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Transformer Overloading and Assessment of Loss-of-Life

for Liquid-Filled Transformers

P.K. Sen, PhD, PE, Fellow IEEE Professor of Engineering Colorado School of Mines

PSERC Project Webinar, April 19, 2011

Presentation Outline

• Introduction and Motivations • Remaining Transformer (Insulation) Life,

Transformer Thermal Model, IEEE Loading Guides

• Modeling and Economic Evaluation • Simulation and Results • Conclusions

2

• Oil-Filled Transformer - <500 kVA (distribution, OA)

- 500 kVA - 100 MVA (distribution power) (OA, OA/FA, OA/FA/FA)

- >100 MVA (transmission power) (OA/FA/FA and OA/FA/FOA)

Transformer Type and Nameplate Rating

• 65°C average winding temperature rise (thermally-upgraded paper insulation)

• 55°C average winding temperature rise (not thermally-upgraded paper, kraft)

• 30/40/50/56 MVA @55o / 65o C TR (OA/FA/FA)

@55°C TR 3

• Thermal Model - Design Consideration (Losses & Cooling) - Temperature (Top & Bottom Oil, Winding Hottest-Spot Temp.)

- Insulation Degradation

- Estimation of Transformer Remaining Life from Its Insulation

• Economic Model - Total Owning Cost (TOC) - Revenue Requirement

- Other Models!!

Issues and Considerations

4

Thermal Model • Design •Temperature • Insulation • Life

Economical Model Revenue Requirement

Optimization (Minimum Cost & Optimum Sizing) • New Design • Retrofit Design

- Replace now - Replace later - Add a second transf. - ??

Uncertainties & Probability Approach • Future load growth projection •Ambient temp. •Transformer Failure

5

Loading Guide Standards

• IEEE Std. C57.91-1995 (USA) – Clause 7 (Classical Model) – Annex G (Detailed Model)

• IEC 354-1991 (EUROPE, CANADA and Others)

• IEEE & IEC Comparisons

IEC is somewhat similar to IEEE Clause 7

6

• Long-term Failure Mode – Mechanical and chemical properties of insulation

deterioration – Dielectric strength reduction (approx. 10% over

the transformer life)

• Short-term Failure Mode – Bubble formation (gassing), temporally dielectric

strength reduction (30% impulse strength reduction @ 180 °C )

Transformer Failure Modes

7

• The Tensile Strength (Mechanical) of cellulose insulation is used as a criteria for loss-of-life estimation.

• Recently, the Degree of Polymerization (DP)

(Chemical) has also become a popular measurement of insulation life.

• If a sample of insulation near hot spot location is

made available, the remaining life of the transformer could be approximately predicted based on specific criteria.

Remaining Transformer (Insulation) Life

8

0

20

40

60

80

100

120

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2

Remaining Life (per unit)

% T

ensi

le S

tren

gth

The normalized remaining life by tensile strength method based on 20% remaining tensile strength (RTS) as end-of-life criteria, created by least square method

Remaining Life by Tensile Strength Method

97.05ln633.01Life Remaining TSR

9

Remaining Life by DP Method

0

100

200

300

400

500

600

700

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2

Remaining Life (per unit)

Deg

ree

of

Po

lym

eriz

atio

n

The normalized remaining life by DP method based on remaining DP of 200 as end-of-life criteria, created by least square method

622ln881.01Life Remaining RDP

10

IEEE Std. C 57.91-1995, Per-Unit Life

• Per-Unit Life

• Relative Aging Factor

• Equivalent Aging

• % Loss-of-Life

273

000,151810 x 80.9 HST

eL

273

000,15 39.164HST

AA edt

dLF

1

0

dtFT

F

T

AAEQA

100 × Life Insulation Normal

Tx F= EQA

• Normal Insulation Life

• Hottest-Spot Temperature (THS) 11

THERMAL MODEL

Hottest-Spot Temperature (T ) HS

Hottest-spot temperature = ambient temperature (TA) + top oil rise over ambient + hot spot rise over top oil (DTG)

(DT TO)

12

GTOA TTTT DDHS

Steady-State Equations

n

TORTOR

RKTT

DD

112

mGRG KTT 2DD

Thermal Model (IEEE Clause 7)

K = Per-Unit Loading (Actual Load/Rated (max) Load)

R = Loss Ratio (Load Loss @ Rated Load/No-Load Loss)

Exponent „n‟ and „m‟ depends on “Cooling” 13

Thermal Model (IEEE Clause 7) Transient Equations

uTOTOTO

TO TTdt

Td,DD

D

n

TORuTOR

RKTT

DD

112

,

,uGGG

G TTdt

TdDD

D

m

uGRuG KTT )( 2, DD

Oil

Winding

14

Modified Transient Equations

AuTOTOTO

TO TTTdt

TdDDD

D,

)(1

1)(1

1)( , sTs

sTs

sT A

TO

uTO

TO

TO D

D

D

15

Thermal Block Diagram (IEEE Clause 7)

16

• Loading cycle, Complex load growth

• Ambient temperature variation Thermal Model

Aging rate, %Loss-of-life

273

000,15383

000,15

HSTeRateAging

LifeNormal

telifeofloss

HST

100* %

273000,15

383000,15

D

Aging Rate and % Loss-of-Life

17

• “Clause 7” thermal model: Simple, Requires minimum information, uses top-oil temperature

• “Annex G” thermal model: More complex, Requires

more information, Focus on duct oil temperature change, uses bottom-oil temperature

IEEE “Clause 7” & “Annex G” Comparisons

18

IEEE Classical Model (Clause 7) IEEE Detailed Model (Annex G)

1. Top oil temperature rise at rated load2. Hot spot temperature rise over top oil at

rated load3. Loss ratio at rated load4. Winding time constant5. Oil time constant or6. Type of cooling system

1 Top oil temperature rise at rated load2 Hot spot temperature rise at rated load3 Average winding temperature rise at rated

load4 Bottom oil temperature rise at rated load5 Losses data from test report6. Weight of Core & coil7. Weight of tank & fittings8. Gallons of fluid9. Type of cooling system10. Type of cooling fluid11. Type of winding material12. Winding time constant13. Location of hot spot14. Per unit eddy current losses at hot spot location

“Clause 7” and “Annex G” Data Requirements

19

H o t s p o t

To p o il

L o a d in g

Te m p e r a tu r e Pr o f ile Plo ts ( IEEE A n n e x G Th e r m a l M o d e l)

T im e ( h r )

1 21 086420

Tem

pera

ture

(C

)

1 2 0

1 0 0

8 0

6 0

4 0

2 0

0

Loading (Per unit)

5

4 .5

4

3 .5

3

2 .5

2

1 .5

1

0 .5

0

IEEE Annex G & Clause 7 Thermal Model (Step Load Response)

20

Economic Evaluation (Total Owning Cost)

Buying a New Transformer

Simplified Practice,

TOC = IPP + A * NLL + B * LL

• Size (MVA) • A & B Factors

Owner Specifies: • Initial purchase price (IPP) • Losses (Winding & Core)

Manufacturer Specifies:

21

Revenue Requirement • Daily load curves • Daily ambient temp. variations • Overloading & end-of-life • Accurate energy loss • Transformer replacement • Refined & flexible method • Detailed economic analysis

Applicable for Investor Owned Utilities

(IOU)

Economic Evaluation (Revenue Requirement)

22

OPTIMIZATION • NEW DESIGN • RETROFIT APPLICATIONS

THERMAL MODEL

ECONOMIC MODEL

23

Daily load curve, Complex load growth

Ambient temperature variation

Economic data - discount rate, tax, - energy cost, etc.

Transformer Data

Thermal Model

Economic Model

Life Expectancy

TOC

Optimization (New Procurement)

24

Existing system

Estimate Remaining Life

Remaining Life Expectancy

Historical load and ambient temp. data

Present load Load growth Load shape Ambient temp. Economic data etc.

Replace with new transformer now

Add a 2nd transformer

Overload existing transf. and replace with new one later

Optimization (Retrofit Design)

25

Probability Tree Structure

ProbabilityDistribution

Path Levelized Probability Revenue Requirement

1 $134,000 0.0016

81 $101,000 0.0016

Probability

Equivalent LevelizedRevenue Requirement (ERR)

Utility’sFinancial

Model

Debt RatioEquity ReturnBorrowed Money RateTax Rate

Depreciation MethodBook Life

HistoricalData

Transformer ThermalModel

Transformer DataSize, Losses, Cost

New TransformerSizing Criteria

Cost of Transformer Cost of Losses

End-of-Life

Load

Ambient Temperature andLoad Profiles

Economic Data

Energy and Demand ChargeEscalation Rate

Estimated Remaining Life

Random Failure ModelThermal Data, Electrical Losses

Cost of Failure

Complete Method Block Diagram

26

SIMULATION CASE STUDIES

AND RESULT

• Case #1 - New Design • Case #2 - Retrofit Applications

27

• Buy new transformer for a new project

• Initial peak load = 20 MVA

• Load growth in first 4 years (Probability)

- High growth = 2.00%

- Moderate growth = 1.75%

- Low growth = 1.00%

• Load growth after the 4th year is 2.00%

Case #1: New Design Example Data

28

Hot SpotTop Oil

Hot Spot and Top Oil Temperature

Year203020282026202420222020201820162014201220102008200620042002

Tem

pera

ture

(Deg

ree

C)

160

150

140

130

120

110

100

90

80

70

60

50

40

Case #1: Hot-Spot & Top-Oil Temperature Plots

29

• Existing transformer rating = 18 MVA

• In service for 25 years

• Estimated remaining life = 0.25 pu.

• Initial peak load = 20 MVA

• Load growth in first 4 year (Probability) - High growth = 2.00% - Moderate growth = 1.75% - Low growth = 1.00%

• Load growth after 4th year is 2.00%

• Replace with new unit now or continue overload ..and replace later ?

Case #2: Retrofit Design Example Data

30

• Graphic interface, Load, Save, Print, and Copy • Transient Loading Analysis (Daily load) • Life Cycle Study (with load growth from table) • Optimize Transformer Size

• Delay Replacement or Replace now Analysis

Windows Based Computer Program

31

Screen Shot (1), Main Menu

32

Screen Shot (2), Annex G Input

33

Screen Shot (3), Load Profile Input

34

Screen Shot (4), Load Growth Input

35

Screen Shot (5), Temperatures Plot

36

Screen Shot (6), Life Cycle Charts

37

Screen Shot (8), Economic Data Input

38

• Developed an Optimization Model for the

“Best Utilization” of a transformer: – Transformer replacement strategy (retrofit

design) – Optimum transformer sizing (new design)

• Computer program is written to facilitate long and complex calculations

• Windows based computer program

• Asset management tools

Conclusions

39

• New programming is required for faster optimization computation

• The different depreciation method (economic

model) shall be explored

• Loss-of-life and hottest-spot calculation shall be updated when more real data is made available

• Other financial model shall be explored

• Sensitivity analysis on Loss Ratio (R)

Future Work

40

Now publicly available on the PSERC Website

PSERC Project Report: Transformer Overloading and Assessment of Loss-of-Life

for Liquid-Filled Transformers

Project Leader: P.K. Sen Professor of Engineering Colorado School of Mines

Golden, CO 80401 psen@mines.edu, (303) 384-2020