prestressed. Whenprestressed, ACSS has much higher self-damping thanstandard ACSR. It can be installed with smaller initialsag, which reduces ice galloping motions and may allowoperation of an existing line at higher voltage as well ashigher current levels.

In lines without vibration dampers, the addition ofdampers may allow the line’s existing conductors to beretensioned and operated to a higher maximum temper-ature without the need for reconductoring.

When bundling new conductors with old, the use of avertical bundle can eliminate the problem of subconduc-tor oscillation while keeping the bundle spacing to nomore than 9 to 12 inches.

Regardless of the uprating method, wind-inducedmotions must be thoroughly considered as part of theredesign.

2.2.5 Electrical Clearance

The National Electric Safety Code (National ElectricSafety Code 1997) specifies minimum spacings fromenergized conductors to ground, to objects passingunder the line, to buildings nearby, and to other conduc-tors (“underbuild”). These clearances must be main-tained under “The maximum conductor temperature forwhich the line is designed to operate” (NESC 232.A.2).Failure to maintain such minimum distances is a publicsafety issue of primary importance.

The National Electric Safety Code also specifies mini-mum horizontal spacings from energized conductors toother conductors and objects such as buildings at theedge of ROW. When subjected to transverse wind, theconductor catenaries “blow out,” and the horizontalspacing of energized conductors to buildings, etc. isreduced. This reduction in horizontal clearance can belimited by using heavier conductors or shorter spanlengths; reducing energized conductor sag under blow-out conditions; using insulators such as V strings, hori-zontal V, and posts that do not move with wind; andproviding generous right-of-way widths. Reducing sagunder horizontal blowout conditions is limited by con-cerns about vibration, but is complementary to upratingmethods such as retensioning.

Minimum electrical clearances must be maintainedunder all line loading and environmental conditions.Since the actual sag clearance of transmission lines isseldom monitored, sufficient allowance for this clear-ance must be included in the process of initial design orin rerating of existing lines.

Applicable Code ClearancesIn all cases, national codes may apply. In the UnitedStates, the National Electric Safety Code (NESC) isapplicable. State codes may also apply. Minimum hori-zontal and vertical distances from energized conductor(“electrical clearances”) to ground, other conductors,vehicles, and objects such as buildings are a function ofthree things: the line-to-ground voltage, the use ofground fault relaying, and type of object or vehicles.

The NESC Rules covers both vertical and horizontalclearances. That is, the code sets minimum spacing forenergized conductors both above and next to people,vehicles, and buildings. This chapter considers only ver-tical clearances since our focus is on high temperatureoperations (see Tables 2.2-5 and 2.2-6). Horizontalclearances are typically specified for high winds wherethe transmission line catenaries are horizontally dis-placed by the wind. In such cases, the conductor tem-perature is low due to high convection cooling.

Ground clearance minimums listed in the NESC codeare primarily due to the height of the object or personthat may pass beneath the span. For example, a personwith an overhead umbrella extended overhead at arm’slength may physically reach 10 ft (3 m) above ground,whereas a railroad car may be as much as 20 ft (6 m)high. The NESC code calls for a minimum groundclearance of 27 ft (8.2 m) for a low-voltage conductorover a railroad and only 16.5 ft (5 m) over “spaces orways” accessible only to pedestrians. The difference inminimum ground clearance is due primarily to theheight of the object under the line. In each case, theclearance between the low-voltage conductor and thetop of the conflicting object is approximately the same.

Essentially, the minimum vertical ground clearance forany “supply” conductor (0 to 750 V) is defined by theNESC code as 16.5 ft (5 m) for lines going over placessuch as roads, streets, driveways, parking lots, and farm-land, or any other type of land which can be traversedby vehicles. Conductors passing over waterways mustgenerally meet greater clearance requirements.

The Influence of Line Voltage on ClearanceFor those lines having a line-to-ground voltage of 750 to22 kV, the ground clearance for the 0 to 750 V supplyconductor is increased by 2 ft to 18.5 ft (0.6 m to 5.6 m).

For lines at higher voltages, the vertical clearance isincreased by 0.4 in. (1 cm) for every kV increase in line-to-ground voltage above 22 kV. Note that the voltageused in these calculations of added electrical clearanceare based on the maximum operating voltage, which istypically 5% or 10% above nominal.

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Reduced Clearance for EHV Lines with Limited Switching Surge LevelsFor lines exceeding 98 kV line to ground, the codeallows clearances to be calculated based on knowledgeof switching surge levels. If the switching surge level isrestrained to 2.2 p.u., the clearance at EHV voltagesmay be decreased.

Power System Conditions when Clearances ApplyIt is impossible to be certain that clearances will bemaintained under all foreseeable circumstances. Forexample, in certain regions, tornadoes may occur, whichmight cause conductors that are energized to fall toearth. However, it is irresponsible to design lines or lineupgrades where clearance violations are likely to occur.

The minimum ground clearances specified by the NESCcode apply to energized conductors under the three con-ditions specified in Rule 232A where the temperaturesspecified are that of the conductor not the surroundingair:

• 50°C (122°F) with no wind displacement.

• At the maximum operating temperature for which theline is designed to operate if greater than 50°C(122°F) with no wind displacement.

• 0°C (32°F), no wind displacement, with radial thick-ness of ice.

Even in these days of heavily utilized transmissionassets, it is unusual for lines to carry electrical loads thatcause the energized conductors to be more than 5°C or10°C above air temperature. However, given the rela-tively rare loss (outage) of a major generating station orEHV transmission circuit, electrical loading on HV linescan increase and cause much higher conductor tempera-tures. Thus, all lines are designed to meet clearances “atthe maximum operating temperature for which the lineis designed to operate” (see above).

Heavy ice loads are also relatively rare events, but in anymodern HV or EHV line, the energized conductor sag at0°C (32°F) with maximum ice is typically less than thesag for high temperature, even when that maximumoperating temperature is only 50°C (122°F). Thus, theassurance of adequate clearance involves the behavior oftransmission conductors at high temperatures, notunder heavy ice load.

Transmission line operators typically meet minimumclearance requirements by limiting the current on theenergized conductors. The specification of any relation-ship between the electrical current on the energized con-ductors and the conductor temperature is left to thediscretion of the operator.

The NESC code describes the minimum clearances inconsiderable detail as a function of voltage and poten-tially conflicting activity. The code also prescribes theconditions under which the clearance minimums must bemet. The code does not, however, specify: (1) how thetemperature of the conductor is to be calculated; (2) howthe physical position of the conductor above ground is tobe related to this maximum operating temperature; nor(3) how adequate ground clearance can be confirmedunder rare occasions of high electrical loading. Conse-quently, methods of ensuring adequate ground clearancevary widely between transmission line operators.

Upgrading BuffersOn older transmission lines, the structure placementalong the ROW is fixed, and the final sag of the conduc-tor is measurable. Thus any initial spacing buffer addedbecause of uncertainties in structure placement and ini-tial sag can be reduced in uprating. There are, however,certain irreducible uncertainties, and some clearancebuffer must be maintained.

The traditional method of determining clearances forexisting transmission lines involves standard surveymethods to determine the conductor attachment pointsand the sag at span mid-point for one or more spans in

Table 2.2-5 Minimum Vertical Ground Clearances According to NESC C2-1997, Rule 232C

L-L/L-GBasic Clear-

ance @ 22 kVClearance Added for

Voltage Streets

kV ft m ft m

69/40 18.5 5.6 0.7 19.2 5.8

138/80 18.5 5.6 2.1 20.6 6.3

161/93 18.5 5.6 2.5 21.0 6.4

230/133 18.5 5.6 3.9 22.2 6.8

345/200 18.5 5.6 7.0 25.5 7.8

500/290 18.5 5.6 9.9 28.4 8.7

765/440 18.5 5.6 15.5 34.0 10.4

Table 2.2-6 Minimum Vertical Ground Clearances According to NESC C2-1997, Rule 232D*

Nominal Voltage L-L/L-G

Reference Height Listed in

Table 232-3Alternate

Clearance Adder

Minimum Clearance for

Streets

KV ft m ft m ft m

69/40 - 19.2 5.9

138/80 - 20.6 6.3

161/93 21.0 6.4

230/133 14 4.3 7.1 2.2 21.0 6.4

345/200 14 4.3 7.1 2.2 21.0 6.4

500/290 14 4.3 12.7 3.9 26.7 8.1

765/440 14 4.3 21.8 6.6 32.4 9.9

* In accord with Rule 232D4, the clearance calculated based on Rule 232D2-3 cannot be less than the clearance calcu-lated for 98 kV under Rule 232C, which is 21.0 ft.

2-11


each line section. These measurements are typicallytaken with the line out of service so that the conductoris at air temperature plus some solar rise. Vertical posi-tion errors of up to a foot (0.3 m) are easily made indetermining the catenary’s position and the attachmentheights. Additional errors may be expected in determin-ing the ground clearance since the ground profile is onlychecked at a few points along the line.

In more recent years, several photographic and laser-based methods have been developed. These methodshelp determine all attachment points at all structures,and provide a complete description of catenary profilesfor all three-phase conductors with much better accu-racy than is possible with conventional survey methods.Such measurements are seldom done with the line out ofservice, so the conductor temperature at the time of thesurvey measurements must be calculated or measured.The result of such detailed survey activity is veryimpressive and can easily convince the novice that buff-ers can be eliminated or reduced when upgrading exist-ing lines. This is not the case.

Knowing the exact ground clearance with perfect cer-tainty at the conclusion of a laser survey does not meanthat one can be certain of adequate clearance undermaximum electrical loading. There still remain severaluncertainties.

2.2.6 Loss of Conductor Strength

Construction codes also require that maximum conduc-tor tension not exceed a certain percentage of the ener-gized conductor’s breaking strength. A significantreduction in the breaking strength can weaken the ener-gized conductor and lead to a tensile failure during sub-sequent high ice and wind loading events. To avoid this,the conductor must not operate at a high enough tem-perature for a long enough period of time so as toreduce its breaking strength more than 10%, and it mustnot be installed at such a high everyday “unloaded” ten-sion that its strands fatigue due to wind vibration.

The American Society for Testing and Materials(ASTM) or the International Engineering Consortium(IEC) standards specify the minimum tensile strength ofaluminum and copper wires, which is the stress at whichthe wire breaks. At temperatures above 75°C, the tensilestrength decreases with time. Temperatures below 300°Cdo not affect the tensile strength of galvanized, alumi-num-clad, or copper-clad steel wires. Thus, extendedexposure of conductors made up largely of aluminum orcopper wires to temperatures above 75oC can eventuallylead to tensile failures during high ice and/or wind load-ing events.

Figure 2.2-7 shows the reduction in tensile strength withtime and temperature for a sample of 0.081 in. (0.2 cm)diameter hard drawn copper wire, as described in (Hick-ernell et al. 1949). There are 8760 hours in a year, so thediagram clearly shows that sustained operation at 65οCyields no measurable reduction of tensile strength, sus-tained operation at 100oC yields a 10% reduction in 600hours (25 days), and that only 40 hours at 125oCreduces the wire tensile strength by 10%.

Figure 2.2-8 shows similar tensile strength reductiondata for 1350-H19 “EC” hard drawn aluminum wire. It

Figure 2.2-7 Annealing of 0.081 in. diameter hard drawn copper wire.

Figure 2.2-8 Annealing of 1350-H19 hard drawn aluminum wire (Aluminum Association 1989).

2-12


is taken from (Aluminum Association 1989). In general,tensile strength reduction of aluminum wires at temper-atures of less than 90oC is considered negligible. At100oC, the tensile strength of the wire is reduced by 10%after 5000 hours, and at 125oC the tensile strength isreduced 10% after 250 hours.

When compared to copper, aluminum appears to annealsomewhat more slowly, though the difference is proba-bly not important in transmission line applications. Thesource of the copper wire data also noted a significantamount of variation in the annealing rates for wireobtained from different manufacturers.

In applying these equations, the cumulative strengthreduction for multiple exposures at the same conductortemperature may be found by simply adding up all thehours and calculating the residual strength. However,for multiple exposures at different conductor tempera-tures, the calculation process is more complex. To deter-mine the cumulative strength reduction for a series ofhigh temperature exposures at different temperaturesand times, all exposures must be expressed in equivalenttime at the highest temperature before adding.

Thus, if an all aluminum conductor consisting of 37-0.1466 in. diameter strands is raised to 125oC for 100hours and then at a later time for 50 hours, then thestrength reduction can be calculated for 150 hours at125 oC. If the same conductor is raised to 125oC for 100hours and then at a later time is raised to 150oC for 50hours, then the following calculation must be per-formed:

For 100 hours @125oC,

2.2-1

At 150oC, RS = 91.0% after 7.2 hours, so the cumulativeloss of strength over the two high temperature exposuresis equal to the remaining strength after 50 + 7.2 hours.It is 82.1%

2.2.7 Constraints on Structural Loads

Existing structures and foundations were designed forcertain maximum transverse wind loads and, for strainstructures, for maximum tension loads. Unless the exist-ing structures are to be replaced, retensioning the exist-ing conductor, or reconductoring the line with a newconductor, must be done without greatly exceeding theoriginal design limits on structure loading. If many ofthe line structures must be replaced, the design solutionis not the sort of minimal capital investment solutionthat this guide emphasizes.

For tangent structures, the governing transverse loadsare primarily a function of the conductor diameter.Thus the replacement conductor diameter must bewithin about 10% of the existing conductor to avoid tan-gent structure modification. For angle and dead-endstructures, the governing loads are primarily related tomaximum conductor tension. The replacement conduc-tor’s maximum tension should not exceed the originalconductor’s initial maximum conductor tension unlessthese structures are to be reinforced.

Before undertaking any uprating project, a review of theexisting structures and operating records of the line isrequired. If structural failures at angle or dead-endstructures have occurred, any attempt at increasingeveryday installed tension is unlikely to succeed. Simi-larly, if occasional high temperature operations haveyielded splice failures, increasing operating temperaturelevels without replacing or inspecting the line is unwise.On the other hand, if a review of structure and founda-tion capacity indicates that the line was conservativelydesigned, and that it has operated for many years with-out any structural or foundation failures, it may be pos-sible to replace the existing conductor with a new largerconductor without structure modifications.

When a conductor span is ice covered and/or exposed tohigh winds, the effective conductor weight per unitlength increases. During occasions of heavy ice and/orwind load, the conductor tension increases dramatically,along with the loads on angle and dead-end structures.Both the conductor and its supports can fail unlessthese high-tension conditions are considered in the linedesign. The National Electric Safety Code (NESC) sug-gests certain combinations of ice and wind correspond-ing to heavy, medium, and light loading regions of theUnited States.

The NESC Code (National Electric Safety Code 1997)also suggests that increased conductor loads due to highwind loads but no ice should be considered as noted inthe last column of Table 2.2-7.

Certain utilities in very heavy ice areas use glaze icethickness as much as 2 to 3 in. (5 to 7.6 cm) in order tocalculate iced conductor weight. This is especially true ifthey have experienced extensive line failures due to iceloads in excess of those recommended by the NESC.Similarly, utilities in regions where hurricane windsoccur may use wind loads as high as 0.236 psi (1630 Pa).

Ice LoadingThe formation of ice on overhead conductors may takeseveral physical forms such as glaze ice, rime ice, or wet

( )%0.91100100 1466.0

1.0095.0125.0

=×=⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛•−−

RS

2-13


snow. The impact of lower density ice formation is usu-ally considered in the design of line sections at highaltitudes.

The formation of ice on overhead conductors has thefollowing influence on line design:

• Ice loads determine the maximum vertical conductorloads that structures and foundations must with-stand.

• In combination with simultaneous wind loads, icedconductor may also yield the highest transversedesign loads on structures.

• In regions of heavy ice loads, the maximum sags andthe permanent increase in sag with time (differencebetween initial and final sags) may be due to iceloading.

In addition to the NESC loading region, ice loads foruse in designing lines may also derive from past experi-ence, state regulations, and analysis of historicalweather data. Mean recurrence intervals for heavy iceloadings are a function of local conditions along variousroutings. Line design software can be used to investigatethe impact of a variety of assumptions concerning iceloading. The calculation of glaze ice loads on conduc-tors is normally done with an assumed ice density of57 lb/ft3 (913 kg/m3).

The ratio of iced weight to bare weight depends stronglyupon the conductor diameter. As shown in Table 2.2-8,for three different conductors covered with 0.5 in. (1.27cm) radial glaze ice, this ratio ranges from 4.8 for #1/0AWG to 1.6 for 1590 kcmil (811 mm2) conductors.

Therefore, small diameter conductors may need to havea higher elastic modulus and higher tensile strengththan large conductors in heavy ice and wind loadingareas to limit the sag.

Wind Loading Wind loading on overhead conductors influences linedesign in a number of ways:

• The maximum span between structures may be deter-mined by the need for horizontal clearance to theedge of the ROW during moderate winds.

• The maximum transverse loads for tangent and smallangle suspension structures are often determined byinfrequent high wind-speed loading.

• Wind loading determines the permanent increase inconductor sag in areas of light ice loads.

Wind pressure load on conductors, Pw, is commonlyspecified in lb/ft2. Equation 2.2-2 gives the relationshipbetween Pw and wind velocity:

2.2-2Where Vw = the wind speed in miles per hour.

The wind load per unit length of conductor, Ww, isequal to the wind pressure load, Pw, multiplied by theconductor diameter (including radial ice of thickness t,if any):

2.2-3

Combined Ice and Wind LoadingIf the conductor weight is to include ice and wind load-ing, the resultant magnitude of the loads must be deter-

Table 2.2-7 Definition of NESC Loading Areas

Loading Districts

Heavy Medium Light

Extreme Wind

Loading

Radial thickness of ice (in.) 12.5 6.5 0 0

Radial thickness of ice (mm) 318 165 0 0

Horizontal wind pressure (lb/ft2)

4 4 9 16 to 22

Horizontal wind pressure (Pa) 190 190 430 16 to 22

Temperature (°F) 0 +15 +30 +60

Temperature (°C) -18 -10 -1 +15

Constant to be added to the resultant (all conductors) (lb/ft)

0.30 0.20 0.05 0.0

Constant to be added to the resultant (all conductors) (N/m)

4.40 2.50 0.70 0.0

Table 2.2-8 Ratio of Iced to Bare Conductor Weight

ACSRConductor D wbare wice

wbare+ wice---------

wbare

(in.) (lb/ft) (lb/ft)

#1/0AWG-6/1“Raven” 0.398 0.1452 0.559 4.8

47-kcmil-26/7“Hawk” 0.858 0.6570 0.845 2.3

1590-kcmil-54/19“Falcon” 1.545 2.044 1.272 1.6

[ ][ ]2

22

)/(0473.0)(

)(00256.0)/(

hkmVPascalsP

mphVftlbP

ww

ww

⋅=

⋅=

[ ]

[ ]1000

)(2)()()/(

12

)(2)()()/(

mmtmmDPascalsPmNW

intinDpsfPftlbW

cww

cww

⋅+⋅=

⋅+=

2-14


mined. Equation 2.2-4 gives the weight of a conductorunder both ice and wind loading:

2.2-4Wherewb = bare conductor weight per unit length.wi = weight of ice per unit length.ww = wind load per unit length.ww+i= resultant of ice and wind loads.

2.2.8 Environmental Effects

The public considers overhead transmission lines asvery visible and, though most power engineers have dif-ficulty in understanding why, unattractive. Thus, one ofthe primary environmental effects of any transmissionline is their visual impact on their surroundings. A greatdeal of effort has been expended on making lines morevisually acceptable with decidedly mixed results. Fortu-nately, when uprating existing lines, most of the normalopposition to new lines is avoided unless the appearanceof the uprated line is significantly changed.

Because lines are highly visible and perceived as unat-tractive, they can have a negative impact on propertyvalues. This is typically much less of an issue with themodification of existing lines than with new lines.

Figure 2.2.9 shows a comparison of the relative impor-tance of some of the major environmental issues involv-ing overhead lines as determined by survey. It isinteresting that the top three factors are primarily amatter of human perception or belief, while the threeleast important issues are matters of physics.

Various attempts to reduce the visual impact of linesand the corresponding impact on property values havebeen made. There have been design competitions to findmore visually acceptable structures and research intomethods of compacting HV lines so they look more likedistribution lines.

Probably the most effective way to reduce public opposi-tion to transmission lines concerns putting them awayfrom where people live and work. Clearly, this is notalways possible, but as shown in Table 2.2-9, it is quiteeffective.

In the specific case of uprating, a variation on the classicphysician’s ethic. “First, do no harm” makes sense. Spe-cifically, uprating techniques that do not raise structurepeaks or make conductors more visible from a distanceare preferred.

This guide emphasizes line uprating methods where thevoltage of the line remains the same but current flow isincreased. Most of the techniques covered herein willleave the original ground level electric field, electricinduction, corona discharge levels and audible noise lev-els unchanged. However, the ground level magnetic fieldand magnetic induction levels will increase with thehigher line currents. Both environmental effects are lin-ear with current so that maximum original levels areeasily estimated by scaling with the increase in rating.

2.3 LINE THERMAL RATINGS

2.3.1 Introduction

The temperature and/or sag of overhead power trans-mission lines can be measured, but seldom are. Rather,in order to avoid excessive sag or loss of strength, a“maximum allowable conductor temperature” is typi-cally specified, and the conductor temperature is keptbelow this maximum by placing limits on the level andduration of power transferred over the line (MVA oramperes). If such limits are based on worst-case weatherconditions, they are called static ratings, and if based onactual weather conditions, they are called dynamic rat-ings. The calculation of thermal ratings for overheadlines is an essential part of the uprating process.

22 )()( wibiw Wwww ++=+

Figure 2.2-9 Median survey results as to why people oppose transmission lines.

Table 2.2-9 The Impact of Distance on Public Opposition to Power Transmission Lines

Distance from Line

Feeling Less than 1 mile More than 1 mile

Like it 2.3% 3.2%

Don’t care 32.6% 71.3%

Dislike it 65.1% 25.3%

2-15


The electrical power conductors of overhead transmis-sion lines carry relatively large electrical currents, areself-supporting, and energized at high voltage. They arestranded from wires of aluminum or copper, which maybe reinforced with a steel core. As the current flowingthrough a conductor increases, its temperatureincreases, and it elongates. This elongation increases thesag of the conductor between support points, decreasingthe clearance to people, ground, other conductors,buildings, and vehicles under the line. Beyond a certain“maximum allowable” sag, the line may flashover,resulting in either a power supply outage or injury to thepublic. If the conductor temperature remains high foran extended period of time, the strength of the conduc-tor and tensioned connectors may decrease, resulting inmechanical failure during the next occurrence of ice orhigh wind loading.

In the design of a new transmission line, the thermal rat-ing required for reliable system operation can beattained either by selecting a large conductor at a mod-erate maximum operating temperature or by using asmaller conductor at a higher maximum temperature.The higher sag resulting from higher operating tempera-tures can easily be accommodated by using taller ormore closely spaced structures.

In uprating an existing line, it is unusual if the existingconductor can be replaced by a significantly larger con-ductor since this would increase both transverse windloads and maximum tension loads, and require costlyand time-consuming rebuilding of existing structures. Itis also unusual if the existing conductor can simply beoperated at a significantly higher temperature withoutraising the existing attachment points or retensioningthe line, since this would lead to unacceptable violationsof minimum electrical clearances under maximum elec-trical loading.

2.3.2 Maximum Conductor Temperature

Modern transmission conductors are typically strandedfrom aluminum wires with a steel core added whereincreased strength is required. The temperature limit onall-aluminum or ACSR conductors is based on the max-imum sag or maximum loss of strength in the alumi-num. Temperature limits for normal ACSR conductorsin use today range from 50°C to 150°C (122°F to302°F). The temperature limit is normally selected atthe time the line is designed. The higher this tempera-ture, the higher the thermal capacity of the line, themaximum conductor sag, and the higher (or closer) thestructures required to maintain ground clearance.

If aluminum or copper conductor temperatures remainhigh (above 95 °C, or 203 °F) for an extended period of

time, the strength of the conductors and tensioned con-nectors may decrease, which eventually results inmechanical failure during ice or high wind occurrences.Generally, rating durations are kept short if maximumconductor temperatures are high (e.g., 4 hour maximumat 115 °C [239 °F] and 15 minutes at 125 °C [257 °F]).

These high temperature effects on conductor, hardware,and fittings are discussed in detail in Section 2.4.

2.3.3 Weather Conditions for Rating Calculation

Traditionally, power utilities use fixed “worst-case”weather conditions in order to calculate (static) line rat-ings. The impact of changes in these weather parametersupon thermal line ratings depends on the specific ratingsituation. Consider an overhead line with 795 kcmil (402mm2) of aluminum, 26/7, “Drake” ACSR conductor,whose static rating is based upon a maximum allowableconductor temperature of 100oC with an air tempera-ture of 40oC, full summer sun, and a wind blowing per-pendicular to the conductor axis at 2 ft/sec (0.61 m/sec).The static rating under these conditions is 1000 A.

Clearly, if the current in this conductor is 1000 A withthe assumed weather conditions, the conductor temper-ature is 100oC. Table 2.3-1 shows how the conductortemperature is affected by small changes in weather con-ditions. For example, the conductor temperature dropsto 92oC if there is no solar heating. The table also showshow the thermal rating (i.e., the current which yields atemperature of 100oC) changes with small changes inweather.

Note that with the conductor at a reasonably high tem-perature and near “worst-case” heat transfer conditions,the overhead line rating and conductor temperature arevery sensitive to wind direction, modestly sensitive to

Table 2.3-1 Variation in Conductor Temperature and Rating with Weather Conditions (for 795 kcmil [404 mm2], 26/7, “Drake” ACSR conductor with a maximum allowable conductor temperature of 100°C, an air temperature of 40oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec)

Range in Weather

Conditions

Line Rating @ 100°C

Conductor Temperature at 1000 A

(amperes) (°C) (°F)

None 1000 100 212

Air temp = 39°C 1010 99 210

No sun 1070 92 198

3 ft/sec (0.91m/sec) 1090 90 194

Parallel wind 750 133 271

2-16


changes in wind speed and solar heating, and lessaffected by small changes in air temperature. Otherminor factors are gradual changes in emissivity andabsorptivity of the conductor with age, and seasonalshifts in solar heating.

2.3.4 How Line Design Temperature Affects Line Ratings

Line design temperature is the maximum allowable con-ductor temperature for a particular line. As noted previ-ously, for normal conventional ACSR, it varies from50oC to 150oC. The impact of changes in the line designtemperature upon thermal line ratings depends on thespecific rating situation, but certain observations arepossible.

Until the early 1970s, the National Electric Safety Code(National Electric Safety Code 1997) suggested thatminimum electrical clearances were to be met at conduc-tor temperatures up to 120°F (49oC). Line thermalcapacity was typically calculated by conductor manu-facturers for a conductor temperature of 75oC, a tem-perature sure to avoid possible annealing problems withaluminum and copper.

In the 1970s, the NESC changed this position and statedthat the electrical clearances listed were to be met at“the maximum conductor temperature for which theline was designed to operate, if greater than 50oC, withno wind displacement” (excerpted from Rule 232.A.2).Thus the maximum allowable conductor temperature(MACT) used in line rating calculations may vary from50oC to 200oC according to available ground clearances,and consistency, with concerns about loss of tensilestrength at temperatures above 90oC.

Consider an existing overhead line with 795 kcmil(402 mm2) of aluminum, 26/7, “Drake” ACSR conduc-tor, whose static rating is based upon an air temperatureof 40oC, full summer sun, and a wind blowing perpen-dicular to the conductor axis at 2 ft/sec (0.61 m/sec).The rating of this existing line depends on the linedesign temperature as is shown in Table 2.3-2, where theline design temperature with this ACSR conductorranges from 50°C to 150oC.

For each line design temperature, the line rating isshown. Also shown is the increase in rating that corre-

sponds to an increase of 10oC in the line design temper-ature. For this ACSR conductor, the increase in sag for a10oC increase in conductor temperature decreases withincreasing line design temperature.

It is clear from this table why simple physical line modi-fications (such as raising support points or using “float-ing” dead-ends) are an effective means of uprating olderlines with relatively low design temperatures. Even mod-est increases in allowable sag result in relatively largeincreases in rating for such lines. It is also clear why suchtechniques are not usually helpful in uprating new lineshaving higher line design temperatures.

2.3.5 Heat Balance Methods

Around the world, utilities perform overhead line ratingcalculations in essentially the same way: by setting theheat input from Ohmic losses and solar heating equal tothe heat loss due to convection and radiation (EPRI1995). The specific formulas used to determine the heatbalance terms vary somewhat, but normally one of threemethods is used – the IEEE method (IEEE 1993), theCIGRE method (CIGRE 1992), or the EPRIDYNAMP method (Black et al. 1983).

Given the same assumed wind speed and direction, thesame conductor temperature and the same conductorelectrical and physical parameters, the thermal ratingfound with the three methods is similar if not identical.

To illustrate typical values of the heat balance terms, theIEEE method is used in the following development for aDrake ACSR conductor at 100oC.

Table 2.3-2 Variation in Line Rating with Design Temperature (for 795 kcmil [405 mm2], 26/7, “Drake” ACSR conductor with an air temperature of 35oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec [0.61 m/sec])

Line Design Temperature Line Rating

Increase in Line Rating for 10°C Change in Line

Design Temperature

(oC) (amps) (amps) (%)

50 374 213 57

75 797 107 13

100 1039 78 7.5

125 1221 63 5.2

150 1370 54 3.9

2-17


RadiationRadiation of heat from an overhead conductor is mod-eled in terms of the absolute temperature of the conduc-tor and its surroundings (taken as the air temperature):

2.3-1

As an example of radiation heat loss from a bare over-head conductor, consider Drake ACSR at 100oC and anair temperature of 40oC:

2.3-2qr = 24.44 W/m qr = 7.461 W/ft

ConvectionNatural ConvectionWith zero wind speed, natural convection occurs, wherethe rate of heat loss is:

2.3-3

Taking our example of Drake ACSR at 100oC, the natu-ral convection heat loss is:

2.3-4where: where:D = 28.14 mm D = 1.108 in.Tc = 100°C TC = 100oCTa = 40°C Ta = 40oC

ρf

= 1.029 kg/m3 ρf

= 0.0643 lb/ft3

qc = 0.0205 (1.029)0.5 qc = 0.283 (0.0643)0.5

(28.14)0.75 (1.108)0.75

(100–40)1.25 (100-40)1.25

= 42.4 W/m = 12.9 W/ft

Forced ConvectionWith the IEEE 738 and the CIGRE methods, forcedconvection is calculated with two separate formulas, andthe larger of the two values for forced convection heatloss is used.

2.3-5

2.3-6

The first two equations apply at low winds, but are toolow at high speeds. The last two equations apply at highwind speeds, being too low at low wind speeds. At anywind speed, the larger of the two calculated forced con-vection heat loss rates is used.

The convective heat loss rate is multiplied by the winddirection factor, Kangle, where φ is the angle betweenthe wind direction and the conductor axis:

2.3-7

0.0178 /

0.138 /

4 + 273Tc 100

= D W mqr 4 + 273Ta100

4 + 273Tc 100

= D W ftqr 4 + 273Ta100

ε

ε

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⋅ ⋅ ⋅⎢ ⎥⎢ ⎥⎛ ⎞−⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⋅ ⋅ ⋅⎢ ⎥⎢ ⎥⎛ ⎞−⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

−⋅⋅⋅=

−⋅⋅⋅=

4

1003134

100373

5.0108.1138.0

4

1003134

100373

5.014.280178.0

rq

rq

0 05 /

83 /

0.5 1.250.75 = 0. 2 ( - W mq )D T Tc ac f

0.5 1.250.75 = 0.2 ( - W ftq )D T Tc ac f

ρ

ρ

⋅ ⋅ ⋅

⋅ ⋅ ⋅

25.1)(5.0283.0

)5(25.1)(75.05.00205.0

aTcTfcq

saTcTDfcq

−⋅⋅=

−⋅⋅⋅=

ρ

ρ

100 + 40 100 40= = 7070

2 2o

film filmC T CT+

= =

ftWaTcTfk

f

wVfD

cq

mWaTcTfk

f

wVfD

cq

/)(

52.0

371.001.11

/)(

52.0

0372.001.11

−⋅⋅⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ ⋅⋅⋅+=

−⋅⋅⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ ⋅⋅⋅+=

μ

ρ

μ

ρ

( )

( ) ftWaTcTfk

f

wVfD

cq

mWaTcTfk

f

wVfD

cq

/

6.0

1695.02

/

6.0

0119.02

−⋅⋅

⋅⋅⋅=

−⋅⋅

⋅⋅⋅=

⎟⎠

⎞⎜⎝

⎛

⎟⎠

⎞⎜⎝

⎛

μ

ρ

μ

ρ

cos cos 0.368 sin (2 )angle = 1.194 - ( ) + 0.194 (2 )K φ φ φ+

2-18


Referring once again to our example of Drake ACSR at100oC we have:

2.3-8

2.3-9

Now select the larger of the two calculated convectionheat losses.

qc = 82.295 W/m qc = 25.052 W/ft

Since the wind is perpendicular to the axis of the con-ductor, the wind direction multiplier, Kangle, is 1.0, andthe forced convection heat loss is greater than the natu-ral convection heat loss. Therefore, the forced convec-tion heat loss will be used in the calculation of thermalrating.

Notice that if the wind had been nearly parallel to theline at 10o from the line direction, the wind directionmultiplier would be 0.517, and convection coolingwould have been similarly reduced.

Also, notice that the heat loss with no wind (naturalconvection) is much less than that for forced convectionwith even the low 2 ft/sec (0.61 m/sec) wind.

Solar HeatingOverhead conductors are typically 5oC to 10oC aboveair temperature due to solar heating alone, even if thecurrent in the conductor is zero. The conductor heatbalance described in these notes applies when there isonly solar heat input as well as when the conductor car-ries electrical current. The solar heat into the conductorin direct sun is a function of the solar heat flux density,

the angle of the solar beam relative to the line direction,and the conductor absorptivity (the fraction of incidentsolar radiation absorbed by the conductor). The result-ing temperature rise above air temperature is a functionof the conductor absorptivity and diameter as well asthe wind speed and direction.

According to the IEEE solar model, the maximum pos-sible conductor solar temperature rise above air temper-ature is on the order of 15oC (for still air). Fieldmeasurements of actual lines indicate that the typicalsolar rise is in the range of 5°C to 10°C.

With reference to Table 2.3-3, with a solar altitude of 70degrees (noon in June in New York) and clear atmo-sphere, the solar heat flux to a surface perpendicular tothe sun’s rays is approximately 1020 watts/ft2 or 95watts/m2. The maximum heat input to the conductor istherefore:

2.3-10

Ohmic LossesConductor resistance per unit length and the electricalcurrent on the line determine the Ohmic losses. Theresistance of a stranded conductor is a function of theconductivity of the component wires, the frequency, thecurrent density, the temperature of the wires, and thestranded construction. Resistance values at 25°C and75oC are readily available from the manufacturer or theAluminum Association.

The IEEE standard suggests that electrical resistancemay be calculated solely as a function of conductor tem-perature, ignoring dependence on current density. Forexample, the values of conductor resistance at high tem-perature, Thigh, and low temperature, Tlow, may be takenfrom the tabulated values in the Aluminum AssociationHandbook (Aluminum Association 1989). The conduc-

28.14 1.029 .60961.01 0.03721 52.04 10

.0295 (100-40) = 82.295 W/m

0.521.108 0.643 72001.01 0.3711 0.0494

.00898 (100-40) = 25.052 W/ft

0.52

= + qc

qc

⎡ ⎤⎛ ⎞⋅ ⋅⎢ ⎥⎜ ⎟⎢ ⎥−⎜ ⎟⋅⎢ ⎥⎝ ⎠⎣ ⎦⋅

⎡ ⎤⋅ ⋅⎛ ⎞⎢ ⎥+ ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⋅

0.6

25

2

0.011928.14 1.029 .6096

2.04 10

.0295 (100-40) = 76.88 W/m

0.61.108 0.0643 72000.1695

0.0494

.00898 (100-40) = 23.464 W/ft

c

c

= q

q

−⋅⎛ ⎞⋅ ⋅⎜ ⎟⎜ ⎟⋅⎝ ⎠

⋅

⋅ ⋅⎛ ⎞= ⋅⎜ ⎟⎝ ⎠

⋅

Table 2.3-3 Total Heat Flux Received by a Surface at Sea Level Normal to the Sun’s Rays

Solar Altitude, Hc

QS for a Clear Atmosphere

QS for an Industrial Atmosphere

Degrees (w/m2) (w/ft2) (w/m2) (w/ft2)

60 1000 92.9 771 71.6

70 1020 95.0 809 75.2

80 1030 95.8 833 77.4

90 1040 96.4 849 78.9

W/ft 4.4092.0955.0

W/m 3.140281.010205.0

=⋅⋅==⋅⋅=

C

C

q

q

2-19


tor resistance at any other temperature, TC, is found bylinear interpolation according to Equation 2.3-11.

2.3-11

This method of resistance calculation allows the user tocalculate the high and low temperature resistance valuesby whatever means is appropriate. See, for example, ref-erences (Douglass and Rathbun 1985 and (Lewis andTuttle 1958).

In the example calculation, the resistance of the DrakeACSR conductor is calculated for a conductor tempera-ture of 100oC:

2.3-12

Steady-State Thermal Rating Now that the radiation heat loss, the convective heatloss, the solar heat input and the resistance of the con-ductor have been determined, the steady-state thermalrating can be calculated as follows:

2.3-13For the example case:

qc = 82.295 W/m qc = 25.052 W/ft qr = 24.44 W/m qr = 7.461 W/ftqs = 14.0 W/m qs = 4.26 W/ft

(from equations) (from equations)R(100) = 9.390⋅10-5 Ω/m R(100) =2.862·10-5Ω/ft

Thermal Rating – Dependence on Conductor ParametersThe rating of bare overhead conductors depends on thevarious conductor parameters including (see Table2.3-4):

• Outside diameter

• Emissivity and absorptivity

• Electrical resistance per unit length

At the time of construction, the choice of conductortype and size defines the resistance and outside diame-ter. Normally, the emissivity and absorptivity of newaluminum conductor are initially in the range of 0.2 to0.3 but increase to values close to 1.0 as the conductorages. Figure 2.3-1 shows this increase in emissivity withtime for energized conductors.

The actual rate at which the conductor emissivity andabsorptivity increase with time is a function of the linevoltage and the density of particulates in the air. Twoobservations, however, can be made. The emissivity andabsorptivity are correlated, so it is unlikely that oneparameter will be high and the other low. Also, new con-ductors will have emissivity and absorptivity values inthe range of 0.2 to 0.3, and old conductors will have val-ues in excess of 0.5.

As stated above, resistance and diameter are tightly cor-related. Thus, aluminum stranded conductors of a givendiameter will have a corresponding resistance per unitlength. The exceptions to this are:

• The component strands have a different conductivityfrom that of standard aluminum (e.g., copper).

• Conducting strands are trapezoidal rather thanround (e.g., TW conductor).

• The steel core strands are not used or are replaced byaluminum-clad steel wires (e.g., ACSR/AW).

)T lowR(+)T low - T c(*

T low - T high

)T lowR( - )T highR(=)T cR( ⎥⎦

⎤⎢⎣⎡

( )

m

RRRR

/10390.9

7550

510283.7510688.8510283.7

251002572

)25()75()25()100(

5 Ω⋅=

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡ −⋅−−⋅+−⋅=

−⋅−−

+=

−

⎟⎠⎞

⎜⎝⎛

( )

ft

RRRR

/10862.2

7550

10220.210648.210220.2

251002572

)25()75()25()100(

5

555

Ω⋅=

⋅⎥⎦

⎤⎢⎣

⎡ ⋅−⋅+⋅=

−⋅−−

+=

−

−−−

⎟⎠⎞

⎜⎝⎛

(100) (100)c r s c r sq q q q q q

I IR R

+ − + −= =

AA

II

994994

10862.2

26.4461.7052.25

5510390.9

0.1444.24295.82

==

⋅

−+=

−−

−+=

Table 2.3-4 Illustration of the Effect of Diameter, Resistance, Emissivity and Absorptivity on Thermal Rating

Conductor Description

OutsideDiameter

(in.)

Resis-tance

@ 25 °C(Ohms/mi)

Emissivity and

AbsorptivityThermal

Rating (A)

Drake 1.108 0.1170 0.5 & 0.5 996

Drake/TW 1.010 0.1170 0.5 & 0.5 976 (-2.0%)

Drake/AW 1.108 0.1129 0.5 & 0.5 1014 (+1.8%)

Arbutus AAC 1.026 0.1200 0.5 & 0.5 962 (-3.4%)

CU 500 kcmil 0.811 0.1196 0.5 & 0.5 909 (-8.7%)

Drake 1.108 0.1170 0.9 & 0.9 1046 (+5.0%)

Drake 1.108 0.1170 0.3 & 0.3 971 (-2.5%)

2-20


2.3.6 Thermal Ratings—Dependence on Weather Conditions

It is clear from the preceding discussion that the thermalrating of an overhead line depends on the weather con-ditions along it, as well as on the type of conductor andits maximum allowable operating temperature. Manyutilities around the world adjust their line ratings forseasonal variation in air temperature, recognizing thatair temperature is lower and ratings can be higher in thewinter than in the summer. Of course, in areas where theseasonal change is small (near the equator), or wherethe fluctuations in any season are larger than the sea-sonal average difference, this does not make sense. Otherutilities adjust thermal ratings for day and night byincluding or ignoring solar heating, and others adjustthe wind speed, using a more conservative (lower) windspeed for continuous ratings than for emergency ratings,which tend to have a low probability of occurrence.

Many utilities have installed real-time monitoring sys-tems, adjusting their line ratings for actual real-timewind speed, wind direction, solar heating, and air tem-perature. This technique is discussed in more detail inSection 2.8.

In order to illustrate the effect of changing weather con-ditions on ratings, consider Table 2.3-5.

Figure 2.3-1 Transmission line conductor emissivity as a function of time (House et al. 1963)

Table 2.3-5 Effect of Weather Conditions on Thermal Ratings. (In all cases, the conductor is 26/7 795 kcmil

(0.61 mm2) ACSR (Drake) with emissivity = absorptivity = 0.5, Direct sun on June 10, clear air, at sea level, latitude = 40° with the conductor at 100°C.)

Air Temperature

(°C)

Wind Speed(ft/sec)

Wind Direction Relative to the

Line(90 =

Perpendicular)Time of

Day

Thermal Rating

Amperes

40 2 90 2 PM 996

40 2 90 12 PM 986 (-0.8%)

40 2 90 6 PM 1045 (+4.9%

30 2 90 2 PM 1081 (+8.5%)

40 0 90 2 PM 838 (-15.6%)

40 3 90 2 PM 1183 (+18.7%)

40 6 10 2 PM 968 (-2.8%)

2-21


By reviewing this limited series of rating calculations, anumber of important aspects of line rating dependenceon weather can be drawn:

• Rating variation due to solar heating changesthroughout the day is less than 5%.

• Air temperature variation is important. A differenceof 10°C in air temperature causes a line rating changeof nearly 10%.

• Relatively small differences in wind speed, in therange of 0 to 3 ft/sec (0.91 m/sec) can make a big dif-ference in the line rating, generally 10% to 20%.

• The wind direction relative to the line is as importantas the speed. A 6 ft/sec (1.8 m/sec) wind blowing nearparallel to the line (10°) yields a slightly lower linerating than a 2 ft/sec (0.61 m/sec) wind blowing per-pendicular to the line.

2.3.7 Transient Thermal Ratings

The need for increased thermal capacity in overheadlines is often driven by occasional, sharp increases inload after certain system contingencies. For example, anHV line might only reach high current levels after theloss of an EHV line or a critical generating facility. Sincethese occasions of high load occur infrequently and maypersist for short time periods, it is often useful to con-sider transient thermal ratings for lines.

The temperature of an overhead power conductor isconstantly changing in response to changes in electricalcurrent and weather. In this method, however, weatherparameters (wind speed and direction, ambient temper-ature, etc.) are assumed to remain constant, and anychange in electrical current is limited to a step changefrom an initial current, Ii, to a final current, If, as illus-trated in Figure 2.3-2.

Immediately prior to the current step change (t = 0–),the conductor is assumed to be in thermal equilibrium.That is, the sum of heat generation by Ohmic losses and

solar heating equals the heat loss by convection andradiation.

Immediately after the current step change (t = 0+), theconductor temperature is unchanged (as are the conduc-tor resistance and the heat loss rate due to convectionand radiation), but the rate of heat generation due toOhmic losses has increased. Therefore, at time t = 0+, thetemperature of the conductor begins to increase at a rategiven by the non-steady-state heat balance equation.

As time passes, the conductor temperature increases,yielding higher heat losses due to convection and radia-tion, and somewhat higher Ohmic heat generation dueto the increased conductor resistance. After a large num-ber of “thermal time constants”, the conductor temper-ature approaches its final steady-state temperature (Tf).

The transient thermal rating is normally calculated byrepeating the preceding calculations of Tc(t) over arange of If values, then selecting the If value that causesthe conductor temperature to reach its maximum allow-able value in the allotted time.

The transient thermal rating of an overhead line isdependent on the duration of the elevated current, themaximum temperature that the conductor is allowed toattain during the rating period, and on the starting tem-perature of the conductor. For example, with the DrakeACSR that was used for rating calculations previously,the transient ratings for various rating durations, maxi-mum temperatures, and starting temperatures are asshown in Table 2.3-6.

The advantage to using transient ratings is that the linecan be loaded above its continuous rating without vio-lating the constraints on sag clearance or annealing, but

Figure 2.3-2 Temperature response of a bare overhead conductor to a step-change in current.

2

c 2c s c r

p

dT c+ + = + R ( )q q qmC I T cpc r sdt1dT = R( ) + - -q q qT I

dt mC⎡ ⎤⎣ ⎦

Table 2.3-6 Transient Ratings Versus Rating Duration

Rating duration

Maximum temp Starting Temp Rating

(Minutes) (oC) (oC) (A)

continuous 100 N/A 1040

60 100 50 1045

30 100 50 1090 (+4.8%)

15 100 50 1230 (+18.3%)

15 100 75 1135 (+9.1%)

2-22


the drawback is that the load must be reduced to thecontinuous rating or below within a short time (15 to 30min). See, for example, (Black and Rehberg 1985) and(Davidson 1969).

2.4 EFFECTS OF HIGH-TEMPERATURE OPERATIONS

2.4.1 Introduction

For any given high-voltage conductor, there are usuallyat least two current limits specified—the conductor’snormal rating, and the emergency rating (see Section2.3). The conductor’s normal rating specifies how muchcurrent may flow in the circuit on a continuous basis,whereas the emergency rating specifies how much cur-rent can flow under emergency conditions for a specifiedamount of time—e.g., 30 minutes. A typical emergencyrating may be applicable in the case where there is anunexpected outage on a parallel circuit requiring ashort-duration increase in the load flow.

The above “normal” current flow that is required duringemergency loading will, if it remains unchecked, result ina thermal overload of the circuit, or significantlyreduced clearances leading to a flashover of the circuit.Regardless of the case, the two issues that require atten-tion are the loss of conductor strength and increasedconductor sag. Ideally, transmission line operators aimto maximize the load on a particular circuit while mini-mizing the annealing (softening) of the circuit’s conduc-tor. Annealing causes a decrease in the conductor’sstrength and performance, necessitating the eventualreplacement of this component. Because of the difficultyassociated with taking a line out of service, and the largeexpense associated with the replacement of a circuit’sconductor, the operator clearly needs to balance theneed for increased load flow with the economic riskassociated with the premature replacement of the com-ponent, and the loss of service life or the safety riskassociated with providing inadequate clearances.

This section reviews issues related to the effects of high-temperature operation, including annealing, calculation

of sag and tension, thermal and creep elongation, andconnectors and conductor hardware at high temperature.

2.4.2 Annealing of Aluminum and Copper

The American Society for Testing and Materials(ASTM) standards and the International EngineeringConsortium (IEC) standards specify the minimum ten-sile strength of aluminum and copper wires, which is thestress at which the wire breaks. For aluminum and cop-per wires, the tensile strength of the materials decreaseswith time if operated at temperatures above 75°C, whilethe tensile strength of galvanized, aluminum-clad, orcopper-clad steel wires remains constant at tempera-tures below 300°C. Thus, the extended exposure of con-ductors made up largely of aluminum or copper wires totemperatures above 75oC can eventually lead to tensilefailures during high ice and/or wind loading events.

Table 2.4-1 shows experimental results for a test con-ducted by Troia (Troia 2000). The high-temperaturesimulation used an ACSR conductor “Raven” with a 6/1stranding ratio. In this study, four sets of conductorsand connectors, and three sample loops, were operatedat a temperature of 100°C, and cycled for 125, 250, and500 cycles, respectively. The fourth set of samples wascontinued to 1000 current cycles at the 100°C tempera-ture rise. A second group of four sets of sample testloops were operated at 175°C, and the current cyclecounts were 125, 250, 500, and 1000. Upon completion,a Rockwell H scale was used to measure the hardness ofeach sample, and as expected, the average hardness wasdetermined to be directly proportional to the tempera-ture and duration of heating. Conductors heated to100°C exhibited a decrease in hardness of up to 22%after 1000 cycles, and conductors heated to 175°Cshowed a decrease in hardness of up to 92.5% after only250 cycles. Thus, annealing of the conductor was exten-sive at the higher operating temperature, and hardnessreadings could not be measured for conductors havingbeen cycled 500 or 1000 cycles.

Clearly, the results of this and other studies indicate thatthe prolonged operation of high-voltage conductorsincluding ACSR at very high temperatures reduces the

Table 2.4-1 Hardness Resultsa

a. Rockwell H scale, 1/8 in. ball, 60 kgs.

Conductor Cycle Temp Average Hardness % Difference Temp Average Hardness % Difference

ACSR (6/1) ‘Raven’

0 - 33 - - 37.3 -

125 100 23.6 28.5 175 15.9 57.4

250 100 19.4 41.2 175 2.8 92.5

500 100 20.8 37.0 175 0b

b. Material hardness too soft for accurate readings on Rockwell H scale.

-

1000 100 22.6 31.5 175 0b -

2-23


mechanical strength, integrity, and performance of theoverhead system. It is also clear that the damage to thealuminum is of a cumulative nature and that the pro-longed high temperature operation will significantlyreduce the expected service life of the delivery system.

Figure 2.4-1 shows the influence of prolonged high-temperature operation on the tensile strength of alumi-num conductor. The graph shown has been developedbased on test data of 1350-H19 “EC” hard drawnaluminum wires. In general, tensile strength reduction ofaluminum wires at temperatures of less than 90oC isconsidered negligible, and the effect of prolonged opera-tion at this temperature will have very little effect on theservice life of the aluminum conductor. At 100oC, the

tensile strength of the wire is reduced by 10% after 5000hours, equivalent to a little more than a half a year, andat 125oC, the tensile strength of the aluminum conduc-tor is reduced 10% after 250 hours, a little more than 10days of continuous operation. The effects of the high-temperature operation on the aluminum conductor areirreversible, and the damages experienced by theconductor are cumulative.

Aluminum anneals at a slower rate than copper wirewhen exposed to identical conditions. Even though theuse of copper conductors has significantly decreasedover the years, a large number of low- to medium-volt-age lines with copper conductors are still operated. Theissues associated with the prolonged operation of thesewires at very high temperatures are similar to the issuesencountered with aluminum conductors.

For example, Figure 2.4-2 shows the reduction in tensilestrength with time and temperature for a sample of 0.081in. (0.2 cm) diameter hard drawn copper wire. Sincethere are 8760 hours in a year, the logarithmic diagramclearly shows that the sustained operation of the copperwire at 65oC yields no measurable reduction in the ten-sile strength, while the sustained operation of a copperwire at 100oC yields a 10% reduction in the tensilestrength in 600 hours (25 days). More critically, the oper-ation of the same wire at a temperature of 125oC for lessthan 40 hours reduces the wire tensile strength by 10%.

The remaining strength of AAC, AAAC, ACAR, andACSR conductor wires can be estimated with the fol-lowing predictor equations. The use of these equations isacceptable even in the case in which several emergency-rating episodes have occurred.

Figure 2.4-1 Annealing of 1350-H19 hard-drawn aluminum wire.

Figure 2.4-2 Annealing of 0.081–in. diameter hard-drawn copper wire (Southwire).

2-24


Definition of Terms:

RS1350

= Residual aluminum (1350 Alloy) strength as apercentage of initial strength [%].

RS6201

= Residual 6201 Alloy strength as a percentageof initial strength [%].

RSCOM

= Residual strength of composite conductor asa percentage of initial strength [%].

T = Temperature [°C].

t = Elapsed time [hours].

d = Strand diameter [mm, in.].

A1350

= Area of aluminum (1350 Alloy) strands [sqmm, sq in.].

A6201

= Area of 6201 alloy strands [sq mm, sq in.].

AT = Total area [sq mm, sq in.].

STR1350

= Calculated initial strength of the aluminum(1350 Alloy) strands [N, lbs].

STRST

= Calculated initial strength of the steel core[N, lbs].

STRT

= Calculated initial strength of the conductor[N, lbs].

Predictor Equations: (Metric)

AAC:

2.4-1If (-0.24T + 134) > 100, use 100 for this term.

AAAC:

2.4-2

If (-0.52T + 176) > 100, use 100 for this term.

ACAR:

2.4-3

ACSR: 2.4-4ACSR:

2.4-5

Predictor Equations: (English)

AAC:

2.4-6

If (-0.24T + 134) > 100, use 100 for this term.AAAC:

2.4-7

If (-0.52T + 176) > 100, use 100 for this term.ACAR:

2.4-8

ACSR:

2.4-9

As previously shown, when applying these equations,the cumulative strength reduction for multiple expo-sures at the same conductor temperature is additive;however, this is not true for multiple exposures at differ-ent conductor temperatures. To determine the cumula-tive strength reduction for a series of high-temperatureexposures at different temperatures and times, each ofthe exposures must be expressed in equivalent time atthe highest temperature experienced by the conductorbefore finding the equivalent time. The following exam-ples illustrate a possible scenario that an ACSR andAAC conductor might experience during one year ofservice.

E x a m p l e 2 . 4 - 1 : T h e c o n d u c t o r i s 7 9 5 k c m i l(405 mm2)ACSR “Drake”. During one year of opera-tion, it is subjected to 7500 hours at 75°C, 1200 hours at100°C, 50 hours at 125°C, and 10 hours at 150°C. Whatis the remaining strength (RS) of the conductor?

Using Equation 2.4-5, we know the following equation:

ACSR:

and, if (134 – 0.24T) >100, use 100; if (0.241- 0.00254T)> 0, use 0.

a) 7500 hours at 75°C

7500 hours at 75°C has 100% remaining, which equals 0minutes at 150°C.

( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+= dRS54.2

0.095 - T 0.001

1350 t 134 T 0.24-

( )( ) ⎟

⎠⎞

⎜⎝⎛−

+= dRS54.2

0.118 - T 0.0012

6201 t 176 T 0.52-

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

TTCOM A

A

A

ARS 6201

62011350

1350 RS RS

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

T

ST

TCOM STR

STR

STR

STRRS 109 RS 1350

1350

( ) ( ) d

COMRS1.0

0.00254T - 0.241t 0.24-134=

( ) ( ) d

COMRS1.0

0.095 - 0.001Tt 0.24-134 −=

( ) ( ) d

COMRS1.0

0.118 - 0.0012Tt 1760.52T- −+=

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

TTCOM A

A

A

ARS 6201

62011350

1350 RS RS

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

T

ST

TCOM STR

STR

STR

STRRS 109 RS 1350

1350

( )0.1

(0.241 - 0.00254T)134-0.24 t d

COMRS⎛ ⎞⎜ ⎟⎝ ⎠=

( ) ( )0.1

0.241 - 0.00254T

0.1 -(0.241 0.00254T)

1.108

134-0.24 t

(134 - (0.24 x 75)) x (7500)

100%

d

COMRS⎛ ⎞⎜ ⎟⎝ ⎠

=

==

2-25


b) 1200 hours at 100°C

1200 hours at 100°C has 99% remaining, which equals20 minutes at 150°C.

c) 50 hours at 125°C

50 hours at 125°C has 99% remaining, which equals 2hours at 150°C.

d) 10 hours at 150°C

10 hours at 150°C has 95% remaining.

To calculate the total loss of conductor strength, thesum of the equivalent times (hours) at 150°C is found.In this example, the sum is:

The remaining strength for the in-service conductor is95%.

Example 2.4-2: The conductor is 37 kcmil (19 mm2)AAC “Arbutus”. During one year of operation, it is sub-jected to 7500 hours at 75°C, 1200 hours at 100°C, 50hours at 125°C, and 10 hours at 150°C. What is theremaining strength (RS) of the conductor?

Using Equation 2.4-6,

AAC:

and, if (134 – 0.24T) >100, use 100.

a) 7500 hours at 75°C

7500 hours at 75°C has 98.3% remaining, which equals1 hour at 150°C.

b) 1200 hours at 100°C

1200 hours at 100°C has 87.4% remaining, which equals125 hours at 150°C.

c) 50 hours at 125°C

50 hours at 125°C has 92% remaining, which equals 15hours at 150°C.

d) 10 hours at 150°C

10 hours at 150°C has 93% remaining.

To calculate the total loss of conductor strength, thesum of the equivalent times at 150°C is found. In thisexample, the sum is:

The remaining strength for the in-service conductor is87%.

As expected, the example calculations predict that thecontinuous high-temperature operation will cause thetensile strength of the AAC conductor to deterioratefaster than in the case of the ACSR conductor. In Fig-ure 2.4-1, the graph showing the loss of strength for

0.11.108-(0.241 - 0.00254T)(134 - (0.24 x 100)) x (1200)

99.17%

⎛ ⎞⎜ ⎟⎝ ⎠=

=

0.11.108-(0.241 - 0.00254T)= (134 - (0.24 x 125)) x (50)

= 99.17%

⎛ ⎞⎜ ⎟⎝ ⎠

0.11.108-(0.241 - 0.00254T)= (134 - (0.24 x 150)) x (10)

= 95.19%

⎛ ⎞⎜ ⎟⎝ ⎠

0.1

0.11.108

-(0.241 - 0.00254T)COM

-(0.241 - (0.00254 x 150))

0 + 0.3 + 2 + 10 = 12.3 hours at 150 C.

RS = (134 - 0.24T) t

= (134 - (0.24 x 150))

x (12.3)

= 95%

d⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

( ) ( )0.1

0.001T - 0.095134-0.24 t d

COMRS −=

0.1d

0.11.026

-(0.001 T - 0.095)

1350

-(0.001(75) - 0.095)

RS = (134 - 0.24 T) t

= (134 - (0.24 x 75)) x (7500)

= 98.3%

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

0.11.026-((0.001 x 100) - 0.095)= (134 - (0.24 x 100)) x (1200)

= 87.4%

⎛ ⎞⎜ ⎟⎝ ⎠

0.11.026-((0.001 x 100) - 0.095)= (134 - (0.24 x 125)) x (50)

= 91.95%

⎛ ⎞⎜ ⎟⎝ ⎠

0.11.026-((0.001 x 100) - 0.095)= (134 - (0.24 x 150)) x (10)

= 92.8%

⎛ ⎞⎜ ⎟⎝ ⎠

0.1

0.11.026

-(0.001 T - 0.095)1350

-(0.001(150) - 0.095)

1 + 125 + 15 + 10 = 151 hours at 150 C.

RS = (134 - 0.24 T) t

= (134 - (0.24 x 150)) x (151)

= 86.9%

d⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

2-26


individual strands of aluminum indicates that after 150hours the remaining strength of the hard-drawn alumi-num wire is 82%. When compared to the remainingstrength value calculated using the predictor equations,the AAC conductor appears to be 5% stronger than pre-dicted by using the data of the individual aluminumstrands. Much of this difference in the prediction of thestrength loss in the AAC conductor can be attributed todifferences in behavior between the stranded conductorand an individual strand of aluminum and to differencesin the nominal and actual dimensions of the manufac-tured product.

Similarly, using strand data, the prediction equationsshow the ACSR conductor to be approximately 13%stronger than the tensile strength predicted by using theindividual aluminum strand data itself. The difference inthe remaining tensile strength can be directly attributedto the presence of the steel reinforcing strands which aresignificantly stronger than a comparably sized alumi-num strand and are also not affected by temperaturesbelow 300°C.

2.4.3 Sag Tension Models for ACSR Conductors

The traditional sag and tension model used throughoutthe industry is the model developed and promoted bythe Alcoa-Fujikura LLC (Alcoa) (Alcoa 2003). TheAlcoa sag and tension prediction model and methodsassume that the magnitude of the compression stressesresulting from the manufacturing process are negligibleand therefore do not affect the behavior of the conduc-tor regardless of the operating temperature. Therefore,the model ignores the effects of aluminum compression.

The Alcoa sag and tension model focuses on the coeffi-cient of thermal expansion phenomenon, whichaccounts for the fact that the aluminum strands expandat nearly twice the rate of the steel strands for the sameincrease in temperature. Consequently, as the tempera-ture of the conductor increases significantly, the alumi-num strands expand more rapidly than the steel strands.This shifts a continuously increasing percentage of thecatenary tension onto by the steel strands (i.e., the alu-minum “unloads” its share of the original tension). Atsome point (i.e., commonly called the “knee point”) thetension in the aluminum strands approaches a value ofzero. At this time, the steel strands of the conductorcarry all of the catenary tension of the composite wire.Based on this premise, and once the knee point temper-ature has been exceeded, the sag of the ACSR conduc-tor is proportional to the rate of thermal expansion ofthe steel strands. It should be noted that the Alcoa sagand tension prediction model was developed in the earlypart of the last century when the stranding of the mostcommonly used ACSR conductors was six aluminum

strands to one steel strand. Nevertheless, the sags andtensions predicted by the Alcoa model generally corre-late very well for most conductors operated at tempera-tures not exceeding 75°C to 100°C.

Today, medium-to-large ACSR conductors may have asmany as four layers of aluminum strands surrounding amultistranded steel core. Based on the constructionmethods used to manufacture these multilayered con-ductors, it is very likely that a significant number of alu-minum strands are capable of supporting limitedcompression forces (as a result of the confinement pro-vided by underlying and overlaying layers) and that theresulting conductor harbors noticeable built-in stresses.The EPRI technical report Conductor and AssociatedHardware Impacts during High Temperature Operations– Issues and Problems, published in December 1997 byShan and Douglass (EPRI, TR-109044) concluded thatit is more likely that such multilayered conductors fol-low a sag and tension model originally proposed byNigol (Nigol and Barrett 1980).

The Nigol sag and tension model, as shown in Figure2.4-3, assumes that the aluminum strands do not changefrom tension to compression until a fixed limiting valueis reached. In Nigol’s sag and tension model, as the alu-minum changes from tensile to compression stresses, theelastic modulus is assumed not to change. Nigolhypothesizes the existence of compression stresses in thealuminum below the “birdcaging” temperature butassumes that the outer layer of aluminum strandsremains in tension. Therefore, Nigol assumes that thetension in the outer layer strands denies the inner layerto expand radially and buckle outward. Nigol concludesthat, since the inner layer is in compression and theouter layer is in tension, and since the outer layerpresses radially inwards against the expanding innerlayer, the aluminum strands of the inner layer arepressed against the steel cores and birdcaging is effec-tively negated. Consequently, based on this hypothesis,Nigol concluded that the elastic modulus remainsunchanged even though the net aluminum stresseschange from tension to compression.

Thus, Nigol’s sag-tension model assumes that, as theconductor temperature increases towards the birdcagingtemperature, the tensions in the outer layers of alumi-num strands and the corresponding inward directedradial forces decrease. At the same time, Nigol’s modelassumes that there is an increase in the radial forces ofthe outer layer and also an increased axial compressionin the strands of the inner layers. Nigol, therefore,concludes that at the time when the birdcaging tempera-ture is reached, the inner and outer radial forces are

2-27


balanced, and the compressive stresses that are createdreach their limiting value.

Barrett’s sag and tension prediction model (Barrett et al.1982) departs from Nigol’s model at this point. Barretthypothesizes that at the birdcaging temperature, theradial forces within each of the aluminum strand layersbalance. Based on Barrett’s hypothesis, the aluminumstrands of a layer move radially outward as the tempera-ture rises, resulting in a different elastic modulus to beused for the aluminum strands. Therefore Barrettdescribes the use of two compression moduli—the firstvalue to be used at temperatures below the “knee point”and the second to be used at temperatures above thebirdcaging temperature.

Contrary to Nigol and Barrett, Rawlins (Rawlins 1998)proposes that there are no compression stresses abovethe knee point, but rather promotes the idea of largebuilt-in tensile stresses that are the result of the manu-facturing process. In Rawlins’s sag and tension predic-tion model, the point at which the aluminum stressesbecome tensile is also the point when there is a changein the elastic modulus. Therefore, Rawlins proposes thatthese stresses cause permanent elongations when com-pared to the other sag and tension models at the samelevel of tension. Figure 2.4-3 shows graphical represen-tations of the four hypotheses explaining the behavior ofhigh temperature conductors.

2.4.4 Axial Compressive Stresses

Work performed previously by Nigol and Barrett (Bar-rett 1982) clearly showed that compression stresses in

the aluminum strands are capable of greatly contribut-ing to the sag of conductors at high operating tempera-tures. A simplified illustration of the influence ofcompression stresses in the aluminum strands at hightemperatures is illustrated in Figure 2.4-4.

The first sketch (Sketch 1) shows a length of the conduc-tor at ambient temperature where the lengths of all ofthe aluminum and steel strands are equal. The secondsketch (Sketch 2) shows an instance of the behavior ofthe conductor once the conductor length is heated to atemperature above ambient conditions. Because of thedifferences in the coefficients of thermal expansion ofthe aluminum and the steel strands (discounting for nowissues such as stranding, manufacturing, etc), thelengths of the aluminum and steel strands will differ byan amount proportional to the temperature differenceand the difference in the coefficients of thermal expan-sion. Of course, this scenario assumes that each type ofmaterial would be free to expand and not restricted inany manner.

Similarly, the third sketch (Sketch 3) shows the behaviorof the same length of conductor heated to a temperaturesignificantly above ambient conditions, with the differ-ence that the two materials are restricted from expand-ing independently of each other. As a result of thedifferences in the coefficients of thermal expansion, theproportion of the stresses carried by each type of mate-rial will change.

Finally, the fourth sketch (Sketch 4) shows the conduc-tor in the case at which the compression in the alumi-num strands is balanced by a tensile load in the steelcore (i.e., the phenomenon most commonly referred toas “aluminum compression”). As the conductor reachesthe birdcaging temperature (i.e., the point at which thealuminum strands expand outward to compensate forthe increase in length), the aluminum strands move out-ward, yielding to the inherent compression stressinduced by the constrained thermal expansion. At this

Figure 2.4-3 Sag-tension models.

Figure 2.4-4 Manufacturing effects of ACSR conductor.

2-28


point (i.e., the point in the loading at which birdcagingis first observed), the tensile stress in the steel core farexceeds the value of the compression stress in the alumi-num strands.

2.4.5 Built–In Stresses

When multistranded conductors are manufacturedusing a combination of steel and aluminum wires, thetemperatures of the individual wire strands during themanufacturing process may vary, especially that of thesteel core when compared to the aluminum strands.Contrary to the manufacturing of these multimaterialconductors, the same problem is not encountered in themanufacturing of All Aluminum Conductors (AAC),since they are constructed from the same homogeneousmaterial. For ACSR conductors, the variance in thetemperatures of the different types of stranding materi-als contributes to the composite behavior of the conduc-tor. Therefore, when the conductor is placed under load,the variance in the temperature during manufacturing islikely to impact the sag and tension characteristics ofthe conductor. Unfortunately, quantitative values usefulin estimating these manufacturing effects are neitherprovided by the manufacturer nor otherwise published.

For example, if one assumes that a cold steel core isstranded with hot aluminum wires around the outside,the resulting conductor’s steel core will be slightlylonger than the outer aluminum layers once the conduc-tor is allowed to reach thermal equilibrium. As a resultof the temperature differences, the commonly namedknee point (i.e., the point at which the temperature ofthe complete length and cross-section has increased to alevel at which the stresses in the aluminum strandsapproach zero) will shift relative to the knee point of aconductor constructed with steel and aluminum strandsat the same temperature.

2.4.6 Sag Tension Calculations

Bare overhead conductors are flexible and uniform inweight. These characteristics allow conductors toassume a catenary shape when suspended between sup-port points. The shape of the catenary assumed by theconductor changes continuously as a result of climaticchanges such as ambient temperature, operating condi-tions such as the amount of current being transferred,service life, and weather-related loads such as wind,snow, and ice.

Because of the threat to human life and property, it iscritical to ensure adequate horizontal and vertical clear-ances under all circumstances. Therefore the linedesigner is challenged to consider all weather and elec-trical loading cases to ensure that the breaking strength

of the conductor is not exceeded and that the suggestedminimum clearances are maintained.

In this subsection the mechanical and thermal proper-ties acquired in the EPRI Conductor High TemperatureProject experiments are presented, and the calculatedsags and tensions are compared to values predictedusing traditional sag and tension prediction data, meth-ods, and tools. For clarity, these comparisons have beenseparated into two parts; the first addresses sags of levelspans, the second addresses sags for inclined spans.

To illustrate the use of the results and to demonstratethe differences in the predicted sags and tensions, threeACSR conductors of varying stranding ratios (low,medium, and high aluminum- to-steel stranding ratios)have been analyzed at different temperatures. The con-ductor sag analyses and comparisons were made atroom temperature (23ºC), at a temperature of 120ºC,and at a temperature of 150ºC. Also, sags computed atlevel spans are compared to values at an inclined span of15° and 30°. The underlying principles behind sag ten-sion calculations for both level and inclined spans areoutlined in the following subsections.

Sag and Tension of Level SpansThe shape of a catenary of a conductor is a function ofthe conductor’s weight per unit length, w, the horizontalcomponent of tension, H, the span length, S, and theconductor sag, D. Figure 2.4-5 shows an illustrationrelating all of these parameters for a level conductorspan. The actual conductor length, L, constitutes thestretched length of conductor (Trash et al. 1994).

Figure 2.4-5 Catenary sag model – level span.

2-29


The exact catenary equation representing the height ofthe conductor, y(x), at its lowest point along the span isgiven by the following equation:

2.4-10

For level conductor spans, the low point is in the centerand the total sag, D, is found by substituting x = S/2 inEquation 2.4-10. The resulting hyperbolic catenary rela-tion for sag then becomes:

2.4-11

The horizontal component of tension, H, is located atthe point in the span where the conductor slope is hori-zontal, or at the midpoint for level spans. The conductortension, T, is found at the ends of the spans at the pointof attachment and is calculated using the followingequation.

2.4-12

Rearranging the hyperbolic catenary equation for a levelspan, along with the substitution of x = S/2 for levelspans corresponds to a conductor length of:

2.4-13

It should be noted that while the above equationsdescribe the behavior of ideal (with perfectly elastic stressand strain characteristics) concentric-lay stranded con-ductors, actual conductors such as ACSR conductorsexhibit nonlinear behavior when loaded from an initialtension to some final value due to ice, wind, or tempera-ture loading. Permanent elongation from creep andheavy loading also affects the resulting sag. Also, high-temperature operations result in thermal elongation ofthe steel and aluminum strands, thus affecting sag.

Therefore, in order to calculate the correct sag, it is nec-essary to separate the effects of conductor elongationdue to tensile loading as well as thermal loading. Thisprocess requires an iterative procedure in which themathematical formulas describing the conductor elon-gation caused by the temperature change are solvedsimultaneously with the tension and conductor lengthrelationship. To calculate the change in length due totemperature loading, the following equation is used:

2.4-14

where:

= coefficient of linear thermal elon-gation for the AL/SW strands.

= final length of the conductor.

= reference length of the conductor.

= change in temperature.

The NESC (National Electric Safety Code 1993) recom-mends limits on the tension of conductors based on apercentage of their Rated Breaking Strength (RBS). Forexample, the tension limits of an ACSR may be 60%under maximum ice and wind loading, 35% upon instal-lation at 60ºF, and 25% final unloaded after maximumloading has occurred at 60ºF. Therefore, if the initialtension in a span is known along with the initial conduc-tor length, the total elongation resulting from the tensileload is calculated as follows:

2.4-15where:

= length of conductor under horizontal reference tension.

= length of conductor under horizontal tension.

= horizontal tension.

= length of conductor under horizontal reference tension.

= modulus of elasticity of the conductor(psi).

= cross-sectional area, in2.

It should be noted that the modulus Ec in Equation2.4-15 is the modulus of the steel and aluminum strandsdetermined by the stress and strain relationship of thecomposite conductor. Since this relationship for a bime-tallic construction of the conductor is quite complex,the relationship of ACSR conductors is typicallydescribed by a third or fourth order polynomial. Inaddition, the thermal and permanent elongation drasti-cally affects the mechanical behavior of ACSR conduc-tors at high temperatures, and this further complicatesthe analysis. Therefore, since ACSR conductors arenonhomogenous, the stress and strain characteristicsare separated into their steel and aluminum componentsas shown in Figure 2.4-6. Numerical methods are usedto calculate the resulting sags and tensions, with the aid

( ) [cosh( ) 1]H wx

y xw H

= −

[cosh( ) 1]2

H wsD

w H= −

T H wD= +

2sinh

2H Sw

Lw H

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Re1 ( )REFT T AS r fL L T Tα⎡ ⎤= + −⎣ ⎦

ASα

TL

TL REF

Re( )r fT T−

1REF

REFH H

c

H HL L

E A

⎡ ⎤−= +⎢ ⎥

⎣ ⎦

REFHL

HL

H

REFH

cE

A

2-30


of software programs such as Alcoa Fujikura’s Sag10package (Alcoa 2003).

2.4.7 Sag and Tension of Inclined Spans

For inclined spans, the length of the conductor betweensupports is divided into two separate sections for con-sideration. One is to the right of the lowest point of theconductor, and one is to the left (see Figure 2.4-7).

The same equation used to represent the height of theconductor, for a level span is valid for inclined spans andis given by the following equation (Trash el al. 1994):

2.4-16

In each part of the span, the sag is dependent upon thevertical distance between support points and can bedescribed by the following equations:

2.4-17

2.4-18

The maximum tension is

2.4-19

2.4-20

Figure 2.4-6 Decomposed ACSR “Tern” conductor at 120°C.

Figure 2.4-7 Catenary sag model—inclined span.

( ) cosh( ) 1H wx

y xw H

⎛ ⎞= −⎜ ⎟⎝ ⎠

2

14R

hD D

D⎛ ⎞= −⎜ ⎟⎝ ⎠

2

14L

hD D

D⎛ ⎞= +⎜ ⎟⎝ ⎠

R RT H wD= +

L LT H wD= +

2-31


2-32

2.4.8 Calculation of Conductor High-Temperature Sag and Tension

Simplified CalculationsSimplified calculations are used for demonstration usinga hand calculator. While most sag and tension calcula-tions are typically performed with an analysis software,the use of the simplified calculation clearly demon-strates the process and provides the reader some insightinto how sags and tensions occur for overhead lines.

Example 2.4-3: What is the sag (D) and slack for a1000-ft level span of 795 kcmil (405 mm2) ACSR“Drake” conductor at ambient temperature (25ºC,77ºF). The weight per unit length is 1.094 lbs/ft (1.6kg/m), the horizontal tension component, H, is 25% ofthe RBS.

H = 0.25 x 31,500 lbs = 7875 lbs (35,196 N)

Use Equation 2.4.11,

The sag for this level span is 17.37 ft (5.3 m).

The following equation is used to calculate the length ofthe conductor:

The conductor slack is the length minus the span length,0.80 ft (0.24 m).

Example 2.4-4: What happens to the conductor length ifthe temperature increases from ambient to 50ºC (122ºF)?What about if it increases to 150ºC (302ºF)? The coeffi-cient of linear thermal expansion is 10.7 x 10-6/ºF.

At 50ºC, the length of the conductor is 1001.28 ft(305.2 m). At 150ºC, the length of the conductor is1003.21 ft (305.8 m).

Example 2.4-5: What is the sag of the conductor at theelevated temperature levels?

The following equation is rearranged to estimate theresulting sag, which only considers the change due tothermal effects, and ignoring any changes that are dueto the changes in tension.

hence

Example 2.4-6: What is the tension of the conductorwhen subjected to the two temperatures?

Rearrange the following equation to obtain the result-ant tension of the conductor.

These values assume that the conductor has an infinitemodulus of elasticity. Actually, the elastic modulus ofthe conductor is finite, and changes in the conductortension do affect the length of the conductor. Therefore,these equations estimate sags that are greater than hasbeen observed in the field.

Estimating the actual change in sag due thermal effectsis complex, because one needs to look at the combinedthermal and elastic effects of conductors. The initialloads of concentrically stranded ACSR conductorsresult in elongation behavior that is different from thatcaused by loading several years later. Software such asAlcoa’s Sag10 program use numerical methods to esti-mate the resulting sags.

2

[cosh( ) 1]2 8

H ws wSD

w H H= − ≈

( )( ) ( )

22 1.094 100017.37 ft 5.29 m

8 8 7875wS

DH

= = =

( )( ) ( )

2

22

2 8sinh

2 3

8 17.3781000 1000.80 ft 305.05 m

3 3 1000

H Sw DL S

w H S

DL S

S

⎛ ⎞ ⎛ ⎞= ≈ +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

= + = + =

( )

( ) ( )

( ) ( )

6122

6302

1

1000.80 1 10.7 10 122 77

1001.28 ft (305.2 m)

1000.80 1 10.7 10 302 77

1003.21 ft (305.8 m)

REFT T AS REFL L T T

L

L

α−

−

⎡ ⎤= + −⎣ ⎦⎡ ⎤= + × −⎣ ⎦

=

⎡ ⎤= + × −⎣ ⎦=

( )2 38becomes

3 8

S L SDL S D

S

−= + =

( )( )( ) ( )

( )( )( ) ( )

122

302

3 1000 1.2821.9ft 6.68m

8

3 1000 3.2134.7 ft 10.58m

8

D

D

= =

= =

2 2

becomes8 8wS wS

D HH D

= =

( )( )

( )

22

122

1.094 10006244 lbs (27,875 N)

8 8 21.9wS

HD

= = =

( )( )

( )

22

302

1.094 10003941lbs (17,594N)

8 8 34.7wS

HD

= = =


The following example uses an AAC, and the effects ofthe elevated temperature levels are estimated.

Example 2.4-7: What is the sag (D) and slack for a 1000ft. (305 m) level span of AAC “Arbutus” conductor atambient temperature (25ºC, 77ºF). The weight per unitlength is 0.746 lbs/ft (1.09 kg/m), the horizontal tensioncomponent, H, is 25% of the RBS.

The sag for this level span is 26.8 ft (8.18 m).

The following equation is used to calculate the length ofthe conductor:

The conductor slack is the length minus the span length,1.9 ft (0.58 m).

Example 2.4-8: What happens to the conductor length ifthe temperature increases from ambient to 50ºC (122ºF)?What about if it increases to 150ºC (302ºF)? The coeffi-cient of linear thermal expansion is 12.8 x 10-6/ºF.

At 50ºC, the length of the conductor is 1002.48 ft(305.56 m). At 150ºC, the length of the conductor is1004.79 ft (306.26 m).

Example 2.4-9: What is the sag at the elevated tempera-ture levels?

The following equation is rearranged to estimate theresulting sag, which only considers the change due tothermal effects, and ignoring any changes that are dueto the changes in tension.

hence

Example 2.4-10: What is the tension of the conductorwhen subjected to the two temperatures?

Rearrange the following equation to obtain the result-ant tension of the conductor.

These high readings reflect the thermal elongationassuming the strands have an infinite modulus of elas-ticity. Fortunately, the modulus is finite, and the changesin the tension levels do affect the conductor length.These equations are a useful way to get a rough idea ofhow an ACSR conductor behaves when compared to anAAC conductor. At 50ºC, the AAC elongates about28% more than the ACSR, and at 150ºC, the AAC elon-gates approximately 50% more than the ACSR.

Using Alcoa Fujikura’s Sag10 SoftwareSoftware programs can be useful to obtain more accu-rate results, since they use an iterative procedure toobtain solutions to complex problems such as the sagand tension calculation of a conductor. This iterativeprocess is commonly referred to as the “binary chop”technique, and it separates the thermal as well as plasticand elastic effects resulting from changes in the conduc-tor’s tension.

Once the results of the iterative calculations have con-verged, the results reflect the conductor length thataccounts for the elastic effects of an increased load aswell as the thermal elongation effects. Since H, andHREF correspond to the first-, second-, third-, andfourth-order composite stress and strain curves thatdescribe the initial and final conductor modulus, it istypically convenient to rearrange the equations in termsof strain elongation to permit the direct substitution ofvalues into the polynomial equations.

H = 0.25 x 13,900 lbs = 3475 lbs. (15,513 N)

( )( ) ( )

22 0.746 100026.8 ft 8.18 m

8 8 3475wS

DH

= = =

( )( ) ( )

22 8 26.881000 1001.9 ft 305.38 m

3 3 1000D

L SS

= + = + =

( )1REFT T AS REFL L T Tα⎡ ⎤= + −⎣ ⎦

( ) ( )6122 1001.9 1 12.8 10 122 77

1002.48 ft (305.56 m)

L −⎡ ⎤= + × −⎣ ⎦=

( ) ( )6302 1001.9 1 12.8 10 302 77

1004.79 ft (306.26 m)

L −⎡ ⎤= + × −⎣ ⎦=

( )3

8

S L SD

−=

( )( ) ( ) ( )

( )( )( ) ( )

122

302

3 1000 2.4830.5 ft 9.3 m

8

3 1000 4.7969.2 ft 21.1 m

8

D

D

= =

= =

2 2

becomes8 8wS wS

D HH D

= =

( )( )

( )

22

122

0.746 10003057 lbs (13,647 N)

8 8 30.5wS

HD

= = =

( )( )

( )

22

302

0.746 10001348 lbs (6,018 N)

8 8 69.2wS

HD

= = =

2-33


2.4.9 Results of High-Temperature Sag Tension Calculations

Three different ACSR conductors were selected to dem-onstrate the high-temperature behavior of conductorsand the calculation of the sag and tension. The ACSRconductors have varying steel-to-aluminum ratios,hence the effects of the construction of the conductoron the sag and tension are demonstrated. The conduc-tors selected for the examples are ACSR “Drake,”ACSR “Mallard,” and ACSR “Tern.” All of theseACSR conductors selected for the demonstration arecommonly used by electric utilities.

ACSR Mallard is constructed using 30 aluminumstrands and 19 steel core strands. The ratio of the alumi-num’s cross-sectional area to the conductor’s total cross-sectional area for the ACSR Mallard conductor is0.814, classifying this conductor as a wire with a “high”steel-to-aluminum ratio. Similarly, ACSR Drake is con-structed using 26 aluminum strands and 7 steel strands.The ratio of the aluminum’s cross-sectional area to theACSR Drake conductor’s total cross-sectional area is0.860, classifying this conductor as a wire with a“medium” steel-to-aluminum ratio. Finally, ACSR Ternis constructed using 45 aluminum strands and 7 steelstrands. The ratio of the aluminum’s cross sectional areato the ACSR Tern conductor’s total cross-sectional areais 0.935, classifying this conductor as a wire with a“low” steel-to-aluminum ratio.

In support of the analysis and the illustration of thehigh-temperature behavior of standard ACSR conduc-tors, stress and strain data acquired in the EPRI Con-ductor High Temperature Operation Project were used.The data used for the prediction of high-temperaturesags included the stress and strain curves and coeffi-cients of thermal elongation.

In order to illustrate the differences in the results, saganalyses were performed for a level conductor span aswell as for inclined spans of 15° and 30°. In each case,sags were calculated for each type of conductor usingtwo different approaches at each of the selected conduc-tor temperatures. The resulting sags are reported at theinitial and final condition at each temperature.

In addition, the span length was varied, and the saganalyses were performed for 500 ft, 1000 ft, and 1500 ftspan lengths. Again, the results were reported at the ini-tial and final condition at each temperature.

In the first approach, sags were calculated using AlcoaFujikura’s Sag10 sag tension analysis program using theprovided stress and strain charts included in the soft-

ware. Values are reported for initial and final conditions,respectively.

In the second approach, sags were calculated usingAlcoa Fujikura’s Sag10 sag tension analysis programand data obtained in the EPRI Conductor High Tem-perature Operation Project. Values are reported for ini-tial and final conditions, respectively. Tables 2.4-2through 2.4-10 provide a summary and comparison ofderived sags at each operating temperature.

For ACSR Drake with the 500 ft (152 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data are lessthan 1ft (0.3 m) greater than comparable values calcu-lated using Alcoa Fujikura’s Sag10 data. For the 15°-inclined span, the differences in the final sag were alsoless than 1 ft (0.3 m). Similar results were obtained forthe 30° incline, which resulted in increased final sagsthat were less than 1 ft (0.3 m).

For ACSR Drake with the 1000 ft (305 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data gener-ally differ by about 2 ft (0.61 m) at ambient, but wasabout 1 ft (0.3 m) higher for elevated temperatures whencompared to Alcoa Fujikura’s Sag10 data. For the 15°inclined span, the difference in the final sags was lessthan 1 ft (0.3 m). Similar results were obtained in thecase of the 30° incline, which resulted in increased finalsags that were minimal.

For ACSR Drake with the 1500 ft (457 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data was upto 3 ft (0.9 m) at ambient, and 1 ft (0.3 m) at the elevatedtemperatures when compared to Alcoa Fujikura’s Sag10data. For the 15° inclined span, the difference in thefinal sags was less than a foot (0.3 m). Similar resultswere obtained for the 30° incline, which resulted inincreased final sags that are less than 1 ft (0.3 m).

For ACSR Tern with the 500 ft (152 m) span, the resultsof the comparison show that final sags calculated usingEPRI High Temperature Conductor data are generallyless by about half a foot (0.15 m) when compared toAlcoa Fujikura’s Sag10 data. For the 15° inclined span,the difference in the final sags was negligible, and simi-lar results were obtained for the 30° incline. Good corre-lation of the data occurred for the 1000 ft (305 m) and1500 ft (457 m) span, and the sag values were less than 1ft (0.3 m) when compared to Alcoa data. In most cases,the predicted sag was less than expected by the Alcoadatabase curves.

2-34


For ACSR Mallard with the 500 ft (152 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data are gen-erally 1 ft (0.3 m) higher than comparable values calcu-lated using Alcoa Fujikura’s Sag10 data. For the 15°inclined span, the difference in the final sags was between0 ft and 1.5 ft (0.46 m). For the 30° incline, the differencein the final sags was between 0 and 1.6 ft (0.49 m).

For ACSR Mallard with the 1000 ft (305 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data are 3 ft(0.9 m) at ambient temperatures and about 2 ft (0.61 m)at elevated temperatures, when compared to values cal-culated using Alcoa Fujikura’s Sag 10 data. For the 15°inclined span, the difference in the final sags was negligi-ble at ambient temperature but 2.5 ft (0.76 m) at ele-vated temperatures. For the 30° incline, the difference inthe final sags was negligible at ambient temperature butup to 2.8 ft (0.85 m) at elevated temperatures.

For ACSR Mallard with the 1500 ft (457 m) span, theresults of the comparison show that final sags calculatedusing EPRI High Temperature Conductor data is anadditional 4 ft (1.2 m) at ambient temperature and isabout 2.5 ft (0.76 m) at elevated temperatures whencompared to values calculated using Alcoa Fujikura’sSag10 data. For the 15° inclined span, the difference inthe final sags was negligible at ambient, and as high at3 ft (0.9 m) and approached 4 ft (1.2 m) for elevatedtemperature levels. Similar results were obtained for the30° incline.

Table 2.4-2 ACSR Drake, Span Length = 500 ftAlcoa Fujikura Sag 10 Software with Alcoa Data

Conductor Temperature Level 15% 30%

Initial Sag (ft) Final Sag (ft) Initial Sag (ft) Final Sag (ft) Initial Sag (ft) Final Sag(ft)

23 Deg 3.26 4.35 3.26 3.37 3.26 3.76

120 Deg 8.61 8.61 8.61 8.30 8.61 9.26

150 Deg 9.21 9.61 9.21 9.52 9.21 10.62

Alcoa Fujikura Sag 10 Software with EPRI Data



23 Deg 3.26 5.23 3.26 3.37 3.26 3.76

120 Deg 8.64 9.26 8.64 8.93 8.64 9.96

150 Deg 9.81 10.29 9.81 10.14 9.81 11.31

Comparison: Alcoa to EPRI


Difference (ft) Difference (ft) Difference (ft) Difference (ft) Difference (ft) Difference (ft)

23 Deg 0 0.88 0.00 0 0 0.88

120 Deg 0.61 0.65 0.63 0.70 0.61 0.65

150 Deg 0.60 0.68 0.62 0.69 0.60 0.68

2-35





23 Deg 13.05 16.27 13.05 13.05 13.05 15.05

120 Deg 22.48 25.32 22.48 23.22 22.48 25.89

150 Deg 25.62 26.94 25.62 26.45 25.62 29.49




23 Deg 13.05 18.32 13.05 13.5 13.05 15.05

120 Deg 23.05 26.23 23.05 23.81 23.05 26.55

150 Deg 26.20 27.87 26.20 27.05 26.20 30.16




23 Deg 0 2.05 0 0 0 0

120 Deg 0.57 0.91 0.57 0.59 0.57 0.66

150 Deg 0.58 0.93 0.58 0.60 0.58 0.67




23 Deg 29.39 34.65 29.39 30.38 29.39 33.88

120 Deg 42.39 47.81 42.39 43.74 42.39 48.77

150 Deg 46.40 49.93 46.40 47.84 46.40 53.34




23 Deg 29.39 37.61 29.39 30.38 29.39 33.88

120 Deg 43.04 48.83 43.04 44.41 43.04 49.51

150 Deg 47.10 50.97 47.10 48.56 47.10 54.14




23 Deg 0 2.96 0 0 0 0

120 Deg 0.65 1.02 0.65 0.67 0.65 0.74

150 Deg 0.70 1.04 0.70 0.72 0.70 0.80

2-36


Table 2.4-5 ACSR Tern, Span Length = 500 ftAlcoa Fujikura Sag 10 Software with Alcoa Data



23 Deg 3.81 5.67 3.81 3.94 3.81 4.39

120 Deg 10.90 12.89 10.90 11.27 10.90 12.56

150 Deg 13.11 13.73 13.11 13.53 13.11 15.09




23 Deg 3.81 5.74 3.81 3.93 3.81 4.39

120 Deg 10.76 12.45 10.76 11.12 10.76 12.40

150 Deg 13.00 13.29 13.00 13.42 13.00 14.96




23 Deg 0 0.07 0 -0.01 0 0

120 Deg -0.14 -0.44 -0.14 -0.15 -0.14 -0.16

150 Deg -0.11 -0.44 -0.11 -0.11 -0.11 -0.13




23 Deg 15.24 19.84 15.24 15.76 15.24 17.58

120 Deg 27.30 34.46 27.30 28.17 27.30 31.41

150 Deg 30.84 35.78 30.84 31.80 30.84 35.45




23 Deg 15.24 19.98 15.24 15.76 15.24 17.58

120 Deg 27.17 33.7 27.17 28.04 27.17 31.27

150 Deg 30.67 35.04 30.67 31.63 30.67 35.26




23 Deg 0 0.14 0 0 0 0

120 Deg -0.13 -0.76 -0.13 -0.13 -0.13 -0.14

150 Deg -0.17 -0.74 -0.17 -0.17 -0.17 -0.19

2-37





23 Deg 34.34 41.10 34.34 35.47 34.34 39.55

120 Deg 49.79 62.49 49.79 51.31 49.79 57.20

150 Deg 54.26 64.30 54.26 55.88 54.26 62.28




23 Deg 34.34 41.27 34.34 35.47 34.34 39.55

120 Deg 49.69 61.51 49.69 51.21 49.69 57.08

150 Deg 54.13 63.26 54.13 55.73 54.13 62.12




23 Deg 0 0.17 0 0 0 0

120 Deg -0.10 -0.98 -0.10 -0.10 -0.10 -0.12

150 Deg -0.13 -1.04 -0.13 -0.15 -0.13 -0.16

Table 2.4-8 ACSR Mallard, Span Length = 500 ftAlcoa Fujikura Sag 10 Software with Alcoa Data



23 Deg 3.02 4.27 3.02 3.12 3.02 3.48

120 Deg 6.21 7.43 6.21 6.42 6.21 7.16

150 Deg 7.77 8.48 7.77 8.03 7.77 8.95




23 Deg 3.02 5.45 3.02 3.12 3.02 3.48

120 Deg 7.63 8.49 7.63 7.89 7.63 8.80

150 Deg 8.67 9.57 8.67 8.96 8.67 10.00




23 Deg 0 1.18 0 0 0 0

120 Deg 1.42 1.06 1.42 1.47 1.42 1.64

150 Deg 0.90 1.09 0.90 0.93 0.90 1.05

2-38


Table 2.4-9 ACSR Mallard, Span Length =1000 ftAlcoa Fujikura Sag 10 Software with Alcoa Data



23 Deg 12.08 15.82 12.08 12.50 12.08 13.94

120 Deg 19.54 22.59 19.54 20.20 19.54 22.52

150 Deg 22.11 24.33 22.11 22.85 22.11 25.48




23 Deg 12.08 18.58 12.08 12.50 12.08 13.94

120 Deg 21.99 24.46 21.99 22.72 21.99 25.34

150 Deg 24.51 26.20 24.51 25.31 24.51 28.22




23 Deg 0 2.76 0 0 0 0

120 Deg 2.45 1.87 2.45 2.52 2.45 2.82

150 Deg 2.40 1.87 2.40 2.46 2.40 2.74

Table 2.4-10 ACSR Mallard, Span Length = 1500 ftAlcoa Fujikura Sag 10 Software with Alcoa Data



23 Deg 27.21 33.36 27.21 28.13 27.21 31.37

120 Deg 38.20 43.22 38.20 39.45 38.20 43.98

150 Deg 41.62 45.51 41.62 42.95 41.62 47.89




23 Deg 27.21 37.38 27.21 28.13 27.21 31.37

120 Deg 40.74 45.76 40.74 42.05 40.74 46.89

150 Deg 45.07 48.03 45.07 46.48 45.07 51.82




23 Deg 0 4.02 0 0 0 0

120 Deg 2.54 2.54 2.54 2.60 2.54 2.91

150 Deg 3.45 2.52 3.45 3.53 3.45 3.93

2-39


2.4.10 Effects of Wind Speed on Thermal Ratings

High-temperature operations are greatly affected bylocal wind conditions. This is discussed in Section 2.3for its effect on clearances. Below, its effect on conduc-tor strength is the focus.

The following will demonstrate the effect of wind on theperformance of the conductor. For the comparison,Power Technologies’ Ratekit was used. Ratekit is a soft-ware tool capable of evaluating the effects of wind speedand operating temperature independently. In the discus-sion, all conductor conditions are assumed steady state.Also, the angle of the wind relative to the conductor is90°, the span is at sea level, and the time of year is sum-mer. The coefficient of emissivity is 0.50, the coefficientof solar absorptivity is 0.50, the conductor resistance at25ºC is 0.1200 ohms/mile (0.075 ohms/km), and the con-ductor resistance at 75ºC is 0.1442 ohms/mile (0.090ohms/m). Atmospheric conditions are clear, and the ori-entation of the conductor relative to the north is 0°. Theambient temperature is 25°C , the ruling span is 1000 ft(305 m), and the conductors used in the comparisonsare ACSR Drake and AAC Arbutus. The operating tem-peratures are 120°C and 150°C , and the wind speedsused are 0 ft/sec, 2 ft/sec (0.61 m/sec), and 4 ft/sec(1.2 m/sec). Table 2.4-11 shows the remaining strength

and sags for the ACSR Drake conductor, and Table 2.4-12 summarizes the results obtained for the AAC Arbu-tus.

At 1180 A and 0 ft/sec wind, the operating temperatureof the ACSR Drake conductor is 150ºC. If subjected tothis high operating temperature for 100 hours, theremaining strength of the ACSR Drake conductordecreases by 1.4% to 98.64% of the rated tensilestrength. If the weather conditions are favorable and thewind speed is 2 ft/sec (0.61 m/sec), the operating temper-ature of the ACSR Drake conductor is 110ºC, and thetensile strength of the conductor remains unaffected. Ifthe wind speed is 4 ft/sec (1.22 m/sec), the temperatureof the ACSR Drake conductor with 1180 A of current isnearly 86ºC, and the strength of the conductor remainsunaffected. Similarly, the sag (final) of the ACSR con-ductor at 1180 A, and 0 ft/sec wind is 39.6 ft (12.1 m),while the sag of the ACSR Drake decreases by nearly3.5 ft (1.1 m) if the wind speed increases from 0 ft/sec to2 ft/sec. If the wind speed increases to 4 ft/sec (1.2m/sec), the sag of the ACSR Drake conductor is 33.8ft/sec (10.3 m/sec), nearly 6 ft (1.8 m) less than in thecase where the wind is 0 ft/sec. If the ACSR Drake car-ries 1000 A and the wind speed is 0 ft/sec, the operatingtemperature of the conductor is 120ºC, resulting in noloss of tensile strength if operated for 100 hours. If thewind speed increases to 2 ft/sec (0.61 m/sec), the operat-ing temperature decreases 86ºC and the sag decreases byapproximately 2 ft (0.61 m). If the wind speed increasesto 4 ft (1.2 m), the temperature decreases to 70ºC andthe sag decreases an additional 2 ft (0.61 m).

The temperature of an AAC Arbutus conductor carry-ing a current of 1130 A at a wind speed of 0 ft/sec is150ºC. If the duration of this operation is 100 hours, thetensile strength of the conductor decreases by nearly30% to 70.12% of the rated tensile strength. However, ifthe wind speed is 2 ft/sec (0.61 m/sec), the operatingtemperature of the AAC Arbutus conductor is 108ºC,and the operation at this condition for a period of 100hours reduces the tensile strength of the conductor byonly 9% instead of 30% at a wind speed of 0 ft/sec. Theremaining strength at these conditions is 92.1% of therated tensile strength, an acceptable value. At a windspeed of 4 ft/sec (1.2 m/sec), an AAC Arbutus conduc-tor carrying a current of 1130 A will operate at a tem-perature of 85ºC, resulting in no loss of the tensilestrength of the conductor. Also, a wind speed of 2 ft/sec(0.61 m/sec) reduces the sag by nearly 4 ft (1.2 m) com-pared to the sag calculated in the no wind scenario, andthe sag is reduced an additional 2 ft (0.61 m) if the windspeed increases to 4 ft/sec (1.2 m/sec).

Table 2.4-11 ACSR Drake

Current (A)

Wind Speed (ft/sec)

Tempera-ture (°C)

Remaining Strength

(%)a

a. The remaining strength is after 100-hours of high operat-ing temperatures.

Initial Sag (ft)

FinalSag (ft)

1180 0 150 98.64 36.1 39.6

2 110 100 32.3 36.1

4 85.7 100 29.8 33.8

1000 0 120 100 33.3 36.9

2 85.8 100 29.8 33.8

4 68.5 100 28.0 32.1

Table 2.4-12 AAC Arbutus

Current (A)

Wind Speed (ft/sec)

Tempera-ture (°C)

Remaining Strength

(%)a

a. The remaining strength is calculated when the conductor is exposed to the high temperature for 100 hours.

Initial Sag (ft)

FinalSag (ft)

1130 0 150 70.12 47.4 49.0

2 108.5 92.11 43.5 45.2

4 84.6 100 41.2 43.0

960 0 120 85.89 44.6 46.3

2 84.9 100 41.2 43.0

4 68.1 100 39.5 41.3

2-40


AAC Arbutus carrying a current of 960 A at a windspeed of 0 ft/sec operates at a temperature of 120ºC,resulting in a loss of 14% of the tensile strength if oper-ated continuously for a period of 100 hours. Theremaining tensile strength is reduced to 86% of the ratedtensile strength of the conductor. If the wind speedincreases to 2 ft/sec (0.61 m/sec), the sag of the conduc-tor decreases by 3 ft (0.9 m), while an increase in thewind speed will decrease the sag by nearly 5 ft (1.5 m)when compared to the no wind case.

2.4.11 Thermal Elongation

Thermal elongation is a metallurgical phenomenonwhere the material increases in length in proportion toan increase in temperature. The rate of linear thermalexpansion for the composite ACSR conductor is lessthan that of conductors that are made entirely of alumi-num because the steel strands in the ACSR elongate atapproximately half the rate of aluminum. The theoreticalcomposite coefficient of linear thermal expansion (CTE)of a nonhomogenous conductor, such as the ACSRDrake may be found from the following equations:

2.4-21

2.4-22whereEAL = modulus of elasticity of aluminum, psi.EST = modulus of elasticity of steel, psi.EAS = modulus of elasticity of aluminum-steel

composite, psi.AAL = area of aluminum strands, square units.AST = area of steel strands, square units.ATOTAL= total cross sectional area, square units.αAL = aluminum coefficient of linear thermal

expansion, per °F.αST = steel coefficient of thermal elongation, per

°F.αAS = composite aluminum-steel coefficient of

thermal elongation, per °F.

Example 2.4-10: Using elastic moduli of 10 and 30 mil-lion psi (68,966 MPA and 206,897 Mpa) for aluminumand steel, find the elastic modulus for ACSR Drake is:

and the coefficient of linear thermal expansion is:

A comparison of three different ACSR conductors ofvarying aluminum-to-steel ratios is used to demonstratethe effect of the steel reinforcing on the composite con-ductor behavior and coefficient of linear expansion.Table 2.4-13 summarizes calculated (ideal) and mea-sured coefficients of linear thermal expansion. The mea-sured coefficient of linear expansion of the ACSR Ternconductor (low steel-to-aluminum ratio) is 10.9% largerthan the calculated value. The measured coefficient oflinear expansion of the ACSR Drake conductor(medium steel-to-aluminum ratio) is approximately 6%higher than the calculated value and the measured coef-ficient of the ACSR Mallard (high steel-to-aluminumratio) is only marginally larger than the calculated value.As the steel-to-aluminum ratio increases, the coefficientof linear expansion of the composite conductorapproaches a limiting value equal to the coefficient ofsteel alone.

Note that the results of the EPRI High TemperatureConductor Project identifies the conductor’s knee point,and that the coefficient of linear expansion does nottypically address the effect of the knee point on the sagand tension calculation. A typical set of test data isshown in Figure 2.4-8. The knee point is shown atapproximately 120ºC. However, to accurately predictsags and tensions at high temperature, the effects of theknee point need to be considered and is discussed inmore detail.

The conditions under which calculations using a simplecomposite modulus and coefficient of linear thermalexpansion fail may be illustrated by considering the ten-sion distribution between steel and aluminum undernormal and high temperature conditions. The precedingequations for composite modulus and CTE are derivedbased on the assumption that the aluminum and steel

ST STAL ALAS AL ST

AS TOTAL AS TOTAL

E AE A

E A E A∂ ∂ ∂

⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

STALAS AL

TOTAL TOTAL

AAE E EST

A A

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

( ) ( )6 6

6 10

0.6247 0.101710 10 30 10

0.7264 0.7264

12.8 10 (8.83 x 10 Pa)

ASE x x

x psi

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

=

66

6

66

6

6

10 10 0.624712.8 10

0.726412.8 10

30 10 0.10176.4 10

0.726412.8 10

10.7 10 /

AS

xa x

x

xx

x

x F

−

−

−

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞ ⎛ ⎞+ ⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

= °

Table 2.4-13 Coefficient of Thermal Elongation for ACSR Conductors

ACSR Conductor

(below 212°F, or 100°C)

Calculated Coefficient of Thermal Elon-gation (CTE)

Measured Coefficient of Thermal Elon-gation (CTE)

Percent Difference

Tern 45/7 11.7 x 10-6 13.0 x 10-6 10.9

Drake 26/7 10.7 x 10-6 11.4 x 10-6 6.09

Mallard 30/19 10.2 x 10-6 10.1 x 10-6 0.64

2-41


strands are of the same length. Based on this assump-tion, the total conductor tension (HAS) is equal to thesum of the component tensions, and the elongation ofthe steel and aluminum is equal:

2.4-23

2.4-24

For example, an ACSR Drake conductor installed in a600 ft (183 m) span at an initial tension of 9450 lbs(42,188 N) carries 3124 lbs (13,946 N) of the tension inthe steel core with the remainder of the tension beingcarried by the aluminum strands. Therefore, the tensioncarried by the steel is roughly 33% of the total tension.If the ACSR Drake conductor is heated to a tempera-ture of 100oC, the sag of the conductor increases, andthe total tension decreases to 4780 lbs (21,339 N), butthe tension carried by the steel core increases from3124 lbs (13,946 N) to 3305 lbs (14,754 N), or nearly70% of the total tension.

As the operating temperature of the conductor increasesfurther, the tension in the aluminum eventuallydecreases to zero while the tension carried by the steelincreases further. At some temperature, commonlyreferred to as the knee point temperature, the linearexpansion of the conductor continues, but the stresses inthe aluminum strands change from tension to compres-sion (as shown in Figures 2.4-8 and 2.4-9). The kneepoint temperature of an ACSR conductor is directlyproportional to the steel-to-aluminum ratio and is lowerfor ACSR conductors with high ratios and higher forconductors with low steel to aluminum ratios.

Conductors made by different manufacturers exhibitdifferent knee-point temperatures because of differencesin the manufacturing practices, processes, and machin-ery. For example, Figure 2.4-8 indicates that the ACSRDrake has a knee point at about 120ºC, while the data inFigure 2.4-8 suggests that the ACSR Drake has a kneepoint of only 70ºC. Disregarding experimental differ-ences, built-in stresses, which are the result of manufac-turing methods and tools, are the primary cause for thisdifference.

In Figure 2.4-8, the coefficient of thermal expansion is17.38 x 10-6 /ºC prior to the knee point, and the corre-sponding value in Figure 2.4-9 is 17.53 x 10-6 /°C, a dif-ference of less than 1%. While the correspondingcoefficient beyond the knee point is also fairly consis-tent, the temperature at which the knee point has beenobserved differs by nearly 50ºC or nearly 70%. The coef-ficient of thermal expansion beyond the knee point in

Figure 2.4-8 is 12.84 x 10-6 /ºC, while the correspondingvalue in Figure 2.4-9 is 13.74 x 10-6 /ºC, a difference ofless than 7%.

2.4.12 Creep Elongation

Once a conductor has been installed to an initial ten-sion, it can elongate further. Such elongation resultsfrom three phenomena—permanent elongation due tohigh-tension levels resulting from ice and wind loads,creep elongation under everyday tension levels, andcreep elongation due to thermal overloads. The creepresulting from thermal loading is discussed below.

High-Temperature Creep ElongationThe definition of “normal” creep is the accumulativenonelastic elongation of a conductor under low tension,over an extended period of time at modest operatingtemperatures. Normal operating temperatures are gen-erally agreed upon as temperatures below 75°C. In any

AS AL STH H H= +

ST AL

ST ST AL AL

H H

A E A E=

⋅ ⋅

Figure 2.4-8 ACSR Drake (26/7) composite thermal elongation, (30% of RBS Pre-Stressing, 10% of RBS Applied Tension, Manufacturer 2).

Figure 2.4-9 ACSR Drake (26/7) composite thermal elongation, (30% of RTS Pre-Stressing, 10% of RTS Applied Tension, Manufacturer 1).

2-42


case, a conductor under tension experiences a nonelasticelongation over a period of time. Time is usually mea-sured in years. The magnitude and rate of creep are afunction of the conductor's composition, stranding, linetension, and operating temperature.

Conductors exhibit creep under everyday tension levelseven if the tension level never exceeds normal operatingconditions. Creep can be determined by long-term labo-ratory creep tests, and the results of the tests are used togenerate charts that document the relationship of creepversus time. On the stress-strain graphs of conductors,creep curves are often shown for 6-month, 1-year, and10-year time periods. Figure 2.4-10 shows a typicalcreep curve (experimental results) for an ACSR Drakeconductor at room temperature. Generally, the creepelongation in aluminum conductors is quite predictable,it is a function of time and temperature, and the rela-tionship is exponential. Thus, knowing the initial condi-tions of the conductor, the permanent elongation due tocreep at everyday tension can be found for any period oftime after the initial installation. Note that the creepelongation of copper and steel strands is minimal, andthat the effects can essentially be ignored.

High-temperature creep occurs when a conductor isoperated for extended periods of time at operating tem-peratures in excess of approximately 75°C. Creep consti-tutes an irreversible, nonelastic elongation occurring inresponse to the molecular realignment in the conduc-tor’s base material. Figure 2.4-10 shows the effects ofcreep on the conductor strain at an operating tempera-ture of 120°C. Because aluminum exhibits a signifi-cantly higher rate of creep elongation than steel, the sagand tension behavior of all-aluminum type conductorssuch as AAC, AAAC, and ACAR is much more suscep-tible to high-temperature creep. Conversely, copper andsteel wire strands supported aluminum conductors (Cu,ACSR, and AACSR) exhibit lower rates of creep, andthe sag and tension behavior of these conductors is lessaffected by the high-temperature operation. AluminumConductor Steel Supported (ACSS) conductor, a con-ductor constructed using fully annealed aluminumstrands and steel strands for the strength member,exhibits negligible creep rates since all of the tension iscarried by the steel strength member, which is essentiallynot affected by creep.

Creep, and the associated rate of creep, are directly pro-portional to the type of conductor, the steel-to-alumi-num stranding ratio, the material characteristics of theconductor, and the tension and operating temperature.For example, using strands that are drawn from continu-ous-cast rod instead of hot-rolled rod reduces the creep

elongation and the associated long-term sag and tensionbehavior of the conductor. Other important parametersrequired in the determination of the rate of creep andthe cumulative effect include the conductor stress orstrain, the operating temperature, the elapsed time, andfor ACAR and ACSR type conductors, the ratio of theconstitutive components.

Figures 2.4-10 and 2.4-11 show experimentally derivedcreep elongation results for ACSR Drake at room tem-perature and at 120°C. In both experiments, the major-ity of the creep elongation occurred during the initial100 hours, a settling phase, so to speak. Note that atambient room temperature conditions (23°C), the finalcreep elongation after 1000-hours was 0.01%, while thefinal creep elongation measured at the increased operat-ing temperature was 0.03%. Thus, an ACSR conductoroperated at a high temperature will reach its “final” sag

Figure 2.4-10 ACSR Drake composite creep at 23°C, Manufacturer 1.

Figure 2.4-11 ACSR Drake composite creep at 120°C, Manufacturer 1.

2-43


)

approximately two to three times faster than a conduc-tor operated at temperatures of 75°C or below.

Creep Predictor EquationsHarvey (Harvey 1969) developed mathematical modelsand associated equations that can be used to estimatethe magnitude of creep elongation. The models andequations were empirically derived, and are able to pre-dict the creep elongation of a conductor at room tem-perature, as well as at an elevated temperature. Therequired definitions, constants, and formulas are listed(see Tables 4-14 and 4-15), along with an example.

Definition of Terms:εc = Primary creep strain (units/unit)ε = Strain - increase in length/original

(units/unit)ΣεT = Increase in conductor strain due to ele-

vated temperature operations (units/unit)σ = Stress - tension/area (N/mm2, lbs/in2)α = Coefficient of thermal expansion

(units/unit/C)t = Elapsed time (hours)T = Conductor temperature (C)ΔT = Temperature change value (C)AEC = Area of aluminum strands (sq. mm., sq.

in.)AST = Area of steel strands (sq. mm., sq. in.)AT = Total conductor area (sq. mm., sq. in.)%RS = Tension as a percentage of the rated

strength (%)

Predictor Equations:All-Aluminum Conductors (Room Temperature, Metric)

2.4-25

2.4-26

2.4-27

All-Aluminum Conductors (Room Temperature, English)

2.4-28

2.4-29

2.4-30

All-Aluminum Conductors (Elevated Temperature, Metric)

2.4-31

2.4-32

2.4-33

All-Aluminum Conductors (Elevated Temperature, English)

2.4-34

2.4-35

2.4-36

Steel Reinforced Conductors (Room Temperature, English)

Aluminum strands drawn from hot-rolled rod:

2.4-37

Aluminum strands drawn from continuous cast rod:

2.4-38

Steel Reinforced Conductors (Elevated Temperature, English)

Only for conductors with less than 7.5% steel by area:

Note: K1, K3, M1, and M3 are for wire bar rolled rod and K2, K4, M2, and M4 are for continuous cast (rolled) rod.

Note: K1, K3, M1, and M3 are for wire bar rolled rod and K2, K4, M2, and M4 are for continuous cast (rolled) rod.

Table 2.4-14 Formula Constants (Metric Units)

7 Strands 19 Strands 37 Strands 61 Strands

K1 1.36 1.29 1.23 1.16

K2 0.84 0.77 0.77 0.71

M1 0.0148 0.0142 0.0136 0.0129

M2 0.0090 0.0090 0.0084 0.0077

G 0.71 0.65 0.77 0.61

Table 2.4-15 Formula Constants (English Units)

7 Strands 19 Strands 37 Strands 61 Strands

K3 0.0021 0.0020 0.0019 0.0018

K4 0.0013 0.0012 0.0012 0.0011

M3 0.000023 0.000022 0.000021 0.000020

M4 0.000014 0.000014 0.000013 0.000012

G 0.0011 0.0010 0.0012 0.00094

1.3 0.16cAAC: = K tε σ

1.3 0.16cAAAC: = G tε σ

1.4 1.3 0.16c EC TACAR: = (0.19 + 1.36 A / A ) (T t )ε σ

1.3 0.16cAAC: = K tε σ

1.3 0.16cAAAC: = G tε σ

1.4 1.3 0.16c EC TACAR: = (0.0003 + 0.0021 A / A ) (T t ε σ

1.4 1.3 0.16cAAC: = M T t ε σ

1.4 1.3 0.16cAAAC: = 0.0077 T t ε σ

1.4 1.3 0.16c EC TACAR: = (0.0019 +0.012 A / A ) (T t )ε σ

1.4 1.3 0.16cAAC: = M T tε σ

1.4 1.3 0.16AAAC: c = 0.000012 T t ε σ

c

1.4 1.3 0.16EC T

ACAR: =

(0.000003 +0.000019 A / A ) (T t )

ε

σ

1.3 0.16cACSR: = 2.4 (%RS) t ε

1.3 0.16cACSR: = 1.1 (%RS) t ε

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2.4-39

Elevated creep in conductors with steel to aluminumratios of greater than 7.5% can be ignored.

Temperature Change ValueThe equivalent temperature change value is a calculatedtemperature that approximates the net increase in themicro-strain due to elevated temperature creep aboveand beyond general creep.

2.4-40

2.4-41

ε@ambient is the strain in the conductor due to room tem-perature creep only, and ε@high is the strain in the con-ductor attributed to the elevated temperature creep.

Method for Using the Predictor EquationsThe process of calculating the predicted elevated tem-perature creep is straightforward and can be accom-plished using sags and tensions derived from graphicalcharts, long-hand calculations, or computer softwarepredictions. The following procedure must be followed:

1. Use the standard graphical charting, long-hand cal-culations, or computer sag and tension methods topredict the sags and tensions without elevated creepfor the given situation.

2. Compute the creep of the conductor at ambient tem-perature.

3. Compute the creep of the conductor at the first ele-vated temperature.

4. Compute the number of hours that would berequired to accumulate an equivalent amount of con-ductor creep at the second elevated temperature.

5. Repeat steps 3 and 4 for each elevated temperature.

6. Calculate the value of the equivalent temperaturechange by subtracting the predicted creep elongationat the everyday temperature from the creep elonga-tion at the elevated temperature.

7. Calculate the final sag of the conductor following ele-vated temperature creep by adding this temperaturechange value to the temperatures used in the stan-dard sag and tension calculation.

Example 2.4-11: A 795 kcmil (405 mm2)ACSR Ternconductor is subjected to 20 hours at 60°F (16°C), 7500hours at 167°F (75°C ) and 1240 hours at 212°F(100°C). What is the sag and tension if creep is a factor?Use a ruling span equal to 1000 ft (305 m). Use Alcoa’sSag10 program to directly calculate the result and com-pare it to the results of the Creep Predictor Equations.Assume Alcoa Heavy Loading applies.

Using Equation 2.4-37, the ambient temperature creep is:

20 hours at 60°F produces a creep of 0.64 micro-in./in.or the equivalent of operating the conductor for 0 hoursat 212°F. Using Equation 2.4-39, the elevated tempera-ture creep is:

7500 hours at 167°F produces a creep of 417.7 micro-in./in. or the equivalent of operating the conductor for1690 hours at 212°F (100°C).

To calculate the total elongation due to creep, the sumof the equivalent times (hours) at 212°F (100°C ) isdetermined. In this example, the sum is:

The temperature change value is calculated using Equa-tion 2.4-40.

where

The final sag following elevated temperature creep isdetermined by adding this temperature change value to

0.16cACSR: = 2.4 (%RS) T t ε

T T = T or T = /ε α ε α∑ Δ Δ ∑

T @high @ambient = - ε ε ε∑

1.3 0.16c

0.16c

c

= 2.4 (%RS) t where %RS is the

Remaining Strength, and is the time (hours)

a) Conductor creep produced for 20 hours

at 60°F (16°C)

= 2.4 x 0.25 1.3 x 20

= 0.64 micro-in/in (1 in. = 2.

t

ε

εε 54 cm)

0.16c

0.16c

c

= 2.4 (%RS) T t

b) Conductor creep produced for 7500 hours

at 167°F (75 C)

= 2.4 x 0.25 x 167 x (7500)

= 417.7 micro-in./in.

ε

εε

0.16c

c

c) Conductor creep produced for 1240 hours

at 212°F (100 C)

= 2.4 x 0.25 x 212 x (1240)

= 397.6 micro-in./in.

εε

0.16c

0.16c

c

0 + 1690 + 1240 = 2930 hours at 212°F (100°C).

= 2.4 (%RS) T t

= 2.4 x.25 x 212 x 2930

= 456 micro-in./in.

ε

εε

TT = /ε αΔ ∑

T @high @ambient

6

= -

T (456 0.64) /(11.8 10 )

38.75 F(3.8 C)

ε ε ε−

∑

Δ = − ×= ° °

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the temperatures used in the standard sag and tensionsoftware calculations. In this example, 60°F (16°C)becomes 98.75°F (37°C), 90°F (32°C) becomes128.75°F (54°C), 120°F (49°C) becomes 158.75°F(70°C), etc. Table 2.4-16 provides a summary compari-son of the calculated sags including the effects of creepat each of the reference temperatures. The differences inthe sags predicted by each method can be mostly attrib-uted to the empirical nature of the predictor equationsand the creep data and numerical analysis methodsdeployed by the Alcoa software. Regardless, the use ofthe predictor equations has been illustrated to conveythe process required whenever dealing with the effects ofelevated temperature creep for conductors. While thepredicted sags vary depending on which analysismethod is used, the critical issue is the significant differ-ence in the predicted sag that is directly attributed to thehigh-temperature operation of the conductor.

As discussed, the results obtained by using the hand cal-culations are in close agreement to the values obtainedusing the software, and the percentage difference rangedfrom only 2.2 to 13%. Note that the correlationimproves as the temperature is increased, with a differ-ence of only 2.2% when the operating temperature is212°F (100°C).

2.4.13 Connectors at High Temperature

Splices and compression fittings, which join sections ofconductor and other components, must provide bothstructural and electrical integrity. Therefore, the integ-rity of these components is critical to the operation of apower line, particularly as the temperature of operationincreases. Connector failures can become very costly toutilities, and the cost of failure can be attributed to oneof four categories. First, there is the cost associated withpotential damages and injuries to the public. Second,there is a cost for loss of revenue from rerouting power.Third is the cost of repairs, which depends heavily onthe labor cost for using line crews and equipment, and

fourth, there is the cost associated with the loss of com-petitive advantage in the marketplace.

Transmission line operators use two types of tensionconnectors: limited-tension connectors and full-tensionconnectors. Limited-tension connectors are primarilydesigned to join conductors that are under little or nomechanical tension. These connectors are typically usedto splice the ends of two conductors together in a low-tension application, tap a second conductor from a con-tinuous run conductor, or terminate the end of a con-ductor in a low-tension application. Typical examples oflimited-tension connectors are bolted connectors, com-pression connectors, formed-wire connectors, wedge-type connectors, and implosive connectors. Becausethese connectors exhibit a limited tensile strength, thepart of the connector directly in contact with the cur-rent-carrying conductor is generally smaller in area thanthat of its full-tension counterpart.

Full-tension connectors are designed to providemechanical strength up to, or in excess, of the rated ten-sile strength of the conductor at all operating tempera-tures and also to provide a low-resistance conductivepath for the current carried by the conductor. Thus,splice connectors are used to join the ends of the con-ductors in spans between supports, and dead-end (alsoreferred to as terminations) connectors are used to joinconductors to the attachment hardware at the end ofeach tension segment, or special heavy angle, or termi-nation structures.

Generally, full-tension connections can be achievedusing one- and two-piece compression connectors,formed-wire splices, implosive connectors, and wedge-type connectors, but the compression-type connectorappears to be the predominant method of creating afull-tension connection on high-voltage conductors.Although the term “full tension” is commonly used tospecify the tensile strength of connectors to match thetensile strength of the conductor, the connectors aretypically designed to exhibit a tensile strength of at least95% of the conductor's rated breaking strength.

The main consideration for connectors when evaluatingelevated conductor temperature operations is its impacton the connector’s short- and long-term performanceand the effect on the service life. Certainly, the high-temperature operation of a circuit greatly increases aconnector’s electrical, mechanical, and thermal stresses.If operated unchecked, these stress increases are likelyto lead to the premature deterioration of the integrity ofthe connector and the eventual failure of this criticalcomponent. Since the prediction of such a failure is

Table 2.4-16 Comparison of the Predictor Equations and Alcoa’s Software Results

Tempera-ture (°F)

Predictor Equations

(ft)Alcoa’s Sag 10

Software (ft)Percentage

Difference (%)

60 27.5 31.6 13.0

90 29.5 33.4 11.8

120 31.4 35.2 10.8

167 34.2 36.6 6.3

212 36.8 37.6 2.2

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difficult, and the consequences are great, the successfulhigh-temperature operation of a circuit requires a care-ful evaluation of all of the issues involved.

Connector Breakdown ProcessA connector facilitates the transfer of current throughnumerous contact points between the connector and theconductor. High current densities and high operatingtemperatures tend to encourage the buildup of resistivecompounds at these contact points, effectively reducingthe size of the contact area, or in some cases completelyrestricting the current flow. Generally, the resultingincrease in the temperature of the connector will thenallow the formation of new contact points within thecomponent at locations where the buildup of resistivecompounds is small. The continuous cycle of closing andreopening of contact points within the connector can bethought of as an “aging” process in which the connectorwill continue to perform well as long as there are loca-tions where contact points can be easily established.

Once the connector has aged sufficiently so that all loca-t ions for easi ly establishing contact points areexhausted, the connector is forced to maintain contactpoints at locations at which resistive compounds arepresent in order to reach the parent metal. Thisincreases the overall resistance of the connector, itsoperating temperature, and current density within theremaining contact points. At this time, the higher cur-rent densities and operating temperatures cause furtherbuildup of resistive compounds, which in turn furtherincreases the current density and operating tempera-tures, leading to the eventual thermal failure of the con-nector. The thermal failure will eventually lead to theelectrical failure of the connector, and eventually resultsin the mechanical failure of the component. Figure2.4-12 shows typical compression deadend connectorsas used on transmission lines, and Figure 2.4-13 showsan infrared image of the connector indicating an imped-ing failure as indicated by the significant temperaturedifferences at the surface of the component.

Elevated temperature operations of conductors willincrease the current density and operating temperatureof associated connectors. This increase in the associatedthermal, electrical, and mechanical stresses will acceler-ate their aging process, effectively reducing service life.The amount of accelerated aging connectors experienceis directly related to the magnitude and frequency of theelevated current and operating temperature operationexperienced by the component. Unfortunately, the rela-tionship between the aging of the connector and theloads served is nonlinear, and little success has beenachieved in directly quantifying that relationship. EPRIis currently conducting research to assess the perfor-mance of transmission-line components when subjectedto increases in operating temperatures. Preliminaryresults indicate that most conductor hardware appearsto operate more efficiently when compared to the con-ductors as long as the components are installed cor-rectly. Results show that failures occur mostly as a resultof improper installation, and that many of these issuescan be addressed effectively using an appropriate qual-ity assurance strategy.

Most well-designed connectors (when properlyinstalled) are capable of operating at high current densi-ties and high conductor temperatures while providingacceptable performance and service life. The currentcycle test, an industry standard, is commonly used toevaluate these connector designs. Current cycling theconnector results in the thermal expansion and contrac-tion of the electrical contact interface and tends tobreak down the contact points between the connectorand the conductor. Although this standard test identi-fies procedures and qualification criteria for connectorsused under normal operating conditions, the applicationof this test does have its limitations. Figure 2.4-14 showstypical test results obtained from a standard heatcycling test.

Figure 2.4-12 Visual image of problem deadend. Figure 2.4-13 IR image of problem deadend.

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Connectors should be considered as approaching failureif the operating temperature approaches or exceeds theoperating temperature of the conductor. Experimentsshow that the operating temperature of an adequatelydesigned and correctly installed compression connectorshould be approximately 10 to 30% lower than the oper-ating temperature of the conductor. The reduced oper-ating temperature can be directly attributed to thesignificantly larger cross section of the compressionconnector relative to the cross-sectional area of the con-ductor, the increase in the surface area of the compres-sion fitting relative to the surface area of a comparableunit length of conductor, and the increase in the convec-tion to occur at any measurable wind speed.

High-Temperature Effects on Connector Joint CompoundMost aluminum connectors, especially compressiontype, employ a viscous compound in the interfacebetween the connector and underlying conductor. Theprimary purpose of the joint compound is to provide abarrier that prevents moisture and other contaminantsfrom leaching into the joint. The ingress of moistureand other contaminants is not desirable since this willlead to the internal corrosion of the connector, which islikely to affect not only the tensile strength of the steelstrength member in the case of an ACSR conductor but

also deteriorate the connector’s ability to effectivelytransfer the current.

The repeated high-temperature operation (connectortemperatures above 200°F (95°C)) degrades the jointinterface by causing the viscosity of the joint compoundto decrease significantly, leading to the eventual outflowof the joint compound or the carbonization of the jointcompound, leading to a reduction in the protection pro-vided by the corrosion inhibitor. Thus, the later scenarioleaves a shrunken and hardened residue that is no longereffective as a moisture barrier. The presence of moistureand contaminants in the joint accelerates the connec-tor’s aging process and effectively shortens the connec-tor’s service life. Figure 2.4-15 shows an infrared imageof a compression splice on which the joint compound isleaking out of the fill hole located at the center of thecomponent.

New and Existing ConnectorsWhen designing overhead power lines for high-tempera-ture operations or contemplating the refurbishment ofexisting facilities, a great deal of consideration should begiven to the conductor temperatures at which the con-nectors were tested. Prudence dictates that connectorsdesigned for high-temperature operation should be

Figure 2.4-14 Mechanical load data of a “new” Hawk conductor.

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tested and qualified for temperatures well in excess ofthose expected in service.

When evaluating existing connectors prior to the opera-tion of a circuit at a higher operating temperature, it isrecommended to evaluate the original performancespecifications of the existing connectors. A review of thestandards against which the connectors were designedand tested assists in evaluating whether these compo-nents are acceptable for operation at significantlyincreased operating temperatures. Operating electricalconnectors at temperatures above those for which theywere designed can be risky, and at the least, a standardcurrent-cycle test should be performed to evaluate theperformance of each connector.

Mitigation of Effects of Connector High-Temperature OperationsA cost-effective and frequently used method used toincrease the operating life of connectors is by using rein-forcing methods such as shunts. Typically, existing con-nectors that are suspected of being inadequate for the

high-temperature operation of a particular line can beshunted to reduce their electrical loading and to prolongtheir service life. Shunts provide an alternate path forthe current flow, thereby reducing a connector’s currentdensity and operating temperature. The reduction in theconnector’s current density retards the aging process,and extends the long-term performance and service life.Similarly, shunting of marginal connectors can be usedto extend the service life and to improve the perfor-mance of components.

Nondestructive Methods to Measure ConnectorsThe degradation of a connector can be observed byincreases in its resistance and temperature. Theincreased resistance is measured with devices such as anOhmstik, developed by SensorLink Corp. The tooltakes advantage of the increased resistance by measur-ing the ac voltage drop across the component that iscaused by the current. Typically, resistance measure-ment devices such as the Ohmstick can operate at cur-rents ranging from 2 to 1400 A and can measureresistances from 5 to 2500 micro-ohms. Figure 2.4-16shows an infrared image of a defective conductor con-nection and a summary of the corresponding resistancemeasurements.

2.4.14 Conductor Hardware

Conductor hardware, as defined in this report, refers tononcurrent carrying devices attached directly to theconductor. Conductor hardware includes componentssuch as suspension clamps (with or without armorrods), dampers, repair sleeves and splices, spacers andspacer dampers, shackles, pins, etc. Generally hardwareis manufactured from cast or forged aluminum, butthere are instances where metallic hardware has beenused, and the issues associated with the use of metallichardware are discussed.

Figure 2.4-15 Leakage of connector joint compound.

Figure 2.4-16 Resistance measurement of connector.

2-49


Metallic Conductor Hardware Metallic conductor hardware for aluminum conductorsis fabricated primarily from aluminum alloys, whilehardware for copper conductors is mostly fabricatedfrom copper alloys. One of the reasons for the strictselection and use of similar metals is the recognition ofthe differences in the galvanic properties of these materi-als. When metals of different galvanic properties arepermitted to react in the presence of moisture, theresulting reaction quickly deteriorates the lower rankedmaterial, resulting in significant corrosion to an assem-bly. Nevertheless, galvanized ferrous hardware and com-ponents have been used extensively in the past becauseof the inherent high strength-to-weight ratio and thefact that the galvanized steel component is relativelyinert to both aluminum and copper in a mild climateand environment.

High-Temperature Effects of Ferrous Conductor HardwareFerrous hardware that either partially or completelysurrounds a current-carrying conductor is subject tohysteresis and eddy current losses caused by the mag-netic flux associated with the current flow. These eddycurrent losses manifest themselves in the form of signifi-cant heat gains within the hardware, and hence signifi-cantly increased operating temperatures. Thus, excessiveheating of the hardware or greatly increased operatingtemperatures within the ferrous hardware at levels abovethe acceptable level of the conductor is likely to causethe annealing of any aluminum components. The exces-sive heating and increased temperatures conveyed by theferrous hardware can anneal the conductor or other alu-minum components, thereby reducing the tensilestrength and the expected service life. While the effect ofthe heating is typically localized and adjacent to the fer-rous component, the effect on the conductor can be det-rimental and sufficiently destructive to mandate theeventual replacement.

Heat gain due to hysteresis and eddy current losses inferrous hardware is a function of the magnitude of thecurrent in the conductor and the hardware’s thermalconductivity. Convection and radiation heat losses fromthe ferrous hardware are primarily a function of thehardware’s surface area and surrounding ambient con-ditions. Hence, the operating temperature of ferroushardware fluctuates in response to changes in the cir-cuit’s load and the ambient conditions.

Conductor hardware is deployed in numerous configu-rations to support and protect the conductor, and isavailable in many different sizes and shapes. Smaller ver-sions of ferrous hardware have a relatively low ratio ofmass to surface area and usually operate at tempera-tures well below that of the conductor, regardless of cur-

rent. Conversely, larger versions of ferrous hardwarehave a mass-to-surface-area ratio that can result inhardware temperatures greater than the conductor’sallowable annealing temperature at higher currents.Hardware large enough to produce localized conductortemperatures of concern are usually confined to suspen-sion and strain clamps, but can occasionally be causedby any ferrous device surrounding the conductor as longas they have a large mass-to-surface-area ratio. Pub-lished literature, which permits the calculation of thelocal temperature increase in a conductor’s temperatureas a function of the load, is limited.

The mitigation of the effects of localized heating underferrous hardware usually involves either limiting thecurrent rating of a line, limiting the cumulative time aconductor can operate at the elevated rating, or replac-ing the hardware with nonferrous hardware. Experienceshows that the number of conductor and hardware con-figurations are extensive, requiring each utility todevelop customized solutions to address this problem.

Nonferrous conductor hardware does not internallygenerate any heat in response to a conductor’s current.Generally, nonferrous hardware operates at tempera-tures well below the conductor’s operating temperaturebecause of the increased surface area and the corre-sponding increase in the convective cooling provided bythe wind, if any.

Nonmetallic Conductor Hardware Nonmetallic conductor hardware is generally limited toelastomeric compounds, which serve as compressive“bushings” within a hardware assembly. Compressionbushings are typically used in spacers, spacer-dampers,and armor grip suspension clamps to provide a resilientinterface between the conductor and the hardware.

Publications concerning the effects of high-temperatureoperations on elastomeric hardware components arelimited. During and after high-temperature excursions,the elastomeric components must retain their resilientand semiconductive properties for long-term survival.Loss of such properties can result in component deterio-ration and/or component failure.

High-Temperature Tests on ACSS Conductor Hardware Reynolds Aluminum performed high-temperature cur-rent cycle tests of ACSS conductors and associated fit-tings. Tests were performed on a loop of 1033.5 kcmil(527 mm2), with a 45/7 Stranding, “Ortolan” SSAC con-ductor with various fittings installed. In all cases, thetemperatures measured at the conductor hardware werewell below the conductor operating temperature. At a200oC conductor operating temperature, the measured

2-50


full-tension splice temperatures ranged from 120o to130oC. The operating temperature of the partial-tensionsplices was observed to be significantly higher, rangingfrom 160o to 170oC. On the contrary, the operating tem-perature at the suspension clamp was 84oC, and thetemperature measured at the first insulator pin was37oC. Operating temperatures at the AGS unit were102oC on the armor rods, 46oC on the clamp surface,and 106oC beneath the neoprene sleeve.

High-Temperature Tests of ACSR Conductor HardwareDetroit Edison conducted tests of ACSR conductorsand hardware to determine if high-voltage power linehardware could be safely operated at temperatures up to200oC. Tests were conducted over a temperature rangefrom 75oC to 200oC. Hardware tested included alumi-num body bolt-type strain clamps, aluminum body sus-pension clamps, armor rods, parallel groove clamps, linedampers, and full-tension splices. Hardware was testedwith 477 kcmil (243 mm2) ACSR Hawk, 795 kcmil (405mm2) ACSR Drake, 954 kcmil (487 mm2) ACSR Cardi-nal, and 1431 kcmil (730 mm2) ACSR Bobolink con-ductors. The aluminum strain clamp temperatureranged from 35 to 61% of the conductor operating tem-perature for the four conductors tested, while the sus-pension clamp temperature ranged from 29 to 43% ofthe conductor temperature. On the contrary, armor rodtemperatures were 68 to 80% higher than the conduc-tor’s temperature.

High-Temperature Tests on Polymer Insulators Test results on polymer insulators indicate that mostinsulators are well equipped to handle high operatingtemperature loads. An EPRI report (EPRI 2002)describes the results of a typical conductor suspensionassembly using a polymer insulator. In the test, temper-atures were measured on the conductor, suspensionclamp, shackle, link, insulator pin, and polymer insula-tor, as well as the ambient temperature. The tempera-tures of the test components at the maximum conductoroperating temperature of 292oC (not referenced toambient temperature) ranged from 163oC at the suspen-sion clamp, to 88oC at the shackle, to 43oC at the link,to 32oC at the insulator pin, to 28oC at the insulator.The ambient temperature at the time of the test wasmeasured at 17oC.

Another set of tests on polymer insulators had similarresults. In these tests, temperatures were measured at theinsulator end fitting near the fiberglass rod end, near thesuspension fitting end, on the suspension fitting conduc-tor keeper, on the suspension fitting body near the con-ductor groove, and on the conductor itself. The testingincluded the mechanical loading of the suspensionassembly and current cycling of the conductor to a max-

imum conductor core operating temperature of 250oC(not referenced to ambient temperature). Tests wereconducted on high-voltage polymer suspension insula-tors of five different manufacturers. The measured insu-lator end fitting temperature, nearest the fiberglass rod,ranged from 47o to 61oC depending on the type of poly-mer insulator. The end fitting temperature nearest theconductor was slightly higher, ranging from 54o to 67oC.After the thermal testing, each insulator was testedmechanically to determine the residual strength. Resultsshowed no measurable degradation of the mechanicalperformance of the five polymer insulators regardless ofthe manufacturer.

A third set of tests reinforces the same conclusions forpolymer suspension insulator assembly. In each test,thermocouples were used to measure the conductortemperature, the insulator end fitting temperature, andthe ambient temperature. Sufficient current was appliedto the conductor to generate a nominal operating tem-perature of 200oC. Tests generated end-fitting tempera-tures ranging from 38o to 46oC at ambient temperaturesranging from 19o to 27oC.

2.5 UPRATING WITHOUT RECONDUCTORING

2.5.1 Introduction

There are two overall strategies to uprating overheadtransmission lines without reconductoring: using deter-ministic methods or probabilistic methods.

With deterministic methods, line rating calculations aredone using tradit ional tools, such as the EPRIDYNAMP program, and assumed ambient conditions.Physical alterations to the line can be made (such asretensioning the conductors or raising their supportpoints) to increase the maximum allowed conductortemperatures, thereby increasing the ratings. Or, theassumed ambient conditions themselves can be changed(such as assuming a higher wind speed).

With probabilistic methods, actual weather data is ana-lyzed statistically to determine the most viable assump-tions and the associated risks.

2.5.2 Deterministic Methods

This subsection focuses on uprating methods that avoidreconductoring, involve minimal capital investment,and do not require field monitors. Typical increases inpower flow resulting from these options range from 5%to 50%, depending on the original design conditions, thepresent rating assumptions, and the type of structureand conductor used in the existing line. These upratingchoices are particularly effective for older lines, perhaps

2-51


designed under the old 120oF (49oC) clearance tempera-ture.

Since the transmission conductors are not to bereplaced, the result will be operation of the line’s exist-ing conductors at increased temperature levels. Conse-quently, the conductor, its hardware, and its connectorsneed to be carefully inspected prior to uprating. Anyquestionable elements need to be replaced.

In addition to a physical inspection, the line upratingprocess must verify that adequate electrical clearanceswill be maintained after the uprating is complete. Typi-cally, this verification should consist of three steps:

1. Measurement of “everyday” sag clearance and sup-port point locations by use of conventional surveyequipment, or airborne digital imaging equipment,with the line out of service or at relatively low electri-cal load.

2. Calculation of maximum sag (minimum groundclearances) under electrical load equal to the pro-posed new thermal rating.

3. Experimental verification of electrical clearancesunder a combination of rated load and worst-caseweather conditions through the use of sag or tensionmonitors.

Since the maximum allowable temperature is to beincreased, these steps are necessary to be certain that theadditional sag does not violate minimum electricalclearance requirements and that any increased anneal-ing of the conductor’s aluminum or copper strands doesnot reduce the line’s loading safety factors to an unac-ceptable level.

Evaluating Sag Clearance Under “Everyday” ConditionsAs discussed in Section 2.3, new lines are designed tomeet certain minimum electrical clearances under allweather conditions at electrical loads less than or equalto their thermal rating. They are also designed to limitthe maximum tension under maximum ice and windloads to the structure design values. To do this, initialunloaded conductor sags are specified such that thefinal sags at high temperatures and the maximum ten-sions under ice and/or wind loading are within theselimiting values. By adjusting the initial sags to these“stringing sags” at the time of construction, minimumclearance and maximum tension limits are maintainedthroughout the life of the line. The “final” sags includean allowance for permanent elongation due to creepelongation of aluminum and to plastic elongation due toice and wind loads. In addition, because of uncertaintiesin these calculations, new lines are typically designedwith clearance buffers of at least 3 ft (1 m).

With existing lines that have been in service for 10 yearsor more, the measured sag may be assumed equal to“final” conditions. That is, the conductor has experi-enced most of the permanent elongation allowed in theoriginal design. Unless the line is retensioned, the errorin estimating final sag at the maximum design tempera-ture is limited to questions about thermal elongation athigh temperature. Also, since the structures have beenlocated and the support point elevations determined,the initial sag buffer requirement may be less than thatrequired for a new line.

Many different techniques are available to determine theelectrical clearance under everyday loadings where theconductor temperature is quite close to air temperature.These techniques range from the use of survey crews atselected spans, to flying the span by airplane or helicop-ter with digital recording devices. The latter providesmore data than required and costs more. The formerprovides less data than one might wish for and costs less.

Particularly with digital recording from the air, the datacan be loaded directly into line profiling and design pro-grams like PLS-CADD™ and TL-CADD™. This allowsa span-by-span verification of sag and a relativelystraightforward calculation of conductor sag at highertemperatures.

While the accuracy of these measurements is in therange of a few inches (several centimeters), the determi-nation of the corresponding conductor temperature atthe time of measurement is less accurate. Generally, theconductor temperature is determined by use of a heatbalance equation such as IEEE738 or DYNAMP withthe line electrical load and local weather data. If theelectrical load of the conductor is less than 0.25 A/kcmil(0.5 A/mm2), then the difference between calculatedconductor temperature and actual should be less than5oC. If the electrical load is higher, then the differencecan also be higher, depending on how the calculation isdone and how the weather data (see Section 2.3) isdetermined.

Raising Conductor Support PointsThe thermal elongation of stranded conductors is essen-tially the same as that of its component strands. There-fore, for an all-aluminum or copper conductor, once thesag at “final” everyday conditions is established, the sagat high temperatures can be calculated with relativelysmall uncertainty.

For example, consider a line section of an all-aluminum,37 strand (Arbutus) conductor having a ruling span of600 ft (183 m) installed to meet the following con-straints: maximum tension of 50%, 33% initial unloaded

2-52


at 15°F (9.4°), and 25% final unloaded at 15°F (-9.4 °C).An equally typical SAG10 program line design sag-ten-sion run is in Table 2.5-1.

As an example, consider that the line was originallydesigned for a maximum conductor temperature of120°F (49 °C) and the line structures were placed suchthat the minimum ground clearances are met with theruling span final sag of 15.5 ft (4.7 m).

To operate the existing line at 167°F (75 °C), the attach-ment points must be raised approximately 2.2 ft (0.67m). To operate at 212°F (100 °C), the attachment pointsmust be raised approximately 4.2 ft (1.28 m).

Given rating conditions of 2 ft/sec crosswind, sun, andan air temperature of 35oC, the rating of the originalline is 345 A. By raising the attachment points by 2.2and 4.2 ft (0.67 and 1.28 m), to allow operation to 75oCand 100oC, the line’s thermal rating is increased to 775and 1010 A, respectively. Note the large increase in ther-mal rating corresponding to modest increase in attach-ment height. Many lines built prior to 1970 originallyutilized 49oC as the maximum conductor temperaturefor clearance estimates.

With wood pole H-frame structures, increasing attach-ment height in order to increase the line thermal ratingmay be particularly attractive. Crossarm attachmentpoints can be raised, hardware replaced, and shieldwires placed on metal pole top extensions at minimalcost. Figure 2.5-1 is a photograph of a wood pole struc-ture where the conductor attachment height has beenraised.

In existing lines having longer ruling span sections, thereare fewer structures per mile (km) to modify but greatersag increases required to offset increased sag at higheroperating temperatures, as shown in Figure 2.5-2.

Retensioning Existing ConductorsRather than replacing existing conductors with new, itmay be possible to increase the everyday tension ofexisting lines in order to reduce sag at high temperatureand therefore increase the line rating. For example, con-sider the following case where an existing line with Mal-lard ACSR is to be uprated.

Table 2.5-2, taken from the SAG10 program, shows thesag and tension (total, aluminum, and steel componenttensions) for initial and final conditions for 30/19, 795kcmil (405 mm2) ACSR (Mallard) initially sagged so as

Table 2.5-1 Sag-tension Calculations for 37 AAC (Arbutus)


Conductor Arbutus 795.0 kcmil 37 Strands AAC Area = 0.6234 sq in. Dia + 1.026 in.



Temp (°F) Ice (in.) Wind (psf) K (lB/°F) Weight (lb/°F) Sag (ft) Tension (lb) Sag (ft) Tension (lb)

15. .25 4.00 .20 1.451 12.02 5446. 10.65 6140

32. .25 .00 .00 1.143 12.00 4294. 10.06 5118

0. .00 .00 .00 .746 8.77 3833. 6.63 5067.

15. .00 .00 .00 .746 9.67 3475.a


7.27 4621.

30. .00 .00 .00 .746 10.58 3179. 7.98 4212.

60. .00 .00 .00 .746 12.34 2727. 9.54 3524.

90. .00 .00 .00 .746 13.99 2406. 11.19 3006.

120. .00 .00 .00 .746 15.54 2167. 12.82 2624.

167. .00 .00 .00 .746 17.78 1897. 15.24 2210.

212. .00 .00 .00 .746 19.73 1711. 17.37 1941.

257. .00 .00 .00 .746 21.54 1570. 19.33 1746.

302. .00 .00 .00 .746 23.22 1457. 21.15 1598.

Figure 2.5-1 Photograph of a wood pole H-frame structure with raised crossarm and pole-top extensions for shield wires.

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not to exceed a final unloaded tension of 15% of Mal-lard’s Rated Breaking Strength at 60oF (15.5oC). NESCMedium Loading conditions and conductor tempera-tures up to 302oF (150oC) are included, but the originalline is rated at 75oC, at which temperature electricalclearance to ground is near the NESC minimum values.

Notice that the knee-point temperature, where the alu-minum tension goes to zero, under final conditions,occurs at only 90oF (32oC).

It is assumed that the existing conductor has beeninspected, and that the increased vibration that will

result from pulling the conductor to a higher everydaytension (up to 25% rather than 15% of RBS at 60°F[16°C]) can be offset by the addition of dampers.

From Table 2.5-2, it can be seen that increasing the ten-sion from 15% to 25% RBS will reduce the high-temper-ature sags at temperatures of 75oC to 150oC by about 4ft (1.2 m). Therefore, the maximum design temperaturecan be increased to 150oC or more without violatingclearance limits.

At the original line’s maximum allowable conductortemperature of 75oC, with an air temperature of 40oC,full summer sun, and a wind blowing perpendicular tothe conductor axis at 2 ft/sec, the thermal rating was 735A. If the retensioned line is rated at 150oC with the sameweather conditions, the new thermal rating is 1345 A(83% higher).

Limitations on Retensioning Existing ConductorThere are several concerns about this method of thermaluprating:

1. The maximum tension exerted on strain structuresduring maximum wind and ice loading has increasedfrom 7800 to 11,300 lbs. (34.8 kN to 50.4 kN). As aresult, it is likely that these structures would need tobe replaced. An alternative solution may be to limitthe increase in everyday tension so that the increasein tension loading of existing structures was accept-able without having to rebuild. This would, of course,reduce the allowable conductor temperature and theresulting increase in thermal rating.

Figure 2.5-2 Change in sag for all aluminum conductor as a function of span length.

Table 2.5-2 Sag-tension Calculations for 30/19, 795 kcmil ACSR (Mallard)a



Conductor Mallard 795.0 kcmil 30/19 ACSR Area = 0.7669 sq in. Dia + 1.140 in.


Design Points Re-tensioned Original Line

Temp(°F)

Ice(in)

Wind (psf)

K(lb/°F)

Weight(lb/°F)

Sag(ft)

Tension(lb)

Sag(ft)

Tension(lb)

15. .25 4.00 .20 1.955 7.80 11283. 11.26 7823

32. .25 .00 .00 1.667 7.68 9773. 11.39 6600

0. .00 .00 .00 1.235 5.30 10495. 8.97 6202

15. .00 .00 .00 1.235 5.79 9600. 9.66 5760

30. .00 .00 .00 1.235 6.34 8775. 10.35 5377

60. .00 .00 .00 1.235 7.56 7357. 11.71 4755

90. .00 .00 .00 1.235 8.65 6432. 12.57 4433

120. .00 .00 .00 1.235 9.26 6010. 13.26 4204

167. .00 .00 .00 1.235 10.27 5422. 14.33 3891

212. .00 .00 .00 1.235 11.27 4939. 15.33 3637

257. .00 .00 .00 1.235 12.30 4528. 16.32 3419

302. .00 .00 .00 1.235 13.34 4178. 17.28 3230

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2. While the conductor in the existing line had reachedits final sag condition, increasing the tension willcause additional creep elongation and must beallowed for in the uprating study (see Section 2.4).

3. The calculation of sag and tension for this MallardACSR ignored the problem of compression in thealuminum strands. If compression is considered, thesag at high temperature will be higher than that indi-cated in Table 2.5-2. This has two effects: the sagclearance of the original line may not have been ade-quate at 75oC, and the change in sag with tempera-ture after retensioning will also be greater thanindicated.

4. Conductors and structures that have been in place formany years will be mechanically and electricallystressed to increased levels. Unless the existing con-ductor, structures, hardware, and connectors arethoroughly inspected, there is a possibility that thereliability of the line will be less than that of a newline or one that was reconductored.

Redefining Weather AssumptionsThrough a careful review of weather conditions, it maybe possible to use less conservative weather assumptionsfor rating calculations. This increases the rating withoutthe need for physical modification of the line. The tech-nique is limited by the increased risk necessarilyassumed by allowing higher current operation withoutincreasing everyday clearances.

Figure 2.5-3 illustrates the difference between actual lineratings and static ratings. The rightmost bell-shapedcurve represents the probability distribution of line ther-mal ratings calculated based upon real-time field mea-surements of weather data. Note that the ratings of theline typically vary over a range of more than 2:1. The

very lowest ratings correspond to still air, maximum airtemperatures, and full sun. A typical static thermal rat-ing of 800 A is shown at the left tail of the rating distri-bution. A less conservative static rating of about 900 Ais also shown. Clearly, the higher the static rating, themore frequently the actual line rating is less than thestatic.

The leftmost distributions are line loadings (which varyas a result of varying customer load levels and systemconfiguration changes) appropriate to each of the staticratings. Note that in this case, the line loadingsapproach, but do not exceed, the static ratings, and foreach loading curve, the load may occasionally exceedthe dynamic rating. This happens more frequently(larger overlap area) for the higher load distribution.

Unless a dynamic line rating system is in use, the opera-tor cannot know when the actual line rating is lowerthan the line load and therefore is unable to avoid occa-sional clearance infringements if the load distribution ishigh enough.

Actual Line Ratings are Normally Higher than Static RatingsIt can be seen from Figure 2.5-3 that most of the timethe line rating is well above the static rating and thatunder these conditions, the line current could safely behigher than the static limit. As long as line loads onlyrarely approach the line rating, it has been argued thatthe static rating can be increased with a negligible effecton electrical safety. This approach is investigated morethoroughly in Section 2.6. The method discussed here ismuch less scientific and much more common. Lines aresometimes uprated simply by using less conservativeweather assumptions.

Concerns About Using Less Conservative Weather ConditionsIn a regulated business environment, under ordinaryoperating conditions, power equipment was lightlyloaded. High electrical loadings were rare; hence, theprecise determination of high-temperature behavior wasnot critical. Some years ago, however, as the regulationof utility business began to decrease, many older high-voltage lines have been operated at higher and higherload levels. This might lead to increased failure ratesand consequent service outages unless the mathematicalmodels used to specify load limits were refined, and crit-ical equipment parameters verified by measurement.

Driven by the advent of open transmission access andderegulation of the utility business, there has been a dis-tinct trend toward the use of less conservative ratingassumptions with little or no basis in science. Field test-

Figure 2.5-3 Probability density distributions for a typical circuit load and dynamic rating.

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ing of dynamic thermal methods offered an opportunityboth to evaluate the possible increase in ratings, and todetect the frequency of occurrences where existingequipment might be damaged due to less conservativerating assumptions.

The calculation of thermal ratings for overhead lines istypically based upon heat balance methods such as thatfound in IEEE 738-1993. Given a maximum allowableconductor temperature, the corresponding maximumallowable current (the thermal rating) is determined for“worst-case” weather conditions. Maximum allowableconductor temperatures typically range from 50°C to150°C. Typical “worst-case” weather conditions are awind speed of 2 ft/sec (0.61 m/sec) perpendicular to theconductor, with full solar heating and an air tempera-ture of 30°C to 40°C.

Table 2.5-3 illustrates the advantage of assuming ahigher wind speed and the consequence of doing so. Useof a higher wind speed for thermal rating calculationsyields an increase in the line rating, even though themaximum conductor temperature (100°C) remains thesame. For example, an increase in assumed wind speedfrom 2 to 3 ft/sec (0.61 m/sec to 0.91 m/sec) yields anincrease in the rating from 990 to 1080 A and, since theassumed conductor temperature remains the same, noline modifications are required.

The major advantage of this method of uprating isclear—it is very inexpensive. Since the maximum allow-able conductor temperature remains the same (100°C),the corresponding maximum sag is unchanged and noline modifications are required.

The major disadvantage of this approach is also clearfrom the rightmost column of Table 2.5-3. This columnshows the temperature attained by the conductor forstill air conditions , with a line load equal to the calcu-

lated rating shown in column 2. Historically, the jointprobability of maximum loading and worst-caseweather was considered a rare event. Recent field studiesindicate that, in certain areas, the probability of still airmay be in excess of 10%. Combined with the previouslynoted increase in normal and emergency line loading,the temperatures indicated in the last column of Table2.5-3 may be a real concern, and the use of a less conser-vative wind assumption may impact line reliability.

2.5.3 Probabilistic Methods

The probabilistic approach uses the actual weather dataand conditions prevailing on the line to determine thelikelihood or probability of a certain condition occur-ring. Such a condition could be, for example, the con-ductor temperature rising above the design temperature(the maximum allowed conductor temperature). Thesemethods have been developed to include a measure ofsafety of the line. This can be used as a means of com-parison of practices between utilities in all countries.

The pros of probabilistic methods are that the risk isbetter known and can be quantified and defended if nec-essary. The designs can be consistent from a risk pointof view in that, if localized weather conditions are usedfor different lines in different geographical areas, thelines can have different ratings, even though their designtemperature and conductor types are the same.

If there is a thermal rating limitation on a line, the prob-abilistic approach can ensure minimal or zero capital isused to uprate the line. The line designers also have farmore parameters to vary in increasing the rating of aline. They could use the load profile, surge, or trafficpatterns to increase the thermal rating of lines. This isnot possible in the deterministic method.

The cons of the probabilistic method are that significantamounts of data are required to determine the rating.This includes weather data as a minimum. If moresophisticated methods are required, the data needs to bedetermined on traffic patterns, surge patterns, and loadprofiles etc. Regarding the weather data, the variation ofthe data with time as well as with area needs to be takeninto account. While the ambient temperature and solarradiation may be consistent over large areas, the windspeed and direction may vary within a few meters. It isalso necessary to know how the parameters will varyinto the future. This is particularly important withregard to the more complicated probabilistic methodswhere, for example, load profile is used. It is thus neces-sary to be aware of these issues in the determination ofratings.

Table 2.5-3 Effect of Assumed Wind Speed on Thermal Rating for Drake 795 kcmil ACSR at 100°C, Assuming Full Sun and an Air Temperature of 40°C.

Assumed Wind Speed for Line Rating Calcula-

tion

Line Rating for 795 kcmil ACSR

@ 100°C

Conductor Temperature When Current =

Rating and Wind Speed = 0 ft/sec (0 m/sec)

(ft/sec) (m/sec) (A) (°C)

0 0 750 100

2 0.61 990 130

3 0.91 1080 145

4 1.22 1160 160

2-56


Three main probabilistic methods are available atpresent:

1. Absolute MethodThe probability of an unsafe condition occurring canbe quantified in this method. The benefit is that anabsolute measure of safety can be achieved. Thedrawback is that the nature of the parameters isextremely difficult to determine. In addition, the cor-relation between the parameters—for example, theweather parameters—must be determined. Thiscould vary from country to country.

2. Exceedence MethodHistorical weather data is used to determine the tem-perature of the line conductors for a given currentflow. The amount of time that the temperatureexceeds the line design temperature can be determinedfor each current level. The utility can then decide onthe current level to use based on the percentage ofexcursion or “exceedence.” The advantage of thismethod is that it is relatively easy to determine thepercentages and decide on a level by which to operate.The disadvantage is that there is no way of determin-ing the difference in safety (to the public) between, forexample, the 5% and 6% exceedence levels.

An adaptation of the above method is to simulate theweather data and the current flow to determine thecumulative distribution of the conductor temperatureas a function of current. This curve could be used todetermine the current and excursion level.

3. Modified Exceedence MethodThe safety of a transmission line is estimated byincorporating all relevant factors. From this method,a measure of safety can be developed whereby thepractices in different countries can be compared onan objective basis. The advantage of this method isthat all factors are considered. The variation of theoccurrence of objects under the line—for example, atraffic pattern—can be related to the safety of a line.Designers can use a wider range of methods, not gen-erally used before, to increase the thermal rating ofthe line. Examples of this are the reduction of surgemagnitudes or the number of surges per year, both ofwhich can be used to increase the current-carryingcapacity of a line.

By using the measure of safety, system planners andline designers are in a position to determine the con-sequences of decisions in a more objective, ratherthan a subjective, way. Similarly by using the measurein conjunction with real-time monitoring systems todetermine exact conductor temperature, operatorscan take more objective decisions. Utilities worldwidewould also be in a position to determine the safety oftheir lines in relation to those of other utilities.

The “Absolute Method” of Determining the Probability of an AccidentResearch to date has primarily been confined toattempts at determining the probability of an unsafecondition arising. This is determined by ascertaining theprobability of each factor occurring and multiplying theprobabilities. This is represented in Equation 2.5-1.

2.5-1Where:P(acc) is the probability of the accident occurring.P(CT) is the probability of a certain temperature

being reached by the conductor, and is cal-culated from existing weather conditions,conductor types, and an assumed current.

P(I) is the probability of the assumed currentbeing reached, and is determined from theactual current being measured on a system.

P(obj) is the probability of the electrical clearancebeing decreased by an object or person.

P(surge) is the probability of a voltage surge occur-ring in the line and may be determinedfrom fault records kept by the power utilityas well as simulations on switching surgeovervoltages on the system. If the surgeoccurs simultaneously with an object beingunder the line, the likelihood of a flashoveris increased.

Each of the above is considered to be determined inde-pendently.

P(CT) is determined by the Monte Carlo simulationtechnique sampling from distributions of ambient tem-perature, wind speed, wind direction, and solar radia-tion to calculate the probability of a certain temperaturebeing reached given a current transfer. The ambienttemperature, solar radiation, wind speed, and winddirection are sampled independently to form a set ofparameters from which the temperature of the conduc-tor is determined.

The problem with the above method is that it assumesno correlation between weather parameters or the cur-rent, object, and surge occurrences. This may not becorrect in all cases. The correlation between the individ-ual weather parameters, as well as the weather parame-ters and the surge occurrences and objects being underthe line, needs to be ascertained.

This problem can be partly overcome by using sets ofweather parameters, nmeasured at the same time. Thesesets will be used to determine the P(CT). Since each setused is determined from actual recordings of ambient

P(acc) = P(CT) P(I) P(obj) P(surge)• • •

2-57


temperature, solar radiation, wind speed, and winddirection taken at the same time, the correlationbetween the parameters is taken care of.

Determination of Line Rating by the “Standard Exceedence Method”This method assumes that the design temperature of theline may be exceeded for a small percentage of time, butthat the line remains safe because of the low probabilityof other factors, such as high current levels and switch-ing surge voltages. The amount of time the conductorexceeds the design temperature expressed as a percent-age of total time is termed the exceedence level. Bydetermining the exceedence level, and keeping it con-stant, the line ratings can be determined using differentweather conditions or different geographical locations.This method is simpler to use than the absolute probabi-listic method described earlier and does ensure consis-tent risk. The standard use of this method assumes thatthe full load current will flow at all times. A modifiedexceedence method uses the load profile of the line inquestion to increase the thermal rating above that of thestandard method.

This (standard) method uses the weather data as well asthe current and conductor characteristics to determinethe frequency of occurrence of each temperature rangeattained for a given conductor current. Alternatively thecurrent that would result in the templating or designtemperature being reached can be calculated for each setof weather conditions. The frequency of occurrence ofeach current range can be determined. The weather data

used can be hourly readings, although the accuracy willincrease with more frequent readings. The steady-statemodel can be used for the determination of the conduc-tor temperature or the current required to reach a cer-tain temperature.

With reference to Figure 2.5-4, the exceedence levelshave been calculated for the same conductor (Bersfort)in two separate locations in South Africa. The solid linerepresents the exceedence levels experienced in Bloem-fontein, a hot semi-arid climate, compared to Volksrust,a small town in a more moderate climatic region. Thenumber of lines for Volksrust indicates the differences inthe weather data from year to year. The dashed line rep-resents the average of the years. The graph indicates aninteresting fact in that the operators utilize a single rat-ing for both sites. The risk or exceedence experienced atboth sites is likely to be different for the same current.The operators are therefore operating “blind” withregard to the risk. The exceedence method has the bene-fit of applying a uniform risk, or probability of exceed-ing the design temperature, by utilizing different ratingsat the different locations.

Difficulty often arises in setting the exceedence limit.One approach could be to determine the exceedencelimits experienced at present for various geographicalareas at different times of the year. This can be achievedby plotting graphs similar to those of Figure 2.5-4. Thepresent current limit is used to determine the exceedencelevel. This level can then be used to determine the

Figure 2.5-4 Graph showing the results of the use of the exceedence method.

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ampacity of different conductors at different design orline design temperatures.

Benefits of Using Standard Exceedence MethodThe Standard Exceedence Method has been in use bythe National Grid Company (UK) for some years. Table2.5-4 gives an example for rating its transmission sys-tem. The percentage excursion time, now called“exceedence,” corresponds to the portion of time thatthe conductor would exceed the stated design tempera-ture if it were operated continuously at the correspond-ing current. These values of current are compared in thetable with their previous ratings assigned on a determin-istic basis. The exceedence to which the deterministicratings actually corresponded, which could not be iden-tified or acknowledged previously, are seen to vary fromapproximately zero to 6%, depending on the rating, sea-son, and the design temperature.

Adopting a consistent 10% exceedence throughout theyear led to increases in rating from 3% to 30%. Moreaccurate meteorological studies may allow a ratingincrease without increasing the exceedance. The methodalso allows greater consistency compared to the otherapproach, since the exceedence can be made constantfor all seasons.

Note that the ratings given in Table 2.5-4 are post-con-tingency values, which are used only in emergency con-ditions. The risk of flashover depends on the coincidentrisk of a maximum voltage surge occurring while worst-case cooling conditions exist in the span with the criticalclearance. This risk is many orders of magnitude lessthan the value of exceedence chosen. In addition to this,

the current is not at the maximum level all the time.These factors vary from area to area and line to line.

Instead of looking to the probability of an unsafe condi-tion arising that relates directly to safety, it has beenassumed that to exceed the design temperature is unsafe.No knowledge exists of exactly how unsafe it is. Thenext method, although more complex, goes some way tosolve this problem.

Modified Exceedence MethodThe Standard Exceedence Method assumes that the linecurrent is constant. For lines having a reasonably pre-dictable electrical load cycle, the load cycle shape can beused. The calculation is then referred to as the ModifiedExceedence Method.

Effect of the Load Profile on Thermal RatingThe effect of a load profile on thermal rating can bequite pronounced. This can be shown in the followingset of graphs (Figure 2.5-5) developed for conditionsprevailing in Cape Town (moderate climate with strongwinds).

This load profile was used to generate the exceedenceand modified exceedence curves. The conductor used inthis case was 196 kcmil (100 mm2), 6/1, “Hare”.

Figure 2.5-6 shows the increase in the ampacity of theconductor using the load profile and local weather data.

The graph shows that the ampacity can be increased, ifwe are using an exceedence level of 5%, for example,from 230 A to 340 A. The two graphs using the load

Table 2.5-4 Comparison of Deterministic and Probabilistic Ratings for 4% - A1/S1 - 54/7 “ZEBRA”

Design Temp

Exceedence% Summer Spring/Autumn Winter

Previous Deterministic

Rating (A)

ProbabilisticRating (A)

PreviousDeterministic

Rating (A)


PreviousDeterministic

Rating (A)


0.1 610 683 770 789 950 847

50 3 745 861 925

6 769 888 954

10 790 912 980

0.1 795 826 896 910 1019 959

65 3 901 994 1046

6 930 1025 1079

10 955 1053 1109

0.1 912 906 1000 981 1090 1025

75 3 989 1071 1118

6 1020 1105 1153

10 1048 1135 1185

2-59


profile for HARE and HARE 95 result from differentyear’s data being used. This shows that in this type ofevaluation it may not be necessary in Cape Town to usemany years’ data to determine ampacity as each year issufficiently variable.

2.5.4 Development of a “Measure of Safety” as a Basis for Line Rating

The above probabilistic methods—the absolute method,the standard exceedence method, and the modifiedexceedence method—do not make use of all the factorsthat affect the thermal rating of a line.

The factors that affect the safety are:

1. Whether or not a surge exists on the line.

2. The magnitude of the surge should one be present.

3. Whether or not an object is present under the line.

4. The size of the object should one be present.

5. The position of the conductor.

6. The probability of flashover as a function of spacingand shape.

Types of Accidents Occurring Relating to Transmission LinesBased on the research conducted to date in Eskom(South Africa), the area in which this probabilisticapproach to the determination of conductor ampacitywould be most beneficial is on lines above 132 kV. Theobjects that would result in an unsafe condition arisingin this case are mainly vehicles. It should be noted thatthese findings may vary from country to country, andsimilar research may be required.

Simulations of transmission-line flashovers indicate thatthe correlation between the various factors make thecalculation of probable safety difficult, if not impracti-cal. It is not merely a matter of multiplying the probabil-ities of each of the factors together, but to include thecorrelation functions, which are extremely difficult todetermine.

Figure 2.5-5 Load profile for exceedence rating example.

Figure 2.5-6 Results of exceedence rating probability example.

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Simulation using actual weather and data for each fac-tor that affects the safety of a line measured at the sametime eliminates the need for correlation evaluation.

Simulation of Unsafe ConditionsThe simulation combines different models to determinewhether a flashover occurs to a vehicle or how close thesituation was to a flashover. At Eskom this is done bymeans of four modules. Each of the modules simulatesthe behavior of the particular parameter. These modulesare:

• Surge Module. This module determines the month,day, hour, minute, and second in which a surgeoccurs. It then determines the magnitude of the surge.

• Object Module. This simulates the size and time that avehicle will be under the line. If the vehicle is underthe line at the same time as the simulated surge, thedata containing the surge time and magnitude, aswell as the vehicle data, is stored.

• Position Module. The position module determines theposition of the conductor at the time of the surge.

• Accident Module. Using the gap-surge relationship, itis possible to determine the surge required to create aflashover. This module determines the differencebetween the surge required to cause a flashover withthe actual simulated surge on the line.

Developing a Measure of SafetyParameters Independent of Current and Line DesignTemperature

The number of surges and vehicles in each categorywere analyzed based on the generation of 572 “counts,”or times at which the surge and the truck were simulta-neously under the line.

• Average counts per year 12.43

• Number of cars 26.4% of vehicles

• Number of small trucks 49.8%

• Number of large trucks 23.8%

• Surges of magnitude 1.6 30.6% of surges

• Surges of magnitude 1.7 40.6%




The probability of surges follows the expected distribu-tion, but the probability distribution for vehicles underthe line is affected by the time span that the differentvehicles remain under the line. Incorporating the surgesgenerated on the line into the measure of safety is diffi-cult. One method investigated was to subtract the surge

required to cause a flashover from the surge generatedat the time. The more positive the mean of the differ-ence, the safer the line. This measure is felt to be themost valid since it takes into account not only the surgesgenerated, but also the surges generated at the time thevehicle is under the line. The designer can readily deter-mine the probability of an accident occurring since theintegral (number of incidents) of the curve below zerowould represent the number of accidents expected. Thedistribution of the new safety measure as a function ofline design temperature is shown in Table 2.5-5.

It appears that the statistical description of the safetymeasure as listed above is a valid and reliable means ofdetermining the safety of a transmission line since themeasure is valid for any line design temperature andtakes into account every parameter dealt with in deter-mining the likelihood of an accident.

Uses of the Established Measure of SafetyA statistical “signature” can now be established describ-ing the safety of a particular line. This can be used asdescribed in the above example to increase current byline design temperature or by reducing surge magnitude.

Utilities are now able to quantify the safety of a trans-mission line. This will enable presentation of the ratio-nale behind any action taken. Uprating an existing lineor establishing a power transfer rating for a new line canbe justified in an objective rather than a subjective way.

The advantage of the above method is that the probabil-ity of an accident occurring can be determined. Thesafety of the line can be quantified and compared withother risks such as that of nuclear facilities. This willassist with objective discussions with regulators.

The model can be used to determine the reliability oflines by comparing statistical signatures of the differencebetween the surge present on the line and that requiredto cause a flashover with the insulator string swingingdue to wind. The wind data as well as the surge modulescan be used in this case. Lines in similar areas with dif-

Table 2.5-5 Probability Distributions versus Line Design Temperature

Line Design Temperature oC

40°C 50°C 60°C 80°C

MeanStd. Dev

Max.Min.

% below 0

1.580.841.95-1.9 4.3%

1.640.783.2

-0.37 4.0%

1.890.703.09

-0.19 0.8%

2.340.563.320.910%

2-61


ferent designs can be compared, and a measure of reli-ability relating to conductor swing can be developed.

2.5.5 Comparison of Probabilistic Rating Methods

Table 2.5-6 summarizes the main points of each proba-bilistic rating method.

2.5.6 Device for Mitigating Line Sag - SLiM

A new class of line hardware, SLiM (Sagging Line Miti-gator) (Figure 2.5-7), can help solve problems where theremay exist excessive line sag. SLiM reduces excessive sagin transmission lines and allows transmission owners torealize higher line ratings and increases transmission sys-tem performance, reliability, and asset utilization. The

passive design of SLiM and its ruggedness allow trans-mission owners to treat SLiM like typical transmissionline hardware such as insulator strings. Its installationprocedure is a relatively simple O&M activity.

SLiM reduces excess sag and allows transmission own-ers to realize higher line ratings, permitting them toincrease asset utilization and maintain safety and reli-ability in a very cost-effective manner. SLiM has multi-ple applications for both new and existing transmissionlines to address a host of challenges for transmissionowners. SLiM provides transmission planners, engi-neers, and asset managers another tool to help themmanage transmission systems in an increasingly chal-lenging environment.

The SLiM can serve as an economic alternative to con-ventional solutions, such as:

• Replacing the existing conductor with a premiumconductor that can operate at high temperatureswithout increased sag.

• Reinforcing line structures and foundations forincreased mechanical loading, and either reconduc-tor with a larger conductor or bundle with the exist-ing size conductor.

• Raising towers and improving foundations at key linelocations to provide for increased clearance.

• Adding intermediate towers at key line locations toincrease ground clearances.

Table 2.5-6 Comparison of Probabilistic Rating Methods

Absolute Method Std Exceedence Method Modified Exceedence Method Safety Method

Establishes the absolute proba-bility of an unsafe condition arising. Can be used to com-pare with other industries such as nuclear safety standards.

Uses relative comparison of risk. Cannot relate to an abso-lute probability.



Complex method that requires explicit equations for the proba-bilities of current, surges, etc.

Uses simulation. Little advanced probabilistic theory required.



Takes into account all factors that affect thermal rating of lines.

Takes only the weather data into account.

Uses weather data and load profile.

Takes into account all factors that affect thermal rating of lines.

Requires analysis of correlation between weather data and weather data and other factors such as surges and load.

Automatically takes care of weather data correlation by using actual wind speed, solar radiation, wind direction, and ambient

Uses simulation that automati-cally takes care of correlation if sets of weather data and load profile data are used.

Uses simulation taking care of correlation if sets of weather data are used.

Can be used on its own.

Can be used in isolation, but may encounter difficulties in determining the exceedence limit to use without reference to an absolute risk

Can be used in isolation, but may encounter difficulties in determining the exceedence limit to use without reference to an absolute risk

Can be used as a comparison between two lines, but needs to refer to the risk level found in the absolute method to deter-mine a reference level.

Analysis of data is required to determine the probabilistic func-tions.

Data can be used directly in the method without statistical analy-sis of the data itself.



Figure 2.5-7 The SLiM device.

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• Installing a sag monitoring system and the infrastruc-ture to process this information.

How SLiM WorksSLiM uses a shape-memory alloy actuator that is acti-vated by the same temperature changes that cause aconductor to change sag. The device is passive, with nomotors or electronic controls. As increasing temperatureincreases conductor length, and hence its sag, SLiMchanges its geometry to decrease line length. As conduc-tor temperature returns to normal, SLiM returns to itsoriginal shape, keeping the conductor always withinacceptable sag and tension limits (see Figures 2.5-8 and2.5-9).

Some Potential ApplicationsHere is a bulleted list of situations where a SLiM devicemay offer a viable solution:

• A system contingency situation can cause loading onparallel transmission lines to exceed their thermallimits. These limits are often established to maintainconductor line-to-ground clearances. Thus, theaction of SLiM, which mitigates the excess sagcaused by high-temperature operation, can allow forsafe line operation during these contingencies. Linecapacity is increased by allowing operation beyondconventional thermal limits, and expensive line modi-fication projects may not be required.

• Many older lines were constructed to 120°F maxi-mum conductor temperature operation. Studies haveshown that SLiM can enable operation of such linesat a conductor temperature of about 200°F withoutcompromise of line clearances or tensions. This canrepresent a substantial increase of rated line capacity.

• System planning may project that certain lines willbecome overloaded as local growth increasesdemand. In this instance SLiM can delay the need foreither a new line or considerable line modificationswhile the anticipated load materializes. Installation ofSLiM is a simple O&M activity and can help bridgeneeds.

• Line routing or line modifications near airports orother unique situations quite often require structures

to be as low-profile as possible. SLiM can beemployed in a cost-effective fashion to minimizetower height for such installations while maintainingrequired ground clearances and higher power flows.

• Limitations on line ratings to maintain clearancesover road or river crossings can be lifted by usingSLiM while maintaining ground clearances andhigher power flows.

• SLiM can be used on new line construction and allowfor use of lower towers, mitigating visual impacts andcommunity objections.

SLiM Specifications

Electrical ConnectionThe SLiM device carries the full line current, splittingthe current between the actuator and the body of thedevice. Standard flexible connectors carry currentbetween the transmission line and the SLiM device. Theelectrical connectors on the device terminate with 4-boltNEMA paddles for easy connection to standard linehardware.

Mechanical ConnectionThe device is installed in series with the transmissionline. Either end of the device is equipped with standardoval-eye end fittings. The mating attachment on the con-ductor is the choice of the utility. The device accepts anyindustry standard dead-end attachment with a 1 in.(2.54 cm) clevis pin. Options include dead-end compres-sion fittings, preformed dead ends, and wedge dead ends.

InstallationThe device can be installed at a dead end, or anywherealong a span using procedures similar to line-splicingtechniques. During installation, a piece of conductorapproximately the length of the SLiM device is removedand replaced by the device. The length of conductor to beremoved as well as the number and locations of devicesalong a section of transmission line can be determinedusing line-sagging software for optimum performance.

Figure 2.5-8 SLiM is strong, maintenance-free, and designed to have a very long life. It is designed for easy installation using hot or cold procedures. Industry standard connectors can be used to attach SLiM to the line. Its operation is configurable to match specific line requirements, and has no negative effects on line electrical performance.

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Operating ParametersTables 2.5-7 and 2.5-8 list some of SLiM’s basic parame-ters and operating characteristics. The standard unit istargeted primarily to 115- and 230-kV lines, but canoperate in 60- and 70-kV class, as well as 345-kV classlines. Standard units can also be configured to actuate atdifferent temperature points based on individualrequirements.

Development and Testing of SLiMSLiM has been through several years of extensive R&Dand testing including laboratory functionality and reli-ability testing as well as actual field demonstration.

Functionality testing was performed at PG&E’s trainingfacility in Livermore, California. The sag differentialbetween the test and control spans at the maximum tem-perature of 100°C was 44 in. (Figure 2.5-10), whichclosely matched the predicted effect of SLiM. Prior toand following the full functionality testing at PG&E,SLiM and its components were extensively tested forload and current-carrying capacity, fatigue, corrosion,and repeatability of performance.

SLiM was also tested at Kinectrics and was subjected toa number of fault current events ranging from 21 kA to40 kA (rms) for a minimum of 10 cycles. After currenttesting, SLiM was subjected to increasing load until itsbreak links failed, as designed, at about 49 Kips, exceed-ing the target range (110% of the conductor breakingload).

The SLiM device was installed on the bottom phase of a69-kV transmission line, in SDG&E’s service area inEscondido, California (Figure 2.5-11), and monitoringequipment was installed directly below the test span on a12-kV distribution pole. The field demonstration wasintended to prove both ease of installation and function-ality and reliability. SDG&E crews called the installation“straightforward.” SLiM has successfully completedover a year of field demonstrations.

Figure 2.5-9 The major components of the SLiM device in its “Dead-End Configuration” and its “In-Line Configuration.”

Table 2.5-7 Operating Parameters for Standarda SLiM

a. Custom sizes for special applications available.

Criteria Application

Voltage Rating 230 kV and below. Higher voltages (345 and 400 kV) possible.

Target Conductor Conductors with a breaking load 40,000 lb (180 kN)

Range of Motion Up to 8 in. (200 mm)

Line Tension @ 110°F Up to 5,000 lbs (22.5 kN)

Functional Temperatures

~120–212°F (50-100°C) (conductor temperature)

Mechanical Failure Load

> 49,000 lbs (218 kN) – Tested per IEC at Kinectrics

Electrical Current Capacity > 1400 A

Short Current Rating 40 kA (rms)– Tested per IEC at Kinectrics

Total Weight ~ 85 lbs (380 N) (Production Version)

End-to-end Dimension

~ 5 ft, 3½ in. (1610 mm) open, 4 ft, 7½ in. (1410 mm) closed

End Connectors Any standard connector with 1 in. clevis pin (utility’s choice)

Installation

“Cold” using standard procedures – or – “Live” using live-line hand procedure (similar to splicing procedure). Detail pro-cedure available upon request.

Table 2.5-8 Example Sag Mitigation for a Drake Conductor

Spanft / m

Conductor Temperaturea

a. Tension at 40°F considered equal to 20% of tensile strength of conductor.

Excess Sag due to Heating Sag

InitialºF / ºC

FinalºF / ºC

Without SLiMft / cm

With SLiMft / cm

Reductionft / cm

750 / 230 110 / 43 212 / 100 5.2 / 158 0.2 / 6 5.0 / 152

1000/300 110 / 43 212 / 100 6.0 / 183 1.9 / 58 4.1 / 125

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2.6 RECONDUCTORING WITHOUT STRUCTURAL MODIFICATIONS

2.6.1 Introduction

By replacing the original line conductors, it is possibleto employ modern conductors having lower resistancefor the same diameter and/or having the same maximumsag as the original conductor but at greatly increasedtemperature. The use of certain new conductors canyield an increase in thermal capacity of as much as100% at a cost of less than half that of a new line. Thissection concerns the application of commercially avail-able conductors, but the analysis methods are applicableto new conductor types.

Existing lines may be uprated using methods discussedin preceding sections of this chapter, all of which involveusing the original conductor. In certain applications, itmay make sense to replace the original conductor with anew one, usually having a diameter near the original andoften capable of operation at higher temperatures. Thissection reviews the various reconductoring choices, andprovides some insight into those line uprating applica-tions where reconductoring is preferred.

Given the low cost, high conductivity, and low densityof aluminum, no other high conductivity material ispresently used. Therefore, any “low-resistance” replace-ment conductor must have increased cross-sectional alu-minum area, and increased wind/ice and tension loadson the existing structures.

Figure 2.6-1 shows how the thermal rating of an existingline may be increased by about 50% by using a replace-

Figure 2.5-10 The sag differential being measured on a control span (bottom) and a test span (top).

Figure 2.5-11 Field demonstration of the SLiM device at SDG&E.

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ment conductor with twice the original conductor’s alu-minum area. Note that this doubles the original strainstructure tension loads and increases transversewind/ice conductor loads on suspension structures byabout 40%. Such large load increases would typicallyrequire structure reinforcement or replacement.

“High-Temperature, Low-Sag” (HTLS) conductors,capable of continuous operation at temperatures above100oC with stable tensile strength and creep elongationproperties, are commercially available or under develop-ment. Practical temperature limits of up to 200oC havebeen specified for some conductors. As is also shown inFigure 2.6-1, use of an HTLS conductor (having thesame diameter as the original) at 180oC also increasesthe line rating by 50%, but without any significantchange in structure loads. Raising the structures mayalso be avoided if the replacement conductor has alower thermal elongation rate than the original.

EPRI is presently engaged in a project to field-test longsamples (several spans) of HTLS conductors in operat-ing lines. This project is in its early stages at the printingof this guidebook, but some preliminary observationsare discussed in the following sections. Future versionsof this guidebook will be updated with the latest pub-lishable results.

The use of a lower-resistance conductor has two advan-tages—losses are reduced, and operating temperaturesremain modest. The use of HTLS conductor has the pri-mary advantage that structure modifications are mini-mized. In either case, the replacement of existingconductor should improve the mechanical reliability ofthe line since conductor, connectors, and hardware areall new.

Sag Constraints for ReconductoringAs shown in Figure 2.6-2, the original conductor’s “Ini-tial installed sag” increases to a final “everyday” sagcondition (typically at 60×F [16×C] with no ice andwind) as a result of both occasional wind/ice loadingevents and the “normal” creep elongation of tensionedaluminum strands over time. This everyday final sagincreases further (but reversibly) due to ice/wind loadingor high electrical loads. For most transmission lines, asshown, maximum final sag occurs as a result of electri-cal rather than mechanical loads.

Any replacement conductor must be installed such that,over time, its final sag under maximum electrical ormechanical load does not exceed the original conduc-tor’s maximum final sag. Otherwise, existing structureswill have to be raised or new structures added. HTLSreplacement conductors are usually applied to existinglines where structure reinforcement or replacement is tobe avoided.

2.6.2 TW Aluminum Wires – ACSR/TW or AAC/TW

While this conductor is limited to operation at moderatetemperatures, the use of compact trapezoidal strandsresults in a resistance reduction of about 20% for thesame diameter as the original conductor. The use of alu-minum trapezoidal wire (TW) wires in place of roundwires potentially increases the cross sectional area of around wire conductor of the same diameter by approxi-mately 20%. Therefore, the use of TW conductor inuprating offers a reduction in conductor resistance of20% with no increase in structure transverse loading. Ifsome increase in conductor diameter over the original ispossible with limited structural reinforcement, the resis-

Figure 2.6-1 Thermal rating as a function of conductor area and maximum temperature.

Figure 2.6-2 Typical transmission line sag as a function of time, load, and temperature.

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tance reduction can be in excess of 20%, and theincrease rating can be 20% or more.

For example, consider an existing line with a 477 kcmil(243 mm2), 26/7 Aluminum Conductor Steel-Reinforced(ACSR) (Hawk) conductor operated to a line designtemperature of 90oC. Given reasonably conservative rat-ing weather conditions, the rating of the line is 650 A.

If this original conductor is replaced by a Calumet/TWconductor (which has the same diameter) and operatedto the same maximum temperature of 90oC, it wouldhave approximately the same sag at 90oC, but its lowerresistance would result in a rating that is on the order of710 A (9% higher). The maximum tension on strainstructures and for broken wire calculations would beabout 10% higher.

To get a larger increase in thermal capacity, a larger-diameter replacement conductor could be used, but thiswould require the existing structures to handle increasedice and wind transverse loads as well as even higher ten-sion loads than Calumet/TW. Other advantages to thisreplacement conductor include reduced electrical lossesover the life of the line, and since the conductor andconnectors are new, one might argue that the reconduc-tored line is capable of safe operation at temperaturesabove 90oC and that installed tensions could beincreased if dampers are used.

In summary, reconductoring with ACSR/TW requiresthat structures, , especially strain structures, be rein-forced. The probable increase in line rating will be mod-est, but the electrical losses over the life of the line willbe less. These conductors are intended to be operated atusual temperatures, and are not part of the EPRI HTLSproject.

2.6.3 ACSS and ACSS/TW

Many millions pounds of Aluminum Conductor SteelSupported (ACSS) have been installed and are operat-ing successfully in the United States. However, for manyit is still considered a relatively new conductor, and itsperformance is not well understood. As such, it is anintegral part of EPRI’s HTLS conductor field testproject. Most of the initial concerns about installationand surface roughness problems due to the use ofannealed aluminum strands have passed. The main limi-tation with ACSS is its relatively low strength and mod-ulus that may limit its application in regionsexperiencing high ice loads. The use of ACSS/TW canoffset this problem to some extent, as can the use ofextra-high-strength steel core wires. The conductor andspecial connectors designed for it allow continuous

operation at temperatures up to 200oC with conven-tional galvanized steel core wires. The conductor can beoperated above 200oC if Alumoweld or special zinc“Galfan” coated steel is used.

ACSS is described in ASTM B 856-95. It consists offully annealed strands of aluminum (1350-H0) strandedaround stranded steel core. The steel core wires may bealuminized, galvanized, or aluminum clad, and are nor-mally “high strength,” having a tensile strength about10% greater than standard steel core wire. In appear-ance, ACSS conductors are essentially identical to stan-dard ACSR conductors (see Table 2.6-1).

By using annealed aluminum, the rated strength ofACSS is reduced by an amount dependent on the strand-ing (e.g., 35% for 45/7, 18% for 26/7, and 10% for 30/7).In fact, a 45/7 ACSS conductor has about the same ratedbreaking strength as a conventional all-aluminum con-ductor (e.g., 16,700 lbs (71.4 kN) for 954 kcmil (487mm2) 45/7 ACSS versus 16,400 lbs (73.2 kN) for 954kcmil (487 mm2) 37 strand AAC [Magnolia]). The ther-mal elongation coefficient, creep rate, and maximumoperating temperature are, however, quite different.

ACSS Conductor DesignsACSS is typically available in three different designs:“Standard Round Strand ACSS,” “Trapezoidal Wire ofEqual Area,” and “Trapezoidal Wire of Equal Diame-ter.” In addition, it is possible to obtain all three ACSSconductor designs with any of the standard types of steelcore wire (galvanized, aluminized, and Alumoweld).

Advantages and Disadvantages of ACSSACSS provides a number of advantages in reconductor-ing. The combined effect of these factors can make iteconomically attractive in thermal uprating applica-tions. It has higher self-damping than conventionalACSR. It has lower thermal elongation over a widerange of conductor temperatures. It can be operated attemperatures as high as 250 °C without damage. It canbe installed at smaller initial sags without dampers if itis prestressed. With reference to the preceding discus-

Table 2.6-1 ACSS Equivalents to Standard Type 16, 795 kcmil, 26/7 ACSR (Drake)

Conductor Name OD

Alum Area AC Resistance

(in.) (mm) (kcmil) (Ω/mile) (Ω/km) (Δ%)

Drake ACSR 1.108 28.14 795 0.1170 0.0727 æ

Drake/ACSS 1.108 28.14 795 0.1137 0.0707 -3%

Suwannee/ACSS/TW 1.108 28.14 960 0.0939 0.0584 -17%

Drake/ACSS/TW 1.010 25.65 795 0.1132 0.0704 -3%

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sion of sag clearance, the conductor properties make itattractive for reconductoring applications as well as cer-tain new line designs.

In reconductoring existing lines, in comparison to con-ventional ACSR conductors, ACSS can yield a muchlarger increase in thermal capacity while minimizing theneed for expensive structure modifications. In new lines,this conductor can yield designs with less environmentalimpact (shorter and/or fewer structures) with greatlyincreased thermal capacity for essentially no increase incost. As discussed in the following, the key advantagesof ACSS are:

• Operate to 250 °C with no loss in strength

• No creep elongation over time

• High self-damping (which yields low levels of Aeo-lian vibration)

• Lower thermal elongation than conventional conduc-tor

• 63% IACS conductivity, not 61.2%

• Equal OD and equal AREA options.

Higher Maximum TemperatureTypically aluminum stranded conductors can be oper-ated at temperatures up to 95°C without significant lossof tensile strength. Aluminum conductors with a steel-reinforcing core can be operated at temperatures of upto 150° C for limited periods. Because the aluminum inACSS is fully annealed at the factory, it can be operatedcontinuously at temperatures up to 250°C or, with spe-cial high-temperature-tolerant galvanizing coatingssuch as “Galfan,” even higher.

Table 2.6-2 shows a comparison of continuous ampacity(with 2 ft/sec (0.61 m/sec) crosswind, 40 °C air tempera-ture, and full sun) for ACSS and ACSR conductors.Note that the ampacity of an ACSS conductor operat-

ing at 250°C is nearly twice that of an ACSR of the samecross-sectional area operating at 100°C.

Thermal ElongationAluminum strands elongate thermally at twice the rateof steel. The sag increase of ACSR conductor is, there-fore, less than it is for AAC. In the case of ACSS, thetension level in the aluminum strands is very small, andthe conductor elongates thermally as though it weresteel. Thus, the sag increase in going from 15°C to150°C with ACSS may be the same as the sag increasefrom 15°C to 95°C with ordinary ACSR.

As an example of this lower thermal elongation ofACSS, consider the data in Table 2.6-3. The ACSS con-ductor has the same sag at 150°C as the ACSR conduc-tor of the same diameter has at 100°C. Therefore, for aclearance-limited line, by reconductoring with ACSS,the thermal capacity of the line increases by about 30%without the need to raise or reinforce structures.

Self-DampingThe tension of conductors in overhead lines is normallydetermined by concern about Aeolian vibration-induced fatigue. It is normal to limit initial tension to nomore than 20% of the rated breaking strength in orderto limit vibration levels. Because it has higher self-damping than ordinary ACSR, ACSS may be installedto smaller initial sags, and because it has a lower modu-lus, it yields lower maximum tensions than ACSR.

Low Creep ElongationWhen reconductoring, one must allow for creep elonga-tion over time with ordinary ACSR. In addition, exceptfor ACSR conductors with a high steel content, onemust consider the possibility of accelerated creep at highoperating temperatures. ACSS does not creep at anytemperature, high or low. Thus, its final and initial sagsare the same as shown in Figure 2.6-3.

Not only is there little or no difference between the ini-tial and final sag, but also the initial sag is less, and thechange in sag due to temperature is less than it is forstandard ACSR.

Table 2.6-2 Continuous Ampacity of Equivalent ACSR and ACSS Conductors as a Function of Maximum Allowable Conductor Temperature

Conductor Temperature

(oC) Drake ACSRaSuwannee ACSS/TW

Drake/ACSS or

Drake/ACSS/TW

75 730 820 720

100 990 1110 980

150 -- 1490 1320

200 -- 1770 1560

250 -- 2000 1740

a. For continuous loads, ACSR is normally limited to about 100oC to avoid annealing of the aluminum strands.

Table 2.6-3 Illustration of the Lower Thermal Elongation of ACSS Conductor

Conductor Temp

Sag of Drake ACSR

Sag of Drake/ACSS Ampacity

(oC) (ft) (m) (ft) (m) (A)

15 31.0 9.4 31.0 9.4 --

100 37.6 11.5 35.3 10.8 1110

150 -- -- 37.8 11.5 1490

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The novel characteristics of ACSS make it attractive asa replacement conductor for HV lines where thermalcapacity is inadequate. ACSS can be substituted forexisting ACSR of the same diameter. Although havingnearly the same resistance and diameter as the conduc-tor it replaces, ACSS can be operated at a much highertemperature without exceeding the original high-tem-perature sag levels. Since the aluminum strands of ACSSare fully annealed, it has a somewhat lower ratedstrength than the same stranding in ACSR. In areaswhere ice and wind loads permit, ACSS may be speci-fied with a reduced steel content. The result is that, withACSS, the maximum tension loads on angle and dead-end structures may be no higher than those generated bythe ACSR conductor that it replaces.

As an example of the advantages of ACSS in reconduc-toring, consider Figure 2.6-4, which shows ampacityand sag as a function of maximum allowable tempera-

ture. The original conductor in the existing line isassumed to be 477 kcmil (243 mm2) ACSR (Hawk). Theproposed replacement conductors are 565.3 kcmil (288mm2) ACSS/TW (Calumet), which has the same diame-ter as the original and 795 kcmil (405 mm2) ACSR(Drake), which has a diameter that is 30% higher. Forcontinuous operation, the 565.3 kcmil (288 mm2)ACSS/TW (Calumet) conductor at 200°C has anampacity about 25% higher than Drake at 100°C andlower maximum sag than the original or replacementACSR conductors.

ACSS/TW: Field Trial in the EPRI HTLS Conductor ProjectAs part of the EPRI HTLS conductor project, anACSS/TW conductor was spliced into a line segment ofan operating 138-kV transmission line. This test seg-ment consists of four spans, and is approximately 2880ft in length, and includes five structures (two dead-endand three suspension towers). The test conductor wasspliced into all three phases of one circuit of a double-circuit vertical line. Various field data associated withconductor performance are intended to be collectedover an extended period of time (about three years).

The conductor is classified as “Trapezoidal Shaped WireConcentric-Lay Aluminum Conductor Steel Supported”(ACSS/TW). It is designated by the name “Suwannee,”and is 1.108 in. (2.814 cm) in diameter. Figure 2.6-5shows photos of the conductor—the outside aluminumstrands and steel center strands are indicated.

Figure 2.6-3 Typical behavior of ACSS conductor, illustrating that initial and final sags are nearly identical.

Figure 2.6-4 Ampacity and sag of original Drake ACSR and Calumet ACSS/TW replacement conductor as a function of maximum allowable temperature. Figure 2.6-5 ACSS/TW cable, manufactured by

SouthWire, installed on operating test line.

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During the course of the project (ongoing for just overtwo years at this time), measurements and observationswere made of the following quantities:

• Sag and Tension

• Weather Parameters

• Average Conductor Temperature

• Current

• Splice Resistances

• Hardware Temperatures via Infrared Measurements

• Corona

• Electric and Magnetic Fields

• Visual Inspections

This project is still ongoing, and final results are not yetavailable

2.6.4 High-Temperature Aluminum Alloy Conductors

T-Aluminum Conductor Steel Reinforced (TACSR) is aconductor widely used in Japan. A special type of steelcore (“Invar”) adds expense but reduces thermal elonga-tion. There is extensive laboratory test data on the Zir-conium aluminum alloy wire materials (TAL andZTAL). There appear to be no special problems withinstallation and termination of (Z)TACSR. TAC can beoperated continuously up to 150oC and ZTAC to 210oCwithout loss of strength.

The various Japanese manufacturers (e.g., FujikuraLtd., Sumitomo Electric Industries, Ltd.) have devel-oped a whole range of special high-temperature conduc-tors. These conductors consist of special temperature-tolerant aluminum alloy wires combined with ordinarysteel or a special low-thermal-elongation steel wirecalled “Invar.” The acronyms for these conductors indi-cate the type of aluminum alloy (TAC, GTA, UTA,XTA, and ZTA); the type of steel core wire (SR or IR);and whether the aluminum strands are trapezoidal; andwhether there is a gap between the inner layer of alumi-num and the steel core (e.g., GACSR or GTACIR).

A partial list of the most common types includes the fol-l owin g n a m e s : TAC S R , G TAC S R , U TAC S R ,GTACSR, UTACIR, XTACSR, XTACIR, ZTACSR,and ZTACIR. The acronyms refer to the type of high-temperature alloy, whether the conductor is “gapped,”and the type of steel core material.

As a simple comparison, consider Table 2.6-4, a sum-mary of the maximum operating temperatures of thevarious Japanese heat-resistant conductors.

High-Temperature Alloys of AluminumTable 2.6-5 is a description of the heat-resistant alloys ofaluminum.

The TAL alloy was developed in the 1960s. The otheralloys were developed in a continuing attempt to keepthe conductivity near that of ordinary electrical conduc-tor grade aluminum (1350-H19). The relationshipbetween conductivity and maximum continuous tem-perature is shown in Figure 2.6-6.

2.6.5 Special Invar Steel Core

ACSR conductors are manufactured with a variety ofsteel wire coatings to prevent corrosion. Normal steelcore wire has a tensile strength of 170 to 190 psi (1170 to1310 Mpa). Invar steel wires have a 15-20% lower tensilestrength but also have a much lower coefficient of ther-mal expansion than conventional galvanized steel wire.The thermal expansion coefficient of conventional steelis 11.5 × 10-6 per-degree-C, whereas the thermal coeffi-cient of Invar steel is only 2.8 × 10-6 per-degree-C.

At high operating temperatures, the aluminum strandsof any high-temperature conductor unload tensionalmost entirely to the steel core. With Invar, this hap-pens at a lower (“knee point”) temperature. In addition,

Table 2.6-4 Maximum Operating Temperatures (°C) for High-Temperature Alloys Made in Japan

Description SymbolMax Temp

ContinuousMax Temp Emergency

Super Heat Resistant UTACSR 200 230

Super Heat Resistant ZTACSR 210 240

Super Heat Resistant XTACSR 230 310

Heat Resistant TACSR 150 180

Normal ACSR 95 125

Table 2.6-5 Conductivity of High-Temperature Alloys Made in Japan

Aluminum Alloy % Conductivity

Max Temp Continuous

Min. Tensile Strength

(IACS) (°C) (kgf/mm2)

UTAL 57.0 200 16.2 to 17.9

ZTAL 60.0 210 16.2 to 17.9

XTAL 58.0 230 16.2 to 17.9

TAL 60.0 150 16.2 to 17.9

1350-H19 61.0 95 16.2 to 17.9

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the rate of increase in sag with further increases in con-ductor temperature is less with Invar steel cores. This isdemonstrated in Figure 2.6-7.

The EPRI HTLS project has begun the field testing of anInvar “Drake” conductor spliced into a five-span sectionof a 230-kV line. The installation process went well, but it

is too early in the project to make any further meaningfulconclusions at this time. The data shown in Table 2.6-6show the physical properties of this conductor.

2.6.6 Gapped Construction

Gapped ACSR has been used both in Japan andEngland. The conventional steel core is surrounded by alayer of trapezoidal aluminum wires, and the gap filledwith grease. Through the use of special terminationsand suspension clamps and by preloading the steel core,the thermal elongation of the conductor is less than thatof conventional ACSR, while maintaining the fullstrength of a conventional ACSR conductor underheavy ice conditions.

The lower temperature range aluminum alloys areoptionally supplied in a “gapped” construction, asshown in Figure 2.6-8—a picture taken from a Sumit-omo Technical Data Sheet.

In the gapped construction, the space between the steelcore and the inner layer of the aluminum alloy strands isfilled with high-temperature grease to prevent corrosion.In addition, the gapped construction conductors areinstalled with full tension on the steel core (and little orno load on the aluminum strands).

It was noted in the preceding comparison of Invar withconventional steel wire that Invar has a reduced tensilestrength. While it is conceivable that a gapped construc-tion conductor could be made with an Invar steel corefor use in a light-loading region such as Arizona, it isnot commonly done in Japan, where heavy ice and windloads commonly occur. Thus, as shown in Figure 2.6-8,

Figure 2.6-6 Plots of conductivity (top) and loss of strength (bottom) for high-temperature Japanese aluminum alloys.

Figure 2.6-7 Comparison of ACSR-type conductors with Invar and conventional steel cores.

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Table 2.6-6 Physical Properties of a Drake Invar Conductor

Item Unit Specifications

Cable designation -- Hi-STACIR/AW 795kcmil (Drake)

Stranding wire compositionSuper thermal-resistant aluminum-alloy wireHigh tensile strength aluminum-clad invar wire

Nos./mmNos./mm

26/4.447/3.45

Minimum rated tensile strength kgf 13,630

Calculated cross-section areaa

Super thermal-resistant aluminum-alloy wireHigh tensile strength aluminum-clad invar wireComplete conductor

a. Tabulated values are for reference calculated on standard diameter and density.

mm2

mm2

mm2

402.5665.44468.0

Calculated overall diametera

High tensile strength aluminum-clad invar wireComplete conductor

mmmm

10.3528.11

Calculated nominal weighta kg/km 1,582

Calculated D.C. resistance at 20°Ca ohms/km 0.0706

Typical modulus of elasticitya

Up to transition point temperatureAbove transition point temperature

kgf/mm2

kgf/mm27,590

15,500

Typical coefficient of linear expansiona

Up to transition point temperatureFrom transition point temperature to 230°CFrom 230°C to 290°C

1/°C1/°C1/°C

17.5 x 10-6

3.7 x 10-6

10.8 x 10-6

Maximumoperating temperature

Continuous °C 210

for emergency °C 240

Calculated current carrying capacityb

b. Current carrying capacity is calculated on the following conditions:Ambient air temperature (°C) 40Maximum temperature (°C) 210Frequency (Hz) 60Wind velocity (m/s) 0.61Total solar and sky radiated heat flux at sea level (W/cm) 0.10Emissivity 0.50Solar absorptivity 0.50

Continuous A 1,628

for emergency A 1,752

The direction of lay of the outer most layer -- Left-hand (S)

Standard length per reel m 200 -0%/+1.0%

Figure 2.6-8 Summary table showing gapped and conventional constructions for Japanese high-temperature conductors.

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Gapped conductors are designed with conventionalhigh-strength steel core wires.

Gapped Conductor: Field Trial in the EPRI HTLS Conductor ProjectThe EPRI HTLS project has begun the field testing of aGap conductor spliced into a four-span section of a 230-kV line. The installation process went well, but it is tooearly in the project to make any further meaningful con-clusions at this time. The data shown in Table 2.6-7show the physical properties of this conductor.

In addition to a field trial on an operating transmissionline, the EPRI HTLS project included a demonstrationand training session on the installation of a Gap con-ductor on a full-scale test line at the EPRI Engineeringand Test Center in Lenox, Massachusetts. The installa-tion of a Gap conductor is somewhat unique, particu-larly in the need to strip back a sizeable amount of thealuminum outer strands in order to expose and splicethe steel core separately from the aluminum layers in a“two-step” splice arrangement.

There are presently no other installations of this con-ductor in North America; however, there are manyapplications in other countries (e.g., Japan, UK, SaudiArabia). Figure 2.6-9 shows a photo of a lineman from aNorth American utility being trained by a specialistfrom Japan on the splicing technique. The participants

Table 2.6-7 Physical Properties of a Drake Invar Conductor

Item Unit Proposal

Construction Nos./mm

16/4/4-ZTAI10/TWa-ZTAI

7/3.2-Est

a. TW Trapezoid wire

Direction of outer lay -- Z-Strand

Minimum breaking strength kN 149.2

Lay ratio (length/diameter)

Aluminum layer Outer layerInner layer times

10-148-16

Steel core 16-26

Maximum D.C. resistance at 20°C σ/km 0.0714

Calculated cross-sec-tional area

Super thermal resistant aluminum alloy

mm2

413.2

Steel 56.29

Total 469.5

Outer diameter mm 27.8

Weight kg/km 1614

Modulus of Elasticity Conductor Steel Core GPa 79.1

205.9

Coefficient of linear expansion

ConductorSteel Core x 10-6/°C

19.411.5

Cross sectional view

Figure 2.6-9 A lineman being trained on the installation of a Gap conductor.

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of the training session generally believed that, althoughthe installation and splicing technique is different thanwhat they are accustomed to, it was easy to learn andvery “do-able.” However, it is recommended that priorto an installation, linemen unfamiliar with the methodsshould be provided training on the techniques involved.

2.6.7 ACCR Conductor

The Aluminum Conductor Composite Reinforced(ACCR) is commercially available in limited quantitiesfrom the 3M Company. Reasonably extensive tests havebeen performed on several sizes of this conductor underlaboratory conditions, and terminations and suspensionclamps are available from Preformed Line Products.Xcel Energy, Hawaiian Electric Company, and WesternArea Power Administration have successfully completedtest installations. The installation of this conductorappears to be fairly straightforward, but may requirespecial large blocks and careful handling.

The key advantage of ACCR is that the composite corestrands have a conductivity of about 40% InternationalAnnealed Copper Standard (IACS) and have the modu-lus and tensile strength of steel but are approximatelythe same density as aluminum.

The ACCR conductor is about to be field tested in theEPRI HTLS conductor project. Future updates to thisguidebook will provide more details as they becomeavailable.

2.6.8 Conductors with Exotic Cores

There are other less well-known conductors that areeither still in the development stage, or in early trialscompared to the other HTLS conductors. One is a fiber-glass core conductor that was a popular topic of discus-sion in the power industry’s research community, butinterest seems to have dwindled recently. Another has acarbon fiber core with a slightly negative coefficient ofthermal expansion. Development of this conductor wassupported by the National Science Foundation, and apatent has been issued. However, no significant labora-tory or field tests have been reported thus far.

Another conductor that involves a carbon and polymerfiber core, referred to as ACCC (aluminum conductorcomposite core), has received some press coveragerecently. Very little laboratory test data have been pub-lished, and there is not much expertise in the industryon it. Apparently, there are other business-related issuesabout the ability to procure it at this time.

The EPRI HTLS project has begun field testing a sam-ple of the ACCC conductor in four spans of a 69-kV

line. The installation process went well, but it is tooearly in the project to make any further meaningful con-clusions at this time. Figure 2.6-10 shows a photo of theconductor’s cross section. The core has the look and feelof a rod that is somewhat rigid, but with some flexibility.This conductor requires some special hardware andinstallation techniques, and linemen would require somedegree of training prior to installation. Also, as with anycore that has a polymer component, there is some con-cern about long-term performance.

2.6.9 Comparing ACSS and High-Temperature Alloy Conductors

The major advantage of using ACSS is its cost (typicallysold at a premium of less than 50%) and its wide avail-ability outside of Japan. Also, ACSS has been usedextensively, and most of the handling and installationdifficulties are well understood.

The major advantage of the High-Temperature Alloyconductors is that they can be used in regions experienc-ing heavy ice and wind loads (ACSS may not), and theyare applicable to EHV lines, where surface roughness ofACSS may yield higher corona noise and radio noiselevels. The cost of these conductors, however, appears tobe relatively high (probably a premium in excess of100% over conventional ACSR). The availability ofthese high-temperature alloy conductors outside ofJapan is uncertain at this point, and shipping costswould simply worsen the cost issue.

The selection process for HTLS replacement conductoris unique to each line uprating, but the most importantaspect is sag as a function of temperature. Consider anexisting line with 795 kcmil (405 mm2) 26/7 DrakeACSR installed in a 1000 ft (305 m) ruling span to aninitial unloaded tension equal to 20% of its rated break-ing strength at 60°F. The everyday initial sag of 21.8 ft

Figure 2.6-10 Cross section of an ACCC conductor.

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(6.6 m) increases to 25.7 ft (7.8 m) over the life of theline. The initial conductor tension is 15,300 lbs(68.3 kN) under maximum ice and wind load.

At the original maximum conductor temperature of100°C (212°F), the ruling span sag is 31.7 ft (9.7 m). Toavoid raising the existing structures, any HTLS replace-ment conductor will also be limited to a sag of 31.7 ft(9.7 m) at its maximum temperature.

The thermal rating of DRAKE at 100°C is 990 A for2 ft/sec (0.61 m/sec) crosswind, 40°C air temperature,and solar heating for summer at noon. The sag behaviorof HTLS replacement conductors (ACSS, ACSS/TW,ACCR(3M), GTACSR, and TACIR) are compared inFigure 2.6-11, where each of the HTLS alternatives hasthe same diameter as Drake and the same finalunloaded sag at 60°F as the original conductor.

From this figure, one can see that the ACCR conductor,with its very low thermal elongation, attains the highestoperating temperature of 370°F (190°C). Given the rela-tively high conductivity of its composite core, the ther-mal rating is 1550 A.

ACSS/TW reaches the maximum sag (31.7 ft (9.7 m)) at120°C, given the thermal elongation of its steel core,which yields a thermal rating of 1270 A with its some-what higher aluminum cross-sectional area.

T-Aluminum Conductor Invar Reinforced (TACIR)reaches the maximum sag at 270°F (132°C) for a ther-mal rating of 1220 A.

Gapped T-Aluminum Conductor Steel Reinforced(GTACSR) reaches the sag limit at 124°C for a thermalrating of 1170 A.

For all of these replacement conductors, the conductortemperature at the maximum sag of 31.6 ft (9.6 m) iswell below their continuous operating temperature limit.The thermal rating comparison could be quite differentif the line were not clearance limited or limited to ahigher sag. Similarly, the results could be quite differentif the final everyday sags of the HTLS conductors weredifferent due to differences in vibration damping orstructure tension load limits.

2.7 DYNAMIC MONITORING AND LINE RATING

2.7.1 Introduction

If dynamic rating methods are applied to increase theeffective rating of an overhead line, real-time weatherdata and, optionally, line temperature or sag-tensiondata must be communicated from multiple remote loca-tions to the operations center where the line rating cal-culations are performed. In all such cases, the line ratingis no longer constant but varies with weather conditions.

This technology has been implemented at a number ofEPRI member utilities and is worth considering in caseswhere there is a need for a modest increase in rating atminimum capital investment. The technology requiresoperational flexibility and available SCADA/EMS com-munications.

2.7.2 Dynamic Ratings Versus Static Ratings

The calculation of thermal ratings for overhead lines istypically based upon heat balance methods such as thatfound in IEEE 738-1993 (see Section 2.3). For static rat-ings, given a maximum allowable conductor tempera-ture, the corresponding maximum allowable current (thethermal rating) is determined for “worst-case” weatherconditions.

As discussed in Section 2.2, for most existing transmis-sion lines, the maximum allowable conductor tempera-tures typically range from 50°C to 150°C. In most cases,the maximum temperature is limited in order to avoidexcessive conductor sag (referred to as a “clearance lim-ited” line), or, in some cases, a loss in conductorstrength (referred to as a “thermally limited” line).

Also, as discussed in Section 2.5, most power utilities(both domestic and foreign) assume “worst-case”weather conditions that are not really worst, but ratherconservative. Worst-case line rating conditions would bethe peak 1-hour air temperature and still air with fullsolar heating. Conservative line rating conditionsassume a wind speed of 2 to 3 ft/sec (0.6 to 1 m/sec) per-pendicular to the conductor with full solar heating and

Figure 2.6-11 Typical plot of sag versus temperature for various HTLS conductor types.

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a reasonably high air temperature of 30°C to 40°C. As aresult, dynamic line ratings are usually higher thanstatic line ratings but can occasionally be less.

Table 2.7-1 illustrates the advantage and consequence ofvarious wind speed assumptions. Use of a higher windspeed for static thermal rating calculations yields anincrease in the line rating, even though the maximumconductor temperature (100 °C) remains the same. Forexample, an increase in assumed wind speed from 2 to 3ft/sec (0.61 m/sec to 0.91 m/sec) yields an increase in therating from 990 to 1080 A and, since the assumed con-ductor temperature remains the same, no line modifica-tions are required.

The major advantage of this method of uprating isclear—it is very inexpensive. Since the maximum allow-able conductor temperature remains the same (100 °C),the corresponding maximum sag is unchanged and noline modifications are required.

The major disadvantage of this approach is also clearfrom the rightmost column of Table 2.7-1. This columnshows the temperature attained by the conductor forstill air conditions, with a line load equal to the calcu-lated rating shown in column 2. Historically, the jointprobability of maximum loading and worst-caseweather was considered a rare event. Recent field studiesindicate that, in certain areas, the probability of still airmay be in excess of 10%. Combined with the previouslynoted increase in normal and emergency line loading,the temperatures indicated in the last column of Table2.7-1 may be a real concern, and the use of a less conser-vative wind assumption may impact line reliability.

2.7.3 Advantages of Dynamic Rating

A Flexible Response to Uncertain Load GrowthIn a regulated utility environment, circuit load growthwas reasonably predictable, and the corresponding needfor increases in circuit capacity could be predicted yearsin advance. In the increasingly “open access” environ-

ment, circuit load growth is much less certain, and pro-viding appropriate increases in circuit capacity is muchmore difficult. Also, in our present economic state, largecapital expenditures are unattractive, especially if thoseexpenditures turn out to be unnecessary. Dynamic mon-itoring leading to modest practical increases in capacityfor equally modest capital investment appears to be anattractive uprating alternative.

Avoid Circuit OutageWith those methods of uprating existing lines thatrequire physical modification of the line—reconductor-ing, raising support points, retensioning—the line mustbe de-energized. This may be expensive if loss of serviceresults in increased generation costs. Installation andcalibration of some line monitoring devices do notrequire taking the line out of service for more than a fewhours. With some noncontact monitors, the line maystay in service during installation.

Monitoring Equipment May be Moved and ReusedMonitoring equipment and communication links are, ingeneral, reusable. Thus they may be applied to lines on atemporary basis, allowing postponement or avoidanceof a more traditional uprating project. If the line is even-tually physically modified, the monitors can be used atanother location. This process is limited by the durabil-ity of monitors and the rate of change in communica-tions equipment.

Improved Clearance AccuracyOne of the benefits of real-time line monitoring is theimproved understanding of how existing transmissionlines behave when subjected to heavy electrical loading.Such high loading events in a regulated environmentwere rare, and errors in clearance estimation were, there-fore, of little concern. Given the difficulty in getting newlines approved and the increased utilization of existinglines under both normal and emergency conditions,accurate determination of electrical clearances along theline is becoming essential. Real-time monitors com-bined with direct communication links to SCADA allowthe system operator to load existing circuits with confi-dence that minimum clearances are being met. Thisallows increased utilization (higher ratings) during mostloading situations and the avoidance of dangerous clear-ance violations during those increasingly frequent timeswhen the line is heavily loaded during a period of poorrating weather conditions (low wind speed, high solarheating, high air temperature).

2.7.4 Disadvantages of Dynamic Rating

Need for Real-time Communication to SCADATransmission owners have not traditionally monitoredoverhead lines, especially in real-time. Whatever type of

Table 2.7-1 Effect of Assumed Wind Speed on Thermal Rating for Drake 795 kcmil ACSR at 100°C, Assuming Full Sun and an Air Temperature of 40°C

Assumed Wind Speed for Line

Rating Calculation

Line Rating for 795 kcmil ACSR

@ 100°C

Conductor Temperature when current =

rating and wind speed = 0 ft/sec (0 m/sec)

(ft/sec) (m/sec) (A) (°C)

0 0 750 100

2 0.61 990 130

3 0.91 1080 145

4 1.22 1160 160

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monitoring device is used, communication of the mea-sured values back to the system operator is essential.This requires two communication links, one from themonitor to a nearby substation, and a second from thesubstation to the operations center. These communica-tion links must be set up and maintained if the dynamicmonitoring and rating method is to be useful.

Installation and Material CostThe cost of any dynamic monitoring system must beweighed against the cost of other uprating methods.Costs include monitors, communications equipment,software, and engineering as well as the cost of main-taining each. In general, the cost of real-time monitor-ing and rating should be significantly less than the costof more conventional uprating methods.

Operational IssuesIn contrast to the other line uprating methods discussedin this report, dynamic monitoring and rating methodsrequire a change in the way system operators limit cir-cuit loading. With such methods, the system operatorsees a circuit load limit that varies significantly withtime, and at certain times can be less than the presentfixed line rating. This typically requires some mentaladjustment by operators that is partly offset by nor-mally higher line ratings. A culture change regardingline ratings needs to take place. This can be facilitatedby performing some upfront dynamic rating studies. Itcan prove very useful to gather data offline for a periodof time, then run real-time simulations on the data. Thiscan help educate operators (and engineers and manag-ers) about the technology and its usefulness. Also, thisdata itself can be very useful in identifying hidden powercapacity in lines.

2.7.5 Real-time Monitors

The maximum electrical power flow down an overheadtransmission line is typically determined by the need tolimit conductor sag and thus maintain minimum groundclearances that are specified by a maximum allowedconductor temperature. Various monitoring methodshave been proposed and tested, all of which are typicallyapplied to determine the line’s sags in all its spans andthe maximum current that can be carried without violat-ing minimum electrical clearance requirements in anyspan.

The following real-time monitors are either commer-cially available or have been field-tested at a number oflocations:

Weather StationsWeather stations generally measure wind speed anddirection, air temperature, solar intensity, and rain. If

the line current and weather conditions are known inreal-time, the conductor temperature near the weathermonitor can be calculated in real-time (EPRI 1995).

Weather stations can include standard propeller-typeanemometers, or the more sophisticated 3-D ultrasonicunits. The latter are quite expensive, but have no movingparts and are therefore very reliable, are very accurateeven at low wind speeds, and can measure vertical airmovement. Figure 2.7-1 shows a photograph of aweather station with both anemometer types.

Conductor Temperature MonitorsConductor temperature monitors incorporate a clamp-on thermocouple, attached directly to the energizedconductor and linked to a ground station by radio. Theaccuracy of temperature monitors depends on how closethe measured conductor temperature at one spot is tothe average line section temperature. It has beenobserved that conductor temperature can vary signifi-cantly along its length due to large variations in windspeed and direction.

Line Tension MonitorsA load cell can be used to determine the line tension.The load cell is placed on the grounded side of dead-endinsulator strings. The measurement of line tension canthen be converted to the average temperature of the linesection.

A base station is mounted on the structure and con-nected to the load cells by cable. Communication to abase station is usually by spread spectrum radio, and theunits can be solar powered. The line is normally de-energized when the load cells are installed.

Figure 2.7-1 A weather station with a 3-D ultrasonic anemometer mounted next to a standard propeller-type anemometer.

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Sag MonitorsEPRI recently developed a device for monitoring con-ductor sag in real-time. It is based on digital video tech-nology, and is called the video sagometer (EPRI 2001).

Figure 2.7-2 provides a very simple illustration of thebasic concept and main components of the video sago-meter system. The main components include a videocamera based on highly light-sensitive charge coupleddevice (CCD) technology, a passive reflective target, asolid-state target illuminator, a communication system, andassociated electronics.

The camera unit is typically mounted on one of thestructures of the line being monitored, but it could bemounted on any appropriate structure in the vicinity. Asmall, passive, reflective target is placed on the conduc-tor being monitored. A low-power solid-state illumina-tor (diode laser or LED-based device) is mounted withthe camera to illuminate the target at night or whenambient light is not sufficient.

Image recognition algorithms residing in local firmwaredetermine the position of the target within the camera’sfield of view. The target’s ground clearance is deter-mined from that position through a calibration proce-dure performed during installation. The conductor’s sagand/or ground clearance is determined at any pointalong the span from the catenary equation. The systemshave proved to be incredibly accurate.

Readings are taken at user defined intervals—typicallyabout every 10 minutes—and stored in an onboard data

logger. In addition to the sag/ground clearance data, thedata logger also records the date, time, temperature, cor-relation factor, and other data described in the reference(EPRI 2001).

Communication of the data back to a control center orengineering office is accomplished via cell phone and/orspread-spectrum radio. Data can be retrieved inarchived blocks or provided in real time, although real-time transmission by cell phone is generally impractical.In addition, the system can be configured to transmitdigitized images of the camera’s field of view.

The systems can be powered by solar-cell/batteryarrangements, or by standard ac distribution power ifavailable at the site. The systems, including the targets,can readily be installed on energized EHV transmissionlines, or readily removed and relocated.

Utilities have used these systems in a variety of ways.Some simply monitor the ground clearance in real timeas a simplified means of rating their lines in real time.Others use the more sophisticated approach of using thereal-time data in conjunction with EPRI’s DynamicThermal Circuit Rating (DTCR) software to perform real-time rating calculations. Some have used the data inuprating studies. Figure 2.7-3 is a photograph of aninstallation of a video sagometer on a wood pole. Thecommunications and associated electronics are mountedin boxes near the base of the pole.

The video sagometer underwent extensive testing at theEPRI-Lenox facility, and now has a proven performancerecord on operating transmission lines throughoutNorth America, and over a line voltage range of 69 kVto 500 kV. The video sagometer offers several features:

Figure 2.7-2 A simplified illustration of the video sagometer concept. Figure 2.7-3 The video sagometer mounted on a wood

pole.

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• It can easily be installed, or moved, without taking aline outage. In fact, of all the systems installed inNorth America, most were installed while the linewas energized.

• It does not have to be installed at a dead-end struc-ture. It can be installed on any of the transmissionstructures, on nearby poles, on its own pole, ormounted anywhere in the vicinity of the line.

• Because conductor sag depends on average conductortemperature, sag measurements are equivalent to tem-perature measurements (and tension measurements).This is important for lines that are thermally con-strained, and makes it possible to use heat balanceequations for rating computations.

• The system has proven to be incredibly accurate, pro-viding sag measurements to better than quarter-inchaccuracy.

• The system provides a direct indication of sag, whichcan be the most relevant quantity for line operation.The system can also be placed at the most criticalspan in the line.

• Its operation can be simply verified at any time bycomparing the measured height of the conductor tothe sagometer’s output. Comparative measurementscan readily be made by any simple means (surveyingequipment, range finder, tape measure, etc.).

• Because of the so-called ruling span effects, measure-ment of sag at one span provides the sag and tempera-ture information for the entire line section.

• The systems can be powered by solar cells and bat-tery pack, or by standard AC power if available at thesite. Both types of systems have been installed inNorth America.

• On-board electronics store the information for laterretrieval and/or provide the information in real-time.

• Information is transmitted back to a control centervia cell phone or spread-spectrum radio. Both typesof systems have been installed in North America.

• The system can also provide other information, suchas ambient temperature, battery voltage, etc. Also, anew device has been developed that works in con-junction with the sagometer that can monitor load atthe site. Load needs to be known in real-time in orderto perform dynamic rating calculations.

• The system is able to transmit a digitized image of theline back to a control center for further scrutiny ifneeded. This feature could be used when thereappears to be anomalous line behavior, such as icingevents or other serious physical damage to the line.

2.7.6 Dynamic Rating Calculations

There is a distinction to be made between the real-timemonitoring and dynamic rating of overhead lines. Real-time monitoring is easier, but less useful in guiding oper-ator actions than providing dynamic ratings.

For example, the conductor temperature, sag clearance,or tension of an overhead line can be monitored with atemperature monitor, a video sagometer or a load cell,and the result reported to the system operator by a vari-ety of communication methods. Such measurements canbe very useful during periods of high electrical loadingin guiding the operator as to the “real-time” state of theline. Such measurements can be used to avoid load shed-ding or load reduction that would be required by staticrating methods. The limitations of such real-time moni-toring involve the operator’s needing to know the spe-cific limits on temperature, sag, or tension for the linesection, and the operator’s needing to estimate howlarge the electrical load can be in order to meet physicallimits.

Dynamic thermal ratings require certain calculationsbased on the real-time sag, conductor temperature, ortension monitor data, however, since such ratings maybe directly compared to electrical load to guide operatoractions even where the operator does not have detailedknowledge of line design limits on temperature or sag-tension. Dynamic thermal ratings are also useful priorto high post-contingency loadings and may therefore beutilized to maximize load flows and minimize the likeli-hood of clearance or over-temperature occurrences dur-ing emergencies.

Dynamic thermal ratings are calculated on the basis ofthermodynamic heat balance in the line conductors(Douglass and Edris 1996, 1999; EPRI 1995). If real-time tension or sag is monitored, the tension or sagmust be converted into an equivalent conductor temper-ature in order to serve as the basis for dynamic ratingcalculations. With both tension and sag monitoring sys-tems, the conductor temperature is not directly mea-sured. Therefore, the temperature of the conductor mustbe inferred from other measurements. This process ofrelating conductor temperature to sag or tension iscalled “line calibration.”

Figure 2.7-4 illustrates how a “line calibration” is donewith a tension monitor (note that a very similar graph isused for sag measurements—i.e., sag versus temperatureis plotted). The vertical axis is the line tension. The hor-izontal axis is the estimated conductor temperature. Inthis case, the conductor temperature is assumed equal to

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that reported by a “net radiation sensor,” which is ashort length of aluminum rod, oriented in the directionof the line section and painted to approximate the emis-sivity of the line. This is a reasonable assumption duringthose times when the line current is low and the lineconductor may be assumed to have nearly the same tem-perature as the painted aluminum rod.

The symbols indicate 15-minute average tension andsolar temperature data taken for the line during periodsof low current. The curve shown in Figure 2.7-1 is takenfrom a normal sag-tension calculation (done withAlcoa’s SAG10 program), where the final unloaded ten-sion at 15°C was set equal to about 6350 lbs (28 kN) inorder to fit the tension field data. The curve has alsobeen expressed as a polynomial, as shown by the fourth-order equation shown in the figure.

Given the tension-temperature (or sag-temperature)equation for a line section, tension (or sag) measure-ments can be converted to equivalent conductor temper-ature and dynamic rating calculations performed.

Weather-Based RatingsInstruments to measure wind speed, wind direction,solar intensity, and air temperature are placed at theapproximate height of the transmission line conductor,preferably in the transmission right-of-way. Weatherdata from airports and other commercial stations islikely to be inappropriate for real-time monitoring oflines. As in most monitoring methods, the line current isobtained from conventional current transformer mea-surements at a nearby substation.

The conductor temperature (and the sag and tension ofthe line) is predicted based on weather conditions, linecurrent, and conductor parameters. Conductor tempera-ture is used to determine the position of the conductor inlight of the sag-tension line design data. Alternatively,the conductor temperature is compared to the line designmaximum allowable conductor temperature, and it isassumed that if the design temperature is reached, thenthe safety limit is exceeded and there is risk to the public.

The highest conductor temperatures are obtained forthe lowest wind speeds, and those winds that are nearlyparallel to the line direction. Therefore, the wind ane-mometer must be of high quality, and be able to mea-sure wind speeds below 3 ft/sec (1m/sec). The propellertype is more accurate than the cup type, but both aresubject to start-up error after stalling at low wind speed.The best results are often obtained from the ultrasonictype (see Figure 2.7-1).

The calculation of line ratings by weather monitoringdoes not require measurement of the line current. Thismethod may therefore be used to supplement the othermonitor based dynamic rating methods.

This method may not cater for variation in parametersthat could affect the conductor temperature. Variationin the value of the parameters can be caused by variabil-ity of the terrain or by the sheltering of a line by trees orbuildings. In addition, wind speed and direction can dif-fer from the point of measurement, (for example, an air-port) to the actual line. To mitigate this, there may be aneed to install a number of weather stations along the(long) lines; associated communication problems totransmit the readings may occur, together with uncer-tainty of the best location of weather stations.

Conductor Temperature-Based RatingsThe sensor is usually located at one position only. It isknown that temperature varies along the span as well asbetween spans. To make a judgment based on this onereading is risky, since the temperature of the conductorcan be very different from span to span, especially if theline changes direction or terrain (sheltered or unshel-tered spans). The cooling is approximately 40% in a linesection parallel to the wind compared to a section per-pendicular to the wind.

Also, the temperature measured is the conductor sur-face temperature, not the average conductor tempera-ture (that affects sag).

Tension-Based Dynamic RatingsOver the last 5 years, use of line tension monitors hasbecome widespread within the U.S. The first commer-

Figure 2.7-4 Example of “line calibration” from a previous EPRI field test at PECO Energy.

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cially available device, known as the CAT-1, is installedat over 30 utilities. There are a number of reasons for thepopularity of these devices. The tension-measuringdevice is a commercial load cell, which appears to bevery reliable and exhibits little drift with varyingweather and line load conditions. The device is mountedon the grounded side of a dead-end insulator string andthus is not subject to high electric fields. Line tensionmonitors are normally installed with the line taken outof service.

Sag-Based Dynamic RatingsAs an example of a typical sagometer installation, arecent field study at TVA is noted in the following (seeFigure 2.7-5). The project involved one of the video sag-ometer’s unique features: the transmission of real-timeimages of the span being monitored. The developmentof firmware and the base-station software needed toimplement this feature has been completed.

One of TVA’s primary objectives was to use these sys-tems in real time—i.e., by communicating clearancemeasurements directly to the control center and deter-mining real-time dynamic ratings for these lines. TVA’sultimate goals are to connect the sagometers and theweather station to its SCADA system, which wouldmake the data available throughout its EMS system,and to use the clearance and weather data, coupled withmodified DTCR software, to calculate real-time ratingsfor the monitored lines that would be available to systemoperators.

As such, these systems were set up and installed to func-tion in real-time, and from the day the system went intooperation, data has been collected at the base station inreal-time. Spread-spectrum radios are used instead ofcell phones to communicate between the base-stationcomputer and the remote video sagometer sites. Thesagometers are all within a radius of 10 miles from thebase-station computer.

A custom-made user interface to display clearance data,along with the available clearance margin, was writtenfor the base-station computer (see Figure 2.7-6). TheTVA’s system operators routinely access the displayscreen during contingency periods and monitor the avail-able clearance margin, which blinks if it gets below 10%.

Based on sag and weather measurements, DTCR wasexecuted to compare actual ratings to the static rating.Figure 2.7-7 shows an example of the results that can beachieved. This is a 24-hour block of rating data. The4-hour and 15-minute dynamic rating data were deter-mined by DTCR operating in conjunction with real-time data from a video sagometer. As can be seen, thedynamic ratings are significantly greater than the static

Figure 2.7-5 The solar-powered Sagometer on a lattice structure at TVA.

Figure 2.7-6 Real-time display for TVA video sagometers.

Figure 2.7-7 A 24-hour block of rating data.

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ratings. Note that, during the morning, the dynamic rat-ings became very high due to precipitation. Results suchas these are typical of all DTCR/sagometer applications.

2.7.7 Field Test Results

EPRI sponsored a series of field tests of dynamic ratingand monitoring techniques at several utility sites. Theoutcome of these field tests were significant, and EPRIrefined both its DTCR circuit rating software andlearned certain fundamental facts about how weatheraffects the rating of overhead transmission lines andhow dynamic rating methods are best applied.

1. Dynamic thermal ratings for overhead lines may becalculated based on either real-time weather, or real-time sag or tension data in conjunction with real-timeweather. For weather-based ratings, the wind angleshould be assumed fixed and near parallel to the linedirection to account for directional variation alongthe line section.

2. In rating longer lines with multiple ruling span sec-tions, it is likely that the line rating (dynamic orstatic) decreases with line length and that dynamicrating of lines requires multiple monitoring locations,and the minimum number of monitors required mustbe based on field measurements.

3. Sag and tension monitors work well in lines havinghigh current density (greater than approximately 1amp/mm2) where they generally yield more accurateratings than single-point weather monitors. However,in lines with low current density (less than 0.5amps/mm2), weather-based dynamic ratings are moreaccurate than those based on sag-tension monitors

4. Sag and tension monitoring allows one to directlymake measurements at high temperatures. Weathermonitoring does not.

For example, the data obtained in these field tests showthat there is a great deal of fluctuation in both windspeed and direction along most line routes, particularlyduring periods of low wind activity. Figure 2.7-8 shows15-minute average wind speeds at locations only 1.5 kmapart along a line route in Philadelphia.

The field tests confirm that not only the wind speed butalso the wind direction varies along the line. This raisesquestions about the usefulness and accuracy of basingdynamic thermal line ratings on weather data from asingle location within a line section. It would seem toimply that multiple weather monitor locations might berequired, especially for long line sections.

Comparison of Weather Monitor and Tension/Sag Monitor-Based Dynamic Line Ratings The main advantages of using weather-based line rat-ings are two-fold:

• The rating calculation is independent of the line current.

• The monitoring equipment is modest in cost.

Weather data may also be used to dynamically ratenearby substation equipment.

The disadvantages are that the anemometers are quitefragile and prone to measurement error unless calibratedfrequently and, being a measurement of weather condi-tions at a single location, may not truly represent theweather along the entire line section, especially the wind,which can be extremely variable from place to place.

Field experiments conducted by Chisholm at OntarioHydro (EPRI 1995) indicated considerable success inestimating average conductor temperature. The instru-ments were placed over a five span ruling span section,and the data was based on real-time line current and onweather monitors placed at a distance from the line, andit was assumed that the wind angle was fixed at an angleof 20° to 30°.

Comparisons of weather-based and tension-based lineratings at three of the four field-test sites indicates thatthere is good agreement between minimum values ofweather-based and line tension-based ratings whenusing a fixed wind angle of 22° relative to the conductoraxis. This is illustrated in Figure 2.7-9.

Figure 2.7-8 Wind speed (15-min average) at two locations 1.5 km apart along a 230-kV line in the eastern U.S.

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Based on such observations at each field test site, itappears that weather-based ratings based on a fixed lineangle of the order of 20° are conservative under nearlyall conditions and that such “weather-based” ratingscan be used as a means of warning the operator duringperiods of “low rating” conditions. When combinedwith the use of less conservative fixed ratings for plan-ning and low load operation, this weather-baseddynamic rating method would be very cost-effective.

Rating Variation in Adjacent Line SectionsFigure 2.7-10 shows the variation in tension-based linerating with time for the 230-kV SRP line. Four rulingspan sections are monitored. I2 is E-W, and the otherthree are oriented nearly N-S. Note that the E-W spangenerally has the lowest rating, but that this is not true forcertain periods such as the three hours starting at 6 am.

Clearly, if the entire line were rated on the basis of amonitor in only one section, the rating would be toohigh some percentage of the time and therefore not con-servative. Multiple monitoring locations are required tocorrectly calculate the real-time line rating; however, itappears that there is good agreement for the three linesections oriented in the same direction (N-S).

It appears that the number of monitoring locations(either weather or tension) required to calculate the real-time line rating correctly must be empirically deter-mined for each location.

Daily Line Rating VariationCertain circuits experience a fairly regular daily loadvariation, others do not. For those circuits that experi-ence a repeatable load cycle, the daily variation in linerating may or may not be coordinated with the load.Consider, for example, the rating variations shown inFigures 2.7-11 and 2.7-12.

Figure 2.7-9 Comparison of weather-based and tension-based cumulative rating distributions.

Figure 2.7-10 Comparison of tension-based rating estimates for four separate line sections.

Figure 2.7-11 Weather-based normal rating for SDGE 138-kV line as a function of time of day for September 1997.

Figure 2.7-12 Weather-based normal rating for SDGE 138-kV line as a function of time of day for December 1997.

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2.7.8 Summary

The calculation of thermal ratings for overhead lines istypically based upon heat balance methods such as thatfound in IEEE 738-1993. Given a maximum allowableconductor temperature, the corresponding maximumallowable current (the static thermal rating) is deter-mined for “worst-case” weather conditions. In mostcases, the maximum temperature is limited in order toavoid excessive conductor sag or, in some cases, a loss inconductor strength.

By using real-time monitors combined with communi-cations, these measurements can be presented to the sys-tem operator, and/or can be used to perform dynamicrating computations whose results can also be provided.Results of several projects have demonstrated that it ispossible both to increase the line rating under most con-ditions and to avoid electrical clearance violations undersevere load and weather situations.

The distinction between real-time line monitoring anddynamic ratings is explained and the various monitoringmethods noted and analyzed.

2.8 CASE STUDIES

2.8.1 Introduction

This section includes a general discussion of the majorfactors that need to be quantified in order to select aneconomic and reliable uprating method for overheadlines. No single method is most economic in all cases,nor are all the important factors economic. Nonethe-less, the selection of an appropriate uprating method isnever made without economic justification. Similarly,no method can be identified as the “best” method sincethe uprating decision depends on predictions of whatwill be, and involves certain irreducible uncertainties. Inspite of these difficulties, the uprating of transmissionlines, as described in the following, should be a logicalprocess, flexible enough to use in most cases, and power-ful enough to yield valuable insight into line behaviorand operation.

2.8.2 Selecting a Line Uprating Method

As described in preceding sections of this chapter, thereare many ways to increase the thermal rating of an exist-ing line. As any experienced line designer knows, thereare a lot of different ways to accomplish the same goal,and the cheapest way may not be the most sensible wayto provide a reliable transmission system. Engineeringjudgment is often required in selecting the most appro-priate method of uprating existing lines. Therefore, thegoal here is to identify the major factors that should be

considered in line uprating, demonstrate a generalmethod of viewing these factors simultaneously for anumber of design cases, and perform a reasonablydetailed application of such methods for a particularline uprating example.

Basic ObservationsCertain observations about line uprating appear to benearly universally accepted by utility designers:

• Public safety is most crucial, and litigation is to beavoided if at all possible. If litigation or public injuryis a possible result, the chosen uprating approach isunacceptable.

• Frequent load shedding is painful, expensive, andmakes distributed generation (DG) more attractive.A marginal line uprating method that results in thefrequent need for operator intervention to drop cus-tomer loads, even interruptible ones, is a poor choicein the long run.

• Avoiding the use of vibration dampers and/or armorrod by keeping everyday conductor tension wellbelow NESC Code or CIGRE safe limits is an expen-sive way to avoid conductor fatigue. However, avibration assessment by damper manufacturersshould precede any uprating decision that involvesthe use of high everyday conductor tensions.

• If the maximum design temperature of an older exist-ing line is to be increased to more than 100oC, com-pression splices should be replaced or shunted, andloss of tensile strength in the aluminum strands mustbe carefully assessed.

• Sag clearance buffers are required in any transmis-sion line because of uncertainties in weather anddesign. The buffer for an existing line may be some-what less than for the design of a new line (sincestructure placement uncertainties do not exist, andconductor elongation uncertainties are less than for anew line), but reducing necessary sag buffers to zerois not a good idea.

• Before considering any uprating method, it must bedetermined if the existing structures are in reasonablygood shape, having load capacities at least equal tothe original design assumptions. If this is not true,then none of the uprating options discussed is appro-priate. The transmission owner should considerreplacing the existing line with a new facility that isboth safe and reliable.

• Before considering any uprating method that doesnot involve reconductoring the line, the present con-dition of the conductors must be evaluated. When theconductor is not replaced, the increased rating willlead to higher conductor operating temperatures, and

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such methods can only be considered practical whenthe existing conductors and compression splices arein “very good” condition or can be made so.

Critical but Qualitative IssuesIn evaluating uprating options for an overhead trans-mission line, there are many issues to be considered.Some issues are hard to quantify. For example, the reuseof existing structures carries with it an uncertain, and toa certain degree unknowable, risk that there may beundiscovered structural flaws. This risk may be perfectlyacceptable in most situations, but not acceptable in lineswhose failure may have enormous consequences. Thesefactors may be hard to put a price on, but their consid-eration is essential in deciding whether, and how, touprate an existing line. Some risks that should be con-sidered are:

• Corporate impact of negative publicity from injuries,death, property damage from downed conductors, orinstances of excessive sag.

• Loss of residential or commercial customers due toservice interruptions.

• Intervention by regulatory bodies in response to ser-vice interruptions.

• Criticality of line to overall system reliability. To whatextent might an outage affect a broader regional ser-vice interruption.

• Certainty of projected electrical overload.

• Certainty of financial return on capital investment.

All of these issues exist and are part of the transmissionowner’s uprating decision, but none is easy to quantify.A consideration of these issues is more likely to producea sense of “comfortable risk” rather than a detaileddecision on uprating method.

Financial Consequence of Electrical Line Losses A very important and peculiar issue in line upratingconcerns the matter of line losses over the life of the line.As is demonstrated in the final detailed uprating exam-ple in this section, when the value of line losses is con-sidered in the uprating problem, the line designer mayselect a significantly different uprating method than ifsuch losses are ignored.

In those cases where the rating of a moderately shorttransmission line is being increased in order to avoidload shedding during relatively infrequent post-contin-gency loadings, it is unlikely that electrical losses shouldbe a factor in uprating. In those cases where the ratingof a reasonably long line is being increased in order toallow increased daily load peaks throughout an entireseason, it is likely that electrical losses should be consid-

ered and that the designer should seek an upratingmethod that reduces them.

Surely, occasional operation of lines at temperaturesapproaching 200oC may be smart engineering, but rou-tine operation at high temperature is not.

2.8.3 Preliminary Selection of Uprating Methods

The “best” solution at one utility may differ from that atanother because the line uprating decision involves agood deal of engineering judgment based on experience.Nonetheless, in every case, the selection of an appropri-ate uprating method depends heavily on the physical,electrical, and thermal characteristics of the existingline, and on the exact nature of the “need” for a highercapacity line. It is possible to identify certain existingline parameters and system analysis results that largelyindicate the “best” uprating solutions.

Since there are many factors that influence the selectionof line uprating methods, it is helpful to list the mostessential ones, and to develop a table summarizing thosemost likely to determine, or at least strongly influence,the line uprating method. The resulting “UpratingAnalysis Table” is intended for use in the preliminarystages of developing an appropriate uprating solution. Itis an aid to focusing the engineering inquiry on the mostproductive uprating methods.

Given the large number of factors that influence theuprating of an existing overhead line, it is crucial toidentify, and then quantify, the most important. Thesefactors in line uprating (with the most important shownitalicized and/or in bold) include the following:

System AnalysisThe impetus for line uprating comes as a result powersystem analysis. Present electrical loads are projectedinto the future, and the impact of various componentoutages (i.e., contingencies) on the electrical loading ofthe existing line is determined. Specific probabilities areseldom associated with post-contingency loadings, andeven the prediction of normal loads is often uncertain,particularly with the advent of “open access” to com-mercial power generators.

Nonetheless, even with such uncertainties, the systemplanner must determine:

• Criticality of the line to overall system reliability(marginal or absolutely critical).

• Certainty of projected electrical overload (very cer-tain or not certain).

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• Frequency of high electrical loads (e.g., daily sea-sonal peak loading or rare post-contingency emer-gency loads).

• Magnitude of the electrical overload in 2 years (e.g.,< 10% or > 50%).

Structural ReviewTransmission structures and the conductors they sup-port are the major cost components of any overheadline. (In comparison, the cost of insulators and hard-ware are almost always minor.) Therefore, the designlimits and actual physical condition of the existingstructures and foundations are a major factor in select-ing a line uprating method. It is fair to say that if theline’s structures are in poor condition, no uprating alter-native makes much sense, reliability-wise or financially.On the other hand, given their initial cost, if the struc-tures are largely in their “as designed” condition, anyuprating method that does not require their extensivemodification is likely to be significantly cheaper than anew line with the same capability.

Given an existing line with structures in reasonablygood condition, there is a large financial incentive touprate the line without needing to make major changesin the structure geometry or load capability. As part ofany preliminary uprating evaluation, for a line withstructures in good condition, it is necessary to deter-mine the limits of “low-cost” structure modifications.For example, in uprating an existing line, how much canthe present structure attachment points be raised with-out incurring significant cost (where significant cost isthat which exceeds 10% of the cost of new structures).Similarly, in considering the possibility of retensioningthe line or reconductoring it, how much can the originalmaximum conductor tension be increased withoutincurring costs that exceed 10% of the cost of new struc-tures. In performing such analysis, the following shouldbe considered:

• Physical condition of the existing structures (“asdesigned” or “10% or more in need of replacement”).

• Maximum increase in transverse load beyond whichthe cost of tangent structure reinforcement exceeds10% of the cost of new structures.

• Maximum typical increase in tangent structure con-ductor attachment height beyond which the costexceeds 10% of the cost of new structures.

• Number of strain structures per mile (km) (0.05 or1.0).

• Maximum increase in maximum conductor tensionload beyond which the cost of strain (and possiblytangent) structure reinforcement or replacementexceeds 10% of the cost of new structures.

• Evaluation of broken wire loads and other conditionsnot considered in the original design.

Conductor ReviewOther than transmission structures, the conductors theysupport are the major cost component of any overheadline. Therefore, the reuse of the existing conductors in aline uprating is very economically attractive. The optionof reusing existing conductors hinges on their physicalcondition, which may not be easy to determine. Theusual signs of conductor deterioration include corrosionof the steel core wires of ACSR, corrosion and fatiguewithin compression splices, and the fatigue of aluminumwires at, or near, the mouth of support clamps due toAeolian vibration. None of these signs is easily deter-mined in the field, yet there is little point in consideringthe reuse of existing conductor without establishing thatit is in good condition.

Assuming that the existing conductor is in reasonablygood condition, the following factors help in selectingan appropriate uprating method:

• Physical condition of the existing conductors (“aspurchased” or “remaining life” < 10 years).

• Unloaded final everyday tension of existing conduc-tors (15% or 25% RBS).

• Existing conductor type (30/7 ACSR or 37 strandAAC).

• Existing line maximum temperature (49°C or 125°C).

• Excess clearances at existing line maximum tempera-ture (most spans < 1ft (3 m) or most > 5 ft (1.5 m)).

• Change in sag with increased temperature(0.2 ft/10°C to 2 ft/10°C [0.06 m/°C to 0.6 m°C]).

• Probability of assumed weather conditions.

• % change in line rating per 10°C change in line designtemperature (50% to 5%).

Preliminary Uprating Analysis TablesTo summarize the various key uprating parameters, thefollowing simple “Uprating Analysis Table” has beendeveloped. By defining the 11 parameters listed in thetable, one can better understand which uprating meth-ods are likely to meet system needs at minimum cost.

Table 2.8-1 is an example.

In this example, it is clear that:

• The predicted overload magnitude is probably toolarge to be accommodated by the use of dynamic rat-ing methods, but not so large as to necessarily requirereconductoring.

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• The predicted high electrical loading will be infre-quent, and the resultant cost of electrical losses willbe low even if the existing conductor is reused.

• Modifying the existing conductor tension or replac-ing it with a larger conductor will require significantexpensive structure modifications, but raising theconductor attachment points appears to be rathereasy (low cost).

• The present line design temperature is moderate andcould be increased without causing annealing byexceeding 100°C.

This preliminary review seems to indicate that raisingthe existing conductor attachment height, while con-tinuing to use the existing conductor and installed ten-sion, may be an economic uprating method.

Uprating analysis tables were developed for each of thefollowing uprating case studies in order to simply sum-marize those aspects of the existing line that are mostimportant to the selection of uprating method.

2.8.4 Uprating Test Cases—Preliminary Uprating Study

Clearly, the uprating method applicable to a particularline depends on a number of different parameters thatmust be defined as part of the uprating process. However,certain aspects of the line design suggest certain upratingmethods, or suggest avoiding certain approaches. Thissection includes a collection of typical candidate lineswith appropriate line uprating methods identified(including references to the section describing themethod) (see Table 2.8-2).

Table 2.8-1 Uprating Analysis Table

Table 2.8-2 List of Case Studies Considered

Case Study # and Section Reference Structure Conductor System

Promising Uprating Method(s)

1– Section 5115-kV single ckt, wood pole H-Frame, I-string insulators

26/7 397.5 kcmil (203 mm2), clearancelimited at 75°C

Normal load in summer reaches 50% of rating, fairly frequent emer-gency loads reach 110%

Raise attachment points by raising crossarm or using floating dead-end concept

2 – Section 3 & 4

69-kV single ckt, single wood pole with cross-arm & post insulators, guyed pole angle and dead-ends

#2AWG copper with original splices, > 3 ft, (1 m) excess clear-ance at 75°C max

Normal load is 20% of thermal, rare emergency load to 120% rating

Inspect conductor and connectors, raise max temp of existing conduc-tor to 90°C

3 – Section 5230-kV double ckt, steel lattice self-supp, I string insul

18/1 477 kcmil (243 mm2), clearance limited at 75°C

Normal load in summer reaches 50% of rating, fairly frequent emer-gency loads reach 110%

Retension existing ACSR conductor to allow operation to 100°C

4 – Section 5132-kV double ckt, steel lattice self-supp, I string insul

30/7 250 mm2 (490 kcmil) ACSR

Normal load profile to exceed 100% rating. Load cycle is predict-able.

Statistical comparison of line rating with other lines in region of low wind and high air temp allows increased rating

5 – Section 7138-kV double ckt, steel lattice, light loading, seacoast area

26/7 636 kcmil (324 mm2) ACSR

Install tension or sag monitors, and use dynamic rating methods

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To be useful, a detailed description of each case study isincluded to make at least some initial decisions aboutwhat approach to take, but a detailed plan profile or sagsurvey data is not included. Similarly, the lines includevoltage ranges of 69 kV to 345 kV—the most commonlines that need uprating.

Case #1 – 115-kV Single-Circuit Wood Pole H-Frame 26/7 ACSR ConductorsThis 115-kV line has a thermal rating of 114 MVA (seeFigure 2.8-1). During the preceding summer period, theload on this line reached 110 MVA during the hottestday, and system planners project the need for a 25%increase in capacity (to 140 MVA). The increasing loadis likely to develop slowly over the next 10 years. Theline experiences relatively high daily loads during thesummer peak period. Post-contingency emergency loadsare not a problem.

The line consists of older wood pole H-frame structureswith 600 ft (180 m) spans. The structures are easily rein-forced. Transverse load limits can be increased with aminimum of additional bracing. Vertical loading can beincreased by hardware replacement, and dead-ends canbe strengthened by use of additional guying. The line isin an NESC light loading area.

The existing conductor is 26/7, 397.5 kcmil (203 mm2)Ibis ACSR strung to a final unloaded tension of 20% ofits rated strength at 32oF. The final everyday sag per 600ft (180 m) span is about 9 ft (3 m) with an existing buffer(excess electrical clearance) that is typically 3 to 6 ft (1to 2 m) at the present line design temperature of 75oC.Occasional fatigue breaks have been observed nearclamps, and about half of the original galvanizing is lefton the core wires.

The summer rating conditions (the line load peaks inthe summer) presently in use are an air temperature of35oC and a crosswind speed of 3 ft/sec (0.91 m/sec).

Uprating Analysis – Case #1The uprating alternatives for test case #1 (see Table2.8-3) include the following:

A. Revision of existing rating conditions based on theuse of monitors (dynamic ratings - Section 7) orthrough a probabilistic analysis of the line rating(probabilistic ratings - Section 5). Given the required25% increase in line rating and the nonconservativeweather assumptions presently in use, it is unlikelythat these methods will yield an increase that large.Also, given the high daily load cycle, electrical losseswill be significant, and neither of these methodsreduces losses.

B. While the structures appear to be in good condition,there is evidence that the existing Ibis conductor hassustained some damage from vibration and that itssteel core strands are certainly not in “like new” con-dition. Given the relatively low cost of structure rein-forcement, one might consider retensioning theexisting conductor (Section 5) and increasing the linedesign temperature to 100oC. Ibis ACSR at 100oChas a thermal rating of 145 MVA. Given the highnormal line loads and the marginal conductor condi-tion, however, this may not be advisable.

C. If the capital is available, the line might be reconduc-tored (Section 6) with a trapezoidal wire conductor

Figure 2.8-1 Case #1—115-kV line.

Table 2.8-3 Uprating Analysis for Case #1

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such as Dove/TW, which has 40% lower resistance(and therefore lower losses), about the same sag asIbis at 80°C, and a thermal rating 25% higher thanthe present line. The transverse structure loads will be10% higher with Dove/TW, but the maximum tensionloads will be nearly 40% higher, and dead-end struc-tures will require extensive reinforcement.

D. An alternative uprating solution may involve the useof a high-temperature, low-sag conductor such asACSS or ACCR, though the relatively modestincrease in line rating (25%) doesn’t require it. ACSSis particularly attractive in applications where theexisting structures cannot easily, or economically, bereinforced. The structures in this case are easily andinexpensively reinforced.

Case #2— 69-kV Single-Circuit Wood-Pole Copper ConductorsTypical of the oldest lines in many systems, the desiredincrease in thermal line rating results from an attempt todeal with a relatively rare single contingency that wouldpersist for up to 24 hours. The addition of a new 345-kV

line section will remove the contingency within 5 years.(See Figure 2.8-2.)

Line Description—Case #2

• 69-kV system voltage, 4 suspension insulator bells.

• No dampers, bolted dead-ends, no armor rod.

• 7 strand, #4/0 AWG Copper conductor, originalsplices.

• Rating conditions—2 ft /sec (0.6 m/sec) perpendicu-lar, 40°C air, sun, 60°C continuous/75°C emergency.

• Mild corrosion area, no broken strands found atclamp locations.

• Normal daily peak annual loading is only 30% ofnormal continuous rating. System analysis by plan-ning needs a 50% increase in emergency rating (post-contingency loading).

• Span lengths range from 150 to 300 ft (45 to 90 m).Ruling span is 250 ft (76 m). Excess electrical clear-ance at 75°C ranges from 2 to 10 ft (0.6 to 3 m). Aver-age clearance is 4 ft (1.2 m). The line length is 10 km(6 miles) with 15 line sections going in a predomi-nantly east-west direction.

• NESC Medium loading area (0.25 in. (0.6 cm) icewith 4 psf wind). Everyday tension at 15 °C equal to12% RBS (Rated Breaking Strength) final.

• Single wood pole structures with zig-zag cross-armsand suspension insulators.

• Built in 1935, 20% damaged poles (rot) replaced in1962. Another 15% replaced in 1988. No extensivestructural failures known. No broken conductors.

Uprating Analysis—Case #2The thermal rating of the existing line is 47 MVA(395 A). The system analysis indicates a need for a 50%higher emergency rating of 70 MVA (590 A). The nor-mal rating of the line remains at 33 MVA (280 A). (SeeTable 2.8-4.)

Figure 2.8-2 Photo of Case #2 69-kV line.


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The structures appear to be in reasonably good shape,yet they are quite old, and the possibility of reconduc-toring such old structures to meet a relatively rare emer-gency load event does not seem economic. The existingstructures cannot be modified to raise the attachmentpoints, nor can they be easily reinforced. Reconductor-ing the line would, therefore, be difficult since the con-ductor maximum tension and diameter could not beincreased at all, and the sag could not be increased.

The predicted occurrence of high, post-contingencyelectrical loading is relatively rare, being the result of anunusual contingency. The copper phase conductorscould be operated at temperatures up to 100oC for shortperiods of time without any significant annealing, butthe existing original splices would have to be replaced toensure reliable operation. This is also true of existinghardware. The original conductor is installed at a rela-tively low tension in short spans and exhibits no evi-dence of fatigue damage. There is insufficient clearanceat 75oC to allow operation of the existing line above thatdesign temperature. Retensioning the existing conductormay be a low-cost uprating method to meet clearancerequirements at a temperature above 75oC.

The present rating weather assumptions are reasonablyconservative. This suggests the possibility of usingdynamic uprating methods, but as discussed in Section2.7, such methods typically produce a usable increase ofonly 10 to 20% in the line rating.

Assuming that samples taken from the existing copperconductor indicate that it retains its original tensilestrength and that a 10% reduction in tensile strengthover the remaining life of the conductor is acceptable,the annealing curves in Section 2.2 indicate that theexisting #4/0 copper conductor can be operated at tem-peratures in excess of 100oC for brief time periods withthe impact on tensile strength, as shown in Table 2.8-5.

With the (emergency) design temperature of the lineincreased to 115oC, the emergency rating with the exist-ing #4/0 copper conductor would be increased to 70MVA, meeting the required emergency rating. At thistemperature, the tensile strength of the #4/0 copper con-ductor would drop by 10% in approximately 100 hours.

If the remaining life of the line is 20 years, and contin-gencies are limited to 24 hours when they occur every 5years, then this is acceptable if the electrical clearancecan be maintained.

At the present emergency design temperature of 75oC,the sag is 7.6 ft (2.3 m). If the unloaded sag of the con-ductor is decreased from 5.1 ft to 3.4 ft. (1.5 m to 1 m)by increasing the everyday tension at 60°F by about 500lbs (2232 N), then the sag at 115oC will be 7.4 ft (2.2 m)and the clearances will be met. The increase in installedtension will cause an increase in the maximum conduc-tor tension from 1570 lbs (7009 N) to 2120 lbs (9464 N)and will require reinforcement or replacement of dead-ends. The transverse loads on tangent structures areunchanged.

Case #3— 230-kV, Double-Circuit Steel Lattice, 54/7 795 kcmil (405 mm2) Condor ACSRTypical of the moderately aged lines in many systems,this double-circuit 230-kV line was built in the 1960susing steel lattice self-supporting structures. The emer-gency thermal rating of the Condor ACSR conductor is1170 A (465 MVA per circuit). The system analysis indi-cates that this short line needs to carry up to 800 MVAas a result of certain severe contingencies. Although thecontingency is likely to occur only every few years, if itdoes occur at all, it is likely to persist for several weeks.


• 230-kV system voltage, double-circuit, 12 suspensioninsulator bells, aluminum clamps.

• Dampers on exposed sections, compression dead-ends, armor rod used at all clamps.

• Existing line has 54/7 strands, 795 kcmil (405 mm2)ACSR conductor, the condition of full tension splicesis uncertain.

• Rating conditions—3ft/sec (1 m/sec) perpendicular,30 °C air, sun, 75°C continuous/100°C emergency.

• Mild corrosion area, no broken strands found in rou-tine climbing inspection.

• Normal daily peak annual loading is 40% of normalcontinuous rating. System analysis indicates that theemergency rating needs to be 800 MVA rather than475 MVA, and that the increased post-contingencyloading would be likely to persist for several days atthe infrequent times when it occurs.

• Span lengths range from 800 to 1100 ft (240 to 330m). Ruling span is 1000 ft (305 m). Electrical clear-ance at 100°C ranges from 1 to 3ft. (0.3 to 3 m). Aver-age clearance at 100°C is 2 ft (0.6 m). The line lengthis 40 km (24 miles) with 20 line sections going in apredominantly north-south direction.

Table 2.8-5 Loss of Tensile Strength

Temperature

Loss in tensile strength after 100

hoursHours for a 10% Loss

in Tensile Strength

100 3% 600

125 20% 40

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• NESC Heavy loading area (0.5 in. [1.3 cm] ice with 4psf wind). Final everyday unloaded tension at 15 °Cequal to 18% RBS (Rated Breaking Strength) final.

• Steel lattice, self-supporting structures. Galvanizingis in good shape. Concrete footing inspection indi-cates they are in “near-original” condition.

• Built in 1963, structures have been inspected by heli-copter. No major line failures have occurred. One linesection failure in 1972 due to a crane accident. Cros-sarm failure and conductor damaged.

Uprating Analysis—Case #3Given the nonconservative nature of the rating weatherassumptions and the need for a large increase in the linerating (465 to 800 MVA), neither the dynamic ratingmethods in Section 2.7 nor the probabilistic methods ofSection 2.5 are applicable. (See Figure 2.8-3 and Table2.8-6.)

Similarly, given the small increase in rating (7%) per10oC increase in the line design temperature, even if theline design temperature of the existing line (with Con-dor) were increased to 200oC, the corresponding linerating (690 MVA) would not be sufficient to meet thesystem requirements (800 MVA).

This reduces our options to reconductoring the line (seeSection 2.6) with a conductor having less resistance thanCondor and capable of operating at 200oC for anextended period of several days. In addition, thereplacement conductor will need to sag (at 200°C) nomore than the original Condor ACSR did at 100oC, yetthe maximum conductor tension cannot exceed that ofCondor by more than 20%. As can be seen from the fol-lowing sag-tension calculations for Condor in the origi-nal line design (Table 2.8-7), the final sag is 37 ft (11 m)at 100oC, and the maximum tension is a little over10,000 lbs (44.6 kN).

As noted in the uprating analysis table, the clearancelimits of the existing line are tight (i.e., excess clearanceof Condor at 100oC is only 1 to 3 ft (0.3 to 1 m). There-fore the replacement conductor cannot have more than37 ft (11 m) sag at 200oC.

Also, the maximum tension load should not exceed thatof the original Condor conductor by more than 20% orthe costs of reinforcement will become prohibitive.

One possible solution involves reconductoring withACSS/TW. For example, 1033.5 kcmil (527 mm2),Curlew/ACSS/TW would yield a rating of 803 MVA at aline design temperature of 200oC as a result of itsgreater aluminum cross section and its ability to operateat 200oC for an extended period of time. The sag-tensioncalculations (of Table 2.8-8) indicate that it is also capa-ble of meeting the 37 ft (11 m) sag constraint at 200oCand the 20% higher maximum tension constraint.Figure 2.8-3 Photo of structure for Case #3.


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Other ACSS conductor designs may also be reviewed tosee if another design can also meet these constraints, butwith in lower capital cost.

Case #4—Double-Circuit 132-kV LineThe existing 132-kV double-circuit line, according toprojected load growth, will soon reach the thermal limitunder normal operating conditions. The line is situatedin an area with mild climate and strong winds. Thephase conductor is “Bear” ACSR (30/7 250 mm2)—aBritish conductor similar to Hen ACSR.

The prediction of increased load is somewhat uncertain,and in order to conserve capital, uprating methods thatrequire a minimum level of capital investment arestrongly preferred by management. As shown in Table2.8-9, two essential features of the existing line thatmake it a candidate for probabilistic uprating are thatthe present rating calculations are based on rather con-servative weather conditions (40°C air temperature,

2 ft/sec [0.6 m/sec] wind, full sun), and the line designtemperature of the existing line is only 60oC. This makesthe rating of the line quite sensitive to changes in airtemperature (> 30% per 10°C).

Probabilistic uprating methods require little or no capi-tal investment since the line is neither physically modi-fied nor monitored. The modified exceedance method(described in Section 5) considers the electrical load pro-file of the line. The conductor temperature (and thus theground clearance) is calculated over an entire seasonusing weather data derived through monitoring alongthe line. The load profile is normalized based on theprofile at the maximum load. This is assumed to be thelikely profile at the time when the thermal rating is likelyto be met.

The present ratings for the existing line are based on theassumption of a flat load profile using weather datafrom a location some distance away from this line, in a

Table 2.8-7 Sag-tension Calculations for Case #3

Table 2.8-8 Sag-tension Calculations for Replacement Conductor of Case #3

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semi-arid region. While it isn’t possible to determine theabsolute probability of ground clearance for the line, therelative probability of ground clearance for this linecould be calculated using more appropriate weather.

When these relative probabilistic methods are applied, itis determined that the thermal capacity of the existingline can be increased from 529 to 863 A for normal, and715 to 1240 A for emergency ratings. The risk is thesame as long as the line integrity from a physical view-point is not jeopardized. It is necessary, therefore, toassess the temperatures that joints are likely to reach.

• This method of uprating must be carefully applied.The rating applies only to a particular line. All jointsin the line must be tested via the resistance methodfor integrity. All joints that are the same or higherresistance than the conductor need to be replaced.

• If the resistance method is found to be too costly,each joint should have a wrap tie placed around it toprevent the conductor falling in case of failure. Thejoints then need to be regularly checked by infraredcamera. All joints at the same, or hotter, temperaturethan the conductor need to be replaced.

Given the managerial decision to seek the lowest costuprating method, probabilistic methods of uprating arevery attractive. The rating of the line can be increasedsufficiently such that a major capital investment projectmight be postponed for several years. It may not even benecessary to increase the tension in the conductor orraise towers. It must be noted, however, that such meth-ods must be used with care. Results are not generic anddepend on the weather conditions at a specific area andthe load profile of a specific line. There are several spe-cific cautions to be observed:

1. The weather data used in the calculation of conduc-tor must be appropriate to line ratings. Data from an

airport weather station 20 miles (32 km) from oneend of the line may not be useful for this.

2. The conclusion that the line can be uprated because itappears to be more conservatively rated than anotherline at another location depends on the assumptionthat the rating of the other line is safe.

3. The inclusion of line current variation over a typicalday means that the resulting probability distributionof conductor temperatures may no longer be valid ifthe line’s daily load variation changes due to changesin the system configuration.

4. Finally, there is no absolute certainty that the result-ing line rating is safe. The uprating decision is basedon a comparison to another line, not on the establish-ment of an absolute clearance assurance probability.

Case #5—169-kV double-circuit, steel lattice, medium loading area, 26/7 636 kcmil (324 mm2) ACSR


• 169-kV system voltage, double-circuit, 10 suspensioninsulator bells, aluminum clamps.

• Dampers on exposed sections, compression dead-ends, armor rod used at all clamps.

• Existing line has 26/7 strands, 636 kcmil (324 mm2)Grosbeak ACSR conductor. The condition of fulltension splices is excellent.

• Rating conditions—2ft/sec (0.6 m/sec) perpendicu-lar, 40°C air, sun, 75°C continuous/90°C emergency.

• Mild corrosion area, no broken strands found in rou-tine climbing inspections.

• Normal daily peak annual loading is 30% of itspresent continuous rating. System analysis indicatesthat the emergency rating needs to be increased to310 MVA rather than the existing line’s 293 MVA.The increased post-contingency loading would be


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likely to persist for no more than an hour at the infre-quent times when it occurs.

• Despite the modest predicted overloads, system oper-ations is particularly interested in finding a way touprate this line without taking it out of service formore than short time periods. Extensive reconstruc-tion is unacceptable.

• Span lengths range from 600 to 800 ft (180 to 240 m).Ruling span is 750 ft (225 m) Electrical clearance at90°C ranges from 3 to 5 ft (1 to 1.5 m). Average clear-ance at 90°C is 4 ft (1.2 m). The line length is 15 km(9 miles) with 10 line sections going in a predomi-nantly east-west direction.

• NESC Heavy loading area (0.5 in. (1.3 cm) ice with 4psf wind). Final everyday unloaded tension at 15°Cequal to 18% RBS (Rated Breaking Strength) final.

• Steel lattice, self-supporting structures. Galvanizingis in good shape. Concrete footing inspection indi-cates they are in “near-original” condition.

Built in 1974, structures have been inspected by helicop-ter. No major line failures have occurred.

Uprating Analysis—Case #5Given the conservative weather assumptions (see Table2.8-10) used in calculating the rating of the existing line,the uncertainty of the predicted overload, and the mod-est magnitude by which the post-contingency loadexceeds the present rating, the use of dynamic ratingmethods appears to be worth considering.

Since system operations does not want this line takenout of service even to uprate it, noncontact or hot stickmounting of line monitors is attractive. Video sagome-ters could be installed at each end of the line, each neara substation where communications to the utility con-trol center is simplest.

The following photograph (Figure 2.8-4) illustrates theinstallation of a sag monitor on a lattice structure.

The primary advantage of this approach is that it meetsthe need for a modest increase in line rating withoutrequiring a large capital investment. Also, if the pre-dicted increase in post-contingency load does not occur,the monitor and communications equipment can bereused in another suitable installation.

The primary concerns center around the need to edu-cate system operations personnel in dealing with lineratings that are not constant. This can be challengingand, if this is the first application of dynamic ratingmethods in the utility, the necessary investment in engi-neering time and operator education should not beunderestimated.


Figure 2.8-4 A Video sagometer mounted on a lattice structure.

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2.8.5 Economic Comparison of Line Uprating Alternatives

This chapter discusses a wide variety of techniques thatallow one to increase the capacity of existing transmis-sion lines. In the preceding part of this section, test casesand methods are presented for performing a preliminaryuprating assessment, the goal of this being to identifythose methods most likely to apply to a particular lineuprating problem. Typically, while several methods canbe eliminated as yielding inadequate ratings increases, orrequiring excessive capital investment, multiple upratingoptions are likely to survive such an initial review.

In this subsection, it’s assumed that a preliminary analy-sis has been successfully completed and that the mostlikely uprating methods have been identified. The goalhere is to prepare a more detailed cost/performancecomparison of likely uprating methods. A test case willbe developed to illustrate the essential features of such adetailed analysis.

In comparing the total cost of viable uprating alterna-tives, the major cost and savings factors for each alter-native need to be determined. The point of the exerciseis to select the minimum cost uprating method thatmeets the need for safe and reliable operation, that ismost likely to meet regulatory constraints on line modi-fications, and that minimizes systemwide costs. In manycases, the lowest-cost uprating solution may not beselected because of the many noneconomic constraintson line design.

Present Worth CalculationsBecause line uprating costs can occur immediately, orover the life of the line, the total costs of each upratingmethod should be developed on a “present worth” basis.

Consider two uprating schemes, which require the sametotal amount of capital but with different annual expen-diture schedules, as shown in Table 2.8-11.

In each case the total cost of uprating is the same,$15,000, if there is no difference in the value of a dollar

at different points in time. The uprating alternativesappear to be economically equivalent. But it is clear thatthe distribution of annual costs—interest on capital andinflation—has been ignored. The concepts of presentand future worth of money are explained in many textsand will be included in the following discussions.

Line Costs and System Savings from Line UpratingWith the exception of electrical losses, and possiblyreduced maintenance from reconductoring, all of thebenefits from line uprating accrue to the power systemat large. In contrast, with the exception of certaindynamic rating methods, all of the costs associated withline uprating are specific to the line being modified.

The most significant economic benefits to be expectedfrom uprating of existing lines include:

• Reduced power generation costs by increased accessto low cost sources.

• Increased revenues from increased sales of low costpower to other utilities.

• Avoidance of litigation involving clearances and envi-ronmental effects.

• Avoidance of extensive regulatory and public hear-ings required for new lines.

• Postponement of major capital investment.

• Reduced maintenance.

• Reduced electrical losses.

The major cost components typical of line upratinginclude at least some of the following:

• Replacement and/or reinforcement of tangent/sus-pension structures.

• Replacement and/or reinforcement of tension/strainstructures.

• Purchase of new conductors.

• Stringing, sagging and clipping of new or existingconductors.

• Replacement or addition of insulators and hardware.

• Addition of wind-motion control devices.

• Purchase and installation of monitors and communi-cations.

• Installation and repair of line monitoring devices andcommunications.

• Increased maintenance associated with higher oper-ating temperatures.

• Increased cost of operator intervention to reduce lineload.

Table 2.8-11 Comparison of Two Uprating Schemes

YearUprating Method A

($)Uprating Method B

($)

0 7,000 15,000

1 2,000 0

2 2,000 0

3 2,000 0

4 2,000 0

TOTAL 15,000 15,000

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• Reduced maintenance access to heavily loaded linesand equipment.

Some of these factors—structure reinforcement, con-ductor cost, etc.—can be quite readily estimated whileothers—increased levels of maintenance, operationcomplexities, etc.—can be difficult to quantify. This dif-ficulty in estimating maintenance is particularly true forthose uprating methods with which the utility has littleor no experience.

In choosing the “best” line uprating approach, the lineengineer typically finds himself with several differentways to accomplish the same (or nearly the same) endresult. Given the high level of uncertainty in the powertransmission business today and the uncertainties aboutthe long-term cost and viability of many of the possibil-ities, the choice of uprating method cannot be solelyeconomic. Nonetheless, economic analysis helps to clar-ify the choices, and is necessary to get funds to do themodifications.

Identifying Potential Power System SavingsMany transmission line uprating projects are not justifi-able on a purely economic basis (i.e., the present worthof savings over the life of the uprated line does notexceed the present worth of construction capital andmaintenance). Considerations of safety or system reli-ability are as likely to prompt the decision to uprate aline, as is the opportunity to reduce electrical losses orto operate the transmission and generation grid at amarginally lower cost per kilowatt-hour. On “tie-lines”between systems or on radial feeds from low-cost gener-ators, however, where major savings from the purchaseof more low-cost power or increased income from thesale of same is at stake, economic justification of uprat-ing is more likely.

Savings in Generation DispatchThe potential savings in electrical losses and/orimproved economic generation dispatch associated withuprating an existing circuit by traditional means—suchas reinforcing the towers and reconductoring—must off-set the very real dollars spent in the rebuilding (typicallyin excess of $100,000 per mile, or $62,000 per km). Someof the lower-cost uprating alternatives—such as the useof dynamic thermal ratings, increased static thermal rat-ings based on weather studies, or the selective rebuildingof critical clearance spans—are more likely to proveeconomically justifiable since the capital investment isso much lower.

Dynamic thermal uprating of all lines throughout a sys-tem on the basis of weather data monitoring has beeneconomically justified in terms of reduced generation

costs in several references. The calculation of such costsavings involves load flow studies and is peculiar to eachsystem. It has been noted, however, that for increases incapacity of any single line beyond about 10%, otherlines serve to limit dispatch, and little is gained by fur-ther increases in the capacity of that particular line.Maximum improvement in economic dispatch is, rather,gained by systemwide increases in line capacity.

Reference (Nabet 1986) is typical of the more generalclaims at economic justification of uprating procedures.Under a section of the paper called Benefits, G. Nabetwrites “...the use of [systemwide] ambient temperatureadjusted [dynamic thermal] ratings ....from January 1,1979 to June 30, 1980 .... resulted in reduced off-costgeneration requirements for transmission control ...[saving] ... 976 MWHR [worth] 1.2 million [dollars].These savings reflect only those occasions in which off-cost operation was invoked.”

Reference (Hall and Deb 1987) presents a more detailedattempt at the economic justification of (again dynami-cally) uprating lines in the PG&E system. The point wasto show that by increasing the thermal ratings of all thedouble-circuit lines shown in [their] Figures 8 and 9from 800 to 1300 A, the total cost of generating powerfor loads and line losses decreased by some 18%. Theauthors do not attempt to justify the use of such a largeincrease in line ratings with dynamic ratings, nor dothey present any cost estimates for the increased opera-tion and maintenance expenses of the dynamic ratingsystem. This paper does clearly illustrate the techniqueof economic justification of line uprating.

Savings in Electrical LossesThe flow of electrical current on the phase conductorsresults in the loss of electrical energy due to conductorheating. As was noted previously in this section, theissue of whether electrical losses are included in an eco-nomic analysis of uprating can have a major impact ofthe selection of uprating method.

For example, consider a 10-mile (16-km) long, 115-kVthree-phase transmission line with Drake conductor.Assume that the current on the phases of the line is con-stant and equal to the static thermal rating of DrakeACSR conductor (995 A for a maximum allowable con-ductor temperature of 75oC without sun, 25oC ambientand a 2 ft/sec (0.6 m/sec) cross-wind). The thermalcapacity is 198 MVA.

At 75oC, the resistance of 795 kcmil (405 mm2) DrakeACSR is 0.1390 ohms/mile (0.09 ohms/km), and thetotal of losses in the three-phase conductors is 413 kWper mile (0.1390 * 9952 * 3/1000 = 413). At a power fac-

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tor of 0.95, carrying its full thermal capacity, the 115-kVline is transmitting 198 MW (0.95 * 995 * 1.732 * 115)and the electrical losses amount to 0.22% of the realpower transmitted per mile of line.

If the 115-kV line were thermally uprated to 236 MVA(1185 A per phase) by increasing the line design temper-ature to 100oC (by raising attachment points and/orretensioning the existing conductor), and if the line cur-rent again equaled its thermal rating, then the line losseswould be increased by 53%, from 413 kW/mile to 632kW/mile (256 to 392 kW/km).

Assuming a wholesale electrical power cost of $0.03 perKW-hr, the cost of electrical losses increases from$123.39 per hour of operation at the thermal limit to$189.60 per hour. Clearly, if operation of the original, oruprated, 10-mile (16-km) long line is operated at or nearits thermal limit for no more than 24 hours per year, thecost of losses is a minor consideration. If, on the otherhand, the line is operated such that its electrical load isat or near its thermal capacity for 2 hours per day, thecost of losses ($189.60 * 2 * 365 = $138,000 annually)can be a major economic consideration in uprating.

Of course, the comparison of electrical losses for variousuprating alternatives is not quite this straightforwardfor a real transmission line. The line loading varies withthe season, the weather, and the time of day. For manylines, even those that are candidates for uprating, thenormal load may be well below the thermal capacity ofthe line (approaching the thermal capacity of the lineonly under occasional contingency loadings resultingfrom emergency operation). In order to account for thevariation in line load over time, it is normally assumedthat the “peak normal load” is that which occurs undernormal operation of the transmission system. The“peak post-contingency load” is that line load thatoccurs only rarely, under emergency operation of thetransmission system. The “average load” is the averageline load over a certain period of normal operation.Since the “contingency peak load” only rarely occurs,the line losses that occur during such times will beneglected.

The line load factor (LoadF) for each of those futureyears is defined as the ratio of average to peak line loadover the year. In order to calculate the present worth ofline losses, however, one needs to know the loss factor(LossF)—the ratio of average annual electrical losses topeak losses—rather than the load factor. If the averagecurrent on a conductor over one year is 500 A, and thepeak current over the same period is 1000 A, then theload factor is 0.50. If the current is quite constant at 500

A, except for brief excursions to 1000 A, then the lossfactor for the conductor is 0.25.

In many cases, the load factor and the loss factor areoften empirically related by a formula such as:

2.8-1

Reduced Emergency ActionsIf the capacity of certain lines is increased, then the prob-ability is reduced that the system operator will be forcedto take emergency actions (e.g., “shedding” load or initi-ating “quick startup” generation). This increase in reli-ability of power supply to interruptible customers andreduced use of relatively expensive generation has a realcost that is very much a function of the particular system.

The reduction of workload for the operator also hasgenuine value to the efficient functioning of the system.Naturally, if the operator has more work to do after theuprating than before, then this should be evaluated as acost of uprating. This is particularly true for “instanta-neous” dynamic thermal rating schemes.

Postponed Capital Investment The selection of uprating method, indeed the initiationof the uprating process itself, is the result of projectedload growth. Clearly a number of unpredictable factorsare involved in the prediction both of systemwide load,and even more so of the load on any particular linewithin the system. Every utility has seen this very clearlyover the last decade as a result of large swings in fuelcosts, generation construction costs, and conservationefforts. Decreases in peak contingency loads on theorder of 20 to 30% have occurred with changes in oilprices. Such major shifts in predicted load render largecapital commitments for uprating hazardous. Similarlylarge changes in projected loading of certain lines canresult from wheeling decisions made by neighboringutilities or from additions of cogeneration.

As a result of the unpredictability of future load growth,marginal uprating methods have real economic value.They are especially attractive if they can be applied andthen supplemented or removed at a future date depend-ing upon whether the projected load growth does ordoes not occur. During the short term, such methodswould require only the minimum capital investment.During the long term, the capital investment in the linewould more closely match the needs of the transmissionsystem.

A number of marginal methods of uprating have beendiscussed. The only commercially available method thatis “portable” is some sort of weather-based dynamic

2LossF = 0.15 LoadF + 0.85 LoadF∗ ∗

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thermal rating technique. The techniques of dynamicrating and selective rebuilding of critical clearance spansare complementary and could follow one another asrequired. Conductor temperature monitors, for exam-ple, could be removed and used on another circuit if theline load did not require them in the future.

Estimating Line Uprating CostsIn comparing alternative methods of line uprating, onemust consider all of the cost components and the likeli-hood that each uprating method can meet the powersystem needs. Line uprating costs are very dependent onthe design details of the existing line. For example, if thestructures were designed to withstand much largertransverse and/or longitudinal forces than are producedby the existing conductors, reconductoring can beaccomplished without the expense of structure modifi-cation. Similarly, if the original design allowed forground clearances that greatly exceed the NESC mini-mums, it may be possible to operate the line at higherelectrical loads without any physical modification orexpense.

Structures and Foundation ModificationsModifications to existing structures should be consid-ered in a two-part process. First, consider only the tan-gent structures, assuming that angle structures will haveto be either rebuilt or replaced if the conductor diameteror tension levels are changed. Determine the cost ofmodifying the tangent structures on the line as a func-tion of the conductor diameter accounting for changesin code or loading since the line was built. Second, if theuprating cost for tangent structures appears to be rea-sonable for the required increase in thermal rating orvoltage, then consider the cost of modifying angle struc-tures and dead-ends, and do a detailed clearance studyof the line for the most economical conductor diameter.

As a rough rule of thumb, if the study of tangent struc-tures shows that necessary structure modifications canbe accomplished for less than 50% of the cost of replac-ing the existing structures with new, then a moredetailed analysis is justified.

Reconductoring Costs If the existing conductors are to be replaced, then anumber of conductor options exist. A new conductormay be bundled with the existing conductor or the exist-ing conductor can be replaced with:

• A conductor having less electrical resistance.

• A special conductor capable of higher unloaded ten-sion.

• A special conductor capable of operating at highertemperatures with reduced sag.

Bundling of new and old conductor doubles loading onthe structure. The cost of installing the second conduc-tor in either a vertical or horizontal bundle costs onlyslightly more than installing a new conductor on thesame structures. The added cost is due to the possibleneed to pre-stress the new conductor and the need towork “around” the existing conductor.

Reconductoring with a larger conductor costs roughlywhat the stringing, sagging, and clipping of new con-ductor usually costs. The old conductor may have signif-icant scrap value if it is all aluminum. In any event, if itcan be reused, the cost of this operation should bereduced accordingly.

Reconductoring with special conductors may cost some-what more than using standard conductors. There isoften a premium of 5 to 15% associated with conductorssuch as SDC or SSAC. Also the use of higher installa-tion tensions and special handling may cause a contrac-tor premium.

Operation and Maintenance CostsUprating an existing line will inevitably lead to higherelectrical loads. This can cause reduced life for conven-tional current-carrying components and/or the need forshorter inspection intervals. The use of real-time moni-tors may also increase the need for maintenance andproblem-solving where none existed before. Also,

• Dynamic rating monitors are installed in a hostileelectromagnetic environment. Though sometimesinstallable with the line in service, their removal fromcertain spans of the line can be a significant expense.It is essential that the manufacturer provides the userwith the possibility of field correction, or at leastdetection of errors, so that recalibrations can be keptto a minimum.

• Reconductoring with novel conductors may be veryattractive, but the aggressive utilization of new mate-rials and products can add to maintenance and repairactivities.

Unless engineers have extensive experience with particu-lar techniques of uprating, they should first move togain experience with a pilot project. Based on this work,one should be certain to allow for any unforeseen prob-lems that might develop years after the uprating occurs.

If line ratings are to be only marginally increased, theneed for operator intervention may increase. Dynamicratings in particular offer added complexity to the sys-tem operator, both in assessing the adequacy of thetransmission system, and in establishing contractualobligations for the transfer of power between systems.

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The operator must help to define his needs for display ofvariable thermal ratings. This need is likely to involveadditional software and display hardware in the energycontrol center.

If the interval between uprating reviews of lines is to bereduced in order to more closely match capital invest-ment to capacity needs, the operator must be closelyintegrated into the process of review and uprating deci-sions. This implies an increase in the time that the sys-tem operator is to spend in communicating hisexperience to planners and engineering personnel.

Miscellaneous Cost IssuesIf a particular method of uprating is applicable to manylines in a particular utility system, then the engineeringcost can be spread over several upratings. Otherwise, thecost of engineering time is a real consideration in mak-ing some of the more complex uprating schemes work.

Traditional uprating of lines by rebuilding with lines ofthe next higher voltage class or reconductoring withlarger standard conductors means that the transmissionsystem planner need only concern himself with certainlines at widely spaced intervals of time—at least 5 to 10years. Marginal uprating techniques imply more fre-quent and more sophisticated studies of line capacity,including the possibility of small changes in capacitythat must be reviewed for sufficiency frequently.

Dynamic thermal uprating techniques offer particularchallenges to the system planner. Standard softwaretools must be modified to consider the probabilisticaspect of thermal limits, which depend on weather and

time of day. This is a very real cost, even though it is dif-ficult to quantify.

2.8.6 Detailed Comparison of Uprating Alternatives—An Example

Consider a 10-mile (16-km) long, 115-kV transmissionline with 336.4 kcmil (172 mm2) Linnet ACSR conduc-tor installed to a final unloaded tension of 16% UTS at60°F. The wood pole H-frame structures are spacedquite uniformly at 600 ft (180 m). According to the util-ity operating this line, it is assumed that the conductorhas a summertime thermal capacity of 430 A (75oC con-ductor, 40°C air, 2 ft/sec (0.6 m/sec) cross-wind, withsun) that corresponds to a thermal line capacity of 85MVA. The sag-tension data for the original conductor isshown below in Table 2.8-12.

The existing structures are in good condition, and it ispossible to reinforce strain structures to allow anincrease in the present maximum conductor tension(6410 lbs or 28.6 kN) of up to 50% for a cost equal toless than 10% of rebuilding all structures. The transverseload capability of the existing tangent structures is suchthat the diameter of the replacement conductor can beup to 10% higher than that of the existing conductor(0.72 in., or 1.8 cm) without reinforcing or replacingtangent structures.

The suspension structure conductor attachment heightmay not easily be increased, and the existing line’sground clearances with a sag of 13.2 ft (4 m) at 75°C arebarely adequate. Therefore this maximum high-temper-ature sag may not be exceeded in any of the upratingalternatives.

Table 2.8-12 ALCOA Sag and Tension Data

ALUMINUM COMPANY OF AMERICA SAG AND TENSION DATA600 ft spans, 16% final, 75C max, w comp

Conductor LINNET 336.4 Kcmil 26/ 7 Stranding ACSRArea = 0.3070 sq in. Dia = 0.720 in. Wt = 0.463 lb/°F RTS = 14100 lb

Span = 600.0 ft NESC Heavy Load ZoneCreep is a Factor Rolled Rod


Temp Ice Wind K Weight Sag Tension Sag Tension

(°F) (in.) (psf) (lb/°F) (lb/°F) (Ft) (lb) (Ft) (lb)

0. .50 4.00 .30 1.650 12.58 5915. 11.61 6409.

-20. .00 .00 .00 .463 5.85 3564. 4.13 5047.

0. .00 .00 .00 .463 6.67 3124. 4.44 4695.

60. .00 .00 .00 .463 9.55 2186. 5.75 3626.

120. .00 .00 .00 .463 12.08 1729. 7.78 2679.

167. .00 .00 .00 .463 13.23 1579. 9.78 2133.

212. .00 .00 .00 .463 14.33 1458. 11.78 1772.

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The existing Linnet conductor is in reasonably goodcondition with an expected life of at least 20 years. It iscapable of operation at a temperature above the presentlimit of 75oC, but only if it can be operated at a highertemperature without exceeding the present sag of 13.2 ft(4 m) at 75oC.

Because the line is short, stability problems are not ofconcern. The voltage drop per mile is considerable, how-ever, with a current of 430 A, a conductor temperatureof 75°C, and a 90% power factor is:

2.8-2

Setting a 10% voltage drop as a limit during emergencyloadings, all lines of this construction, having a thermallimit of 85 MVA are voltage constrained at lengthsgreater than 35 miles (56 km). Note that as the thermalrating of the line is increased, the line length at whichthe line is voltage drop limited decreases. Thus increas-ing the thermal rating of a 25-mile (40-km) line of thisdesign to 125 MVA would make it voltage drop ratherthan thermally limited. In the present example, however,the 10-mile-long line’s rating would have to be increasedto 300 MVA before it became voltage-drop limited.

The projected growth of the peak emergency line load-ing is shown in Figure 2.8-5. Note that the thermalcapacity of the line will be exceeded by the peak contin-gency loading in 2 to 5 years for the pessimistic (1%)and the optimistic (3%) projections, respectively.

Preliminary Uprating AnalysisA preliminary uprating assessment of the line has beenperformed, as shown in this Uprating Analysis Table(Table 2.8-13). Certain uprating methods seem inappro-priate. For example, since the line is presently clearancelimited with Linnet at 75oC and the tangent structureswill not allow an increase in conductor attachmentheight, it is not possible to lift the conductor attachmentpoints in order to increase the line design temperature.Alternatively, the relatively modest increase in thermalrating and its uncertainty indicates that dynamic ratingmethods may work well.

After considering the capabilities and conventions of thetransmission owner, the following three alternativeuprating methods are identified as possible:

A. Reconductor the line with a lower resistance, trape-zoidal wire, Hawk/TW ACSR conductor, reinforcingthe strain structures. The 10% larger diameter ofHawk/TW can be accommodated by the existingstructures.

B. Install a dynamic thermal rating system based uponthe use of conductor sag-tension monitors along theline. After some period of time depending upon theline load growth rate, remove the dynamic rating sys-tem, and increase the tension of the existing Linnetconductors to allow operation at higher temperaturefor the same maximum sag.

( )

( )

100 cos sin%

3

100 430 0.328 0.90 0.336 0.436

115

3

0.286%

LL

I Rac XVoltDrop

kV

per mile

φ φ⎡ ⎤• • +⎣ ⎦=⎡ ⎤⎢ ⎥⎣ ⎦

⎡ ⎤• • • + •⎣ ⎦=⎡ ⎤⎢ ⎥⎣ ⎦

=

Figure 2.8-5 Example of projected growth of peak emergency line loading.

Table 2.8-13 Uprating Analysis Table

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C. Reconductor the line with Linnet ACSS withoutmodifying either tangent or strain structures.

Reconductoring with ACSR/TW ConductorReconductoring with 477 kcmil (243 mm2), 26/7 HawkACSR/TW conductor will yield a thermal rating of 525A (105 MVA) at 75oC and 700 A (139 MVA) at 100oCdue to the reduced resistance of Hawk/TW. Theincreased thermal capacity with Hawk/TW will be ade-quate for at least 10 years under the least-conservativeassumption of 3% annual load growth.

In order to meet the maximum sag limit of 13.2 ft (4 m)at 75oC , Hawk/TW must be installed to an initialunloaded tension of 29% UTS at 0°F (-18°C) and a cor-responding maximum tension under NESC Heavy load-ing conditions of 7750 lbs (35 kN) (21% above theexisting Linnet ACSR). If the initial unloaded tension at0°F (-18°C) is increased to 33%, the sag limit is met at100oC, but the maximum tension increases to 8310 lbs(37 kN) (30% above the present line). In either case, themaximum tension is well within the 50% increase limitin maximum tension load.

Hawk/TW has a diameter of 0.781 in. (2 cm) (8.5%greater than Linnet), so it is likely that the existing tan-gent structures will not require reinforcement.

Having established the increase in thermal capacity pos-sible by reconductoring with Hawk/TW, other substa-tion equipment limits and replacement costs need to bereviewed.

The total line construction cost (i.e., strain structuremodifications, replacement conductor, vibration damp-ers, labor cost, etc.) is a weak function of maximum ten-sion, since only strain structures need to be modified.It’s assumed that the reinforcement of strain structurescosts 5% of the structures for a new 115-kV line. It isfurther assumed that this amounts to $5,000 per mile($3k per km).

In addition to the cost of upgrading structures, the mostsignificant cost is that of the new conductor minus thescrap value of the old. Typically, one may obtain con-ductor costs and scrap value from a manufacturer. Wewill assume that the new Hawk/TW ACSR conductorcosts $2.00 per ft ($6.70 per m) and that the scrap valueof the old conductor is $0.50 per ft (1.50 per m). Recon-ductoring the line with Hawk/TW involves a total mate-rial cost of $24,000 per mile ($14,400 per km).

Other costs include stringing, sagging, and clipping thenew conductor, new hardware, and engineering designcosts. We will assume that this cost equals that of theHawk/TW material.

Finally, the present worth of electrical losses over thelife of the reconductored line should be calculated. It isassumed that the normal annual peak line load that ispresently 50 MVA will increase to 65 MVA over an esti-mated 20-year useful life of the reconductored line. It isalso assumed that the peak contingency load is 1.6 timesthe peak normal annual load of the line, and that theloss factor is 40%.

Economic Parameters for Loss Calculation

• Years of Analysis: 20 years

• Interest Rate: 8%

• Energy charge: $0.020/kW-hour

• Energy charge Escalation Rate: 7%

Using the economic data in the preceding paragraphand in Table 2.8-14, the present worth of electrical losseswith the existing Linnet conductor over the 20-yearperiod is $610k. The resistance of Hawk/TW is approxi-mately 70% (336.4/477 = 0.71) that of Linnet. Therefore,the savings in present worth of electrical losses forHawk/TW is $18k/mile ($11k/km).

During the reconductoring of the line, the system opera-tor cannot use the circuit. Construction could takemonths and higher cost generation may have to be pur-chased during this period. The cost of this loss of thecircuit could be determined by a system load flow analy-sis. The cost is primarily due to higher costs of genera-tion due to non-optimum generation dispatch duringconstruction and increased losses on other lines whoseloads increase

Table 2.8-14 summarizes the costs and savings associ-ated with reconductoring the line with Hawk/TW con-ductor.

Table 2.8-14 Summary of Cost Savings Associated with Reconductoring

Conductor Name Hawk/TW

OD (in.) 0.782

Structures $5,000/mi

Conductor $24,000/mi

Conductor labor $24,000/mi

Total construction $53,000/mi

Cost of increased losses during construc-tion ?

Savings in PW losses over 20-year life $18,000/mi

Net PW cost of line operation over 20 years (ignore losses) $53,000/mi

Net PW cost of line operation over 20 years (include losses) $35,000/mi

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Dynamic Uprating MethodIf the existing Linnet conductor is in good condition,the line rating can be increased through the installationof sag-tension monitors along the line. Many papershave dealt with these techniques.

Before doing any economic calculations, it is essentialthat one determines just how much the use of a dynamicrating method increases the thermal rating of the line.As was discussed previously, the dynamic thermal ratingof the line is both random and chronological—that is,there is a certain amount of uncertainty combined witha certain degree of predictability based on season andtime of day. Based on reference (Hall and Deb 1987), fora line in upstate New York, one may expect that thedynamic thermal rating of the 115-kV line with Linnetconductor will be:

• 10 to 20% above the static rating 50% of the time.

• Above the static rating 90% of the time.

• Below the static rating 10% of the time (usually atnight).

One must decide how to interpret these numbers interms of traditional planning criteria. One must recog-nize that the operator will have to intervene occasionallyto reduce the loading of this line during times of peakloading and minimal rating. During these times whenthe load is high and the dynamic rating is low, the sys-tem will be operated in an uneconomic mode or loadmay need to be shed. It’s assumed that operating per-sonnel feel that they can intervene during 10% of thepeak loading events without incurring significant costs.Then one may credit the dynamic rating system withincreasing the thermal rating of the line by 10%, or from85 to 94 MVA.

For a 2% annual growth rate, the peak contingency loadwill reach 94 MVA in 8 years. Therefore, one mayassume that the useful life of this dynamic ratingapproach is 8 years, after which the line must be modi-fied in some other manner to increase its thermal rating(e.g., raise structures, reconductor, etc). The installationof the dynamic rating system does nothing to reducelosses since the conductor resistance is unchanged.

It may be assumed that the dynamic rating equipmentcosts about $100,000 for a 10-mile (6.2 km) line. Themonitoring system is reusable on other lines after 8years, or earlier if the load increases more rapidly thanpredicted.

Line monitors are usually installed by bucket truck ifterrain permits. Installation expenses vary widely since

they depend on terrain and accessibility along the line.This is also true for maintenance. The monitors pres-ently available require periodic recalibration and proba-bly should be checked annually. A guess for initialinstallation cost of the line monitors might be $10,000with an annual maintenance cost of the order of $5,000.

Prior to beginning the dynamic rating of the line, onemust allow for a complete inspection of the structuresand conductor to spot bad splices and impaired clear-ances. An inspection of the 10-mile (6.2-km) line isrequired for any of the three alternatives. The use of linemonitors offers the unique advantage of establishing anexperimental basis for high-temperature clearance.

Any line outage required to install the line monitors isbrief, typically less than 24 hours. For EPRI’s video sag-ometer, no outage is needed.

Assume that at the end of 8 years the dynamic ratingmonitor system is worth 50% of its initial purchaseprice. After 8 years, the dynamic rating system will beremoved and reused elsewhere in the system. The linewould then be surveyed, certain critical spans selectedfor increase in clearance, the allowable conductor tem-perature increased, and 50 MVA of power transformercapacity added. The use of dynamic ratings would bediscontinued at this point.

It’s estimated that the cost of retensioning the existingLinnet ACSR to 20% UTS at 60°F will be equal to halfthat of installing new conductor or approximately$12,000/mile ($7,400/km). The increased everyday ten-sion will require the use of dampers costing about$2,000/mile ($1240/km). The retensioned line will thenhave a line design temperature of 100oC and a rating of575 A (115 MVA). If load growth is faster than antici-pated, then this may not be adequate, and the line willhave to be either reconductored or rebuilt.

The present worth of $14,000/mile 8 years in the futureis $10,000/mile, so the total present worth cost of thisuprating approach is $21,000/mile.

Reconductor with Linnet/ACSSLinnet/ACSS can be applied to the line without the needto rebuild or reinforce any of the structures. If the theLinnet/ACSS is installed to maximum NESC Code lim-its at 60oF, it reaches the sag limit of 13.2 ft (4 m) atabout 150oC. The line rating is, therefore, 770 A(153 MVA).

The cost of reconductoring is limited to the conductorand its installation. Given the premium typical of ACSSof $2.00 per ft ($6/m) for the conductor and an equal

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amount for stringing, sagging, and clipping it in place ofthe original Linnet, the total cost is $63,000 per mile($39k/km).

Dampers will also be required because of the high initialtension levels. Therefore, the total estimated cost is$65,000 per mile ($40k/km).

Economic Comparison of Uprating Alternatives The total present worth of construction and losses tomeet the increased thermal rating requirements of this10-mile line in the three different uprating methods aresummarized in Table 2.8-15.

Clearly, the use of dynamic ratings followed by a reten-sioning of the existing conductor (if required by actualload growth) is the most flexible approach, and requiresthe least initial and total capital investment. The majordrawbacks involve the need to modify standard operat-ing procedures to utilize real-time ratings and the mod-est rating increase that results.

The use of ACSS requires an absolute minimum ofstructure reinforcement since Linnet/ACSS has the samediameter as the original Linnet ACSR and yieldsreduced maximum tension because of its reduced modu-lus. There is no reduction in electrical losses since theLinnet/ACSS has nearly the same resistance as the orig-inal Linnet. In pursuing other alternatives, it is likelythat an ACSS/TW conductor with a slightly largerdiameter than Linnet would be a better choice.

The uprating option requiring the largest capital invest-ment is the reinforcement of strain structures and theaggressive use of vibration dampers in order to recon-ductor the line with Hawk/TW ACSR. This option isunique in that it reduces electrical losses as well asincreasing the line rating.

Review of other line uprating options and refinement ofthese three is clearly worthwhile. The means for identify-ing other possible uprating options and selecting themost appropriate has been presented in the precedingnotes.

2.8.7 Conclusions

The impetus for line uprating comes as a result powersystem analysis. Present electrical loads are projectedinto the future, and the impact of various componentoutages (i.e., contingencies) on the electrical loading ofthe existing line is determined. Specific probabilities areseldom associated with post-contingency loadings, andeven the prediction of normal loads is often uncertain,particularly with the advent of “open access” to com-mercial power generators.

For uprating to be possible, the existing line must be ingood condition. Having established this, the identifica-tion of possible uprating methods depends upon thephysical, electrical, and thermal characteristics of theexisting line. An “Uprating Analysis Table” is developedhere that simplifies the analysis of the existing line andprovides a basis for identifying promising upratingmethods in each specific line. Once the most promisinguprating methods have been identified, a detailed analy-sis comparing the costs and capabilities of each methodis required.

The final selection of an uprating method and its suc-cess in providing the necessary increase in line capacitywhile maintaining system reliability and minimizingcapital cost involves a good deal of engineering judg-ment, as well as the application of suitable numericaltools.

Table 2.8-15 Present Worth of Three Uprating Options

Option A1 – Reinforcing strain structures, adding dampers, and reconductoring with Hawk/TW for a line design temperature of 100oC.

$53,000/mile (ignoring losses)

Option A2 – Same as A1 but include loss savings

$35,000/mile (allowing for loss savings)

Option B – Apply dynamic rating monitors and retension existing Linnet ACSR if pre-dicted load growth requires it.

$20,900/mile

Option C – Reconductor with Linnet/ACSS and go to a line design temperature of 125oC.

$65,000/mile

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CHAPTER 3 Underground Cables

3.1 INTRODUCTION

Many factors need to be considered when evaluating uprating and upgrading options forunderground transmission cables. Chapter 3 provides a general description of conceptsthat a utility engineer should consider in understanding underground power cables andselecting uprating technologies that are appropriate. While this chapter focuses on trans-mission, many of the concepts are equally valid for distribution cables, although the cost-benefit ratio of applying these techniques to distribution is less easy to justify.

Chapter 3 includes nine sections:

• Section 3.2, Cable System Types, provides an overview on underground cable systemsand a very brief background on each of the major transmission cable types.

• Section 3.3, Power Flow Limits and System Considerations, considers aspects external toa specific cable circuit that may limit power flow regardless of the cable circuit’s rating.

• Section 3.4, Underground Cable Ratings, provides an overview of cable system ampac-ity, including worked examples, to understand the basic approach to calculating ratingsand the areas where uprating or upgrading could be applied.

• Section 3.5, Uprating and Upgrading Constraints, lists some of the major barriers touprating that are inherent to each cable system type or installation location.

• Section 3.6, Increasing the Ampacity of Underground Cable, is the major focus of thischapter, describing how to increase capacity on existing circuits. Other sections of thechapter have been provided to support this chapter.

• Section 3.7, Reconductoring (Upgrading), discusses topics related to replacing cables toincrease capacity, possibly combined with other uprating considerations.

• Section 3.8, Dynamic Ratings of Underground Cable Systems, includes information onthe state-of-the-art methods used for optimizing the rating on a cable system, includingtopics on real-time monitoring and ratings.

• Section 3.9, Case Studies for Underground Cable Circuits, describes real-world upratingapplications that have been implemented by utility-users, along with their respectiveexperiences.

• Section 3.10, Summary of Uprating and Upgrading Approaches and Economic Fac-tors, lists the various uprating and upgrading approaches with qualitative comparisonsof each concept.

While readers of this chapter are encouraged to have a background in underground cablesystems, the various sections provide a general overview so that those readers who areunfamiliar with underground technologies may also come away with an understandingand be able to utilize some of the technologies discussed on their own cable systems.Readers are also encouraged to review appropriate industry standards and guides from

3-1

Chapter 3: Underground Cables Increased Power Flow Guidebook

the Institute of Electrical and Electronics Engineers(IEEE), Association of Edison Illuminating Companies(AEIC), International Electrotechnical Commission(IEC), Insulated Cable Engineers Association (ICEA)and others. In addition to providing valuable back-ground on cable manufacturing, rating and installationpractices, these documents also include supportinginformation about testing (type, routine and commis-sioning) that may be done in conjunction with upratingactivities.

3.2 CABLE SYSTEM TYPES

Underground transmission is often used to transferpower where overhead lines are impractical. Issues thataffect the selection of underground cables vary but aregenerally focused around reduced rights-of-way require-ments, aesthetics, and minimizing the environmentalimpact associated with installing transmission systems.

There are three major types of cables systems:

• High-pressure fluid-filled (HPFF) or gas-filled(HPGF), pipe-type

• Extruded dielectric (XD), including cross-linkedpolyethylene (XLPE) and ethylene-propylene-rubber(EPR) cable types

• Self-contained liquid-filled (SCLF) or self-containedoil-filled (SCOF)

When evaluating uprating and upgrading strategies forunderground cable systems, it is first important to con-sider the unique characteristics of each of these cablesystem types. This section describes the constructionfeatures and operational characteristics of each cablesystem.

3.2.1 High-Pressure Pipe-Type (Fluid- and Gas-Filled)

Cable ConstructionPipe-type cables incorporate three cable phases installedin a common steel pipe (see Figure 3.2-1). Each cablephase consists of a stranded copper or aluminum con-ductor, with a layer of metallic (steel or copper) bindertapes intercalated with a carbonized black paper tape.Larger conductors above 800 mm2 (1500 kcmil) may besegmented to reduce ac resistance, and hence reduce aclosses. Over the conductor shield is a laminated Kraftpaper or, for higher voltages, a laminated paper-polypropylene insulation. The insulation thickness isgoverned by voltage. Typical AEIC insulation thick-nesses are listed in Table 3.2-1.

The insulation wall thickness is important when evalu-ating reconductoring options or for considering the freearea within the pipe for circulating dielectric liquid.These concepts are discussed in Section 3.7.

Table 3.2-1 Typical Pipe Cable Insulation Thicknesses

Rated kV Phase-to-Phase Size of Conductors Insulation Thickness

(kcmil) (mm2)

Laminated Paper Polypropylenea mils

(mm)

a. Large conductor sizes using laminated paper polypropylene insulation may require increased insulation wall thicknesses to control the minimum electrical stress to 1750 volts/mil (68.9 kV/mm) so as not to exceed the design limits of terminals and splices.

Papermils (mm)

69 167.8-4000 85 – 2027 n.a.270 (6.86)

300b (7.62b)

115 350-750800-4000

177-380405-2027

250 (6.35)250 (6.35)

420 (10.67)375 (9.53)

485b (12.32b)

120 350-750800-4000

177-380405-2,027 n.a. 435 (11.05)

405 (10.29)

138500-900

1000-4000253-456507-2027

300 (7.62)270 (6.86)

490 (12.45)440 (11.18)

585b (14.86b)

161 759-9001000-4000

380-456507-2027 n.a. 575 (14.61)

515 (13.08)

230 1000-20002250-4000

507-10131140-2027 450 (11.43) 745 (18.92)

605 (15.37)

345 1000-12501500-4000

507-633760-2027 600 (15.24)

1020 (25.91)905 (22.99)

500 2000-4000 1013-2027 745 (18.92) 1100 (27.94)

765 2000-4000 1013-2027 1200 (30.48) n.a.

b. High-pressure gas-filled (HPGF) cable insulation thicknesses.

3-2

Increased Power Flow Guidebook Chapter 3: Underground Cables

Over the insulation, it is common to see one or two met-alized Mylar tapes applied over a carbonized blackpaper tape. The Mylar tape acts as a moisture seal tolimit insulation contamination and dielectric liquiddrainage prior to installation. Metal shield tapes arethen applied over the Mylar tape. Over the shield andmoisture barrier tapes is one or two helical metal skidwires, typically constructed of stainless steel, zinc, brass,or bronze. The skid wires provide mechanical protectionwhen the three cables are pulled into the installed cablepipe. On a few cable designs, a plastic “compressionjacket” is applied over the insulation shield (more oftenon HPGF cables than HPFF cables) to limit the insula-tion impregnate from draining from the insulation andmixing with the dielectric media within the cable pipe.

Cable PipeThe pipe is generally ASTM A-523 Schedule 20 or 40line pipe, 6.35 mm (¼-in.) wall with flared ends to facili-tate welding with chill rings. A cable trench is excavatedfor the installation of the cable pipe. Typically, the trenchis usually backfilled with “thermal sand” or a FluidizedThermal Backfill (FTB) that helps ensure good heattransfer away from the cable pipes (Figure 3.2-2).

JointsPipe cables may be 32 km (20 miles) long, but mostinstallations are only a few kilometers (miles). Installa-tion sections are on the order of 350-1000 m (1200-3300 ft) and require manholes and joints to connectcable sections. Cable pipes enter both ends of the man-hole to facilitate joining the cables. Inside manholes,section casing lengths of 1-1.5 m (3-5 ft)— generally 1.5-3 times the cable pipe diameter—are used to connectpipe sections. Inside the casing, each cable phase isjoined together using a compression connector andhand-applied paper or laminated-paper-polypropylenetapes. Joints may be one of three types:

• Normal Joint. The cable conductors are connectedthrough the casing, and hydraulic continuity is per-mitted (see Figure 3.2-3).

• Semi-Stop Joint. The cable conductors are connectedthrough the casing and hydraulic flow is stopped fordifferential pressures below 350 kPa (50 psi). Valvesmay allow complete hydraulic isolation from one sideof the joint to the other.

Figure 3.2-1 Example of high-pressure fluid-filled (HPFF) pipe-type cable.

Figure 3.2-2 Pipe-type cable trench being backfilled with FTB.

Figure 3.2-3 Pipe-type cable manhole with joint casing.

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• Full Stop Joint. The cable conductors are connectedthrough the casing, but there is no hydraulic continu-ity as the full stop joint supports rated line pressuredifferential.

Terminations (Potheads)The ends of a pipe-type circuit are terminated with agraded insulation that controls electrical stress from thepaper-insulated cable to the air-insulated terminal. A“cone” of insulation is applied within a porcelain termi-nation to provide hydraulic and electrical isolation forthe cable end. Leading up to the terminations, the threecables within the common cable pipe are separated intoindividual stainless steel pipes through a trifurcatingjoint (see Figure 3.2-4). Nonmagnetic stainless steelpipes are used between the trifurcating joint and the ter-mination to avoid the high circulating currents and eddycurrent heating that would otherwise result if conven-tional carbon steel pipe were used. Stand-off insulatorsare used at the base of the potheads to isolate the pot-head from the support structure so that circulating cur-rents are not induced in the riser pipes between thetrifurcator joint and pothead.

Fluid-Filled CablesHigh-pressure fluid-filled (HPFF, also known as high-pressure oil-filled) cables are installed in cable pipeswhere the pipe is filled with very clean, very low mois-

ture dielectric fluid. Older HPFF cable systems (before1970) typically used mineral oil for the pipe fillingdielectric fluid. HPFF cable systems installed after 1970have used alkyl benzene or polybutene dielectric fluid(polybiphenyl chlorine-based liquids were never used asan insulating liquid in pipe cables). The dielectric fluid ispressurized to 1400 kPa (200 psi) and is generally free tomix with the insulation impregnant, although thismovement is limited.

Gas-Filled CablesHigh-pressure gas-filled (HPGF) cables use pressurizeddry nitrogen gas inside the cable pipe. HPGF cables stillutilize dielectric-fluid impregnated into paper insulatingtapes as insulation, but the dielectric fluid is generally ofa much higher viscosity than fluid-filled cables to limitdrainage. Also, the insulation thickness on HPGFcables is slightly greater than in HPFF cables as shownin Table 3.2-1. Nitrogen pressure is typically on theorder of 1400 kPa (200 psig). Bottled nitrogen and apressure regulator located near the terminal ends areused to maintain the pressure within the cable pipe.Low-pressure alarms are utilized to ensure that thecable pipes are maintained at the required pressure toavoid damaging the pipe cable.

Other Equipment

Pumping PlantsAs was mentioned above, pipe-type cables are pressur-ized with either dry nitrogen or dielectric liquid. For theliquid-filled cables, a “pumping plant” or “pressuriza-tion plant” is needed to maintain and regulate the typi-cally 1400 kPa (200 psi) pressure within the cable pipe(Figure 3.2-5).

Cathodic Protection EquipmentThe carbon steel pipe must be protected from corrosionto avoid leaks and deterioration of the pipe. The firstlevel of protection is a corrosion protection layer that isapplied over the outside of the pipe. Older cable systemsused a hot applied tar coating or a somastic coating thatis similar to concrete. More recent HPFF cable systemsuse pipe that is coated with a polymeric material such ashigh-density polyethylene. These corrosion protectioncoatings are effective in preventing corrosion if there areno holes (“holidays”) or cracks in the coatings. How-ever, some damage inevitably occurs to the pipe coatingduring installation or subsequent digging after the cablesystem has been placed in service. Consequently, it isnecessary to further protect the cable pipe withimpressed current cathodic protection systems or sacri-ficial anodes.

Some HPFF cable system pipes are corrosion protectedwith magnesium sacrificial anodes that are connected to

Figure 3.2-4 Above ground trifurcator (spreader head) and pipe-type cable potheads.

3-4


the pipe at manhole locations as well as at the substa-tions where the cable terminations are located.

Impressed current cathode protection systems must pro-vide enough current to maintain the cable pipe at apotential of –1.0 volt dc (or in some cases higher) withrespect to the surrounding earth. The impressed cur-rent/pipe grounding system must also be designed toaccommodate the maximum line-to-ground fault cur-rent while keeping the pipe potential close to groundpotential.

Several types of impressed current systems have beenused to cathodically protect and ground the cable pipe.These are:

Resistor/Rectifier Cathodic Protection. In this type ofcathodic protection system, the ends of the pipe aregrounded through low resistance connections (severalmilliohms), and a relatively high-capacity dc currentsupply forces enough current through the resistor tomaintain the dc pipe potential at approximately -0.85 to-1.0 V.

Polarization Cells with Rectifiers. In this type of cathodicprotection system, a passive device called a polarization

cell is used to ground the cable pipe at the end pointsubstations. A polarization cell, which is about the sizeof a car battery, is characterized by a relatively highresistance to dc voltages of several volts and a low resis-tance to ac currents. A relatively low-capacity dc recti-fier then supplies enough current to the pipe to maintainthe pipe potential at -0.85 to -1.0 V.

Solid-State Pipe Grounding Devices with Rectifiers. Themost recent development for pipe cathodic protectionincludes power electronic devices that are capable ofconducting line-to-ground fault currents. These devicesare direct replacements for the polarization cellsdescribed above.

3.2.2 Extruded Dielectric

Cable ConstructionExtruded dielectric cables are so named because the insu-lation is extruded onto the conductor core (Figure 3.2-6),as compared to paper-insulated cables (HPFF or SCFF),where the insulation is a laminar application of paper.The cables consist of a stranded copper or aluminumconductor. Larger conductors above 800 mm2 (1500kcmil) may be segmented to reduce ac impedance, and

Figure 3.2-5 Pumping plant pressure charts and control system (left) and fluid reservoir (right).

3-5


hence reduce ac losses. The typical extruded insulationtypes are as follows:

• Cross-linked Polyethylene (XLPE). This cable insula-tion is the most common on modern XD cable sys-tems with applications up to 500 kV. The insulation iscross-linked (vulcanized), forming long polymerchains that are joined to one another at intermediatecarbon atoms. XLPE cable manufacturing isextremely sensitive to cleanliness and quality controlduring the manufacturing process. “True triple extru-sion” process, where the conductor shield, insulation,and insulation shield are extruded together, is thestandard extrusion process. This ensures that there isgood adhesion between the insulation-shield bound-aries and limits the likelihood that contaminants getinto the insulation. XLPE insulation is extremely sen-sitive to the presence of moisture or water, whichcould lead to water and electrical trees.

• Ethylene-Propylene-Rubber (EPR). This insulationtype is often considered for distribution cables andtransmission cables up to 138 kV. The insulation isvery “lossy” as compared to XLPE insulation, result-ing in high dielectric losses and charging current. Forthis reason, EPR insulation is rarely considered forhigher voltage cable systems. The insulation materialis relatively forgiving about operation in the presenceof water, so that the cable may not include a hermeticmoisture barrier like the one required on XLPEcables.

• Linear Low or Medium Density Polyethylene (LLPE,MDPE). This insulation type is less common for newinstallations, although there are several installations,

predominantly in France. As compared to XLPEinsulation, LLPE and MDPE were first used at thehigher voltage levels because the extrudate could beraised to higher temperatures without forming cross-linking agents present. This permitted filtering theextrudate at higher temperatures with finer-grademesh screens. The disadvantage is that the maximumnormal operating temperature for cables with LLPEand MDPE is much lower, limiting the power trans-fer for a given conductor size as compared to an oth-erwise similar XLPE cable.

Typical insulation thicknesses for extruded insulationare summarized in Table 3.2-2.

After the conductor and insulation shields and insula-tion are applied, the outer layers of an extruded cablevary depending on the application. All XLPE cablesand most other extruded transmission cables have sometype of metallic sheath consisting of a lead extrusion,corrugated copper, aluminum or stainless steel, or cop-per or aluminum foil laminate. There may be additionalcopper or aluminum wires applied under the moisturebarrier for additional fault current capability. Over themetallic moisture barrier is typically an extruded insu-lating jacket of linear low, medium, or high-densitypolyethylene. The jacket electrically isolates the metallicmoisture barrier to control circulating currents andinsulate to induced voltages. The jacket also providescorrosion protection. Extruded dielectric cables do notutilize any dielectric liquid, which has increased the useof this cable type as it represents a low-maintenancecable system with minimal potential for environmentalimpact.

Installation ConsiderationsMost extruded transmission cables are manufactured assingle phases that are connected into three-phase sys-tems (there are three-core extruded cables that may beused for transmission voltages, but these are less com-mon). The cable phases may be installed directly buriedin the ground or pulled into conduits. Direct buriedinstallations are generally less expensive and haveslightly better ampacity capability for a given conductorsize, but require that the trench for an entire installationsection be open, which is generally not possible withurban installations. Duct bank installations are installedin similar manners as pipe-type cables in that the con-duit system is installed first and backfilled with concrete,thermal sand, or Fluidized Thermal Backfill (FTB)(Figure 3.2-7). The cables are then pulled into the con-duits later. The cost for duct bank installations is nor-mally greater than direct buried, both for materials andinstallation, but later changes to the cable system do notrequire surface excavation.

Figure 3.2-6 Example extruded dielectric (XLPE) transmission cable.

3-6


Extruded dielectric cables may also be installed underwater. The submarine installations often utilize astranded armor around the outside of the cables but areotherwise similar in construction to land cables.

JointsAs with pipe-type cables, extruded cables are typicallyinstalled in sections of 300–850 m (1000-2800 ft) thatmust be joined together. For direct buried systems, thejoints may be directly buried and backfilled withthermal sand. Duct bank installations utilize manholessimilar to pipe-type cables. Older joint technology forXLPE cables utilized “field-molded” joints whereunvulcanized polyethylene tapes were applied around aconnector and cables and then heated and vulcanized

using specialized equipment. This approach requiredadditional time and was more sensitive to workmanshipthan the present technology that utilizes “pre-fabricated” joints where the cable ends are inserted intothe factory-molded joint (Figure 3.2-8).

Each cable phase is joined separately. Depending on thesheath bonding scheme (single-point bonded, cross-bonded, or multi-point bonded—see Section 3.6.8 for a

Table 3.2-2 Typical Extruded Cable Insulation Thicknesses

Rated kV Phase-to-Phase

Size of Conductors Insulation Thickness

(kcmil) (mm2)XLPE

mils (mm)LLPE

mils (mm)EPR

mils (mm)

63-70 500-2000 253-1013 650 (16.5)a

433 (11.0)b

a. AEIC CS7-1993 “full wall” insulation thicknesses.

b. Typical minimum insulation thicknesses used on commercial cable.

650 (16.5)433 (11.0) 650 (16.5)

110-120 4744,000

2402000

800 (20.3)a

620 (15.7)b709 (18)630 (16) 800 (20.3)

132-138 750-3000 380-1520 850 (21.6)a

650 (16.5)b 850 (21.6)

150-161 5923,947

3002000

24.521.2

19.519.5

220-230 7893,947

4002,000

906 (23)c

866 (22)906 (23)866 (22)

330-400 1243-2368 630-1200 1063 (27) 1063 (27)

500 2000-4000 1013-2027 1260 (32) 1260 (32)

c. Initial applications of 230-kV XLPE cable in North America used insulation thicknesses of approximately 29-mm (1142 mils).

Figure 3.2-7 Duct bank installation for extruded dielectric cables. Figure 3.2-8 Factory pre-molded joint for XLPE cable

(“Click-Fit” joint from Pirelli).

3-7


detailed discussion), the joint may have sheath inter-rupts built into the joint. This allows electrical isolationof the sheath from one side of the joint to the other andpermits transpositions of sheath connections in a cross-bonding link box or connection of the ungroundedsheath end to a sheath voltage limiter.

The cable joints are often placed on racks on the sides ofthe manhole and mechanically supported so that thejoint does not move as a result of thermal-mechanicalbending. One distinction between pipe-type cable man-holes and manholes for other cable types is that parallelpipe circuits may pass through the same manhole whileXLPE cables typically have individual manholes for eachcircuit unless all the XLPE circuits connect to a com-mon bus at the terminals (e.g., as shown for the manholein Figure 3.2-9). Pipe circuits can pass through a com-mon manhole since utilities generally allow work on onepipe circuit while a parallel circuit is still energized.Extruded cables, lacking the robust steel cable pipe andjoint casing, are generally not operated this way both forconcerns about faults and the possibility of inducedvoltages and currents from nearby parallel circuits.

TerminationsTerminations (terminators) provide a means of gradingthe high electrical stress in the cable insulation to an air-insulation where the cable is connected to other equip-ment (Figure 3.2-10). Most termination designs forextruded dielectric transmission cables utilize a smallamount (200–400 liters, 50–100 gallons) of silicone oil.The metallic and semiconducting shields are removedfrom the outside of the insulation, and the insulation issanded smooth prior to installing a stress cone and plac-ing a polymer or porcelain termination housing over theprepared cable end.

The terminations typically have polymer or porcelainstand-off insulators that isolate the base plate from the

support structure. For cable systems with cross-bondedor single-point bonded sheaths, the stand-off insulatorscontrol circulating currents. During maintenance, thestand-off insulators allow the cable jacket to undergo a10-kV dc test to insure cable jacket integrity.

3.2.3 Self-Contained Liquid-Filled (SCLF)

Cable ConstructionSelf-contained liquid-filled (SCLF) (also known as self-contained oil-filled [SCOF] or low-pressure oil-filled[LPOF]) cables utilize the dielectric liquid-impregnatedlaminated-paper insulation similar to pipe-type cables,but three separate cables are installed for the threephases. The cable is called “fluid-filled” because there isa hollow fluid channel in the center of the conductorthat allows dielectric liquid to move through the cablewith thermal expansion and contraction (Figure3.2-11). As compared to pipe-type cables, the SCLFcable typically operates at a lower pressure of 105–525 kPa (15–75 psi). Two different methods are used toconstruct the stranded hollow conductors. Smaller con-ductors typically consist of a helical steel support for thefluid channel, over which is applied the conductor

Figure 3.2-9 Extruded dielectric cable manhole.Figure 3.2-10 Termination for a 145-kV class extruded dielectric cable.

3-8


strands (usually copper but may be aluminum). Largerconductors are manufactured by using “keystone”shaped copper strands to form the fluid channel, andthe helically-applied round strands are then applied overthe first layer of formed strands. Large conductors (i.e.,1000 mm2 or larger) are typically assembled with 4, 5, or6 segments that are brought together around the fluidchannel. For larger conductor sizes, a binder tape (met-allized paper tape, carbon black tape, or copper or steeltape) is applied around the outside of the high-voltageconductors to maintain the circular construction, par-ticularly around segmented conductors. A carbonizedblack paper tape may be intercalated with the bindertape for a conductor shield. Many layers of insulatingtapes are then wound around the cable conductor usinga tape “lapping” machine in a low-humidity environ-ment (see Figure 3.2-12). Both conventional celluloseand laminated paper polypropylene (LPP) tapes areused to insulate SCLF cables. The cable cores are thenimpregnated with low-viscosity dielectric liquid, such asalkyl- or dodecyl-benzene. Over the insulation, carbonblack paper tapes and metallic shield tapes are applied.A metallic sheath is then applied around the outside ofthe cable core to facilitate pressurization of the cablesystem and to exclude moisture. The cable sheaths aretypically tubular lead or corrugated aluminum or cop-per. In some cases, lead sheaths must be reinforced withnonmagnetic metal tapes to withstand the cable fluidpressure.

On some SCLF submarine cables, a concentric copperconductor may be installed to reduce induced sheathcurrent and armor wire losses. This is common on sub-marine cables where there may be large phase spacing,resulting in induced currents that approach the magni-tude of the phase currents. An insulating plastic jacket,

similar to extruded cables, is applied over the metallicsheath.

Installation ConsiderationsSCLF cables are typically installed directly buried orsuspended from the walls of underground tunnels, par-ticularly in Europe and Asia. Concrete-encased ductbank installations have been the most common installa-tion method used in North America. SCLF cables arefrequently used for submarine cable installationsbecause SCFF cables can be manufactured in longlengths (greater than 15 km or 9 miles) without factoryor field joints.

One of the significant differences between the installa-tion of SCLF cables and other types of transmissioncables is that dielectric fluid pressure must be maintainedat all times. The cables are shipped from the factory onreels with integral pressure reservoirs to maintain thefluid pressure during shipment and storage.

JointsSCLF cable joints are, in general, more complicatedthan joints for other cable types. Two different types ofjoints are required for most SCLF transmission cablecircuits that have elevation differences greater than150 m (500 ft) or that are longer than 5 km (3 miles) inlength.

The normal, or straight-through, joint is designed toelectrically connect the conductor between two adjacentcable sections and to provide hydraulic continuitybetween the two cable sections. The splice casing mustalso act as a pressure vessel and in some cases electri-

Figure 3.2-11 Example self-contained liquid-filled cable.

Figure 3.2-12 SCLF tape lapping machine for paper cable.

3-9


cally isolate the metallic cable sheaths to eliminateinduced sheath currents.

Stop joints are designed to withstand dielectric fluidpressure between the two sides of the joint in order tohydraulically isolate adjacent cable sections. In this case,the joints are fitted with hydraulic connections tonearby fluid pressurization reservoirs.

The installation of SCLF cable joints requires a highlevel of skill by the cable jointer (Figure 3.2-13). Thesespecial skills include tape lapping and conductor joining(while maintaining a continuous flow of dielectric fluid).Lead wiping of the joint casing to the cable sheath alsorequires special skills.

TerminationsSCLF cable terminations require the installation of animpregnated paper stress cone similar to that of HPFFcables to maintain acceptable electrical stresses at thepoint where the cable insulation shield is terminated.

The terminations typically have epoxy or porcelainstand-off insulators that isolate the base plate from thesupport structure. For cable systems with cross-bondedor single-point bonded sheaths, the stand-off insulatorscontrol circulating currents. During maintenance, thestand-off insulators allow the cable jacket to undergo a10-kV dc test to ensure cable jacket integrity.

Other Equipment

Fluid ReservoirsSCLF cables commonly utilize fluid reservoirs on oneor both ends of the circuit and sometimes at intermedi-ate locations along the cable route. Pumping plants orpressurization plants similar to pipe-type systems arealso used for very large installations. The fluid reservoirsconsist of a nitrogen-pressurized bladder that expandsor compresses against a sealed dielectric liquid con-tainer, allowing the dielectric liquid in the cables toexpand and contract with load cycling. Reservoirs forSCLF cables are sometimes gravity fed, as shown in Fig-ure 3.2-14.

3.2.4 Other Cable Types

There are other cable types, but most are less commonfor transmission applications than pipe-type, extrudeddielectric, or self-contained.

Mass Impregnated (MI) or Paper Insulated Lead Cov-ered (PILC) cables are sometimes used up to 69 kV forac systems, although they are not that common at this

Figure 3.2-13 Jointing a self-contained liquid-filled cable. Figure 3.2-14 SCLF fluid reservoirs.

3-10


voltage. Uprating approaches would be somewhat simi-lar to those of extruded or self-contained cables. Thesecables have paper tapes that are impregnated with ahigh-viscosity dielectric fluid. They do not have externalpressurization systems, as in the case of HPFF or SCLFcable systems. MI cables are used for ac applications butare more common for HVDC submarine applicationswhere there may be a significant change in elevationalong the cable route that would otherwise be compli-cated by hydrostatic head pressures. A moisture barrieron the outside of the MI cable prevents moisture ingress.

Compressed Gas Insulated Transmission (CGIT) lineshave many similarities to isolated phase bus or gas insu-lated substation (GIS) equipment. A system of SF6 gasand epoxy insulators are used to insulate a hollow, rigidaluminum conductor from a tubular aluminum enclo-sure. Factory-assembled elbows are required to accom-modate turns in the cable route, and sections withbellows in the enclosure are required to accommodateexpansion and contraction. A CGIT bus is generally notburied because the aluminum enclosure is highly suscep-tible to corrosion, although some manufacturers in theearly 21st century are promoting an insulated enclosurefor buried applications. The most common applicationsfor CGIT lines are situations where very high ampaci-ties are required (i.e., > 2000 A), usually to connect withoverhead lines entering a station or as a high-capacitybus within a station.

3.3 POWER FLOW LIMITS AND SYSTEM CONSIDERATIONS

Generally, this section considers methods to improvethe thermal capacity, and therefore the rating, of under-ground cable systems. However, transmission circuitsmay be limited by factors external to the cable circuitbeing considered. Specifically, system considerationsmay not allow a cable circuit to be fully loaded to itsthermal capacity. This section describes these factors.

3.3.1 Thermal, Stability, and Surge Impedance Loading Limits

Transmission circuits, in general, may be constrainedbased upon one of three limits—thermal, stability, andsurge impedance loading—each of which is summarizedin the sections that follow.

Thermal LimitsAll transmission cables are limited by thermal consider-ations. “Weak link” analysis applies to undergroundcable ratings where the section of cable that has theworst thermal conditions limits the overall circuitcapacity. The causes of these thermal limits will be dis-cussed in more detail in Section 3.4.5. Sections of the

route that result in the cable having a higher operatingtemperature for a given load condition will limit theoverall line capacity. These limits may result fromgreater soil thermal resistivity, deeper burial depth,higher ambient soil temperature, or possibly mutualheating from multiple cables in the same trench or otherexternal heat sources. Conceivably, conditions along afew meters of cable may limit the rating for several kilo-meters of an underground line.

Cables also have much higher charging current per unitlength as compared to overhead lines, and the chargingcurrent must pass through the conductor. Although thecable charging current is 90° out of phase from the cur-rent for real power transfer, it significantly reduces theamount of real power that may flow through the cableconductor for some underground lines. The cable charg-ing current per unit length is given by Equation 3.3-1.

3.3-1Where:f is the power frequency. C is the capacitance in Farads per meter.E0 is the line-to-ground voltage. ε is the dielectric constant.

The natural log term contains the insulation and con-ductor shield diameters.

In determining the allowable real power transfer for acable circuit, the square of the capacitive current (leadsthe real current by 90°) is subtracted from the square ofthe maximum allowable current (e.g., the normal ratingor “ampacity”), as described in Equation 3.3-2.

3.3-2

Cable circuits are always limited by thermal constraints,which is generally consistent with overhead lines thatare less than 80 km (50 miles) in length. Although eco-nomic considerations constrain the lengths for under-ground cables, the maximum length ac cable circuitsbetween shunt compensation reactors are technicallylimited by the charging current. The charging currentincreases proportionally with length and representsactual amperes that flow through the cable.

Figure 3.3-1 shows the magnitude of the charging cur-rent for cable circuits with the charging from one endand from both ends of the line.

]Amperes[10ln182

2 900arg

−×=CONDUCTOR

INSULATION

DDingCh

EffCE = I

εππ

Amperes][2arg

2Re ingChMaximumal III −=

3-11


As the length of the underground line is increased, apoint is reached where the total charging current equalsthe cable ampacity. This occurs at what is called the“critical length” of the cables, where no real power maybe transferred without overloading the cable circuit. Thecritical length can be calculated from Equation 3.3-3.

3.3-3Where:INormal is equal to the normal ampacity. ICharging is equal to the charging current per meter.

It is obvious that the maximum feasible line length mustbe significantly less than the critical length in order totransmit reasonable amounts of real power. However,the concept of critical line length quantifies the absolutemaximum lengths between shunt compensation that canbe achieved for different types of underground cables.Table 3.3-1 shows critical line lengths based on typicalinsulation thicknesses and parameters.

In real situations, economic considerations, rather thanthe critical length considerations, limit the constructionlength for most land cables. However, charging currentlimitations have been a significant factor for long sub-marine cable circuits. In these cases, owners sometimesconsider using HVDC cables where there are only resis-

tive losses to consider and the cost of the HVDC valvesand convertor stations is more easily justified relative tothe cable cost. In some other cases, shunt compensationreactors were installed on intermediate islands.

Note that reactive compensation can mitigate cablecharging current effects on the system to which thecables are connected, but the charging current still flowsin the cables, potentially limiting the real power transfer.It is common practice to install shunt reactors at one orboth ends of relatively long underground transmissionlines to mitigate the effects of cable-generated chargingcurrent on the power system. The amount of shunt com-pensation depends upon the ability of the power systemto “absorb” the reactive MVARs generated by the cablesduring light load conditions. The amount of leadingreactive MVARs that generation units can absorb isgenerally less that the amount of lagging MVARs thatthey can generate. During normal and peak load condi-tions, the leading MVARs generated by the cable capac-itance are typically offset by lagging power factor loads.Consequently, high-voltage load-switching devices (i.e.,circuit switchers) are typically used to disconnect shuntcompensation reactors during periods of relatively highload. The reactors are then connected to the power sys-tem during periods of light load. The reduction of trans-mission system losses is another consideration in sizingshunt compensation reactors for underground transmis-

Figure 3.3-1 Charging current magnitude profile.

[Meters]Length Criticalarg ingCh

Normal

II

=

Table 3.3-1 Critical Lengths for Underground Cable Circuits with Typical Insulation Thicknessesa

a. Assuming 3158 kcmil (1600 mm2) segmental copper con-ductor.

Voltage Kraft Paper

Laminated Paper

Polypropy-lene

Cross-Linked

Polyethyl-ene

Ethylene-Propylene-

Rubber

Critical Lengths, miles (km)

69 kV 63 (101) n.a.b

b. Laminated paper-polypropylene is not generally used for voltages below 161 kV.

163 (262) 120 (193)

115 kV 48 (77) n.a.b 130 (209) 82 (132)

138 kV 45 (72) n.a.b 120 (193) 70 (113)

161 kV 42 (67) 52 (84) 114 (183) n.a.c

c. The relatively high dielectric constant and dissipation factor for EPR insulation limit the application of these cables to 138 kV or below.

230 kV 30 (48) 36 (58) 81 (130) n.a.c

345 kV-400 kV 20 (32) 29 (47) 53 (85) n.a.c

500 kV n.a.d

d. At this voltage, with conventional Kraft paper insula-tion, the dielectric losses are so great that the ampacity is zero.

23 (37) 47 (76) n.a.c

3-12


sion lines. Typically, the shunt reactors are chosen sothat the lagging MVARs created by the shunt reactorsare between 60% and 100% of the leading MVARs gen-erated by the cable capacitance. In most cases, a series ofload flow cases must be performed for light and heavyload conditions to determine the optimum amount andlocation for cable system shunt compensation.

Voltage Profile and Stability LimitsSome overhead lines may have voltage regulation prob-lems (i.e., excessive voltage drop) when transmittingpower to lagging power factor loads. As the line lengthincreases, the voltage on the line tends to drop. This cancause problems in transferring power from the sendingend to the receiving end of a line.

The relatively high capacitance of cable circuits mayhave adverse effects on the voltage profile in the vicinityof underground transmission lines. Since a capacitivecurrent flowing through an inductance causes a voltagerise across the inductor, the charging current created bythe capacitance of a cable circuit can cause high systemvoltage by two related phenomena. The first and mostcommon situation is for the cable charging current tocause voltage rises across the inductive impedancesexternal to the cable circuits. This situation, which isworst during light load conditions, is illustrated in Fig-ure 3.3-2.

In this circuit, the reactances, XL and XT, representinductive impedances of transmission lines and trans-former impedances between the generator and the cablecircuit. Since the voltages at the load must be held nearrated voltage, the system voltages rise significantlyabove the rated voltage as the cable charging currentflows through the inductive impedances, XL and XT, tothe generation units. During light load conditions(assumed in Figure 3.3-2), this voltage rise may causevoltages above the maximum rated voltage that mostpower system components are designed for (105%) with-out shunt compensation.

Cable circuits are not generally associated with voltagestability problems because of their capacitive nature—they are generally shorter as compared to overheadlines, are naturally compensated, and generate voltage-supporting vars.

Surge Impedance Loading (SIL) LimitsSurge impedance loading (SIL) limits involve a greaterthan allowable phase shift in power frequency from oneend of a transmission system to the other. As a result,the two ends of the system cannot remain synchronous,resulting in instability and outages. This system stabilityconsideration is generally an issue on overhead trans-mission lines that are 80-320 km (50-200 miles) inlength.

The positive sequence surge impedance, ZS, of a trans-mission line is defined by Equation 3.3-4

3.3-4

where, L and C are the positive sequence series induc-tance and shunt capacitance, respectively.

Cables have lower series inductances and much highershunt capacitances compared to overhead lines. Conse-quentially, cables have very low surge impedance relativeto overhead lines. Typical surge impedances for over-head and underground lines are 375 ohms and 30 ohms,respectively.

The SIL limit, based on the line-to-line voltage (VLL), isdefined by Equation 3.3-5

3.3-5

SIL power transfer limits are rarely a problem forunderground transmission lines because of their lowsurge impedance and relatively short lengths.

Figure 3.3-2 Voltage rise due to cable charging current.

OhmsCLZ S =

MVALimitSIL2

S

LL

ZV

=

3-13


3.3.2 Load Flow Considerations

Low cable system series impedances, and the resultingunequal distribution of load flow between overhead andunderground lines, are important considerations whenevaluating the uprating potential on underground cablecircuits.

The reactive loading of various transmission lines in apower system is controlled by the magnitude of the volt-ages across the system and can be adjusted by generatorexcitation and transformer taps. The flow of real powerover the lines is a function of the relative voltage anglesaround the system and the interconnecting impedances.Unfortunately, the distribution of real power flow is notas easily controlled as reactive power flow because thecircuit impedances are fixed in most cases, and it is noteconomical to control power flows by changing anglesat the generation units. Therefore, where transmissionline loadings are not approximately equal to the thermalcapacities of the circuits, the power transfer cannot beincreased once a circuit is loaded to its thermal limiteven though the other circuits may be lightly loaded.Because underground cables have much lower seriesimpedances than overhead lines, a higher portion ofpower will flow over the underground lines compared tooverhead lines in the same area. Figure 3.3-3 shows anextreme situation where an underground cable is con-nected electrically in parallel with an overhead line.

The sending and receiving end phasor voltages are thesame for both overhead and underground circuits. Thenthe power flow between the two buses along the cableand line is defined by Equations 3.3-6 and 3.3-7.

3.3-6

3.3-7

Since the series impedance of cables is typically 25-30%of length compared to those for overhead lines, thepower flow along the cable circuit is greater, perhapsexceeding the ampacity of the cable circuit or resultingin underutilization of the overhead line. While the aboveexample is extreme, cables may be put in parallel withoverhead lines indirectly in a conventional power sys-tem. Is some cases, relatively expensive phase shiftingtransformer must be placed in series with undergroundcables to more evenly distribute power flows with over-head lines in the same area.

3.3.3 Uprating Hybrid (Underground and Overhead) Circuits

Hybrid transmission circuits contain sections of bothoverhead lines and underground cables. The reasons forthese types of installations are numerous (rights-of-waycongestion, available ROW, water crossings, tunnels, air-ports, etc.), but the issues with uprating these types ofcircuits are complicated by considering all of the equip-ment along the circuit. Overhead lines are typicallyoperating at only 30-40% of their rated capacity, and inhybrid circuits usually have a normal rating that is 40-60% greater than the connected underground sections.As a result, the cable section is usually studied first fromthe standpoint of increasing a circuit’s capacity since thecircuit will be limited by the section with the lowest rat-ing – often the cable.

From the standpoint of typical design limits, an over-head line usually can obtain 1 ampere of capacity foreach kcmil (2 amperes per square millimeter), while acable will generally have half that capacity. Also, over-head lines do not suffer from mutual heating effectsamong phases or circuits, but this is a significant consid-eration where cables are installed in the same trench.Therefore, additional overhead conductors added toincrease capacity cannot be equally matched by thesame number of underground conductors, since the bur-ied cables will experience a net de-rating from mutualheating.

While overhead lines typically have greater ampacity fornormal operating conditions, the large thermal timeconstant of buried transmission cables – typically 50-150 hours – compared with overhead lines (5-15 min-utes) means that for short-duration emergencies, cablestypically have a higher emergency rating. Also, becauseof the relatively short time constant of overhead lines,the load cycle on the overhead line does not have a sig-nificant impact on the normal or emergency capacity.However, with buried cables, the long thermal time con-stant has a big impact on ratings. This is factored intodaily ratings by considering a 24-hour loss factor (essen-

Figure 3.3-3 Simplified power system network with parallel overhead and underground circuits.

( )1221 θθ −= Sin

ZVVP

CableCable

( )1221 θθ −= Sin

ZVV

PLineOH

LineOH

3-14


tially, the daily load factor of the losses). This is dis-cussed in greater detail in Section 3.4.

3.4 UNDERGROUND CABLE RATINGS

3.4.1 Introduction

This section provides a brief overview of the ampacityprocedures used to determine cable ratings. While thereare subtle differences in constructions among the vari-ous cable types, this section focuses on the most com-mon constructions to provide the reader with enoughbackground to understand how the uprating approachesdiscussed in later sections can be applied.

Many ampacity calculations are based on a 1957 paperby Neher and McGrath (Neher and McGrath 1957).Later work by CIGRÉ documented an ampacity proce-dure into an international standard (International Elec-trotechnical Commission 1982, 1987) that provides astep-wise approach to calculating ampacity based uponcable construction. The two calculation approaches givesimilar results, although their treatment of daily loadcycles is different.

The paper by Neher and McGrath assumes a sinusoidalload shape and uses a 24-hour (daily) loss factor toaccount for an overall “averaging” effect of heat outputfrom the cable beyond a certain diameter (called DX).Within this diameter, the temperature rise across thethermal resistances in the cable and nearby soil is pro-portional to the peak heat output from the cable. At dis-tances greater than this diameter away from the cablecenter, the temperature rise is proportional to the aver-age daily heat output.

Many system planners are familiar with a “load factor,”which relates the peak load to the average daily load. Incable systems, the focus is on heat output—a function ofI2R—so the term daily “loss factor” is used, which isessentially the load factor of the losses as defined byEquation 3.4-1.

3.4-1

The loss factor can be estimated from the load factorusing an empirical relationship. One such relationship isas shown in Equation 3.4-2.

3.4-2

Distribution cables sometimes fol low a s imilarrelationship, Loss Factor = 0.2 (Load Factor) + 0.8(Load Factor)2, but it is important to note that theseload factor-to-loss factor relationships are specific to agiven system and should not necessarily be appliedarbitrarily. The IEC method in its basic form assumesthat the load remains constant (e.g., a loss factor of100%), but ratings by this method can be modified by acompanion document, IEC-60853 (International Elec-trotechnical Commission 1989), to account for the dailyload variations, particularly when the load is not closelysinusoidal. The IEC approach to account for load varia-tions does not easily lend itself to hand calculations andgenerally gives close agreement to the “Neher andMcGrath” method under typical loading patterns.

The approach described in this section is focused on theuse of the IEC method—generally recognized as provid-ing better accuracy for ac losses and being easier to fol-low—but accounts for cyclic loading by using the “lossfactor” approach from the paper by Neher andMcGrath.

Chapter 3 does not specifically address emergency rat-ings, except conceptually in later sections. For the typi-cal user of this chapter, both normal and emergencyrating calculations can be handled by a computer pro-gram such as UTWorkstation and DTCR that are avail-able from EPRI, as well as other commercial sources.For additional background on emergency rating calcu-lations, the reader should review relevant referenceslisted at the end of this chapter.

3.4.2 Concept of Ampacity

An underground cable circuit rating, or “ampacity,” isthe solution to a basic heat transfer problem. Heat gen-erated in the cable is removed by thermal conduction toambient earth and, ultimately, air. Engineers familiarwith Ohm’s Law know that electrical current flowingthrough an resistance will produce a voltage drop (orrise) according to Equation 3.4-3.

3.4-3

An analogous relationship may be used to describe ther-mal conduction where heat flowing through a thermalresistance produces a temperature drop (or rise) accord-ing to Equation 3.4-4.

3.4-4

This basic concept is extended to model heat out of aburied cable through the various cable layers, trenchbackfill and native earth.

2max

24

1

2

24Factor Loss

I

Ii

i

⋅=∑=

( ) ( )2Factor Load7.0Factor Load3.0Factor Loss +=

ACRCurrentVoltage ⋅=Δ

ThermalRHeateTemperatur ⋅=Δ

3-15


3.4.3 Losses

Losses (heat) from a cable are the source of temperaturerise above ambient earth. Heat is generated from bothdielectric heating and ac resistance heating, as describedin the following sections.

Dielectric HeatingDielectric heating comes from charging and dischargingthe insulating dielectric at 50 or 60 times per second.The dielectric heat loss, WDielectric, can be found fromEquation 3.4-5.

3.4-5Where:C = Capacitance, Farads/meter.f = power frequency, Hz.ε = specific inductive capacitance (dielectric

constant).tan δ = insulation dissipation factor.Vl-g = line to ground voltage applied across the

insulation, volts.

Some typical insulation parameters are listed in Table3.4-1.

Charging CurrentDielectric losses are generated on a per-meter basis andaffect the radial heat escaping from the cable, ultimatelyaffecting normal ampacity. Charging current—energyused to charge and discharge the insulation at power fre-quency—is consumed when the cable is energized andultimately limits the allowable real power transfer (seeSection 3.3.1).

Electrical Losses

DC ResistanceElectrical losses are generated from current flowingthrough the resistance of the phase conductors, concen-tric metallic shields, sheaths or skid wires, and the pipes(depending on cable system type). The resistance is afunction of the cross-sectional area of the material andis defined by Equation 3.4-6.

3.4-6Where:ρ = electrical resistivity of metal in ohm-m at

20°C.Area = cross-sectional area of metal in mm2.

The dc resistance of the conductor is usually increasedby 2.5% or so to account for the lay of the wires in thestranded conductor.

The dc resistance can be adjusted to other temperatures,usually the rated conductor temperature, using Equa-tion 3.4-7.

3.4-7Where:τ = inferred temperature of zero resistance.T = temperature of the conductor.

Some typical values of electrical resistivity are listed inTable 3.4-2, along with their temperature correctioncoefficients.

AC Skin and Proximity EffectsLosses in the conductor are affected by self and mutualinductance; the self inductance causes the current toconcentrate near the conductor surface – called “con-ductor skin effect” – and the magnetic field of neighbor-

[W/meter]ln18

10tan22

922

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅==

−−

−

Conductor

insulation

glglDielectric

DD

VffCVW

δεππ

Table 3.4-1 Typical Cable Insulation Material Parametersa

Insulation Material

Dielectric Constant Dissipation Factor

Range Typical Range Typical

Impregnated Paper 3.3-3.7 3.5 0.002-0.0025 0.0023

Laminated Paper-Polypropylene 2.7-2.9 2.7 0.0007-

0.0008 0.0007

Cross-linked Polyethylene 2.1-2.3 2.3 0.0001-0.0003 0.0001

Ethylene-Propylene-Rubber 2.5-4.0 3.0 0.002-0.08 0.0035

a. Values from 1992 EPRI Underground Transmission Systems Reference Book.

r][Ohms/mete10 620 −⋅

=Area

Rdcρ

]Ohms/meter[2020 τ

τ−−

⋅=TRR dcdcT

Table 3.4-2 Electrical Resistivities and Temperature Factors for Common Cable Metals

MaterialElectrical Resistivity

Ohm-metersInferred Temperature

of Zero Resistance, °C

Aluminum 2.8264 x 10-8 -228.1°C

Brass 6.317 x 10-8 -912.0°C

Bronze 3.5 x 10-8 -564.0°C

Copper 1.7241 x 10-8 -234.5°C

Lead 21.4 x 10-8 -236.0°C

Stainless Steel 70 x 10-8 n.a.a

a. There is almost no variation in the resistance of stainless steel with respect to temperature over the typical operating range of a cable.

Zinc 6.633 x 10-8 -218.7°C

3-16


ing conductors affects the distribution of current acrossthe conductor – called “conductor proximity effect.”When the total losses from the cable conductor arebeing calculated, these two parameters must be deter-mined. The impact of these effects on the dc resistance –called the “ac-dc ratio” – is a function of the conductortype and construction. Values of the conductor skineffect correction factor, ks, and proximity effect correc-tion factor, kp (also known as the transverseconductivity factor) are listed in Table 3.4-3.

The ac resistance increment for conductor skin effect,YCS, can be found from Equation 3.4-8, where kS is theskin effect factor based on the conductor construction.

3.4-8

The ac resistance increment for conductor proximityeffect, YCP, can be found from Equation 3.4-9, where kP

is the proximity effect factor based on the conductorconstruction.

3.4-9

The conductor resistance including skin and proximityeffects can be calculated using Equations 3.4-10 and3.4-11.

3.4-10

3.4-11

Shield, Sheath and Skidwire ResistanceDepending on the cable type, there are various metalliclayers outside of the cable insulation. A summary oftypical layers is as follows:

Pipe-Type:helically applied metallic tape(s), helicallyapplied skid wire(s).

SCFF: extruded lead, corrugated copper, or corru-gated aluminum sheath, possibly with addi-tional copper wires or tapes.

Extruded: concentric stranded copper or aluminumwires, copper or aluminum tapes, extrudedlead, corrugated copper, corrugated alumi-num or corrugated stainless steel.

Regardless of the cable type, the resistance of the metal-lic layers outside of each cable phase must be evaluated.These resistance values are then be adjusted for the tem-perature of the respective layer. Three basic equationsmay be used. For a helical metallic layer (e.g., a helicallyapplied tape or skid wire), Equation 3.4-12 can be used.

3.4-12Where:ρ = electrical resistivity of layer in Ohm-

meters.DLayer = average diameter of the helical layer.LayLayer = distance along the cable for one turn of

the tape or wire (e.g., the “lay”).Area = cross-sectional area of the tape, wire or

skid wire.

For an extruded or welded metallic layer (e.g., thesheath on an extruded or self-contained cable), the areaof the layer can be calculated by knowing the difference

Table 3.4-3 Skin and Proximity Effect Factors for Various Conductor Types

Conductor Type ks kp

Concentric round, dry 1.0 1.0

Concentric round, in oil 1.0 0.8

Compact round, in oil 1.0 0.6

Compact segmental, dry 0.435 0.6

Compact segmental, in oil 0.435 0.37

Compact segmental, in oil 0.39 0.35 (trefoil), 0.46 (cradled)

Compact segmental (aluminum), in oil 0.35 0.29 (trefoil), 0.36 (cradled)

Hollow core, 6 segment, in oil 0.39 0.33

Hollow core, 6 segment (aluminum), in oil 0.26 0.19 (trefoil),

0.27 (cradled)

Hollow core, 4 segment, in oil 0.435 0.37

dcT

SS R

fkX

7108 −⋅=

π2

2

8.0192 S

SCS X

XY

⋅+=

dcT

PP R

fkX

7108 −⋅=

π

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

+⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅+=

27.0

18.1312.0

8.0192

2

2

2

2

2

phase

Conductorphase

Conductor

phase

Conductor

P

PCP

dDd

D

d

D

X

XY

( ) soilor air in cablesfor 1 CPCSdcTacc YYRR ++⋅=

( )( ) pipe steel ain cablesfor 5.11 CPCSdcTacc YYRR +⋅+⋅=

r][Ohms/mete110

2

620 ⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅+⋅

⋅=

−Layer

Layerdc Lay

D

AreaR

πρ

3-17


in diameters above and below the layer, as shown inEquation 3.4-13.

3.4-13

For a stranded shield, the area of a single strand must becalculated and then multiplied by the number, N, of wirestrands. The resistance can then be calculated as aboveby dividing the area into the electrical resistivity of thematerial (see Equation 3.4-14).

3.4-14

Once the resistances for all of the shield layers are deter-mined, they should be taken electrically in parallel tofind the overall resistance, as shown in Equation 3.4-15.

3.4-15

Shield Loss Increments for Circulating CurrentsCirculating currents exist when a cable metallic shield,sheath, neutral or skidwire is grounded at both ends(e.g., multi-point bonding – see Section 3.6.8). Thephase currents induce a circulating current in these lay-ers depending on the geometry and resistance of thelayer that opposed the phase current according toLenz’s Law. Circulating currents exist in pipe-typecables because the skidwire and metallic shield are con-tinuously grounded to the cable pipe. Circulating cur-rents also exist in single-core cables (e.g., extrudeddielectric or self-contained cable types) when the metal-lic sheath is grounded at both ends or on cross-bondedsystems where the minor section lengths are not equal inlength.

Calculation of the circulating current increment requiresdetermining the mutual reactance between adjacentcable phases and depends on the configuration of thephases. Equations 3.4-16, 3.4-17, and 3.4-18 should beapplied appropriately, depending on the cable configu-ration that most closely matches the indicated cablepositions. S, the center-to-center phase spacing, and,DS, the average diameter of the shield/sheath/skidwirelayer are used in the equations.

3.4-16

3.4-17

3.4-18

The incremental increase in resistance from circulatingcurrents can then be found using Equation 3.4-19.

3.4-19

Shield Loss Increments for Eddy CurrentsEddy current losses occur when a continuous concentricmetallic layer exists around the cable core (e.g., a corru-gated or extruded metal sheath or longitudinally tapedmetallic shield, but not to stranded shields). Also, eddycurrents are negligible for pipe-type cables.

The mechanics for calculating the eddy current losses issomewhat onerous but not particularly complicated. Theequations to perform these calculations were derivedempirically and are listed in Equations 3.4-20 through3.4-24. For a more detailed explanation, see IEC-287(International Electrotechnical Commission 1982).

3.4-20

3.4-21

3.4-22

3.4-23

( )

r][Ohms/mete10

][mm4

620

222

−⋅=

−=

AreaR

DDArea

dc

InnerOuter

ρ

π

][mm4

22strandDN

Area⋅⋅

=π

1 2

1 1 1 1....

S s s snR R R R= + + +

7 24 10 ln [Ohms/meter]

for cables in equilateral (triangular) configuration

ms

SX f

Dπ − ⎛ ⎞⋅

= ⋅ ⋅ ⎜ ⎟⎝ ⎠

7 2.34 10 ln [Ohms/meter]

for cables in cradled configuration

ms

SX f

Dπ − ⎛ ⎞⋅

= ⋅ ⋅ ⎜ ⎟⎝ ⎠

7 2.524 10 ln [Ohms/meter]

for cables in flat/vertical configuration

ms

SX f

Dπ − ⎛ ⎞⋅

= ⋅ ⋅ ⎜ ⎟⎝ ⎠

2

1

1

SSC

acc S

m

RY

R RX

= ⋅⎛ ⎞

+ ⎜ ⎟⎝ ⎠

7

'

2 10

S

fm

Rπ −⋅

=

22

0 2

1.4 0.73.08

1

621

0.862

for flat formation

SSe

mS

Se

DmY

Sm

DY m

S

⋅ +

⎛ ⎞ ⎛ ⎞= ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⋅+ ⎝ ⎠⎝ ⎠

⎛ ⎞= ⋅ ⋅ ⎜ ⎟⋅⎝ ⎠

( )

22

0 2

0.92 1.662.45

1

321

1.14 0.332

for trefoil formation

SSe

mS

Se

DmY

Sm

DY m

S

⋅ +

⎛ ⎞ ⎛ ⎞= ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⋅+ ⎝ ⎠⎝ ⎠

⎛ ⎞= ⋅ + ⋅⎜ ⎟⋅⎝ ⎠

( )

2

1 7

1.743

1

8

10

1 10 1.6

Shield

Shields S

S

f

tg D

D

πβρ

β −

=⋅

⎛ ⎞= + ⋅ ⋅ ⋅ −⎜ ⎟

⎝ ⎠

3-18


3.4-24

where RS’ is the resistance of only the layer(s) whereeddy currents may occur and tShield is the thickness ofthe shield layer.

AC Resistance Including Circulating Current and Eddy Current IncrementsThe conductor resistance including skin, proximity, cir-culating current, and eddy current effects can be calcu-lated using Equations 3.4-25 and 3.4-26.

3.4-25

3.4-26

Pipe Loss Increments for Pipe-Type CablesPipe cables have additional losses from eddy current andhysteresis heating in the cable pipe as a result of the accables within the pipe. The increment losses associatedwith the pipe can be calculated using Equations 3.4-27and 3.4-28.

3.4-27

3.4-28

Note that the pipe loss increment is greater for cables incradled configuration, so cradled configuration shouldgenerally be assumed unless the cables are known to layin close trefoil configuration.

Equations 3.4-27 and 3.4-28 are for 60 Hz. If the powersystem is 50 Hz, the values of YP should be multipliedby 0.76.

Ac resistance including skin, proximity, circulating cur-rent, eddy current, and pipe loss effects is determinedusing Equation 3.4-29.

3.4-29

Other LossesAdditional losses may be experienced in some cableinstallations. Single-core submarine cables may havesteel or other armor wires that can have both circulatingcurrent and hysteresis (for iron-based armor) losses.Also, utilities use steel casings for road crossing or direc-tionally drilled installations that can have significanthysteresis and eddy current losses. Neutral continuityconductors may generate heat if the phase currents areimbalanced, but this is most often an issue on distribu-tion systems.

3.4.4 Equivalent Thermal Circuit and Thermal Resistances

As was discussed in Section 3.4.2, thermal conduction isthe principal means by which heat leaves a buried cablesystem. The thermal equivalent to Ohm’s Law is appliedto this model by developing an “equivalent thermal cir-cuit” that describes the various layers of cable materialsand surrounding earth which heat must pass through toreach ambient. Thermal circuits for extruded/self-con-tained and pipe-type cables are shown in Figures 3.4-1and 3.4-2. The thermal resistances and heat sources areshown, analogous to electrical resistances and currentsources in a conventional Ohm’s Law circuit. The tem-perature of the conductor, Tc, is determined by addingup the temperature rises above the ambient earth tem-

( ) ( )41

0 1 121

12 10ShieldS

EC s Se Seacc

tRY g Y Y

R

β⎛ ⎞⋅⎛ ⎞ ⎜ ⎟= ⋅ ⋅ ⋅ + +⎜ ⎟ ⎜ ⎟⋅⎝ ⎠ ⎝ ⎠

( )1

for cables in air or soilacs dcT CS CP SC ECR R Y Y Y Y= ⋅ + + + +

( )( )1 1.5

for cables in a steel pipe

acs dcT CS CP SC ECR R Y Y Y Y= ⋅ + ⋅ + + +

610

0.0438 0.0226

for cables in cradled configuration

Skidwire PipeP

dcT

D IDY

R ⋅

⋅ + ⋅=

610

0.115 0.01485

for cables in trefoil configuration

Skidwire PipeP

dcT

D IDY

R ⋅

⋅ − ⋅=

( )( )1 1.5acp dcT CS CP SC EC PR R Y Y Y Y Y= ⋅ + ⋅ + + + +

Figure 3.4-1 Equivalent thermal circuit for extruded dielectric and self-contained fluid-filled cable types.

Figure 3.4-2 Equivalent thermal circuit for pipe-type cables.

3-19


perature, Tearth, as heat passes through the various ther-mal resistances.

The thermal capacitances shown in the figures accountfor the fact that changing load (e.g., heat output) fromthe cable does not instantaneously result in a change intemperature. This is consistent with the Ohm’s Law anal-ogy, where a change in applied voltage does not instantlychange the voltage across an electrical capacitor.

Temperature RiseTo calculate the ampacity, the conductor temperature isdetermined for a given current and checked against themaximum allowable conductor temperature based onthe insulation material. For the above thermal circuits,the temperature rise above ambient is found usingEquation 3.4-30, where the ac losses (I2R) and dielectricheat losses (Wd) pass through the various thermal resis-tances to give a temperature rise:

3.4-30

Typical ampacity calculations assume that the voltageremains constant, so dielectric losses are fixed. Then,the only unknown in Equation 3.4-30 is the current asshown in Equation 3.4-31 (as a convention, thermalquantities are shown with an over-line to distinguishthese values from electrical quantities):

3.4-31

Cable Thermal ResistancesThe thermal resistances for each cable layer out to theearth interface – where the cable contacts the soil – mustbe determined to complete the thermal circuit. The ther-mal resistivities of common cable materials are listed inTable 3.4-4.

For layers where the inner and outer diameters are con-centric (e.g., cable insulation, cable jackets or pipe coat-ings, or the thermal resistance of a conduit), the thermalresistances may be found using the Equation 3.4-32

3.4-32

where n is the number of cables within the diameter,DInner.

The thermal resistance between a cable and the inside ofa conduit or pipe can be determined using Equations3.4-33.

3.4-33Where:Tmean= mean temperature of the duct air, or nitro-

gen gas or dielectric liquid in the pipe.Dcable= outer diameter of the cable.n = number of cables within the conduit or pipe.U, V, and Y as defined in Table 3.4-5.

Earth Thermal ResistancesThe cable thermal resistances describe components ofthe thermal circuit out to the interface with the sur-rounding soil. For direct buried cables, this is the pipecoating (on pipe-type cables) or the jacket on single-conductor cables. Single core cables installed in conduitshave an earth interface at the outside of the conduit. Atthat point, the earth portion of the thermal circuitstarts.

Three thermal resistances must be considered in theearth portion of the thermal circuit:

• Thermal resistance to heat escaping from the cable orpipe itself

( )2max

2max

ac d thermal ambient

d ambient ac thermal

T I R W R T

T T T T I R R

= + × +

Δ = − Δ − = ×

ac thermal

TI

R R

Δ=

⋅

ln [C°-m/Watt]2

Outer

Inner

DR n

Dρπ

⎛ ⎞= ⋅ ⋅ ⎜ ⎟

⎝ ⎠

Table 3.4-4 Thermal Resistivities of Common Cable Materials

MaterialRange

(C°-m/Watt)Typical

(C°-m/Watt)

Impregnated Paper 5.0-6.0 6.0

Laminated Paper-Polypropylene 5.0-6.0 6.0

Crosslinked Polyethylene 3.5-4.0 3.5

Ethylene-Propylene-Rubber 4.5-5.0 4.5

Somastic 1.0 1.0

Transite 2.0 2.0

PVC 4.0-4.5 4.0

Neoprene 3.8-5.8 4.0

Epoxy 0.7-4.45 1.0

Thermoplastic Pipe Coating 3.5-4.5 4.0

( )[ / ]

1 0.1 mean cable

n UR C m Watt

V Y T D⋅

= ° −+ + ⋅ ⋅

Table 3.4-5 Pipe and Duct Thermal Resistance Constants

Configuration U V Y

Fiber Duct or PVC in Concrete 5.2 0.91 0.010

Asbestos Cement in Concrete 5.2 1.1 0.011

Pipe-Type, HPGF 0.95 0.46 0.0021

Pipe-Type, HPFF 0.26 0.0 0.0026

Earthenware Ducts 1.87 0.28 0.0036

3-20


• Thermal resistance resulting from mutual heatingamong other cables or pipes

• Thermal resistance correction to account for nativesoil materials outside of the trench having a higherthermal resistivity than backfill materials

The equations in this section describe each of these. Thebasis for these calculations is application of superposi-tion of the heat fields generated by each buried cableand the assumption that the earth’s surface may betreated as an isotherm. These assumptions are substan-tiated by the Kennelly Hypothesis, and the reader isencouraged to review relevant references (Anders 1997)for more details.

The thermal resistivity of the soil is an importantparameter, which will be discussed in detail later. Table3.4-6 summarizes some typical values of soils and back-fills.

Earth Thermal ResistanceThe earth thermal resistance is mainly a function ofcable burial depth. For installations where the cable isinstalled in a special backfill, the thermal resistivity ofthe special backfill—directly in contact with the cable—should be used for the earth thermal resistance calcula-tion. The fact that the native soil outside of the trenchmay have a greater thermal resistivity will be corrected,as shown in Equation 3.4-34.

3.4-34Where:

L = centerline burial depth of the center of thecable, pipe or conduit, mm.

Dearth = diameter of the earth interface (cable OD,pipe OD, or conduit OD), mm.

ρ = the thermal resistivity of the soil in contactwith the cable, C°-m/Watt.

n = number of cables within diameter, Dearth.

LF = the 24-hour loss factor for the load on thecables, per-unit.

Dx = diameter where average daily heat outputapplies, as defined below.

Diameter, Dx, is the diameter beyond which 24-houraverage ac heat losses apply and is a function of the soilthermal diffusivity. An empirical relationship for findingthe soil thermal diffusivity, αsoil, as a function of thenative soil thermal resistivity, , is as shown inEquation 3.4-35.

3.4-35

From this, the diameter, Dx, may be found (typicallyabout 210 mm or 8.3 in.), using Equation 3.4-36.

3.4-36

Mutual Heating Thermal ResistanceWhen multiple cables are installed in the ground, heatgenerated by each cable impacts the temperature of theother cables. For the purposes of this section, all cablesare treated as though they are carrying equal loadingsuch that the heat output from each cable is the same.With the assumption that the earth’s surface is an iso-therm, a “method of images” is used to model the heatleaving each cable and its mutual heating effects on theother cables. Figure 3.4-3 shows examples for a two-pipe

Table 3.4-6 Typical Soil Thermal Resistivity Values

Soil Type

Thermal Resistivity

5% Moisture(C°-m/Watt)

0% Moisture(C°-m/Watt)

Fluidized Thermal Backfill 0.4 0.75

Concrete 0.6 0.8

Stone Screenings 0.4 1.0

Thermal Sand 0.5 1.0

Uniform Sand 0.7 2.0

Clay 1.0 2.5

Lake Bottom 1.0 (50% moisture) >3.0

Highly Organic Soil >3.0 >6.0

2 2

ln

[C°-m/Watt]2 2 4

ln

x

earth

earthearth

x

DLF

DR n

L L D

D

ρπ

⎛ ⎞⎛ ⎞+⎜ ⎟⎜ ⎟

⎜ ⎟⎝ ⎠⎜ ⎟= ⋅ ⋅ ⎛ ⎞⎜ ⎟⋅ + ⋅ −⎜ ⎟⋅⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

ρnative

( ) /hour][mm100

1071.6 28.0

4

⋅

×=

native

soilρ

α

1.02 24 [mm]x soilD α= ⋅

Figure 3.4-3 Illustration of mutual heating effects.

3-21


cable circuit (left) and for a single extruded dielectric orself-contained cable circuit (right).

The mutual heating effect is evaluated knowing the dis-tance from a given cable to the image of an adjacentcable divided by the actual distance separating thecables, as shown in Equation 3.4-37.

3.4-37

with N being the number of conduits, cable pipes, orcable positions with energized cables. It is important toevaluate the mutual heating effect for the cable that willrun at the highest temperature to ensure that none of thecables exceeds the maximum allowable temperature.

Then, the thermal resistance from mutual heating canbe evaluated using Equation 3.4-38.

3.4-38

where n is the number of energized cables at each loca-tion. For a pipe-type cable, n equals three. For directburied cables or conduit installations of transmissioncables, n generally equals one. If the cables are installedin special backfill, the thermal resistivity used to calcu-late the mutual heating thermal resistance should bethat of the backfill.

Thermal Resistance Correction for Native SoilUp to this point, the thermal resistances of the earthand mutual heating have used a value of the backfillthermal resistivity. However, in actual installations, thethermal resistivity of the soil outside of the trench is typ-ically greater, and this must be factored into the ampac-ity calculations. To make this correction, an additionalthermal resistance term is needed. The approach consid-ers the length and width of the backfill envelope, asshown in Figure 3.4-4.

If the short, x, and long, y, dimensions of the backfillenvelope are known, it is possible to determine a cir-cumscribing circle having a diameter, Db, with the samevolume of backfill material as the rectangular backfillenvelope, as shown in Equation 3.4-39.

3.4-39

Then, if the center-line depth, Lb, of the backfill enve-lope is known, a geometric factor for the backfill can becalculated, as shown in Equation 3.4-40.

3.4-40

The thermal resistance correction for native soil withdifferent thermal resistivity, ρnative, than the backfillthermal resistivity, ρbackfill, can be calculated using theabove geometric correction factor as shown in Equation3.4-41.

3.4-41

where n is the number of cables per pipe, conduit orlocation, and N is the number of pipes, conduits or loca-tions within the backfill envelope.

The procedure described above is valid as long as theratio of the long dimension of special backfill to theshort dimension of the special backfill is 3 or less. Apaper by El-Kady and Horrocks (1995) describes geom-etry factors that may be used for special backfill enve-lopes with dimensions outside the acceptable range ofthe method used above.

Temperature Rise from Dielectric HeatingThe ac and thermal resistances complete the equivalentthermal circuit so that ampacity can be calculated.However, it is also important to consider the tempera-ture rise caused by dielectric heating. Losses are gener-ated throughout the insulating dielectric, but for thepurposes of ampacity calculations, the dielectric losses,Wd, are assumed to enter the thermal circuit half waythrough the insulation. This can be seen by referringback to the thermal circuit figures.

13 112

12 13 1

' ''... N

N

d ddF

d d d

⎛ ⎞ ⎛ ⎞⎛ ⎞= ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( )ln [ / ]2mutualR n LF F C m Wattρπ

= ⋅ ⋅ ° −

( )2

2

1 4exp ln 1 ln

2bx x y

D xy y xπ

⎡ ⎤⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞= − + +⎢ ⎥⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

Figure 3.4-4 Trench backfill width and height.

2 22 4ln b b b

bb

L L DG

D

⎛ ⎞⋅ + ⋅ −⎜ ⎟=⎜ ⎟⎝ ⎠

[ / ]2

native backfillcorrection bR n N LF G C m Watt

ρ ρπ−

= ⋅ ⋅ ⋅ ⋅ ° −

3-22


The thermal resistances used for dielectric temperaturerise are calculated in the same manner as for ac losses,except that the loss factor is 100% (1.0 per unit) sincethe voltage is constant. Therefore, it is necessary to con-sider the thermal resistance values used for dielectrictemperature separately from those used for ac losses,which are a function of the daily load variation.

The temperature rise caused by dielectric heating can bedetermined as shown in Equations 3.4-42 through3.4-44.

For extruded and self-contained cables in conduit:

3.4-42

For direct buried extruded and self-contained cables:

3.4-43

For pipe-type cables:

3.4-44

Ambient Soil Temperature“Ambient” soil temperature is the temperature at theburial depth of the cable in the absence of any non-native heat sources. These temperatures are usuallyestablished during a route thermal survey (described inSection 3.6.1). Some typical values of ambient soil tem-perature are listed in Table 3.4-7.

3.4.5 Calculating Ampacity

Once the thermal circuit is complete and the dielectrictemperature rise is known, it is possible to determine theallowable conductor temperature rise for ac loading(ampacity). The temperature at the conductor is high-est, and the temperature of the insulation nearest theconductor limits the ampacity. Some industry-acceptedmaximum allowable conductor temperatures are listedin Table 3.4-8.

The “summation of electrical and thermal resistances”(units of the “summation of electrical and thermal

resistances” are C°/ampere2) is determined using thethermal circuit parameters, as shown in Equations 3.4-45 through 3.4-47.

For extruded and self-contained cables in conduit:

3.4-45

12 insulation jacket

d d jacket duct duct

earth mutual correction

R R

T W R R

R R R

−

⎛ ⎞+⎜ ⎟⎜ ⎟Δ = + +⎜ ⎟⎜ ⎟+ + +⎝ ⎠

12 insulation jacket

d d


R RT W

R R R

⎛ ⎞+⎜ ⎟Δ =⎜ ⎟+ + +⎝ ⎠

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++++

+=Δ

−

correctionmutualearthngpipe coati

pipecableinsulationdd

RRRR

RRWT 2

1

Table 3.4-7 Example Ambient Soil Temperatures at Typical Installation Depthsa

a. E.g., 1.1 m (42 in.).

LocationMaximumSummer

MaximumWinter

Atlanta 25°C 20°C

Boston 22°C 18°C

Chicago 22°C 18°C

Denver 22°C 17°C

Honolulu 30°C 15°C

Johannesburg 22°C 15°C

London 18°C 8°C

Miami 30°C 25°C

New York 25°C 18°C

Palo Alto 22°C 20°C

Singapore 30°C 25°C

Table 3.4-8 Industry-Accepted Maximum Conductor Temperatures

Insulation Material

Maximum Normal (Con-

tinuous)Temperature

Maximum EmergencyTemperature

Impregnated Paper 85°C 105°C peak at end: up to 100 hours

100°C peak at end: 100-300 hours

Laminated Paper

Polypropy-lene

85°C 105°C peak at end: up to 100 hours100°C peak at end: 100-300 hours

Cross-Linked Polyethylene 90°C 105-130°Ca, 72 hours continuousb

105°C- peak at end of 100-300 hours

a. Depends on shield construction and agreement from manufacturer.

b. Based on Association of Edison Illuminating Companies CS-7 standard.

Ethylene Propylene

Rubber90°C 130°C

Linear Low Density

Polyethylene75°C 90°C

( )AC th acc insulation

jacket jacket duct ductacs


R R R R

R R RR

R R R

−

Σ ⋅ =

⎛ ⎞+ +⎜ ⎟+⎜ ⎟+ + +⎝ ⎠

3-23


For direct buried extruded and self-contained cables:

3.4-46

For pipe-type cables:

3.4-47

Then, the ampacity may be calculated, as shown inEquation 3.4-48.

3.4-48

Appendices 3.1 and 3.2 have worked examples for calcu-lating ampacity of pipe-type and extruded dielectriccables.

3.4.6 Effect of Various Parameters on Ampacity

This section briefly highlights the effects of variouscable and installation parameters on ampacity. Therange of variation shown is not applicable to allinstalled cable systems, but the trend is generally consis-tent for all cable installations.

Effect of Burial DepthAs the burial depth increases, the thermal resistance toheat leaving the cable and reaching the earth’s surfacealso increases (see Equation 3.4-34). As a result, theampacity declines with increasing burial depth. This isillustrated in Figure 3.4-5.

Barring other factors, it is generally better to have amore shallow burial depth to minimize the earth ther-mal resistance. However, ambient soil temperatures aregenerally greater near the surface (potentially reducingampacity) and soils tend to be drier above the watertable (potentially reducing soil moisture content andincreasing thermal resistivity). So, although a shallowburial depth reduces thermal resistance, other installa-tion factors must be considered when evaluating ampac-ity and placement of cables.

Effect of Phase and Circuit SpacingMutual heating among cable circuits and cable phasescause elevated temperatures that reduce the availabletemperature rise for ac current. As a result, increasedphase and circuit spacing reduce mutual heating andtend to increase ampacity. Some considerations for themutual heating might be the placement of cable phaseswithin a duct bank. For example, if a 3x3 duct bank isbeing used, the outer duct positions should be filled firstbefore the center ducts to minimize mutual heating. Fig-ure 3.4-6 shows the effect of circuit spacing on ampacity.

A similar trend would apply to phase spacing except inthe case of multi-point bonded cables. For multi-pointbonded cables, metallic shield/sheath circulating cur-rents are generally higher when the phase spacing islarge, particularly for sheath constructions designed forhigh fault currents. For this reason, multi-point bondedcables (mostly at distribution voltages) are placed in asingle conduit or in close-trefoil (triangular) configura-tion.

Effect of Native Soil and Backfill Thermal ResistivityExcept for conductor size, most of the cable construc-tion is fixed based upon the voltage class of the cable.The native soil outside the cable trench is also fixed (andrepresents a large part of the total thermal resistance asseen in the examples at the back of this guide) but mustbe factored into the ampacity calculations. Higher soilthermal resistivity results in a higher thermal resistanceto heat leaving the cable and lower ampacity.

( )( )

AC th acc insulation

acs jacket earth mutual correction

R R R R

R R R R R

Σ ⋅ =

+ + + +

( )( )( )correctionmutualearthngpipe coatiacp

pipecableacs

insulationaccthAC

RRRRR

RR

RRRR

++++

+

=⋅Σ

−

[amperes]max

thAC

ambientdimum

RRTTT

I⋅Σ

−Δ−=

Figure 3.4-5 Graph of ampacity versus burial depth. Figure 3.4-6 Graph of ampacity versus circuit spacing.

3-24


Soils may also have great variability in soil conditionsover a few meters of cable route, contrary to overheadlines where weather conditions may apply for a few kilo-meters. Therefore, it is important to find the worst con-ditions along the cable route – “weakest link” – andbase ratings on that limiting location.

From the standpoint of installations, the installer hascontrol over the material put back into the trench. Fig-ure 3.4-7 shows the effect of special backfill placed inthe cable trench as a function of various native soil con-ditions. Using a good quality thermal backfill (thermalsand, Fluidized Thermal Backfill – FTB) can improvethe allowable current carrying capacity. Section 3.6.1describes soil testing and backfill materials.

Effect of Ambient Soil TemperatureLike native soil thermal resistivity, there is little controlover the ambient soil temperature, but it must be fac-tored into the cable ratings. One consideration about theambient temperature is the burial depth. Greater tem-perature extremes are experienced close to the surface,so summer ambient temperatures will be more signifi-cant at shallow depths. Also, surface coverings have animpact on ratings. Soil ambient temperatures may be 3-5°C warmer below asphalt than other areas because ofthe increased solar absorptivity of the surface. Figure3.4-8 shows the impact of ambient temperature onampacity.

Effect of Conductor Size and Sheath BondingConductor size directly impacts the allowable currentcarrying capacity of a circuit. Larger conductor sizesallow for more current. Also, the circulating currentsfrom multi-point bonded cable sheaths cause significantlosses (heat) that reduce ampacity by 20% or more(depending on factors like sheath construction andresistance and the phase spacing). Figure 3.4-9 showsthe impact of these parameters on ampacity.

3.4.7 Emergency Ratings

Emergency ratings reflect a temporary increase in circuitcapacity during a contingency. For cables, the emergencyratings take advantage of a higher allowable conductortemperature for a period of time (usually not longer than300 hours) and the heat storage capacity – long thermaltime constant – of the cable and soil around the cables.This is somewhat different from overhead transmissionlines where the thermal time constant is measured inminutes. With buried transmission cables, the thermaltime constant is 35 to 150 hours. Figure 3.4-10 shows an

Figure 3.4-7 Graph of ampacity versus native and special backfill thermal resistivity.

Figure 3.4-8 Graph of ampacity versus ambient soil temperature.

Figure 3.4-9 Graph of ampacity versus conductor size as a function of sheath bonding mode.

Figure 3.4-10 Graph of emergency ampacity versus emergency duration.

3-25


example of emergency ampacity versus duration for a230-kV XLPE cable. The normal ampacity at 100% loadfactor is also shown on the graph.

The calculation of emergency ratings is described in apaper by Neher (1963) and IEC-853 (International Elec-trotechnical Commission 1989). The reader is encour-aged to review these documents or obtain suitablesoftware such as EPRI’s ACE (Alternative Cable Evalu-ation) or DTCR (Dynamic Thermal Circuit Rating) toperform these calculations.

From the standpoint of uprating, the techniquesdescribed in this chapter apply to both normal andemergency ratings.

3.4.8 Inferring Conductor Temperatures from Measured Temperatures

Some cable installations have temperature monitoringusing thermocouples or distributed fiber optic tempera-ture sensing (DFOTS) (both described in Section 3.6.4).The temperature measurements are commonly availablein one or more locations:

• Under the cable jacket (for DFOTS)

• Outside of the cable jacket or cable pipe (for thermo-couples) when direct buried

• Duct air temperature (either DFOTS or thermocou-ples)

• Parallel conduit or cable pipe (either DFOTS or ther-mocouples)

The conductor temperature of a neighboring cable canbe inferred by comparing the measured and calculatedtemperatures at one of the above locations until theyagree, usually while varying the inferred native soil ther-mal resistivity.

During in situ or laboratory soil thermal resistivity mea-surements using a thermal property analyzer (describedin Section 3.6.2), a constant heat is injected into the soil(or soil sample) using a thermal probe. A sensitive ther-mistor is used to monitor changes in temperature overtime while the heat is being injected into the soil. Theslope of the change in temperature with respect to timeshows the soil thermal resistivity.

For a buried cable circuit, it is possible to infer the soilthermal resistivity using measured cable temperatures –essentially making the cable a thermal probe. Althoughthe loading (heat input) is not constant, a reasonableassessment of the soil thermal resistivity can be deter-mined and is often a better indication of the effectivesoil thermal resistivity “seen” by the power cable (e.g.,

including effects of moisture migration, etc.) over the insitu measurements or soil samples collected some dis-tance away from the cables.

By using the equivalent thermal circuit to calculate thetemperature at a location where measurements aremade, the effective soil thermal resistivity can beadjusted until the calculated values match the measuredvalues. The effective soil thermal resistivity, combinedwith historical load data—usually 2-4 weeks—can beused to find the temperature of a conductor in thetrench. A more elegant approach is to use the dynamicrating model described in Section 3.8 of this chapter.

3.5 UPRATING AND UPGRADING CONSTRAINTS

Underground cable systems have unique characteristicsthat must be considered when exploring upratingoptions. This section describes the characteristics of eachcable system and installation conditions that may limituprating options and that should be considered beforeexploring any of the uprating methods described later.

3.5.1 Direct Buried Cable Systems

Direct buried cable systems have several limitations foruprating and upgrading mainly due to the fact that thecable is relatively inaccessible, there is generally noopportunity to provide active cooling, and the civilworks cost would eliminate most practical reconductor-ing options. A hot spot along the cable route that isidentified and of relatively short length might be miti-gated. Spot temperature monitoring might also be con-sidered, but retrofitting continuous monitoring is just asimpractical as reconductoring. Soil remediation using alower thermal resistivity soil or, for very short distances,applying heat pipes, could mitigate a hot spot that islimiting a circuit.

If overburden has developed above the cables and this isdetermined to be the cause of a hot spot, the overburdencould be removed to reduce the cable burial depth andthereby improve ampacity.

3.5.2 Fluid-Filled Cable Systems

The pipe in a pipe-type cable system offers the greatestflexibility for uprating and upgrading an undergroundcable system of any cable type. While the pumping orpressurization plant generally requires greater mainte-nance than the other cable types, particularly extruded,the ability to circulate the dielectric liquid (for HPGF,fill the pipe with dielectric liquid and then circulate)allows for both thermal smoothing of a hot spot orforced cooling.

3-26


The pipe size may be a limiting factor because it canconstrain the voltage upgrading (requiring thicker insu-lation wall), or ampere upgrading (requiring a largerconductor) may be limited.

Note that mitigating a hot spot on a pipe-type or self-contained fluid-filled cable system, allowing a greateroverall ampacity, may mean that other sections of thecircuit will be operating at a higher temperature. Thiswould generally result in greater fluid expulsion in pipetype and, in particular, SCFF cables, which may requirethat the pressurization plant be recalibrated, that thefluid reservoir tanks be resized, or the nitrogen blanketpressure above the oil adjusted to accommodate thelarger volume of dielectric liquid. Alarm settings mightalso need to be adjusted.

3.5.3 Duct Bank Installations

Duct bank installations do not offer significant optionsfor uprating. The concrete encasement that is commonto duct banks generally has good thermal resistivity.The impact of overburden on the circuit might be inves-tigated and, in extreme cases, the native soil around asection of duct bank might be replaced with lower ther-mal resistivity material.

Often a problem associated with duct banks is the rela-tively high congestion of cable circuits in those loca-tions. Sometimes expensive transmission cables aresignificantly derated by a low-cost and relatively verylow power transfer distribution cable. One possibleremediation method could be to remove the distributioncircuits entirely, or replace the distribution cables with alarger conductor or multiple cables per phase to reducethe heat output and mutual heating effects.

Duct bank installations allow for upgrading options inthat existing cables may be removed and new onesinstalled relatively easily. If a particular section of a cableroute is found to limit overall ampacity and a section ofcable with a larger conductor is available, that particularsection could be replaced to mitigate the hot spot.

Ducts may also be filled with water or grouted with alow-thermal resistivity grout to improve thermal con-duction between the cable surface and conduit.

3.5.4 Trenchless Installations

Trenchless installations – horizontal directional drilling(HDD), pipe jacking, or microtunneling – have some ofthe limitations of the direct buried system such as beingessentially inaccessible. However, trenchless installa-tions typically use inner ducts – some with spare pipesor conduits – that may be used to mitigate hot spots andimprove ampacity. The inner ducts allow a cable phase

to be removed and replaced, possibly with a larger con-ductor size. To improve ampacity, the casing in a trench-less installation may be filled with water or a low-thermal resistivity grout to improve heat transfer awayfrom the cables and conduits. Filling the annular spacebetween the inner ducts and the casing will allow heat topass through a low thermal resistivity grout (0.8 C°-m/Watt) or water (1.6 C°-m/Watt) rather than air(45 C°-m/Watt).

3.5.5 Other Installation Locations

TunnelsTunnel installations offer some unique considerationsfrom the standpoint of uprating. First, the cables aregenerally more accessible than for buried cable systems,so this more easily facilitates maintenance and repairs.However, tunnel installations do not benefit as muchfrom the long thermal time constant of direct buried,pipe, or conduit installations because the cables areessentially installed in air. Some tunnel installationsmay be limited by the maximum allowable air tempera-ture from the standpoint of work safety or heating/ven-tilation/air conditioning (HVAC) limits. Depending onthe tunnel configuration, it may be difficult to addforced air ventilation to the tunnel to improve capacity.Also, extruded or self-contained cables that are rackedin troughs or by mechanical supports could be subjectedto damage from thermal-mechanical bending (TMB)effects during increased temperature operation.

“Deep” Installations Including Water CrossingsSomewhat like trenchless installations described above,“plowing in” cables or cable pipes in water crossingsmakes installation of a specialized thermal backfillimpractical. Also, mitigating a hot spot at one of theselocations is not easily accomplished because there is lit-tle control over the sedimentation that can build abovethe cables. The best approach is to properly account forthe soil conditions – both thermal resistivity and ambi-ent temperatures – in developing ratings.

Overhead (In Air) InstallationsCables installed in air, for example on bridges or risers,do not benefit from the long earth thermal time con-stant of buried cable systems. In most cases, the in-airnormal ampacity is greater than the buried normalampacity.

However, the cables may be exposed to high ambient airtemperatures and possibly solar radiation and also lackthe long earth thermal time constant of buried cables,possibly limiting the emergency rating capacity of in-airsections. Mitigating ampacity limits for in-air sectionsmay be difficult, particularly if solar radiation is an issuesince shielding the cables from solar heating can beimpractical.

3-27


3.5.6 Hot Spot Identification

Hot spot identification is sometimes difficult to dobecause of restrictions on accessing the cables. Distrib-uted temperature sensing (DTS) fiber—the state-of-the-art for cable temperature monitoring—is often difficultto retrofit. More traditional approaches to finding hotspots involve studying plan and profile drawings andevaluating the impact of other known heat-producingservices in the area around cables.

If DTS can be applied, the hot spots can be readily iden-tified, although the causes may not always be obvious.

3.5.7 Accessories

JointsFor the most part, joints do not normally limit a cablecircuit’s ampacity, particularly when the joints areinstalled in manholes that often run cooler than thedirect buried soil sections. However, directly-buriedjoints on pipe-type cables may limit ampacity because ofthe added layers of hand-applied paper tape insulationthat are used to construct the joint, adding additionalthermal resistance to heat leaving the joint. Forced-cooled pipe-type cables may result in a thermal limit atjoints. The forced-cooling fluid circulation essentiallymakes the surface of the cable an isotherm. With theadded insulation applied over the joint resulting inincreased thermal resistance, the connector may be run-ning hotter, limiting the rating.

TerminationsIn general, terminations are not the limiting factor foruprating cable systems except on forced-cooled pipe-type cables or in areas with a very high ambient air tem-perature. In forced-cooled pipe systems, the dielectricliquid circulation cannot cool the termination, so theterminations rather than the cable sections become alimiting factor. EPRI report EL-2233 on high-capacityterminations gives additional details about this subject(EPRI 1982).

3.5.8 Hydraulic Circuit

In pipe-type cables, the hydraulic circuit may limituprating opportunities under some circumstances.

For example, if there is no return pipe or there is onlyone pipe circuit, it would not be possible to circulatedielectric liquid within the pipe. Some utilities are reluc-tant to use fluid circulation where the hydraulic circuitinvolves moving liquid down one energized cable pipeand back another, mainly because if a failure occurred,the “healthy” circuit could be contaminated frombyproducts of the fault. Although there will be lessmutual heating with the parallel circuit out of service,

the rating on the healthy circuit will probably dropbecause fluid circulation cannot continue.

A small amount of fluid movement might be achievedby oscillating the dielectric liquid within the pipe usingthe 7500–11,000 liter (2000–3000 gallon) fluid reservoirtanks on either end of the circuit if at least 3,750 liters(1000 gallons) of additional dielectric fluid can beaccommodated in the existing reservoirs on each end.

The extent of pipe filling—degree to which the cables fillthe free area of the pipe—may also limit dielectric liquidcirculation rates because the pressure drop betweenpumping plants may be too great even when using a lowviscosity dielectric liquid.

3.6 INCREASING THE AMPACITY OF UNDERGROUND CABLES

Once there is an understanding of the possible limita-tions associated with each cable type, it is necessary toconsider how uprating might occur on a given circuit.This section describes various techniques that may beapplied to investigate ampacity limitations and thenways to improve ampacity, or at least have a betterunderstanding of what is limiting the ampacity.

3.6.1 Route Thermal Survey

A route thermal survey has traditionally involved evalu-ating the entire cable route in a detailed manner tounderstand ampacity limitations. Many North Ameri-can utilities adhere to Association of Edison Illuminat-ing (AEIC) standards regarding cable design. One of theprinciples of these standards is that if the soil character-istics are not well known, the design ampacity should bebased upon a maximum operating temperature that is10°C below the allowable operating temperature (e.g.,values in Table 3.4-8).

Regardless of following the AEIC standards or not, util-ities have sometimes designed cable circuits without agood knowledge of the route characteristics, particu-larly on older circuits. In these cases, the ambient soiltemperature and soil thermal resistivity were not wellknown, so assumed values were often incorporated intorating calculations. Those following the AEIC guide-lines obtained some additional conservatism in the rat-ings by using the lower 10°C operating temperature inthe event that the assumed parameters were inaccurate.However, as the circuits age and load growth continues,many utilities are revisiting the rating assumptions tosee if additional transmission capacity is available with-out major investment in infrastructure.

Also, during the process of uprating a cable circuit, hotspot mitigation may require removing existing trench

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backfill materials and replacing it with a good qualitythermal backfill.

The following subsections discuss some of the tech-niques employed for a route thermal survey anddescribe soil and backfill characteristics that are impor-tant to consider in evaluating methods for upratingcable systems.

Thermal Property AnalysisIn the equivalent thermal circuit, the earth thermalresistances are the largest component, typically repre-senting over 50% of the total thermal resistance. Theyare also the least understood. As compared with over-head lines, where weather parameters (wind speed anddirection, solar radiation, temperature) may be valid for1-2 km of line length, soil characteristics along under-ground cable routes can vary over a few meters. If thecables are buried in city streets, there exists a strong pos-sibility of encountering “borrowed fill” instead of nativesoils. These “fills” may satisfy civil/construction require-ments, but if topsoil, cinders, or organic soils are used,the thermal performance may be very poor. For this rea-son, it is very important to test the soils so that appro-priate values of thermal resistivity may be used in designcalculations.

Thermal property analysis based on transient heat flowwas first suggested as early as 1888 (Wiedman 1888).During the mid-1900s, significant research and otherwork were conducted in North America (Mason andKurtz 1952; Blackwell 1954; Carslaw and Jaeger 1959).This demonstrated the practical use of a thermal needle“line heat source” method. The Insulated ConductorsCommittee, organized in 1947, performed a specialproject on soil thermal resistivity in 1951. A special sub-committee (No. 14) headed by Professor H. F. Win-terkorn of Princeton University continued work in thisfield for 10 years and published the AIEE CommitteeReport in 1960.

In the 1970s, EPRI-sponsored research resulted in thedesign and development of the Thermal Property Ana-lyzer. The basic approach was to develop a portable,fully automated test instrument with standardized test-ing procedure that could be employed for both field andlaboratory with results that could be extended to powercable systems.

Thermal ResistivityThermal resistivity, sometimes call “rho,” is a propertyof a material. In the contents of cable installation andfield measurements, the thermal resistivity is measuredfor a soil or trench backfill. The most commonapproach to thermal resistivity measurements now is the“transient thermal needle” method, which is based onthe “line heat source theory.”

Essentially, an underground cable is a long distributedheat source. The “transient thermal needle” methodtakes advantage of this characteristic by using a “ther-mal probe,” which contains a heating coil throughout itslength and a thermistor type temperature sensor at themid-point of the heater. The length-to-diameter ratio ofthe probe is high enough so that end effects do notimpact the measurements. An example thermal probe isshown in Figure 3.6-1.

Once the probe is installed in the soil sample or in thenative soil (field), the heater in the thermal probe isenergized with a constant power while the change intemperature is recorded over time (usually 20–30 min).The slope of the log time-temperature curve is propor-tional to the thermal resistivity of the soil sample. Athermal property analyzer (TPA) was developed toautomate this process and is commonly used for bothfield and laboratory measurements (Figure 3.6-2).

The transient thermal probe method (e.g., IEEE Stan-dard 442) is a relatively quick and accurate approach tomeasuring soil thermal properties, provided the theoret-ical assumptions are understood and care is taken in thetest setup to stay within the limits of the theory. The testassumes various conditions:

Figure 3.6-1 Thermal probe used for field thermal resistivity measurements.

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• The probe is an instantaneous and constant heatsource (no thermal capacitance).

• Heat flow is radial.

• Conduction is the only mechanism of heat transfer.

• No contact resistance exists at the soil/probe interface.

• An infinite sample boundary exists.

• The test sample is homogeneous and at moisture andthermal equilibrium.

• No moisture migration occurs during the test.

For these assumptions to be valid, it is important thatthe probe insertion and testing be performed carefully,usually by a qualified specialist, to ensure that theresults are valid. Contact resistance is very importantand a critical part of inserting the probe into the soil.Also, it is important to keep the probe temperature atreasonable values to avoid drying the soil.

A drill rig with a hollow stem auger is used to drill downto the required depth for soil sampling and to performin situ thermal resistivity measurement tests. Sometimesa backhoe or hand digging down to the required depthis also used to access the soil where testing will be done.In the case where the hole is advanced using a drill rig,the thermal probe is attached to an extension rod andthen tapped into the native soil at the required depth.The testing is then performed from the surface (see Fig-ure 3.6-1).

In addition to field measurements, called in situ mea-surements, soil samples are collected during soil boring

for detailed laboratory analysis and to evaluate parame-ters such as dry-out curves (thermal resistivity as a func-tion of moisture content under constant dry density; seeFigure 3.6-3) or thermal stability that cannot be doneeffectively in the field. The samples are collected in thin-wall Shelby tubes. If the soil is very loose or noncohesive(granular), a split spoon sampler or large diameter Cali-fornia sampler with liners is used to collect undisturbedsamples. If soil conditions (granular, very hard or rocky)are such that undisturbed tube samples cannot be col-lected, either disturbed bulk samples or auger cuttingsare taken. If bedrock is encountered, core samples of 5–8 cm (2–3 in.) diameter are collected to be tested in thelaboratory. Standard ASTM procedures should beimplemented for soil boring, sampling, storage, andtransportation.

Borehole logs, which characterize the soil types withdepth, are often made so that if the cable burial depthvaries, the type of native material – and its thermal resis-tivity – can be known for rating purposes. A typical borehole log is shown in Figure 3.6-4. The borehole loginformation may also be used for other geotechnicalpurposes such as designing structural loads, laying outdirectional drilling route, etc. This geotechnical infor-mation is very useful for the civil contractor to deter-mine the type of equipment required for excavation,

Figure 3.6-2 Thermal Property Analyzer (TPA) used for field and laboratory thermal resistivity measurements.

Figure 3.6-3 Example thermal dry-out curves for various soil types with pores between soil grain particles saturated with water (A), and dry (B).

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Figure 3.6-4 Example borehole log.

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dewatering, backfilling, and other activities. The ambi-ent temperature recorded at the start of an in situ ther-mal resistivity test is an important value to record forthe cable designer.

In the laboratory, a soil sample is prepared to evaluatethermal dry-out characteristic– the variation in thermalresistivity of the material as a function of moisture con-tent. The results of these tests (dry-out curves) are pre-sented on charts that show thermal resistivities at the insitu moisture content (if known), at “critical moisturecontent,” and in totally dry condition (worst case). Somedegree of drying beyond the native moisture levels shouldbe expected in the presence of energized power cables, soan adjusted soil thermal resistivity that factors in the dry-ing should be incorporated into ampacity calculations.

Once the soil thermal resistivity results are known, theycan be used in ampacity calculations. For the case ofinstalled cable systems, it may be necessary to do testingoutside the cable trench to get native conditions, andwithin the cable backfill to characterize the special ther-mal backfill that may have been used around the cables.If the trench is known to have a common materialthroughout, testing of the backfill material may only beneeded at a few selected locations.

Thermal DiffusivityAlthough thermal diffusivity is not commonly recorded(typical transient needle TPA equipment can measurethis parameter) for most applications, its application is in“transient” calculations. In simple terms it can be treatedas the “inertia” in the heat and mass transfer equation.The three terms—resistivity (ρ), diffusivity (α) and heatcapacity (C)—are related by Equation 3.6-1.

3.6-1

Thermal StabilityThermal stability is a system-driven parameter and is asoil characteristic that describes how well a soil main-tains a constant thermal resistivity when exposed tocable heating. The main issue is to consider if the heatleaving a cable would result in the soil being below itscritical moisture content, in which case the soil wouldexperience net drying and an increase in thermal resis-tivity. Smaller diameter cables with direct contact to thesoil are more likely to result in thermal instabilitybecause of a larger heat flux (temperature gradient) atthe cable-soil interface.

A classic example of a thermally instable material ismodeling clay. The clay can be dried at room tempera-ture over time. If the dried sample is then placed inwater, it does not readily reabsorb water to return to a

malleable substance. Some soils—including soils withhigh clay and silt contents—have these characteristics. Acommon situation where this may be an issue for powercables is the use of bentonite as a grout material eitherin trenchless casing installations or for cable conduits;pure bentonite has high thermal resistance and is proneto drying. Bentonite is prone to shrinkage and cracking(leaving voids) if drying does occur. A better solution isto use as much sand as possible while minimizing thebentonite content, and to seal the ends of the casing orducts so that the grout cannot dry.

Moisture Migration in the SoilFor any given soil or backfill, the major influence on thethermal resistivity is the moisture content. In a dry state,the pore spaces between soil particles are filled with air(thermal resistivity of about 45°C-m/W). As water (ther-mal resistivity of about 1.65°C-m/W) replaces air, thesoil resistivity decreases substantially by as much as 3 to7 times, as the good heat conduction paths are expanded(additional thermal “thermal bridges”). This is illus-trated by the “thermal dry-out curve” (thermal resistiv-ity vs. soil moisture content) shown in Figure 3.6-3. Asoil that is better able to retain its moisture, as well asbeing able to efficiently re-wet when dried, will have bet-ter thermal performance characteristics. The soil watercontent is expressed as a percentage of the weight ofwater to the dry weight of soil solids, as determined byoven drying at 105°C.

The heat generated by energized cable tends to cause soilmoisture to migrate away from the cable/backfill inter-face. In unstable backfills or soils, this drying increasesthe resistivity substantially, inducing further heating ofthe cable and thus more drying of the soil. Eventuallythis cycle may create a totally dry zone of the backfillaround the cable, resulting in excessive heating andpotential thermal runaway. In a stable backfill, the heat-induced drying raises the resistivity marginally, thusminimizing the potential for thermal runaway.

Thermal stability is best illustrated by means of thermaldry-out curves (Figure 3.6-3). The “critical moisture” isdefined as the moisture content below which the rela-tively flat nature of the thermal dry-out curve gives wayto a disproportionate increase in the thermal resistivity.Above the critical moisture a soil will resist thermal dry-ing (by means of capillary suction), whereas below thisvalue, thermal runaway is inevitable (unless soil mois-ture is externally replenished, (i.e., rain).

Although some native soils at high moisture content(10–25%) may exhibit fairly low thermal resistivity (0.4to 0.6 °C-m/W), this value may increase a few fold whendry. Well-graded sands and stone-dust containing 10–

1Cρ α⋅ ⋅ =

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15% fines (-200 Sieve size material) make good correc-tive thermal backfills.

Cable Route Soil Test SpacingThe soil testing and sampling frequency for thermalresistivity testing along the cable route can vary depend-ing on the area and the length of the route. In ruralareas, where the use of fills is minimal and historicalconstruction has not been significant, sampling and in-situ testing every 500 m might be done. In urban areasor locations where fill materials have been used, sam-pling might be done every 200–500 m. Known varia-tions in geology or other conditions might affect howoften along the route testing and sampling are done.The goal of testing is to capture test results for anyunique soils and potential hot spots along the cableroute while categorizing where each soil type is found.

Factors Affecting Soil Thermal Resistivity

Soil CompositionThe soil composition is an important characteristicaffecting soil thermal resistivity. Soils are typically aconglomerate of various materials, and the ratio of thesematerials within a soil affects the thermal resistivity.Table 3.6-1 summarizes the dry thermal resistivity val-ues of various components.

Because the soil components are so important in affect-ing the thermal resistivity, a good understanding of thegeology along a cable circuit is valuable to assessingwhere soil testing should be performed and how muchvariation might be expected along a given cable route.

It is important to note from Table 3.6-1 and Figure3.6-3 that dry soils have a much higher thermal resis-tance than moist soils because the thermal resistivity ofwater (1.65 C°-m/Watt) is much lower than that of air(~45 C°-m/Watt). In addition to the air having higher

thermal resistivity, heat transfer takes place by radiationinstead of conduction that is much less efficient.

Soil Texture and Dry DensityThe soil texture is also critically important to thermalresistivity. The grain size distribution and grain shapeare evaluated by a sieve analysis (e.g., ASTM D422,etc.) to determine the variation in particles both inbackfill materials and native soils. Figure 3.6-5 shows asieve analysis for four materials and a band of “good”granular thermal backfill.

Water Content and Ground Water LevelAs is seen in Figure 3.6-3, soils with higher moisturecontent generally speaking have better thermal resistiv-ity. Some soils naturally retain water better than others.Certain soils may not retain water well—e.g., they havea high hydraulic porosity—but are below the water tableso they remain saturated even though the dry density islow and dry thermal resistivity would otherwise be high.

Dry DensityThe dry density of a soil determines its ideal ability toconduct heat away from the cables. Factors that influ-ence the dry density are porosity, solids content, inter-particle contacts and pore size distribution. Having awell-graded material with a range of particle sizesimproves the dry density and minimizes pores and voidsin the material.

Other Subsurface CharacteristicsConcerns for solutes and hysterisis apply only in areaswhere significant fluctuation in the water table may“wash out” fines from the backfill, making it thermallypoor. For most applications, this is not a concern forcable system uprating and, in any case, would be foundduring soil thermal resistivity testing.

Surface Characteristics and VegetationSurface conditions have an impact on soil thermal resis-tivity. For example, soils below asphalt roadways gener-ally will not gain or loose moisture readily under normalconditions. However, in the presence of cables, the dry-ing that does occur may not be mitigated by heavy rainssince the water will not be easily reabsorbed.

Surface vegetation can be significant factor affectingsoil thermal resistivity. The root systems on large treesand plants will draw moisture out of the soil, drying it.Also, the decaying components of plants and their rootsystems will tend to increase the organic component ofsoils, which tends to increase the soil thermal resistivity(see Table 3.6-1).

Surface cover has strong influence over earth ambienttemperatures, especially at shallower depths. A differ-ence of 4–5°C has been measured between grasses ver-sus asphalt cover over cables.

Table 3.6-1 Thermal Resistivities of Soil Components

ComponentDry Thermal Resistivity

C°-m/Watt

Quartz 0.12

Granite 0.30

Limestone 0.40

Sandstone 0.50

Shale (sound) 0.60

Shale (highly friable) 2.00

Mica 1.70

Ice 0.45

Water 1.65

Organics (peat, etc.) ~5.00

Petroleum Oil ~8.00

Air ~45.00

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Engineered Thermal BackfillsThe general goal of engineered thermal backfills (ETB)is to enhance the removal of heat away from buriedcables. In most cases, the native soil materials have ahigher thermal resistivity than good quality backfillsand, in any case, are difficult to reconstitute in thetrench with the same density as the native soil. For thisreason, special backfill materials are often designed foruse in a cable trench. These include well-graded sands,stone screenings, and concrete or Fluidized ThermalBackfill. In addition to having excellent thermal proper-ties, they are engineered to meet civil requirements(strength and ease of voids-free installation) that areassociated with the particular application. The criteriaconsidered for these ETB are:

• Low thermal resistivity over the expected range ofoperating conditions

• Low critical moisture content and high thermal sta-bility limits

• No adverse affects on materials used for cable con-duits, cable jackets, or pipe coatings

• Easy to install

• Inexpensive and locally available to the locationwhere the materials will be used

Types of engineered thermal backfills are discussed inthe following sections.

Granular Backfill MaterialsThese materials should be composed of hard, well-graded, natural or crushed mineral aggregate (limestone,granite, quartz or other similar rock). The materialshould be sound (porosity less than 2%) and be free ofany organic material (peat, root matter, topsoil, vegeta-tion) and foreign matter (wood, rubble, cinders). Thesieve analysis should match closely to that given in 3.6-5.The maximum particle size should be no larger than 1/4-in. sieve size with a fines content (material finer than#200 sieve size) of 12% to 18%.

During supply and installation of this material, qualityassurance is very important. Sieve analysis on the deliv-ered materials should be performed periodically to checkand verify its compliance with the above characteristics.

Figure 3.6-5 Grain size distribution for soil samples.

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Fluidized Thermal Backfill (FTB)One of the difficulties with any granular backfill is thatit must be installed properly, regardless of its ideal ther-mal properties. Granular backfills should be installed inshallow lifts 15 cm (6 in.) at a time and well compactedto give good density. This is labor intensive, and greatcare must be used when working close to directly-buriedcables or conduits so as not to damage either.

Leading up to and during installation, FTB delivered tothe project site should conform to the respective mixdesign and performance specifications of low-strengthand/or high-strength FTB. This should be checked withsamples collected during the project. When installed bypouring into the cable trench, the material should befree flowing and without any segregation. This will helpensure that the material completely surrounds thecables, conduits, or pipes. The amount of water in theFTB mix may be adjusted to increase or decrease theflow (slump) as directed by the field engineer. If lowerslump FTB is required for a particular area, it is gener-ally better to adjust the water content at the batch plantrather than as the material goes into the trench. Air con-tent (natural trapped) should not be higher than 2%.Mixing at the batch plant and transportation to theproject site should be done in accordance with ASTMor American Concrete Institute (ACI) specifications.

If trench shoring and sheathing is being used, theseshould be removed immediately after the installation ofFTB, unless otherwise required by the field engineer. IfFTB is installed in cold conditions, care should be takento protect the installed FTB from freezing. This appliesto both low-strength and especially high-strength FTB.ASTM or ACI specifications should be followed forsuch installations. Sampling and testing for quality con-trol/assurance should be performed on FTB samplestaken every 250 ft along the cable trench, or every 100cubic yards of material installed, or as directed by thefield engineer.

Component materials from an FTB mix design areshown in Figure 3.6-6.

Grouts for Cable Conduits and Trenchless CasingsFor extruded or self-contained cables in ducts or thespace between inner-ducts and trenchless (directionaldrilling, pipe jacking, etc.) casings, the air space betweenthe cable and conduit or conduit and casing is often filledwith air, which is a poor thermal conductor. Filling theduct with a thermally conductive material improves thecable ampacity by 5–10%, depending on the configura-tion and the type of filler. The annular space is generallysmall, and utilities usually want to retain the ability toremove the cables from the conduits later in the event ofa failure or for upgrading. Therefore, it is not practical tofill the annular space with a solid filler material (or one

Figure 3.6-6 Component materials used in a typical Fluidized Thermal Backfill.

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that becomes solid over time), so a pumpable materialthat will not hard set is ideal.

IEC-60287 allows that cables with grouted conduits maybe treated as direct-buried cables for the purposes ofampacity. Various materials that have been consideredfor conduit grouts are:

• Bentonite and sand/bentonite slurry

• Sand-cement grout

• Flyash-cement grout

• Grease and viscous oil, along with other compounds

• Water

Factors that must be considered when selecting a groutare the total length that must be filled and the amount ofannular space. For trenchless installations, the potentialsoftening of a plastic duct at elevated temperatures—including potentially the heat generated as cement-basedgrouts cure—could soften ducts and cause partial col-lapse. The safe pumping pressure for the grout materialmust therefore be considered when a grout is pumped onthe outside of air-filled cable conduits.

The grout material typically will have a thermal resistiv-ity of 0.4 to 1.4 C°-m/Watt, which is much lower thanair (45 C°-m/Watt) at the set moisture content. A sand-bentonite slurry backfill with a thermal resistivity ofapproximately 0.7 C°-m/Watt is easy to formulate andgenerally easy to install. Varying the amount of sand,bentonite and water affects the pumpability of thegrout. Bentonite tends to absorb a lot of water, so thismust be factored into the mix. Mixing the sand/bento-nite slurry also requires special equipment (i.e., colloidalmixer). The thermal resistivities of these componentsare as follows:

• Sand: 0.12-0.20 C°-m/Watt—optimizes the thermalresistivity but negatively affects pumpability.

• Water: 1.65 C°-m/Watt—optimizes the flowabilitybut negatively affects shrinkage.

• Bentonite: 3.50 C°-m/Watt—optimizes the pumpabil-ity but negatively affects thermal resistivity.

These materials are combined by a soil specialist for useby the contractor or utility during installation.

3.6.2 Review Circuit Plan and Profile

A classical approach to performing uprating on under-ground cable circuits is to review the circuit plan andprofile drawings, preferably the “as-built” versions,which may show additional details about the locationsof the buried power cables, as well as better illustrate the

locations of other underground utilities that may impactcable ratings.

The plan drawings will show a variety of factors thatmay be relevant to determining the cable ampacity andpossible locations where uprating could be considered:

• Phase and circuit or pipe spacing among the cablesbeing studied, which would impact mutual heatingeffects.

• The locations of other utilities that cross the cables,especially other transmission or distribution cablecircuits that could produce mutual heating effects.Also, steam lines may be present.

• Sections of the route that parallel other utilities,including power cables. Parallel cables within a cer-tain range may produce sufficient mutual heating tocause derating. A general guideline is, if the horizon-tal spacing is within 25% of the depth, mutual heat-ing may be a factor (e.g., if the cables being studiedare at 4 m depth, parallel cables or other heat sourceswithin 1 m horizontal spacing should be examinedfor mutual heating effects).

• Topographical profiles may show areas where over-burden has accumulated above the cable route.

Profile drawings mainly indicate the cable circuit’s depthof cover below grade and usually the locations of otherutilities that cross the cable circuit. Areas that areimportant to note on the profile drawing are:

• Entry/exit to manholes since cables frequently dip toenter a manhole

• Road crossings where the cable burial depth may beincreased to accommodate the required road beddingmaterials

• Directional drilling locations where the burial depthis significantly greater than conventionally-trenchedsections

3.6.3 Evaluate Daily, Seasonal, or Other Periodic Load Patterns

Load shape is generally not that important for mosttransmission equipment, particularly overhead lineswhere the thermal time constant is relatively short. Withunderground transmission cables, the long thermal timeconstant—35–150 hours—can significantly impactloading patterns for both normal and emergency rat-ings, particularly for short-duration emergencies.

In typical normal ampacity ratings on cables, daily loadcycles are modeled by rating techniques through theapplication of a load factor or loss factor. The load fac-

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tor relates the average daily load to the peak load, usu-ally following a relationship similar to the following:

Loss Factor, p.u. = 0.3 (Loss Factor, p.u.) + 0.7 (LossFactor, p.u.)2

This relationship is graphed in Figure 3.6-7. As men-tioned earlier, the loss factor (or load factor of thelosses) considers the average daily heat output relativeto the peak heat output. Consider Figure 3.6-8, whichshows several load shapes that all have the same peakcurrent but substantially different load and loss factors.

All of the curves in Figure 3.6-8 have the same peak cur-rent (1000 A), but substantially different loss factors.On a daily basis, the different loads shown will releasedifferent amounts of energy into the surrounding soil.This has a significant impact on conductor sizing for adesired rating or on the available current for a givenconductor size. Note that the loss factor is also the per-unit power delivered on a daily basis.

If the cable construction and installation conditions areheld constant and the loss factor is varied, the cable rat-ings will vary substantially.

From the standpoint of uprating, increases in loss factorover time mean that the ampacity will tend to decrease.For example, on a recent uprating study for a NewEngland utility, the loss factor in 1959 when the circuitwas built was 57% but had grown to 83% in 2001. Whilethe utility was able to increase capacity on the circuitwith some extraordinary methods, the normal book rat-ing actually decreased with respect to time because ofthe increasing loss factor.

Load shape may also play an important role from thestandpoint of emergency ratings. If the daily load cycleis such that the load during portions of the day (typi-cally at night) is lower than at other times of the day(typically mid-afternoon), short duration emergenciescan vary greatly. This is illustrated in Figure 3.6-9,where the normal ampacity (1.0 per unit), A, is deter-mined for a peak temperature of 90°C, and two 4-houremergency ratings are determined:

• Emergency Rating B: The peak temperature is 105°Cwith a rating of 2.6 per-unit (as compared to the nor-mal rating). This emergency starts going into a low-load period, so the pre-emergency load temperatureis about 73°C.

• Emergency Rating C: The peak temperature is also105°C with a rating of only 1.3 per-unit (as comparedto the normal rating). This emergency starts goinginto a peak load period, so the pre-emergency tem-perature is about 85°C.

The above example illustrates that considering the loadshape for emergency ratings is important. Dynamic rat-ings (see Section 3.8) is a main benefit for this type ofanalysis in optimizing—and generally increasing—thecurrent carrying capacity of an underground cable circuit.

Figure 3.6-7 Ampacity as a function of loss factor.

Figure 3.6-8 Graph of load profiles showing the same peak current with different load and loss factors. Figure 3.6-9 Temperature plots and ratings as a

function of rating starting time.

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3.6.4 Temperature Monitoring

Using ThermocouplesTemperature measurements are an important part ofverifying assumptions when calculating ampacity andstudying ways to improve ratings. Ideally, one wouldwant to measure the cable conductor temperature—thehottest location in the cable system—to be sure thatinsulation temperature limits are not exceeded. How-ever, because the conductor is energized, this is typicallydifficult to do. Instead, it is common to measure thetemperature on the outer surface of the cable either onthe pipe coating of a pipe-type cable or the jacket of theother cable types. For conduit installations, tempera-tures might be measured in the conduits.

To perform these measurements, thermocouples areoften used. Thermocouples are temperature sensorsbased on the principle that when two dissimilar metalsare joined, a predictable voltage will be generated thatrelates to the difference in temperature between themeasuring junction and the reference junction (connec-tion to the measuring device). The types of metals thatare used depend on the application (temperature range,location, cost, etc.). There are varieties of thermocoupletypes (T, F, N, J, etc.). For cable-related measurements,“Type-T” thermocouples are most often used becausethey have a temperature range most closely matched totypical cable operating temperatures. The Type-T ther-mocouple has a blue outer jacket in the United States,France and the United Kingdom (up until 1993) or darkbrown outer jacket in the United Kingdom (since 1993)and Germany. Inside, the thermocouple wire consists ofa copper electrode (positive, +) and a constantan elec-trode (negative, -). Each electrode has an insulatingcoating that varies in color depending on the country oforigin (United States is blue on the positive and red onthe negative; the United Kingdom is white on the posi-tive and blue on the negative (pre-1993) or brown on thepositive and white on the negative; France is yellow onthe positive and blue on the negative; and Germany isred on the positive and brown on the negative). Whenconnecting thermocouple wire to a meter, data logger,or other measuring device, it is important to verify thatthe polarity is correct. Otherwise, the schematic willessentially create three thermocouple junctions in series(rather than one), which could provide misleadingresults. Also, the thermocouple wire or extension gradethermocouple wire must also be run from the measure-ment location all the way to the test instrument.

A thermocouple junction is created by joining the cop-per and constantan wires together as shown in Figure3.6-10. The junction can be left bare, which minimizesthermal capacitance and increases temperature mea-

surement response. However, depending on the environ-ment, the junction may need to be coated or soldered toprotect the thermocouple junction from corrosion, etc.Laboratory-grade thermocouples are typically weldedtogether. A thermocouple has an accuracy of typicallyless than 1 C°.

A key advantage to thermocouple temperature measure-ment is that the wire itself and the equipment to mea-sure thermocouple temperatures are both relativelyinexpensive and minimal training is required to use thetechnology. Several companies including Telog Instru-ments, Omega, and Fluke make data loggers that costless than US $1000 to read and possibly record thermo-couple temperatures. Battery-powered recorders can logdata for 6–18 months, recording temperatures every 15minutes for an extended period. Once suspected orknown cable circuit hot spots are identified, low-costthermocouples and data loggers may be placed at theselocations and checked periodically, particularly duringperiods of high load.

By comparing measured temperatures with those pre-dicted using load history and the equivalent thermal cir-cuit from ampacity calculations, it is possible toevaluate the assumptions used in ampacity calculations.From an operations standpoint, monitoring the cabletemperatures gives some assurance that the cables arenot exceeding their allowable temperature during typicalload cycles.

The main disadvantage to thermocouple measurementsis that they only take a temperature measurement at onelocation. It is, therefore, possible to miss hot spots ifthey are not already identified. Also, the practical leadlength limit of thermocouples is about 300 m (1000 ft),and each thermocouple requires its own pair of wires to

Figure 3.6-10 Thermocouple wires (copper and constantan with U.S. color scheme – left) and completed junction (right).

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make a measurement. Therefore, it is difficult to instru-ment more than a few tens of locations.

Distributed Fiber Optic Temperature Sensing (DFOTS)Distributed fiber optic temperature sensing (DFOTS)uses a specialized optical time-domain reflectometer(OTDR) to measure the temperature along a multimodeoptical fiber. The process works by taking advantage oftemperature-dependent reflections (called “backscatter”based on the Raman Effect) in the fiber. The specialOTDR instrument, such as York Sensors (Sensa) DTS-80 or SensorTran’s Model 5000 (see Figure 3.6-11),records the magnitude of the reflection (proportional totemperature) and the time for reflections to return aftersending an incident 1080 nm laser pulse into the fiber,which, when combined with the fiber’s propagationvelocity, gives the distance to the measurement location.By successively sending light pulses into the fiber, thespecial OTDR can scan the entire fiber and obtain atemperature trace along the fiber with a spatial resolu-tion of approximately 1 m and a temperature accuracyof 1°C. The obvious advantage of DFOTS is that a con-tinuous end-to-end temperature measurement is possi-ble, allowing the ampacity study to reveal all of the hotspots along the cable route. Later, these hot spots couldbe instrumented with thermocouples for extended tem-perature measurements at key locations.

Depending on the configuration of the fiber (number ofsplices, etc.) and the temperature measurement mode(single or double ended), a fiber length of 5–10 km maybe scanned. Equipment is also available that works withsingle-mode fiber and can measure up to 30 km. How-ever, this equipment suffers from both lower spatial res-olution (4–10 m) and lower accuracy (2–3°C). All fibertest loops are limited by the losses in the system, sofusion splicing is the preferred method for joining fibers.

Fiber used for DTS measurements is typically installedin a parallel conduit or directly buried alongside anexisting cable or pipe. Retrofitting a fiber on a direct-

buried system is impractical unless there is a conduit(communications or power) within a meter or so of theenergized cables in which the fiber may be installed. Anexample of fiber that might be installed directly buriedor in a conduit is shown in Figure 3.6-12.

The fiber optic cable typically consists of four to six 50 x125 μm fibers, each with a 900 μm tight buffer (only 1 or2 fibers are needed, but some may be damaged duringinstallation so spares are desirable), Kevlar strengthmembers to improve pulling strength (usually only3000N, 675 lb), and a fire-retardant PVC jacket.

Some XLPE cable manufacturers are embedding opticalfibers under the jacket of the cable to facilitate tempera-ture measurements (Figure 3.6-13). Since this is physi-cally closer to the conductor—ultimately where wewould like to know the temperature—this has someadvantages.

A disadvantage of DTS equipment is the cost of theelectronics to measurement the fiber temperature, whichmay be upwards of US $60,000. Also, the equipment is

Figure 3.6-11 Distributed temperature sensing equipment.

Figure 3.6-12 Optical fiber cable used for DTS measurements.

Figure 3.6-13 XLPE cable with integrated optical fiber under the jacket.

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not well suited for operation in the field on an extendedperiod of time, which makes “spot” measurements orextended measurements in manholes or stations diffi-cult. Most of the equipment has an operating range of10–35°C, which is fairly limited in particularly warm orcool climates.

3.6.5 Ampacity Audit

An “ampacity audit” involves investigating ampacityfor a cable circuit by applying the various techniquesdescribed in this chapter. The basic concepts includeperforming a soil thermal survey to determine soil char-acteristics and ambient temperatures, evaluating loadhistory, and then calculating ampacity. If AEIC guide-lines are being followed on a circuit that previously hadused assumed soil parameters, the 10°C increase in con-ductor temperature by itself generally allows a 20%increase in ampacity.

The ampacity audit is geared towards verifying theampacity by whatever means are available and assessingwhich locations along the route limit the overall circuitampacity. This might possibly include obtaining aDFOTS temperature trace for the route to find hotspots, or looking at route plan and profiles to find limit-ing installation conditions. These “hot spots” wouldthen be investigated further to see how they might bemitigated.

3.6.6 Remediation of “Hot Spots”

Remediation of hot spots is sometimes possible if thescope of the hot spot is limited.

If the hot spot is the result of overburden, or increasedburial depth, it might be possible to remove some of theoverburden above the cables. This reduces the thermalresistance to heat leaving the cable and may improveampacity.

Poor soil thermal resistivity can often lead to hot spots,particularly if a low quality thermal backfill was used –or not backfill at all. A hot spot may be eliminated orpartially mitigated by excavating around the cables andinstalling a good quality thermal backfill. This willimprove the heat transfer characteristics away from thecable, lowering the operating temperature for a givenload condition.

Heat PipesIn extreme cases, usually where one circuit experiences ahot spot from mutual heating of another circuit, theinstallation of heat pipes can help. The heat pipe is apassive device that takes advantage of the heat of vapor-ization to remove heat from a location. A heat pipe is

constructed using an alcohol-water or ammonia-watermixture in a partially filled copper tube. A partial vac-uum is drawn on the tube to adjust the vapor pressure tothe operating temperature range for the particularapplication. The heat pipe is then installed at an anglewith the low point installed near the heat source (cable,steam main, etc.). Heat from the source is absorbed bythe liquid alcohol-water or ammonia-water solution,causing a phase change to vapor, which rises, carryingthe heat away. The gaseous vapor then condenses backto a liquid away from the hot spot and then drains backto the hot spot location. This continuous processremoves heat from the location. The number and instal-lation geometry of the heat pipes are typically designedby a specialist.

An example of a heat pipe installation to mitigate theeffects of crossing cable circuits is shown in Figure3.6-14.

3.6.7 Active Uprating

The following methods are mostly applicable to pipe-type cables, although there are applications that couldextend to extruded or self-contained cables.

Figure 3.6-14 Heat pipes being installed to mitigate a hot spot where a steam main crosses a pipe-type cable.

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Fluid FillingGas-filled pipe-type cables may be uprated slightly byreplacing the dry nitrogen gas with a dielectric liquidsuch as polybutene or alkylbenzene. Since a liquid is amore efficient heat transfer media than a gas, fluid-fill-ing alone provides a small ampacity improvement (~2-3%). However, this allows for additional uprating meth-ods to be applied.

Fluid CirculationFluid circulation is a relevant uprating technique when ashort section, relative to the overall circuit length, is lim-iting the pipe-cable rating. By circulating the dielectricliquid within the cable pipe, the heat generated in thehot section will be transferred to other portions of theroute, mitigating the hot temperatures at that location.One requirement for this to be implemented is to have afluid return pipe or a parallel cable pipe that will permita continuous circulation path as shown in Figure 3.6-15.Flow rates may be up to 800 liter/min (200 gpm), butslow circulation with only 20 liter/min (5 gpm) may beused for small hot spots or where the fluid viscosity lim-its the flow rate.

If no fluid return pipe or parallel cable pipe is present,fluid oscillation may be used. In this configuration, fluidis moved through the pipe at 4–40 liter/min (1–10 gpm)and cycled between the 4,000–11,000 liter (1000–3000gallon) fluid reservoirs at either end of the pipe circuit.

Major considerations for fluid circulation are the freearea in the pipe and the viscosity of the dielectric liquidused in the pipe. As a result, the pressure rise whenpumping dielectric fluid through a pipe could be tooexcessive for practical uses. If the flow rate is limited to avalue below what is necessary to mitigate a hot spot, cir-culation may not be possible to mitigate a hot spot; theutility might consider changing to a lower viscositydielectric liquid or re-examining pressure rise limitations.

The basic principle of fluid circulation is based on workdone by CIGRÉ and discussed in Electra (CIGRÉ1979). The approach is to evaluate sections of the fluidcirculation route that have basically the same character-istics and then use boundary conditions to match theflow rate from one section to the next. Dielectric liquid(or water in parallel circulation/cooling tubes) is rela-tively noncompressible, although the density varies withtemperature around the circulation loops. To considerthis, the dielectric fluid characteristics—density and spe-cific heat—are adjusted for each section that is beingmodeled. As fluid circulates through the pipes, the tem-perature of the fluid leaving one section is assumed to bethe temperature entering the next section, satisfying theboundary conditions.

To model each section, the “un-cooled” (temperaturethat would result absent of any cooling or circulationmovement in the pipes) temperature is calculated basedon circuit loading, the cable construction, and installa-tion conditions at each section. Then, heat absorbed orremoved would cause increases or decreases in thedielectric fluid temperature as it moves through thepipes. The temperature change with respect to distanceis of the form shown in Equation 3.6-2.

3.6-2

In the equation, x is the distance, K is a value propor-tional to the maximum change in temperature possiblefor a section of infinitively long length, A is a valuerelating the mutual heating affects among the pipes(either cabled or fluid return), and P is a value charac-terizing the rate of temperature change as air movesalong the pipe section. There is one exponential term foreach pipe in which fluid is circulating.

Figure 3.6-15 Example pipe cable dielectric fluid circulation loop with heat exchangers.

( ) exp( )UN COOLEDT x T K A P x−= − ⋅ ⋅ ⋅

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The “un-cooled” temperature is the steady-state temper-ature of the dielectric liquid inside the cable pipe thatwould result if the loading remained fixed on the ener-gized cables and no fluid circulation was in place. As theflow rate is reduced, the value of K approaches zero. Asthe flow rate increases, the value of K approaches thedifference between the inlet temperature of the dielectricliquid and the uncooled temperature for a given section.

Changes in dielectric liquid temperature as it passesthrough the cable pipes provide an indication of the heatbeing removed in each section based on the mass flowthrough the section as defined by Equation 3.6-3.

3.6-3Where:

is the mass flow rate in kg/sec.ρ is the density in kg/m3.

A is the free area within the pipe in m2.

υ is the velocity in m/sec.

The heat removed, Watts, in a given section can then befound from Equation 3.6-4.

3.6-4Where:CP is the specific heat in kJ/kg-°C. TOUT and TIN represent the outlet and inlet temper-

atures, respectively, of the dielectric liquid in agiven section.

By knowing the net heat absorbed or lost in a given sec-tion and the length of that section, it is possible to eval-uate the net heat removed (or gained) in a given section.For a forced-cooled system (described next), the netheat gained by the system will assist with sizing theforced-cooling plant and heat exchangers.

Fluid circulation could be applied to extruded dielectricor self-contained liquid-filled cables by installing parallelwater cooling pipes next to the cables and then circulat-ing water through those pipes. Although technically fea-sible, this is not often done. In addition, some utilitiessuch as National Grid in the United Kingdom circulatethe dielectric liquid in the fluid channel of self-containedliquid-filled cables. Again, this is relatively rare.

Forced Cooling (Water or Oil)Forced cooling is an extension of fluid circulation. Themain difference is that, rather than just moving heataround from “hot spots” to “cold spots” in the cableroute, the dielectric liquid (or water in the case of watercooling of extruded or self-contained cables) is diverted

from the cable pipe, passed through a heat exchanger toremove heat, and then reintroduced to the cable pipe.This has the potential of increasing the ampacity by 50–70%, although the cost and maintenance of these activesystems can be high.

Considerations for Active UpratingWith fluid circulation or forced cooling in pipe-typecables, there are some cautions associated with usingthese uprating methods. Pressures along the hydraulicloop may become excessive as a result of hydrostatichead pressure, fluid flow restrictions near joints, andcross-over plumbing between feeders and fluid returnpipes. The high pressures could cause the terminationhousing to fracture, potentially resulting in a cable fail-ure, dielectric fluid leak, and fire.

Pressure drop along long circulation loops must be con-sidered. The degree of snaking of the cable phaseswithin the pipe can affect the fluid flow and pressuredrop, potentially limiting the flow rate. The pressuredrop as a function of length can found by evaluating theDarcy-Weisbach equation, as shown in Equation 3.6-5.

3.6-5Where:f is the friction factor, empirically determined

based upon the Reynolds Number cable-to-pipe inner diameter ratio.

γ is the density, kg/m3.V is the flow velocity, m/sec.Dh is the hydrostatic diameter, m.

The pumping plant, in particular the fluid circulationpump, must be able to accommodate the circulationpressure. The density and viscosity of the dielectric liq-uid will impact the allowable pressure drop, in additionto the free area within the pipe and the degree of cablesnaking. On long circulation loops, multiple loops maybe needed with intermediate fluid circulation stations tolimit the pressure drop. Complex control systems, par-ticularly in the event of a cable failure, must also bedeveloped to manage the various cooling loops and tostop fluid circulation in the event of a fault.

Fluid circulation is often considered for the buried pipesections. However, when forced cooling is used, the risersections—lengths of pipe between the trifurcator andtermination—may become limiting and could requirespecialized plumbing to allow circulation in these areas.Diffusion chambers may also be necessary to avoiddamaging the outer layers of insulation. A factor toconsider for uprating older pipe circuits, where the riser

υρ ⋅⋅=•

Am

•m

( )P OUT INq m C T T•

= ⋅ ⋅ −

2

2 h

dP Vf

dL Dν ⋅

=⋅

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section may be limiting, is that installation of a diffusionchamber on a riser that is not so equipped can be diffi-cult. This is because working “close in” on the riser pipewould be difficult with the cable already in place, andremoving and installing a new termination to put in thediffusion chamber may be impractical.

3.6.8 Shield/Sheath Bonding Scheme

As discussed to some extent in Section 3.4, there arethree methods for grounding the shield/sheath on single-conductor (extruded dielectric, self-contained fluid-filled) cable systems: multipoint bonding, single-pointbonding and cross-bonding. Multipoint bondinginvolves tying the shield/sheath connections togetherand to local ground at both terminals and usually atintermediate manholes, resulting in a path for inducedcirculating currents but with minimal induced voltages.Single-point bonding involves grounding theshield/sheaths at only one location along a given sec-tion, preventing circulating currents but leaving theother end un-grounded where a standing voltage willappear. Cross-bonding involves dividing the cable sec-tions into groups of three minor sections that are closeto the same length and transposing sheath connectionsat the one-third and two-third locations, thereby elimi-nating net circulating currents and minimizing inducedvoltages.

Generally, single-conductor transmission cables aredesigned with cross-bonding or single-point bonding tominimize shield/sheath circulating currents in the pres-ence of relatively high phase currents. The one exceptionto this common practice is submarine cable installa-tions, where multipoint bonding of the sheath is almostmandatory because of the long installation lengths andtypically wide phase spacing. Contrary to transmissionpractice, most distribution circuits are multipointbonded where the utility transformer and customer ser-vice panel are both grounded for safety and so the neu-tral can carry imbalance currents. The circulatingcurrents in multipoint bonded systems generate addi-tional I2R losses (heat) in the shield/sheath that impactsampacity.

Multipoint bonding systems generally have about 20-30% lower ampacity than single-point bonded or cross-bonded systems constructed with similar cable sizes. Ifthe ampacity audit reveals that a circuit has lowerampacity than desired and happens to be multipointbonded, the shield/sheath connections might be recon-figured for sectionalized single-point bonding or cross-bonding to eliminate the circulating current and gain asignificant improvement in ampacity. The reconfigura-tion may require changing out some or all joints since

the joints must have shield interrupts to provide for sin-gle-point bonding or to facilitate transposing the sheathconnections for cross-bonding. If a system that was pre-viously multipoint bonded is being reconfigured for sin-gle-point bonding, a ground continuity conductorshould be installed to provide a low impedance path forfault current; the shield breaks will otherwise block theflow of fault current. Also, single-phase or three-phaselink boxes or cross-bonding boxes will be needed.

If uprating using a reconfigured sheath bonding schemeis being considered, and utility practice is typically withmultipoint bonding systems, care should be used toclearly mark all manholes where standing voltages mayappear. A shield that is not grounded locally, but is con-nected to ground at the adjacent manhole, may experi-ence a significant voltage rise with respect to localground during nearby system fault conditions from acombination of induced voltages and system potentialshifts. This is not a phenomenon peculiar to single-pointgrounded arrangements, as any shielded cable is suscep-tible when the shield is connected to a remote groundyet remains ungrounded locally. The remedy for this sit-uation is to provide secure, temporary shield groundingas appropriate. This has always been a recommendedpractice. This is particularly important when workingon a de-energized single-point bonded circuit that paral-lels an energized circuit, since the parallel circuit caninduce a voltage.

Also, single-point bonded or cross-bonded cable sys-tems require periodic maintenance to check the jacketintegrity and ensure that there are no unexpected cur-rent circulation paths. Fault location efforts may also becomplicated by single-point bonded or cross-bondedsheaths, possibly requiring that the bonding connectionsbe reconfigured during cable fault location. Jacket faultlocation in duct bank installations is difficult unless theducts are under the water table. Although not techni-cally necessary, many cross-bonded cable systems areinstalled with a parallel ground continuity conductor.Induced currents in this parallel conductor can generateenough I ^ 2 x R losses to produce mutual heating thatcan affect ampacity of the phase conductors.

3.7 RECONDUCTORING (UPGRADING)

3.7.1 Introduction

In contrast to uprating, which is generally defined asimproving the capacity of existing equipment, upgrad-ing considers using available infrastructure to economi-cally put in new cables, replacing existing conductors.This section discusses some of these issues.

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A basic assumption for this section is that the cable sys-tem is either pipe-type or a duct installation. Reconduc-toring a direct buried cable is impractical and reallyshould be considered a new installation, along with theinstallation of a parallel circuit when there is no existinginfrastructure (pipe or conduits). Neither of these casesis covered by this chapter.

One possible scenario might be reconductoring one oftwo parallel cable circuits. The condition of the oldercircuit should be evaluated to see if loss of life or higheroperating temperatures might affect reliable perfor-mance. The upgrading topics in this guidebook wouldapply to the scenario, although the details of evaluatingthe impact on the older circuit or other connectedequipment are beyond the scope of this chapter.

3.7.2 Larger Conductor Sizes

The main issue with considering a larger conductor sizeis whether the cable will fit within the same conduit orpipe. Paper-insulated insulation thicknesses are fairlystandardized based upon voltage class, but the designermight consider using a larger conductor size combinedwith a switch from conventional Kraft paper insulationto laminated paper polypropylene paper (PPP) insula-tion, which has a higher dielectric strength and, there-fore, a lower insulation wall thickness. With pipe-typecables, the issue is to maintain sufficient clearance in thecable pipe. The traditional guideline for new pipe instal-lations is to have at least 12.5 mm (0.5 in.) of clearancein the pipe, as determined by Equation 3.7-1. However,with older pipes, where upgrading would more often beconsidered—either pipes that have cables to be replacedor old but unused empty pipes that might have newcables installed—a minimum clearance of 25 mm (1 in.)is often considered prudent to allow for the possibilitythat overburden or settling may have increased the oval-ity of the pipe that possibly could affect a successfulinstallation.

3.7-1Where:

D is the inner diameter of the cable pipe. d is the diameter of the cable over the insula-tion, plus 1.5 times the height of a skidwire, allvalues in inches.

Figure 3.7-1 shows the clearance in a pipe-type cable.

For extruded or self-contained cables where normally asingle phase would be installed in each conduit, theclearance is simply the difference between the inner

diameter of the conduit and the outer diameter of thecable. Again, it is typical to have 12.5–25 mm (0.5–1.0 in.) of clearance in the conduits. If cables are notalready in the conduits, a mandrel through the conduitsshould be used to check the maximum size cable thatcan pass through the pipe or conduit.

For extruded cables in particular, the construction ofthe metallic moisture barrier and metallic shield couldbe adjusted to allow for a larger cable. As an example,Commonwealth Edison (now ComEd, An Exelon Com-pany) removed 138-kV paper-insulated cables fromducts to be replaced by cross-linked polyethylene cables.If the typical 3.2 mm (0.125 in.) lead sheath moisturebarrier and full-wall 138-kV insulation 21.6 mm (0.85in.) were used, it would have meant the standard XLPEcable design could not fit in the existing conduits.Instead, the installation included a reduced insulationwall (16.5 mm, 0.65 in.), a copper laminate tape withcopper shield wires, and a reduced jacket wall (as com-pared to typical industry practice for that size cable),greatly reducing the outer cable diameter and allowingthe cable system to fit in the conduits.

The relative effect of reconductoring on ampacity is dis-cussed in Section 3.4.

3.7.3 Cupric Oxide Strand Coating

Some cable manufacturers have investigated usingcupric oxide coated strands to make conductors. Bycoating the strands with cupric oxide, each strand has aslightly increased resistance (in the radial direction) toeach adjacent strand. This improves the skin and prox-imity effect factors of the conductor—reportedly downto 0.3 for both values—over conventional copperstranded insulations. This reduction in ac incrementallosses significantly improves the ac to dc resistance ratioand ampacity. To illustrate, the pipe-type cable example

( )2

11.366 1

2 2D d

C d D dD d

⎛ ⎞= − + − − ⎜ ⎟−⎝ ⎠

Figure 3.7-1 Clearance in a pipe-type cable.

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in Appendix 3.1 would show an increase in ampacity byalmost 3% if a cupric oxide strand coated conductorwere used.

3.7.4 Voltage Upgrading

Voltage uprating, possibly combined with an increase inconductor size, would significantly improve the powertransfer limits. As an example, an 8-in. cable pipe that istypically used for 138-kV cables with 11.2 mm (0.44 in.)of Kraft paper insulation might be reconductored with11.4 mm (0.45 in.) of PPP insulation, allowing anincrease to 230-kV cable with virtually no change in theouter cable diameter and a 67% increase in power trans-fer. Additional improvements in capacity might be pos-sible if a larger conductor size can also be used. Section3.2 lists typical insulation thicknesses for the variouscable constructions and insulation materials.

The main issue with voltage upgrading is that, in addi-tion to possibly significant costs in new cables, severalpieces of substation equipment must also be replaced toaccommodate the new voltage level. This is sometimesnot so significant if the higher voltage level being con-sidered for voltage upgrading already exists within bothterminals. Otherwise, the cost and effort generally makevoltage upgrading infeasible.

3.7.5 Superconducting Cables

At the time this chapter is being prepared, supercon-ducting cables are largely in the research stage. Limitedsections of cable have been installed in controlled set-tings (e.g., parallel to a 100% redundant overhead line,in a “laboratory” setting, or in a nonessential capacityunderground). Several high-temperature superconduct-ing (HTS) cable projects have been demonstrated largelywith U.S. Department of Energy funding, using eitherwarm or cold dielectric technology (Figure 3.7-2).

As the names imply, the “warm dielectric” cable usesinsulation that is at or above room temperature to sup-port the energized line-to-ground voltage, while “colddielectric” cable utilizes cryogenic (liquid nitrogen~80°K) insulating medium. Examples of recent researchin superconducting cables are summarized below:

1996-1999

• Pirelli/EPRI: 50 m of 115-kV cable with 2000 A.

• Sumitomo/TEPCO: 30 m of 66-kV cable with 1000 A.

2000-2002

• Pirelli/Detroit Edison: 130 m of 24-kV with 2500 A(system could not be energized because of a vacuumleak in the cryostat).

• Sumitomo: 100 m of 66-kV cable with 1000 A.

• Southwire: 30 m of 12.5-kV cable with 2600 A (oper-ated in parallel to an overhead line on Southwire'sproperty).

• NKT: 30 m of 30-kV cable with 3000 A (utility sub-station).

• Condumex: 5 m of 2000 A (Condumex test facility).

• Nexans / American Superconductor / LIPA: 610 mcircuit 138-kV cable with 2510 A is being developedfor a new installation on Long Island.

Figure 3.7-2 Examples of superconducting cables (courtesy of American Superconductor Inc.).

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While favorable results have been observed, the availabletechnology is not yet practical for typical transmissionvoltages, and the operating lengths have not beenincreased sufficiently to allow “transmission” at whathave typically been considered medium-voltage levels(e.g., transferring bulk power at high-current/low-volt-age). At this point, superconducting cables do not yetoffer a commercially viable means for uprating existingtransmission circuits, though this is likely to changewithin the next decade.

3.8 DYNAMIC RATINGS OF UNDERGROUND CABLE SYSTEMS

3.8.1 Background

As discussed in Section 3.3.1, the thermal time con-stants of underground transmission lines are signifi-cantly longer than those of overhead lines and powertransformers. This is a result of the thermal inertia (orheat capacitance) of the earth that surrounds the cables.As a result of this thermal inertia, the dynamic rating ofunderground transmission lines significantly exceedstheir steady-state ratings, provided that there are signifi-cant variations in the line loading. Conversely, thedynamic rating of underground transmission lines is notmuch higher than their steady-state ratings if the linesare consistently loaded near their steady-state ratings.The term “dynamic rating” means the present rating ofa line, taking into account its load history and real-timemeasurement of parameters (mainly ambient earth tem-perature).

In actuality, the “normal” ampacity of a circuit does notchange, except for changing ambient temperature, sinceit is generally based on an assumed daily loss factor andinstallation conditions. Therefore, a “dynamic” normalrating remains relatively constant unless some decisionabout future loading is evaluated. Predicting futureloading patterns is difficult since unplanned systemchanges may affect loading patterns, but the use of pre-dicted load patterns, usually based on utility SCADAsystems, does allow for some future load estimations(usually limited to 24 hours).

Tracking the cable conductor temperature is the maingoal of dynamic ratings, since this is ultimately whatlimits the power transfer on the circuit. For paper-insu-lated cables, tracking the conductor temperature alsopermits an assessment of insulation aging and ulti-mately the life of the cable system. EPRI funded adetailed investigation of paper-insulated pipe-typecables in the 1990s. Transformer ratings have been basedon a variety of factors including the insulation agingand loss-of-life criteria. However, application of insula-

tion aging and “acceptable loss of life” has not oftenbeen considered for underground cable ampacity.

The main benefit to dynamic ratings is the ability totrack the cables’ temperatures with time and changingload conditions and then base emergency ratings on theactual, rather than assumed, pre-emergency tempera-tures. The benefits of this type of evaluation were illus-trated in Section 3.6.3 and Figure 3.6-9.

3.8.2 EPRI Dynamic Ratings on Cables

Development of the EPRI Dynamic Thermal CircuitRating (DTCR) system was started in 1991 withadvanced models for overhead transmission lines, powertransformers, and underground cables. The cable modelused in DTCR was initially based largely on the under-ground cable ampacity program “Alternative CableEvaluation (ACE)” in the EPRI Underground Trans-mission Workstation (UTW) that was started in 1990.ACE was an off-line ampacity program that woulddetermine normal and emergency ratings based on user-specified input data. The ratings generated by ACE weresimilar to what many utility engineers refer to as “bookratings” in that they were static ratings based onassumptions (usually worst-case) and then tabulated forreference by engineers and operators.

As the utility industry changed dramatically during the1990s, toward achieving higher profits, there wasincreased pressure to get more capacity from existingequipment while minimizing new construction wheneverpossible. To this end, DTCR was developed to take real-time data from “off the shelf ” monitoring hardware,and determine optimal ratings (not worst-case) for theconditions at the time the ratings were performed.Although this required some philosophical changes atutilities to consider circuit ratings as moving, changingentities rather than fixed parameters, the overall benefitwas to demonstrate a greater capacity in transmissionassets, including underground transmission cables.

The general theory behind DTCR is that, probabilisti-cally, there are relatively rare circumstances where theworst-case rating conditions occur at the same time thatthe greatest possible circuit loading is required ordesired. As a result, by evaluating the ratings on a real-time basis using actual, rather than worst-case condi-tions, the real-time rating is much higher and the allow-able power transfer is greater. This is illustratedgraphically in Figure 3.8-1.

In Figure 3.8-1, there is a relatively small region (ratingregime) where the dynamic rating distribution overlapsthe loading, indicating that at most times, the dynamic

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rating is greater than the “book” ampacity. DTCRallows the circuit to operate closer to the limit by per-forming a real-time rating evaluation using measured(rather than conservative or worst-case estimates)parameters.

Cable ModelsOne approach to dynamic ratings on cables—that usedin the Underground Cable Module in DTCR—is basedon the paper by Neher and McGrath (1957), and on theInternational Electrotechnical Commission (IEC) Pub-lications 287 and 853 (International ElectrotechnicalCommission 1982, 1989). These same calculation meth-ods are used in off-line rating tools such as EPRI’sUTWorkstation ACE program.

The numerical technique used in DTCR to track con-ductor temperatures is an “additive wave method,”whereby the temperature response to a constant heatinput is tracked into the future. For cables, DTCR looksat “small” intervals (< 0.5 hours), over which the loadcan be treated as constant. The temperature response tothe load with respect to time is a function of the heatinput to the cable (either positive for increasing load ornegative for decreasing load). Each time the loadchanges, a new temperature response “wave” islaunched. As the load changes from interval to interval,the total temperature response at a given time is thesummation of all the previous temperature responsefunctions from each change in heat from the cable (as afunction of load and the change in resistance with tem-perature). This basic concept is described in a paper byNeher (Neher 1963) and illustrated in Figure 3.8-3 withan arbitrary load.

The numerical calculations are based on equations fromIEC-287 and IEC-853 and make use of attainment fac-

tors for changes in heat output from the cables. Thecable temperature changes with respect to time andchanging load based on the thermal response of thecable and environment. The cable or pipe temperatureresponse is defined by Equation 3.8-1.

3.8-1Where:Wi is the heat output from the cable.RA, RB is the thermal resistance at steady state.a, b are time constants representing how the

temperature changes with respect to timefor a given heat input.

For the temperature response of the environment, thereare two models in DTCR: one that assumes all cir-cuits/cables carry identical currents, and a second wheretwo circuits may carry unequal loading.

Equal LoadingFor the case of two three-phase circuits of extruded orself-contained cable, all six (6) cables are assumed tocarry the same load even if the circuits are electricallydisconnected. The temperature rise above ambient fromac loading is described by Equation 3.8-2, utilizingexponential integrals, for the cable that is identified tobe the hottest cable in the trench.

3.8-2

Figure 3.8-1 Probabilistic view of dynamic ratings and actual circuit loads.

( ) ( )( ) 1 exp( ) 1 exp( )Cable i A Bt W R at R btθ ⎡ ⎤= − − + − −⎣ ⎦

2 2

2 26

2

16( )

4 '

4 4

earth

sHottestCable i

j j

j

D LEi Ei

t tt W

r rEi Ei

t t

δ δρθ

π

δ δ=

⎡ ⎤⎛ ⎞ ⎛ ⎞− − + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠

= ⎢ ⎥⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟+ − − + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∑

3-47


Where:Wi is the heat generated by each cable.Ei is an exponential integral.Dearth is the earth diameter for the cable or conduit.L is the burial depth for the “hottest” cable

among the group.rj is the actual distance between the hottest

cable and adjacent cables.r’j is the distance between the hottest cable and

the image of adjacent cables.

The watts generated by each cable, Wi, are identical forall cables in the group.

Unequal LoadingFor the case of two circuits with unequal loading, theheat output from the second circuit is defined separatelyfrom the first circuit. The mutual heating effects withrespect to time are then evaluated as shown in Equation3.8-3.

3.8-3

Where:Wi1, Wi2 are, respectively, the heat generated by

each cable in circuit 1 and circuit 2.

Cable Dynamic Rating ModelThe combined effects of the two temperature responsefunctions gives the complete temperature response ofthe cable conductor to a given cable heat output. Whenthere is changing load, typical of most transmission cir-cuits, the accumulated temperature responses for eachchange in load will give the conductor temperature withrespect to time. The general procedure and flow of theDTCR cable model are illustrated in Figure 3.8-2.

Graphically, the changing load is illustrated in Figure3.8-3, where the top graph shows an arbitrary load pat-tern, with loads that are both increasing and decreasingover time. The bottom graph shows the individual tem-perature response waves to each change in load (finelines) and the summation of all the temperatureresponse waves (dark line). Also shown in the graph isthe addition of the dielectric temperature rise, whichremains constant with respect to time as long as the line-to-ground voltage remains constant (this is an assump-tion). As compared to other modules (overhead linesand power transformers) within DTCR, the cable modelrequires extensive computations since the long earththermal time constant requires “looking back” hun-dreds of hours in the loading history. As a result, ratingsare normally not performed more often than once every15 minutes or so. Fortunately, the long thermal time

2 2

Pr 1 1 2 23

2

2 26

24

16( )

4 '

4 4

'

4 4 4

earth

simaryCable i

j j

j

j jsi

j

D LEi Ei

t tt W

r rEi Ei

t t

r rW Ei Ei

t t

δ δρθ

π

δ δ

ρπ δ δ

=

=

⎡ ⎤⎛ ⎞ ⎛ ⎞− − + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠

= ⎢ ⎥⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟+ − − + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟+ − − + −

⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∑

∑

Figure 3.8-2 General flow of information in DTCR cable model. (“STE” means “Short Time Emergency” rating, and “LTE” means “Long Time Emergency” rating.)

3-48


constant also means that there are limited temperaturechanges over that time.

Because of the considerable heat storage capacity ofunderground cables, the operating power levels prior toa contingency loading have a large effect on the actualthermal behavior during emergency loading events.EPRI’s DTCR technology allows continuous monitor-ing and establishment of such power equipment’s actualpre-contingency thermal state. As a result, load shed-ding during emergencies can often be avoided and capi-tal investment in new equipment postponed.

3.8.3 Benefit of Dynamic Ratings

The thermal rating of underground cables is tradition-ally calculated using worst-case seasonal loads and soiltemperatures. Underground cable thermal parametersare based on manufacturer’s data, installation assump-

tions, and industry standards. Rating calculations aretypically performed “off-line” using worst-case assump-tions to derive seasonal limits (maximum soil tempera-ture, worst-case loss factors).

With dynamic ratings, actual soil temperatures and loaddata are used in place of worst-case approximations,allowing higher operating limits under most conditionsand more accurate thermal modeling under all condi-tions.

Other than cable parameters and configuration,dynamic thermal rating calculations for undergroundcable require soil characteristics and temperature.

The equipment parameters can be verified by compar-ing calculated to measured equipment temperatures,which in the case of high-voltage underground cable isthe earth interface temperature, or a more general com-parison between a measured temperature and calculatedtemperature in a location near the power cables. Themeasured temperature from a thermocouple or DFOTScan be compared to the dynamic rating system-calcu-lated temperature, as described in Section 3.4.7.

DTCR Circuit RatingsThe DTCR software allows the user to calculate real-time equipment temperatures, multiple thermal ratings,and “remaining-time” (or “Time to Temperature Over-load,” TTO) during emergency loadings, given real-timeload and ambient ground temperature for undergroundcable circuits. “Circuit” ratings, rather than “equip-ment” ratings, are possible by modeling all of the powerequipment on a given circuit (e.g., series-connectedtransformers, overhead lines, cables, etc.), or in the caseof cables, each unique installation section along a givenroute, and then letting DTCR calculate ratings for allequipment and locations on a circuit. Then, DTCRselects the lowest rating for each category (normal, LTE,STE) and reports these values as circuit ratings.

Utility Implementation of Dynamic RatingsSome dynamic rating systems interface directly withmonitoring hardware. This has some disadvantages:

• The hardware is probably redundant to monitoringalready done by the utility.

• The hardware is sometimes very specialized, meaningthat the original vendor must be recalled for mainte-nance and repairs, usually at a high cost.

• Telemetry for any monitoring outside of a substation isoften complex, expensive, and prone to interruption.

• The computer system used to perform rating calcula-tions, by virtue of the direct connection to the moni-

Figure 3.8-3 “Additive Wave” model for temperature tracking in underground cables.

3-49


toring hardware, must be located in the field whereweather and security are difficult to manage.

• Any changes to the hardware usually require anew custom-designed interface to collect the moni-tored data.

• There is an issue of getting calculation results fromthe remote location back to the utility’s operationscenter, where it can be used by engineers and opera-tors to optimize circuit capability.

For these reasons, dynamic rating systems may be inter-faced to the utility SCADA system so that the SCADAsystem can handle all of the utility-specific telemetryissues, and the dynamic rating system can concentrateon just the rating and temperature calculations. Somefavorable characteristics are as follows:

• The preferred mode of operation is one whereinremote monitors provide data to the SCADA/EMSdatabase using utility-specific communication links,and the dynamic rating system obtains its real-timedata from that database rather than directly from theremote monitors.

• The utility SCADA/EMS system must transfer real-time monitor data from the database to a simple real-

time input data file on the dynamic rating systemcomputer through use of “Network Access calls” orother operational programs.

• The real-time input data on the dynamic rating sys-tem is read from the ASCII file created by a SCADANetwork Access call.

• A specific “SCADA” input file containing real-timetemperatures and ratings is continually updated bythe dynamic rating system and made available to theutility SCADA/EMS system. This allows dissemina-tion of the calculation results to anywhere within theutility.

All calculations can now be performed in an engineeringoffice or operations center environment (rather than in asubstation) without the need for special monitoringdevice communication links. Utility operations pro-grammers need only develop simple SCADA NetworkAccess calls to write ASCII input data files to thedynamic rating computer, rather than spending a lot oftime writing equipment-specific interface programs. Fig-ure 3.8-4 shows the general layout of EPRI’s dynamicrating system (DTCR), which utilizes this approach.

Input

Data

File*

Input

Data

File*

Input

Data

File*

Input

Data

File*

Real-Time

Historical

Data File

(mmddyy.###)

Real-Time

Output File

(ratings,

temps., etc.)

Real-Time

SCADA Output

File (ratings,

temps, etc.)*

File

HandlerFile

DTCR

Calculation

Algorithms

User Interface

DTCR Software ProductTelephone

Communications

Program

Direct Connect

Communications

Program

Radio Link

Communications

Program

Modem

Cell

or

Land Line

Wire or

Fiberoptic

(RS232)

PC in Engineering

Office or Operations

Center

wireless

SCADA/EMS

Database

Network Access

Call

Network Access

Call

Monitor

Monitor

ModemMonitor

Output to Engineering

or Operations Center

DTCR Functional Diagram

* File with most recent real-

time data appended.

Dir

ec

t M

on

ito

r In

pu

t

Figure 3.8-4 Schematic overview of DTCR’s location within the utility architecture.

3-50


3.8.4 Required Monitoring

Underground cable dynamic rating systems require vari-ous monitored parameters. Some of the parameters thatcould be evaluated are summarized as follows:

Ambient Soil TemperatureThe ambient temperature is a fundamental parameter tobe monitored since it directly affects the allowable tem-perature rise from ac loading. Soil temperature monitor-ing should be located where it is representative of theambient conditions imposed on the cable system. Usu-ally, this means being at least 10 m (30 ft) away from anenergized cable circuit at typical installation depths. Athermocouple tree—a series of thermocouples installedat various depths at the same location—is ideally suitedfor this type of monitoring, since it gives a range of tem-peratures that may be used for the variation in burialdepth encountered along the circuit.

LoadThe load is also an important parameter to know, even ifdoing quasi-dynamic ratings (described in Section 3.8.4).The load serves two purposes. First, it allows the conduc-tor temperature to be calculated as a function of load.Second, it allows a correlation between any measuredtemperatures and the circuit load (see Section 3.4.7). Thisis important for verifying ampacity capability.

Soil Thermal ResistivityReal-time monitoring of soil thermal resistivity is notcommon, mostly because the soil thermal resistivitydoes not change rapidly. Some utilities permanentlyinstall a thermal probe so that additional thermal resis-tivity measurements can be made to account for sea-sonal variations or weather effects.

As discussed in Section 3.6, thermal resistivity is a veryimportant parameter, since earth components of ther-mal resistance represent more than half of the total ther-mal resistance to heat leaving the cable.

Pipe-Type Cable MonitoringSome parameters are uniquely important to pipe-typecable dynamic ratings, particularly those that utilizefluid circulation or forced cooling. Inlet and outlet pres-sure to a cooling loop, fluid flow rates through the cool-ing loop, inlet dielectric liquid temperature, and coolingsystem outlet temperature all may be monitored to eval-uate the performance of a pipe-type cable system withactive forced cooling. The capability of the cooling plantto remove heat from the dielectric liquid is very impor-tant, since this ultimately dictates how much forcedcooling can be applied to the pipe-type system.

3.8.5 Quasi-Dynamic (Real-Time) Ratings

“Quasi-dynamic ratings” utilize many of the principlesof real-time ratings except they may not be done on acontinuous basis. For example, a utility may have acable circuit that is only heavily loaded two months ofthe year. On that basis, the cost to implement a dynamicrating system may not be justified, but the ratings dur-ing that two-month window are still critical.

Quasi-dynamic ratings might be applied by monitoringload and temperatures for a period of time and then cal-culating what the conductor temperature might be as aresult of that load. From this, the temperature of thecable conductor at rated temperature can be extrapo-lated for rating purposes. For example, the earth inter-face temperature of a cable system may be monitoredwith thermocouples for several months until a period ofhigh loading occurs. At that time, the utility may down-load measured temperatures from a thermocouple datalogger and compare measured to calculated tempera-tures to evaluate the assumptions used for rating mod-els, both real-time and off-line ratings.

Quasi dynamic ratings may also apply to reviewing his-torical load profiles using dynamic rating algorithms.The load history on a circuit for a year or two—perhapscovering high-load periods during summer months—could be run through a dynamic rating tool to evaluatepeak loading periods and study loss-of-life criteria (onpaper cables).

3.9 CASE STUDIES FOR UNDERGROUND CABLE CIRCUITS

Section 3.9 describes uprating projects recently con-ducted at utilities. It is hoped that these case studies helpto illustrate the general application of uprating tech-niques described in this chapter.

3.9.1 CenterPoint Energy

Description of Circuit and Summary of Rating Constraints and Utility GoalsA 138-kV HPFF underground transmission line wasconstructed in 1969 from CenterPoint Energy’s Polksubstation (located at the intersection of Polk and LaBranch Streets in Houston, Texas) to CenterPoint’sGarrott Substation (located at the intersection of Gar-rott Street and Blodgett). The total length of this138-kV underground transmission line is approximately2.37 miles (12,500 ft). A 2500-kcmil, compact segmentalcopper, 138-kV HPFF cable with 505 mils of insulatingtapes was used to construct the Polk – Garrott transmis-sion line.

3-51


In March 2001, a loop feed to a new CenterPoint sub-station, Midtown Substation, was constructed by tap-ping into the existing Polk to Garrott undergroundtransmission line. This loop feed to the Midtown Sub-station (located on La Branch Street between Taum andDrew Streets) segregated the Polk to Garrott under-ground transmission line into two parts with the lengthsof 0.96 and 1.41 miles. CenterPoint wanted to evaluatethe power transfer capabilities of the Polk-Midtown-Garrott and Polk-Downtown 138-kV undergroundtransmission lines in light of these changes and to opti-mize the current-carrying capacity of the circuits. Theampacity audit was based on an evaluation of recentand historical data including:

• Long-term load current, ambient soil temperatures,and cable pipe temperatures during summer operat-ing conditions

• Distributed fiber optic temperature sensing (DFOTS)measurements performed on the circuits in February2002 for hot spot identification

• As-built plan and profile drawings for the two cablecircuits

• Cable manufacturing data

CenterPoint Energy also wanted to evaluate the condi-tion of the thirty-two-year-old Polk-Garrott HPFFcables in coordination with the ampacity analysis. Con-sequently, two investigations were performed for thispurpose. First, Detroit Edison (DECo) performed dis-solved gas analysis (DGA) and laboratory testing ofcable paper tape samples obtained during constructionof the loop feed to the new Midtown Substation. PowerDelivery Consultants (PDC) also performed cable dissi-pation factor measurements at rated voltage usingEPRI-developed instrumentation. A previous EPRIproject (Transmission Cable Life Evaluation and Man-agement) indicated that cable tape physical propertymeasurements, DGA, and dissipation factor measure-ments are the best diagnostic tests to determine cableloss-of-life.

The primary focus of the DTCR project was to examinethe ratings on the Polk-Midtown-Garrott circuit. Thiscircuit consists of two segments: 5,060 ft from Polk toMidtown Substation, and 7,440 ft from Midtown Sub-station to Garrott Substation. DTS measurementsshowed that the hotspot for the Polk-Midtown-Garrottunderground line is a crossing with the Polk-Downtown138-kV underground transmission line at the intersec-tion of Polk and La Branch (just outside of the PolkSubstation). The cable used for the Polk to Downtown138-kV line is identical to the Polk to Garrott line. Thedepth of cover over the Polk-Midtown-Garrott line isapproximately 11 ft-2 in. at the hot spot location, and

the vertical clearance to the Polk-Downtown line (aboveit) is approximately 3 ft. CenterPoint placed a thermo-couple on the Polk to Garrott cable pipe near the inter-section. Initially, the thermocouple temperature wasmonitored with a data logger, but this thermocouple isnow connected directly to CenterPoint's SCADA sys-tem. A thermocouple was also placed on the Polk-Downtown circuit at the location of the crossing andconnected to SCADA.

In 2000, CenterPoint Energy (Houston Lighting &Power) began this investigation (completed in December2002 – EPRI Report 1007539) to increase the circuitcapacity on the high-pressure fluid-filled (HPFF) pipe-type cable connecting the Polk and Garrott Substations.Various studies were performed to evaluate upratingpossibilities for this circuit, including the application ofdistributed fiber optic temperature sensing (DFOTS).Results of DFOTS revealed that a hot spot existed whereanother pipe-type cable (CenterPoint’s Polk-Downtowncircuit) crossed over the Polk-Garrott circuit. Althoughan overall increase in ampacity was found for the generalcable circuit, a net decrease in ampacity resulted fromthe modeling of the mutual heating of the two cable cir-cuits where they cross. This was anticipated prior tobeginning the project, so DTCR was implemented onthe Polk-Garrott circuit in an effort to optimize availablecircuit capacity.

The principal goal of the project was to investigate anoptimized circuit rating in light of the interference tem-perature effects detected by DFOTS and experienced bythe crossing pipes. A secondary objective was to demon-strate that, under normal loading patterns, the maxi-mum normal temperature (85°C) of the conductorwould infrequently be exceeded.

Results of Uprating and Benefits to UtilityThe following conclusions may be reached from review-ing the application of DTCR at CenterPoint:

• The DTCR modifications and subsequent data anal-ysis showed that CenterPoint Energy’s Polk-Mid-town-Garrott and Polk-Downtown pipe-cablecircuits can benefit from dynamic ratings. DTCR’spredicted load pattern assumes a typical 24-hour lossfactor cycle consistent with static ratings. However,the emergency loading is a function of pre-load con-ditions, and DTCR accurately calculates the conduc-tor pre-load temperature based on historical loadingpatterns. Also, DTCR uses the present loading topredict time to temperature overload (TTO).

• While a detailed ampacity study indicated there waseffectively a reduction in the established book ratingof 3.4%, applying DTCR allowed for a net increase inthe normal rating of 20.7%, based on considering a

3-52


“dynamic” rating using summer 2000 load data for a“quasi-real-time” dynamic rating analysis.

• In summary, the real-time dynamic ratings of thePolk-Midtown-Garrott and Polk-Downtown under-ground transmission lines are expected to be signifi-cantly higher than the static ratings that werecalculated under a separate project, assuming there issimilar load pattern variability to that observed dur-ing the summer 2000.

The following conclusions are a result of the cable con-dition assessment testing performed on the Polk-Gar-rott 138 kV underground transmission line.

• DGA testing of pipe fluid samples and laboratorytesting of a cable sample indicated that Polk-Garrott138-kV cable offers an exceedingly long life, which ischaracteristic of HPFF cables.

• Results of the dissipation factor measurements con-firmed that the Polk-Garrott 138-kV HPFF cables donot show any signs of insulation deterioration aftermore than 30 years of operation.

3.9.2 United Illuminating Company

Description of Circuit and Summary of Rating Constraints and Utility GoalsIn 1989, United Illuminating Company (UI) performedan engineering evaluation on the ampacity of the exist-ing 1.4-mile-long UI 115-kV high-pressure gas-filledcable Circuits 1710 and 1730, which connect UI’sPequonnock Substation to the Seaview Tap in Bridge-port, Connecticut, where the lines transition to over-head conductors. A 1600-ft section under BridgeportHarbor, where the cables were buried approximately25 ft under high-resistivity sediments, appeared to limitthe overall circuit rating. UI’s construction records indi-cated that the cable configuration under the harbor con-sists of three pipes in a 5-ft trench, with a spare (empty)pipe centered between the two cabled pipes.

Results of the 1989 thermal tests showed that soil resis-tivity ranged widely, from 90º to 250º C-cm/Watt. Thisrange of values produced a degree of uncertainty in theratings. In addition, the degree of siltation and theactual pipe positions since the cable pipes were installedin 1961 was unknown. Because of the uncertainty of thepipes’ locations, 1989 soil tests were done at least 50 ftaway from the expected pipe position to avoid possiblydamaging the pipes with the soil-coring equipment. Theuncertainty of some parameters from the 1989 study,the limiting of the entire circuit’s ampacity by the har-bor section, combined with UI’s interest in increasingthe total power transfer on the circuit, precipitated UIin undertaking a more thorough ampacity evaluation of

the harbor section. An additional goal was to considermeans for increasing ampacity on the circuit.

Power Delivery Consultants, Inc. (PDC) was contractedin 2001 to perform a very detailed evaluation of theBridgeport Harbor portion of UI’s 1710 and 1730 linesusing sophisticated modeling and state-of-the-art tech-nology to gather information about the installation andenvironment. The evaluation included several technolo-gies:

• Gyroscopic testing on the empty cable pipe todevelop accurate cable pipe plan and profile informa-tion for the harbor crossing.

• Hydroscopic surveying of the harbor bottom to eval-uate the degree of siltation over the cable pipes sincethey were installed in 1961 and, ultimately, to deter-mine the cable depth of cover.

• Distributed temperature sensing (DTS) using EPRI’sDTS equipment and fiber optic cable installed in thespare cable pipe

• Continuous thermocouple temperature monitoringusing installed thermocouples and data loggers

• Updated soil sample testing to characterize the soilsat the depths of interest

• Forced air ventilation to characterize possible uprat-ing by removing heat from the cabled pipes

An EPRI report (1007534) documents the results ofthese evaluations and a detailed ampacity study todetermine the actual capacity of UI’s 1710 and 1730lines under both normal and emergency ampacity con-ditions, and describes possible approaches for increasingthe ampacity on the lines.

In 2002, UI implemented two of the recommendationsof the ampacity study:

• Applied forced-air cooling on the parallel cable pipe.

• Implemented DTCR to monitor conductor tempera-ture and evaluate real-time temperatures on the cir-cuit as the result of circuit loading.

Results of Uprating and Benefits to UtilityThe initial ampacity study resulted in several recom-mendations to mitigate the rating limits on UI’s cablecircuits. These are summarized in Table 3.9-1. Two ofthe options, forced air cooling on a parallel empty cablepipe and dynamic ratings, were later implemented.

The forced-air cooling equipment is shown in Figure3.9-1. The actual cost to install the forced-air coolingequipment was substantially higher than the initial esti-

3-53


mate, largely due to some complications associated withthe civil works of the installation.

The following conclusions and recommendations werereached based upon implementing DTCR on UnitedIlluminating Company’s 1710/1730 circuits:

• DTCR shows that the maximum normal operatingtemperature of paper-insulated pipe-type cables (e.g.,85°C) is rarely exceeded, even though there are fre-quent occasions when the actual circuit loadingexceeds the normal book ratings.

• The combined effects of circuit loading on 1710 andmutual heating from circuit loading on 1730 some-times result in the conductor temperature on the 1730circuit exceeding its maximum normal temperature.

As was indicated in an earlier study, this results fromthe typically increased load levels on the 1710 and1730 circuits, the increased daily loss factors, and thefact that loads on the 1730 circuit are increasinglyapproaching the loads on the 1710 lines.

• UI may want to consider performing a long-termloss-of-life evaluation on the 1710 and 1730 circuitsto see how the calculated operating temperatures onthe circuits have influenced accumulated loss-of-life.Despite the occasional incursions above rated tem-perature, the evaluation would likely show that dur-ing a typical calendar year, the below 85°C operatingtemperatures for most of that time indicate that lessthan a calendar year of life has been consumed. Thiswould provide increased confidence to UI that thisoccasional high-temperature operation should notadversely affect the future operation of the circuit. Ifpursued, this additional work would apply paper-insulated pipe cable aging characteristics developedduring EPRI work on accelerated aging at WaltzMill.

• From the standpoint of evaluating normal ratings,the book ratings were previously found to be 743 A(on the 1710 circuit). Real-time ratings show a rangeof improvements (10–25%) depending on the condi-tions (Table 3.9-2).

• If the 1710 and 1730 circuits are ever decommis-sioned, an evaluation of the paper insulation agingshould be performed to determine if the typicallyhigher operating temperatures on the 1710 cablesshow increased aging over the 1730 cables, since bothcircuits are made of similar vintage cable and havehad similar in-service lives.

Table 3.9-1 Summary of United Illuminating Pipe Cable Uprating Methods

Forced Air Cooling

Recondi-tioning

Fluid Filling Circulation

Forced Cooling

Reconduc-toring XLPE

Water Cooling

Dynamic Rating

Location Harbor only Harbor only Circuit Circuit Circuit Circuit Circuit Harbor only Circuit

Maximum estimated increase

4.0%a

a. Based on testing in September-October 2001; small additional increase possible.

5.6%b

b. Land rating becomes limiting.

<3.0% 7.8% 25–50% 18.0% c

c. Not recommended for pipe-type retrofit with conventional technology.

5.6%d

d. Not recommended; air-cooling could achieve same result.

e

e. Rating improvements by dynamic ratings vary depending on circumstances.

Additional mainte-nance

Minimal None Moderate Moderate High None None Moderate None

Environ-mental Con-

cernsLow None High High High None None Moderate None

Estimated Cost $100k $1.2M $1.5M $200kf

f. Increase in cost minimal after fluid filling.

$1.5Mg

g. Assumes fluid filling already done.

$3M c $500kd $200k

Figure 3.9-1 Blower assembly for forced-air cooling on pipe-type cable circuits.

3-54


• Further work on DTCR may be warranted to pro-vide for a cyclic rating factor on emergency ratings oflonger than 24 hours to fully take advantage of the“dynamic normal rating” concept.

3.10 SUMMARY OF UPRATING AND UPGRADING APPROACHES AND ECONOMIC FACTORS

Tables 3.10-1 and 3.10-2 summarize the major improve-ments in ampacity that may be realized by the variousuprating and upgrading techniques described in thischapter. The specific costs for each depend largely onthe unique aspects of each installation or project, butqualitative costs, along with many other factors, arelisted in the tables for reference.

The case studies in Section 3.9 give an indication of spe-cific costs for one of the uprating projects.

Table 3.9-2 Comparison of Normal “Book” Rating to Real-Time and Dynamic Ratings

Rating Type Minimum Maximum

Normal Book (Previous Study) 743A

Real-Time Normal 621A 817A

Dynamic Normal (100% Loss Factor) 0A (722A) 877A

Dynamic Normal (with Cyclic Rating Factor) 0A (774A) 929A

Table 3.10-1 Summary of Uprating and Upgrading Techniques Applicable to All Cable Types

Evaluation Criteria

Measure Soil Rho, Heat Pipes,

Mitigate Hot Spots

Real Time Monitoring

ReplaceConductors

Voltage Upgrading

Thermo-couples (Temp.)

Dist. Fiber Optic (Temp.)

Dynamic Ratings

Rating Incremental Increasea

a. Incremental increase in ampacity over previous options.

20% N.A.b

b. Monitoring the cable circuit alone, does not provide for rating improvements. Real-time monitoring, with the monitored parameters fed into rating calculations provides for optimum ampacities.

10-20% 3-20% 66-80%

Reliability High High High High High High

Maintenance Low Low Low Low Low Increased, but Low

Losses None None None Low Low Increased, but Low

Lead Time

Installation 2 mos. 3 mos.c

c. If not done during the original installation of the cable system.

3 mos. 2 mos. 14 mos. 24 mos.

Operating None Real Time Real Time Real Time None None

CostInstallationd

d. Including material costs.

Low Low-Med Low-Med Low High High

Operating None Low Low Low Med.-High Med.-Highe

e. Generally, higher voltage equipment requires more extensive and expensive maintenance.

Table 3.10-2 Summary of Uprating Techniques Predominantly for Pipe-Type Cables

Evaluation Criteria Fluid Filling Circulation Forced Cooling

Slow RapidPassive Heat Exchanger

Forced-Air Heat Exchanger Refrigerated Cooling

Rating Incremental Increase 2% 21% 8% 16% 31% 16%

Reliability High Medium Medium Medium Low Low

Maintenance Medium Medium Medium Medium High High

Losses None Low Medium Medium High High

Lead Time

Installation 10 mos. 2 mos. 2 mos. 2 mos. 3 mos. 6 mos.

Operating N.A. Lowa

a. Typically less than 24 hours.

Lowa Lowa Lowa Lowa

CostInstallation High Low Low Medium High High

Operating Low Low Medium Medium Medium High

3-55


REFERENCES

The following references were used for this chapter andmay be useful to the reader for additional backgroundon the topics discussed.

Anders, G. J. 1997. Rating of Electric Power Cables, IEEE Press/McGraw Hill.

Bascom, III, E. C., D. A. Douglass, G. C. Thomann, and T. Aabo. 1996. “Hybrid Transmission: Aggressive Use of Underground Cable Sections with Overhead Lines.” CIGRÉ 21/22-10.

Bascom, III, E. C. and J. A. Williams. 2002. “Taking Your Cable’s Temperature.” Transactions of the T&D World Expo. 7-9 May. Indianapolis, Indiana.

Bascom, III, E. C. and J. A. Williams. 2002. Ampacity Evaluation and Distributed Fiber Optic Testing on Pipe-Type Cables Under Bridgeport Harbor. Electric Power Research Institute Publication 1007534. December.

Bascom, III, E. C. and J. H. Cooper. 2002. Condition and Power Transfer Assessment of CenterPoint Energy’s Polk-Garrott Pipe-Type Cable Circuit. Electric Power Research Institute Publication 1007539. December.

Bascom, III, E.C. 2003. “Underground Cable Uprating and Upgrading Tutorial.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0362 (Panel Session). Dallas, Texas. 7-12 September.

Bascom, III, E. C., J. A. Williams, M. A. Pasha, S. M. Rahman, and W. Zenger. 2003. “Ampacity Evaluation of High-Pressure Gas-Filled (HPGF) Pipe-Type Cables Under Bridgeport Harbor.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0093. Dallas, Texas. 7-12 September.

CIGRÉ 1979. “The Calculation of Continuous Ratings of Forced-Cooled Cable.” Working Group 21.08. Study Committee 21. Electra. No. 66. pp. 59-84. October.

CIGRÉ. 1987. “The Calculation of Continuous Rating for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cables.” Working Group 21.08. Study Committee 21. Electra. No. 113. pp. 97-120.

El-Kady, M. A. and D. J. Horrocks. 1995. “Extended Values of Geometric Factor of External Thermal Resis-tance of Cables in Duct Banks.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-104.

EPRI. 1982. High Ampacity Terminations. EL-2233. January.

EPRI. 1985. Volume 1: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs - Designer's Guide. EL-3977.

EPRI. 1985. Volume 2: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs - Details of Mathematical Derivations. EL-3977.

EPRI. 1992. Underground Transmission Systems Refer-ence Book. TR-101670.

EPRI. 1997. Thermal Properties Manual for Under-ground Power Transmission. TR108919. November.

EPRI. 1998. Transmission Cable Life Evaluation and Management. TR-111712. September.

EPRI. 2002. Increased Power Flow Guidebook – Over-head Transmission Lines. 1001817. December.

Holman, J. P. 1997. Heat Transfer. 8th Edition. McGraw-Hill. New York.

IEEE. 1988. “IEEE Guide for Application of Sheath-Bonding Methods for Single- Conductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths.” 575-1988.

Iizuka, K. 1974. Power Cable Technology Hand Book. DenkiShoin, Tokyo. pp. 80.

International Electrotechnical Commission. 1982. IEC-287. “Calculation of the Continuous Current Rating of Cables (100% Load Factor).” International Electrotech-nical Commission.

International Electrotechnical Commission. 1989. IEC-853-2. “Calculation of the Cyclic and Emergency Cur-rent Rating of Cables.” International Electrotechnical Commission. 1st Edition.

Neher, J. H. and M. H. McGrath. 1957. “The Calcula-tion of the Temperature Rise and Load Capability of Cable Systems.” Paper 57-660. AIEE Insulated Conduc-tors Committee. June.

Neher, J. H. 1963. “The Transient Temperature Rise of Buried Cable Systems.” Paper 63-917. IEEE Insulated Conductors Committee. June.

3-56


Parmar, D. and J. Steinmanis. 2003. “Underground Cables Need a Proper Burial.” Transmission & Distribu-tion World. April. pp. 44-51.

Purnhagen, D. W. 1984. “Designer’s Handbook for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cable Systems.” Electric Power Research Institute. EL-3624. Project 7801-5. July.

Stevenson, Jr., W. D. 1982. Elements of Power System Analysis, 4th Edition. McGraw-Hill. New York.

Williams, J. A., T. R. Grave, and E. Kallaur. 1986. “Uprating of High Pressure Gas-Filled Feeders by Fluid Filling and Rapid Circulation.” IEEE Confer-ence. Anaheim, CA. September 15-19.

Williams, J. A., E. C. Bascom III, B. Horgan, and T. Aabo. 1991. “Field Test Program and Results to Verify HPFF Cable Rating.” IEEE Transactions.

Williams, J. A. and J. H. Cooper. 1998. “Distributed Fiber Optic Temperature Monitoring and Ampacity Analysis for XLPE Transmission Cables.” Electric Power Research Institute. TR-110630. June.

Williams, J. A. 2000. “Application of Fiber-Optic Tem-perature Monitoring to Solid Dielectric Cable.” Electric Power Research Institute. Publication 1000469. Novem-ber.

3-57


APPENDIX 3.1 PIPE-TYPE AMPACITY EXAMPLE

This appendix contains a sample calculation of pipe-type cable ampacity using the procedures outlined inthis chapter and detailed in the references.

The cable configuration is as shown in Figure A3.1-1.

Figure A3.1-1 Cable configuration for pipe-type ampacity example.

3-58


tis 0.005:= Thickness of insulation shield tapes, inches

ρ shield 0.7:= ohm-meters Electrical resistivity of stainless steel shield tapes

Skid W ire Size/Type 0.1in. x 0.2in., 2 x 3in. lay

ρ skidwire 0.7:= ohm-meters Electrical resistivity of stainless steel skidwire

f 60:= Hz

LF 0.62= Daily (24-hour) loss factor, per unit (entered below)

n 3:= Number of cables within pipe or conduit

N 2:=

Pipe Data:Pipe is HPFF

ODpipe 10.75:= Pipe outside diameter, inches

IDpipe 10.25:= Pipe inner diameter, inches

tcoating 0.07:= Pipe coating (Somastic) thickness, inches

ρ coating 3.5:= Thermal resistivity of the pipe coating, C°-m/w

Pipe-Type Cable Ampacity Worked Example

Cables are 345kV HPFF cables with 2500kcmil segmental copper conductors, 905 mils kraft paper insulation, 0.1x0.2, 2x3in. lay stainless steel skid wires in an 10-inch cable pipe, 2 circuits, 0.62 loss factor.

Cable Data:

A 2500:= Conductor area, CI

ρ conductor 0.017241:= ohm-meters Electrical resistivity, copper conductor

ks 0.39:= Conductor skin effect factor, in oil

kp 0.46:= Conductor proximitty effect factor, in oil, cradled

Dc 1.824:= Diameter of the segmental conductor, inches

Tc 85:= Maximum normal conductor operating temperature, °C

tcs 0.005:= Thickness of conductor semiconducting shield, inches

ti 0.905:= Insulation wall thickness, inches Values for Paper InsulationSIC 3.5:= Dielectric constant of the insulation

tanδ 0.0023:= Dissipation factor of the insulation, numeric

ρ insulation 6.00:= Thermal resistivity of the insulation, C°-m/Watt

3-59


Center_Depthcbf 39:= Value for center-line depth of cbf is arbitrary

Calculate Cable Geometry:Dcs Dc 2tcs+:= Diameter over the conductor shield, inches

Dinsulation Dcs 2ti+:= Diameter over the insulation, inches

Dis Dinsulation 2tis+:= Diameter over the insulation shield, inches

Dskidwire Dis 1.5 0.1×+:= Diameter over 0.1" skid wires, inches

Dearth ODpipe 2tcoating+:=

ClearanceIDpipe

21.366Dskidwire−

IDpipe Dskidwire−( )2

1Dskidwire

IDpipe Dskidwire−⎛⎜⎝

⎞⎟⎠

−⎡⎢⎣

⎤⎥⎦

0.5+:=

Clearance in pipes, inchesDcs 1.834=

Dinsulation 3.644=

Dis 3.654=

Dskidwire 3.804=

Dearth 10.89=

Clearance 1.992=

Installation Data:x1 15−:= x2 15:= Horizontal location of pipe center, inches

burial1 42:= burial2 42:= Burial depth to pipe center, inches

Ta 25:= Ambient earth temperature, °C

f 60:= Power frequency, Hz

E 345000 1.05×:= System maximum line to line voltage, volts

ρ native 0.9:= Thermal resistivity of the native earth, C°-m/w

ρ backfill 0.5:= Thermal resistivity of the duct concrete, C°-m/w

Widthcbf 53:= Heightcbf 29:= Width and height of backfill, inches

3-60


x1 x125.4:= x2 x225.4:= x1 381−=

Widthcbf Widthcbf25.4:= Width cbf 1.346 103×= mm

Heightcbf Heightcbf25.4:= Heightcbf 736.6= mm

Center_Depthcbf Center_Depthcbf25.4:= Center_Depthcbf 990.6= mm

Calculate the dielectric losses:

Wd

2πfSICE

3⎛⎜⎝

⎞⎟⎠

2tanδ10 9−

18lnDinsulation

Dcond_shield

⎛⎜⎝

⎞⎟⎠

:= Wd 10.741= W/m/phase

Calculate Conductor Resistance:

Rdc20ρ conductor

Areaconductor:= RdcT Rdc20

Tc 234.5−( )−20 234.5−( )−

⎡⎢⎣

⎤⎥⎦

:= Rdc20 1.361 10 5−×=

RdcT RdcT1.025:= Assume 2.5% Stranding of Conductor Ohms/meter

Xs8πf ks( ) 10 7−

RdcT:= Xp

8πf kp( ) 10 7−

RdcT:=

YcsXs2

192 0.8Xs2+:= S Dskidwire:= Ycs 0.056=

YcpXp2

192 0.8Xp2+

⎛⎜⎜⎝

⎞⎟⎟⎠

Dconductor

S⎛⎜⎝

⎞⎟⎠

2

0.312Dconductor

S⎛⎜⎝

⎞⎟⎠

2

1.18

Xp2

192 0.8Xp2+

⎛⎜⎜⎝

⎞⎟⎟⎠

0.27+

+

...⎡⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎦

:=

Ycp 0.061=

Racc RdcT 1 1.5 Ycs Ycp+( )+⎡⎣ ⎤⎦:=

Metric Conversion of Variables

AreaconductorA

1.9735:= Areaconductor 1.267 103×= mm2

Dconductor Dc25.4:= Dconductor 46.33= mm

Dcond_shield Dcs25.4:= Dcond_shield 46.584= mm

Dinsulation Dinsulation25.4:= Dinsulation 92.558= mm

Dinsl_shield Dis25.4:= Dinsl_shield 92.812= mm

Dskidwire Dskidwire25.4:= Dskidwire 96.622= mm

ODpipe ODpipe25.4:= ODpipe 273.05= mm

IDpipe IDpipe25.4:= IDpipe 260.35= mm

Dearth Dearth25.4:= Dearth 276.606= mm

burial1 burial125.4:= burial2 burial225.4:= burial1 1.067 103×= mm

3-61


Ohms/meter

Calculate Mutual Reactance (assume cradled configuration)

Xm 2 2πf( ) 10 7− ln2.3Dinsl_shield

Dskidwire

⎛⎜⎝

⎞⎟⎠

:= Xm 5.977 10 5−×= Ohms

YscRs

Racc

1

1Rs

Xm

⎛⎜⎝

⎞⎟⎠

2

+

:=Ysc 1.314 10 3−

×=

Racs RdcT 1 1.5 Ycs Ycp+ Ysc+( )+⎡⎣ ⎤⎦:=

Calculate the pipe loss increments to AC resistance:

Yp0.0438Dskidwire 0.0226IDpipe+

RdcT106:= Yp 0.578=

Racp RdcT 1 1.5 Ycs Ycp+ Ysc+( )+ Yp+⎡⎣ ⎤⎦:=

Racc 2.06 10 5−×= Racs 2.063 10 5−

×= Racp 3.075 10 5−×= Ohms/meter

QsRacs

Racc:= Qp

Racp

Racc:= Qs 1.002= Qp 1.493= AD/DC resistance ratios

Calculate the shield and skidwire loss increments:

Area of shield tape is width of tape times thickness. Resistance of shield tape is the area times the helical length times the resistivity divided by the area. Shield tape thickness is 0.005in stainless steel, with 1/8" lapped, with typical tape width of 7/8". Assume there are 2 tapes.

widthshield_tape78

25.4:= thickness shield_tape 0.005 25.4×:= lapshield18

25.4:=

areashield_tape thickness shield_tape widthshield_tape:= layshield widthshield_tape lapshield−:=

Rshieldρ shield

areashield_tape1

πDinsl_shield

layshield

⎛⎜⎝

⎞⎟⎠

2

+:= Rshield 3.804= Ohms/meter

Skid wire resistance

Area of elipse is pi * major_radius * minor_radius. Area of skid wire is half this. Skid wire is 0.1 x 0.2, 3-inch lay, 2 wires. Material is stainless steel.

minor_radius 0.1 25.4×:= major_radius 0.225.4

2:= areaskidwire

π

2minor_radius major_radius:=

layskidwire 3 25.4×:=

Length of a hel ix is (1 + (pi*D/Lay)̂ 2)^.5

Rskidwireρ skidwire

areaskidwire1

πDskidwire

layskidwire

⎛⎜⎝

⎞⎟⎠

2

+:= Rskidwire 0.284= Ohms/meter

Rs1

1Rskidwire

1Rskidwire

+1

Rshield+

1Rshield

+:= Rs 0.132=

3-62

3-63


Db 985.973=

Lb Center_Depth cbf:= Lb 990.6=

Gb ln2Lb 4Lb

2 Db2−+

Db

⎛⎜⎜⎝

⎞⎟⎟⎠

:= Gb 1.322=

Calculate diameter Dx

αsoil6.71 104

×

ρ native100( )0.8:= Thermal diffusivity of native soil mm2

hourαsoil 1.834 103×=

Dx 1.02 αsoil24:= Diameter beyond which 24 hour average losses apply, mm Dx 213.978=

Earth thermal resistance for AC losses at loss factor

Rearthρ backfill

2πn ln

Dx

Dearth

⎛⎜⎝

⎞⎟⎠

LFln2burial1 4burial12 Dearth

2−+

Dx

⎛⎜⎜⎝

⎞⎟⎟⎠

+⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Rearth 0.381=

Earth thermal resistance for dielectric losses at 100% loss factor

Rearth'ρ backfill

2πn ln

Dx

Dearth

⎛⎜⎝

⎞⎟⎠

ln2burial1 4burial12 Dearth

2−+

Dx

⎛⎜⎜⎝

⎞⎟⎟⎠

+⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Rearth ' 0.652=

Calculate Cable Thermal Resistances

Riρ insulation

2πln

Dinsl_shield

Dconductor

⎛⎜⎝

⎞⎟⎠

:= Ri 0.663=

U 0.26:= V 0:= Y 0.0026:= Constants for HPGF

Tmoil 66.827= Estimate of mean temperature in duct

Roiln U

1 0.1 V YTmoil+( )Dinsl_shield2.15+:= Roil 0.175=

Rpipe_coatingρ coating

2πn ln

Dearth

ODpipe

⎛⎜⎝

⎞⎟⎠

:= Rpipe_coating 0.022=

Calculate External Thermal Resistances

Calculate geometric correction factor for backfill envelope:

x Height cbf:= x=short dimension of backfill y Width cbf:= y=long dimension of backfil l

Db e

1

2⎛⎜⎝

⎞⎟⎠

x

y⎛⎜⎝

⎞⎟⎠

4

π

x

y−⎛

⎜⎝

⎞⎟⎠

ln 1y2

x2+

⎛⎜⎜⎝

⎞⎟⎟⎠

ln x( )+⎡⎢⎢⎣

⎤⎥⎥⎦:=


ΔTd WdRi

2Roil+ Rpipe_coating+ Rearth'+ Rmutual'+ Rcorrection '+

⎛⎜⎝

⎞⎟⎠

:= ΔTd 20.896=

ΔT Tc ΔTd− Ta−:= ΔT 39.104= Adjust "iterated" values below until they equal "calculated".

IratedΔT

∑RacRth:= Irated 940.2=

Itotal 2Irated:= Itotal 1880.4=

Tccalc Irated2 RaccRi Racs Roil+ Racp Rpipe_coating Rearth+ Rmutual+ Rcorrection+( )+⎡⎣ ⎤⎦

ΔTd Ta++...:=

Tccalc 85=

Tshield calc Tccalc Irated2Racc Ri− Wd

Ri

2−:= Tshield calc 69.357= Tshield 69.357≡

Toilcalc Tshield calc Irated2Racs Wd+⎛

⎝⎞⎠

Roil

2−:= Toilcalc 66.827= Tmoil 66.827≡

Tearth_interface Toilcalc Irated2Racs Wd+⎛

⎝⎞⎠

Roil

2− Irated

2Racp Wd+⎛⎝

⎞⎠Rpipe_coating−:=

Tearth_interface 63.477=

Mutual thermal resistance between two pipes (just for normal ampacities)

d'12 x1 x2−( )2 burial1 burial2+( )2+⎡⎣ ⎤⎦

.5:= Distance between one cable pipe and image

of other cable pipe

d12 x1 x2−( )2 burial1 burial2−( )2+⎡⎣ ⎤⎦

.5:= Distance between one cable and the other

F12d'12

d12:= Rmutual

ρbackfill

2πn LFln F12( ):= Rmutual 0.161=

Rmutual'ρ backfill

2πn ln F12( ):= Rmutual' 0.26=

Thermal resistance correction for native soil for AC losses

Rcorrection LFρ native ρbackfill−( )

2πn N Gb:=

Rcorrection 0.313=

Thermal resistance correction for native soil for dielectric losses

Rcorrection 'ρ native ρbackfill−( )

2πn N Gb:=

Rcorrection' 0.505=

Calculate Normal Ampacity on primary cable

∑RacRth RaccRi Racs Roil+ Racp Rpipe_coating Rearth+ Rmutual+ Rcorrection+( )+:= LF 0.62≡

3-64


APPENDIX 3.2 EXTRUDED AMPACITY EXAMPLE

This appendix contains a sample calculation for a cross-linked polyethylene (extruded) cable ampacity using the

procedures outlined in this chapter and detailed in thereferences.

The cable configuration is as shown in Figure A3.2-1.

Figure A3.2-1 Cable configuration for extruded ampacity example

3-65


3-66

n 1:=

System line to line voltage, voltsE 230000:=

24 hour loss factorLF 0.60:=

Power frequency, Hzf 60:=

Earth ambient temperature summer, °CTa 20:=

Distance between adjacent circuits, inchesdcircuits 20:=

Distance between adjacent phases, inchesdphases 10:=

Depth to center of top conduit, inchesBurial 42:=

Installation Data:

Duct inside diameter, inches

Width and height of backfill, inchesHeightcbf 33:=Width cbf 33:=

Thermal resistivity of the duct concrete, C°-m/wρ backfill 0.50:=

Thermal resistivity of the native earth, C°-m/wρ native 1.00:=

Thermal resistivity of the duct, C°-m/wρ duct 6.00:=

Thermal resistivity of the jacket, C°-m/wρ jacket 3.50:=

Thermal resistivity of the insulation, C°-m/wρ insulation 3.50:=Thermal Resistivities:

Number of occupied ductsN 6:=

Number of conductors per duct

Thickness of conductor semiconducting shield, inchestcs 0.0787:=

Maximum allowable normal conductor operating temperature, CTc 90:=

Diameter of the segmental conductor, inchesDc 1.416:=

Conductor proximitty effect factor, dry segmentalkp 0.6:=

Conductor skin effect factor, dry segmentalks 0.435:=

ohm-metersρ conductor 0.017241:=Conductor area, CIA 1750:=

Cable Data:

The ampacity calculation is for a 230kV 1750 kcmil segmented copper conductor circuit, with866mils XLPE insulation, and lead metallic sheath, 2 circuits installed in a vertical duct bank and0.60 loss factor. The sheath is cross bonded to minize circulating current.

Extruded Dielectric Cable (XLPE) Ampacity Worked Example

IDduct 6.065=IDduct ODduct 2 0.28⋅−:=

PVC Duct outside diameter, inchesODduct 6.625:=

Duct Data:

Dissipation factor of the insulation, numerictanδ 0.001:=

Dielectric constant of the insulationSIC 2.3:=

Jacket thickness, inchestj 0.125:=

Thickness of lead moisture barrier / metallic sheathtms 0.125:=

Thickness of insulation semiconducting shield, inchestis 0.0984:=

Insulation wall thickness, inchesti 0.866:=

3-67


ODduct 168.275=ODduct ODduct 25.4⋅:=mmDjacket 101.656=Djacket Djacket 25.4⋅:=

mmtms 3.175=tms tms 25.4⋅:=

mmDmet_shield 95.306=Dmet_shield Dms 25.4⋅:=

mmDmean_shield 92.131=Dmean_shield Dmms 25.4⋅:=

mmDinsl_shield 88.956=Dinsl_shield Dis 25.4⋅:=

W/mWd 1.144=Wd

2 π⋅ f⋅ SIC⋅E

3⎛⎜⎝

⎞⎟⎠

2⋅ tanδ⋅ 10 9−

⋅

18 lnDinsulation

Dcond_shield

⎛⎜⎝

⎞⎟⎠

⋅

:=

Calculate the dielectric losses:

mmdcircuits 508.000=dcircuits dcircuits 25.4⋅:=

mmdphases 254.000=dphases dphases 25.4⋅:=

mmBurial 1.067 103×=Burial Burial 25.4⋅:=

mmIDduct 154.051=IDduct IDduct 25.4⋅:=

mm

Djacket Dms 2 tj⋅+:=

Dmms 3.627=Mean metallic shield diameter, inchesDmmsDis Dms+

2:=

Dms 3.752=Diameter over the metallic shield/moisture barrier, inchesDms Dis 2 tms⋅+:=

Dis 3.502=Diameter over the insulation shield, inchesDis Dinsulation 2 tis⋅+:=

Dinsulation 3.305=Diameter over the insulation, inchesDinsulation Dcs 2 ti⋅+:=

Dcs 1.573=Diameter over the conductor shield, inchesDcs Dc 2 tcs⋅+:=

Calculate Cable Geometry:

mmDinsulation 83.957=Dinsulation Dinsulation 25.4⋅:=

mmDcond_shield 39.964=Dcond_shield Dcs 25.4⋅:=

mmDconductor 35.966=Dconductor Dc 25.4⋅:=

mm2Areaconductor 886.749=AreaconductorA

1.9735:=

Metric Conversion of Variables

Clearance 2.063=Clearance in conduit, inchesClearance IDduct Djacket−:=

Djacket 4.002=Diameter over jacket, inches


3-68

Racc Rdc90 1 Ycs+ Ycp+( )⋅:= Racc 2.638 10 5−×= ohms/meter

Calculate the shield losses:

Assume that the conductors will lie in a flat (vertical) configuration for purposes of calculating shieldlosses. The metallic sheath consists of lead, and the bonding scheme is cross-bonded, so there willbe no circulating current and only eddy current losses.

Sheath material is lead ρ lead 21.410 8−⋅:=

Areasheath πDmet_shield

2 Dinsl_shield2

−⎛⎝

⎞⎠

4⋅:= Areasheath 918.965= mm2

Areasheath Areasheath 10 6−⋅:= m2

Rsheathρ lead

Areasheath:= Rsheath 2.329 10 4−

×=

Tmshield 73.856=Estimated sheath temperature:

Rsheath RsheathTmshield 236.0−( )−

20 236.0−( )−⋅:= Rsheath 2.819 10 4−

×=

Calculate Conductor Resistance:

Rdc20ρ conductor

Areaconductor:= Rdc20 1.944 10 5−×= ohms/meter

Rdc90 Rdc20234.5 Tc+234.5 20+

⎛⎜⎝

⎞⎟⎠

⋅:= Rdc90 2.479 10 5−×= ohms/meter

Assume 2.5% Stranding of Conductor

Rdc90 Rdc90 1.025⋅:= Rdc90 2.541 10 5−×= ohms/meter

Xs8 π⋅ f⋅ ks( )⋅ 10 7−⋅

Rdc90:= Xs 2.581=

YcsXs2

192 0.8 Xs2⋅+:= Ycs 0.034=

Xp 8 π⋅ f⋅ kp( )⋅ 10 7−⋅

Rdc90:= Xp 3.561=

YcpXp2

192 0.8 Xp2⋅+

⎛⎜⎜⎝

⎞⎟⎟⎠

Dconductordphases

⎛⎜⎝

⎞⎟⎠

2

⋅ 0.312Dconductor

dphases

⎛⎜⎝

⎞⎟⎠

2

⋅

1.18

Xp2

192 0.8 Xp2⋅+

⎛⎜⎜⎝

⎞⎟⎟⎠

0.27+

+

...⎡⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎦

⋅:= Ycp 4.468 10 3−×=

3-69


Rduct 0.084=Rductρ duct

2 π⋅ln

ODduct

IDduct

⎛⎜⎝

⎞⎟⎠

⋅:=

Rcable_to_duct 0.304=Rcable_to_duct5.2

1 0.1 0.91 0.01 Tmduct⋅+( )⋅ Djacket( )⋅+:=

Estimate of mean temperature in ductTmduct 67.629=

Rj 0.036=Rjρ jacket

2 π⋅ln

Djacket

Dmet_shield

⎛⎜⎝

⎞⎟⎠

⋅:=

Ri 0.504=Riρ insulation

2 π⋅ln

Dinsl_shield

Dconductor

⎛⎜⎝

⎞⎟⎠

⋅:=

Calculate Cable Therm al Resistances

Racs 2.734 10 5−×=Racs Rdc90 1 Ycs+ Ycp+ Ysc+ Yse+( )⋅:=

Single point bonded so no circulating currentsYsc 0:=

Yse 0.038=YseRsheath

Racc

⎛⎜⎝

⎞⎟⎠

gs YSe0⋅ 1 YSe1+( )⋅β1 tms⋅( )4

12 1012⋅

+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

gs 1.008=gs 1tms

Dmean_shield

⎛⎜⎝

⎞⎟⎠

1.74β1 Dmean_shield⋅ 10 3−

⋅ 1.6−⎛⎝

⎞⎠⋅+:=

β1 47.050=β1

8 π2

⋅ f⋅

ρ lead 107⋅

:=

YSe1 3.852 10 4−×=YSe1 0.86 m( )3.08

⋅Dmean_shield

2 dphases⋅

⎛⎜⎝

⎞⎟⎠

1.4 m⋅ 0.7+

⋅:=

YSe0 3.468 10 3−×=YSe0 6

m2

1 m2+

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅Dmean_shield( )

2 dphases⋅⎡⎢⎣

⎤⎥⎦

2⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

m 0.134=m2 π⋅ f⋅ 10 7−

⋅

Rsheath:=

Eddy current loss increment


3-70

Diameter beyond which 24 hour average losses apply, mm Dx 205.148=

The self and mutual earth thermal resistances each consist of two terms. The first term assumesthat the concrete resistivity appl ies everywhere, the second term corrects for the excess of thenative earth resistivity over the concrete resistivi ty.

Middle phase has highest total thermalresistanceL Burial dphases+:= L 1.321 103×= mm

Rearthρbackfill

2 π⋅ln

Dx

ODduct

⎛⎜⎝

⎞⎟⎠

LF ln2 L⋅ 4 L2⋅ ODduct

2−+

Dx

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:= Rearth 0.171=

Earth thermal resistance for AC losses

Rearth'ρbackfill

2 π⋅ln

Dx

ODduct

⎛⎜⎝

⎞⎟⎠

ln2 L⋅ 4 L2⋅ ODduct

2−+

Dx

⎛⎜⎜⎝

⎞⎟⎟⎠

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:= Rearth' 0.274=

Earth thermal resistance for dielectriclosses

Rcorrection LFρnative ρbackfill−( )

2 π⋅⋅ n⋅ Gb⋅:= Rcorrection 0.082=

Correction for native backfill thermal resistancefor AC losses

Rcorrection 'ρnative ρbackfill−( )

2 π⋅n⋅ Gb⋅:= Rcorrection ' 0.136=

Correction for native backfill thermal resistancefor dielectric losses

Calculate External Thermal Resistances

Calculate geometric correction factor for backfill envelope:

x Widthcbf:= x x 25.4⋅:= x 838.200= y Heightcbf:= y y 25.4⋅:= y 838.200=

Db e

1

2⎛⎜⎝

⎞⎟⎠

x

y⎛⎜⎝

⎞⎟⎠

⋅4

π

x

y−⎛⎜

⎝⎞⎟⎠

⋅ ln 1y2

x2+

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅ ln x( )+⎡⎢⎢⎣

⎤⎥⎥⎦:= Db 921.455=

Lb Burial dphases+:= Lb 1.321 103×=

Gb ln2 Lb⋅ 4 Lb

2⋅ Db2−+

Db

⎛⎜⎜⎝

⎞⎟⎟⎠

:= Gb 1.714=

Calculate diameter Dx

αn6.71 104⋅

ρnative 100⋅( )0.8:= Thermal diffusivity of native soil mm2

hourαn 1.685 103×=

Dx 1.02 αn 24⋅⋅:=


IratedΔTcond

ΣRacRthermal:= Ampacity per phase group, amperes: Irated 1101.4=

Ito tal 2 Irated⋅:= Total ampacity, amperes Itotal 2202.8=

Check and adjust the estimated shield and duct air temperatures:

Wc Irated2 Racc⋅:= Loss at the conductor, w/m Wc 32.003=

T's Tc Wc Ri⋅−:= Check temperature of shield which was estimated at T's 73.856=

Tmshield 73.856≡

Ws Irated2 Racs⋅:= Ws 33.169=

T'm T's Ws RjRcable_to_duct

2+

⎛⎜⎝

⎞⎟⎠

⋅−:= Check mean temperature between cable surface andinside of duct w hich was estimated at:

T'm 67.629=

Tmduct 67.629≡

Mutual Heating

F12 Burial⋅ dphases+

dphases

⎛⎜⎝

⎞⎟⎠

2 Burial⋅ 3 dphases⋅+

dphases

⎛⎜⎝

⎞⎟⎠

⋅:= F212 Burial dphases+( )⋅⎡⎣ ⎤⎦

2dcircuits

2+⎡

⎣⎤⎦

.5

dcircuits

⎡⎢⎢⎣

⎤⎥⎥⎦

:=

F222 Burial⋅ dphases+( )2 dcircuits

2+⎡

⎣⎤⎦

.5

dcircuits2 dphases

2+⎛

⎝⎞⎠

.5

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

2 Burial⋅ 3 dphases⋅+( )2 dcircuits2

+⎡⎣

⎤⎦

.5

dcircuits2 dphases

2+⎛

⎝⎞⎠

.5

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅:=

F F1 F21⋅ F22⋅:= F 1.262 104×=

Mutual thermal resistance for AC losses:

Rmutualρ backfill

2 π⋅LF⋅ ln F( )⋅ N 1−( ) n⋅ LF⋅

ρ native ρ backfill−( )2 π⋅

⋅ Gb⋅+:= Rmutual 0.860=

Mutual thermal resistance for dielectric losses:

Rmutual'ρ backfill

2 π⋅ln F( )⋅ N 1−( ) n⋅

ρ native ρ backfill−( )2 π⋅

⋅ Gb⋅+:= Rmutual' 1.434=

Calculate temperature rise from dielectric heating

ΔTd Wd12

Ri⋅ Rj+ Rcable_to_duct+ Rduct+ Rearth'+ Rmutual'+ Rcorrection'+⎛⎜⎝

⎞⎟⎠

⋅:= ΔTd 2.884=

Calculate the Ampacity

ΣRacRthermal Racc Ri⋅Racs Rj⋅+

...

Racs Rcable_to_duct⋅+...

Racs Rduct⋅+...

Racs Rearth⋅+...

Racs Rcorrection⋅+...

Racs Rmutual⋅+...

:= ΣRacRthermal 5.533 10 5−×=

C° / A^2

ΔTcond Tc ΔTd− Ta−:= ΔTcond 67.116=

3-71


CHAPTER 4 Power Transformers

4.1 INTRODUCTION

Power transformers are a crucial link in the electric power system. Power transformer fail-ures can result in extremely high financial losses, both in lost revenue and the capitalexpenditure of unit itself. Therefore, it is essential that power transformers be operated ina safe and prudent manner. In addition, given the high equipment cost, power transform-ers must be operated in a manner to give a reasonable service life in order to realize a pos-itive return on investment.

Power transformers represent a significant portion of capital investment costs. Underexisting conditions in the industry, utility budgets are reduced and networks are beingforced to support greater power transfer over existing transmission circuits than everbefore. As such, there is increased interest in safely utilizing all available capacity ofpower transformers.

The thermal design of power transformers is based on an assumed daily average ambienttemperature of 30°C, with a maximum of 40°C. It is also based on continuous loading atthe rated maximum current. These assumptions are essential to the specification anddesign of power transformers; however, they are probably never realized in service. Inmost cases, these assumptions result in very conservative thermal ratings for liquid-filledpower transformers. Safe utilization of this “latent capacity” is the subject of this chapter.

In general, transformer load capacity is limited by equipment (winding and oil) tempera-tures. Industry standards (IEEE C57.12.00 in the U.S.) specify a maximum average wind-ing rise that defines the rated load. In other words, when operating at rated nameplatecurrent, the average winding rise shall not exceed the given value. For newer transformerswith thermally upgraded insulation, manufactured starting in the late 1960s, this maxi-mum average winding rise is 65°C. Combined with the 30°C ambient and a 15°C gradientbetween the winding hottest spot temperature and the average winding temperature, thepeak temperature in the winding is 110°C. This temperature represents a somewhat arbi-trary benchmark temperature that gives a reasonable life expectancy based upon the col-lective experience of the industry. Earlier transformers built before the introduction ofthermally upgraded insulation were based upon a rated average winding rise of 55°C, or ahot spot of 95°C.

4-1

Chapter 4: Power Transformers Increased Power Flow Guidebook


• Section 4.2, Transformer Design, describes the gen-eral construction of power transformers, types ofcooling, losses generated by transformers, and fac-tory testing.

• Section 4.3. Risks of Increased Loading, outlinesshort- and long-term risks related to the loading oftransformers.

• Section 4.4, Thermal Modeling, provides an overviewof heat transfer mechanisms and describes the fourmost prevalent thermal models.

• Section 4.5, Thermal Ratings, discusses factorsbehind thermal ratings, including ambient air tem-perature, load, and maintenance considerations.

• Section 4.6, Winding Temperature Measurement,describes methods of measuring and monitoringwinding temperature.

• Section 4.7, Modest Increases in Capacity from Exist-ing Transformers, outlines methods of increasingcooling.

• Section 4.8, Examples, provides two examples ofincreasing capacity.

4.2 TRANSFORMER DESIGN

4.2.1 General Construction

Power transformers are commonly categorized into twomain construction configurations: core form and shellform. These two categories are clearly defined in thecase of three-phase power transformers. The definitionbecomes less distinct in the case of single-phase trans-formers, especially in the smaller sizes. In this range, thedistinction is of minor importance, however.

Core-Form ConstructionA core-form power transformer is constructed withwindings that are in the general form of concentric cyl-inders (Figures 4.2-1 and 4.2-2). The magnetic core con-sists of stacks of laminated grain-oriented silicone steelsheets. The width of these sheets is varied so that, asstacked, the cross section of each leg conforms as nearlyas practical to the circular form of the innermost wind-

ing. With very few exceptions, the winding assembliesand core legs are assembled with their axis in a verticalor upright plane.

The magnetic circuit is completed with yoke assembliesthat bridge the three legs at the top and bottom. Onsome of the larger transformers, part of the requiredcross section of the yokes might be provided by outerlegs at each end. These are referred to as “fifth legs” andallow a reduction in the vertical dimensions of both thetop and bottom yokes. This reduction is often an impor-tant factor in meeting shipping clearances since coreform power transformers are shipped with the coils andcore legs in an upright or vertical position.

The legs and yoke assemblies are joined with miteredinterfaces that have alternating steps that overlap toprovide good magnetic coupling. Modern practices areto use laminations of 0.009-in. thickness with at leastfive overlapping steps. This pattern is repeated acrossthe entire build of the core assembly. The legs and yokesare maintained as an independent assembly by bandingthe legs with a nonconducting material such as fiber-glass and in some cases, metallic bands that must beprovided with an insulating gap to prevent circulatingcurrents to flow around the band.

Ducts for the flow of cooling oil are provided betweenconcentric winding sections and sometimes within wind-ing sections if required by the thermal characteristics ofthe design (Figures 4.2-3 and 4.2-4).

Cooling ducts may also be required in the core legsand/or yokes (Figures 4.2-5 and 4.2-6). These ducts areformed by providing spacers between laminations at dis-crete intervals determined by the dimensions of the core.These ducts between laminations are usually mirrored inthe top and bottom yokes.

Figure 4.2-1 Typical core-form construction (front view). Figure 4.2-2 Typical core-type internal assembly.

4-2

Increased Power Flow Guidebook Chapter 4: Power Transformers

4-3

In a core-form transformer, the winding design permitscooling oil to flow vertically through the concentricwindings and the core leg ducts (Figure 4.2-7).

Shell-Form ConstructionIn shell-form power transformers, the windings consistof phase assemblies produced by winding individual sec-tions in a flat plane on a winding machine (Figures 4.2-8and 4.2-9). These windings are initially assembled flatwith insulation and cooling ducts between sections.Complete phase assemblies are then clamped and ori-ented in a vertical direction so that the plane of the indi-vidual sections are upright. The core laminations areinserted through and around the windings in the final

Figure 4.2-3 Core-type winding assembly with concentric cooling ducts.

Figure 4.2-4 Cooling duct being assembled on winding.

Figure 4.2-5 Inner winding assembled on core (note oil ducts in core and below windings).

Figure 4.2-6 Cross section of core form construction.

Figure 4.2-7 Oil flow in core-type winding.


assembly process. The core and coil assembly is notdesigned to be lifted as a unit in most cases.

In shell-form construction, the oil flows verticallythrough the ducts between individual winding sections(Figure 4.2-10). The spacers in these ducts are posi-tioned to direct the oil across the width of each windingsection.

Directed Flow DesignsWhen forced oil cooling is employed, the transformerinternal assembly may be designed with oil manifoldsthat direct the incoming cool oil to the lower part of thecore and windings. In a nondirected flow transformer,the incoming cool oil is pumped into the bulk oil of thelower tank and moves through the core and windings inmuch the same manner as normal convection currentsbut with greater velocity (Figures 4.2-11 and 4.2-12).

A directed flow design is normally used with larger sizesof transformers equipped with heat exchangers ratherthan radiators (Figures 4.2-13 and 4.2-14).

Figure 4.2-8 Typical shell-form construction (plan view).

Figure 4.2-9 Shell-form transformer.

Figure 4.2-10 Shell-form phase assembly under construction (cooling ducts are assembled between sections).

Figure 4.2-11 Core-form transformer designed for directed flow.

4-4


4.2.2 Types of Cooling

Oil-immersed power transformers are cooled by fourdifferent cooling configurations, each with unique heattransfer. They are as follows:

• ONAN (OA) – Also referred to as self-cooled, nopumps are used to circulate oil, and no fans are usedto increase airflow over the radiators. Oil circulatesupward through the windings and down through theradiators by natural thermosiphon flow.

• ONAF (FA) – No pumps are used to circulate the oil.Fans are used to force air over the radiators toincrease heat transfer from the bulk oil to the sur-rounding air. As with ONAN, oil circulates upwardthrough the windings and down through the radia-tors by natural thermosiphon flow.

• OFAF (Non-directed FOA) – Pumps are used to cir-culate the oil. Fans are used to force air over the radi-ators. The forced circulation of the oil increases theconvective heat transfer from the windings to the oil.The forced air increases the convective heat transferfrom the oil to the air. With OFAF, there are no ductsto direct the oil over the winding. In general, the bulkof the forced oil flow passes upward between thewinding and the tank, bypassing the windings. Natu-ral convection is still the predominant mode of heattransfer from the windings to the adjacent oil.

• ODAF (Directed FOA) – Pumps are used to circulatethe oil. Fans are used to force air over the radiators orheat exchangers. The forced circulation of the oilincreases the convective heat transfer from the wind-ings to the oil. The forced air increases the convectiveheat transfer from the oil to the air. With ODAF,ducts are added to direct the oil over the winding.This forces a significant portion of the forced oil toflow upward through the vertical winding ducts.Washers may also be employed in a zig-zag fashion toforce the oil to flow back and forth between disk sec-tions of a disk winding, further increasing the convec-tive heat transfer from the winding to the oil.

4.2.3 Losses

As with all electrical apparatus, transformers generatelosses. These losses are manifested in the form of heat.This heat increases the temperature of the transformercomponents, and therefore limits the load capacity.Therefore, it is essential to discuss losses when discuss-ing loading. The losses in a transformer are due toseveral different mechanisms, but are generally lumpedinto two categories: load losses and no-load losses(Figure 4.2-15). Load losses are losses that vary withload current, but not with excitation. No-load losses arelosses that do not vary with load current, but rathervary with excitation or voltage.

Figure 4.2-12 Directed oil flow in core-form construction.

Figure 4.2-13 Heat exchangers assembled on transformer.

Figure 4.2-14 Radiators assembled on transformer.

4-5


Load losses and no-load losses may be further brokendown. Load losses consist of three components: windingI2R losses, winding eddy losses, and stray losses. Wind-ing I2R losses are the Ohmic losses due to the load cur-rent flowing in the windings. Skin effect is generallyignored, but would be included in the I2R losses.Depending upon the conductor dimensions, the increasein winding I2R losses may or may not be negligible.

In addition to the intended load current, unintendededdy currents flow within the winding conductor due tothe presence of leakage flux, or flux that does not flowwithin the core. These eddy currents result in additionalOhmic losses in the winding conductors. The eddy lossescan be reduced by using a stranded conductor, breakingthe path for eddy current flow into smaller regions.

If parallel strands or conductors are used, circulatingcurrents between parallel sections can flow due to differ-ing amounts of flux linkage. These losses can be reducedby transposing the cable, as in the cases of CTC (contin-uously transposed cable) or transposing the windingconductors at various points along the winding.

Stray losses comprise the remainder of the load losses.Stray losses are losses due to currents induced in variousmetallic structures of the transformer, including thewinding clamping structure, tie plates, core bolts, etc.Stray losses are parasitic in nature, and difficult to cal-culate. In some cases, the losses can result in high local-ized temperatures of various metal components. Often,in larger power transformers and GSUs (generation stepups), this is a serious concern and must be carefullyexamined during design and construction.

No-load losses are composed mainly of losses in thesteel core. The steel that comprises the core containsmany microscopic regions of like magnetic polarity,called magnetic domains. When magnetic flux passesthrough the core, these domains shift to orient theirmagnetic poles in the direction of the flux. Since the fluxvaries sinusoidally, the domains must change directionas the flux changes direction. This continuous move-

ment of the magnetic domains produces losses. Theselosses are termed hysteresis losses.

Like the winding conductors, the flux passing throughthe steel core, which is electrically conductive, induces acurrent flow around the core. The magnitude of theseinduced currents is reduced by dividing the core cross sec-tion into thin sheets or laminations. Each sheet is coatedwith an insulating film. This reduces the total eddy cur-rent, and therefore the eddy loss, in the steel core.

The core losses in any transformer are dependent on thecore flux density. The core flux density is determined bythe magnitude and frequency of the primary voltageand the cross-sectional area of the core leg according toEquation 4.2-1.

4.2-1Where:Bm = maximum flux density in Tesla.f = operating frequency.A = cross-sectional area of core in mm2.V = primary voltage (RMS) per phase.T = number of primary winding turns per phase.

The flux density, and therefore the principal core losses,are thus independent of load. There may be some local-ized heating of the outer core laminations or the coresupport structure by stray flux due to winding currentthat will be exacerbated by overloads. These losses areusually of little consequence to either short-term orlong-term reliability of the transformer because they areremoved from the winding insulation and affect the oilonly in the local area involved.

If a transformer has displayed a tendency, in normalservice, to produce methane or ethane close to or inexcess of condition #1 as described in ANSI C57.104,dissolved gas analyses should be performed at dailyintervals when overloading to a level that has not beenpreviously experienced. Continued operation at thatlevel may normally be considered safe from this point ofview if gas accumulation rates do not exceed condition#2 as detailed in ANSI C57.104.

4.2.4 Factory Testing

Little information on a particular power transformer isavailable to the user. Generally, the only information auser has on a unit is the information given on the fac-tory test report and on the nameplate. Combined, thesereports give the user key performance characteristicsneeded to operate the transformer. Included in thisinformation is the heat run data, giving the temperaturerises of the windings and the oil at the benchmark load-ing of the nameplate rating, and the loss data. In order

Figure 4.2-15 Transformer equivalent circuit.

310225 −××=

T

V

fABM

4-6


to interpret the data given on a factory test report prop-erly, at least a passing understanding of the underlyingtest is necessary. This understanding will assist thereader in interpreting the numbers and any remarks thatmay be associated with the test values.

Factory Loss Tests

No-Load Loss TestingNo-load loss testing is performed with one windingopen-circuited and rated voltage applied to the otherwinding. For practical reasons, voltage is usually appliedto the low-voltage winding. This results in full excitationon the transformer, with only the exciting current flow-ing through the excited winding (Figure 4.2-16).

Load Loss TestingThe load losses in an operating transformer consist of:

• I2R losses in the current carrying components due toload current in all active windings.

• Joule losses caused by circulating currents in windingconductors due to impedance inequalities in parallelconductors.

• Eddy currents in winding conductors due to radialgradients in the induced voltages.

• Stray losses due to induced currents in the tank wallsand internal support structures.

Load losses are measured by short-circuiting either thehigh-voltage or low-voltage winding and then applyinga voltage to the other winding that results in rated cur-rent flowing through the windings (Figure 4.2-17). Thepower loss measured, as measured by the wattmeter, isthen the load loss at the temperature of the windingsduring the test. Since losses are dependent upon temper-ature, the load losses must be corrected to a standardreference temperature.

Prior to the test, the transformer is allowed to sit de-energized long enough for the oil temperature to stabi-lize. The temperature of the windings is then assumed tobe equal to the average oil temperature. The load lossesare corrected to a standard reference temperature of

20°C plus the rated average winding rise. For 55°C or55/65°C transformers, the reference temperature is gen-erally 75°C. For 65°C rise transformers, the referencetemperature is generally 85°C. This should be explicitlyspecified on the test report.

The I2R losses vary with temperature in a predictablefashion. The difficulty is in determining the appropriatetemperature for an operating condition since the tem-perature variation between parts of a winding can beconsiderable.

ANSI standards require reporting of transformer lossesat a reference temperature of 85°C for 65°C transformerratings and 75°C for 55°C transformer ratings.

For copper, these I2R losses are corrected to an operat-ing temperature (T) as shown in Equation 4.2-2.

4.2-2Where:Pr(T) = I2R loss due to load current at operating

temperature T (°C).Tm = reference temperature of the test report

losses.PR(Tm) = test report I2R losses at Tm.

(The test report will give total load losses at the refer-ence temperature and the measured winding resistancescorrected to this temperature. The tested I2R can be cal-culated using the test report resistance at the referencetemperature and rated winding current. Note that thetest report resistance values for each winding are equalto the sum of the three phases as required by ANSIstandards. Use of rated winding phase current with thetest report resistance allows calculation of the three-phase I2R loss for each winding.)

The stray and eddy losses vary inversely with tempera-ture. For copper, these losses are corrected as shown inEquation 4.2-3.

Ps(T) = Ps(Tm) (234.5 + Tm)/(234.5 + T) 4.2-3

Figure 4.2-16 Basic circuit for no-load loss testing. Figure 4.2-17 Basic circuit for load loss testing.

m mPR(T) PR(T ) (234.5 T)/(234.5 T )= + +

4-7


Where:Ps(T) = stray losses at operating temperature

T (°C)Tm = reference temperature of the test report

lossesPs(Tm) = test report load losses at Tm minus PR(Tm)

calculated above.

The load losses at operating temperature T are the sumof PR(T) and Ps(T).

Factory Temperature Rise TestsThe basis for all practical transformer thermal modelsused in the evaluation of transformer loading is the fac-tory heat run. The factory heat run provides a directmeasurement of the thermal performance of a trans-former at a particular benchmark, the nameplate rating.Given the temperature rises at this benchmark loading,it is possible to estimate the temperature rises underother loading conditions. Therefore, to understand thethermal models and their application to transformerloading and rating calculations, one must know thebasic principles behind the factory heat run. Thisknowledge will prove invaluable when interpreting thedata presented on the certified test report.

This test must be performed on the tap position andwinding connection that gives the highest winding tem-perature as required by ANSI standards. The tempera-ture rises over ambient should be given in the certifiedtest report for each winding—along with the tap posi-tion, total losses, and line currents. The calculated wind-ing hot spot temperature rise over ambient should givenfor the maximum transformer rating.

Two methods are used to perform factory heat runs: the“short-circuit” method and the “loading-back” method.Of these two methods, the short-circuit method is by farthe most common and will be covered in the greatestdepth here. In addition to these two methods, it is alsopossible that a heat run may be performed by connect-ing the transformer to a load and loading the trans-former at rated voltage and current simultaneously. Thismethod is generally only practical for small power trans-formers and is not often used.

Short-Circuit MethodThe short-circuit method, also sometimes referred to asloss injection, consists of two segments. In both seg-ments of the test, one winding is short-circuited and avoltage is applied to the other winding. In this manner,each winding temperature can be checked. For trans-formers with multiple windings, the test load levels areusually agreed upon before hand, and each winding istested with the other windings short-circuited.

For the initial segment of the test, one winding is short-circuited and a voltage is applied to the other windingsuch that the active power supplied equals the totallosses (load losses plus no-load losses) previously mea-sured by other means (refer to IEEE C57.12.90 or IEC76-1). Note that temperature rise tests are usually per-formed at the combination of taps that gives the highestlosses. The power is applied continuously to bring theoil temperatures up to their steady-state values. Steady-state is defined in the respective test standards, but usu-ally is such that the average oil temperature has notincreased more than 1°C (or 2.5%, whichever is greater)for three consecutive hours. The purpose of this segmentof the test is to establish the oil temperature rise overambient.

The second segment of the test is to measure the windingtemperature rises. Once a steady-state average oil tem-perature has been reached, the applied voltage is reducedsuch that rated current flows in the windings under test.This load is held continuously for one hour. At the con-clusion of one hour, the winding resistance is measuredshortly after the windings have been disconnected,allowing just enough time for the inductance effects todissipate. The winding resistance is measured several dif-ferent times after shutdown, recording the resistance andtime after shutdown each time (Figure 4.2-18). Thesepoints are then used to extrapolate the winding resis-tance back to the instant of shutdown. With this wind-ing resistance and the cold winding resistance (measuredprior to the heat run with the windings at a known ambi-ent temperature), the average winding rise at the instantof shutdown can then be determined. This proceduremay have to be repeated for each winding unless theavailable test equipment and transformer design allowsimultaneous resistance readings on all windings.

After completion of the above procedures, the oil tem-perature rises and average winding rises for each wind-ing are known, given the test conditions. Since it is not

Figure 4.2-18 Example winding cooldown curve illustrating extrapolation of resistance measurements to shutdown.

4-8


always possible to maintain the exact loadings requiredto give the total loss or rated current, the raw resultsobtained above must be corrected to the rated losses andloads. This is done using simple empirical equations asshown in Equations 4.2-4 and 4.2-5.

For oil temperatures:

4.2-4

For winding temperatures:

4.2-5Where:θo,corr = oil temperature corrected to rated losses.θo,meas = oil temperature measured during the heat

run.Pt,rated = total losses at rated load.Pt,meas = total losses applied during oil rise portion

of the heat run.m = oil rise exponent (0.8 for ONAN, ONAF,

OFAF; 1.0 for ODAF).θw,corr = average winding rise corrected to rated

load.θw,meas = average winding rise measured during

test.Iw,rated = rated winding current.Iw,meas = winding current measured during the

winding rise portion of the test.n = winding rise exponent (0.8 or ONAN; 0.9

for ONAF; 1.0 for OFAF, ODAF).

Loading-Back MethodThis method is rarely used, and as such will not bedescribed in any great detail here. For more informa-tion, consult the relevant test standards, IEEEC57.12.90 and IEC 76-2.

4.3 RISKS OF INCREASED LOADING

Any energized transformer has a finite risk of failure.This risk of failure is generally very low. Loading trans-formers above the nameplate rating results in higherrisks, eventually reaching the extreme where failurewould be certain. The challenge is to determine loadinglevels that represent an acceptable level of risk, given thecircumstances.

There are several risks related to the loading of trans-formers. The most significant of these risks are long-

term degradation of the insulation paper and short-termreduction in dielectric strength due to bubble formation.Understanding these risks and their mechanisms isessential to any discussion on transformer loading.Users must be aware of the risks, take steps to assessthese risks, and develop a methodology for maintainingrisks at acceptable levels.

4.3.1 Short-Term Risks

Risks classified as “short-term” are those that wouldresult in the immediate failure of the transformer.Reduction in dielectric strength due to gas evolutionfrom the winding conductor insulation is the principalshort-term risk. Additional short-term risks include gasevolution from lead conductors, gas evolution fromwood and cellulose materials adjacent to metallic hotspots from stray flux heating, delamination of phenolicresin tap boards, and reduction of short-circuit with-stand capability in epoxy-bonded CTC. Some of theserisks will not result in failure in and of themselves, butwhen combined with an abnormal transient voltage orthroughfault, may result in failure.

Bubble EvolutionThrough destructive testing of model coils, researchershave discovered that under certain loading conditions, asignificant decrease in dielectric strength of the windingassembly occurs. In the transformers considered here,specially refined petroleum oil is used as an electricalinsulation material and, concurrently, as a heat transferfluid. Gas-filled bubbles can be formed in the trans-former oil in units in service. The electrical breakdownstrengths of these gases are significantly lower than thatof the transformer oil surrounding these bubbles. Bub-bles that find their way into an electrically stressed oilgap can significantly reduce the breakdown voltage ofthe gap and interfere with the functioning of a trans-former (Figure 4.3-1).

m

meast

ratedtmeasocorro P

P⎟⎟⎠

⎞⎜⎜⎝

⎛=

,

,,, θθ

n

measw

ratedwmeaswcorrw I

I2

,

,,, ⎟

⎟⎠

⎞⎜⎜⎝

⎛= θθ

Sixty-Hertz Breakdown Voltage in Percent of 25C Strength

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Hot Spot Temperature, C

Bre

akdo

wn

Volta

ge, % Paper Insulated

Winding Conductor - Dry (<0.5%)

Paper Insulated Cable - Dry (<0.5%)

Paper Insulated Winding Conductor - Wet (3%)

Figure 4.3-1 Example of 60-Hz breakdown vs. temperature illustrating bubble formation.

4-9


Henry’s Law states that the concentration, Ci, of a singleideal gas, i, dissolved in a liquid is proportional to thepartial pressure of that gas, Pi, over the liquid:

Ci = Ki * Pi 4.3-1

At equilibrium, the drive of the dissolved gas to escapeis balanced by the drive of the gas over the liquid toenter the liquid. Ki is a constant dependent on tempera-ture, T, in a typical exponential manner:

Ki ~ exp (Bi /T) 4.3-2

The magnitude of Ki and its dependence on temperaturereflect the particular intermolecular interactions of agiven gas – liquid combination and are unique to thatcombination. Bi can be either positive or negative alge-braically; it is negative for gases whose solubilityincreases as the temperature decreases.

If, at constant temperature, the partial pressure of thegas over a liquid is decreased, the liquid will be supersat-urated and gas will vaporize in order to reach a newequilibrium concentration as defined by Henry’s Law.Likewise, if the temperature changes so that Ki becomessmaller while the pressure of the gas over the liquid isheld constant, additional gas will make its escape. In thereverse of these happenings, gas will dissolve.

When the reduction in pressure of the gas over the liq-uid is slow or the local mass transport processes are rel-atively fast, the dissolved gas will diffuse through theliquid to and across the gas-liquid interface. The gas will“steam” away. The escape of the gas tracks the slowdecrease in the external partial pressure.

If, however, the pressure of the gas over the liquid dropsso rapidly that dissolved gas does not have time to moveto the surface, local supersaturation can occur and bub-bles can nucleate. The bubble presses aside the sur-rounding liquid, and continues to grow as it absorbssupersaturating gas from the liquid. A bubble will growso long as the pressure within the bubble exceeds theexternal pressure. The primary constraint to bubblegrowth is the pressure of the atmosphere over liquid.The effect of surface tension of the liquid at the bubblesurface and the hydrostatic pressure of the liquid overthe site of bubble growth are minor.

An example – warm beer bubbles and foams when thebottle cap is removed and the pressure of carbon dioxide(CO2) in the neck of the bottle is suddenly released.Colder beer bubbles and foams less, in part because thepressure to be released in the neck of the bottle is less,but also because CO2 is more soluble in cold water(BCO2 is algebraically negative).

Oil in transformers normally contains more than onegas. Some transformers are designed to allow access ofair to the interior. The gases dissolved in the oil arethose present in air: nitrogen, oxygen, carbon dioxide,and traces of other gases. Other transformers are sealedand evacuated and then filled with nitrogen. The pri-mary gas dissolved in the oil is nitrogen. Only smallamounts of oxygen and traces of carbon dioxide remain.

In general, gases dissolved in transformer oil behave asideal dilute solutions in that the solubility of one gas isindependent of the presence of any other gas; e.g., KN2

is the same whether CO2 is present or not, and CN2 isnot affected by PCO2. However, in forming bubbles,gases behave collectively. Each gas dissolved in the oilcontributes to the internal pressure of the bubbleaccording to Henry’s Law, shown in Equation 4.3-3.

4.3-3

A bubble forms when the sum of the partial pressuresresulting from local concentrations of gases in the liquidexceeds the pressure over the surface of the liquid phase– Patm.

The major solid electrical insulation in typical trans-formers is cellulose in the form of paper and press boardimpregnated with transformer oil. Water is absorbed bythe cellulose. It distributes itself between the bulk oiland paper so that the concentrations of water in thesolid and liquid media are in equilibrium with the watervapor pressure over the insulation system. Unlike nitro-gen and oxygen, water vapor is a condensable gas.

A very high percentage of the total mass of water in thesystem is contained in the paper. In most transformersthe amounts of free oil and impregnated cellulose arecomparable. In a subsystem containing equal volumesof paper (with 0.5% moisture content by weight) andtransformer oil and equilibrated at 80°C, the paper willcontain approximately 99.9% of the total weight ofwater. In effect, the paper in a transformer acts as analmost infinite reservoir supplying additional water tothe oil at the higher internal temperatures occurringduring operation. Water will re-absorbed on the paperwhen the electrical load on the transformer is reducedand will again be available for desorption when thetransformer is next loaded.

Desorption of water from the cellulose in the oil/paperinsulations system is an example of a physical reactionthat can increase the local concentration of gases in theoil to produce bubbling. Local concentrations can alsochange as a result of chemical reactions within the system.

bubble i i i atmP = P = (C / K ) > P∑ ∑

4-10


Thermal decomposition of cellulosic insulation canoccur in an operating transformer. The decompositionreaction can increase the local concentration of gases inthe oil. The primary products of thermal decompositionof cellulose are water vapor, CO2, and CO. Decomposi-tion of the oil/paper insulation at a sufficiently hightemperature generates gases more rapidly than they candiffuse away into the surrounding oil. Again, the localconcentration of gases builds to the point where thesummation of partial pressures exceeds the pressure inthe transformer and a bubble forms.

To summarize, formation of bubbles in transformer oilreflects a complex interplay of variables in an operatingtransformer. Bubbles result from an abrupt departurefrom equilibrium between dissolved gas and oil – result-ing from some change in pressure and/or local tempera-ture in a transformer. Bubbles form when a localincrease in gas concentration results in a local pressurethat exceeds the pressure over the oil.

Evaluation of bubble formation is difficult. The mecha-nisms are complex and dependent upon local condi-tions. The most influential factor is the moisturecontent of the paper. The temperature at which bubblesform is highly dependent upon moisture content, asillustrated in Figure 4.3-2. Note that this plot is for anexample loading condition, and therefore, the valuesdepicted are not to be taken as absolute truths.

Given the importance of moisture in the determinationof bubble evolution risk, accurate determination ofmoisture content would be necessary to use any sort ofanalytical model. Currently, there are no means ofdetermining the moisture content distribution through-out an operating transformer with the required preci-sion. Moisture content in oil is often related to moisturecontent in the paper using equilibrium curves. This,

however, has two problems. First, the moisture distrib-utes throughout the winding inversely proportional totemperature. The moisture in oil could only give anaverage content of the entire bulk insulation. Second,the paper-oil system is rarely at equilibrium. The timeconstant of moisture diffusion is on the order of severaldays or weeks.

Without any practical means to precisely assess the riskof bubble evolution, we must fall back on general guide-lines that have been proven by experience. The generalconsensus in the industry is that bubble evolution doesnot occur at hot spot temperatures up to 140°C. This isprobably valid for moisture contents up to 1.5–2%.Newer, dryer transformers could probably be safelyloaded to temperatures approaching 160°C. Transform-ers in service for less than 6 months should be limited totemperatures of 120°C.

Oil ExpansionAs with any fluid, oil expands as temperature increases.Specifically, the coefficient of expansion for oil is0.000756, or the oil expands 0.08% for every degree Crise in temperature. This expansion is anticipated, andtransformers are equipped with devices to handle oilexpansion to some degree. IEEE C57.12.10, the IEEEstandard for power transformers below 230 kV, requiresthat a transformer be capable of operating with temper-ature to 105°C. If the oil temperature exceeds 105°C, theoil may expand beyond the capacity of the gas space orconservator tank, resulting in operation of the mechani-cal pressure relief device and the expelling of oil. Notonly does this present a maintenance and environmentalheadache, this can cause problems if enough oil isexpelled such that upon cooling the oil level drops to alevel exposing the active parts. This could result in adielectric failure.

4.3.2 Long-Term Risks

Aging of Cellulose and Oil in TransformersFor liquid-immersed transformers, the insulation systemconsists of the paper and pressboard solid insulation(cellulose) and the oil liquid insulation. Both the cellu-lose and liquid insulation are adversely affected by heat.However, while the liquid insulation can be replaced orreprocessed relatively easily, the properties of the solidinsulation cannot be easily or effectively restored, norcan the insulation be economically replaced. Therefore,the loss of the paper insulation life is of utmost impor-tance when considering transformer load capability.

Oil AgingOils in transformers are mainly mineral oils. The oilscan be grouped in two types: inhibited oils, which areheavily refined, reducing the amounts of aromatics and

100

110

120

130

140

150

160

170

180

190

200

0 0.5 1 1.5 2 2.5 3 3.5

Moisture Content (% dry weight)

Gas

Evo

lutio

n Te

mpe

ratu

re (d

eg C

)

Figure 4.3-2 Gas evolution temperature vs. moisture content for example conditions.

4-11


polyaromatics, and then inhibited with an antioxidantto reduce oxidation, and the uninhibited oils, where nat-ural aromatics and polyaromatics are natural inhibitors.

When oils are subjected to oxygen and heat, they startto oxidize: the aldehydes, ketones, and finally carboxylicacids, presumably with a high molecular weight, areformed. The neutralization value and loss factor of theoil gradually increase, and the interfacial tension isreduced. At an even later stage, sludge may form. Theoxidation rate increases with increasing temperature.

For an inhibited oil, first the inhibitor is consumed (theperiod this takes is called the induction period). When itis fully consumed, the oils quickly start to oxidize.Before the inhibitor is gone, one may re-inhibit the oil,but the induction period is now be shorter, unless the oilis reclaimed.

The main risk from the oil aging is sludge formation andclogging of cooling channels. The oil aging is not gov-erned by the oxygen concentration but by catalytic pro-cesses, where hydroxyl radicals are formed via interactionwith active metals like copper and iron.

The oil condition may be followed by several diagnosticmarkers: Neutralization value, interfacial tension, lossangle, inhibitor content, and sludge measurement. It isimportant to take maintenance precautions before thecondition becomes too severe.

Cellulose AgingPaper and pressboard are made from cellulose fibers(Figure 4.3-3). They contain 93% cellulose, with mole-cules that are long, straight polysaccharide chains,which may form crystalline regions. The average number

of cellulose molecules, called the degree of polymeriza-tion (DP), describes the length of the cellulose molecule.The cellulose also contains 5-6% hemicelluloses, whichare polysaccharide chains with branches that do not eas-ily crystallize, and lignin, which is a large branched mol-ecule. The last two act as a thermoplastic.

When cellulose ages, the cellulose chains are cut in aprocess called chain scission, reducing the averagelength of the cellulose chains and resulting in shorterfibers. The number of chain scissions (η) is defined asη= DPnew/DPold –1, where the DP value is taken beforeand after the aging period.

Paper may be chemically modified to allow for opera-tion at higher temperatures (thermally-upgraded paper).Upgraded paper is paper that is chemically changed bydifferent chemical additives that reduces the aging ratecompared to untreated kraft paper. A paper is consid-ered “thermally upgraded” if it meets the life criteria asdefined in ANSI/IEEE C57.100—50% retention in ten-sile strength after 65,000 h in a sealed tube at 110°C.However, upgrading can be done in various ways, so it isnot a uniform group and may react differently to chemi-cal aging accelerators. To retard aging, one can ther-mally upgrade the paper by linking bulky substituentssuch as cyanoethyl ether groups to the HO-groups in thecellulose and hemicellulose; or add weak, organic basessuch as dicyandiamide, urea, or melamine (a cyclic tri-mer of urea) so as to neutralize acids produced by oxi-dation of the oil and paper. Beginning in the late 1960s,transformers in the U.S. were manufactured using ther-mally-upgraded paper, whether specified or not.

Cellulose degrades at any temperature. The rate of deg-radation is very slow at room temperature. At elevatedtemperatures, however, the rate of degradation increasesexponentially, effectively doubling for approximatelyevery 8°C increase in temperature. Management of insu-lation degradation is necessary to maintain a reasonablelife expectancy for the transformer.

The shortening of the cellulose chains results in a reduc-tion of the mechanical properties of paper and board,such as tensile, bursting, and folding strength. It is wellknown that the aging rate increases with increasing tem-perature; Montsinger states that the aging rate doubles(or life is halved) by every 6-8 oC temperature increase(Montsinger 1930).

The insulation aging rate has been studied extensively,and several mathematical models have been proposed.The most accepted of these models for insulation agingis that given in IEEE C57.91-1995 (IEEE 1995b), which

Figure 4.3-3 Graphic depiction of cellulose chain (light gray is carbon, dark gray is oxygen, white is hydrogen).

4-12


expresses insulation aging as an Arrhenius reaction rateequation. The equation is as shown in Equation 4.3-4.

(IEEE 1995b, Section 5.2, Equation 2) 4.3-4Where:FAA is the insulation aging rate.A is a constant equal to 15,000 for most insula-

tion types.θHS,R is the reference hot spot temperature for the

insulation.θHS is the hot spot temperature at which aging is

evaluated.

The IEEE insulation model requires two parameters,the constant A and the reference hot spot temperature.For all cases, it is safe to assume that A is 15,000. Thereference hot spot temperature varies depending uponwhether the insulation is thermally upgraded and whatstandard is applied. For 55°C insulation, the referencehot spot temperature is 95°C. For 65°C insulation, thereference hot spot temperature is 110°C.

Equation 4.3-4 can also be expressed in a form for perunit life:

4.3-5Where:B describes how sensitive the ageing is to tem-

perature (15,000 in C57.91).THot is the hotspot temperature of the trans-

former.At is a factor describing the influence of the

environment on the change in tensile strength(9.8 x 10-18 in C57.91).

The base of all this is a definition of a material testwhere the criterion is that paper aged under a certaincondition (e.g., THot = 110oC) should not lose morethan a certain percentage of its functional property (ten-sile strength) within the period. This is referred to as theexpected life of a transformer (e.g., 30 years) at nominalload under specified ambient conditions where thehotspot condition has to be mastered.

The dependence of aging on temperature is fairly wellknown; However, the big problem for a utility whenmanaging an aging transformer population is thatEquations 4.3-4 and 4.3-5 are based on experimentsunder optimum clean conditions for the paper, and thatquantitative information on the importance of the

transformer condition on aging is hard to find. It is allabout getting information about the At factor.

Chemical Description of AgingFor the purposes of insight, aging considerations can bebased not on changes of a functional property like ten-sile strength, but on changes of the chemical propertiesof the paper—the degree of polymerization. A disadvan-tage of doing this is that the link is lost to the directlyrelevant mechanical properties, though only applicableon laboratory aged samples. The main advantages arethat the approach uses a property that can be measuredfrom samples from service-aged transformers and that itis closer to considerations on the chemical kinetic pro-cesses taking place. If the aging analyses are based onDP changes, a correlation between the functional criti-cal tensile strength and the DP, as shown in Figure4.3-4, is needed.

One usually considers aging under normal conditions(nameplate conditions and specified overload) to be dueeither to hydrolysis or to oxidation, and that a third pro-cess (pyrolysis) may take place under failure conditions(thermal defects). The aging due to one kinetic mecha-nism follows Equation 4.3-6

4.3-6

where the DP is given before and after an aging period(t) at a temperature T. E is the so-called activationenergy, which describes the sensitivity to the tempera-ture, A depends on the chemical environment, and R isthe molar gas constant. Note that this is of the sameform as the Arrhenius reaction rate equation first pro-posed by Dakin in 1948 (Dakin 1948). Usually thepaper has a DP around 1000 in a transformer after

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+= 273273, HSRHS

AA

AA eFθθ

273−= HotT

B

t eALifeUnitPer

Figure 4.3-4 Correlation between tensile index and DP value for nonthermally upgraded kraft paper.

( 273)1 1E

R T

old new

Ae tDP DP

−⋅ +− = ⋅

4-13


vapor phase drying, and often a DP of 200 is used as anend-of-life criterion.

We can rearrange and change the equation to:

4.3-7

and further to

4.3-8

where η is the chain scissions and k the aging rate. Wecan see that the aging rate depends on temperature (T),the activation energy (E), and the environment (A). Fora first-order single process, this dependence can bedescribed by an Arrhenius plot, plotting the natural log-arithm of the rate versus the inverse absolute tempera-ture (T + 273) as shown in Figure 4.3-5.

The principle here is that, if the points end along astraight line, this aging can be described by one singleaging process.

Thus far, focus has been on the temperature depen-dence. Recent investigations indicate that the environ-ment may be of even greater importance. Let us firstconsider non-upgraded kraft paper.

Kraft PaperOne major mechanism of paper aging is oxidation. Theoxidizing agent in this environment is oxygen from airingress. The ultimate end products of oxidation are thesame as for combustion—i.e., water and carbon dioxide.The mechanism of low-temperature oxidation is quitedifferent from that of combustion, though. The oxygen

concentration is, of course, an important parameter todetermine the rate of oxidation. However, most experi-mental studies show that the aging rate is not sostrongly influenced by oxygen content. Typically, theoverall degradation rate no more than doubles in exper-iments with oxygen present, compared to when oxygenis totally excluded. We can, therefore, say that theimportance of oxygen is limited.

The other major mechanism of paper aging is hydroly-sis. The significance of water content is paramount: ahumidity of 3-4% may increase the degradation rate ofpaper by a factor of 10 or more, compared to dry paper.In addition, it is commonly acknowledged that a highacidity in the oil accelerates aging but in a nonspecificway. Lately, models have been developed outside thepower engineering community (Lundgaard et al. 2004).It is now understood that the hydrolysis is specific-acidcatalyzed and unimolecular. This means that it is cata-lyzed exclusively by hydrogen ions from dissociatedacids; undissociated carboxylic acids do not depolymer-ize cellulose. It is the hydrogen ion activity (or “pH”)that matters, not the total (undissociated) acid concen-tration. It also means that water does not participate inthe rate-controlling step. Water does, however, affect theacidity by causing carboxylic acids to dissociate, and inthis way it exerts a profound influence upon the agingprocess. During this process, carboxylic acids (like for-mic, acetic, and laevulinic acids) are produced, whichmakes the process auto-acceleratory. These acids mainlyreside in the cellulose and may to a large degree beextracted from oil and paper using water extraction.This applies to kraft paper. The processes for thermally-upgraded papers are more complicated.

It is likely that the activation energy of oxidation is dif-ferent and lower than for hydrolysis, and that for pyroly-sis, it is even higher than for hydrolysis. This can beillustrated by the plot in Figure 4.3-6, where lines withdifferent slopes are plotted for the different mechanisms.

( 273)11

ER Tnew

new Old

DPAe t

DP DP

−⋅ +⎡ ⎤

− = ⋅⎢ ⎥⎣ ⎦

1

new

k tDP

η⋅ = ⋅

Figure 4.3-5 Arrhenius plot and significance of parameters for kraft paper at 0.5% (dry) and 3% (wet) moisture.

1/T

ln (

reac

tion

rat

e)

O2H2O

1/T

ln (

reac

tion

rat

e)

O2H2O

Figure 4.3-6 Total aging as a sum of several mechanisms.

4-14


Thermally Upgraded PaperUpgraded paper is paper that is chemically changed bydifferent chemical additives that reduce the aging ratecompared to untreated kraft paper. A paper is consid-ered “thermally upgraded” if it meets the life criteria asdefined in ANSI/IEEE C57.100—50% retention in ten-sile strength after 65,000 h in a sealed tube at 110°C.However, upgrading can be done in various ways, so it isnot a uniform group and may react differently to chemi-cal aging accelerators. To retard aging, the paper can bethermally upgraded by linking bulky substituents suchas cyanoethyl ether groups to the HO-groups in the cel-lulose and hemicellulose, or weak, organic bases such asdicyandiamide, urea or melamine (a cyclic trimer ofurea) can be added so as to neutralize acids produced byoxidation of the oil and paper.

In one study it was found that the aging rate for oneupgraded paper type (Insuldur from Avery Dennison)showed both lower reaction rates at a specific tempera-ture, and that the acceleration due to presence of waterwas lower, as shown in Figure 4.3-7 (IEEE 1995c). Inanother study on an upgraded paper (Rotherm) fromTullis Russel, a similarly reduced sensitivity to water wasobserved (Schroff 1985).

The different sensitivity to water indicates that the acidcatalyzed hydrolysis is suppressed. In (Lundgaard et al.2004), the experimental results indicated that aging foroxygen-rich oil could increase by a factor of about sevenin the temperature range below 90oC, while water (3%)increased it around 3 times as shown in Figure 4.3-7.

Plastic Deformation and Winding SlacknessThe transformer winding is clamped with a pressurestrong enough to give friction forces between windingsthat may withstand the forces from a short-circuit cur-rent. The cellulose can undergo plastic deformation;

water will in this context act as a plasticizer. Changes inpressure may result from the following reactions:

• Increased moisture will cause swelling and increasethe pressure.

• Drying may cause shrinking of the insulation andreduced pressure.

• Thermal cycling will cause expansion and retractionof the materials, cyclic pressure variation, and loss ofpressure.

Diagnostics of the CelluloseAccurately diagnosing the condition of the cellulose,and therefore the remaining useful life of the trans-former, is a most difficult, if not impossible, task. Theonly way of accurately determining the condition of thecellulose insulation system is to take samples from vari-ous places throughout the transformer and measure theDP. This is impractical for several reasons. First andforemost, this involves disturbing the solid insulation inareas of high electrical stress. Additionally, many areasare simply inaccessible.

A limited sampling can be done by taking paper fromrelatively accessible areas. This, however, involves drain-ing all of the oil, physically breaching and entering thetank, collecting the sample while avoiding contamina-tion, and refilling the unit under vacuum. Breaching thetank introduces the possibility of contamination by par-ticulates or moisture and carries a finite risk.

Without entering the tank, the only remaining alterna-tive for measurement is to draw an oil sample and mea-sure the level of a chemical marker indicative ofcellulose aging. Fortunately, several furanic compounds,measurable by High-Performance Liquid Chromatogra-phy, are produced during the aging process. By measur-ing the levels of these compounds in the oil, the averagecondition of the entire insulation system can be esti-mated. This method, however, carries with it severaldrawbacks. First, the measurement represents only theaverage of all of the cellulose in the unit. In reality, onlya small percentage of the cellulose is subject to hightemperatures during overload. It is this cellulose, and inparticular the cellulose that is exposed to high tempera-tures and high electrical stress, that is important. Inaddition, furan analysis is incapable of discerning local-ized defects that result in high heating in a small area.Furan production is also a function of the paper-to-oilratio of a transformer, which varies widely dependingupon winding construction, BIL, and rating. Finally, ifthe oil is replaced or reclaimed, the aging informationderived from furan analysis up to that point is lost.

A final method of estimating the condition of the cellu-lose is to simply examine the typical loading and ambient

Figure 4.3-7 Arrhenius plots of aging rate for standard Kraft paper and thermally-upgraded insuldur paper (IEEE 1995c).

4-15


air temperatures over the transformer’s service life andapproximate the cumulative insulation aging by the stan-dard thermal models and insulation aging models. Whilenot precise, this method is remarkably simple and gives ageneral feel for the serviceability of a particular unit.

Concluding Remarks on Thermal Aging of the InsulationHistorically, too little attention has been given to thechanges in thermal performance of a transformer due tochanges in the condition of the insulation system.Depending on the materials used, the acceleration ofaging due to chemical contamination may exceed thatfrom increased temperature. Together with a poor con-dition of the transformer, a long-term temperatureincrease may result in a very short life. The life may beestimated using the formulae below.

The life expectancy of the solid insulation is difficult todefine precisely. The “end-of-life” of any device or systemis when the system can no longer perform its intendedfunction. In the case of electrical insulation, this is whenthe insulation no longer provides sufficient dielectricstrength to prevent dielectric breakdown. In the case ofcellulose insulation, such as that used in power trans-former, the electrical properties of the paper do not sig-nificantly degrade until well after the mechanicalproperties become unworkable. The paper will becameextremely brittle and crack or tear at the slightestmechanical disturbance. If this were to occur in an oper-ating transformer, the loss of solid insulation by displace-ment could detrimentally weaken the insulationstructure. Therefore, the mechanical strength of the paperis the defining evaluation criterion with respect to aging.

Several different mechanical strength properties havebeen used by various investigators to quantity the deg-radation of cellulose. The burst strength, fold strength,elongation to break, abrasion resistance, and tensilestrength have all been used as indicators of mechanicalstrength. In addition, degree of polymerization (a mea-sure of average polymer chain length of the cellulosemolecule) has been used. Degree of polymerization, DP,varies nearly proportionally to reduction and mechani-cal strength. Of these measures, tensile strength and DPare used most commonly to define end-of-life criteria.Table 4.3-1 lists several different end points for insula-tion thermal life based upon 50% tensile strength reten-tion, 20% tensile strength retention, and a degree ofpolymerization value of 200 (McNutt 1992). Also illus-trated in this table are the detrimental effects of mois-ture and oxygen.

Since there are many different valid end-of-life criteria,it is ultimately up to the user to select a criterion. Therecommendation of this guide is that the DP of 200 endpoint be used when evaluating life consumption. As analternative, the user could forgo the definition of aninsulation life end point and instead consider aging inrelative terms—i.e. per unit aging rate (FAA) or equiva-lent aging hours. However, the question still remains ofwhen to remove a unit from service.

The failure risk of transformers has often been repre-sented by the “bathtub” curve, so named for its shape(Figure 4.3-8). This curve represents the failure risk overtime for a particular transformer, with all else constant.External factors, such as loading, throughfault fre-

Table 4.3-1 Insulation Thermal Life Expectancies for Various Endpoint Criteria, Moisture Contents, and Oxygen Levels (McNutt 1992)

Basis Moisture in Paper (%) Oxygen Level Life (hrs)

50% Tensile

0.5% Low 65,020

1.0% Low 32,510

2.0% Low 16,255

0.5% High 26,000

1.0% High 13,000

2.0% High 6,500

20% Tensile

0.5% Low 152,000

1.0% Low 76,000

2.0% Low 38,000

0.5% High 60,800

1.0% High 30,400

2.0% High 15,200

200 D.P.

0.5% Low 158,000

1.0% Low 79,000

2.0% Low 39,500

0.5% High 63,200

1.0% High 31,600

2.0% High 15,800

4-16


quency, and maintenance (or lack thereof) all shift por-tions of the curve in some fashion.

If the failure rate with time is represented by a bathtubcurve, the time axis can be viewed as a “cumulative ther-mal aging” rather than actual age of the unit. As theinsulation system ages thermally, the system approachesthe “wear out” portion of the curve, where failure riskincreases, although failure is not necessarily imminent.The transition point from a relatively flat failure risk toan increasing failure risk is the thermal end-of-life, inrough terms. Of course, this is only approximate andvaries with several factors, including condition, design,vintage, etc.

One major point of confusion and misunderstandingwhen performing loading calculations and making load-ing decisions is the discussion of percent loss-of-life (inpercent total life expectancy) and of the end-of-life orlife remaining.

In rough terms, the “end of life” for an insulation sys-tem is the point at which the insulation no longer per-forms reasonably. For electrical insulation, this meansthe point at which the insulation system no longer main-tains a majority of its original dielectric strength. Asinsulation ages, the dielectric strength of the paper doesnot decrease significantly until well after the paper hasbecome brittle. Given the need for transformer insula-tion to withstand mechanical forces, especially duringthroughfault, the point at which the paper loses enoughstrength to withstand the mechanical forces is the prac-tical end of life for the insulation system.

Given this, a precise definition becomes difficult becausethis is dependent upon the application of the material,both electrically and mechanically. Therefore, generalmeasures of mechanical strength have been historically

used. Some criteria include 50% tensile strength reten-tion, 20% tensile strength retention, and more recently,a degree of polymerization of 200. In addition, func-tional life testing has been performed on distributiontransformers subjected to impulse voltages and short-circuits. Each of these criteria gives a different life endpoint, ranging from 65,000 hrs to 180,000 hrs. Thesevalues are largely artificial. A transformer that is notsubject to high throughfault duty may operate reliablywell after the 180,000-hr end point.

Therefore, if %loss of life (LOL) is discussed, the valuefor a given temperature can vary by a factor of three.

It is well known that insulation aging rates increase withthe presence of increased moisture and oxygen. Theoriginal equations in the IEEE Loading Guide (IEEE1995b) are based mostly upon sealed tube aging testswith moisture contents less than 0.5% and presumablylower oxygen contents. This does not reflect the realityof operating transformers and misleads the user on theactual aging rate. The importance of keeping transform-ers dry and oxygen free are not reflected in the guide,and are best addressed by including quantitative esti-mates of the effects of moisture and oxygen in the agingequation. It is proposed that this be done by applyingmultiplying factors to the “Age Acceleration Factor”calculated as shown in Equation 4.3-9.

4.3-9Where:FAA is the insulation aging rate.A is a constant equal to 15,000 for most insula-

tion types.θHS,R is the reference hot spot temperature for the

insulation.θHS is the hot spot temperature at which aging is

evaluated.kH2O and kO2

are determined from Tables 4.3-2 and 4.3-3,respectively

Figure 4.3-8 Example bathtub curve demonstrating thermal end-of-life.

ekk = F 273 +

B -

273 +

B

OOHAA HSo ΘΘ22

Table 4.3-2 Aging Rate Correction Factor for Moisture in Paper

Moisture Content in Paper (roughly) kH2O

Dry (< 0.5%) 1

Moist (0.5-2.5%) 2

Wet (> 2.5%) 4+

Table 4.3-3 Aging Rate Correction Factor for Oxygen Content of Oil

Oxygen Content kO2

Low 1

High 3-5

4-17


The factors developed in the tables were derived fromdata published by Emsley, Lundgaard and McNutt(Emsley and Stevens 1994; Lundgaard et al. 2004; andMcNutt 1992). They are approximations. However,insulation aging calculations, as a whole, are grossapproximations.

By applying these factors directly in the equation, usersare well aware of the importance of moisture and oxy-gen, and are given a method for evaluating the impact ofmoisture and oxygen, as well as estimated life consump-tion for transformers with moisture contents in papergreater than 0.5% and with increased oxygen levels.

4.3-10Where:t is the number of hours at the hot spot tempera-

ture.

Expected life is a value selected from Table 4.3-1.

4.3.3 Additional Risks

Ancillary ComponentsFollowing insulation loss of life and bubble formation,the most significant risk associated with transformeroverload is damage to the ancillary components, such asbushings, on-load tap changers (LTCs), off-load tapchangers (DETCs), and current transformers (CTs).This risk is often overlooked as a rating consideration.Generally, these components are oversized due to theirrelative cost when compared to the transformer itself.However, it is possible that some limitation on the over-load capability of a particular transformer may be dueto an ancillary component.

BushingsOil-impregnated, paper-insulated, capacitance-gradedbushings are designed with 105°C bushing hot spot limitat rated load and 95°C top oil temperature average over24 hrs. Overload, based upon the rated bushing current,is possible. Overload risks of bushings include:

• Pressure build-up due to oil expansion.

• Deterioration of gaskets and seals.

• Thermal deterioration of paper insulation.

• Increase in dielectric loss, possibly resulting in ther-mal runaway.

• Gas evolution at extreme hot spots.

Overload limits, as specified in C57.19.100-1995:

• 40°C ambient temperature

• 110°C transformer top oil temperature

• 2x rated bushing current

• 150°C bushing hot spot temperature

The bushing hot spot is usually located adjacent to thecentral conductor in the area of the mounting flange. Itis here that the insulation is the thickest and the externalheating, via the bulk oil, is highest. The hot spot tem-perature of the bushing conductor may be calculated asshown in Equation 4.3-11 (IEEE 1995c).

4.3-11Where:ΔθHS is the bushing hot spot temperature.K1 is a bushing-specific constant, typically rang-

ing from 15 to 32.K2 is a bushing-specific constant, typically rang-

ing from 0.6 to 0.8.n is a bushing-specific constants, typically rang-

ing from 1.6 to 2.0 with 1.8 typical.I is the bushing current in per unit of the rated

bushing current.ΔθO is the bushing immersion oil temperature

(transformer top oil).

The transient temperature rise may then be calculated asshown in Equation 4.3-12.

4.3-12Where:ΔθHS,2 is the bushing hot spot rise at time t1 + Δt.ΔθHS,1 is the bushing hot spot rise at time t1.ΔθHS,U is the steady-state temperature given in the

previous equation.τB is the bushing time constant.

The determination of the constants is the greatest obsta-cle to the use of these equations. Accurate determina-tion can only be made through tests on duplicatebushings. These tests are not performed routinely by thebushing manufacturer. This information may berequested from the manufacturer. If the data is notavailable, however, typical default values can be usedwithout a significant sacrifice in accuracy.

The paper used in paper-insulated bushings is not ther-mally-upgraded, unless otherwise specified. As such, thestandard loss-of-life model given in C57.91-1995 for65°C rise insulation systems should not be used to cal-

LifeExpected

tFLOL AA ⋅=%

On

HS KIK θθ Δ+=Δ 21

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ+Δ=Δ

Δ−

B

t

HSUHSHSHS e τθθθθ 1)( 1,,1,2,

4-18


culate the loss-of-life for bushing insulation. Instead,Equation 4.3-13 should be used:

4.3-13Where:FAA is the aging acceleration factor.

Percent loss-of-life and cumulative aging can be calcu-lated as outlined in C57.91-1995.

The above method may be applied to resin-bonded orresin-impregnated bushings. The above method doesnot apply to draw-lead connected bushings. Draw-leadconnected bushings are limited by the temperature riseof the draw-lead. Therefore, the bushing temperature isdetermined by the size and construction of the draw-lead. Accurate determination of draw-lead current car-rying capability would require detailed information onthe lead and its application. However, in a properlydesigned application, the draw-lead does not limit thethermal rating of the transformer.

On-Load Tap Changers (LTCs)The critical component of an on-load tap changer, froma thermal standpoint, is the contacts. LTCs are properlydesigned with a contact rise over oil of less than 20°C at1.2 times rated load (rated load here is the rated load ofthe LTC, not the transformer itself). In addition, LTCsare designed to break twice rated current at least 40times without detrimental degradation of the contacts.In some instances of high overloads, it may also beadvisable to switch an LTC to manual control and mini-mize or eliminate operation. Overload risks of LTCsinclude:

• Increased contact wear and ablation with increasedload during break operations

• Increased contact temperature increases probabilityand rate of coking of contacts (>120°C)

• Higher overloads result in prolonged arcing duringbreak operation. Dragging the arc across the contactscould result in short-circuiting the regulating winding.

Overload limits, as specified in C57.131-1995 (IEEE1995a):

• 120°C contact temperature (higher is OK, but mayresult in greater maintenance).

• 2x LTC rated load current (limit breaking operationsat high load level to few times/year).

The temperature rise of the contacts is calculated asshown in Equation 4.3-14 (IEEE 1995c)

4.3-14Where:ΔθC is the LTC contact temperature rise over oil.ΔθC,R is the LTC contact temperature rise over oil at

rated load.I is the LTC current in per unit of the rated LTC

current.n is an exponent that varies from 1.6 to 1.85,

with 1.8 as the default.

4.3-15Where:θC is the total contact temperature.θA is the ambient air temperature.θTO is the transformer top oil temperature.K is a constant to account for the difference

between transformer top oil temperature andLTC compartment oil temperature. This is typi-cally around 0.8.

It is important to note that the main difficulty associ-ated with elevated temperatures in LTCs is the increasedtendency toward contact coking. Since coking increasesthe electrical resistance across the contact assembly,coking can result in even higher temperatures and possi-ble thermal runaway. If frequent high loading periodsare expected, the temperature differential between themain tank oil and the LTC compartment oil should bechecked, if possible. In addition, the LTC oil should beclean oil with high interfacial tension (IFT) and lowacidity.

Reduced Capacity TapsThe load dependent losses, and therefore the heating ofthe transformer windings, is a function of the windingcurrent. Often the transformer load is expressed interms of apparent power, or MVA, since this number isessentially the same for all windings (neglecting losses).However, in the case of rated MVA when taps arepresent, the rated current varies inversely proportionalto the voltage. The consequence for loading is that, forlower voltage taps, the rating in MVA for a given sizeconductor decreases.

Often, to maintain the same MVA load capability for alltaps, the conductors are sized according to the currentat the lowest voltage time. However, occasionally, toreduce cost, the transformer may be specified withreduced capacity taps. In this case, the conductors aresized for the rated current at the neutral position. Forhigher-voltage taps, the transformer is capable of carry-ing full rated MVA. However, for lower voltage taps, the

273

000,15

368

000,15

+−

= HSeFAAθ

nRCC I,θθ Δ=Δ

CTOAC K θθθθ Δ++=

4-19


transformer is capable of carrying only a reduced MVA,corresponding to the rated current at the neutral tap.Transformers with reduced capacity taps can easily beidentified by referring to the table of tap positions, volt-ages, and rated currents on the nameplate. Transformerswith reduced capacity taps have the same rated currentfor all taps at voltages below neutral. An example of thisis shown in Table 4.3-4.

It is important to examine the nameplate when deter-mining the load capability of a particular transformer todetermine if the unit was designed with reduced capacitytaps. If it was designed with reduced capacity taps, andthe unit is operated at taps below neutral, the load capa-bility in MVA will be lower than the nameplate MVA.

Table 4.3-4 Nameplate Showing Tap Positions, Voltages, and Currents

CONNECTIONS

WINDING VOLTAGEMAXIMUM FOA

AMPERES

CRT LOAD TAP CHANGER

PCS

CONNECTS IN EACH PHASE

P1 TO P3 TO R TO

“H”VOLTAGE WYE

120175 432 16L 11 11 3

119495 435 15L 11 10 3

118610 437 14L 10 10 3

118130 440 13L 10 9 3

117445 442 12L 9 9 3

116765 445 11L 9 8 3

116080 448 10L 8 8 3

115395 450 9L 8 7 3

114715 453 8L 7 7 3

114030 456 7L 7 6 3

113350 458 6L 6 6 3

112665 461 5L 6 5 3

111980 464 4L 5 5 3

111300 467 3L 5 4 3

110615 470 2L 4 4 3

109935 473 1L 4 3 3

109250 476 NEUT 11 11 11

108565 476 1R 11 10 11

107885 476 2R 10 10 11

107200 476 3R 10 9 11

106520 476 4R 9 9 11

105835 476 5R 9 8 11

105150 476 6R 8 8 11

104470 476 7R 8 7 11

103785 476 8R 7 7 11

103105 476 9R 7 6 11

102420 476 10R 6 6 11

101735 476 11R 6 5 11

101055 476 12R 5 5 11

100370 476 13R 5 4 11

99690 476 14R 4 4 11

99005 476 15R 4 3 11

98325 476 16R 3 3 11

WINDING VOLTAGE AMPERES

NO LOAD TAP CHANGER

POSCONNECTS IN EACH PHASE

A B

“X”VOLTAGE WYE

59000 753 2 1 TO 19 13 TO 15

06000 787 1 1 TO 18 13 TO 14

4-20


Bushing or Internal CTsDetailed evaluation of bushing CTs is difficult, if notimpossible. The location of the CT can be in the bushingadapter or “turret,” or mounted on the active assemblyin the tank. Bushing CTs are usually limited by trans-former top oil temperature. Maintaining a top oil tem-perature of less than 110°C should avoid excessivetemperatures. Aging rates should be lower than that ofthe winding insulation over the average of the loadingconditions.

De-Energized Tap Changers (DETCs)De-energized tap changers are similar, in a thermalsense, to on-load tap changers, albeit much simpler. Thesame general considerations and risks apply to DETCsas to LTCs. Coking may become a greater problem forDETCs, as they are seldom operated. It may be advis-able to periodically operate the DETC over the range oftaps to “wipe” the contacts clean of any deposits.

Lead HeatingInternal connecting leads may be a concern. The samehot spot limits, and associated risks, apply for leads asfor windings. In general, it is impossible to evaluate leadheating without detailed design data. In a properlydesigned transformer, the connecting leads should notlimit the overload capability. However, lead hot spotshave been a limitation in the load carrying capability ofmany transformers because of lack of attention in thedesign stage or manufacturing practices that permittedor even encouraged liberal application of insulating tapeat lead connection points.

Evaluation of lead heating problems outside of the fac-tory is rather difficult. Even with dimensions of theleads and construction details, it is difficult to assess theoil flow conditions in the vicinity of the lead. The bestmethod for assessing lead heating problems is by exam-ining the DGA records for the unit for any hint of heat-ing gases involving cellulose decomposition, particularlyCO and CO2, and eventually CH4 and C2H6. If thesegases are present in significant quantity or have a gener-ation rate that increases sharply with load, load shouldbe reduced immediately. At the earliest convenience, aninternal inspection should be performed to locate thesource of the gassing. In addition to DGA, partial dis-charge detection and perhaps Furan analysis may alsoyield useful information.

Stray Flux HeatingHeating of non-current carrying metal components bythe leakage flux of the windings and leads is termed“stray flux heating.” The leakage flux induces eddy cur-rent in any conducting material that it passes through.This includes the steel clamping structure, tie rods or tieplates, metal core bands, and the tank wall itself. Since

leakage flux varies proportionally with load current, thestray flux heating increases roughly with the square ofwinding current. For larger power transformers andGSUs in particular, the problem of stray flux heatingcan be substantial. Special design measures must betaken to reduce the induced currents.

The most common areas of stray flux heating problemsare tie plates, used to connect the upper and lower coreyoke clamping structure, and bushing penetrations. Aswith lead heating, evaluation of stray flux heatingpotential is difficult. The best method for assessing strayflux heating problems is by examining the DGA recordsfor the unit for any hint of hot metal gases, specificallymethane and ethane. Should either of these gases exceed120 ppm or 65 ppm, respectively, high loading should bediscontinued and the source of the gases investigated. Inaddition, sudden increases in these gas levels concurrentwith increased loading should be considered additionalcause for alarm.

In addition to DGA, stray flux heating in the tank wallcan be evaluated by examining the transformer with aninfrared camera. Particular attention should be paid inthe area of bushing penetrations and bushing adapters.A visual examination for discolored paint could alsoreveal stray flux heating.

4.4 THERMAL MODELING

Given the extreme complexities of heat transfer within atransformer, as well as the lack of information typicallyavailable, drastic simplifications must be made. It isimportant to recognize the simplifications and to knowthe areas in which these simplifying assumptions are notsufficiently accurate. Therefore, this section begins witha brief and somewhat academic overview of the variousheat transfer mechanisms involved. Following this, thesection describes available thermal models.

4.4.1 Mechanisms of Heat Transfer

In a power transformer, two heat transfer mechanismsare predominant: radiation and convection. Conductionplays a smaller role and will not be described at lengthhere. It should also be noted that even the most moderntreatments of the subject are largely empirical. This ini-tial discussion parallels that of Montsinger in (Mon-tsinger 1951), with additional emphasis on variablesthat may not be constant.

RadiationAll bodies at a temperature above their surroundingsradiate heat energy to the surroundings. The mathemati-cal relationship between heat lost due to radiation and

4-21


the temperature rise are fairly well known, as shown inEquation 4.4-1 (Cengel 1997)

4.4-1

This relationship can be simplified to a simple powerrelationship of the form shown in Equation 4.4-2.

4.4-2

This relationship, for a given exponent x, is generallyvalid over a limited temperature range (Figure 4.4-1).

The curve fits in Figure 4.4-1 are generally valid from a0°C rise to about a 70°C rise. The exponents vary from1.133 for a 0°C ambient to 1.117 for a 40°C ambient.Note that the emissivity will change the multiplicativeconstant but not the exponent.

This relationship could also be expressed inversely as:

4.4-3

where m = 1/x. For the ranges of x derived above, m var-ies from 0.883 for a 0°C ambient to 0.895 for a 40°Cambient.

The absorption rate in the infrared region for transpar-ent liquids such as transformer oils is relatively high.Therefore, the radiant energy from transformers wind-ings is absorbed by even a thin layer of oil, and is there-fore negligible. Air, on the other hand, has a negligibleabsorption rate, and radiant energy loss must be consid-ered when determining the heat loss from the tank, andtherefore the oil.

Forced ConvectionWhen heat is transferred from a solid to a moving fluidmedium, the adjacent fluid is heated by conduction.Since the fluid medium is moving, the heated fluid isquickly replaced by cooler fluid. This results in anincreased rate of heat transfer than would occur by con-duction alone. The heat loss due to convection can beexpressed by Newton’s Law of Cooling, as shown inEquation 4.4-4 (Cengel 1997).

4.4-4Where:Q is the rate of heat loss.h is the heat transfer coefficient.Tc is the temperature at the surface of the object

(solid).Ta is the temperature of the surrounding fluid.

For cross-flow over a cylinder or similar-shaped object(Cengel 1997):

4.4-5Where:C is a constant.Re is the Reynold’s Number.Pr is the Prandtl Number.k is the thermal conductivity of the fluid.D is the characteristic length of the immersed

object (diameter of cylinder).ρ is the density of the fluid.V is the velocity of the fluid.μ is the viscosity of the fluid (varies with tem-

perature).Cp is the specific heat of the fluid.m, n are constants.

From this, it can be seen that h is a function of severalparameters, including geometry, fluid velocity, and fluidviscosity. The exponent n is typically 1/3. The exponentm, determined empirically, ranges from about 0.3 to 0.8,depending upon the geometry. Note that if the expo-nents are equal, the viscosity cancels out and is nolonger a factor. Summarizing, the heat loss can beexpressed by:

4.4-6

or, solving for the temperature rise:

4.4-7

Natural ConvectionNatural convection is slightly more complex than forcedconvection. The heat transfer is still a function of the

)( 44abrad TTAQ −= εσ

xrad KQ θΔ=

Figure 4.4-1 Radiative heat transfer at various ambient temperatures.

mradCQ=Δθ

)( ac TThAQ −=

np

m

nm

k

CVDC

D

kCh ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⋅⋅=

μ

μρ

PrRe

θΔ= KQ

KQ=Δθ

4-22


velocity of the fluid, as described above. However, nowthe velocity of the fluid is the result a varying fluid den-sity with temperature. This is known as thermosiphonflow. The basic relationship is the same as for forcedconvection.

4.4-8

However, h is now a function of the temperature rise aswell. For natural convection along a vertical plate (alsoapplicable to a vertical cylinder), h is given by:

4.4-9

m varies from 1/3 to 1/4. Note that h is also a function ofviscosity, μ, to the -m power.

Combining the temperature component of h with theequation for convection heat transfer:

4.4-10

Taking the inverse to solve for the temperature rise:

4.4-11

Since m varies from 1/3 to 1/4, the exponent in Equation4.4-11 varies from 0.75 to 0.80.

Combined Heat TransferSummarizing the above discussion, the temperature rise(or, conversely, the heat loss) for a particular mechanismof heat transfer can be expressed in the following form:

4.4-12or

4.4-13Where:Δθ is the temperature rise above the surrounding

medium.K is a constant.Q is the heat loss (or gain).x is an exponent that varies with mechanism as

shown in Table 4.4-1.

The constant K is generally constant over the range oftemperatures and materials considered in transformerthermal modeling. The only variable that changesappreciably with temperature is the viscosity of oil. For

forced convection, the viscosity is generally not a factor.For natural convection, the temperature rise is a func-tion of viscosity as follows:

4.4-14

Transient FormulationFor any temperature rise, the temperature at any time, t,can be determined by equating the heat input to the sumof the change in heat storage and the heat loss:

Heat generated = Change in heat storage + Heat loss.

4.4-15

Traditionally, transient temperatures have been calcu-lated by approximating an instant of time as a step-change in load and calculating the temperature at theend of the time step as follows:

4.4-16Where:Δθ is the calculated temperature at time t + Δt.Δθi is the initial temperature at time t.Δθu is the ultimate steady-state temperature.Δt is the time step.e is the time constant.

This closed form solution to the transient differentialequation has several drawbacks. First, it is difficult tocorrect for the change in losses with temperature. Thelosses at the ultimate temperature rise are a function ofthe ultimate temperature. The ultimate temperature is,of course, a function of these losses, requiring an itera-tive calculation at each time step to find the ultimatetemperature rise. In addition, the closed form solutionabove is only truly correct for heat transfer functionwith an exponent of 1.0 (i.e., forced convection).

A more robust approach is to solve the differentialequation using a finite difference approach, as taken byPierce (Pierce 1994) and Lesieutre (Lesieutre et al. 1997)

)( ac TThAQ −=

( ) ( ) m

pacm

k

CLTTg

L

kCGr

L

kCh ⎟

⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅⋅=⋅⋅⋅=

μ

μβρ

2

32

Pr

1+Δ= mKQ θ

)1(1 +=Δ mnatKQθ

xKQ=Δθ

1xQ K θ= Δ

Table 4.4-1 Exponents for Radiation, and Forced and Natural Convection

Mechanism Exponent

Radiation 0.883-0.895

Forced Convection 1.0

Natural Convection 0.75-0.8

mmnatKQ −+ ⋅=Δ μθ )1(1

xpgen K

dt

dmCQ θ

θΔ+=

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−Δ−Δ+Δ=Δ

Δ−

τθθθθt

iui e1

4-23


Referring to the differential equation above, the differ-ence equation would take the form:

4.4-17

4.4.2 Top Oil Model (IEEE C57.91-1995, Clause 7)

The following is an outline of the temperature calcula-tion methods presented in Clause 7 of IEEE C57.91-1995 (IEEE 1995b) (Figure 4.4-2).

The thermal mechanisms of a transformer are extremelycomplex and difficult to model. To reduce complexity,the transformer is analyzed as a lumped system, andseveral assumptions are made. The transformer is essen-tially reduced to two systems, the bulk oil and the wind-ing, with an additional “hot spot” temperature locatedat the top of the winding.

The oil temperature is presumed to be lowest at the bot-tom of the winding. As the oil rises upward along thewinding, the oil adjacent to the winding is heated at aconstant rate. Therefore, the oil temperature is assumedto increase linearly from the bottom of the winding tothe top of the winding, with the highest oil temperaturelocated at the top of the winding.

At rated load, the winding temperature distribution isassumed to be higher than the oil temperature distribu-tion by a constant value, Δw, and thus parallel to the oiltemperature distribution. Due to stray flux concentra-tion near the top of the winding, a further increase in

temperature, the hot spot temperature, is located at thetop of the winding. This hot spot temperature representsthe hottest temperature endured by the insulation andtherefore the highest aging rate (1995b).

The IEEE top oil method relates the steady-state oiltemperature rises to the total losses by a power function.The steady-state winding rises are also related to thewinding current by a power function. In addition, cer-tain corrections are made to account for additional con-siderations such as increased mixing due to forced-oilcooling systems and change in winding resistance withtemperature.

The following is an outline of the temperature calcula-tion method presented in IEEE C57.91-1995, Clause 7.

Symbols:

C is the thermal capacity (Watt-hours/deg C).

WCC is the weight of the core and coils (kg).

WTank is the weight of the tank and fittings in contactwith the oil (kg).

VFluid is the volume of oil (L).

τO is the oil thermal time constant (min).

τw is the winding time constant (min).

t is the time (min.).

Δt is the calculation time step (min).

ΔθTO is the top oil rise over ambient temperature (deg C).

xpgen K

tmCQ θ

θθΔ+

Δ

−= 12

2,

Figure 4.4-2 Graph of temperature rises vs. height for IEEE Clause 7 Model.

4-24


ΔθHS is the hot spot rise over the top oil temperature(deg C).

PT is the total loss (W).

K is the load (per unit of the nameplate rating).

R is the ratio of load loss to no-load loss at the nameplate rating.

m is the winding temperature rise exponent.

n is the oil temperature rise exponent.

θHS is the hot spot temperature (deg C).

θA is the ambient temperature (deg C).

Subscripts:

R indicates a rated quantity.

i indicates an initial quantity.

U indicates an ultimate or steady-state quantity.

Oil Thermal Time Constant:

In order to calculate the transient response of the bulkoil, it is necessary to calculate an oil thermal time con-stant. The thermal time constant of the bulk oil at ratedtemperature equals:

τO,R = C * ΔθTO,R / PT,R 4.4-18Where:τO,R is the oil thermal time constant at rated load

(min).C is the combined thermal capacity of the

transformer (W-min/lbs-C).ΔθTO,R is the measured oil temperature rise over

ambient at rated load (C).PT,R is the total loss at rated load (W).

The thermal capacity, C, is the combined thermalcapacity of all transformer components in contact withthe bulk oil. This includes the core, windings, tank andfittings, and the oil itself. The specific heat for each com-ponent material is shown in Table 4.4-2.

A combined thermal capacity can be calculated by com-bining the specific heats of the various component mate-rials with the component weights. However, thecomponents are not at a uniform temperature. The oiltemperature varies from the bottom of the tank to thetop. For OA (ONAN) and FA (ONAF), the assumptionhas been made that the mean oil temperature is 76% ofthe maximum top oil temperature. In addition, 2/3 ofthe tank weight is used.

For OA and FA (ONAN and OFAF), the thermalcapacity, C, equals:

C = 0.06 * WCC + 0.04 * WTank + 1.33 * VFluid 4.4-19

For DFOA and NDFOA (ODAF and OFAF), the ther-mal capacity, C, equals:

C = 0.06 * WCC + 0.06 * WTank + 1.93 * VFluid 4.4-20

At top oil temperatures other than rated, the time con-stant must be corrected as follows:

4.4-21

Initial Temperatures:

The following equations are used to calculate the initialtemperatures based upon the assumption that the loadprior to the calculation period was constant longenough for the temperatures to reach their steady-statelimits. This assumption is reasonable if the load is fairlyconstant for a period of time prior to the overload equalto two to three times the oil thermal time constant.

4.4-22

Transient Temperatures:

The following equations are used to calculate the tran-sient temperature rises based upon the oil time constantcalculated above, the user-determined winding time con-stant, load, losses, and initial and ultimate temperaturerises. For a graphical representation of the various tem-perature rises, see Figure 4.4-2.

Table 4.4-2 Specific Heat for Copper, Steel, and Oil

Material Specific Heat (W-min/lbs-C)

Copper 0.05

Steel 0.06

Oil 14.6

n

RTO

iTOn

RTO

UTO

RTO

iTO

RTO

UTO

ROO 1

,

,

1

,

,

,

,

,

,

,

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ−⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ−⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ

=

θ

θ

θ

θ

θ

θ

θ

θ

ττ

( )( )

miRHSiHS

n

iRTOiTO

K

R

RK

2,,

2

,, 1

1

⋅Δ=Δ

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

θθ

θθ

4-25


For all cooling modes:

The top oil rise at time t2 = t1 + Δt is given by the follow-ing:

4.4-23

4.4-24

The hot-spot rise over top oil at time t2 = t1 + Δt is givenby the following:

4.4-25

4.4-26

The hot-spot temperature at time t2 = t1 + Δt is given by:

4.4-27

The above calculation is repeated for each time step ofthe overload period, with the initial temperatures risesequal to the temperature rises from the previous timestep. In addition, loss-of-life calculations are performedat each time step (IEEE 1995b).

4.4.3 Bottom Oil Model (IEEE C57.91-1995, Annex G)

This model was originally developed by Linden Piercewith GE in the early 1990s based upon detailed temper-ature measurements on a model coil (Pierce 1992, 1994).The model was included in the 1995 revision of IEEEC57.91 as Annex G (IEEE 1995b).

In the top oil model, the hot spot temperature consistedof three components: ambient temperature, top oil riseover ambient, and hot spot rise over top oil (Figure4.4-3). In the bottom oil model, which is the approachthat will be developed here, the hot spot temperatureconsists of four components: ambient temperature, bot-tom oil rise over ambient, top-of-duct oil to bottom oilgradient, and hot spot rise over top of duct oil. Thesecomponents are shown schematically below. In additionto these components, the average winding rise over aver-age duct oil needs to be developed, as the winding lossesare a function of this temperature and not the hot spottemperature.

4.4-28

Average Winding Rise over Average Duct OilIt will be assumed that the temperatures of the windingand the duct oil vary linearly from bottom to top, andboth are parallel. This results in a winding temperaturerise over adjacent duct oil that does not vary over theheight of the winding, and a constant heat flux from thewinding to the duct oil. In line with the finite differencetransient formulation described above, a heat balancewill be developed for the winding-duct oil system.

The heat generated by the winding at time t2 = t1 + Δt isgiven by:

4.4-29Where:Qgen,W is the average heat generated by the

windings.L is the winding current, in per unit rated.PI2R is the Ohmic losses in the windings due to

the winding current at rated current.PE is the eddy losses in the windings at rated

current.

4.4-30Where:θW,1 is the average winding temperature calculated

at the previous time step, t1.

θW,R is the average winding temperature at ratedload.

θK is 234.5°C for copper windings and 225°C foraluminum windings.

The heat lost by the windings to the duct oil is depen-dent upon the mechanism of heat transfer. For ONAN,ONAF, and OFAF, the predominant mode of heat

( )( )

n

URTOUTO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

1

12

,, θθ

( ) 1,1,,2, 1 TO

t

TOUTOTOOe θθθθ τ Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ

Δ−

mURHSUHS K 2

,, ⋅Δ=Δ θθ

( ) 1,1,,2, 1 HS

t

HSUHSHSWe θθθθ τ Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ

Δ−

2,2,2,2, HSTOAHS θθθθ Δ+Δ+=

DOHSBODOBOAHS // θθθθθ Δ+Δ+Δ+= Figure 4.4-3 Components of bottom oil model.

θA θBO

θDO

θHS

( )WEWRIWgen KPKPLQ +⋅= 22

,

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

+=

KRW

KWWK

θθ

θθ

,

1,

4-26


transfer is natural convection. As outlined above, theheat loss for natural convection can be expressed by:

4.4-31Where:Qloss,Wis the average heat lost by the windings to the

average duct oil.θW,1 is the average winding temperature at the pre-

vious time step.θDO,1 is the average duct oil temperature at the pre-

vious time step.θW,R is the average winding temperature at rated

current.θDO,R is the average duct oil temperature at rated

current.μW,R is the oil viscosity at a temperature equal to

the average of the average winding tempera-ture and average duct oil temperature at ratedload.

μW,1 is the oil viscosity at a temperature equal tothe average of the average winding tempera-ture and average duct oil temperature at theprevious time step.

m is a constant, usually between 1/3 and 1/4.

For ODAF transformers (directed forced oil), the pre-dominant mode of heat transfer is forced convection.The heat loss for OFAF can then be expressed by:

4.4-32

Note that it is assumed that the effect of the change inoil viscosity with temperature is negligible for this case.

Completing the heat balance, the heat absorbed by thewindings is given by:

4.4-33Where:Qabs,W is the heat absorbed by the winding during

incremental time step, Δt.mW is the mass of the windings.CP,W is the effective specific heat of the windings.θW,1 is the average winding temperature at time

t1.

θW,2 is the average winding temperature at timet2 = t1 + Δt.

Δt is the incremental time step.

The term mWCP,W is usually not known directly. Instead,this term can be calculated from a winding thermal time

constant calculated from the winding cooldown curvestaken during the factory heat run. From the definitionof a thermal time constant:

4.4-34

Summing the three terms of the heat balance and solv-ing for θW,2:

4.4-35

Duct Oil Gradient over Bottom OilThe oil entering the winding ducts is at a temperatureequal to the bottom oil temperature. The oil is thenheated as it rises up the winding duct, either by forcedoil flow or natural thermosiphon flow. The temperatureat the duct exit, for a constant heat flux along the duct,is dependent upon the mass flow rate, as follows:

4.4-36Where:Te is the temperature of the fluid exiting the duct.Ti is the temperature of the fluid entering the

duct.qs is the constant heat flux along the duct.As is the surface area of the duct.ρ is the density of the fluid.V is the fluid velocity (average).Ac is the cross-sectional area of the duct.Cp is the specific heat of the fluid.

For ODAF, the mass flow rate through the duct remainsessentially constant for varying load levels. For ONAN,ONAF, and OFAF, the oil flow through the duct is bynatural thermosiphon flow. The flow rate through theduct in these cases is a complex function of the tempera-ture rise in the duct, the temperature drop through theradiators, and the relative height of the windings and theradiators. The temperature rise in the duct, in turn, is afunction of the mass flow rate through the duct (Figure4.4-4).

Lacking sufficient data, the following simple approachwill be taken, relating the temperature rise through thevertical ducts (top-of-duct oil – bottom oil) to the lossby an exponent, y, as follows:

4.4-37Where:ΔθDO/BO is the duct oil rise over bottom oil.

( )ERI

m

W

RW

m

RDORW

DOWWloss PPQ +⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−=

+

21,

,

1

,,

1,1,, μ

μ

θθ

θθ

( )ERIRDORW

DOWWloss PPQ +⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

−= 2

,,

1,1,, θθ

θθ

( )t

CmQ WWWPWWabs Δ

−= 1,2,

,,

θθ

( )( )RDORW

ERIWWPW

PPCm

,,

2, θθ

τ−

+=

( )1,

,

,,2, W

WPW

WlossWgenW Cm

tQQθθ +

Δ−=

Pc

ssie CVA

AqTT

ρ+=

yRBOTDOHSBODO LH 2

,/2,/ *θθ Δ⋅=Δ

4-27


HHS is the height of the winding hot spot in perunit of the winding height (1.0 = top).

ΔθTDO/BO,R is the top-of-duct oil rise over bottom oilat rated load (see discussion below).

L is the per unit load.y is an exponent.

In almost all cases, it can be assumed that the hot spot isat the top of the winding, and hence adjacent to the topduct oil temperature, making HHS equal to 1.0. The datafrom tests done on model coils in Pierce (1994) suggeststhat, for most cases, the hot spot is within the top 10%of the winding. When the increased eddy loss at the topof the winding is factored in, the hot spot should beeven closer to the top, most often within a few turns ordisc sections. However, HHS has been included to allowthe engineer to assume a hot spot position below the topof the winding.

The exponent, y, is as yet undetermined. Lacking mea-sured data, the values given by Pierce (1994) can beused. For ONAN, ONAF, and OFAF, y is given as 0.5.For ODAF, y is given as 1.0. Since the mass flow ratedoes not change for ODAF over varying loads and theheat flux is proportional to the losses, the exponent of1.0 for ODAF should be correct. For the other coolingmodes, however, the mass flow rate is a function of boththe oil temperatures within the duct and the oil temper-atures in the bulk oil and radiators. Therefore, a morecomplex relationship is needed.

The temperature of the oil exiting the ducts, expressedas the rise over bottom oil ΔθDO/BO, at rated load is diffi-cult to determine. It cannot be measured easily. Evenwhen measurements are made, the values vary consider-ably for the various vertical ducts around the circumfer-ence of the winding (Pierce 1992). Pierce (1994) suggests

that, for ONAN, ONAF, and ODAF, this value is equalto the rated top oil rise. For OFAF, Pierce suggests usingthe average winding rise. These recommendationsappear to be based upon the tests of the model coil in(Pierce 1992).

Hot Spot Rise over Top Duct OilBy following a development similar to the average wind-ing rise over average duct oil, only considering an incre-mental portion of the winding at the hot spot (top ofwinding), the hot spot temperature rise over top duct oilcan be calculated.

The heat generated by the winding at the hot spot attime t2 = t1 + Δt is given by:

4.4-38Where:Qgen,HS is the heat generated by the windings at the

hot spot.L is the winding current, in per unit rated.PI2R is the Ohmic losses in the windings due to


current.

4.4-39Where:θHS,1 is the winding hot spot temperature calculated


θHS,R is the winding hot spot temperature at ratedload.


The heat lost by the windings to the duct oil is depen-dent upon the mechanism of heat transfer. For ONAN,ONAF, and OFAF, the predominant mode of heattransfer is natural convection. As outlined above, theheat loss for natural convection can be expressed by:

4.4-40Where:Qloss,HS is the heat lost by the winding hot spot to

the top duct oil.θHS,1 is the winding hot spot temperature at the

previous time step.θDO,1 is the duct oil temperature at the previous

time step.θHS,R is the winding hot spot temperature at rated

current.

Figure 4.4-4 Oil flow throughout the duct. ( )HSEHSRIHSgen KPKPLQ +⋅= 22

,

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

+=

KRHS

KHSHSK

θθ

θθ

,

1,

( )ERI

m

HS

RHS

m

RDORHS

DOHSHSloss PPQ +⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−=

+

21,

,

1

,,

1,1,, μ

μ

θθ

θθ

4-28


θDO,R is the duct oil temperature at rated current.μHS,R is the oil viscosity at a temperature equal to

the average of the winding hot spot tempera-ture and top.

μHS,1 is the oil viscosity at a temperature equal tothe average of the winding hot spot tempera-ture and top duct oil temperature at the pre-vious time step.

m is a constant, usually between 1/3 and 1/4.

For ODAF transformers (directed forced oil), the pre-dominant mode of heat transfer is forced convection.The heat loss for OFAF can then be expressed by:

4.4-41

Note that it is assumed that the effect of the change inoil viscosity with temperature is negligible for this case.

Completing the heat balance, the heat absorbed by thewindings is given by:

4.4-42Where,Qabs,HS is the heat absorbed by the winding during

incremental time step, Δt.mW is the mass of the windings.CP,W is the effective specific heat of the windings.θHS,1 is the average winding temperature at time

t1.

θHS,2 is the average winding temperature at time t2

= t1 + Δt.θt is the incremental time step.

Summing the three terms of the heat balance and solv-ing for θHS,2:

4.4-43

Bottom and Top Bulk Oil RisePierce (1994) calculates the average oil rise and thenapplies a top-to-bottom oil gradient to that average oilrise. This gradient is calculated as a function of thelosses raised to an exponent. This exponent is given byPierce (1994) as 0.5 for ONAN and ONAF, and 1.0 forOFAF and ODAF.

The heat generated by the active assembly (core andcoils) at the hot spot at time t2 = t1+ Δt is given by:

4.4-44Where:Qgen,O is the heat generated within the transformer.L is the winding current, in per unit rated.PI2R is the Ohmic losses in the windings due to


current.PS is the stray loss.PC is the core (no-load) loss.

4.4-45Where:θW,1 is the average winding temperature calculated


θW,R is the average winding temperature at ratedload.


The heat loss is given by:

4.4-46Where:Qloss,AO is the heat lost by the bottom oil to the sur-

rounding air.θA,1 is the ambient temperature at the previous

time step.θA,R is the ambient temperature during the heat

run.θAO,1 is the average oil temperature at the previous

time step.θAO,R is the average oil rise at rated load.y is an exponent equal to 0.8 for ONAN, 0.9

for ONAF and OFAF, 1.0 for ODAF.

Completing the heat balance, the heat absorbed by thebulk oil is given by:

4.4-47Where:Qabs,AO is the heat absorbed by the average bulk oil

during incremental time step, Δt.θAO,1 is the average bulk oil temperature at time t1.

θAO,2 is the average bulk oil temperature at time t2

= t1 + Δt.Δt is the incremental time step.

( )ERIRDORHS

DOHSHSloss PPQ +⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

−= 2

,,

1,1,, θθ

θθ

( )t

CmQ HSHSWPWHSabs Δ

−= 1,2,

,,

θθ

( )1,

,

,,2, HS

WPW

HSlossHSgenHS

Cm

tQQθθ +

Δ−=

( )( ) CWSEWRIOgen PKPPKPLQ +++⋅= 22

,

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

+=

KRW

KWWK

θθ

θθ

,

1,

T

y

RARAO

AAOAOloss PQ

1

,,

1,1,, ⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

−=

θθ

θθ

( )t

mCQ AOAOPAOabs Δ

−=∑ 1,2,

,

θθ

4-29


The value ΣmCP is a sum of product of the masses of thetransformer in contact with the oil, as well as the oilitself, and the specific heat of those components:

4.4-48

Summing the three terms of the heat balance and solv-ing for θAO,2:

4.4-49

Once the average bulk oil temperature has been deter-mined, a top-to-bottom bulk oil gradient must be calcu-lated. This is done by the following equation:

4.4-50Where,θTO/BO is the top-to-bottom bulk oil gradient, C.θTO,R is the top oil rise at rated load, C.θBO,R is the bottom oil rise at rated load, C.Δt is the incremental time step.z is an exponent (0.5 for ONAN, ONAF; 1.0

for OFAF, ODAF).

The top and bottom oil temperatures are then solved forby adding and subtracting, respectively, half of the top-to-bottom bulk oil gradient:

4.4-51

4.4-52

4.4.4 IEC Model (IEC 354-1991)

The IEC 354-1991 (McNutt 1992) model is similar tothe IEEE Clause 7 model (Figure 4.4-5). The two mod-els differ in a few important respects. First, the calcula-tion of the rated hot spot rise is done by applying a “hotspot factor” to the average winding rise over average oiltemperature gradient. This “hot spot factor” is a designspecific constant that generally varies between 1.0 and1.4, with 1.2 being typical for power transformers.

Note: The winding temperature rise exponent in thisdocument differs slightly from that described in IEC354. The equations listed below apply a multiple of 2 tothis exponent, whereas in IEC 354, this multiple isincluded in the exponent definition. Therefore, the wind-ing temperature rise exponent listed here is equal to halfof the winding temperature rise exponent in IEC 354.

Oil Thermal Time Constant:

In order to calculate the transient response of the bulkoil, it is necessary to calculate an oil thermal time con-stant. Since IEC 354 does not include this information,the IEEE C57.91-1995 equations can be offered as anoption:

For OA and FA (ONAN and OFAF), the thermalcapacity, C, equals:

C = 0.0272 * WCC + 0.01814 * WTank + 5.034 * VFluid(1) (IEEE Clause 7) 4.4-53

For DFOA and NDFOA (ODAF and OFAF), the ther-mal capacity, C, equals:

C = 0.0272 * WCC + 0.0272 * WTank + 7.305 * VFluid(2) (IEEE Clause 7) 4.4-54

( )∑ ++= fluidfluidPTankCCsteelPP WCWWCmC ,&,

( )1,

,,2, AO

P

AOlossOgenAO

mC

tQQθθ +

Δ−=

∑

( )z

Ogen

AOlossRBORTOBOTO tQ

Q⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ−=

,

,,,/ θθθ

2/ BOTO

AOTO

θθθ +=

2/ BOTO

AOBO

θθθ −=

Figure 4.4-5 Diagram illustrating assumed temperature profile within transformer for IEC model.

0.1( )1.108

4-30


The thermal time constant of the bulk oil at rated tem-perature equals:

τO,R = C * ΔθTO,R / PT,R (3) (IEEE Clause 7) 4.4-55

At top oil temperatures other than rated, the time con-stant must be corrected as follows:

(4) (IEEE Clause 7) 4.4-56

Initial Temperatures:

The following equations are used to calculate the initialtemperatures based upon the assumption that the loadprior to the calculation period was constant longenough for the temperatures to reach their steady-statelimits. This assumption is reasonable if the load is fairlyconstant for a period of time prior to the overload equalto two to three times the oil thermal time constant.

(5) (IEC 2.4.1, Equation 1) 4.4-57

(6) (IEC 2.4.2, Equation 2) 4.4-58

(7) (IEC 2.4, Equation 1+2) 4.4-59

g is difference between average winding and average oiltemperatures.

H is a multiplier that equals 1.3.

Hg is the hot spot rise above top oil.

Transient Temperatures:

The following equations are used to calculate the tran-sient temperature rises based upon the oil time constantcalculated above, the user-determined winding time con-stant, load, losses, and initial and ultimate temperaturerises. For a graphical representation of the various tem-perature rises, see Figure 4.4.5.

For OA and FA (ONAN and ONAF) cooling modes:

The top oil rise at time t2 = t1 + Δt is given by the follow-ing:

(8) (IEC 2.4.1, Equation 1) 4.4-60

(9) (IEC 2.5) 4.4-61

The hot-spot rise over top oil at time t2 = t1 + Δt is givenby the following:

(10) (IEC 2.4, Equation 1+2) 4.4-62

In addition, for DFOA (ODAF) cooling modes a cor-rection factor is applied to account for the change inwinding Ohmic losses due to temperature as follows:

(11) (IEC 2.4.3, Equation 3) 4.4-63

For other types of cooling, the change in windingOhmic losses is negligible. Note that the IEEE methodneglects the change in winding resistance with tempera-ture for all cases, assuming that this change is alwaysoffset by the change in oil viscosity with temperature.

The transient hot spot rise is then:

(12) (IEC 2.5) 4.4-64

The equation form is the same as IEEE if the hot spotrise over top oil term is calculated with the IEC method.

Note that the IEC method calculates the hot spot riseover top oil temperature at rated load through the use ofa multiplier, H, applied to the difference between theaverage winding temperature from test and the averagetop oil temperature from test. For power transformers,H is typically approximately 1.3.


(13) (IEC 2.4.1, Equation 1) 4.4-65

n

RTO

iTOn

RTO

UTO

RTO

iTO

RTO

UTO

ROO 1

,

,

1

,

,

,

,

,

,

,

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ−⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ−⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ

=

θ

θ

θ

θ

θ

θ

θ

θ

ττ

( )( )

n

iRTOiTO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

1

12

,, θθ

( )( )

n

iRBOiBO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

1

12

,, θθ

miRiHS KHg 2

, ⋅=Δθ

( )( )

n

URTOUTO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

1

12

,, θθ

( ) 1,1,,2, 1 TO

t

TOUTOTOOe θθθθ τ Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ

Δ−

mURUHS KHg 2

, ⋅=Δθ

( )RHSUHSUHSUHS ,,,, 15.0 θθθθ −+=′

( ) 1,1,,2, 1 HS

t

HSUHSHSWe θθθθ τ Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ

Δ−

2,2,2,2, HSTOAHS θθθθ Δ+Δ+=

4-31


For NDFOA and DFOA (OFAF and ODAF) coolingmodes:

For forced-oil cooling modes, the increased mixingintroduced by the forced circulation of the oil increasesthe complexity of the model. The top oil temperatureleaving the winding is greater than the measured top oil.Therefore, the top oil temperature leaving the winding iscalculated using the sum of the ambient temperature,the bottom oil temperature rise, and the differencebetween the top oil and the bottom oil rises. Note thatthis differs from the IEEE methodology. The IEEEmethod assumes that the measured top oil temperatureis equal to the temperature of the oil leaving the top ofthe winding for all cooling modes.

The bottom oil rise at time t2 = t1 + Δt is given by:

(14) (IEC 2.4.2, Equation 2) 4.4-66

(15) (IEC 2.5) 4.4-67

The top-to-bottom oil rise at time t2 = t1 + Δt is given bythe following:

(16) (IEC 2.4.2, Equation 2) 4.4-68

(17) (IEC 2.5) 4.4-69

The hot-spot rise above top oil, ΔθHS, is calculated usingthe same equations as used for OA and FA coolingmodes described above.


(18) (IEC 2.4.2, Equation 2) 4.4-70

The above calculation is repeated for each time step ofthe overload period, with the initial temperatures risesequal to the temperature rises from the previous timestep. In addition, loss-of-life calculations are performedat each time step (IEEE 1995b).

4.4.5 Proposed IEC Model

The proposed IEC model (IEC 1991) takes a bit of a rad-ical departure from the earlier models. The authors of

this new model recognized that the hot spot temperatureincreases more rapidly initially than is currently predictedwith traditional equations. This is commonly attributedto an increase in the duct oil that occurs more quicklythan the increase in bulk oil. This phenomenon theyhave dubbed the "hot spot bump" (see Figure 4.4-6).

Rather than taking an analytical approach to the prob-lem, as had been taken by Pierce with the IEEE AnnexG model, the authors of the model took the approach ofapplying corrective factors and multiple time constants.The constants would be adjusted empirically to fit mea-sured temperature data. Like the IEEE Clause 7 model,the revised IEC model lumps the hot spot temperatureinto a top oil rise over ambient and a hot spot rise overtop oil.

4.4-71

The computation of the constituent rises is a complexarrangement of factors and time constants. The intentof these factors is to simulate the “hot spot bump” byinclusion of an additional exponential term in the calcu-lation of the hot spot rise over top oil.

The calculation of the top oil temperatures proceeds in asimilar fashion to the IEEE Clause 7 model. First, theultimate top oil temperature for the given load level iscalculated:

4.4-72Where:ΔθTO,U is the ultimate top oil temperature rise, C.ΔθTO,R is the rated top oil temperature rise, C.K is the per unit load.R is the ratio of load losses to no-load losses.x is a constant exponent.

( )( )

n

URBOUBO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+Δ=Δ

1

12

,, θθ

( ) 1,1,,2, 1 BO

t

BOUBOBOOe θθθθ τ Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ

Δ−

mURBOTUBOT K 2

,, −− Δ=Δ θθ

( ) 1,1,,2, 1 BOT

t

BOTUBOTBOTWe −

Δ−

−−− Δ+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ=Δ θθθθ τ

2,2,2,2,2, HSBOTBOAHS θθθθθ Δ+Δ+Δ+= −

Figure 4.4-6 Example of “hot spot bump.”

TOHSTOAHS /θθθθ Δ+Δ+=

x

RTOUTOR

RK⎥⎦

⎤⎢⎣

⎡

++

Δ=Δ1

12

,, θθ

4-32


4-33

The transient top oil rise is then calculated by the fol-lowing equation (note the additional constant applied tothe time constant):

4.4-73Where:ΔθTO,2 is the top oil temperature rise at the current

time step, C.ΔθTO,1 is the top oil temperature rise at the previous

time step, C.Δt is the time step, minutes.k11 is a transformer specific constant.τO is the oil thermal time constant, minutes.

The hot spot rise over top oil is then calculated. Theultimate hot spot rise over top oil is calculated in thetraditional manner:

4.4-74Where:ΔθHS/TO,U is the ultimate hot spot rise over top oil, C.ΔθHS/TO,R is the rated hot spot rise over top oil, C

(IEC defines this as H*g, where H is a hot spotfactor between 1.1 and 1.5 and g is the averagewinding to average oil gradient).

K is the load in per unit.y is a constant exponent.

The most significant difference between this new IECmodel and more traditional calculations is in the tran-sient formulation of the hot spot rise over top oil. Thenew IEC model breaks the rise into two componentswith different time constant, one on the order of thewinding time constant and the other on the order of theoil time constant. The transient hot spot rise over top oilis calculated as follows for increasing load:

4.4-75Where:ΔθHS/TO,2 is the hot spot rise over top oil at the

current time step, C.ΔθHS/TO,1 is the hot spot rise over top oil at the

previous time step, C.k21 & k22 are transformer specific constants.Δt is the time step, minutes.τW is the winding thermal time constant,

minutes.τO is the oil thermal time constant, minutes.

For decreasing loads, the effects of thermal capacity areignored, and the hot spot rise over top oil is taken as the

ultimate hot spot rise over top oil. The individual termsare then summed to give the hot spot temperature:

4.4-76

The various k-constants and the exponents x and y aretransformer specific. The recommended method fordetermining these values is via extrapolation from theheating curves of a prolonged factory heat run test. Thisinformation would not be available for existing trans-formers, and it is unclear whether it could even be derivedusing standard factory heat run procedures. In lieu ofmeasured values, Table 4.4-3 provides suggested values.

4.5 THERMAL RATINGS

To this point, this chapter has examined the risks ofincreased loading and determined ways to predict thepertinent equipment temperatures. Now a method formaintaining reasonable risk levels under everyday oper-ation must be developed. The manner in which trans-former ratings are calculated and communicated variesfrom utility to utility, depending upon operating proce-dures. Thermal ratings are used for various purposes,ranging from planning to operation. The form and com-plexity of the presentation of calculated ratings varywith the preference of the user.

The loading of transformers is ultimately an economicaldecision. The increased risk of failure and reducedusable life must be balanced with the capital investmentof the unit and, to a smaller degree, increased mainte-nance costs. In addition, the impact of the loss of theunit on the integrity of the system must be factored in.Therefore, the ultimate decision on rating limits is up tothe individual utility. Presented here are general recom-mendations.

Ratings can be viewed as a function of several factors:

• Ambient temperature—magnitude—diversity

• Load Shape (diversity)

• Pre-Load

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−Δ−Δ+Δ=Δ

Δ−

Ok

t

TOUTOTOTO e τθθθθ 1111,,1,2,

yRTOHSUTOHS K,/,/ θθ Δ=Δ

( )

( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛−

Δ−Δ+Δ=ΔΔ−Δ−

2222 /2121

1,/,/1,/2,/

111 k

t

k

t

TOHSUTOHSTOHSTOHS

OW ekek ττ

θθθθ

TOHSTOAHS /θθθθ Δ+Δ+=

Table 4.4-3 Suggested Values for Constants in Revised IEC Model

ONAN ONAF OFAF ODAF

Oil exponent, x 0.8 0.8 1.0 1.0

Winding exponent, y 1.3 1.3 1.3 2.0

Constant k11 0.5 0.5 1.0 1.0

Constant k21 2.0 2.0 1.3 1.0

Constant k22 2.0 2.0 1.0 1.0

Oil Time Constant (min) 210 150 90 90

Winding Time Constant (min) 10 7 7 7


• Rating Duration

Power transformer ratings are traditionally calculatedover a 24-hour period. The general procedure is to cal-culate the temperatures and loss-of-life over the 24-hourperiod and compare these to pre-selected limits. Theload is adjusted accordingly such that none of the limitsis exceeded and one or more limits are met. This is thenthe definition of the rating. The steps to calculating therating are as follows:

1. Determine initial temperatures.Since transformers have a significant thermal capac-ity, the initial temperatures prior to the rating becomean important factor, particularly with rating dura-tions less than twice the oil thermal time constant.Therefore, the initial operating temperatures of thetransformer must be estimated by some means. Theinitial temperatures can be estimated directly (possi-bly from measured temperatures) or calculated bycalculating the temperatures at the end of a 24-hourperiod of assumed loading.

2. Calculate equipment temperatures and loss-of-life forrating period.Using any available means, such as those outlined inSection 4.4, the operating temperatures, principallyhot spot and top oil, are calculated throughout therating period. In addition, loss-of-life is calculated.

3. Compare maximum temperatures and loss-of-lifefrom Step 2 to selected limits.

4. Adjust load level and return to Step 2.

4.5.1 Ambient Air Temperature

Obviously, the ambient air temperature is a major factorin the load capacity of a power transformer (Figure4.5-1). Each degree that average 24-hour air tempera-ture is below 30°C represents additional capacity. There-fore, seasonal variations in air temperature can be usedto give higher thermal ratings for cooler periods.

Seasonal VariationDepending upon geographical location, the temperaturecan vary widely between seasons. This allows forincreased capacity during cooler months. Dependingupon the nature of the load, this can be a significantadvantage, especially in cooler climates. If the load islargely heating and lighting loads, then the peak systemloading tends to occur in the winter, when ambients arethe lowest and thermal capacity the highest. On the flipside, in areas with summer peaking loads, the peak loadcoincides with the peak ambient temperatures and con-sequently the minimum capacity periods.

Often times, users produce thermal ratings based uponseasonal peak or average ambients. This allows the userto take advantage of the additional capacity during peri-ods where the ambient is below the rated ambient. Rat-ings of this kind are simple and safe. Significantadditional capacity can be realized without even exceed-ing the rated hot spot temperature of 110°C.

Diurnal VariationDiurnal variations in ambient temperature are oftenpredictable. Due to the thermal capacity of the trans-former, cyclic variations in ambient temperature can beused to advantage.

MeasurementAmbient temperature should be measured as close aspossible to the transformer. Ideally, one would want thetemperature of the air in the vicinity of the radiators orheat exchangers. This is generally not practical. Temper-atures measured within the substation should be suffi-cient. Weather bureau data may be used with theunderstanding that temperatures can vary significantlyover a short distance.

For transformers located in any sort of enclosure suchas a kiosk or vault, temperatures should be used that aremeasured in the vicinity of the transformer. If this is notpossible, an offset should be added to the ambient tem-perature to account for the increased local temperatures.

4.5.2 Load

Pre-loadFor transient ratings, the thermal mass of the trans-former makes the rating dependent upon the initial tem-peratures at the start of the rating period. These initialtemperatures are governed by the loading for the previ-ous 24 hours. Therefore, for rating durations less thanapproximately twice the oil thermal time constant, pre-load is a significant factor. An illustration of this isshown in Figure 4.5-2.

Load ShapeAlso due to the long thermal time constant of the trans-former, load shape can be a factor in rating calculations.

Figure 4.5-1 Example plot of rating vs. air temperature for various durations with pre-load = 0.7 PU.

4-34


A load shape that is flat will achieve higher tempera-tures than a diverse (large difference between minimumand maximum) load shape for a given peak magnitude.This can often be used to advantage if the loading on aparticular unit is cyclic and predictable.

4.5.3 Rating Type and Duration

A thermal rating is a statement of the load capability ofa transformer under a given set of conditions. Theseconditions represent various typical operating scenariosthat a system operator may run into. The system opera-tor then selects the rating scenario that most representsthe current operating scenario to determine the loadcapability of the transformer for the current operatingscenario. Depending upon the application of the trans-former, the system conditions impacting the trans-former, and company operating policies, various ratingscenarios may be developed. However, these rating sce-narios can generally be lumped into three categories:

- Normal life-expectancy loading

- Long-term emergency (LTE)

- Short-term emergency (STE)

Normal Life-Expectancy LoadingNormal life-expectancy loading represents the normaloperating state of the transformer. A transformer repre-sents a large capital investment, and therefore it makesgood business sense to get a full life expectancy out ofthe unit. Increased temperatures result in acceleratedaging rates, and therefore a lower return on investment.The “normal rating” represents the load limit for con-tinuous operation.

Long-Term EmergencyThe definition of a long-term emergency rating (LTE)varies within the industry. Typically, it denotes a ratingwhere the thermal capacity of the equipment does notgreatly impact the rating. For power transformers, the

length of the oil time constant makes this definition abit unclear given the cyclic variation in load and air tem-perature. For the sake of discussion and throughout thischapter, a long-term emergency rating is defined as arating greater than 4 hours in duration.

Short-Term EmergencyAs with LTEs, the definition of short-term emergencyratings (STE) varies. Short-term ratings are usuallydefined as extremely short duration ratings that takeadvantage of the thermal capacity of the equipment.These ratings range from a few minutes in duration to afew hours. In this document, STEs are defined as ratings4 hours and less. An example of a 4-hour STE rating isshown in Figure 4.5-3, demonstrating the pre-load, rat-ing period, and post contingency period.

It is important to note here that short-duration ratingsare highly sensitive to the inaccuracies in the transienttemperature modeling of transformers. Therefore, cau-tion should be exercised when calculating ratings lessthan 1 hour in duration.

4.5.4 Rating Procedure

As a guideline, the following procedure for initial ratingor re-rating of a transformer is proposed.

1. Gather informationInformation essential to the loading calculationsmust be gathered. This information must include, atminimum, the factory test report and the nameplatedrawing. It is highly recommended that maintenancehistory (DGA, oil quality, etc.) and loading historybe obtained. Outline drawings may be of use as well.

2. Assess conditionThe full scope of this step is beyond this guide; how-ever, it is important to recognize the importance ofcondition. Guidelines for condition assessment withregard to loading are given below.

Figure 4.5-2 Example plot of rating vs. pre-load for various rating durations. Figure 4.5-3 Example 4 Hr STE rating.

4-35


3. Examine long-term risksWhen considering a particular loading event, the firstthings examined are the long-term risks. This mainlyconsists of evaluating the loss of insulation life out-lined above. This is an economic decision, balancingthe cost benefit of the increased load levels with thedecreased return on capital investment. If the loadingis short duration, the loss of life may be negligible,and therefore the only concern is avoiding immediatefailure.

4. Examine short-term risksIf the increased life consumption is acceptable, theconcern then shifts to avoiding immediate failure.This means limiting operating temperatures, particu-larly hot spot temperature.

5. Check auxiliary equipmentMost of the attention when presented with a poten-tial overload scenario is on the oil and winding tem-peratures. However, the auxiliary equipment(bushing, LTCs, etc.) should not be neglected. Whilethese should be sized properly to avoid limiting thetransformer rating, this is not guaranteed. Beforeproceeding with increased loading, it is often advis-able to verify the thermal capability of these devices.

6. Follow-up post loadingOnce the decision has been made to permit withincreased loading, any significant overload eventsshould be followed up with a site inspection and oilanalysis. This should be done to verify that there wereno unintended consequences of the increased loadingevent and to determine suitability for future overload.

4.5.5 Condition-Based Loading

Rather than proposing a static set of limits for variousloading situations, a condition-based methodology ispresented here. Limits are first given for healthy trans-formers. These are to be viewed as maximum limits.

These maximum limits are then reduced based upon theassessed condition of the unit. Conditions necessitatingthe reduction of the temperature limits include:

• moisture content of bulk insulation

• oxygen content

• gassing history

• criticality of service

For this guide, three condition categories are proposed:Good, Moderate, and Marginal. Transformers areplaced in each category using the several different crite-ria outlined above. The lowest category for any particu-lar criterion is the category for the unit. For example, ifa unit has an Ethylene content of less than 36 ppm, buthas a moisture content of 2%, the unit falls in the “Mar-ginal” category (Table 4.5-1).

Once the unit has been placed in a condition category,the criticality of service, or the impact of failure, shouldbe considered. If the unit is crucial to system integrity,or is the only GSU for a generation plant with no spare,it may be advisable to use the rating limits for a “Mod-erate” or “Marginal” unit, even if the condition suggests“Good.” The rating limits for each condition categoryare given in Table 4.5-2. These should be taken as guide-

Table 4.5-1 Criteria for Condition Categories Used to Determine Rating Limits

Good Moderate Marginal

Moisture < 0.5% 0.5%-1.5% > 1.5%

Oxygen < 3% TDG 3%-5% TDG > 5% TDG

Methane < 120 ppm 120-400 ppm > 400 ppm

Ethane < 65 ppm 65-100 ppm > 100 ppm

Ethylene < 50 ppm 50-100 ppm >100 ppm

Table 4.5-2 Condition-Based Rating Limits for Transformers

Condition Normal LTE (> 4 hrs) STE (< 4 hrs)

GOOD

Top Oil 95 105 110

Hot Spot 120 140 160

LOL (hrs) 24 - -

Normal LTE (> 4 hrs) STE (< 4 hrs)

MODERATE

Top Oil 95 105 105

Hot Spot 120 130 140

LOL (hrs) 24 - -

Normal LTE (> 4 hrs) STE (< 4 hrs)

MARGINAL

Top Oil 95 100 100

Hot Spot 110 120 120

LOL (hrs) 24 - -

4-36


lines and not necessarily as God-given rules. Each userhas different policies and risk tolerances.

4.5.6 Maintenance Considerations

Given the multitude of unknowns in loading powertransformers, it is essential that increased vigilance beexercised. The reasons for this are twofold. First, theassumptions made in evaluating the risks of loadingneed to be verified. Second, the unit must be maintainedin top working order to prevent conditions that may beexacerbated by increased loading.

Throughout the thermal rating process, assumptions aremade to turn a problem of enormous complexity into amanageable process. This is what distinguishes engineer-ing from science. The most important of these assump-tions are the location of the thermally l imitingtemperature near the top of the winding, adequatelysized and applied leads, and proper construction anddesign.

These assumptions need to be verified in some manner.Direct measurement of the temperatures of the windingis impossible unless fiber optic probes had been installedduring manufacture. Even with the probes installed, thisdoes not preclude the existence of an unintended hotspot elsewhere in the transformer.

Increased Preventive MaintenanceOne often neglected consideration in the loading oftransformers is the need for increased maintenance. Thecooling equipment must be maintained in top workingorder. Loss of even partial cooling could be disastrous.If a unit were loaded to the nameplate rating of thehighest cooling mode of an OA/FA/FA and all coolingfans were lost, the unit would be overloaded by roughly66%, resulting in temperatures exceeding 200°C. Inaddition, various components will age or wear morequickly.

Prior to initial re-rating or increased load, a field inspec-tion should be scheduled. At this time, the unit shouldbe subjected to careful scrutiny. In particular, the fol-lowing should be checked:

• Make sure all pumps and fans are operational. Manu-ally switch the cooling on and off to ensure properoperation. Listen to the pumps, if possible, forsounds of cavitation. Occasionally, phases on thepumps are reconnected in the wrong phase order,causing the pump to run in reverse. Note the positionof all radiator valves. If a radiator or bank of radia-tors is valved off, do not open the valve. Make a noteof this, and derate the unit accordingly.

• Calibrate and check all gauges. This is particularlyimportant if the cooling equipment is switched on/offby the temperature gauges. Oil temperature should bedouble-checked by placing a handheld thermocoupleon the tank wall as close to the thermal well as safetyallows. Once the oil gauge has been calibrated, theestimated hot spot temperature should be calculatedfor the measured top oil temperature and the givenload. The ratio of the CT feeding the heating elementof the analog WTI (winding temperature indicator)(if equipped) should be adjusted until the gauge readsthe calculated value. Finally, check that all snapswitches or setpoints for cooling switching andalarms are properly set. Be sure the alarm and tripsettings coincide with appropriate rating limits. Cal-culated ratings do no good if the unit will trip atlower temperatures!

• Check the oil level. Make sure the oil is at the levelspecified in the operating manual for the measuredoil temperature. As mentioned previously, oil willexpand with increasing temperature. Too much oilwill result in operating of the pressure relief deviceand expulsion of oil. Too little oil could result inexposing the active assembly upon cooling.

• Check all gasketed surfaces for leaks. Specifically,check the bushings, both at the tank cover and at thetop of the bushing, and any other tank penetrations.Gaskets in particular will harden and become brittlemore rapidly than at normal operating temperatures.As this happens, the gaskets can begin to leak, result-ing in reduced oil levels and ingress of moisture andoxygen. Should this occur, the unit must then betaken out of service at some point to replace the gas-kets. If this occurs with sufficient frequency, it may beadvisable to replace the gaskets with a higher temper-ature material such as Viton.

• Check the tank wall for discolored paint. Areas of hightemperatures due to stray flux heating in the tankwall may result in noticeable discoloration of thepaint. Pay close attention to bushing penetrations.

• Check conservator and gas blanket systems. Make surethe oil conservator, if equipped, is filled to the properlevel and all piping is leak free. Make sure any desic-cant canisters are filled with a suitable desiccant. Ifequipped with an inert gas blanket system, make surethat the pressure regulator is operating properly andthat sufficient gas quantity is available in the canister.Gas over-pressure can cause supersaturation of the oilat high temperatures. Upon cooling, the gas wouldcome out of solution and free bubbles would form.

• Check the LTC for proper operation, if equipped. Ifpossible, measure the temperature of the LTC com-partment oil. If the differential between the LTC oil

4-37


and the main tank exceeds 15°C, consider schedulingan outage to investigate the cause. If system condi-tions permit, consider cycling the LTC throughoutthe tap range, in particular exercising the reversingswitch.

• Draw an oil sample for DGA and oil quality. Safe over-loading requires the oil to be in good condition. Inaddition, DGA provides a useful tool for spottinglead heating or stray flux heating problems, or anyother unknown thermal conditions. In addition, unitswith possible incipient problems should never be con-sidered for overload. If an evaluation of insulationcondition with respect to thermal aging is desired,Furan analysis could be performed as well.

The above checks should be repeated as part of apreventive maintenance program at the usual scheduledinterval. If a unit is frequently loading near or abovenameplate, and increased preventive maintenance sched-ule should be considered. In addition, following moresevere emergency overloads, a site inspection should bescheduled at the earliest convenient time to ensure thatno damage was done and that the unit is operatingnormally.

4.6 WINDING TEMPERATURE MEASUREMENT

Temperature monitoring and measurement is an impor-tant tool in loading power transformers. It providesfeedback on the cooling performance of the trans-former, confirmation of calculated temperatures, and areliable assessment of the current operating condition ofthe transformer. That said, accurate temperature mea-surement is difficult and can be expensive. Dependingupon the technology, it may not be economical forsmaller units.

Simulated WTISimulated WTIs (winding temperature indicators) areby far the most common devices for measuring windingtemperatures (Figure 4.6-1). In reality, however, thesedevices do not actually measure the winding tempera-ture. They simply measure the temperature of a speciallycalibrated heating element that is immersed in the topbulk oil near the tank wall. These devices simulate theactual winding temperature.

These most common analog devices consist of a brasstube, or well, that is mounted on the side of the tank,such that it is immersed in the top oil. A separate heat-ing element is the placed in the tube, and a current pro-portional to the winding current is passed through theheating element. This current produces a temperaturerise that, at rate load, equals the expected hot spot tem-perature.

Since these devices do not directly measure the windingtemperature, they are inherently inaccurate. The ther-mal characteristics of the devices do not exactly matchthat of the transformer windings. At higher loads, theerror can be significant. In addition, these devices have alonger time constant, making them inaccurate duringtransient shifts in load (Teetsel 2003). This can be signif-icant, especially if the cooling equipment is switched bythe WTI temperature.

Fiber Optic Temperature MeasurementFirst introduced in the early 1980s, use of fiber optictemperature probes provides a method for direct tem-perature measurement of a point on the surface of thewinding insulation. This is possible due to the inherentdielectric strength of the silica fiber optic material.There are essentially two viable competing technologiesin this area: fluoroptic thermometry and abortion shiftof GaAs semiconductor.

Fluoroptic thermometry probes utilize a phosphor coat-ing at the tip. When the coating is excited with a pulse oflight sent down the fiber optic, the coating fluoresces.The rate of decay of this fluorescence is temperaturedependent. Therefore, by measuring the rate of decay atthe far end of the fiber optic, the temperature of theprobe tip can be determined.

GaAs semiconductor devices utilize a GaAs semicon-ducting wafer topped with a reflective coating at the endof the probe. A pulse of white light is sent down thefiber, passing through the GaAs wafer. Some of the lightis absorbed by the GaAs, while the remainder passesthrough and reflects off the reflective coating. The lightthen returns down the fiber where the magnitude of thereceived light is measured for the various wavelengths ofthe spectrum of the light pulse. Light at different wave-lengths is absorbed by the GaAs, with the magnitude ata particular wavelength a function of temperature of theGaAs semiconductor. Therefore, the absorption spec-

Figure 4.6-1 Schematic drawing of winding temperature indicator.

4-38


trum is a function of the temperature of the GaAs. Thecharacteristic curve of the absorption spectrum shiftstoward higher wavelengths with increasing tempera-tures. By measuring the shift in the absorption spec-trum, the temperature of the probe is determined.

Regardless of the technology used, fiber optic tempera-ture probes have a few significant disadvantages. First,these probes must be installed during manufacture. Theprobes must be inserted in the winding at the expectedhot spot location. Since this location is difficult to pin-point, several probes at different locations must be used.In addition, hot spot locations can move with differingoil flow regimes, making precise hot spot determinationimpossible. These probes are also extremely delicate.Even with the newer, ruggedized probes, breakage oftenoccurs. The manufacturer must take extra precautionsduring winding and final assembly not to break thefibers. This in turn increases the cost of manufacture forthe unit as a whole. The measuring units for reading theprobes are also rather expensive, making them economi-cal only for larger, critical units.

4.7 MODEST INCREASES IN CAPACITY FROM EXISTING TRANSFORMERS

When additional capacity is required, and higher tem-peratures are not practical or acceptable, there are lim-ited options for increasing the rating of a transformer byadding additional cooling. This can be effective to someextent, but care must be taken to ensure that the wind-ing hotspot is not excessive.

There are essentially two ways to reduce transformertemperatures: reduce the losses or increase the heattransfer. The former would require a redesign andrewind of the transformer and is therefore not economi-cal unless the unit is already being rewound following afailure. Even then, other design constraints will limit theamount of additional capacity. The only viable optionis, therefore, to increase the heat transfer. To be costeffective, any cooling upgrades must be installable in thefield. This precludes any internal modifications.

Additional pumps and fans may be added, with limitedincrease in capacity. There is a practical maximum topump flow rates or fan capacities, above which there willbe no increase in heat transfer. For units employing heatexchangers, larger heat exchangers may be added if thecost of the retrofit is justified by the increased capacity.

Methods of increasing the cooling capacity include:

• addition of fans, or higher flow rate fans, to radiatorsor heat exchangers

• retrofit radiators or heat exchangers with higher cool-ing capacity units

• water spray cooling over radiator fins

• retrofit with oil-water heat exchangers

All of the methods listed above increase the heat trans-fer from the oil to the surrounding environment. Theeffect would then be to decrease both the average oil riseand the top-to-bottom oil gradient. In non-directedflow designs, this reduction in oil temperature increasesthe thermal pressure of the natural thermosiphon flowthrough the windings. Assuming that the duct size is notlimiting the oil flow in the area of the hot spot, the hotspot temperature is then decrease.

However, this leads to a major caveat in the applicationof supplemental cooling: the drop in oil temperaturedoes not necessarily give a corresponding drop in thehot spot temperature. In other words, if the oil tempera-ture is reduced 10°C, the hot spot temperature will bereduced somewhere between 0° and 10°C. Withoutdetailed design data or embedded fiber optics, it isimpossible to determine the actual decrease in hot spottemperature. Therefore, the excess capacity, if any,gained by applying supplemental cooling should not berelied upon for planning or operating purposes unlessthe manufacturer has reviewed the application.

4.8 EXAMPLES

Example 1:

This first example will illustrate a simple 6 hr transientrating with a flat preload and load cycle, followed by a6 hr transient rating with a cyclical preload and loadcycle. The unit is a 220/69-kV autotransformer rated at224 MVA with directed forced-oil cooling (DFOA).

For this unit, the bottom oil temperature rise at ratedload is known, so the more accurate IEEE Annex Gmodel is used. The parameters for the thermal calcula-tion are as shown in Table 4.8-1.

As mentioned previously, the preload and load cyclesare flat. A flat preload enforces a conservative assump-tion that the transformer temperatures have reachedsteady-state (and therefore the maximum) prior to theonset of the contingency. The contingency onset isassumed to occur at 12 pm to coincide with the peakambient. The load shape during the contingency is alsoassumed to be flat, again giving a conservative answer(Figure 4.8-1).

The ambient temperature used for the calculation is arepresentative peak day for the summer months mea-sured at the substation. This represents the worst-case

4-39


scenario where the contingency occurs on the hottestday of the season (Figure 4.8-2).

This particular unit was manufactured in 1997 and is ingood working order. Therefore, the temperature limits

for this LTE rating shall be set at 140 hot spot tempera-ture and 110°C top oil temperature. Given the aboveload and air temperature cycles and the temperaturelimits, the load over the 6 hour rating interval isincreased until either the hot spot temperature or thetop oil temperature meets the temperature limit. This isdemonstrated in Figure 4.8-3. The 6 hr LTE rating forthis specific scenario is 278 MVA.

In the above scenario, the conservative approximationof assuming a flat preload and load cycle was used.Where the load follows a predictable cyclical pattern,increased capacity can be safely realized by using theactual load shapes. Recalculating the rating above utiliz-ing the preload and load cycles, shown in Figure 4.8-4,reveals a slight increase in the rating from 278 MVA to291 MVA.

Note that the preload in this example peaks higher at0.88 pu than the flat preload of 0.7 pu assumed above.However, the preload is below 0.7 the majority of the 24hour cycle, with an average load of 0.53. Given the ther-mal time constant of the transformer bulk oil, the oper-ating temperatures with a diverse load shape will befractionally less than the temperatures with a flat loadshape (Figure 4.8-5).

Table 4.8-1 Parameters for Example 1

MVA Base for Loss Data 200 MVA

Temperature Base for Loss Data 75 C

Winding I2R Losses 525072 W

Winding Eddy Losses 0 W

Stray Losses 0 W

Core Losses 54560 W

Cooling Mode Type ODAF

Nameplate MVA 224 MVA

Guaranteed Average Winding Rise 65 C

Rated Average Winding Rise 50.6 C

Rated Hot Spot Rise 62.2 C

Rated Top Oil Rise 32.2 C

Rated Bottom Oil Rise 29.2 C

Rated Ambient Temperature 30 C

Winding Conductor Copper

Per Unit Eddy Loss at Winding Hot Spot 0

Winding Time Constant 5 min

Per Unit Winding Height to Hot Spot 1

Weight of Core & Coils 225500 lbs

Weight of Tank & Fittings 102600 lbs

Fluid Type Mineral Oil

Oil Volume 21696 gals

Load

00.20.40.60.8

11.21.4

0 10 20 30 40 50 60

Time (hrs)

Load

(Per

Uni

t)

Figure 4.8-1 Preload and load cycle for Example 1.

Ambient Temperature

05

101520253035

0 10 20 30 40 50 60

Time (hrs)

Am

bien

t Tem

p (d

eg C

)

Figure 4.8-2 Air temperature cycles for Example 1.

Figure 4.8-3 Calculated transformer temperatures for Example 1.

Load

00.20.40.60.8

11.21.4

0 10 20 30 40 50 60

Time (hrs)

Load

(Per

Uni

t)

Figure 4.8-4 Preload and load cycles for Example 1 with cyclical load.

4-40


Example 2

This second example will answer a question: A substa-tion transformer is feeding a circuit in parallel with twoother transformers. One of the three transformers mustbe removed from service for 48 hours. Can the remain-ing two units handle the increased load safely?

The unit in this example is a 220/138-kV autotrans-former rated at 180/240/300MVA OA/FA/FA. Again,the Annex G model is used with the parameters shownin Table 4.8-2.

The predicted load for the days of the outage is shownin Figure 4.8-6. The lower curve shows the predictedload with all units in service. The upper curve shows theload with two units in service. Figure 4.8-7 shows the

predicted air temperatures in the vicinity of the substa-tion for the 48 hour period under question.

Figure 4.8-8 reveals that the hot spot temperature peaksat about 140°C and the top oil temperature reachesapproximately 100°C. Given the short duration of theevent, these temperatures should be safe, assuming thein-service units are in good working order.

Figure 4.8-5 Calculated transformer temperatures for Example 1 with cyclical load.

Load

00.20.40.60.8

11.21.4

0 10 20 30 40 50 60

Time (hrs)

Load

(Per

Uni

t)

Load (PU)Original Load

Figure 4.8-6 Predicted load during outage for Example 2.

Ambient Temperature

0

10

20

30

40

50

0 10 20 30 40 50 60

Time (hrs)

Am

bien

t Tem

p (d

eg C

)

Figure 4.8-7 Predicted air temperature for outage.

Table 4.8-2 Parameters for Example 2

MVA Base for Loss Data 180 MVA

Temperature Base for Loss Data 65 C

Winding I2R Losses 146265 W

Winding Eddy Losses 0 W

Stray Losses 0 W

Core Losses 47894 W

Cooling Mode Type FA

Nameplate MVA 336 MVA

Guaranteed Average Winding Rise 55 C

Rated Average Winding Rise 53.6 C

Rated Hot Spot Rise 68.6 C

Rated Top Oil Rise 38.2 C

Rated Bottom Oil Rise 12.4 C

Rated Ambient Temperature 40 C

Winding Conductor Copper

Per Unit Eddy Loss at Winding Hot Spot 0

Winding Time Constant 5 min

Per Unit Winding Height to Hot Spot 1

Weight of Core & Coils 190600 lbs

Weight of Tank & Fittings 145750 lbs

Fluid Type Mineral Oil

Oil Volume 26973 gals

Figure 4.8-8 Calculated transformer temperatures during outage

4-41


Figure 4.8-9 shows the cumulative aging during the out-age, in hours, for the in-service units. The total agingover the 48 hour period is approximately 220 hours. Ifthis event is relatively rare, this increased aging shouldbe acceptable over the expected 180,000 hour life of theunit.

Insulation Aging

0

50

100

150

200

250

0 10 20 30 40 50 60

Time (hrs)

Cum

ulat

ive

Agi

ng (h

rs)

0

5

10

15

20

25

Age

Acc

eler

atio

n R

ate

Total Aging (hrs) Age Acceleration Rate

Figure 4.8-9 Insulation aging during outage.

4-42


REFERENCES

Aubin, J. and T. Langhame. 1992. “Effect of Oil Viscos-ity on Transformer Loading Capability at Low Ambient Temperatures.” IEEE Trans. on Power Delivery. Vol. 7. No. 2. pp. 516-524. April.

Cengel, Y. A. 1997. Introduction to Thermodynamics and Heat Transfer. McGraw-Hill. Boston, MA.

Dakin, T. W. 1948. “Electrical Insulation Deterioration Treated as a Chemical Rate Phenomenon.” AIEE Transactions. Vol. 67. pp. 113-122. November.

Emsley, A. M. and G. C. Stevens. 1994. “Review of Chemical Indicators of Degradation of Cellulosic Elec-trical Paper Insulation in Oil-filled Transformers.” IEE Proc. Sci. Meas. Technol. Vol. 141. No. 5. pp. 324-334. September.

IEC. 1991. IEC 60354: 1991. Loading Guide for Oil-immersed Power Transformers. January.

IEC. 2004. IEC 60076-7. Power Transformers – Part 7: Loading Guide for Oil-immersed Power Transformers. Committee Draft 2.

IEEE. 1995a. Standard Requirements for Load Tap Changers. IEEE Standard C57.131-1995. March.

IEEE. 1995b. Guide for Loading Mineral-Oil-Immersed Transformers. IEEE Standard C57.91-1995. June.

IEEE. 1995c Guide for Application of Power Apparatus Bushings. IEEE Standard C57.19.100-1995. August.

Lundgaard, L., W. Hansen, D. Linhjell, and T. Painter. 2004. “Ageing of Oil Impregnated Paper in Power Transformers.” IEEE Trans. on Power Delivery. Vol. 19. No. 1. pp. 230-239. January.

Lesieutre, B. C. Hagman, W.H. and J. L Kirtley Jr. 1997. “An Improved Transformer Top Oil Temperature Model for Use in An On-Line Monitoring and Diag-nostic System.” IEEE Trans. on Power Delivery. Vol. 12 No. 1. pp. 249-256.

McNutt, W. J. 1992. “Insulation Thermal Life Consid-erations for Transformer Loading Guides.” IEEE Transactions on Power Delivery. Vol. 7. No. 1. pp 392-401. January.

Montsinger, V. M. 1930. “Loading Transformers by Temperature.” Trans. AIEE. Vol. 49. pp 776-790.

Montsinger, V. M. 1951. Transformer Engineering. John Wiley & Sons. New York. pp. 275-351.

Pierce, L. W. 1992.“An Investigation of the Thermal Performance of an Oil Filled Transformer Winding.” IEEE Trans. on Power Delivery. Vol. 7. No. 3. pp. 1347-1358. July.

Pierce, L. W. 1994. “Predicting Liquid Filled Trans-former Loading Capability.” IEEE Trans. on Industry Applications. Vol. 30. No. 1. pp. 170-178. January/Feb-ruary.

Schroff, D. H. and A. W. Stannett. 1985. “A Review of Paper Ageing in Power Transformers.” IEE Proc. Vol. 132. Pt. C. No. 6. pp. 312- 319. November.

Teetsel, M. 2003. “Winding Temperature Measurement: Techniques, Devices and Operation.” From presentation before IEEE/PES Transformers Committee. October.

4-43


CHAPTER 5 Substation Terminal Equipment

5.1 INTRODUCTION

In comparison to overhead lines, underground cables, and power transformers, substa-tion terminal equipment is usually much less expensive to replace, and since terminalequipment is within the utility substation boundaries, its replacement does not requirepublic hearings or regulatory approval. Nonetheless, in many cases, the benefits ofincreasing the rating of lines, cables, and transformers may be limited by one or morebreakers, line traps, or current transformers, and replacement of such equipment can beboth time consuming and disruptive due to required circuit outages. Finally, just as withlines, cables, and transformers, when relatively modest increases in terminal equipmentrating are required, more detailed knowledge of thermal behavior can often be obtainedquite easily.

Substation terminal equipment consists of many different types and designs of powerequipment. Included in this classification are line traps, oil circuit breakers, SF6 circuitbreakers, rigid tubular bus, line disconnects, current transformers, bolted connectors, andinsulator bushings.

In a recent Electra article entitled “Dynamic Loading of Transmission Equipment – AnOverview” (CIGRE 2002), representatives of Study Committee 23 concluded, “there isscope for implementing dynamic loading principles for a wide range of transmissionassets.” The need for increased power flow in substation terminal equipment is illustratedin Figure 5.1-1 taken from (New York Power Pool 1982). It shows that the thermal ratingof over 50% of the transmission circuits in New York State are thermally limited by sub-station equipment.

Figure 5.1-1 Thermally limiting transmission circuit equipment.

5-1

Chapter 5: Substation Terminal Equipment Increased Power Flow Guidebook

The increase in circuit rating, resulting from applyingthe various methods of increasing power flow in over-head transmission lines, underground cable, and powertransformers is often limited by terminal equipment, asshown in Figure 5.1-2. This figure illustrates the unex-pected conclusion that relatively modest investments interminal equipment (replacement of the CT in CircuitA) yields an increase in that circuit rating and a 50-MWincrease in the rating of the complex interface. Here alarge increase in circuit rating is obtained for a verymodest expenditure on terminal equipment rather thana relatively large investment in lines, cables, or trans-formers.

This chapter is limited to studying practical, rather sim-ple methods of increasing the power flow through lesscapital-intensive equipment such as switches, bus, linetraps, breakers, and power transformer auxiliary equip-ment. Because the substation equipment being upratedis generally less expensive to replace than lines, cables,and transformers, some of the more elaborate methodsof monitoring are difficult or even impossible to justifyeconomically. Also, because of the large number ofswitches, circuit breakers, etc., in any power system, andthe variety of designs, both the thermal models that rep-resent the equipment and the requirements for weathermonitoring must be kept simple.

This chapter includes four sections:

• Section 5.2, Summary: Equipment Types and IPF Oppor-tunities, is a summary of terminal equipment types, theirthermal response to changes in weather and current, andthe risks associated with high current loading.

• Section 5.3, Thermal Models for Terminal Equipment,describes specific thermal models for each type ofequipment and suggests common limits on temperature.

• Section 5.4, Uprating of Substation Terminal Equip-ment, reviews dynamic thermal rating of terminalequipment, including a discussion of the need forweather and load data.

• Section 5.5, Thermal Parameters for Terminal Equip-ment, describes methods of determining specific ther-mal parameters from field test, laboratory test, andmanufacturer heat-run tests.

5.2 SUMMARY—EQUIPMENT TYPES AND IPF OPPORTUNITIES

Substation terminal equipment includes a wide varietyof equipment types with varying opportunities forincreased power flow. This section provides a broadoverview of the types of equipment that might limitpower circuit thermal ratings.

5.2.1 Equipment Rating Parameters

For each type of terminal equipment, the followingissues are compared:

• Primary reasons for temperature and deteriorationlimits

• Type of thermal model used in rating calculations

• Consequences of over-temperature

• Degree of thermal interaction with other equipment

• Sensitivity to weather parameters

• Response to short-time emergency loads

The comparisons included here are not intended to beexhaustive, but rather to be an initial guide as to whatcan be expected to result from the various methods ofincreasing power flow.

Temperature and Deterioration LimitsManufacturers of terminal equipment usually followANSI or IEEE or IEC standard recommendations withregard to maximum operating temperatures of substa-tion terminal equipment. One clear exception is bus.While there are manufacturing standards for strain busand tubular bus, temperature limits and thermal modelsare not typically included in the standards.

Figure 5.1-2 Diagram showing the limiting element for each of multiple circuits making up a complex power flow interface. The total interface transfer limit is shown at the top labeled “Transfer (MW)”. Note that replacing the CT in Circuit A yields an increase in the transfer limit from 450 to 500 MW! (Diagram courtesy of N. Dag Reppen, Niskayuna Power Consultants, Inc.)

5-2

Increased Power Flow Guidebook Chapter 5: Substation Terminal Equipment

One obvious way to increase the rating of substation ter-minal equipment involves the use of higher than recom-mended equipment component temperatures, especiallywhen this is done for limited periods of time and whensuch events occur infrequently. However, when theexceedence of normally recommended maximum equip-ment temperatures are to be allowed, the consequenceof such events on the life and proper function of termi-nal equipment must be known.

Thermal ModelsThermal models for substation terminal equipment fallinto one of two categories. The first category is similarto the power transformer “top oil” model (see Chapter4). In this “ambient-adjusted” model, the temperaturerise above ambient for critical components of the equip-ment (e.g., switch contact temperature), determined byreference to the appropriate standard, by a manufac-turer test report (if available), or by field or laboratorymeasurement, is specified for a known current (typicallythe rated current of the equipment). This “reference”temperature rise is then adjusted for other currentsaccording to an equation of the form:

5.2-1Where:θ2 is the temperature rise to be calculated.θR is the “reference” temperature rise.I2 is current for which the temperature rise is to be

calculated.IR is the “reference” current which causes θR.

n is an exponent, generally close to 1.0.

The second category of thermal model consists of anactual heat balance similar to that used for overheadlines and underground cables. In this model, the temper-ature rise is calculated with a heat balance equation ofthe form:

5.2-2Where:I is current in amps.R is the ac resistance of the component.qs is the solar heat gain.qr is the radiation heat loss.qc is the convective heat loss.

With either sort of thermal model, heat storage in theequipment can be included in order to simulate tran-sient thermal response to changes in current flow.

Circuit breakers, CTs, and line traps are usually mod-eled with the “ambient adjusted” thermal model. Strain

and tubular bus, bolted connectors are usually modeledwith the heat balance approach. Switches and line trapscan be modeled either way, but the heat balanceapproach usually requires too many dimensional andmaterial parameters to be practical.

Determination of Equipment Thermal ParametersAs discussed in Section 5.5, the determination of otherthan default thermal parameters for substation terminalequipment is one of the most challenging parts of deter-mining and increasing power flow through them. Unlikepower transformers, for which certified heat run data istypically available, thermal test data from the manufac-turer is seldom required by the utility and, if it was orig-inally supplied, it may no longer be available for olderequipment. For newer equipment, it should be possibleto obtain documentation of a thermal design test. Thisdocumentation will contain measurements of the tem-perature rises above ambient of critical equipment partsat rated current. Thermal time constants and exponentsare not typically available and must be determined bymeasurement or assumed.

Estimate and Consequences of Over-temperatureUnless one chooses to be extremely conservative, themagnitude and consequences of equipment over-tem-perature must be evaluated when rating substationequipment. For example, strain bus is seldom rated forstill air conditions, because this would yield extremelylow thermal ratings. But when strain bus is rated at100oC on the basis of a 3-foot-per-second crosswind,then the temperature that it might obtain under still airconditions (the “temperature rise”) must be estimated,and the consequences of occasionally attaining such atemperature on bus strength and clearance evaluated.

Degree of Thermal Interaction with Other EquipmentSpacing of equipment in most substation designs isdriven by electrical clearance considerations. At dis-tances sufficient to meet these electrical clearance needs,there is little or no thermal interaction by means of con-vection or radiation. On the other hand, substationequipment is connected by electrical conductors thatmay conduct heat as well as current. The source of suchheat may be either other electrically connected equip-ment or the conductor itself. Fortunately, the conduc-tion of heat between equipment by means of typical busconductors is unlikely to be significant. The impact ofheat from conductors that are themselves hot, however,is a source of concern.

Sensitivity to Weather The thermal rating of most substation equipment is sen-sitive to air temperature, solar heating, and wind speedand direction. Nonetheless, within the typical substa-tion, because of the many equipment orientations and

2

22

n

RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

2s r cI R q q q+ = +

5-3


the degree of sheltering by other equipment and build-ings, determination of reasonable values for solar heat-ing, wind speed, and wind direction is very difficult. Airtemperature, on the other hand, is easily determined forall equipment at a particular location. Therefore, withthe possible exception of strain and rigid bus work, windand solar effects are typically ignored.

Response to Short Time Emergency OverloadsIn transmission power systems, normal power flows inmost circuits are modest (i.e., less than 30% of the cir-cuit thermal capacity). This occurs because the systemmust be capable of transmitting sudden increases inpower flows due to the sudden loss (outage) of key com-ponents (e.g., generators and bulk transmission cir-cuits). In order to limit the magnitude of such sudden“emergency” loads, the operator may intervene within ashort period of time (e.g., 15 minutes) in order to reducepower flow levels to normal continuous ratings orbelow. In such situations, short-time emergency ratingsof substation terminal equipment may be useful.

Two factors determine the short-time emergency (STE)rating of substation terminal equipment (and otherpower equipment). These factors are the equipment’sthermal time constant and its ability to withstand occa-sional high temperature events with an acceptabledegree of deterioration. The thermal time constant isdefined as that time, after a sudden increase in electricalcurrent, after which the equipment temperature riseequals 63% of that which will ultimately occur if the newhigher load continues indefinitely. An example of with-

standing occasional high temperature exposure is theaging of free-standing current transformer insulation,which may shorten the life but not cause short-term cat-astrophic failure.

Maximum Multiple of Nameplate RatingFor short-time and long-time emergency ratings, thethermal rating calculation formulas may allow for oper-ation at many times the continuous “nameplate” rating,but there may be perfectly good engineering reasons tolimit these transient rating to a multiple of the name-plate rating. For example, this is done with power trans-formers, which are normally limited to 200% ofnameplate regardless of the STE or long-time emer-gency (LTE) rating calculations.

5.2.2 Thermal Rating Parameter Comparison

Tables 5.2-1 and 5.2-2 compare thermal rating parame-ters of substation terminal equipment.

5.3 THERMAL MODELS FOR TERMINAL EQUIPMENT

As noted in the preceding section of this chapter, thereare many types and designs of terminal equipment, anddetailed thermal test data, particularly for older equip-ment, is unlikely to be available. As a result, simplicity ispreferred in modeling terminal equipment.

5.3.1 Bus Conductors

Bus conductors in substations come in a wide variety ofsizes and types. To keep things reasonably simple, three

Table 5.2-1 Summary of IPF Characteristics for Substation Terminal Equipment (Part I)

Substation Terminal Equipment Type

Temperature or Temp Rise Limits (oC) Thermal Models

Consequence of Over-Temperature

Thermal Interaction with Other Equipment

Strain Bus 75 to 125 (cont.) Heat balance Loss of strength, sag clearance Possible

Rigid Bus 75 to 125 (cont.) Heat balance Loss of strength Possible

Switches (Air Disconnects)

70/93 rise normal105/120 rise LTE Ambient Adjusted Contact damage,

annealing of parts None

Line Traps 90 to 115 rise (cont.) Ambient AdjustedDamage to Insulation or reduction in tensile strength of aluminum

None

Bushings 150 conductor temp Adjusted for top oil of PT or OCB.

Reduction in insulation life, overpressure, gas-ket deterioration

Directly influenced by oil temp in OCB or PT

CTs - Bushing 120 hot spot Adjusted for top oil of PT or OCB.

Decrease in insulation life

Can be directly influ-enced by oil temp in OCB or PT

CTs – Free-standing 45 rise oil55 to 80 winding rise.

PT model, ambient adjusted

Decrease in insulation life None

Circuit Breakers 90 (metal in oil)80 (top oil) Ambient Adjusted Damage to contacts,

annealing of parts None

Current Limiting Reactors 55 or 80 rise Ambient Adjusted Damage to insulation None

5-4


types of substation bus are recognized: rigid bus, strainbus, and jumpers:

• Rigid bus is normally tubular, functionally similar tocopper or aluminum conduit or pipe, but some olderrigid bus may be square or “L” shaped in cross-sec-tion.

• Strain bus is under tension (thus the name “strain”),and usually identical to stranded conductor used inoverhead transmission lines. It usually is strandedaluminum wires with a steel wire core (i.e., ACSR).

• Jumpers are also made from stranded transmissionconductor but are not under tension.

The three types of bus conductor are shown in Figure5.3-1.

The thermal model for these bus types are similar tothat of an overhead line (CIGRE 1997, IEEE 1993),consisting of a heat balance between Ohmic and solarheat input and convective and radiation heat losses.

The steady state temperature given a constant load,ambient temperature, and effective wind speed must besolved by iteration so as to satisfy the following heatbalance equation:

5.3-1Where:I is current in amps.R is the ac resistance at temperature T in

ohms/meter.

qs is the solar heat gain (W/m).qr is the radiation heat loss (W/m).qc is the convective heat loss (W/m).qcond is heat loss/gain due to conduction (W/m).

One difference between substation bus and overheadlines is that reflected solar heating is negligible for lines,but not for substation bus, where the conductor aresomewhat closer to the ground.

There are other important thermal rating differences,even for the same conductor applied as substation strain

Table 5.2-2 Summary of IPF Characteristics for Substation Terminal Equipment (Part II)

Substation Terminal Equipment Type

Practical Sensitivity to weather

Thermal Time Constant (min)

Sensitivity of cont. rating to air temp. (% change per oC)

Maximum Multiple of Nameplate

Strain BusWind speed and direc-tion, air temp, solar heating

5 to 15 0.6% to 0.8%10% per fps wind None

Rigid BusWind speed and direc-tion, air temp, solar heating

10 to 30 1.0% to 0.8%10% per fps wind None

Switches(Air Disconnects) Air temp 30 0.8% for new 53oC rise

1.2% for older 30oC rise200%

Line Traps Air temp 15 0.2% None

BushingsIndirectly through trans-former or breaker oil temperature

Adjusted for top oil of PT or OCB.

Reduction in insulation life

Directly influenced by oil temp in OCB or PT

CTs - Bushing Air temp 15 Same as PT Same as PT

CTs – Free-standing Air temp 15 Similar to PTs with OA cooling.

Circuit Breakers Air temp 30 1% 200%

Current Limiting Reac-tors (Dry-type) Air temp 15 to 30 0.8% for 55oC rise

0.4% for 80oC rise200%

2s r c condI R q q q q+ = + +

Figure 5.3-1 Three types of substation bus conductor.

5-5


bus and as a phase conductor in an overhead line. Thesedifferences include:

• The decrease in electrical clearance at high tempera-ture is less likely to be a problem for substation buswhere strain bus spans are short.

• The issue of loss in strength due to annealing is lesslikely to be a concern in bus applications since theincrease in tension under ice and wind load is lessthan for lines.

• High electrical losses in bus are not a concernbecause of the short length involved.

• Inspection of connectors is much simpler in a substa-tion than in a line, which might be 50 or more milesin length.

On the other hand, the temperature attained under highload conditions for both strain bus and line conductorsis very sensitive to wind cooling (forced convection).

Given these observations, it seems reasonable that sub-station bus could be rated “less conservatively” thanoverhead lines.

Consider Drake ACSR used as both substation bus andas the phase conductor in a line. One end of the line ter-minates at the substation with the Drake bus conductor.Assume that both conductors are rated at 990 A for aconductor temperature of 100oC, wind speed 2 ft/secperpendicular to the conductor, air temperature of40oC, and full sun. If the wind drops to 0 ft/sec, the con-ductor temperature with full rated load would increaseto 130oC. This is acceptable in both applications.

Now consider the impact of increasing the assumedwind speed from 2 ft/sec wind to 3 ft/sec. The risk asso-ciated with this change in the assumed rating conditionsappears to be greater for the line than for the strain busin the substation. Any possible deterioration in thephysical conductor and associated hardware is easier tospot by a single trip to the substation. A line inspectionis far more expensive, requiring more time and travel.Any permanent increase in sag is a genuine safety con-cern along the line, not within the substation. Any lossin conductor strength is more likely to result in a hightension failure of the line during the next severe icestorm than in the shorter substation span.

Oddly enough, however, substation bus is normallyrated more conservatively than lines in terms of weatherassumptions. Thus, one simple possible approach to

increasing power flow in substation bus might be the useof less conservative weather assumptions.

5.3.2 Switch (Air Disconnect)

ANSI standards (ANSI 1979) specify certain require-ments for high-voltage air disconnect switches. Thestandards specify the rated current (thermal rating) ofthe switch and the weather conditions and equipmenttemperatures under which the rating is calculated. Forexample, modern switches, produced after 1971, with sil-ver contacts, are rated for continuous operation at atemperature rise of 53oC, whereas those manufacturedafter 1971 are rated for continuous operation at a rise of30oC. In both cases, the continuous rating is calculatedfor an air temperature of 40oC. A typical, rather simpleswitch design is shown in Figure 5.3-2.

The PJM Interconnection has published detailed ratingdata (PJM 1999) for air disconnects. The conclusionsdrawn in the PJM documents reflect the operating phi-losophy of PJM and should be considered by anyoneutilizing the analysis. For example (New York PowerPool 1995), the NY Power Pool (presently NY ISO) uti-lizes limits of 93oC, 120oC, and 140oC in calculating therating of pre-1971 air disconnects for normal continu-ous, long-time emergency (LTE) and short-time emer-g e n c y ( S T E ) rat i n g s. T h e m o s t re c e n t P J Mrecommendations are 93oC, 115oC, and 125oC for thesame ratings. The PJM standard also considers the tem-perature of conducting material joints, switch terminalswith bolted connections, and flexible connectors.

The PJM discussion also considers annealing of copperand aluminum component parts as a factor in high-tem-perature limits, while the NY ISO discussion does not.

Figure 5.3-2 Typical air disconnect (switch).

5-6


Simple Dynamic Rating Switch ModelThe adjustment of steady-state switch rating, IR, withair temperature, TA, may be approximated as follows:

5.3-2

Table 5.3-1 shows the variation of steady-state switchrating with air temperature, using this simple equation.Notice that the variation in the rating of the newerswitches, having a higher allowable contact temperaturerise over air temperature, is less. In any event, Table5.3-1 indicates that the switch rating can be 5% to 20%higher on a cool day.

The following, more general equations, are given inANSI C37.30. They allow adjustment of manufacturernameplate rating for both steady-state and transientloads. The critical contact temperature may also betracked with these equations as load and air tempera-ture vary over time.

5.3-3

5.3-4

5.3-5

5.3-6Where:θU is the ultimate contact temperature rise.θR is the rated contact temperature rise.I2 is switch current at the present time step, t2.IR is the rated switch current.n is an exponent, generally between 0.7 and 1.0

(default 0.8).

θ2 is the contact temperature rise at the presenttime step, t2.

TA is the ambient temperature.θ1 is the contact temperature rise at the previous

time step, t1.Δt is the time step.τ is the switch thermal time constant (default

30.0 min).

The switch rating can be determined by one of several“observable temperature” rises with different limitingtemperatures. It seems likely that the switch contactswill most often be the limiting temperature. In addition,it must be assumed that the contacts are kept in goodcondition such that there is not an appreciable increasein contact resistance.

Thermodynamic Dynamic Rating Switch ModelsAs part of the development of the EPRI DTCR soft-ware, thermodynamic models of certain switches weredeveloped (Coneybeer 1992) and verified through labo-ratory testing. For example, Figures 5.3-3, 5.3-4, and5.3-5 show a comparison of contact temperature mea-

12

2 40R A

RR

T TI I

T

⎛ ⎞−= ⋅⎜ ⎟−⎝ ⎠

Table 5.3-1 Impact of Air Temperature on the Normal Rating of Air Disconnects

Ambient Temperature

(oC)

Thermal Rating (53°C rise in silver

contact temp)%Nameplate (after

1971)

Thermal Rating (30°C rise in silver

contact temp)%Nameplate (before 1971)

45 95 91

40 100 100

35 105 108

30 109 115

25 113 122

20 117 129

12

2 40

nR A

RR

T TI I

T

⎛ ⎞−= ⋅⎜ ⎟−⎝ ⎠

2

2

n

U RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( )2 1 1 1 tU e τθ θ θ θ −Δ= + − −

2 2AT T θ= +Figure 5.3-3 Laboratory current step-sequence for switch tests.

Figure 5.3-4 Comparison of laboratory measurements of contact segment temperature to IEEE/ANSI and EPRI Dynamp thermodynamic model with adjusted parameters.

5-7


sured in a laboratory to temperature calculated with athermodynamic switch model.

The thermodynamic switch model consists of modelingthree switch segments separately—the contact segment,the bus bar segment, and the shunt. The model is basi-cally a heat balance much like that used to model a bareoverhead line. The detailed model had the advantagethat it adjusted ratings for wind cooling, but it had anumber of disadvantages, primarily consisting of therequirement for detailed geometrical dimensions andelectrical and thermal parameters as illustrated by thefollowing list:

• Outer and inner diameters of the bus segment.

• Contact material and surface emissivity/absorptivity.

• Switch rated current, contact temperature at ratedcurrent, and ratio of contact resistance to that of anew contact.

• Dimensions of contacts.

• Shunt material and emissivity/absorptivity.

• Shunt width and thickness.

Utility advisors on the project concluded that theserequirements were onerous and impractical, given thenumber of switch designs being used in large utilities. Inaddition to these problems, the tests indicated that theswitch contact temperature calculation was adequatelymodeled with the simpler ANSI/IEEE equations andwith previously developed utility models (Bendo et al.1979). This is illustrated in Figure 5.3-5.

In addition, the laboratory testing of an old weatheredswitch with contacts that were in poor condition showedthat the ANSI/IEEE model (or presumably the Dynampthermal model with default parameters) underestimatedthe contact temperature, as shown in Figure 5.3-4. Thegood agreement between the measured temperature andthe EPRI Dynamp thermal model was accomplished bynoting the poor condition of the switch contacts andadjusting the parameters accordingly—hardly a practi-cal solution to a “bad” switch. In reality, this switchshould have been de-rated or replaced if part of aheavily loaded power circuit.

Field Testing of SwitchesBoth as part of the original series of substation terminaltests and as part of more recent field measurements ofswitch temperature in operating substations, it was con-cluded that even in heavily loaded circuits, switch tem-peratures rarely reach levels that allow for meaningfulmeasurements. The older DTCR tests concluded that thetemperature rise due to solar heating was generallyhigher than the temperature rise due to electrical current.

The more recent tests utilized infrared (IR) imagingcameras and prepared (white painted) switch surfaces. Itwas found that this approach to measurement providesa noncontact measurement of temperature with anaccuracy of within 1° to 2° C. The camera used was notunusual, but the experience of the operator was.

The primary impediment to field testing involves the rel-atively low current levels that most switches and othersubstation equipment experience. At a current equal to30% of the switch's thermal rating, the temperature riseis only about 10% of the rated rise.

5.3.3 Air-core Reactor

Series-connected air-core reactors are governed byANSI standards (ANSI 1996, 1965). The rating is lim-ited by the hot-spot temperature rise of the conductor incontact with the insulation or encapsulation material.The limiting temperature varies depending upon theinsulation material (as indicated by the temperatureindex). For specific limits, refer to Table 5.3-2. No ther-

Figure 5.3-5 Comparison of laboratory test results to the ANSI/IEEE model and the EPRI Dynamp thermodynamic model.

Table 5.3-2 Temperature Limits for Air-Core Reactors

Insulation Tem-perature Index

(°C)

Average Winding Rise by Resistance

(°C)Hottest-spot Winding Temperature Rise (°C)

105 55 85

130 80 110

155 100 135

180 115 160

220 140 200

5-8


mal model is specifically outlined in the applicable stan-dards. The following simple model should reflect areasonable compromise between accuracy and efficiency.

5.3-7

5.3-8

5.3-9Where:θU is the ultimate winding hot spot temperature

rise.θR is the rated winding hot spot temperature rise.I2 is winding current at the present time step, t2.

IR is the rated current.n is an exponent, generally between 0.7 and 1.0

(default 0.8).θ2 is the winding hot spot temperature rise at the

present time step, t2.

θ1 is the winding hot spot temperature rise at theprevious time step, t1.

Δt is the time step.τ is the winding thermal time constant (default

5.0 min).T2 is the winding hot spot temperature at the

present time step, t2.

TA is the ambient temperature.

5.3.4 Oil Circuit Breaker

ANSI standard (ANSI 1998) gives an expression forallowable continuous current at different ambients. Thisexpression can be rearranged to give the temperaturerise as a function of the current as follows:

5.3-10

Equation 5.3-10 is for steady state. To calculate the tem-perature during transient loading periods, it is necessaryto break the contact temperature rise over ambient intotwo components with different time constants: contactrise over oil and oil rise over ambient (ANSI 1979). Thismay cause some difficulty in application, as the ratedcontact rise over oil may not be available. In addition,an expression or some guidance needs to be developedin estimating the time constant.

The transient formulation is as follows:

5.3-11

5.3-12

5.3-13

5.3-14

5.3-15Where:θO,U is the ultimate oil temperature rise.θO,R is the rated oil temperature rise.I2 is current at the present time step, t2.IR is the rated current.m is an exponent, generally between 1.5 and 2.0

(default 1.8).θO,2 is the oil temperature rise at the present time

step, t2.θO,1 is the oil temperature rise at the previous time

step, t1.Δt is the time step.τO is the oil thermal time constant.θHS,U is the ultimate hot spot temperature rise over

oil.θHS,R is the rated hot spot rise over oil.n is an exponent, generally between 1.5 and 2.0

(default 1.8).θHS,2 is the hot spot rise over oil at the present time

step, t2.

2

2

n

U RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( )2 1 1 1 tU e τθ θ θ θ −Δ= + − −

2 2AT T θ= +

1.8

,C C RR

II

θ θ⎛ ⎞

= ⎜ ⎟⎝ ⎠

Figure 5.3-6 Oil circuit breaker.

2, ,

m

O U O RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( ),2 ,1 , ,1 1 OtO O O U O e τθ θ θ θ −Δ= + − −

2, ,

n

HS U HS RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( ),2 ,1 , ,1 1 WtHS HS HS U HS e τθ θ θ θ −Δ= + − −

,2 ,2 ,2HS A O HST T θ θ= + +

5-9


θHS,1 is the hot spot rise over oil at the previoustime step, t1.

τW is the winding thermal time constant (default5.0 min).

THS,2 is hot spot temperature at the present timestep, t2.

TA is the ambient temperature.

5.3.5 SF6 Circuit Breaker

The equations given in (ANSI 1998) and (ANSI 1979)also apply to SF6 breakers. However, whereas it is neces-sary to divide the contact temperature rise into twocomponents for oil circuit breakers, it should be suffi-cient to consider only the temperature rise of the con-tacts over ambient for SF6 breakers.

There should be no appreciable thermal capacitancebetween the contacts and the ambient air.

5.3-16

5.3-17Where:θU is the ultimate contact temperature rise.θR is the rated contact temperature rise.I2 is breaker current at the present time step, t2.IR is the continuous current rating of the breaker.n is an exponent, generally between 0.7 and 1.0

(default 0.8).

θ2 is the contact temperature rise at the presenttime step, t2.

TA is the ambient temperature.θ1 is the contact temperature rise at the previous

time step, t1.Δt is the time step.τ is the breaker contact thermal time constant

(default 5.0 min).

5.3.6 Bushings (Oil-immersed Equipment Only)

This model (ANSI 1995a) applies to capacitance graded(condenser) bushings with oil-impregnated paper orresin-impregnated paper. Draw-lead bushing applica-tions are not considered, because the temperature riseswill depend upon the size of the draw lead conductorand the amount of insulation on the draw lead.

Note that use of this model requires tested values for K1,K2, and n.Figure 5.3-7 SF6 circuit breaker.

2

2

n

U RR

I

Iθ θ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( )2 1 1 1 tA UT e τθ θ θ θ −Δ= + + − −

Figure 5.3-8 Bushings.

5-10


The bushing model is as follows:

5.3-18

5.3-19

Note: Equations 5.3-18 and 5.3-19 are for the calcula-tion of the oil temperature that the bushing is immersedin, and are included for the sake of completeness. Equa-tions 5.3-18 and 5.3-19 can be substituted by simplyspecifying the oil temperature.

5.3-20

5.3-21

5.3-22Where:θO,U is the ultimate oil temperature rise.θO,R is the rated oil temperature rise.I2 is current at the present time step, t2.IE,R is the rated current of the equipment (trans-

former, OCB, etc.).m is an exponent, generally between 0.7 and 1.0

(default 0.8).θTO,2 is the oil temperature rise at the present time

step, t2.θTO,1 is the oil temperature rise at the previous time

step, t1.Δt is the time step.τO is the oil thermal time constant.θHS,U is the ultimate bushing hot spot temperature

rise over oil.K1 is constant equal to the rated bushing hot spot

rise over oil (15-32).IB,R is the rated bushing current.n is an exponent, generally between 1.6 and 2.0

(default 1.8).θHS,2 is the bushing hot spot rise over oil at the

present time step, t2.θHS,1 is the bushing hot spot rise over oil at the pre-

vious time step, t1.τb is the bushing thermal time constant (default

5.0 min).THS,2 is bushing hot spot temperature at the present

time step, t2.TA is the ambient temperature.K2 is a bushing-specific constant between 0.6 and

0.8.

5.3.7 Current Transformers

The rating of CTs can be complex. They are rated accord-ing to (ANSI 1993), but unlike other substation terminalequipment, the limits on current are a function of the tapselection and the secondary burden as well as the CTitself. No single set of rating factors can be specified forall applications, even in the same utility substation.

To develop continuous ratings, the continuous thermalcurrent rating factor (CTRCF), defined in (ANSI 1993),must be used. The standard does not consider LTE orSTE ratings, so these must be determined by nonstand-ard methods, which should be different for free-standingand for bushing-type CTs.

In general the rating of bushing-type CTs is consideredequal to that of the circuit breaker or power transformerin which the CT is installed.

If the tap setting on a bushing CT is less than its maxi-mum ratio, then the thermal capacity may be greaterthan that of the CT when set to its full winding tap posi-tion. The adjustment of thermal capacity for tap posi-tion can allow operation at currents above the rating forfull tap position. For example, at the 50% tap position,the CT rating would be 140% of its full winding positionrating.

The adjustment of a free-standing CT whose tap posi-tion rating is Itap, and whose rated maximum tempera-ture rise is θR, the rating for air temperature (θair), canbe obtained in much the standard ambient adjustmentmethod using the tap rating as a basis:

5.3-23

Noncontinuous ratings can be calculated based on thepower transformer model loading guide with 55oC aver-age winding rise and OA cooling mode parameters. Thewinding rise exponent of 2 is typically used to be conser-vative.

5.3.8 Line Traps

Line traps consist of an air-core inductance coil. Theyare described by reference (ANSI 1981), but the stan-dard does not make rating adjustments terribly clear,and there is some disagreement between sources. Fol-lowing the method and suggestions outlined in the PJMdocument on rating of line traps (PJM 1999), suitabletemperature limits are a function of the manufacturer asshown in Table 5.3-3.

( )2

2 ,, ,

1

1

m

E R

TO U TO R

I I R

Rθ θ

⎛ ⎞+⎜ ⎟=⎜ ⎟+⎝ ⎠

( )( ),2 ,1 , ,1 1 OtTO TO TO U TO e τθ θ θ θ −Δ= + − −

( ), 1 2 ,

n

HS U B RK I Iθ =

( )( ),2 ,1 , ,1 1 btHS HS HS U HS e τθ θ θ θ −Δ= + − −

,2 2 ,2 ,2HS A TO HST T K θ θ= + +

1230

* R airtap

R

I Iθ θθ

⎡ ⎤− −= ⎢ ⎥

⎣ ⎦

5-11


The adjustment of line trap continuous rating for airtemperature is obtained using the usual equation formwith an exponent of 2.0 in (PJM 1999). Other sourcesuse 1.8.

The calculation of an STE rating can be obtained usingthe temperature limits shown in Table 5.3-3 in an equa-tion of the form similar to transient calculations withother substation terminal equipment. For a 2-hour STErating with a GE Type CF, pre-1965 line trap, having a30-minute thermal time constant, the STE rating is:

5.3-24

Because of the lack of a clear rating adjustment methodin the ANSI standard, the engineer should review thevarious assumptions before doing such adjustments.

5.3.9 Other Types of Terminal Equipment

Other types of substation terminal equipment, while notspecifically described here, are derived similarly. Twoexcellent articles on increased power flow for substationterminal equipment are noted as references (Cronin1972, Conway et al. 1979).

5.4 UPRATING OF SUBSTATION TERMINAL EQUIPMENT

Overhead lines and underground cables are not consid-ered in this chapter but are considered elsewhere. Thereplacement or physical modification of overhead orunderground transmission lines is very expensive andcan be extremely difficult to schedule given the need forreliable power service. Failure of lines and cables occursoutside of the restricted access of a substation and canresult in legal and safety issues. Because of this, real-time monitoring and dynamic rating of lines and cablesis relatively easy to justify even though the monitoringand communications can be expensive and complex.

Similarly, power transformers (the primary cost compo-nent of substations) and their replacement typicallyinvolve large capital outlays and extended service out-

ages. Failure of transformers can occur in a number ofways, and cooling equipment can be complex. As withlines and cables, real-time monitoring of transformersand the development of dynamic thermal rating meth-ods are often easily justified.

Substation terminal equipment considered here fall intoone of four categories:

• Conductors that connect current-carrying (and non-current-carrying) equipment (strain bus, jumpers,rigid tubular bus, bolted and welded connectors).

• Air-insulated terminal equipment (line disconnects,free-standing current transformers, series reactors,and power line carrier [PLC] line traps).

• Oil-insulated equipment associated with a powertransformer (load tap changers, transformer bush-ings).

• Oil circuit breakers and associated bushings.

None of the terminal equipment considered have associ-ated forced cooling equipment (fans, circulating pumpsfor oil, etc.). All have much simpler failure modes thancables, lines, and power transformers. All are consider-ably less expensive to replace. As a result, as the come-dian Rodney Dangerfield might have said, they don’t getthe same “respect.”

There are several ways in which the rating of substationterminal equipment is unique. A large substation mayhave only a few power transformers and three or fourlines connected to it, yet it may have tens or hundreds ofline disconnects, bus segments, connectors, etc. Even amoderately short overhead line has miles of conductorthat the public can stand under or ride under, whereasall of the substation equipment at a location is enclosedby a fence and warning signs. Imminent failures inpower transformer windings, underground cables, andoverhead conductor splices are not directly visible ormeasurable, but in many cases overheated terminalequipment can be detected with a simple infrared scan.

As shown previously, ANSI, IEEE, and IEC standardsfor substation terminal equipment usually allow thenameplate rating of the equipment to be adjusted for airtemperatures other than 40oC. Numerous technical

Table 5.3-3 PJM Recommended Temperature Limits for Line Traps

Line Trap ManufacturerLimit of Rise for Rated

Continuous Current (°C)Normal Max

Temperature (°C)LTE (>24 hrs) Max Temperature (°C)

STE (<24 hrs) Max Temperature (°C)

GE Type CF (1954-1965) 90 130 145 160

Westinghouse Type M 110 150 165 180

Trench Type L 110 150 170 190

GE Type CF (after 1965) 115 155 170 190

30160 130

1 0.0183 134%90STEI

⎛ ⎞+ −⎜ ⎟−= =⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

5-12


publications suggest that the equipment thermal ratingcan be further adjusted for heat storage capacity, andthat the attainment of equipment temperatures higherthan the continuous limits is acceptable for short peri-ods of time.

In reference (Coneybeer 1992), basic thermodynamicmethods are applied to switches, bus, and wave traps.The experiments (sponsored by EPRI) and resultingthermal algorithms account for solar heating and forcedconvection (wind) cooling. In these models, the terminalsubstation equipment is modeled by multiple, thermo-dynamically coupled components. While shown to beaccurate, the dynamic rating algorithms based on thiswork required a great deal of detailed weather data, andequipment parameters and dimensions not readily avail-able to the utility engineer.

Choosing practical thermal models for the varioustypes, sizes, and designs of substation terminal equip-ment is a matter of maximizing accuracy while minimiz-ing complexity. As discussed in the following, thecomplexity of thermal models and monitoring methodsmust be balanced against the cost and complexity ofimplementation, the practicality of maintenance proce-dures, and the consequences of equipment failure.

Increasing the thermal rating of terminal equipmentcan be accomplished by one or more of the followingmethods:

1. Accepting increased deterioration rates by usinghigher equipment temperature limits.

2. Using actual equipment temperature rise data frommanufacturer or field tests rather than conservativeestimates.

3. Adjusting the rating for actual weather conditions(e.g., air temperature) and precontingency circuitloading.

Unless detailed experimental data is available, the firstof these methods can result in unexpected equipmentfailures. The use of manufacturer or field test data is dis-cussed in Section 5.5.1. Adjusting ratings by monitoringweather conditions and circuit load is discussed in Sec-tion 5.4.1.

5.4.1 Monitoring and Communications

Communications is an essential part of dynamic ther-mal monitoring and rating of any power circuit compo-nents. Dynamic rating of overhead lines may requirecommunication of measured data from multiple remotelocations along the line route to a nearby substation,where the data is collated and communicated to an

operations center by means of RTU channels. This pro-cess can be complex and require frequent maintenancevisits to unprotected sites.

Dynamic rating of power transformers and terminalsubstation equipment is much simpler, since any equip-ment or weather monitoring equipment is kept withinthe secure boundaries of the substation, and the com-munications link to the utility operations center is nearat hand.

Given the number of switches and other terminal sub-station equipment, the use of equipment monitors (e.g.,a switch contact temperature monitor) is impracticaland almost certainly uneconomical. On the other hand,a single weather station located in or near the substationis probably sufficient to dynamically rate all equipmentin the station.

5.4.2 Maintenance and Inspection Procedures

An initial inspection and periodic inspection visits arecrucial to reliable operation of dynamically rated termi-nal substation equipment, since it is not economic tomonitor the equipment in real-time. In contrast to over-head lines, the inspection of most terminal equipmentcan be performed quickly and easily with infrared imag-ing equipment and a trip to the single substation loca-tion. Clearly, algorithms for the dynamic rating assumethat the equipment is operating in excellent condition.

It may be very difficult to detect imminent failures ofoverhead lines (particularly full tension splices) orunderground cables, but thermal problems in substationterminal equipment can usually be spotted before anunexpected outage can occur.

5.4.3 Reliability and Consequences of Failure

Substations are designed to be reliable with alternateconfigurations available if certain equipment shouldfail. Thus the consequences of failure of a single substa-tion component may be less than for a critical line orcable.

Failures may occur as the result of metallic deteriora-tion (e.g., switch contact plating), annealing (e.g., strainbus), or insulation aging (e.g., wave traps or free-stand-ing CTs). The mechanism of failure depends on the typeof terminal equipment.

In any event, the consequence of failure may be less forsubstation terminal equipment. Overhead lines andunderground cables are placed in corridors that are notsecured against public access. If either fails, the publicor property may be harmed. Substation equipment is

5-13


enclosed by fencing designed to limit access, and neitherthe public nor nonutility property is likely to be dam-aged in the event of a failure.

On the basis of this observation, certain dynamic ratingcalculation methods that yield higher thermal ratings inexchange for an increased (but low) probability of tem-perature limit exceedence may be justified. Suchapproaches can seldom be justified for overhead lineswhere the public safety may be directly involved.

5.5 THERMAL PARAMETERS FOR TERMINAL EQUIPMENT

Given the various thermal models for terminal equip-ment, the calculation of thermal ratings depends onhaving certain thermal parameters. There are three basicmethods by which these thermal parameters can befound. In order of preference the methods are:

1. The manufacturer provides laboratory test data forthe device, including transient behavior.

2. Laboratory tests or field measurements are per-formed to obtain thermal parameters.

3. Typical thermal parameters are selected from thetechnical literature or from the appropriate stan-dards.

5.5.1 Manufacturer Test Report Data

Two examples of manufacturer test reports are includedhere. The first involves temperature measurements atrated load for an SF6 circuit breaker. The second is foran air disconnect switch.

With the SF6 circuit breaker, the design margins for thevarious components vary somewhat, but are surpris-

ingly large for most parts. For example, the 44oC tem-perature rise of the main contact is the highest measuredfor the various CB components, yet it is considerablyless than the default rise of 65oC. The current in the cir-cuit breaker would need to exceed the rated current bymore than 20% before the main contact temperature risereaches 65oC, but at this current level the bushing termi-nal would exceed its rise limit of 50oC. Considering allthe measured temperature rises for all the circuitbreaker components, the equipment could be operatedat about 15% over nameplate without exceeding the nor-mal ANSI limits.

For the air disconnect, the maximum temperature riseoccurs for TC #1. Assuming an allowable temperaturerise of 53oC, the measured rise of 42.5oC would allow fora switch load above nameplate of approximately 15%.

5.6 CONCLUSIONS AND SUMMARY

In the preceding discussion of increasing power flow forsubstation terminal equipment, certain methods of cal-culation are presented that allow safe, reliable operationof terminal equipment above its “nameplate” rating.Thus a 1200 A switch may be operated at more than1200 A by considering actual air temperature (ratherthan 40oC), the manufacturer’s test data for temperaturerise at rated load (rather than default ANSI values), andpossible operation at higher than usual temperature lim-its. In addition, for emergency ratings, the limited dura-tion emergency rating may be higher if the heat storagecapacity of the switch is considered.

Figure 5.5-1 SF6 circuit breaker with measuring locations for laboratory tests.

Table 5.5-1 Steady-State Temperature Measurements for SF6 Breaker

Location of TC Measurement

Measured Temperature

Rise (oC)

Specified Maximum

Temperature Rise (oC)

1 – Conductor for test 41 -

2 – Bushing terminal 38 50

3 – Bushing conductor 42 -

4 – Conductor junction 41 65

5 – Conductor junction 40 65

6 – Finger contact 42 65

7 – SF6 gas 29 -

8 – Enclosure 22 70

9 – Main contact 44 65

10 - Conductor junction 40 65

11 - Conductor junction 41 65

12 - Bushing conductor 41 -

13 - Bushing terminal 38 50

14 - Conductor for test 40 -

Ambient temp 32

Loading duration 12 hours

5-14


If air temperature at the substation and the electricalloading of the equipment are reported to SCADA/EMSin real-time, substation terminal equipment can bedynamically rated. This is particularly useful in increas-ing the circuit rating when overhead lines, power trans-formers, or underground cables, in series with theterminal equipment, are also dynamically rated.

Field verification of substation equipment thermalbehavior is particularly important since the basic ratingof the equipment and all methods of increasing the rat-ing depend upon the equipment being in excellent con-dition. Field measurements made with infrared imagingcameras are an excellent way to affirm the thermal con-dition of substation equipment. Not only is it possibleto use infrared imaging cameras to spot high tempera-tures and detect damaged equipment, but if small areasof the surface of bus, switches, etc. are prepared bypainting, a high-quality camera in the hands of an expe-rienced operator can be used to measure temperatureswithin a few degrees centigrade. Under high currentload conditions, equipment temperature measurementcan serve to verify the thermal models and parameterassumptions.

In summary, it is possible to operate substation terminalequipment at current levels exceeding “nameplate” by5% to 15% in most cases without reducing reliability,

but the condition of the equipment must be verified byperiodic inspections.

REFERENCES

ANSI. 1965. Appendix to C57.99-1965. Application Guide for Loading Dry-type and Oil-Immersed Cur-rent-Limiting Reactors.

ANSI. 1979. C37.37-1979. Loading Guide for AC High-Voltage Air Switches (in excess of 1000 volts).

ANSI. 1981.C93.3-1981. Requirements for Power-Line Carrier Line Traps.

ANSI. 1988. C37.010-1979. Application Guide for AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis. Reaffirmed 1988.

ANSI. 1993. C57.13-1993. Requirements for Instru-ment Transformers.

ANSI. 1995a. C57.19.100-1995. Guide for the Applica-tion of Power Apparatus Bushings.

ANSI. 1995b. C57.91-1995. Annex B. Effect of Load Transformers Above Nameplate Rating on Bushings, Tap Changers, and Auxiliary Components.

Table 5.6-1 Laboratory test data for switch at rated loading.

5-15


ANSI. 1995c. C57.131-1995. IEEE Standard Require-ments for Load Tap Changers. March.

ANSI. 1996. C57.16-1996. Requirement, Technology, and Test Code for Current-Limiting Reactors.

Bendo, I. S. et al. 1979. “Loading of Substation Electri-cal Equipment with Emphasis on Thermal Capability, Part II – Application.” IEEE Transactions. PAS-98. No.4. July/August. pp. 1403-1419.

CIGRE. 1997. Working Group 12-22. Thermal State of Overhead Line Conductors. Electra. No. 121. pp.51-67.

CIGRE. 2000. Working Group 22.12. Description of State of the Art Methods to Determine Thermal Rating of Lines in Real-Time and Their Application in Opti-mising Power Flow. CIGRE 2000. Paper 22-304.

CIGRE. 2002. Study Committee 23. “Dynamic Load-ing of Transmission Equipment–An Overview.” Electra. No. 202. June.

Coneybeer, R. T. 1992. “Transient Thermal Models for Substation Transmission Components.” Master's The-sis, School of Mechanical Engineering, Georgia Insti-tute of Technology.

Conway, B. J. et al. 1979. “Loading of Substation Elec-trical Equipment with Emphasis on Thermal Capabil-ity.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-98. No. 4. July/August. pp. 1394–1419.

Cronin, J. 1972. “Rate Substation Equipment for Short-time Overloads.” Electrical World Magazine. April 15.

Douglass, D. A. and Edris, A. 1999. “Field Studies of Dynamic Thermal Rating Methods for Overhead Lines.” IEEE T&D Conference Report. New Orleans. April 7. New Orleans, LA.

Douglass, D. A., Edris, A. et al. 2002. “Dynamic Load-ing–Lessons Learned.” CIGRE Report. September 2002, Paris, France.

IEEE. 1993. Standard 738-93. “IEEE Standard for Cal-culation of Bare Overhead Conductor Temperatures.”

New York Power Pool. 1982. “New York Power Pool Task Force on Tie Line Ratings.” Final Report. Final Issue. June.

New York Power Pool. 1995. Tie-Line Ratings Task Force. “Final Report on Tie-Line Ratings.” November.

PJM. 1999. PJM Interconnection Planning & Engineer-ing Committee. “Air Disconnect Switch Ratings.” Feb-ruary.

PJM. 1999. PJM Interconnection Planning & Engineer-ing Committee. “Guide for Determination of Line Trap Normal and Emergency Ratings.” August.

Seppa, T. O. et al. 1998. “Use of On-Line Tension Mon-itoring Systems for Real Time Ratings, Ice Loads and Other Environmental Effects.” CIGRE Report 102-22. September. Paris, France.

5-16

20011108_air_disconnect_switches.pdf







CHAPTER 6 Dynamic Thermal Ratings Monitors and Calculation Methods

6.1 INTRODUCTION

The opening of the transmission system to independent power generators and the reduc-tion in traditional regulation has led many utilities, both in the United States and aroundthe world, to employ methods where transmission lines and equipment can be operatedreliably at higher loadings. Since the mid-1980s, considerable attention has been paid toincreasing the power flow of overhead lines, power transformers, underground cables, andsubstation terminal equipment by means of monitoring weather and the equipment ther-mal state and by developing more accurate thermal models. The resulting dynamic ther-mal rating techniques have typically yielded increases of 5 to 15% in capacity.

Chapter 6 provides an overview of dynamic thermal rating methods. Each of the otherchapters in this book includes a section dealing with the dynamic rating of each type ofequipment (lines, cables, power transformers, and substation terminal equipment). Thegoal of this chapter is to present a balanced overall view of when dynamic rating methodsare appropriate, how they are best implemented in a practical operational application,and how such methods can be applied to complex interconnections consisting of multiplecircuits and many circuit elements. Though the EPRI DTCR software is used to illustratepractical methods of implementation, the observations and technical insights are gener-ally applicable.


• Section 6.2, Issues Related to Dynamic Thermal Rating Methods, discusses concernsrelated to dynamic ratings, including where calculations should be performed, theimpact of ratings on engineering, planning and operations functions, and the connec-tion between ratings and increased utilization.

• Section 6.3 Power Equipment Condition Assessment and Real-Time Monitors, outlinesthe need for inspections and/or real-time monitors and the problems that may arisewithout them.

• Section 6.4, Dynamic Thermal Rating Models for Power Equipment, provides an over-view on models for overhead lines, transformers, underground cables, and substationterminal equipment.

• Section 6.5, EPRI’s DTCR Technology, describes the use of DTCR software.

• Section 6.6, Operating with Dynamic Thermal Ratings, identifies operating issuesrelated to dynamic thermal ratings.

• Section 6.7, Field Studies of Dynamic Ratings, describes field studies of dynamic ratingsused for overhead lines, transformers, underground cables, substation terminal equip-ment, and power circuits.

• Section 6.8, Conclusions, summarizes a number of observations concerning dynamicratings.

6-1

Chapter 6: Dynamic Thermal Ratings Monitors and Calculation Methods Increased Power Flow Guidebook

6.2 ISSUES RELATED TO DYNAMIC THERMAL RATING METHODS

Utilities around the world are undergoing a majortransformation, seeking to increase the utilization ofexisting power equipment within the electric transmis-sion network while attempting to increase, or at leastnot decrease, service reliability. Traditionally, power util-ities operated in a tightly regulated and predictable busi-ness environment where capital investments ingeneration and transmission were carefully plannedmany years in advance and return on investment wasguaranteed. In this environment, there was little reasonto load power equipment to levels close to thermal lim-its, and there was little need for exact thermal models.

More recently, in many countries, power utilities aremoving to an “open access” business environment inwhich transmission rights are not assured to theowner/investor in generation. Those who own and oper-ate the transmission system must respond to the trans-mission capacity needs of new generators with little orno ability to make long-term plans, yet anticipating onlymoderate and regulated return on investment. At thesame time, environmental hurdles and legal battles limitthe construction of new transmission media (overheadlines and underground cables) and inhibit the placementand construction of new substations. Thus significanttransmission network additions and reinforcementshave been at a virtual standstill for over 25 years whileload growth has continued.

As a result of the difficulties in financing, planning, andgaining approval for new facilities, the normal and post-contingency loading of exist ing equipment hasincreased. This has occurred both system-wide and(with the addition of new generation in “unplanned” butcommercially or environmentally attractive locations)on specific circuits. In response, dynamic loading andreal-time monitoring of power equipment has becomean important tool in attempting to maintain system reli-ability while allowing increased power flows. Theimproved thermal models of power equipment, devel-oped in pursuit of higher utilization levels, can improveour understanding of high-temperature operation.

In the mid-1980s, EPRI initiated research projectsinvolving the dynamic rating of both overhead lines andunderground cables. The overhead line project wasreferred to as Dynamp. It produced a thermal ratingmodel for bare overhead conductor that gives resultssimilar to both the IEEE and CIGRE thermal models.

In 1993, EPRI initiated research into the “real-time ther-mal monitoring of transmission circuits.” As described

in (Douglass and Edris 1996), certain existing thermalmodels for underground cable, overhead lines, powertransformers, and substation equipment such as linetraps, circuit breakers, bus, switches, and current trans-formers were included in an integrated software modelcapable of calculating the dynamic thermal rating oftransmission circuits consisting of one or more such ele-ments. The resulting software was tested and improvedas a result of an extensive series of field tests. The resultof the initial series of field tests, primarily on overheadlines, was summarized in (Douglass and Edris 1999).

During the same period, a number of real-time tempera-ture and condition monitoring devices have been devel-oped and refined. These include the EPRI Sagometer,the Valley Group’s CAT-1 line tension monitor, manytypes of oil monitoring devices for power transformers,and optical time-domain reflectometry instruments tomeasure temperature along underground cables. Inaddition, low power communication methods havematured, simplifying the process of real-time monitor-ing for lines and cables that may extend over manymiles. Computerized database and storage techniquesused by utilities have also evolved until it has becomerelatively easy to obtain real-time data and to storeequipment thermal parameters in utility SCADA andmaintenance systems.

This section explores a number of key issues related tothe use of dynamic ratings.

6.2.1 Where Should Dynamic Thermal Circuit Rating Calculations Be Performed?

In early field tests, the dynamic thermal rating software,developed by EPRI and others, was installed on com-puters placed in the substation environment, close to thepower equipment being monitored. This generallyyielded unsatisfactory and unreliable results. Problemsincluded hardware thefts, travel to remote locations toinvestigate problems, and unreliable communications. Inconsequence, the software was modified in its mostrecent version to obtain real-time input from, and sendcalculated output to, volatile ASCII files on the PC.These files are read and written by simple SCADA-based software programs.

In this newer arrangement, real-time monitors are inter-faced with the SCADA system, not with the dynamicloading computer. Calculated dynamic thermal ratings,based on real-time data obtained through SCADA, areread back into the SCADA database from which theycan be displayed according to the needs of each utilityor utility function. The advantage of this arrangement isprimarily one of simplicity and reliability. Other benefits

6-2

Increased Power Flow Guidebook Chapter 6: Dynamic Thermal Ratings Monitors and Calculation Methods

include centralizing the DTCR application onto onecomputer, and having this computer near computermaintenance personnel.

Communication between remote monitors and the util-ity SCADA database is handled by separate commercialsoftware and hardware that has nothing to do with thedynamic rating calculation software. Utilities may haveexisting interface methods, in use for other applications,and may choose the most appropriate interface basedon maintenance and ease of use criteria.

This arrangement also allows the utility operations peo-ple to display or utilize the calculation results in thefashion they prefer, rather than being forced to use anembedded display. The information may be dynamicallylinked to transmission/generation scheduling or genera-tion shedding systems. The calculated and measuredinformation is available for data storage by a compo-nent of an Energy Management System (EMS) makinghistorical information available to dispatchers.

The advantage of this arrangement is primarily one ofsimplicity and reliability. The communication betweenremote monitors and the utility SCADA database ishandled by separate commercial software and hardwarethat has nothing to do with the dynamic rating calcula-tion software. This arrangement also allows the utilityoperations people to display the calculation results inthe fashion they prefer rather than being forced to usethe output screen provided.

6.2.2 Costs—Capital and Otherwise

Traditionally, in regulated power utilities, the engineer-ing, planning, and operations functions are somewhatsegregated. Where dynamic loading (rating) methodsare implemented, it is likely to have an impact on allthree of these areas. This can make the implementationand use of dynamic rating methods challenging.

Figure 6.2-1 shows a typical statistical distribution ofline current and dynamic ratings for a circuit consistingof an overhead line. The figure applies equally well tonormal loadings and normal dynamic ratings or to post-contingency loadings and long-time emergency ratings.

With reference to this figure, consider how such datamay be utilized differently within the utility:

• Unless dynamic rating methods are employed, thesystem operator does not have to take action for anyof the load levels shown since all are below the staticrating. If the line is dynamically rated, the operatormay have to take action very occasionally when theline current exceeds the dynamic rating. If the average

line current increases over time, the operator willneed to take action more frequently.

• Unless dynamic ratings are implemented, the systemplanner would need to upgrade the capacity of thiscircuit before the line current begins to exceed thestatic line rating. If the line is dynamically rated, thenecessary upgrade may be postponed since thedynamic rating is typically higher than the static.

• Unless line monitors are used, the equipment engi-neer’s thermal model for the line cannot be testedexperimentally. With line monitors installed, thedetailed temperature and sag clearance response ofthe line can be improved by comparison with thefield data.

The implementation of line monitors and the calcula-tion of dynamic ratings for the line have an impact onthe interaction of the three groups. The planner may beable to postpone capital investment in uprating the line,and the design engineer may be able to improve theaccuracy of existing thermal models, but the operatormay need to act more frequently to reduce line current.The improved accuracy of the design engineer’s thermalline model may improve reliability by avoiding flash-overs to trees and other electrical circuits, but the systemplanner may find that a reduction in line rating leads todifficulties in operating the system and the need forincreased capital investment in line upgrades.

In summary, dynamic rating technology may allow thepostponement of capital investment and lead to betterthermal modeling and physical reliability, but its appli-cation may also require increased operator actions and,if the static rating is too high, it may lead to the need forphysical line upgrades.

Figure 6.2-1 Current load versus dynamic rating probability distributions.

6-3


6.2.3 Why Dynamic Ratings Go With Increased Utilization

The original EPRI dynamic thermal circuit ratingproject (3022-7) was proposed as part of the EPRI Flex-ible AC Transmission System (FACTS) technologyresearch program (Edris 2000). FACTS is a power elec-tronic-based technology for enhancing controllabilityand increasing power transfer capability of transmissioncircuits. FACTS controllers provide the system operatorwith the means of rapidly controlling loads on particu-lar circuits in order to maximize power transfer capabil-ity of transmission corridors. The ultimate goal ofFACTS controllers is to bring the power transfer stabil-ity limit as close as possible to the thermal rating oftransmission circuits.

Dynamic thermal ratings of power equipment vary overtime, of course. As such, while dynamic equipment rat-ings may often be higher than manufacturers’ ratings,there may be times when thermal capacity is inadequate,and the load needs to be reduced quickly in order toprevent damage.

One of the most attractive applications for dynamicequipment ratings involves automatic actions after(“post”) contingency occurrences. Here, after loss of amajor system component, the thermal capacity in real-time is tested against actual loads. Utilizing the thermaltime delay, certain pre-programmed actions can beundertaken if the temperature limits might otherwise beexceeded and no action is taken when capacity is ade-quate.

Given the ability to control circuit load, the knowledgeof both predicted load and dynamic ratings may be uti-lized to warn the operator well in advance of potentialoverloads. The EPRI dynamic rating software does thisby providing a parameter called Time-To-Overload(TTO). TTO indicates to the system operator how muchtime is left until equipment temperatures exceed safelimits. In the case of most distribution station trans-formers and other transmission circuits, the load profileis repeated daily with only a variation in magnitude.With this predicted load and predicted weather for over-head lines, the TTO can be calculated and updated inreal-time. This allows the dispatcher to shed load orredispatch generation in a precise manner.

6.3 POWER EQUIPMENT CONDITION ASSESSMENT AND REAL-TIME MONITORS

As part of increasing power flow, is it necessary to trackthe condition of power equipment? This section dis-cusses the need for periodic inspections and monitoring.

Two of the results of utility deregulation and growingpublic opposition to new lines and substations are theaging of the transmission system and the increased utili-zation of existing equipment. When building new facili-ties was easier and when the regulated economicenvironment allowed a fixed return on investment,power equipment was typically operated at lower utili-zation levels and was easily replaced as it aged.

While the goal of increased utilization of aging equip-ment is understandable in the present utility environ-ment, it can lead to a reduction in system reliabilityunless the equipment is carefully maintained and moni-tored, either by frequent inspections or by real-timeinstrumentation or both. Real-time instrumentation hasan additional advantage in that field data from heavilyloaded equipment can be analyzed in order to improveour thermal models.

Dynamic ratings of lines, transformers, cables, and sub-station terminal equipment can be calculated on thebasis of weather data alone. For example, the operatingconductor temperature and dynamic rating of an over-head line can be calculated based on air temperatureand wind data from a nearby weather station. This isattractive because no instruments need to be installedon the structures or energized high voltage conductors.The resulting instrumentation cost is low and the instru-ments can be installed without taking an outage.

The drawback to this approach is that there is no directmeans of confirming that the dynamic ratings are cor-rect or that the estimated conductor temperature andsag are correct. Some simple examples of the kind ofproblems that can result are:

1. Electrical clearances may be inadequate, even thoughthe conductor temperature does not exceed the maxi-mum allowable design temperature, because the linesags are not in accordance with design plan-profiledrawings.

2. Conductor temperature may exceed the calculatedconductor temperature because of broken or cor-roded strands at certain points along the line. Thismay, in turn, lead to local annealing and/or tensilefailure.

6-4


3. The conductor sag at high temperature may begreater than that calculated in the original designbecause of incorrect ruling span assumptions orerrors in the estimate of thermal elongation rates.

The first problems can be prevented by continuing phys-ical inspections both before the dynamic rating calcula-tion method is initiated and as long as it continues. Thesecond problem is difficult to detect without climbinginspections since IR scans and video recordings may notshow such damage. The last problem, cannot bedetected by physical inspection of the line at normalelectrical load levels since the unfortunate result (i.e.,inadequate electrical clearance) only occurs duringextremely high line loadings. Continuous sag or tensionmonitoring can be used to detect such problems.

6.4 DYNAMIC THERMAL RATING MODELS FOR POWER EQUIPMENT

A number of distinctions can be made between real-timemonitoring and the determination of dynamic thermalequipment ratings. Equipment monitors provide the sys-tem operator with an indication of the thermal state(e.g., critical temperatures) of remote power equipmentbut offer no guide to safe load levels. Weather monitorsprovide air temperature, wind speed, wind direction,and solar heating data. Dynamic ratings provide the sys-tem operator, and system security assessment programs,with an upper bound on circuit electrical loading that, ifadhered to, keeps equipment temperatures below user-specified maximums. Monitor parameters may be in anyone of a variety of units (degrees C or pounds of linetension). Dynamic ratings are expressed in amps orMVA, the same units as electrical load, so the compari-son is obvious.

Real-time equipment monitors may report equipmenttemperatures (or for overhead lines, possibly sag or ten-sion), electrical current, and/or weather data such as airtemperature, solar heating, and wind speed and direc-tion. When communicated to the dispatcher, this datamay be useful in establishing the present thermal stateof the monitored equipment (e.g., the top oil tempera-ture of a power transformer) or in developing a roughidea of dynamic load capability. For example, many util-ities may allow substation equipment to be loadedabove normal operating limits if the air temperature isrelatively low or if the critical equipment temperaturesare well below safe limits during an emergency. Analysisof monitor data is often dependent on the operator’sknowing specific equipment temperature limits, how-ever, and is seldom useful to system planners makingcapital investment decisions.

Dynamic thermal ratings are calculated with mathemat-ical thermal models, which require equipment parame-ters (e.g., maximum conductor temperature, resistanceper unit length), real-time equipment monitor data (e.g.,underground cable shield temperature or sag-tension forlines), real-time weather data (air temperature, windspeed, solar heating, etc.), and real-time load current.The calculation determining a safe dynamic load limittypically consists of repeated calculation of equipmenttemperature(s) for some period of time into the future todetermine the load current that just meets the safe limitson equipment temperature. These calculations includethe present equipment temperature(s) and use predictedweather data. The resulting maximum allowable loadcurrent, expressed in amperes or MVA, is the dynamicload limit (thermal rating) and may be compareddirectly to the actual equipment load.

Certain types of real-time monitors (line sag or tensionmonitors, transformer oil or winding monitors, andunderground cable thermocouples) are essential to theverification of any dynamic safe loading method. Theyprovide verification that the dynamic rating methodworks. Without such verification, incorrect or inaccu-rate dynamic rating methods could damage powerequipment. In some cases this process of verificationmay only be required during startup, after which thereal-time equipment monitors may be removed.

Therefore, real-time equipment monitors are importantto the verification of dynamic load limits but are not ofthemselves a reliable guide to the safe loading of equip-ment. Both real-time monitors and dynamic load limitcalculation methods are important to the reliable opera-tion of transmission power equipment at high load levels.

6.4.1 Accounting for Heat Storage (Pre-load Monitoring)

Thermal time constants of power transmission equip-ment vary significantly. For example, Figure 6.4-1 showsthe relative time constants of typical lines and cables.The time constant of the overhead line is about 10 min-utes, while the buried cable time constants are greaterthan 1000 minutes. These time constants are importantwhen considering emergency ratings (temporary appli-cation of load beyond the normal continuous rating).The long thermal time constant of buried cables yieldsvery high, short-duration, emergency ratings as com-pared to overhead lines. Transformers are somewhere inbetween.

6-5


6.4.2 Overhead Lines

For overhead lines, dynamic ratings can be calculatedbased on weather monitors alone or in combinationwith conductor temperature, tension or sag monitors.Each type of monitoring has its own advantages anddisadvantages but dynamic ratings based on data fromsag or tension monitors appear to have significantadvantages over the use of weather monitoring alone.

Weather-Based Dynamic Line RatingsWeather-based dynamic line ratings can be based on:

• Air temperature alone

• Air temperature and solar heating

• Air temperature, solar heating, and wind speed

• Air temperature, solar heating, wind speed, and winddirection.

In all cases, the dynamic line rating is calculated with aheat balance method and if the real-time current is mea-sured, then the line conductor temperature can also becalculated.

Equation 6.4-1 is the heat balance equation, consistingof heat input, output, and storage terms. It is based onthe fact that at steady state, the heat input must equal theheat output. In the steady state, where dT/dt is zero, thiscan be solved for current, as shown in Equation 6.4-2.

6.4-1Where:Qgen = Heat input by ohmic losses, I2R [watts/m],

a function of current and resistance.Qsun = Heat input by solar [watts/m].

This can be directly measured or calculated.

Qrad = Heat loss by radiation [watts/m],a function of temperature rise, diameter, andemissivity.

Qconv= Heat loss by convection [watts/m],a function of temperature rise, diameter, andheat transfer coefficient (wind speed).

MCp*dT/dt=Heat storage term [watts/m]. This is zero inthe steady state.

6.4-2

The weather-based model is very accurate if the weatherstations are positioned appropriately to measure theweather actually seen by the line conductors. Multipleweather stations may be required if the weather isexpected to vary along the line route.

The weather-based model, which uses standard weatherinstruments, is usually the simplest method of dynamicline rating to implement. No instruments need to bemounted on the line itself, and therefore they do notneed to survive in a high electromagnetic stress environ-ment. The measurement of wind speed and direction byan anemometer is not dependent on the line’s electricalloading, so the method works equally well under pre-and post-contingency loading.

Conductor Temperature-Based Dynamic Line RatingsThis system is capable of calculating dynamic line rat-ings based on direct conductor temperature measure-ments in combination with the line current, airtemperature and solar heating. To calculate line ratings,the real-time conductor temperature is converted to anequivalent wind speed perpendicular to the line. Thenthe wind speed is used in combination with the otherweather data to calculate the dynamic line rating.

The advantage of temperature-based ratings is that theuser has a direct measurement of conductor tempera-ture. If the line rating is intended to limit the loss of con-ductor strength at high temperature, then this directmeasurement of the primary parameter makes sense.

The disadvantage of using conductor temperature mon-itors is that these instruments must function in the veryhigh electrical stress immediately around the energizedconductor on which they are mounted. The measuredconductor temperature must be communicated to aground station some distance away, and the conductortemperature may or may not be a good estimate of theaverage conductor temperature along the line, which isrelated to the line sag and tension. Additionally, it ispossible for the process of temperature measurement to

Figure 6.4-1 Temperature response to step changes in current load.

*p

dTQgen Qsun Qrad Qconv mC

dt+ = + +

AC_conductorRconv rad sun

rating

Q Q QI

+ −=

6-6


actually interfere with the temperature being measured.That is, if the measurement device introduces significantmass and/or shielding in the measurement area, the tem-perature being recorded might not be representative ofconductor temperatures a few meters away.

Sag/Tension-Based Dynamic Line RatingsThe fundamental parameter of interest on most over-head lines is the sag or clearance at maximum allowableconductor temperature. Thus real-time measurement ofsag or tension provides a direct measurement of the lim-iting parameter. Also, sag-tension monitors respond tothe weather conditions along an entire line section beingmonitored rather than to weather conditions at a singlepoint along the line. Therefore, ratings based on a singlesag-tension monitor are equivalent to several weatherstations along a line section. Of course, most lines con-sist of multiple line sections, so that one sag-tensionmonitor does not indicate the rating of the whole line.

DTCR is capable of calculating dynamic line ratings forcommercial conductor tension monitors such as thewidely used “CAT-1” line tension monitor. The CAT-1uses load cells placed in series with the insulators at astrain structure. Air temperature and solar heating aremeasured at the same structure. The monitors are linkedby radio or cellular telephone to a PC running DTCRor to the utility SCADA/EMS system. Tension monitorscan be installed with the line in service but are normallyinstalled with the line de-energized.

As with the use of temperature monitors, the real-timetension is converted to an equivalent wind speed. This isdone in two steps. First the tension is converted to anaverage conductor temperature along the line sectionbased on field calibration data. Second, the average con-ductor temperature (in combination with the line cur-rent, air temperature, and solar heating) is converted toan effective average wind speed along the line section.The line rating is then calculated using the weather-based heat balance algorithm. DTCR allows for a simi-lar process based on a real-time sag monitor, but nosuch commercial device presently exists.

6.4.3 Power Transformers

The dynamic rating algorithms used to rate power trans-formers are usually based on the IEEE Top Oil model(IEEE 1996), the IEEE Bottom Oil model (IEEE 1996)or the “IEC” model (IEC 1991). Each of the modelsrequires slightly different transformer test data (theIEEE Bottom Oil model requiring considerably moredetailed test data than the other two), and the morecomplex Bottom Oil model does a better job modelingshort time loads.

Transformer ratings are primarily a function of air tem-perature and electrical load. Solar heating of equipmentin unshaded areas and wind effects on transformers thatdo not have forced air cooling are secondary but occa-sionally important parameters. Since wind is less impor-tant to power transformers, the calculation of dynamicratings and the prediction of ratings are simpler than foroverhead lines.

However, in comparison to overhead lines and under-ground cable, real-time monitoring and dynamic load-ing of power transformers present some specialdifficulties:

• The critical transformer temperature is the windinghot spot. Normally, it is impossible to directly mea-sure the hottest spot winding temperature in oldertransformers without a fiber optic hot spot monitor,so there is a level of uncertainty as to the differencebetween the hot spot and the average winding tem-perature.

• All of the transformer dynamic loading calculationmodels require laboratory test data for hot spot riseover top oil and oil rise over air temperature at ratedelectrical load. This data may be difficult or impossi-ble to find for a 40 year-old unit.

• In addition to maximum winding current limits, thedynamic thermal rating of power transformers maydepend on loss of insulation life, maximum oil tem-perature, maximum hot spot temperature, or the for-mation of bubbles in winding insulation. The presentstate of insulation may be difficult to determine.

• Auxiliary equipment such as bushings, conductorleads, tap-changers, and associated protection limitsmay limit transformer dynamic loading. This can bedealt with either by replacing such limiting elementswith ones of higher capacity or by dynamically ratingthe auxiliary equipment as well as the transformeritself.

• Protection settings must also be considered.Unwanted tripping could occur in overload situa-tions.

• Older units may be in poor condition, requiring thatlimits on winding temperature and insulation loss-of-life be reduced below those of newer units.

Rating Constraints for Power TransformersDynamic (and static) thermal ratings for overhead linesand underground cables are typically calculated for asingle rating constraint (conductor temperature). How-ever, the dynamic rating of power transformers is typi-cally determined by simultaneous constraints onmaximum winding hot spot temperature, maximumbulk top oil temperature, maximum % loss of insulation

6-7


life per loading event, and avoidance of gas bubble for-mation in the winding insulation (Figure 6.4-2). Thuswhile the thermal model itself may not be more compli-cated than that of overhead lines or underground cables,the multiple constraints often complicate the rating cal-culation.

Also, while dynamic and static thermal ratings for over-head lines may utilize higher temperatures for shorterrating durations (e.g., 75°C for continuous operationand 100°C for emergencies), power transformers aretypically rated using multiple rating limits as shown inTable 6.4-1.

These limitations are used to calculate thermal ratingswith either the “Top Oil” or “Bottom Oil” thermalmodels and apply to both static and dynamic rating cal-culations. The possibility of gas bubble formation intransformer windings is also considered but only forshort time emergency loadings where the sudden changein electrical loading may lead to the formation of gasbubbles in regions of high electrical stress near thetransformer windings.

Transformer “Top Oil” Thermal ModelIn this thermal rating model, the transformer is repre-sented with only two temperatures, the bulk oil tempera-ture at the “top” of the tank and the winding hot spottemperature. The “Top Oil” model is described in IEEEStandard C57.91-1995, section 7-2 (IEEE 1996).

Given a constant measured load, the “ultimate top oiltemperature rise over air” is:

6.4-3Where:ΔΘTO,U = Ultimate top oil temperature reached

with measured load.ΔΘTO,R = Top oil temperature at rated load.

Ku = Ratio of measured load to rated load,Imeas/IR.

R = Ratio of load loss at rated load to no-load loss.

N = Empirical constant, typically between0.8 and 1.

The hot spot temperature rise over the top oil tempera-ture for a constant load is:

6.4-4Where:ΔΘH,U = Ultimate hot spot temperature reached

with measured load.ΔΘH,R = Hot spot temperature at rated load.Ku = Ratio of measured load to rated load,

Imeas/IR.

m = Empirical constant, typically between0.8 and 1.

After the winding and oil thermal time constants havebeen entered, the calculation of dynamic thermal ratingsfor the transformer involves tracking the hot spot wind-ing temperature and bulk top oil temperatures in real-time, as the electrical load and air temperature change,and based on the present thermal state of the trans-former, calculating its thermal response to predicted airtemperature and electrical loadings. For any type ofdynamic rating (continuous, long-time emergency, orshort-time emergency), the maximum allowable electri-cal load is calculated such that one or more of the ratingconstraints (hot spot or top oil temperatures, loss of life,bubbles) is reached but none are exceeded.

Daily 24-Hour Dynamic Rating ExampleIn the power transformer dynamic rating exampleshown in Figure 6.4-3, the tracking of the top oil tem-perature over the preceding 24 hours is shown to theleft. The predicted hourly average air temperatures over

Table 6.4-1 Temperature Limits for Ratings From IEEE C57.91-1995

Rating Constraint

[°C] ContinuousLong-Time Emergency

Short-Time Emergency

Insulated Winding

Temperature [°C]120 140 180

Top Bulk Oil Temperature [°C]

105 110 110

Loss-of-Insulation Life [%]

0.0133% [per day]

0.1% [per event] 1% [per event]

n

URTOUTO R

RK

⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

⋅ΔΘ=ΔΘ1

12

,,

Figure 6.4-2 Dynamically rated 93 MVA power transformer at Con Ed.

mURHUH K 2

,, *ΔΘ=ΔΘ

6-8


the next 24 hours are shown. The predicted electricalload is also shown. As part of the dynamic rating calcu-lation process, the top oil temperature that results fromthe predicted air temperatures and loads is calculatedfor the shown pre-load.

In this example, the transformer has a nameplate ratingof 1000 A (HV winding), and the oil temperature onlyreaches a peak value of a bit more than 70°C about 18hours from “NOW”.

Given the thermal model, the historical values of airtemperature and electrical loading for the last 24 hours,and the predicted air temperature and load shape (notabsolute magnitude), the maximum electrical load forthe next 24 hours can be calculated. Since we areassumed to be using real-time air temperature and elec-trical loading, this is a dynamic rating calculation.

With reference to Figure 6.4-4, it may be seen that,although the “nameplate rating” of this transformer is

Figure 6.4-3 Example of 24-hour daily dynamic rating calculation considering only top oil temperature limits.

Figure 6.4-4 Dynamic rating calculation for the next 24 hours.

6-9


1000 A (HV winding), the peak loading predicted tooccur 18 hours from NOW can reach 1200 A withoutexceeding the 100°C limit on top oil temperature. Thisrather busy figure also shows that the allowable electri-cal load is a function of the predicted load shape beingonly 1120 A with a “flat” load.

Transformer “Bottom Oil” Thermal ModelThe “Bottom Oil” model is a newer and more complexthermal model. It is more of a physical model than theempirical “Top Oil” model. Bottom oil and duct oiltemperatures, as well as the top oil temperature, repre-sent the thermal state of the transformer fluid. Varia-tions of viscosity and winding resistance withtemperature are included. The “Bottom Oil” model isdescribed in Annex G of IEEE Standard 57.91-1995(IEEE 1996).

When applied to dynamic rating calculations, however,the results of using the bottom oil model in place of theTop Oil model, are small except during certain short-time emergency loading events.

6.4.4 Underground Cables

The dynamic thermal rating module for cables is basedupon the 1957 paper prepared by J.H. Neher and M.H.McGrath (Neher and McGrath 1957), and includesnumerical methods from IEC-287 and IEC-853 (IEC

1982, 1989). The cable rating algorithms in DTCR arebased on EPRI's ACE (Alternative Cable Evaluation)program from UTWorkstation. The approach essen-tially solves an analogous equivalent thermal circuit(Temperature = Heat x Thermal Resistance, see Figure6.4-5) to Ohm’s Law (Voltage = Current x Resistance)for electrical circuits.

Heat is transferred away from the conductor by thermalconduction through the thermal resistances in the insu-lation, jacket, duct (if present), and earth out to ambientsoil (for a solid dielectric cable). The thermal resistancescan all be calculated based on knowledge of the cableconstruction, details of the installation configuration,and assumptions about the earth thermal parameters(thermal resistivity and ambient temperature).

The equivalent thermal circuit from Figure 6.4-5 isdescribed in Equation 6.4-5 (thermal quantities areshown with an overline).

Since the system voltage is generally held to be a con-stant, the dielectric heating is constant, and the temper-ature rise caused by dielectric heating is fixed. Then, if amaximum conductor temperature (limited by insulationmaterial) is selected, the conductor current can be foundby solving Equation 6.4-5 for current as shown in Equa-tion 6.4-6.

Figure 6.4-5 Cable equivalent thermal circuit (extruded dielectric cable).

6.4-5

6.4-6

( )( )

( ) AmbientEarthDuctJacketInsulationDielectric

EarthDuctJacket

EarthDuctJacketInsulationConductor

TRRRRRW

RRRRW

RRRRRWT

++++++

++++

++++=

Duct Jacket to21

Duct Jacket toathShield/She

Duct Jacket toConductor

Earth and CableACR RTTT

I AmbientDielectricConductor

Σ−Δ−

=

6-10


The thermal capacitance of each cable component andthe earth determine the temperature response of thecable to changing load conditions, both during emer-gency rating calculations and normal load cycling. Thetime constant for buried cables is typically 24 hours ormore. As a result, the change in conductor temperatureas a function of time, in response to a sudden change incurrent, is quite slow as shown in Figure 6.4-6.

As a consequence of the long thermal time constantsassociated with underground cable, and the stable envi-ronment (soil temperature and thermal resistivity) inwhich it is immersed, the dynamic thermal rating ofunderground cable is primarily a function of the loadshape over considerable time periods. Thus the reducedloading of an underground cable circuit over the week-end may yield a significantly higher load capability onMonday, whereas the same phenomenon has no impacton the rating of an associated overhead line.

6.4.5 Substation Terminal Equipment

Early in the research into dynamic thermal ratings, sub-station terminal equipment (bus, switches, CTs, linetraps, bushings, LTCs, circuit breakers, etc. ) were eithernot considered or represented by only the simplest ofthermal models. Almost all of the researcher’s attentionwas focused on overhead lines, underground cables, andpower transformers. This “benign neglect” of substationterminal equipment seemed justified because the ther-mal model data requirements were considerable, thecondition of old equipment was uncertain, and the eco-nomic benefit of dynamically rating relatively inexpen-sive substation terminal equipment was questionable.

The replacement or physical modification of overheador underground transmission lines is very expensive andcan be extremely difficult to schedule, given the need for

reliable power service. Failure of lines and cables occursoutside of the restricted access of a substation and canresult in legal and safety issues. Because of this, real-time monitoring and dynamic rating of lines and cablesare relatively easy to justify, as is the use of sometimesexpensive and complex monitoring systems.

Similarly, power transformers are usually the primarycost component of substations. Their replacement typi-cally involves large capital outlays and extended serviceoutages. Failure of transformers can occur in a numberof ways, and cooling equipment can be complex.Because of this, as with lines and cables, real-time moni-toring of transformers and the development of dynamicthermal rating methods is also easily justified.

On the other hand, after dynamically rating lines,cables, and transformers, the useful increase in circuitrating is often found to be limited by substation termi-nal equipment, and the replacement of switches, linetraps, etc. can be both difficult operationally and expen-sive in terms of required outages. Also the dynamic ther-mal rating of substation terminal equipment can oftenbe accomplished with the same real-time weather andelectrical load data used for other more capital-intensivepower equipment, and the dynamic rating of lines andpower transformers is usually highly coordinated withthe dynamic rating of terminal equipment in circuit rat-ing for little additional complexity and investment.

Thermal Models for Substation Terminal EquipmentSubstation terminal equipment falls into one of fourcategories:

1. Conductors, which connect current-carrying (andnon-current-carrying) equipment (strain bus, jump-ers, rigid tubular bus, bolted and welded connectors)

2. Air-insulated terminal equipment (line disconnects,free-standing current transformers, series reactors,and PLC line traps)

3. Oil-insulated equipment associated with a powertransformer (load tap changers, transformer bushings)

4. Oil circuit breakers and associated bushings.

None of these types of terminal equipment has associ-ated forced cooling equipment (fans, circulating pumpsfor oil, etc.). All have much simpler failure modes thancables, lines, and power transformers. All are consider-ably less expensive to replace. As a result, as RodneyDangerfield might have said, they don’t get the same“respect.”

There are several ways in which the dynamic rating ofsubstation terminal equipment is quite different than forlines, cables, and transformers. Even a large substation

Figure 6.4-6 Tracking underground cable temperature.

6-11


may have only a few power transformers and three orfour lines connected to it, yet it may have tens or hun-dreds of line disconnects, bus segments, connectors, etc.Even a moderately short overhead line has miles of con-ductor, which the public can stand under or ride under,whereas all of the substation equipment at a location isenclosed by a fence and warning signs. Imminent fail-ures in power transformer windings, undergroundcables, and overhead conductor splices are not directlyvisible or measurable in most cases, whereas an over-heated line disconnect is readily apparent with a simpleinfrared scan.

ANSI, IEEE, and IEC standards (ANSI 1978, 1979a,1979b, 1981) for substation equipment usually allow thenameplate rating of the equipment to be adjusted for airtemperatures below 40°C. Numerous technical publica-tions suggest that the equipment thermal rating can befurther adjusted for heat storage capacity and that theattainment of equipment temperatures higher than thecontinuous limits is acceptable for short periods of time(Cronin 1972, Conway et al. 1979, Massey 1971).

In (Coneybeer 1992), basic thermodynamic methods areapplied to switches, bus, and wave traps. The experi-ments and resulting thermal algorithms account forsolar heating and forced convection (wind) cooling. Inthese models, the terminal substation equipment is mod-eled by multiple, thermodynamically coupled compo-nents. While shown to be accurate, the dynamic ratingalgorithms based on this work required a great deal ofdetailed weather data, and equip-ment parameters anddimensions not readily available to the utility engineer.

The choice of a practical dynamic thermal model for thevarious types, sizes, and designs of substation terminalequipment is a matter of maximizing accuracy withoutrequiring excessive complexity in monitoring or charac-terizing the equipment. The complexity of dynamicthermal models and monitoring methods must be bal-anced against the cost and complexity of implementa-tion, the practicality of maintenance procedures, theconsequences of equipment failure.

Monitoring and Communications for Substation Terminal EquipmentCommunications is an essential part of dynamic ther-mal monitoring and rating of any power circuit compo-nents. Dynamic rating of overhead lines, may requirecommunication of measured data from multiple remotelocations along the line route to a nearby substationwhere the data is collated and communicated to anoperations center by means of RTU channels. This pro-cess can be complex and require frequent maintenancevisits to unprotected sites.

Dynamic rating of power transformers and terminalsubstation equipment is much simpler since any equip-ment or weather monitoring equipment is kept withinthe secure boundaries of the substation, and the com-munications link to the utility operations center is nearat hand.

Given the number of switches and other terminal sub-station equipment, the use of equipment monitors (e.g.,a switch contact temperature monitor) is impracticaland almost certainly uneconomical. On the other hand,a single weather station located in or near the substationis probably sufficient to dynamically rate all equipmentin the station.

Maintenance and Inspection Procedures – Substation Terminal EquipmentAn initial inspection and periodic inspection visits arecrucial to reliable operation of dynamically rated termi-nal substation equipment since it is not economic tomonitor the equipment in real-time. In contrast to over-head lines, the inspection of most terminal equipmentcan be performed quickly and easily with infrared imag-ing equipment and a trip to the single substation loca-tion. Clearly, algorithms for the dynamic rating assumethat the equipment is operating in excellent condition.

It may be very difficult to detect imminent failures ofoverhead lines (particularly full tension splices) orunderground cables, but thermal problems in substationterminal equipment can usually be spotted before anunexpected outage can occur.

Reliability and Consequences of FailureSubstations are designed to be reliable with alternateconfigurations available if certain terminal equipmentshould fail. Thus the consequences of failure of a singlesubstation component may be less than for a critical lineor cable.

Failures may occur as the result of metallic deteriora-tion (e.g., switch contact plating), annealing (e.g., strainbus), or insulation aging (e.g., wave traps or free-stand-ing CTs). The mechanism of failure depends on the typeof terminal equipment.

Overhead lines and underground cables are built in cor-ridors that are not secured against public access. If eitherfails, the public or property may be harmed. Substationequipment is enclosed by fencing designed to limitaccess, so neither the public nor nonutility property islikely to be directly involved in the event of a failure.

On the basis of these observations, dynamic rating cal-culation methods that yield higher thermal ratings in

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exchange for an increased (but low) probability ofexceeding temperature limits may be justified whenapplied to substation terminal equipment. Suchapproaches can seldom be justified for overhead lineswhere the public safety may be directly involved.

6.5 EPRI'S DTCR TECHNOLOGY

In the 1990s, EPRI developed a software product calledDynamic Thermal Circuit Rating (DTCR) for the pur-pose of rating transmission circuits in real time. DTCRcalculates dynamic thermal ratings of power equipmentbased on actual load and weather conditions that aregenerally accessed through the utility’s SCADA/EMSsystem. Given series or parallel combinations of equip-ment, the software determines dynamic circuit ratings byevaluating all equipment ratings on a circuit and findingthe most limiting ampacity for each rating scenario.

This section describes how the software is used.

6.5.1 Power Circuit Modeling

Circuits may be modeled using series-only or parallelcircuit branches. Series-only circuits are analyzed byevaluating ratings of all circuit elements (assumed to beconnected in series) and then picking the lowest ratingof any of the elements (circuit rating). Parallel circuitbranches are modeled assuming each branch is com-prised of one or more series elements, but the softwareaccounts for the effects of one of the parallel branchesbeing out of service and impacting the loading on theother branches. Three types of data are entered into thesystem:

• Data Channels – This input specifies the source ofmonitored parameters – whether from “real-time”sources or from “override” files. The data mayinclude load, air and soil temperatures, wind speedand direction, solar radiation, and line tension/sag.

• Circuit Data – This data specifies overall circuitparameters such as emergency rating periods and therating that is evaluated for time-to-overload. Thedata channel to use for incoming load data is selectedfrom one of the data channels.

• Circuit Element Data – This data is specific to theequipment being modeled – conductor sizes, maxi-mum allowable temperatures, and installation condi-tions. The data channels associated with weatherparameters or other monitored physical data are alsospecified.

The main input screen for the program is shown in Fig-ure 6.5-1. Double-clicking on a cell brings up datascreens specific to that item.

6.5.2 DTCR Output

The software tracks critical equipment temperaturesand calculates up to four dynamic thermal ratings foreach power circuit element. These are saved to the out-put file and displayed on the screen (see Figure 6.5-2).Typical dynamic ratings might include the following:

• 24 hour “continuous” rating

• 1 to 24 hour “long-time emergency” rating

• 1 to 60 minute “short-time emergency” rating

• 1 to 24 hour “maintenance” starting at some time inthe next 24 hours

Emergency ratings up to 300 hours can be specified forunderground cables to calculate ampacities based on thetypical repair times of these systems at some utilities.The system also determines the limiting circuit elementfor each circuit and displays that element’s dynamic rat-ing as that of the circuit. Finally, if the electrical loadcurrent exceeds one of the calculated ratings (selected bythe user), the software estimates the time until theequipment temperature will begin to exceed a critical

Figure 6.5-1 Setting up two circuits in DTCR.

Figure 6.5-2 DTCR output screen.

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temperature for the equipment – this is called “Time toTemperature Overload.”

6.5.3 DTCR is a Calculation Engine for SCADA

While the software provides a simple spreadsheet-likeoutput on a PC monitor, it is intended that each utilityuser will integrate the output within the standardSCADA operational displays. In most setups, thedynamic rating programs will run on a PC that is net-worked to SCADA.

Figure 6.5-3 illustrates the methods of obtaining real-time data and supplying output to SCADA. Data caneither be supplied to the system by SCADA itself or bynon-SCADA monitors. A file-based method of inputand output is used, so that any monitor that can write afile to the PC hard drive or network can be used for real-time data. SCADA can also retrieve the output calcula-tions from the DTCR output files.

6.5.4 Modeling Complex Interfaces—California “Path 15”

In a recent EPRI research project, a dynamic thermalsoftware model was developed and tested for the Cali-fornia “Path 15” power transmission interface. Thiscomplex dynamic thermal model incorporated real-time

rating calculations for four 230-kV lines and three sin-gle-phase 500/230-kV autotransformers, which supplythe 230-kV lines at the Gates substation. Either theautotransformer or one of the 230-kV lines can deter-mine the Path rating depending upon system operatingconditions.

As shown in Figure 6.5-4, Path 15 is a complex interfacewhose total pre-contingency power flow rating candetermine maximum power flow from southern tonorthern California under certain system operating con-ditions. One of the most important power flow limita-t ions through this interface concerns the post-contingency power flow on the four 230-kV lines if bothof the 500-kV lines are suddenly taken out of service.

Independent of any dynamic thermal rating procedures,if the two 500-kV lines are suddenly taken out of service,the power flow on the 230-kV lines is reduced through aprocess of automatic load shedding of interruptibleloads and a manual generation reduction at the DiabloCanyon nuclear plant. The 230-kV lines that are mostheavily loaded after the loss of the two 500-kV lines arethose between Gates and Panoche substations. Theselines were dynamically rated in order to reduce the needfor post-contingency load reduction and/or to increasethe pre-contingency power flows on the 500-kV lines.

Figure 6.5-3 Real-time data transfer flowchart for DTCR.

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The Path 15 rating (maximum pre-contingency loading)is calculated as follows (refer to Figure 6.5-4):

1. Tension monitors and weather stations were installedon the two 230-kV lines between Gates and Panochesubstations. Real-time air temperature from theweather station near Gates is used for the trans-former rating calculations. Electrical loads are avail-able for all components, as is the list of loads thatmay be shed if the 500-kV double-line outage occurs(“remedial actions or RAS”).

2. The post-contingency electrical loads on the Gates-Panoche (GP) line (singular again) and on the GatesPower Transformer (GPT) are calculated through the

use of “effectiveness factors” relating the pre-contin-gency loads on the 500-kV lines and the other moni-tored components to the post-contingency loads.“Effectiveness factors” are decimal fractions (derivedby studying numerous load flow solutions) that equalthe fraction of load shed at a particular location thatreduces the load on Path 15.

3. The calculated post-contingency loads are reducedaccording to the list of nearly instantaneous remedialactions (load reductions and generation reductions)and the ramp load reduction undertaken manually atDiablo Canyon. The post-contingency loads for theGP 230-kV lines and the Gates Power Transformersare calculated as shown in Figure 6.5-5.

Figure 6.5-4 Circuit diagram for California’s “Path15”.

Temperature Curve

Conductor Loading (Amps)

Loading Curve

Conductor Temp (C)

2 4 6 8 10 12 14 16

Preloading

PostLoading

Peak Loading

0

Pre-outage temp

Max Temp. 100C

Time (min)

Los Banos South DLO

Diablo CanyonRamp Down

Figure 6.5-5 Post-contingency load shape for Gates-Panoche 230-kV line and Gates 500/230-kV autotransformers with the temperature response of the 230-kV line.

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4. The temperature of the GP lines and the oil/windingtemperatures of the GPT are limited in the dynamicrating calculation.

5. The loss-of-life and the possibility of gas bubble for-mation due to the post-contingency power flow in theGPT windings are limited.

6. The pre-contingency Path 15 power flow is adjusteduntil the post-contingency power flow through boththe GPT and the GP 230-kV lines is less than theirdynamic ratings. This pre-contingency Path 15 ratingdoes not incorporate other system limiting condi-tions such as voltage and stability limits.

6.5.5 Conclusions about the Dynamic Rating of Complex Interfaces

The Path 15 dynamic thermal rating is calculated suchthat, in the event of a “double-line outage” (DLO),where both 500-kV lines are suddenly taken out of ser-vice, the post-contingency power flow in the two Gates-Panoche 230-kV lines and in the Gates 500/230-kVtransformers does not exceed the dynamic rating of theequipment.

Path 15 is probably the most complex transmissioninterface in the California power system. The successfuldevelopment and field-testing of this dynamic model ofPath 15 strongly suggests that similar dynamic modelscan be developed for other less complex transmissioninterfaces. It appears that any such dynamic modeldevelopment requires:

• System analysis to define the power flow relation-ships (distribution factors) and the impact of loadand generation reduction events.

• Installations of line and power transformer monitorsand communication links from remote locations to aserver through SCADA.

• Development of a real-time software “shell,” whichallows the calculation of pre-contingency and post-contingency loads on critical interface componentsand includes iterative calculation of interface rating.

• Inclusion of previously developed and tested thermalmodel algorithm objects such as the EPRI DTCRlibrary.

• Inclusion of off-line power flow limits reflecting con-cerns about voltage and stability limits.

• Economic trade-off analysis.

The Path 15 dynamic modeling project serves as a pro-totype for managing complex transmission interfacepower flow with state-of-the-art technology.

6.6 OPERATING WITH DYNAMIC THERMAL RATINGS

The implementation of dynamic thermal ratings usuallyrequires certain changes in operating rules and proce-dures. The biggest change is simply incorporating thevariability of dynamic ratings into operating rules andcalculations. Historically, ratings for power equipmenthave been defined for “worst-case” conditions and donot vary with time and weather or system conditions.The increased capacity attainable with dynamic ratingmethods requires a major shift in thinking for opera-tions personnel.

6.6.1 Traditional Rating Definitions

Traditionally, transmission circuits have one or moreassigned limits on power flow that the operator mustheed. These limits may be set in order to avoid excessivevoltage drop or electrical phase shift, to maintain sys-tem reliability under certain contingencies, or to avoidoverheating equipment in the circuit. This discussionconcerns only thermal limits (i.e., ratings) specified inorder to avoid damaging power equipment by causingexcessively high temperatures in power equipment.

A good example of a fairly complex definition of tradi-tional thermal circuit ratings is as follows:

• Continuous (Normal) rating – Power flows at thislevel may continue indefinitely without infringingminimum electrical clearances of bare energized con-ductors in lines and substations, without exceedingagreed-upon maximum (Normal) temperatures forconductors in all types of power equipment, and, forup to 7665 hours over the life of such equipment,without reducing the 40-year assumed life of suchpower equipment or reducing the strength of lineconductors by more than 10%.

• Long-time Emergency (LTE) rating – Power flowsmay continue at this level for infrequent nonconsecu-tive four-hour periods without infringing minimumelectrical clearances of bare energized conductors inlines and substations, without exceeding agreed-uponmaximum (LTE) temperatures for conductors in alltypes of power equipment, and, for up to 300 hoursover the life of such equipment, without reducing the40-year assumed life of such power equipment orreducing the strength of line conductors by morethan 10%.

• Short-time Emergency (STE) rating – Power flowmay continue at this level for very infrequent post-contingency periods of up to 15 minutes withoutinfringing minimum electrical clearances of bareenergized conductors in lines and substations, with-out exceeding agreed-upon maximum (STE) temper-

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atures for conductors in all types of powerequipment, and, for up to 12.5 hours over the life ofsuch equipment, without reducing the 40-yearassumed life of such power equipment or reducingthe strength of line conductors by more than 10%.

• The “agreed-upon” maximum temperatures, and lossof life per event, are usually allowed to increase ingoing from Normal to LTE to STE ratings. Forexample, with an overhead line having ACSR con-ductors, if the Normal maximum temperature is95ºC, the LTE maximum might be 115ºC, and theSTE maximum temperature, 125ºC. Similarly, forpower transformers, if the loss of insulation life perevent for Normal ratings is 0.0133% (per 24 hours),then the loss of life during an LTE rating could beincreased to 0.25%.

• The shorter duration emergency ratings, heat storageshould be considered. This may be a factor is the STErating of lines and the STE and LTE rating of trans-formers.

For example, an overhead transmission line with 1590kcmil 45/7 ACSR (Lapwing) might have a Normal Sum-mer rating of 1794 amps (100%), an LTE rating of 1924amps (107%), and an STE rating of 2247 amps (125%),all calculated for the same weather conditions.

In many transmission systems, the available thermal rat-ing categories are often simpler. For example, the systemoperator may be given a single rating for lines (andtransformers) with the understanding that normal loadswill be no more than 60% of the rating and that emer-gency loads not exceed it. In this case, the duration ofthe emergency rating is typically indefinite and equip-ment damage is avoided by defining modest temperaturelimits on equipment.

6.6.2 Traditional Operating Rules

Given a rating hierarchy, the transmission system opera-tor is also normally given rules that govern his/heractions in keeping circuit loads below these limits. Thegoal of these operating rules is that the power systemshould remain “secure.” That is, all equipment is operat-ing below “normal” ratings and, contingency analysisprograms determine that, even with a major generatingstation or bulk transmission circuit out of service, noequipment exceeds its long-time emergency rating.

Should the system be found not to be “secure,” then theoperator must take action to restore system security.The type of action and the speed with which it is to be

implemented depend on the severity of the equipmentoverloads.

For example, given the Normal LTE and STE ratingsfor a circuit, the system operator is instructed to applythem in this fashion:

1. As long as the circuit load is below the Normal rat-ing, no action is required.

2. If the circuit load exceeds the Normal rating but isless than the LTE rating, the circuit load must bereduced until it is below the Normal rating withinfour hours.

3. If the circuit load exceeds the LTE rating but is lessthan the STE rating, the circuit load must be reduceduntil it is below the Normal rating within 15 minutes.

4. If the circuit load exceeds the STE rating, the circuitload must be reduced until it is less than the Normalrating immediately.

Thermal ratings for other durations can also be definedif useful with the operating rules functioning in a similarfashion.

In addition to this desire to keep the power system oper-ating in a secure mode, there is considerable economicmotivation to maximize the utilization of low cost gen-eration to meet load demands. To accomplish this,short-term and longer-term economic dispatch calcula-tions are performed.

6.6.3 Operating with Dynamic Ratings

When circuit flows are limited by thermal concerns(rather than stability limits), dynamic thermal ratingsoffer advantages (and challenges) compared to tradi-tional static thermal ratings. Since dynamic thermal rat-ings are normally higher than static ratings, theadvantages to their use are:

• When dynamic normal ratings are available, the oper-ator may determine that normal load levels thatexceed the static rating do not require action since theload does not exceed the dynamic rating.

• When dynamic emergency ratings are available, low-probability, post-contingency loads that exceed staticemergency ratings may be less than dynamic emer-gency ratings, thus avoiding the need for operatorintervention to reduce load.

• Dynamic ratings may allow for considerable cost sav-ings during generation dispatch calculations becausethey are higher than static ratings, though this mayrequire accurate prediction of dynamic rating valuesup to a day ahead.

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A number of challenges may arise with the use ofdynamic ratings, which results in their not being morewidely integrated into power system operations. Thesechallenges include:

• SCADA/EMS flexibility and capability

• Instrumentation reliability

• Availability and reliability of communication links toSCADA

• Rating variability

• Engineering acceptance

The purpose of this discussion is not be exhaustive butrather to identify obvious barriers to implementationand suggest solutions that might overcome them.

SCADA/EMS Flexibility and CapabilitySCADA/EMS systems are constantly being upgraded,and some older systems may not possess the capabilityto incorporate dynamic ratings. This limitation is muchless common today than it was 5 to 10 years ago. It islikely that any new operational software will be capableof updating circuit ratings if provided by dynamic ratingcalculation programs.

Instrumentation ReliabilityInstruments may be used to monitor power transformeroil and winding hot spot temperatures, soil tempera-tures, weather conditions, and tension or sag of over-head lines. Instruments within the substation perimeterare generally safe from vandalism and protected to someextent from lightning and extreme weather conditions.Instruments mounted on overhead line structures and inunderground cable manholes are more vulnerable.

Verification of proper instrument function needs to beconsidered as part of any dynamic rating calculationsoftware. Ideally, indications of malfunction would bereported to system operations in conjunction withdynamic rating values to help in assessing the accuracyof dynamic ratings.

Availability and Reliability of Communication Links to SCADAIn many power systems, the number and capability ofcommunication links connecting remote substations toSCADA may be a limitation in implementing dynamicratings.

For overhead lines, where multiple monitors may berequired to ensure that worst-case locations areincluded, the number of real-time data values cominginto SCADA may be 10 or more. In this case, placementof computation in a substation location might be prefer-able to placement at a central location, since only the

line rating need be communicated to SCADA/EMS. Nosimilar advantage exists for substation equipment.

Communication of monitor data from remote locationsto a substation has been successfully accomplished bymeans of spread spectrum radio and by Cellular DigitalPacket Data (CDPD). Solar power sources are usuallyadequate for such low power transmitters and avoid allthe reliability issues inherent in supplying distributionpower in remote locations.

Rating VariabilityTo many system operators, one of the most annoyingaspects of dynamic ratings involves their variability. It isdifficult to establish system security if ratings are chang-ing rapidly.

There are several ways to minimize the variability ofdynamic ratings. The simplest method is to be sure thatthe rating variability is not based on monitor inaccuracyor communication problems.

Another method of limiting variability is through acombination of averaging and limiting the range ofdynamic rating values. Expressing dynamic ratings asthe moving average of values calculated over the lastseveral time intervals can reduce variability with little orno loss of accuracy. Limiting dynamic rating values tono more than 30% above static can be a simple methodof limiting variability.

Figure 6.6-1 illustrates how the use of a moving averagecalculation can reduce the variability of dynamic ratingsfor an overhead line.

Engineering AcceptanceEngineering personnel, both in asset management andoperations, typically question the accuracy of important

1500

1700

1900

2100

2300

2500

2700

0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48

Time-of-Day

Rat

ing

& L

oad

- am

pere

s

LTE-4Hr 6 per. Mov. Avg. (LTE-4Hr)

Figure 6.6-1 Dynamic ratings with moving average to reduce variability.

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calculated equipment parameters such as ratings. Cer-tainly, fundamentally, dynamic ratings need to be basedon the same equipment limitations as are used for staticratings. For example, with an overhead line, conven-tional static ratings are calculated for a maximum con-ductor temperature. That same maximum conductortemperature would also be used in performing dynamicrating calculations.

One way to improve engineering acceptance of dynamicratings is by using the same calculation method fordynamic ratings as is used for static ratings. For exam-ple, the EPRI DTCR software models power transform-ers with the same “Top Oil” and “Bottom Oil” modelsthat are used in the IEEE Loading Guide C57.92-1995and in the engineering program PTLOAD. The provi-sion of the PTLOAD software for static rating calcula-tions has been very helpful in gaining acceptance for theDTCR dynamic rating calculation method and eases theset-up and results checking necessary to verify thedynamic rating results.

6.7 FIELD STUDIES OF DYNAMIC RATINGS

Dynamic ratings have been employed to allow increasedloading of lines, power transformers, and undergroundcables. More recently, substation equipment has beenincluded in the list of equipment for which dynamic rat-ings may be applicable.

Real-time thermal algorithms have been developed foroverhead lines, underground cables, power transform-ers, and substation switches, bus, and line traps. Most ofthe research has centered on verifying these algorithmswith field test data.

6.7.1 Overhead Lines

The potential increase in thermal rating of overheadlines through the use of dynamic rating methods islarger than for other power equipment. As a result,there have been many field studies of lines.

A variety of overhead line thermal model algorithmshave been field tested. (Examples are the EPRI“DYNAMP” algorithm [Black and Byrd 1983], theIEEE P738 thermal model, and a slightly differentmodel proposed by CIGRE Study Committee 22[CIGRE 1997].) Each algorithm is capable of trackingthe present conductor temperature based on real-timeweather station data and on line current or on sag ortension monitor data.

A study by Schmidt (Schmidt 1997) indicates that anydifference between these algorithms and the IEEE Stan-dard 738-1993 (IEEE 1993) is quite small, particularly

when compared to differences produced by measure-ment methods. That is, given a certain series of chrono-logical weather and load values, each real-timealgorithm will yield very similar calculated temperatures(and consequently, dynamic ratings).

Conclusions based on these field measurements includethe following:

1. For a line section (multiple suspension spans havingnearly the same tension), limited by electrical clear-ance, dynamic ratings based on a single sag or ten-sion monitor are more accurate than those based ona single weather station or temperature monitor.

2. For lines consisting of many line sections, multiplemeasurement locations coupled by radio communi-cation links are necessary for accurate dynamic ratingcalculations of the whole line.

3. At low wind speeds, when the dynamic rating is low-est and most sensitive to weather, the prediction ofwind direction and persistence is nearly impossibledue to limitations on equipment and the turbulentnature of low speed winds.

In particular, Figure 6.7-1 illustrates the need tomonitor multiple line sections for long lines. It showsthe dynamic rating of each of four different line sec-tions (from the same line) over a 24- hour period.Note that the limiting line section (the section withthe lowest rating) varies during the day. Thus allwould need to be monitored to ensure a safe dynamicrating for the whole line.

4. At current levels less than 0.5 A per kcmil, dynamicthermal ratings determined by sag or tension moni-tors are not accurate.

Figure 6.7-1 Variation in limiting line section for a monitored 230-kV line.

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6.7.2 Power Transformers

Three distinct dynamic loading algorithms are availablein the DTCR software to model power transformers.These are based on the IEEE Top Oil model (IEEE1996), the IEEE Bottom Oil model (IEEE 1996) and the“IEC” model (IEC 1991). As is the case for overheadlines, except for very short time loads, the calculateddynamic loadings using the three models for powertransformers are relatively similar. Each requires slightlydifferent transformer test data (the IEEE Bottom Oilmodel requiring considerably more detailed test datathan the other two). The more complex Bottom Oilmodel does a better job modeling short-time loads.

In comparison to overhead lines and undergroundcable, real-time monitoring and dynamic loading ofpower transformers offer some special difficulties:

• The critical transformer temperature is the windinghot spot. Normally, it is impossible to directly mea-sure the hottest spot winding temperature in oldertransformers without a fiber optic hot spot monitor.

• All the transformer dynamic loading calculationmodels require laboratory test data for hot spot riseover top oil, which may be difficult or impossible tofind for a 40 year-old unit.

• In addition to maximum winding current limits, thedynamic thermal rating of power transformers maydepend on loss of insulation life, maximum oil tem-perature, maximum hot spot temperature, or the for-mation of bubbles in winding insulation.

• Auxiliary equipment such as bushings, conductorleads, tap changers, and associated protection limitsmay limit transformer dynamic loading.

• Protection settings must also be considered.Unwanted tripping could occur in overload situa-tions.

• Older units may be in poor condition requiring thatlimits on winding temperature and insulation loss-of-life be reduced below those of newer units.

6.7.3 Underground Cables

Many field tests of dynamic rating for undergroundcable circuits have been undertaken. By and large thisapplication of dynamic rating methods is the most suc-cessful. The dynamic rating of underground cable isdetermined by the loading of the cable (which varies)and the thermal resistivity of the surrounding soil, whichvaries between locations but not very much with time.

The thermal time constants associated with under-ground cables are much larger than those of other ele-

ments, even power transformers. As a result, short-timeemergency ratings for underground cable are normallymuch higher than for other types of power equipment.

Chapter 3 in this IPF Guidebook discusses the thermalrating of underground cable in considerable detail.

6.7.4 Substation Terminal Equipment

Substation terminal equipment consists of many differ-ent types and designs of power equipment. Included inthis classification are line traps, oil circuit breakers, SF6

circuit breakers, rigid tubular bus, line disconnects, cur-rent transformers, bolted connectors, and insulatedbushings.

The dynamic thermal rating of substation terminalequipment centers on practical, rather simple methodsthat avoid the use of monitoring instruments and dedi-cated communication links. In dynamically ratingequipment such as switches, bus, line traps, breakers,and power transformer auxiliary equipment, it must bekept in mind that replacement is generally less expensivethan for lines, cables, and transformers, and thereforethe more elaborate methods of monitoring are difficultor even impossible to justify economically. Also,because of the large number of switches, circuit break-ers, etc., in any power system, and the variety of designs,thermal models and weather monitoring must be keptsimple.

6.7.5 Power Circuits

Power systems are operated with the goal of maintain-ing a secure system wherein normal circuit loads are lessthan circuit normal ratings and post-contingency loads(mostly for the loss of a single major system compo-nent) are less than circuit emergency ratings. Most cir-cuits consist of multiple series circuit elements. Figure6.7-2 shows a simple circuit consisting of a switch andan overhead line segment. The static rating of the switchis 1200 A, and the line, consisting of Bunting ACSRconductor, is rated at 1310 A at 90°C. The static circuitrating is therefore 1200 A, limited by the switch.

Switch

Line Segment

Line Current

Figure 6.7-2 Circuit diagram for a simple transmission circuit.

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Using DTCR3 to model this circuit, we find that the linesegment limits the circuit for short-time emergency rat-ings, and either element can determine the LTE rating,depending on the wind speed (see Figure 6.7-3).

6.7.6 Communications and Monitoring

In early field tests, the DTCR software was installed oncomputers placed in the substation environment. Thisgenerally yielded unsatisfactory results, which includedhardware thefts, travel to remote locations to investigateproblems, and unreliable communications. In conse-quence, the software was modified in its most recent ver-sion to obtain real-time input from and send calculatedoutput to, volatile ASCII files on the PC. These files areread and written by simple SCADA-based software pro-grams.

Real-time monitors are interfaced with the SCADA sys-tem not with the dynamic loading computer, and calcu-lated dynamic thermal ratings are read into the SCADAdatabase from which they can be displayed according tothe wishes of each utility. The advantage of this arrange-ment is primarily one of simplicity and reliability. Otherbenefits include centralizing the DTCR applicationonto one computer, and having this computer near com-puter maintenance personnel.

The communication between remote monitors and theutility SCADA database is handled by separate com-mercial software and hardware, which has nothing to dowith the dynamic rating calculation software. Utilitieslikely have existing interface methods in use for otherapplications. They may choose the most appropriateinterface based on maintenance and ease of use criteria.

This arrangement also allows the utility operations peo-ple to display the calculation results in the fashion theyprefer rather than being forced to use the output screenprovided. The information may be dynamically linkedto transmission/generation scheduling or generationshedding systems. The calculated and measured infor-mation is available for data storage by a component ofan Energy Management System (EMS), making histori-cal information available to dispatchers.

The advantage of this arrangement is primarily one ofsimplicity and reliability. The communication betweenremote monitors and the utility SCADA database ishandled by separate commercial software and hardware,which has nothing to do with the dynamic rating calcu-lation software. This arrangement also allows the utilityoperations people to display the calculation results inthe fashion they prefer rather than being forced to usethe output screen provided.

6.8 CONCLUSIONS

Dynamic thermal rating methods apply to all powerequipment, indeed to all power circuits. By monitoringthe thermal environment and perhaps the equipmentitself in real-time, the utilization of thermal capabilitymay be safely increased.

Dynamic methods are capable of yielding an increase of5 to 15% in the effective thermal rating of most powerequipment, which can result in both more economicoperation and in postponement of equipment capitalinvestment in low growth areas.

Certain specific observations about dynamic ratings canbe made:

1. Real-time monitoring of power equipment may beused in evaluating dynamic loading methods, butmonitoring alone does not predict the future conse-quences of present loading. Dynamic loading meth-ods allow time for remedial action.

2. Dynamic rating methods require the cooperation oftransmission planners, operators, and engineers inorder to gain maximum benefit.

3. Wind is the most crucial factor in rating overheadlines correctly. Because of the variability of windalong the line, multiple monitoring locations arerequired, especially for long lines.

4. Power transformers are the most complex equipmentto rate dynamically since such methods involve limitson insulation life, oil and winding temperature, gasbubbles, and auxiliary equipment.

5. The most attractive candidates for dynamic thermalrating are those requiring the most capital to replace.

Figure 6.7-3 Short-time and long-time emergency dynamic thermal ratings of 1200 A switch and Bunting line segment.

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6. Dynamic thermal rating methods and the accurateprediction of post-contingency loadings are mostuseful in combination with fast-reaction load con-trols.

7. Real-time data should be obtained from directSCADA links rather than by direct telephone orradio communication with remote monitors.

8. Probabilistic ratings offer an attractive alternative todynamic rating methods for certain types of trans-mission equipment, provided the thermal models andfield data are accurate.

REFERENCES

ANSI. 1978. ANSI C57.13-1978. Requirements for Instrument Transformers.

ANSI. 1979a. ANSI C37.37-1979. Loading Guide for AC High-Voltage Air Switches (in excess of 1000 volts).

ANSI. 1979b. ANSI C37.010-1979. Application Guide for AC High Voltage Circuit Breakers rated on a Sym-metrical Current Basis.

ANSI. 1981. ANSI C93.3, 1981. Requirements for Power-Line Carrier Line Traps.

Black, W. Z. and W. R. Byrd. 1983. “Real Time Ampac-ity Model for Overhead Lines.” IEEE Transactions. Vol. PAS-102. No. 7. July. pp. 2289–2293.

CIGRE. 1997. CIGRE WG12-22. “Thermal State of Overhead Line Conductors.” Electra. No. 121. pp. 51-67.

Coneybeer, Robert T. 1992. “Transient Thermal Models for Substation Transmission Components.” Master's Thesis. School of Mechanical Engineering, Georgia Institute of Technology.

Conway, B. J. et al. 1979. “Loading of Substation Elec-trical Equipment with Emphasis on Thermal Capabil-ity.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-98. No. 4. July/August. pp. 1394–1419.

Cronin, John. 1972. “Rate Substation Equipment for Short-time Overloads.” Electrical World Magazine. April 15.

Douglass, D. A. and A. Edris. 1996. “Real-time Moni-toring and Dynamic Thermal Rating of Power Trans-mission Circuits.” IEEE Transactions on Power Delivery. Vol. 11. No. 3. July.

Douglass, D. A. and A. Edris. 1999. “Field Studies of Dynamic Thermal Rating Methods for Overhead Lines.” IEEE T&D Conference Report. New Orleans. April 7. New Orleans, LA.

Edris, A. 2000. “FACTS Technology Development: An Update.” IEEE Power Engineering Review. Vol. 20. No. 3. March.

IEEE. 1993. IEEE Standard 738-1993. “Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors.”

IEEE. 1996. IEEE Standard C57.91-1995. “IEEE Guide for Loading Mineral-Oil-Immersed Transform-ers.” April 25.

International Electrotechnical Commission. 1982. IEC-287. “Calculation of the Continuous Current Rating of Cables (100% Load Factor).”

International Electrotechnical Commission. 1989. IEC-853-2. “Calculation of the Cyclic and Emergency Cur-rent Rating of Cables.” 1st Edition.

International Electrotechnical Commission. 1991. IEC International Standard 354. 2nd Edition, “Loading Guide for Oil-immersed Power Transformers.”

Massey, D. E. et al. 1971 “Determination of Discon-necting Switch Ratings for the Pennsylania-New Jersey– Maryland Interconnection.” IEEE Symposium on High Power Testing. Portland, OR. July.

Neher, J. H. and M. H. McGrath. 1957. “The Calcula-tion of the Temperature Rise and Load Capability of Cable Systems.” Paper 57-660. AIEE Insulated Conduc-tors Committee. June.

Schmidt, N. 1997. “Comparison between IEEE and CIGRE Ampacity Standards.” IEEE PE-749-PWRD-0-06-1997. Berlin, Germany. July.

Seppa, T. O. et al. 1998. “Use of On-Line Tension Mon-itoring Systems for Real Time Ratings, Ice Loads and Other Environmental Effects.” CIGRE Report 102-22. September. Paris, France.

6-22


G-1

Glossary

AAAC. All Aluminum Alloy Conductor. (Chapter 2)

AAC. All Aluminum Conductor. (Chapter 2)

ACAR. Aluminum Conductor Alloy Reinforced. (Chapter 2)

ACCR. Aluminum Conductor Composite Reinforced.(Chapter 2)

ACSR. Aluminum Conductor Steel Reinforced. (Chapter 2)

ACSS. Aluminum Conductor Steel Supported. (Chapter 2)

AEIC. Association of Edison Illuminating Companies.(Chapter 3)

Aeolian Vibration. Most common type of wind-inducedmotion of conductors. The vibration is caused by thealternate shedding of wind-induced vortices from thetop and bottom sides of the conductor. This action cre-ates an alternating pressure unbalance, inducing theconductor to move up and down at right angles to thedirection of the air flow. This vibration occurs at rela-tively low wind speeds, and conductor fatigue damage iscumulative in nature. (Chapter 2)

Aluminum Conductor Steel Supported (ACSS). Conduc-tor design consisting of fully annealed strands of alumi-num (1350-H0) stranded around stranded steel core.The steel core wires may be aluminized, galvanized, oraluminum clad, and are normally “high strength,” hav-ing a tensile strength about 10% greater than standardsteel core wire. (Chapter 2)

Ampacity. The ampacity of a conductor is that maxi-mum constant current that will meet the design, secu-rity, and safety criteria of a particular line on which theconductor is used. In this Guidebook, ampacity has thesame meaning as “steady-state thermal rating.” (Chap-ter 2)

Annealing. Process wherein the tensile strength of cop-per or aluminium wires is reduced at sustained hightemperatures. (Chapter 2)

ASTM. American Society for Testing and Materials.(Chapter 2)

Bottom Oil Model. One of several methods of modelingthe winding temperature of power transformers. Tem-perature calculation methods presented in the 1995 revi-sion of IEEE C57.91 as Annex G. See also Top OilModel and IEC Model 354-1991. (Chapter 4)

CGIT. See Compressed Gas Insulated Transmission.(Chapter 3)

Compressed Gas Insulated Transmission (CGIT) Cables.A system of SF6 gas and epoxy insulators used to insu-late a hollow, rigid aluminum conductor from a tubularaluminum enclosure. The most common applicationsfor CGIT lines are situations where very high ampaci-ties are required (i.e., > 2000 A), usually to connect withoverhead lines entering a station or as a high-capacitybus within a station. (Chapter 3)

Conductor Hardware. Noncurrent carrying devicesattached directly to the conductor. Conductor hardwareincludes components such as suspension clamps (withor without armor rods), dampers, repair sleeves andsplices, spacers and spacer dampers, shackles, pins, etc.(Chapter 2)

Continuous (Normal) Rating. Current at this level (MVAor amperes) may continue indefinitely without withoutexceeding agreed-upon maximum (Normal) tempera-tures for conductors or critical components in all typesof power equipment. (Chapter 6)

Core-Form Construction. Power transformer design con-structed with windings that are in the general form ofconcentric cylinders. (Chapter 4)

Glossary Increased Power Flow Guidebook

G-2

Creep Elongation. Creep constitutes an irreversible,plastic elongation occurring in the aluminum strands ofbare overhead conductor, which occurs as a result oftension over extended periods of time. Higher rates ofcreep occur when a conductor is operated for extendedperiods of time at operating temperatures in excess ofapproximately 50°C. (Chapter 2)

Cross-Linked Polyethylene (XLPE) Cables. Most com-mon on modern XD cable systems with applications upto 500 kV. The insulation is cross-linked (vulcanized),forming long polymer chains that are joined to oneanother at intermediate carbon atoms. (Chapter 3)

Deterministic Methods. Method of uprating overheadtransmission lines (without reconductoring) using tradi-t ional ca lcu lat ion methods, such as the EPRIDYNAMP program, with fixed, worst-case weathercondition assumptions. (Chapter 2)

Direct Flow Design. Design of power transformeremploying forced oil cooling. The transformer internalassembly is designed with oil manifolds that direct theincoming cool oil to the lower part of the core andwindings. A directed flow design is normally used withlarger sizes of transformers equipped with heat exchang-ers rather than radiators. (Chapter 4)

DTCR. See Dynamic Thermal Circuit Rating. (Chapter 3)

Dynamic Rating. Limits on the level and duration ofpower carried by power equipment based on actualweather conditions. (Chapter 2)

Dynamic Thermal Circuit Rating (DTCR). EPRI softwaredeveloped to take real-time data from “off the shelf ”monitoring hardware, and determine optimal ratings(not worst-case) for the conditions at the time the rat-ings were performed. (Chapter 3)

Emergency Rating. Conductor rating that specifies howmuch current can flow through power equipment underemergency conditions for a specified amount of time—e.g., 30 minutes. (Chapter 2)

EPR. See Ethylene-Propylene-Rubber. (Chapter 3)

Ethylene-Propylene-Rubber (EPR) Cables. Insulationtype often considered for distribution cables and trans-mission cables up to 138 kV. The insulation is very“lossy” as compared to XLPE insulation, resulting inhigh dielectric losses and charging current. (Chapter 3)

Exceedance Level. Amount of time a conductor exceedsthe design temperature expressed as a percentage oftotal time. (Chapter 2)

Extruded Dielectric (XD) Cables. Cables are so namedbecause the insulation is extruded onto the conductorcore, as compared to paper-insulated cables (HPFF orSCFF), where the insulation is a laminar application ofpaper tapes. Three types of XD cables include: cross-linked polyethylene (XLPE) cables, ethylene-propylene-rubber (EPR) cables, and linear low- or medium-densitypolyethylene (LLPE, MDPE) cables. (Chapter 3)

Factory Heat Run. A direct measurement of the thermalperformance of a transformer at a particular bench-mark, the nameplate rating. Two methods are used toperform factory heat runs: the “short-circuit” methodand the “loading-back” method. (Chapter 4)

Flexible AC Transmission System (FACTS). A powerelectronic-based technology for enhancing controllabil-ity and increasing power transfer capability of transmis-sion circuits. FACTS controllers provide the systemoperator with the means of rapidly controlling loads onparticular circuits in order to maximize power transfercapability of transmission corridors. (Chapter 6)

Fluidized Thermal Backfill (FTB). Fill used in trenches forunderground cable that helps ensure good heat transferaway from the cable pipes. (Chapter 3)

Gapped ACSR (GTACSR). Type of high-temperature con-ductor invented in Japan, which consists of a conven-tional steel core surrounded by layers of trapezoidalzirconium aluminum wires, and the gap filled with grease.The zirconium aluminum does not anneal until reachingtemperatures in excess of 200oC. Through the use of spe-cial terminations and suspension clamps and by preload-ing the steel core, the thermal elongation of theconductor is less than that of conventional ACSR, whilemaintaining the full strength of a conventional ACSRconductor under heavy ice conditions. (Chapter 2)

High-Pressure, Fluid-Filled (HPFF) Pipe-Type Cables.One of two kinds of pipe-type cables (the other beingHPGF). HPFF cables are installed in cable pipes wherethe pipe is filled with very clean, very low moisturedielectric fluid. Older HPFF cable systems (before 1970)typically used mineral oil for the pipe filling dielectricfluid. HPFF cable systems installed after 1970 have usedalkyl benzene or polybutene dielectric fluid. (Chapter 3)

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Increased Power Flow Guidebook Glossary

High-Pressure, Gas-Filled (HPGF) Pipe-Type Cables. Oneof two kinds of pipe-type cables (the other beingHPFF). HPGF cables use pressurized dry nitrogen gasinside the cable pipe. (Chapter 3)

High-Temperature, Low-Sag (HTLS) Conductors. Con-ductors capable of continuous operation at tempera-tures above 100oC with stable tensile strength and creepelongation properties. Such conductors are commer-cially available or under development. (Chapter 2)

HPFF. See High-Pressure, Fluid-Filled. (Chapter 3)

HPGF. See High-Pressure, Gas-Filled. (Chapter 3)

HTLS. See High-Temperature, Low-Sag Conductors.(Chapter 2)

ICEA. Insulated Cable Engineers Association. (Chapter 3)

Ice Galloping. Wind-induced conductor motion occur-ring with both single and bundled conductors, andrequiring high winds and ice on the conductors. (Chap-ter 2)

IEC. International Electrotechnical Commission (Chap-ter 3) or International Engineering Consortium (Chap-ter 2)

IEC Model 354-1991. One of several methods of model-ing the winding temperature of power transformers. Seealso Top Oil Model and Bottom Oil Model. (Chapter 4)

IEEE. The Institute of Electrical and Electronics Engi-neers. (Chapter 3)

Invar Steel. A type of steel core wire used in transmis-sion conductors, which has a high nickel content. It hasa 15-20% lower tensile strength than conventional gal-vanized steel wire and a much lower coefficient of ther-mal expansion than regular high-strength steel wire.(Chapter 2)

Knee-point Temperature. The conductor temperatureabove which the aluminium strands of an ACSR con-ductor have no tension or go into compression. (Chap-ter 2)

Linear Low- or Medium-Density Polyethylene (LLPE,MDPE) Cables. Insulation type less common for newinstallations, although there are several installations,predominantly in France. As compared to XLPE insula-tion, LLPE and MDPE were first used at the highervoltage levels because the extrudate could be raised to

higher temperatures without forming cross-linkingagents present. (Chapter 3)

LLPE. See Linear Low-Density Polyethylene. (Chapter 3)

Load Losses. Losses generated by transformers thatvary with load current but not with excitation.(Chapter 4)

Long-Term Emergency (LTE) Rating. A rating where thethermal heat storage capacity of the equipment does notgreatly impact the rating. For power transformers, thebulk oil time constant makes this definition a bit uncleargiven the cyclic variation in load and air temperature.Sometimes defined as a rating greater than 2 to 4 hoursin duration. (Chapter 4)

Mass Impregnated (MI) Cables. Cables sometimes usedup to 69 kV for ac systems, although they are not thatcommon at this voltage. These cables have paper tapesthat are impregnated with a high-viscosity dielectricfluid. MI cables are used for ac applications, but aremore common for HVDC submarine applications wherethere may be a significant change in elevation along thecable route that would otherwise be complicated byhydrostatic head pressures. (Chapter 3)

MDPE. Medium-Density Polyethylene. (Chapter 3)

MI. See Mass Impregnated. (Chapter 3)

NESC. National Electric Safety Code. (Chapter 2)

No-Load Losses. Losses generated by transformers thatdo not vary with load current but rather vary with exci-tation or voltage. (Chapter 4)

Normal Rating. Power equipment thermal rating thatspecifies how much current may flow in the circuit on acontinuous basis. (Chapter 4)

ODAF (Directed FOA). One of four cooling configurationsused by oil-immersed power transformers. Pumps areused to circulate the oil. Fans are used to force air overthe radiators or heat exchangers. The forced circulationof the oil increases the convective heat transfer from thewindings to the oil. The forced air increases the convec-tive heat transfer from the oil to the air. With ODAF,ducts are added to direct the oil over the winding. Thisforces a significant portion of the forced oil to flowupward through the vertical winding ducts. (Chapter 4)

OFAF (Non-directed FOA). One of four cooling configu-rations used by oil-immersed power transformers.Pumps are used to circulate the oil. Fans are used to

Glossary Increased Power Flow Guidebook

G-4

force air over the radiators. The forced circulation of theoil increases the convective heat transfer from the wind-ings to the oil. The forced air increases the convectiveheat transfer from the oil to the air. With OFAF, thereare no ducts to direct the oil over the winding. In gen-eral, the bulk of the forced oil flow passes upwardbetween the winding and the tank, bypassing the wind-ings. (Chapter 4)

ONAF (FA). One of four cooling configurations used byoil-immersed power transformers. No pumps are usedto circulate the oil. Fans are used to force air over theradiators to increase heat transfer from the bulk oil tothe surrounding air. As with ONAN, oil circulatesupward through the windings and down through theradiators by natural thermosiphon flow. (Chapter 4)

ONAN (OA). One of four cooling configurations used byoil-immersed power transformers. Also referred to asself-cooled, no pumps are used to circulate oil, and nofans are used to increase airflow over the radiators. Oilcirculates upward through the windings and downthrough the radiators by natural thermosiphon flow.(Chapter 4)

Paper Insulated Lead Covered (PILC) Cables. Cablessometimes used up to 69 kV for ac systems, althoughthey are not that common at this voltage. Upratingapproaches would be somewhat similar to those ofextruded or self-contained cables. These cables havepaper tapes that are impregnated with a high-viscositydielectric fluid. (Chapter 3)

PILC. See Paper Insulated Lead Covered. (Chapter 3)

Probabilistic Line Rating Methods. Methods that use theactual weather data and conditions prevailing on a con-ductor to determine the likelihood or probability of acertain condition occurring. Probabilistic methodsinclude the Absolute Method, the Exceedance Method,the Modified Exceedance Method, and the SafetyMethod. (Chapter 2)

Quasi-Dynamic (Real-Time) Ratings. Quasi-dynamicratings are applied by monitoring load and tempera-tures for a period of time and then calculating what theconductor temperature might be as a result of that load.From this, the temperature of the cable conductor atrated temperature can be extrapolated for rating pur-poses. (Chapter 3)

Rated Breaking Strength (RBS). Breaking strength of abare overhead conductor as calculated by the methodsdescribed in appropriate ASTM or IEC manufacturingstandards. (Chapter 2)

Ruling (Effective) Span. Hypothetical level span lengthwherein the variation of tension with conductor temper-ature is the same as in a series of suspension spans.(Chapter 2)

Sagging Line Mitigator (SLiM). A new class of line hard-ware that uses a shape-memory alloy actuator, activatedby increased temperature, to reduce excessive sag in con-ductors. (Chapter 2)

Sag-Tension Calculations. Calculations performedusing numerical programs in order to determine the sagand the tension of a conductor catenary as a function ofice and wind loads, conductor temperature, and time.(Chapter 2)

Self-Contained Liquid-Filled (SCLF) Cables. Cables uti-lizing the dielectric liquid impregnated laminated paperinsulation similar to pipe-type cables, but with three sep-arate cables installed for the three phases. The cable iscalled “fluid-filled” because there is a hollow fluid chan-nel in the center of the conductor that allows dielectricliquid to move through the cable with thermal expan-sion and contraction. Also known as self-contained oil-filled (SCOF) or low-pressure oil-filled (LPOF). (Chap-ter 3)

Self-Contained Oil-Filled (SCOF) Cables. Cables utiliz-ing the dielectric liquid impregnated laminated paperinsulation similar to pipe-type cables, but with three sep-arate cables installed for the three phases. Also knownas self-contained liquid filled (SCLF). (Chapter 3)

Shell-Form Construction. Power transformer design inwhich windings are initially assembled flat with insula-tion and cooling ducts between sections. Completephase assemblies are then clamped and oriented in avertical direction so that the plane of the individual sec-tions are upright. (Chapter 4)

Short-Term Emergency (STE) Rating. Short-term rat-ings are usually defined as extremely short duration rat-ings that take advantage of the thermal capacity of theequipment. These ratings range from 5 to 30 minutes induration. (Chapter 4)

SIL. See Surge Impedance Loading. (Chapter 3)

Simulated Winding Temperature Indicator (WTI). Themost common device for measuring winding tempera-tures in power transformers. These devices simply mea-sure the temperature of a specially calibrated heatingelement that is immersed in the top bulk oil near thetank wall. (Chapter 4)

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Increased Power Flow Guidebook Glossary

SLiM. See Sagging Line Mitigator. (Chapter 2)

Static Ratings. Limits on the level and duration ofpower transferred over a line based on specified worst-case weather conditions. (Chapter 2)

Stray Flux Heating. Heating of non-current carryingmetal components by the leakage flux of the windingsand leads. The leakage flux induces eddy current in anyconducting material that it passes through. Thisincludes the steel clamping structure, tie rods or tieplates, metal core bands, and the tank wall itself. Sinceleakage flux varies proportionally with load current, thestray flux heating increases roughly with the square ofwinding current. For larger power transformers andGSUs in particular, the problem of stray flux heatingcan be substantial. (Chapter 4)

Subconductor Oscillation. Wind-induced conductormotion occurring with bundled phase conductors whenwind speeds exceed a certain critical velocity. (Chapter 2)

Surge Impedance Loading (SIL) Limits. Limits involvinga greater than allowable phase shift in power frequencyfrom one end of a transmission system to the other. As aresult, the two ends of the system cannot remain syn-chronous, resulting in instability and outages. This sys-tem stability consideration is generally an issue onoverhead transmission lines that are 80-320 km (50-200miles) in length. (Chapter 3)

TACSR. See Thermal-resistant Aluminum ConductorSteel Reinforced. (Chapter 2)

Thermal Elongation. Metallurgical phenomenon in con-ductors where the material increases in length in pro-portion to an increase in temperature. (Chapter 2)

Thermal Property Analyzer (TPA). Device used for fieldand laboratory measurement of thermal resistivity.(Chapter 3)

Thermal-resistant Aluminum Conductor Steel Rein-forced (TACSR). Conductor widely used in Japan, with aspecial type of aluminum strand capable of operating attemperatures up to 150oC without losing tensilestrength. (Chapter 2)

Time-To-Overload (TTO). Parameter indicating to thesystem operator how much time is left until equipmenttemperatures exceed safe limits. (Chapter 6)

Top Oil Model. One of several methods of modeling thewinding temperature of power transformers. Tempera-ture calculation methods presented in Clause 7 of IEEEC57.91-1995. See also Bottom Oil Model and IECModel 354-1991. (Chapter 4)

Trapezoidal Wire (TW). Aluminum trapezoidal wire usedin conductors in place of round wires, which therebypotentially increases the cross-sectional area of a roundwire conductor of the same diameter by approximately20%. (Chapter 2)

Upgrading. Using available infrastructure to economi-cally put in new cables. (Chapter 3)

Uprating. Improving the capacity of existing equipment.(Chapter 3)

Video Sagometer. EPRI device, based on digital videotechnology, for monitoring conductor sag in real time.(Chapter 2)

Voltage Drop. Limit placed on power flow correspond-ing to the maximum allowable decrease in voltage mag-nitude. (Chapter 2)

“Worst-case” Weather Conditions for Line Rating Calcu-lation. Weather conditions that yield the maximum ornear-maximum value of conductor temperature for agiven line current. (Chapters 2 and 5)

XD. See Extruded Dielectric. (Chapter 3)

XLPE. See Cross-Linked Polyethylene. (Chapter 3)

ZTACIR. ZTAL aluminium alloy conductor reinforced byan Invar steel core. (Chapter 2)

ZTAL (“Super Thermal-resistant Aluminium”). An alu-minium zirconium alloy that has stable mechanical andelectrical properties after continuous operation at tem-peratures of up to 210oC. (Chapter 2)


I-1

Index

All references are to section or subsection numbers.

AAAC

Sag-tension calculations, 2.2.3ACCR, 2.6.7ACSR

High-temperature sag, 2.2.3Sag-tension models, 2.4.3

ACSS, 2.6.3Air-core reactor, 5.3.3Ampacity, 3.4.2

Ampacity audit, 3.6.5Calculating ampacity, 3.4.5Effect of various parameters, 3.4.6Increasing ampacity (of underground cables), 3.6

Annealing, 2.4.2

BBus conductors, 5.3.1Bushings, 5.3.6

CCase studies

Overhead, 2.8Underground, 3.9

CGIT (Compressed Gas-Insulated Transmission) cables, 3.2.4

Compressed gas-insulated transmission cables, 3.2.4Conductor blowout, 2.2.4Conductor hardware, 2.4.14Constraints on uprating overhead transmission lines, 2.2Constraints on uprating underground cables, 3.5Continuous (normal) rating, 6.6.1Creep elongation, 2.4.12Cross-linked polyethylene, 3.2.2Current transformers, 5.3.7

DDTCR (Dynamic Thermal Circuit Rating), 2.7.5, 3.8.2,

3.8.3, 6.5Dynamic monitoring, 2.7

Real-time monitors, 2.7.5Video sagometer, 2.7.5

Dynamic ratings (overhead transmission), 2.3.1, 2.7.2Advantages, 2.7.3, 3.8.3Calculations, 2.7.6Disadvantages, 2.7.4Underground cables, 3.8

Dynamic ratings (underground cables), 3.8, 6.4.4Benefits, 3.8.3Dynamic Thermal Circuit Ratings, 3.8.2Monitoring, 3.8.4Quasi-dynamic ratings, 3.8.5

Dynamic Thermal Circuit Rating (DTCR), 2.7.5, 3.8.2,3.8.3, 6.5

DTCR output, 6.5.2Power circuit modeling, 6.5.1

Dynamic Thermal RatingsCondition assessment and real-time monitors, 6.3Costs, 6.2.2Field studies, 6.7Models, 6.4

Accounting for heat storage, 6.4.1Overhead lines, 6.4.2Power Transformers, 6.4.3Substation terminal equipment, 6.4.5Underground cables, 6.4.4

Operating with dynamic thermal ratings, 6.6

EElectric field, 1.3.5Electrical clearance, 2.2.5Elongation

Creep elongation, 2.4.12Thermal elongation, 2.4.11

Emergency ratings, 2.4.1, 3.4.7Environmental limits (for overhead transmission lines),

1.3.5, 2.1.4EPR (Ethylene-Propylene-Rubber) cables, 3.2.2Ethylene-Propylene-Rubber cables, 3.2.2Extruded dielectric, 3.2.2

FFACTS (Flexible AC Transmission Systems), 1.3.3, 6.2.3Flexible AC Transmission Systems, 1.3.3, 6.2.3

Index Increased Power Flow Guidebook

I-2

GGapped Construction, 2.6.6

HHeat balance methods, 2.3.5

Convection, 2.3.5Ohmic losses, 2.3.5Radiation, 2.3.5Solar heating, 2.3.5Steady-state thermal rating, 2.3.5

High-temperature operations (of overhead transmissionlines), 2.4

Connectors at high temperature, 2.4.13High-pressure fluid-filled cables, 3.2.1High-pressure gas-filled cables, 3.2.1High-pressure pipe-type cables, 3.2.1Hot spots

Identification (underground cables), 3.5.6Remediation (underground cables), 3.6.6

HPFF (High-Pressure Fluid-Filled) cables, 3.2.1HPGF (High-Pressure Gas-Filled) cables, 3.2.1Hybrid (underground and overhead) circuits, 3.3.3Hydraulic circuit, 3.5.8

IIce loading, 2.2.7Invar steel core conductor, 2.6.5

LLimiting conditions, 1.3

Circuit power flow limits, 1.3.1Environmental limits, 1.3.5Surge impedance loading of line, 1.3.2, 3.3.1Thermal limits, 1.3.4, 3.3.1Voltage drop limitations, 1.3.3

Linear low-density polyethylene cables, 3.2.2Line traps, 5.3.8LLPE (Linear Low-density Polyethylene) cables, 3.2.2Long-time emergency rating, 6.6.1Losses (underground cables), 3.4.3

MMagnetic field, 1.3.5Mass impregnated cables, 3.2.4MDPE (Medium-Density Polyethylene) cables, 3.2.2Medium-density polyethylene cables, 3.2.2MI (Mass Impregnated) cables, 3.2.4Modeling

Complex interfaces, 6.5.5Power circuits, 6.5.1

Monitoring (underground cables), 3.8.4

NNational Electric Safety Code, 2.2.5NESC (National Electric Safety Code), 2.2.5Normal rating, 2.4.1

OOhmic losses, 2.3.5Oil circuit breakers, 5.3.4Operating with dynamic thermal ratings, 6.6Overhead transmission lines

Case studies, 2.8Dynamic monitoring and line rating, 2.7

Disadvantages, 2.7.4Dynamic rating calculations, 2.7.6Dynamic ratings versus static ratings, 2.7.2Real-time monitors, 2.7.5

Dynamic thermal rating models, 6.4.2Effects of high-temperature operations, 2.4

Annealing of aluminum and copper, 2.4.2Axial compressive stresses, 2.4.4Built-in stresses, 2.4.5Calculation of conductor high-temperature sag

and tension, 2.4.8Conductor hardware, 2.4.14Connectors at high temperature, 2.4.13Creep elongation, 2.4.12Sag and tension of inclined spans, 2.4.7Sag-tension calculations, 2.4.6Sag-tension models for ACSR conductors, 2.4.3Thermal elongation, 2.4.11Wind speed effects on thermal ratings, 2.4.10

Line thermal ratings, 2.3Heat balance methods, 2.3.5Line design effects on line ratings, 2.3.4Maximum conductor temperature, 2.3.2Transient thermal ratings, 2.3.7Weather conditions for rating calculations, 2.3.3,

2.3.6Reconductoring without structural modifications, 2.6

ACCR conductor, 2.6.7ACSS and ACSS/TW, 2.6.3Gapped construction, 2.6.6High temperature aluminum alloy conductors,

2.6.4Invar steel core, 2.6.5TW aluminum wires, 2.6.2

Uprating constraints, 2.2Constraints on structural loads, 2.2.7Electrical clearance, 2.2.5Environmental effects, 2.2.8High-temperature sag, 2.2.3Loss of conductor strength, 2.2.6Sag-tension calculations, 2.2.2Wind-induced conductor motion, 2.2.4

Uprating without reconductoring, 2.5Deterministic methods, 2.5.2“Measure of Safety” as a basis for line rating,

2.5.4Probabilistic methods, 2.5.3Sagging Line Mitigator, 2.5.6

I-3

Increased Power Flow Guidebook Index

PPipe-type cables, 3.2.1Power flow example, 1.2Power flow limits, 3.3

Load flow considerations, 3.3.2Stability limits, 3.3.1Surge impedance loading limits, 3.3.1Thermal limits, 3.3.1Uprating hybrid circuits, 3.3.3

Power system issues, 1.2Power transformers

Design, 4.2Cooling types, 4.2.2Core-form construction, 4.2.1Directed flow designs, 4.2.1Factory testing, 4.2.4Losses, 4.2.3Shell-form construction, 4.2.1

Dynamic thermal rating models, 6.4.3Examples, 4.8Modest increases in capacity, 4.7Risks of increased loading, 4.3

Long-term risks, 4.3.2Short-term risks, 4.3.1

Thermal modeling, 4.4Bottom oil model, 4.4.3, 6.4.3IEC model, 4.4.4, 6.4.3Mechanisms of heat transfer, 4.4.1Proposed IEC model, 4.4.5Top oil model, 4.4.2, 6.4.3

Thermal ratings, 4.5Ambient air temperature, 4.5.1Condition-based loading, 4.5.5Load, 4.5.2Maintenance considerations, 4.5.6Rating procedure, 4.5.4Rating type and duration, 4.5.3

Winding temperature measurement, 4.6

QQuasi-dynamic ratings (underground cables), 3.8.5

RRatings

Continuous (normal) rating, 6.6.1Emergency ratings, 2.4.1, 3.4.7Long-time emergency rating, 6.6.1

Short-time emergency rating, 6.6.1Traditional rating definitions, 6.6.1Underground cable ratings, 3.4

Reconductoring Overhead transmission lines, 2.6Underground cables, 3.7

Resistances (underground cables), 3.4.4Route thermal survey, 3.6.1

SSag

High-temperature sag with aluminum conductors,2.2.3

High-temperature sag with ACSR, 2.2.3High-temperature sag-tension calculations, 2.4.9SAG10, 2.2.2, 2.4.8, 2.4.9Sag and tension of inclined spans, 2.4.7Sag-tension calculations, 2.2.2, 2.4.6, 2.4.8, 2.5

Tension-elongation diagram, 2.2.2Sag-tension models, 2.4.3

Sagging Line Mitigator, 2.5.5SCLF (Self-Contained Liquid-Filled) cables, 3.2.3Self-contained liquid-filled cables, 3.2.3SF6 circuit breakers, 5.3.5Shield/sheath bonding scheme, 3.6.8Short-time emergency rating, 6.6.1SIL (Surge Impedance Loading), 1.3.2, 2.1.1, 3.3.1SLiM (Sagging Line Mitigator), 2.5.5Stability limits, 3.3.1Static ratings, 2.3.1STESS software, 2.2.3Substation terminal equipment

Dynamic thermal rating models, 6.4.5Equipment types and IPF opportunities, 5.2

Rating parameters, 5.2.1Thermal models, 5.3

Air-core reactor, 5.3.3Bus conductors, 5.3.1Bushings, 5.3.6Current transformers, 5.3.7Line traps, 5.3.8Oil circuit breaker, 5.3.4SF6 circuit breaker, 5.3.5Switch (air disconnect), 5.3.2

Thermal parameters, 5.5Uprating, 5.4

Maintenance and inspection procedures, 5.4.2Monitoring and communications, 5.4.1Reliability and consequences of failure, 5.4.3

Superconducting cables, 3.7.5Surge impedance loading, 1.3.2, 2.1.1, 3.3.1Switches (air disconnect), 5.3.2

TT-Aluminum Conductor Steel Reinforced (TACSR),

2.6.4Temperature monitoring (underground cables), 3.6.4Tension-elongation diagram, 2.2.2Thermal elongation, 2.4.11Thermal limits, 1.3.4, 2.1.3, 3.3.1Thermal models

Substation terminal equipment, 5.2.1, 5.3Underground cables, 4.4

Index Increased Power Flow Guidebook

I-4

Thermal ratingsOverhead transmission lines, 2.3

Dependence on weather conditions, 2.3.6Dynamic ratings, 2.3.1Heat balance methods, 2.3.5Maximum conductor temperature, 2.3.2Static ratings, 2.3.1Transient thermal ratings, 2.3.7Weather conditions for rating calculation, 2.3.3Wind speed, 2.4.10

Power transformers, 4.5Ambient air temperature, 4.5.1Condition-based loading, 4.5.5Load, 4.5.2Maintenance considerations, 4.5.6Rating procedure, 4.5.4Rating type and duration, 4.5.3

Transformers. See Power transformers.TW aluminum wires, 2.6.2

UUnderground cables

Cable system types, 3.2Compressed gas insulated transmission, 3.2.4Extruded dielectric, 3.2.2High-pressure pipe-type, 3.2.1Mass impregnated, 3.2.4Paper insulated lead covered, 3.2.4Self-contained liquid-filled, 3.2.3

Case studies, 3.9Dynamic ratings, 3.8, 6.4.4

Benefits, 3.8.3Dynamic Thermal Circuit Ratings, 3.8.2Monitoring, 3.8.4Quasi-dynamic ratings, 3.8.5

Increasing ampacity, 3.6Active uprating, 3.6.7Ampacity audits, 3.6.5Evaluation of load patterns, 3.6.3Remediation of “hot spots,” 3.6.6Review circuit plan and profile, 3.6.2Route thermal survey, 3.6.1Shield/sheath bonding scheme, 3.6.8Temperature monitoring, 3.6.4

Power flow limits and system considerations, 3.3Load flow considerations, 3.3.2Stability limits, 3.3.1Surge impedance loading limits, 3.3.1Thermal limits, 3.3.1Uprating hybrid circuits, 3.3.3

Ratings, 3.4Ampacity, 3.4.2, 3.4.5, 3.4.6Emergency ratings, 3.4.7Equivalent thermal circuit and thermal

resistances, 3.4.3

Inferring conductor temperatures from measuredtemperatures, 3.4.8

Losses, 3.4.3Reconductoring, 3.7

Cupric oxide strand coating, 3.7.3Larger conductor sizes, 3.7.2Superconducting cables, 3.7.5Voltage upgrading, 3.7.4

Uprating and upgrading constraints, 3.5Accessories, 3.5.7Direct buried cable systems, 3.5.1Duct bank installations, 3.5.3Fluid-filled cable systems, 3.5.2Hot spot identification, 3.5.6Hydraulic circuit, 3.5.8Trenchless installations, 3.5.4

Uprating, active (underground cables), 3.6.7Uprating case studies

Overhead transmission lines, 2.8Underground cables, 3.9

Uprating constraints (overhead transmission lines), 2.2Constraints on structural loads, 2.2.7Electrical clearance, 2.2.5Environmental effects, 2.2.8Limiting high-temperature sag, 2.2.3Loss of conductor strength, 2.2.6Sag-tension calculations, 2.2.2Uprating constraints related to wind-induced

conductor motion, 2.2.4Uprating constraints (underground cables), 3.5

Direct buried cable systems, 3.5.1Duct bank installations, 3.5.3Fluid-filled cable systems, 3.5.2Trenchless installations, 3.5.4

Uprating hybrid (underground and overhead) circuits, 3.3.3

Uprating substation terminal equipment, 5.4Uprating without reconductoring (overhead

transmission lines), 2.5Deterministic methods, 2.5.2Probabilistic methods, 2.5.3

Absolute method, 2.5.3Exceedance method, 2.5.3Modified exceedance method, 2.5.3

VVideo sagometer, 2.7.5Voltage drop, 1.3.3, 2.1.2Voltage limits, 3.3.1Voltage upgrading, 3.7.4

WWind-induced conductor motion, 2.2.4Wind loading, 2.2.7Wind speed, effect on thermal ratings, 2.4.10

I-5

Increased Power Flow Guidebook Index

XXD (Extruded Dielectric), 3.2.2XLPE (Cross-Linked Polyethylene), 3.2.2

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