M.I.E.T. ENGINEERING COLLEGE

(Approved by AICTE and Affiliated to Anna University Chennai)

TRICHY – PUDUKKOTTAI ROAD, TIRUCHIRAPPALLI – 620 007

DEPARTMENT OF ELECTRICAL AND ELECTRONICS

ENGINEERING

COURSE MATERIAL

EE6004 - FLEXIBLE AC TRANSMISSION SYSTEMS

IV YEAR – VIII SEMESTER

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING (SYLLABUS)

Sub. Code : EE6004 Branch/Year/Sem : EEE/IV/VIII

Sub Name : FLEXIBLE AC TRANSMISSION SYSTEMS Staff Name : D.Jayaraj

L T P C 3 0 0 3

Course Code Course Title Topics

EE6503 Power Electronics Thyristor, Voltage source inverter,

UNIT I INTRODUCTION 9

Reactive power control in electrical power transmission lines -Uncompensated transmission line - series compensation – Basic concepts of Static Var Compensator (SVC) – Thyristor Controlled Series capacitor (TCSC) – Unified power flow controller (UPFC).

UNIT II STATIC VAR COMPENSATOR (SVC) AND APPLICATIONS 9

Voltage control by SVC – Advantages of slope in dynamic characteristics – Influence of SVC on system voltage – Design of SVC voltage regulator –Modelling of SVC for power flow and fast transient stability – Applications: Enhancement of transient stability – Steady state power transfer – Enhancement of power system damping.

UNIT III THYRISTOR CONTROLLED SERIES CAPACITOR (TCSC) AND

APPLICATIONS 9

Operation of the TCSC – Different modes of operation – Modelling of TCSC – Variable reactance model – Modelling for Power Flow and stability studies. Applications: Improvement of the system stability limit – Enhancement of system damping.

UNIT IV VOLTAGE SOURCE CONVERTER BASED FACTS CONTROLLERS 9

Static Synchronous Compensator (STATCOM) – Principle of operation – V-I Characteristics. Applications: Steady state power transfer-enhancement of transient stability - prevention of voltage instability. SSSC-operation of SSSC and the control of power flow –modelling of SSSC in load flow and transient stability studies.

UNIT V CO-ORDINATION OF FACTS CONTROLLERS 9

Controller interactions – SVC – SVC interaction – Co-ordination of multiple controllers using linear control techniques – Control coordination using genetic algorithms.

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TOTAL : 45 PERIODS

TEXT BOOKS:

1. R.Mohan Mathur, Rajiv K.Varma, “Thyristor – Based Facts Controllers for Electrical

Transmission Systems”, IEEE press and John Wiley & Sons, Inc, 2002.

2. Narain G. Hingorani, “Understanding FACTS -Concepts and Technology of Flexible AC Transmission Systems”, Standard Publishers Distributors, Delhi- 110 006, 2011.

3. K.R.Padiyar,” FACTS Controllers in Power Transmission and Distribution”, New Age International(P) Limited, Publishers, New Delhi, 2008.

REFERENCES:

1. A.T.John, “Flexible A.C. Transmission Systems”, Institution of Electrical and

Electronic Engineers (IEEE), 1999.

2. V.K.Sood,HVDC and FACTS controllers – Applications of Static Converters in

Power System, APRIL 2004 , Kluwer Academic Publishers, 2004.

3. Xiao – Ping Zang, Christian Rehtanz and Bikash Pal, “Flexible AC

Transmission System: Modelling and Control” Springer, 2012.

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EE6004 FLEXIBLE AC TRANSMISSION SYSTEMS

COURSE OBJECTIVE

1. To introduce the reactive power control techniques

2. To educate on static VAR compensators and their applications

3. To provide knowledge on Thyristor controlled series capacitors

4. To educate on STATCOM devices

5. To provide knowledge on FACTS controllers

COURSE OUTCOME

1. Ability to understand the concept of reactive power control techniques

2. Ability to explain the operation of SVC controllers and its application

3. Explain the operation of TCSC controller and its application

4. Explain the operation of UPFC and STATCOM and its modeling

5. Understand the concept of FACTS Co-ordination

Prepared by Verified By Mr.D.Jayaraj HOD

Approved by

PRINCIPAL

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UNIT 1

INTRODUCTION

2 MARKS

1. What is the necessity of compensation?

The reactive power through the system can significantly improve the

performance / parameters of the power system such as voltage profile, power angle

characteristics, stability margin and Damping to power oscillations

2. What are the objectives of line compensation?

(i) To increase the power transmission capacity of the line

(ii) To keep the voltage profile of the line along its length within acceptable

bounds to ensure the quality of supply to the connected customer as well

as to minimize the line insulation costs

3. How is the reactive power controlled, using FACTS devices?

The SVC is a shunt device of the FACTS group, regulates voltage at its

terminals by controlling the amount of reactive power injected in to or absorbed from

the power system. When a system voltage is low, the SVC generates reactive power

(SVC Capacitive). When a system voltage is high, it absorbs reactive power (SVC

inductive)

4. How is reactive power controlled in electrical network?

Traditionally, rotating synchronous condensers and fixed or mechanically

switched capacitors or inductors have been used for reactive power compensation.

However, in recent years static VAR compensators are used to provide or absorb the

required reactive power have been developed.

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5. Explain the objectives of FACTS controllers in the power system network.

(i) Better the control of power flow (Real and Reactive) in transmission

lines.

(ii) Limits Short circuit current and increase the loadability

(iii) Increase dynamic and transient stability of power system

(iv) Load compensation

(v) Power quality improvement

6. What are the advantages of FACTS controllers?

(i) The flow of power is ordered. It may be as per the contract or as per the

requirements of the utilities

(ii) It increases the loading capability of the lines to the thermal capability

(iii) It improves the stability of the system and thus make the system secure

(iv) Provides secure Tie Line connection to the neighboring utilities and

regions, thereby decreasing overall generation reserve requirements on

both sides

7. List the disadvantage of fixed series compensation.

(i) It is effective only during heavy loads

(ii) Whenever an outage occurs on a line, with series compensation, the

series compensation is removed. This may cause overloading of other

parallel lines

(iii) If series compensation is added to an existing system, it is generally

necessary to have it on all the lines in parallel.

(iv) One major drawback in the series capacitance compensation is that

special productive devices are required to protect the capacitors and

bypass the high current produced when a short circuit occurs.

8. What is meant by Thyristor Controlled Series Capacitor?

TCSC is a capacitive reactance compensator, which consists of series capacitor

bank shunted by a thyristor-controlled reactor.

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9. Define the term Static VAR compensator.

The SVC is a shunt device of FACTS group using power electronics to control

power flow and improve transient stability on power grids. The SVC regulates voltage

at its terminals by controlling the amount of reactive power injected into or absorbed

from the power system.

10. What are the different types of compensation schemes?

Mainly two types of compensation are carried out,

(i) Load compensation

(ii) Line compensation

11. Define the term FACTS.

Alternating current transmission system incorporating power electronics based

and other static controllers to enhance controllability and increase power transfer

capability

12. What is best location for SVC?

In general the best location is at a point where voltage swings are greatest.

Normally, the midpoint of a transmission line between the two areas is a good

location.

13. What are the main areas of application of FACTS devices?

FACTS mainly find application in following areas,

(i) Power transmission

(ii) Power Quality

(iii) Wind power grid Connection

(iii) Cable Systems

14. What is load compensation?

Load compensation is a management of reactive power to improve the quality

of supply especially the voltage and power factor levels

Three main objectives of the load compensation are

(i) Better voltage profile

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(ii) Power factor correction

(iii) Load balancing

15. Define VAR compensation.

It is defined as the management of reactive power to improve the performance

of AC power systems: Maximizing stability by increasing flow of active power.

16. What are various categories of FACTS controllers?

(i) Series FACTS controllers

(iii) Shunt FACTS controllers

(iv) Combined Series- Series FACTS controllers

(v) Combined Series- Shunt FACTS controllers

17. What is IPFC?

Interline power Flow Controller is a combination of two or more independently

controllable static synchronous series compensator (SSSC) which are solid state

voltage source converters which inject an almost sinusoidal voltage at variable

magnitude and couples via a common DC link.

18. What are reactive power compensation and Compensators?

Reactive power control for a transmission line is often called reactive power

compensation. External devices or sub systems that control reactive power on

transmission line are known as compensators.

19. What is shunt compensation?

The Shunt compensators are connected parallel to the transmission lines with

the help of Circuit breakers. Shunt reactors compensate for the line capacitance, and

they control over voltages at no loads and light load conditions. The shunt

compensators need careful system design because of high charging in-rush currents.

20. What is series compensation?

The Series compensators are connected series with the transmission lines.

Series compensators are used to partially offset the effects of the series inductances of

transmission lines. It provides automatic adjustment of reactive power compensation.

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21. What are the methods used for compensating the uncompensated

transmission lines?

(i) Load compensation- One capacitor is connected parallel across the load

(ii) System compensation - In addition with the parallel capacitor the power

utility devices are also connected.

22. List the advantages of SVC

(i) In high-power networks, SVCs are used for voltage control and for

attaining several other objectives such as damping and stability control.

(ii) Increase in Steady-State Power-Transfer Capacity

(iii) Enhancement of Transient Stability

*********************

16 MARKS

1. (i) Give the complete analysis of lossless distributed parameter transmission

lines and derive power equations for symmetrical case (12)

(ii) Write a brief note on IPFC (4)

1. (i) Give the complete analysis of lossless distributed parameter transmission

lines and derive power equations for symmetrical case (12)

Most power-transmission lines are characterized by distributed parameters:

series resistance, r; series inductance, l; shunt conductance, g; and shunt

capacitance, c—all per-unit (pu) length.

These parameters all depend on the conductors’ size, spacing, clearance above

the ground, and frequency and temperature of operation.

In addition, these parameters depend on the bundling arrangement of the line

conductors and the nearness to other parallel lines.

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The characteristic behavior of a transmission line is dominated by its l and c

parameters. Parameters r and g account for the transmission losses. The

fundamental equations governing the propagation of energy along a line are the

following wave equations:

𝒅𝟐𝑽

𝒅𝒙𝟐= 𝒛𝒚𝑽 (𝟏)

𝒅𝟐𝑰

𝒅𝒙𝟐= 𝒛𝒚𝑰 (𝟐)

where zy = (r + jωl)(g + jωC).

For a lossless line, the general solutions are given as

𝑽 𝒙 = 𝑽 𝒔𝒄𝒐𝒔𝜷𝒙 − 𝒋𝒁𝒐𝑰 𝒔𝒔𝒊𝒏 𝜷𝒙 (𝟑)

𝑰 𝒙 = 𝑰 𝒔𝒄𝒐𝒔𝜷𝒙 − 𝒋𝑽 𝒔

𝒁𝒐

𝒔𝒊𝒏 𝜷𝒙 (𝟒)

These equations are used to calculate voltage and current anywhere on line, at a

distance x from the sending end, in terms of the sending-end voltage and current

and the line parameters. From the above equations we get

𝑰 𝒔 =𝑽 𝒔𝒄𝒐𝒔𝜷𝒂 − 𝑽 𝒓

𝒋𝒁𝟎𝒔𝒊𝒏𝜷𝒂

(𝟓)

Where

𝑍𝑜 = 𝑙

𝑐 Ω = the surge impedance or characteristic impedance

𝛽 = 𝜔 𝑙𝑐 rad/km = the wave number

𝛽𝑎= 𝜔 𝑙𝑐𝑎 = the electrical length of an a-km line

l is the line inductance in henries per kilometer (H/ km), c is the line shunt-

capacitance in farads per kilometer (F/ km), and 1/ 𝑙𝑐 is the propagation

velocity of electromagnetic effects on the transmission line.

If 𝑉 𝑠 = 𝑉 𝑠 00 and 𝑉 𝑟 = 𝑉 𝑟 - δ = 𝑉𝑟 (cos δ − j sin δ), then

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𝑰 𝒔 =𝑽𝒓𝒔𝒊𝒏𝜹 + 𝒋(𝑽𝒓𝒄𝒐𝒔𝜹 − 𝑽𝒔𝒄𝒐𝒔𝜷𝒂)

𝒁𝟎𝒔𝒊𝒏𝜷𝒂

(𝟔)

Therefore, the power at the sending end is given as

𝑺𝒔 = 𝑷𝒔 + 𝒋𝑸𝒔 = 𝑽 𝒔𝑰 𝒔∗ (𝟕)

𝑺𝒔 =𝑽𝒔𝑽𝒓𝒔𝒊𝒏𝜹

𝒁𝟎𝒔𝒊𝒏𝜷𝒂

+ 𝒋𝑽𝒔

𝟐𝒄𝒐𝒔𝜷𝒂 − 𝑽𝒔𝑽𝒓𝒄𝒐𝒔𝜹

𝒁𝟎𝒔𝒊𝒏𝜷𝒂

(𝟖)

Likewise, power at the receiving end is given as

𝑺𝒓 = 𝑷𝒓 + 𝒋𝑸𝒓 =𝑽𝒔𝑽𝒓𝒔𝒊𝒏𝜹

𝒁𝟎𝒔𝒊𝒏𝜷𝒂

+ 𝒋𝑽𝒓

𝟐𝒄𝒐𝒔𝜷𝒂 − 𝑽𝒔𝑽𝒓𝒄𝒐𝒔𝜹

𝒁𝟎𝒔𝒊𝒏𝜷𝒂

(𝟗)

Figure 1.1: The power on a lossless distributed line.

Comparing Equations (8) and (9) and taking the directional notation of Fig. 1.1

into account, it is concluded that for a lossless line, 𝑃𝑠 = −𝑃𝑟 , as expected.

However, 𝑄𝑠 ≠ 𝑄𝑟 , because of the reactive-power absorption/ generation in the

line. From Equations (8) and (9), the power flow from the sending end to the

receiving end is expressed as

𝑷 =𝑽𝒔𝑽𝒓

𝑿𝒍

𝒔𝒊𝒏𝜹 (𝟏𝟎)

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Accordingly, the maximum power transfer is seen to depend on the line length.

When the power-transfer requirement for a given length of a line increases

higher transmission voltages of 𝑉𝑠 and 𝑉𝑟 must be selected.

(ii) Write a brief note on IPFC (4)

In its general form the Interline Power Flow Controller employs a number of

dc-to-ac converters each are providing series compensation for a different line.

In other words, the IPFC comprises a number of Static Synchronous Series

Compensators. However, within the general concept of the IPFC, the

compensating converters are linked together at their dc terminals.

With this scheme, in addition to providing series reactive compensation, any

converter can be controlled to supply real power to the common de link from its

own transmission line. Thus, an overall surplus power can be made available

from the underutilized lines which then can be used by other lines for real

power compensation.

In this way, some of the converters, compensating overloaded lines or lines

with a heavy burden of reactive power flow, can be equipped with full two-

dimensional, reactive and real power control capability, similar to that offered

by the UPFC.

Evidently, this arrangement mandates the rigorous maintenance of the overall

power balance at the common de terminal by appropriate control action, using

the general principle that the under loaded lines are to provide help, in the form

of appropriate real power transfer, for the overloaded lines.

2. What are the objectives of line compensation? Explain the effect of shunt

and series compensation on power transmission capacity of a short symmetrical

transmission line (Or) Explain the effect of shunt and series compensation on

power transmission capacity (Or) Explain the detail about effect of shunt and

series compensation on transmission line. (16)

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Objectives of line compensation

Reduces line voltage drops

Limits load-dependent voltage drops

Influences load flow in parallel transmission lines

Increases transfer capability

Reduces transmission angle

Increases system stability

Effect of shunt and series compensation on transmission line

Shunt compensation

Shunt reactors compensate for the line capacitance, and because they control

over voltages at no loads and light loads, they are often connected permanently

to the line, not to the bus.

Shunt capacitors are used to increase the power-transfer capacity and to

compensate for the reactive-voltage drop in the line. The application of shunt

capacitors requires careful system design.

Effect of Shunt compensation on Transmission Line

The midpoint-capacitor compensation of a short, symmetrical line

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Reconsider the short, symmetrical line; apply a shunt capacitor at the midpoint

of the line so that a shunt susceptance is incrementally added (∆Bc), as shown in

figure. For the system in this figure, the power transfer in terms of the midpoint

voltage on the line is

𝑷 =𝑽𝑽𝒎

𝑿𝒍

𝟐

𝒔𝒊𝒏𝜹

𝟐 (𝟏)

The differential change in power, DP, as a result of a differential change, ∆Vm,

is given as

∆𝑷 =𝟐𝑽

𝑿𝒍

𝒔𝒊𝒏𝜹

𝟐∆𝑽𝒎 (𝟐)

∆𝑰𝒄 = 𝑽𝒎∆𝑩𝒄 (𝟑)

The current ∆Ic in the midline shunt capacitor modifies the line currents in the

sending and receiving ends of the line to the following:

𝑰𝒍𝒔 = 𝑰𝒍 −∆𝑰𝒄

𝟐 𝒂𝒏𝒅 𝑰𝒍𝒓 = 𝑰𝒍 +

∆𝑰𝒄

𝟐 (𝟒)

As 𝑽𝒎 = 𝑽𝒓 + 𝒋𝑰𝒍𝒓𝑿𝒍/𝟐,

∆𝑽𝒎 =∆𝑰𝒄𝑿𝒍

𝟒=

𝑽𝒎𝑿𝒍

𝟒∆𝑩𝒄 (𝟓)

Substituting the results of Eq. (5) in Eq. (2), we get

∆𝑷 =𝑽𝑽𝒎

𝟐𝒔𝒊𝒏

𝜹

𝟐∆𝑩𝒄 (𝟔)

If the midpoint voltage of the line is approximately equal to V cos 𝛿/2, then the

Incremental rating of the shunt-capacitor compensation will be∆𝑄𝑠ℎ = 𝑉𝑚2∆𝐵𝑐 ,

or

∆𝑷

∆𝑸𝒔𝒉

=𝟏

𝟐𝒕𝒂𝒏

𝜹

𝟐 (𝟕)

By comparing the above, we deduce that for an equivalent power transfer on a

short electrical line,

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∆𝑸𝒔𝒆

∆𝑸𝒔𝒉

= 𝒕𝒂𝒏𝜹

𝟐

𝟐

𝒕 (𝟖)

Series compensation

Series capacitors are used to partially offset the effects of the series inductances

of lines. Series compensation results in the improvement of the maximum

power-transmission capacity of the line.

The net effect is a lower load angle for a given power-transmission level and,

therefore, a higher-stability margin.

The reactive-power absorption of a line depends on the transmission current, so

when series capacitors are employed, automatically the resulting reactive-power

compensation is adjusted proportionately.

Also, because the series compensation effectively reduces the overall line

reactance, it is expected that the net line-voltage drop would become less

susceptible to the loading conditions.

Effect of Series compensation on Transmission Line

The consideration of series compensation invariably raises the issue of its

comparison with shunt compensation. A simple system analysis can be

performed to develop a basic understanding of the effect of shunt and series

compensation on power-transmission capacity.

Consider a short, symmetrical electrical line as shown in figure for an

uncompensated line, and assuming Vs = Vr =V, the power equation becomes

𝑷 =𝑽𝟐

𝑿𝒍

𝒔𝒊𝒏𝜹 =𝑽𝟐

𝑿𝒍

𝟐𝒔𝒊𝒏𝜹

𝟐𝒄𝒐𝒔

𝜹

𝟐 (𝟗)

From the voltage-phasor equations and the phasor diagram in Figure,

𝑰𝒍 =𝟐𝑽

𝑿𝒍

𝒔𝒊𝒏𝜹

𝟐 (𝟏𝟎)

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If the effective reactance of a line is controlled by inserting a series capacitor,

and if the line terminal voltages are held unchanged, then a ∆Xl change in the

line reactance will result in a ∆Il change in the current, where

∆𝑰𝒍 =𝟐𝑽

𝑿𝒍𝟐 𝒔𝒊𝒏

𝜹

𝟐𝑿𝒍 = − 𝑰𝒍

∆𝑿𝒍

𝑿𝒍

(𝟏𝟏)

Series compensation of a short symmetrical transmission line

Therefore, from Eq. (2.21), the corresponding change in the power transfer will be

∆𝑷 =𝑽𝟐

𝑿𝒍

𝟐𝒔𝒊𝒏𝜹

𝟐𝒄𝒐𝒔

𝜹

𝟐 ∆𝑿𝒍 (𝟏𝟐)

Using Eqs. (11) and (12), Eq. (13) may be written as

∆𝑷 =𝟏

𝟐𝒕𝒂𝒏𝜹𝟐

−∆𝑿𝒍𝑰𝒍𝟐 (𝟏𝟑)

As

−∆Xl is the reactance added by series capacitors, −∆𝑋𝑙𝐼𝑙2 = ∆𝑄𝑠𝑒 represents the

incremental var rating of the series capacitor. Therefore

∆𝑷

∆𝑸𝒔𝒆

=𝟏

𝟐𝒕𝒂𝒏𝜹𝟐

(𝟏𝟒)

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3. (i) Explain the concept and need for reactive power. (8)

(ii) Discuss the possible control actions to maintain the voltage at rated

value in transmission line (8)

3. (i) Explain the concept and need for reactive power. (8)

Concept

The portion of electricity establishes and sustains the electric and magnetic

fields of alternating-current equipment. Reactive power must be supplied to most types

of magnetic equipment, such as motors and transformers. It also must supply the

reactive losses on transmission facilities. Reactive power is provided by generators,

synchronous condensers, or electrostatic equipment such as capacitors and directly

influences electric system voltage. It is usually expressed in Kilovars (KVAR) or

Megavars (MVAR).

Need for reactive power

Voltage control in an electrical power system is important for proper operation

for electrical power equipment to prevent damage such as overheating of

generators and motors, to reduce transmission losses and to maintain the ability

of the system to withstand and prevent voltage collapse.

Decreasing reactive power causing voltage to fall while increasing it causing

voltage to rise. A voltage collapse may be occurs when the system try to serve

much more load than the voltage can support.

When reactive power supply lower voltage, as voltage drops current must

increase to maintain power supplied, causing system to consume more reactive

power and the voltage drops further . If the current increase too much,

transmission lines go off line, overloading other lines and potentially causing

cascading failures.

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If the voltage drops too low, some generators will disconnect automatically to

protect themselves. Voltage collapse occurs when an increase in load or less

generation or transmission facilities causes dropping voltage, which causes a

further reduction in reactive power from capacitor and line charging, and still

there further voltage reductions.

If voltage reduction continues, these will cause additional elements to trip,

leading further reduction in voltage and loss of the load. The result in these

entire progressive and uncontrollable declines in voltage is that the system

unable to provide the reactive power required supplying the reactive power

demands

(ii) Discuss the possible control actions to maintain the voltage at rated value

in transmission line (8)

Voltage stability is concerned with the ability of a power system to maintain

acceptable voltage at all buses in the system under normal conditions and after

being subjected to a disturbance

To maintain security of such systems, it is desirable to plan suitable measures to

improve power system security and increase voltage stability margins.

The only way to counteract this problem is by reducing the reactive power load

in the system or by adding new reactive power generation systems in the

weakest points of the system, thereby, increasing the voltage at those points.

The flexible AC transmission system (FACTS) controllers are capable of

supplying or absorbing reactive power at faster rates. The introduction of

FACTS controllers are increasingly used to provide voltage and power flow

controls.

Insertion of FACTS devices is found to be highly effective in preventing

voltage instability and minimize the active or real power loss on transmission

lines.

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Series and shunt compensating devices are used to enhance the static voltage

stability margin and reduce the real power loss appreciably

When a series-connected compensating voltage is used to control the

transmission line voltage, the compensating voltage is also at any phase angle

with the prevailing line current.

In the process, it emulates in series with the line a capacitor that increases the

power flow of the line or an inductor that decreases the power flow of the line,

and a positive resistor that absorbs active power from the line or a negative

resistor that delivers active power to the line. Therefore, the desired

compensating voltage is actually an impedance emulator.

A shunt-connected compensating voltage can also modify the transmission

line’s sending- end voltage. In certain special cases for point-to-point transfer of

power between two isolated networks or interconnection of two transmission

lines with different voltages or phase angles (or frequencies), this scheme is a

preferred choice.

*********************

4. Explain the basic construction, working and characteristics of any one type

of SVC (16)

SVC

Static var compensators (SVCs) are used primarily in power systems for voltage

control as either an end in itself or a means of achieving other objectives, such as

system stabilization. The performance of SVC voltage control is critically dependent

on several factors, including the influence of network resonances, transformer

saturation, geomagnetic effects, and voltage distortion.

Types of SVC

Saturable reactor

Thyristor controlled reactor

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Thyristor switched capacitor

Thyristor switched reactor

Thyristor controlled transformer

(1). The Thyristor-Controlled Reactor (TCR)

Construction

A TCR is one of the most important building blocks of Thyristor-based SVCs.

Although it can be used alone, it is more often employed in conjunction with fixed or

thyristor-switched capacitors to provide rapid, continuous control of reactive power

over the entire selected lagging-to-leading range.

Schematic diagram of a TCR

One line diagram of a TCR compensator with fixed-shunt capacitors

21 | P a g e

A basic single-phase TCR comprises an anti-parallel–connected pair of

thyristor valves, T1 and T2, in series with a linear air-core reactor, as illustrated

in Figures 1&2.

The anti-parallel–connected thyristor pair acts like a bidirectional switch, with

thyristor valve T1 conducting in positive half-cycles and thyristor valve T2

conducting in negative half-cycles of the supply voltage.

The firing angle of the thyristors is measured from the zero crossing of the

voltage appearing across its terminals. The controllable range of the TCR firing

angle, a, extends from 900 to 180

0.

A firing angle of 900 results in full thyristor conduction with a continuous

sinusoidal current flow in the TCR. As the firing angle is varied from 900 to

close to 1800, the current flows in the form of discontinuous pulses

symmetrically located in the positive and negative half-cycles.

Once the thyristor valves are fired, the cessation of current occurs at its natural

zero crossing, a process known as the line commutation. The current reduces to

zero n for a firing angle of 1800.

Thyristor firing at angles below 900 introduces dc components in the current,

disturbing the symmetrical operation of the two anti parallel valve branches.

A characteristic of the line-commutation process with which the TCR operates

is that once the valve conduction has commenced, any change in the firing

angle can only be implemented in the next half-cycle, leading to the so-called

thyristor dead time.

Operating Characteristics of a TCR

Operating Characteristics without Voltage Control

The sinusoidal current flowing in this reactor is equal to the fundamental

component of the non sinusoidal current flowing in the TCR.

22 | P a g e

For a general SVC, this can be considered as a black box with an unknown but

purely reactive circuit inside, the overall compensator susceptance BSVC can be

defined with the following equation:

𝑰𝑺𝑽𝑪 = 𝑽𝒋𝑩𝑺𝑽𝑪 (𝟏)

In the simple case of a TCR, the compensator susceptance is

𝑩𝑺𝑽𝑪 = 𝑩𝑻𝑪𝑹 (𝟐)

The voltage–current (V-I) characteristics without voltage control

This shows the SVC current as a function of the system voltage for different

firing angles, as depicted in Figure.

This V-I characteristic is given in a very general sense. No control system is

assumed to vary the firing angle, and any operating point within the two limits

is possible depending on the system voltage and the setting of the firing angle.

This characteristic clearly illustrates the limits of the operating range, and it

may include the steady-state characteristics of the various possible controls.

This characteristic is the usual way in which the system engineers prefer to look

at the compensator, because the characteristic shows the steady-state

performance of the SVC plant.

23 | P a g e

Operating Characteristic with Voltage Control

Two system characteristics such as system 1 and system 2 are depicted in

Figure, that illustrate the decline in system node voltage when the node is

loaded inductively and reactive power is absorbed.

The corresponding operating points for the two system conditions are A1 and A2.

If the system voltage of system 2 rises will creates new characteristic system 2′.

The voltage–current (V-I) characteristics with voltage control

Operating point A then moves to the right and reaches the absorption limit of

the compensator.

Any further increase in system voltage cannot be compensated for by the

control system, because the TCR reactor is already fully conducting.

The operating point A2 will, therefore, move upward on the characteristic,

corresponding to the fully on reactor connected to the system.

The compensator then operates in the overload range, beyond which a current

limit is imposed by the firing control to prevent damage to the thyristor valve

from an over current.

At the left-hand side, the compensator will reach the production limit if the

system voltage drops excessively; the operating point will then lie on the

characteristic of the under voltage range.

24 | P a g e

(2) A Thyristor switched capacitor (TSC)

A thyristor switched capacitor (TSC) is a type of equipment used for

compensating reactive power in electrical power systems.

It consists of a power capacitor connected in series with a bidirectional thyristor

valve and, usually, a current limiting reactor (inductor).

The thyristor switched capacitor is an important component of a Static VAR

Compensator (SVC), where it is often used in conjunction with a thyristor

controlled reactor (TCR).

Static VAR compensators are a member of the Flexible AC transmission

system (FACTS) family

A TSC is usually a three-phase assembly, connected either in a delta or a star

arrangement.

Unlike the TCR, a TSC generates no harmonics and so requires no filtering. For

this reason, some SVCs have been built with only TSCs.

This can lead to a relatively cost-effective solution where the SVC only requires

capacitive reactive power, although a disadvantage is that the reactive power

output can only be varied in steps.

Configuration

A basic single-phase TSC consists of an anti-parallel–connected thyristor-valve

pair that acts as a bidirectional switch in series with a capacitor and a current

limiting small reactor, as shown in Fig.(a).

The thyristor switch allows the conduction for integral number of half-cycles.

The capacitor is not phase controlled, as is a TCR.

The small-series inductor is installed to limit current transients during

overvoltage conditions and planned switching operations, as well as when

switching at incorrect instants or at the inappropriate voltage polarity.

The inductor magnitude is chosen to give a natural resonant frequency of four

to five times the system nominal frequency, which ensures that the inductance

25 | P a g e

neither creates a harmonic-resonant circuit with the network nor hampers the

TSC control system.

Another function of this series inductor is to act in combination with the

capacitor as a filter for harmonics generated by the associated TCR.

In some cases, discharge circuits are provided with the capacitors to rapidly

dissipate the remnant charge on the capacitor after a switch-off.

Voltages after turn-off to the TSC: (a) a circuit diagram and (b) the

Voltage – Current waveforms

A practical TSC compensator involves n 3-phase TSC banks of equal rating

connected in shunt.

The overall TSC susceptance at any given instant is the sum of conducting

TSC. In some cases, the ratings of different constituent TSC steps may be

chosen based on a binary system.

26 | P a g e

In this scheme, n−1 capacitors are rated for susceptance B and one capacitor is

rated for susceptance B/ 2.

Thus the total number of possible TSC steps gets extended to 2n. The TSC

provides a fast response—typically between one-half to one cycle.

However, this response time may be extended because of any delays in the

measurement and control systems. The TSCs provide virtually unlimited

switching operations, in stark contrast to MSCs.

Operating Characteristic

The operating characteristic of a TSC

The TSC has a discrete voltage–current operating characteristic, as shown in

Figure. The shape of this characteristic is a function of the number of TSC

units, their individual ratings, and a hysteresis voltage ∆V, which is built in to

avoid undesirable frequent switching of capacitors.

In a closed-loop voltage control operation, the TSC regulates the bus voltage

within the range Vref ± ∆V/ 2.

**************************

27 | P a g e

5. Explain in detail about the classification of different FACTS controllers. (16)

Flexible AC Transmission System (FACTS) is defined as `Alternating current

transmission systems incorporating power electronic-based and other static

controllers to enhance controllability and increase power transfer capability.

The FACTS controller is defined as a power electronic based system and other

static equipment that provide control of one or more AC transmission system

parameters.

The FACTS controllers can be classified as

1. Shunt connected controllers

2. Series connected controllers

3. Combined series-series controllers

4. Combined shunt-series controllers

Series Controllers

The series Controller could be variable impedance, such as capacitor, reactor,

etc., or power electronics based variable source of main frequency, sub

synchronous and harmonic frequencies (or a combination) to serve the desired

need.

In principle, all series Controllers inject voltage in series with the line. Even

variable impedance multiplied by the current flow through it, represents an

injected series voltage in the line.

28 | P a g e

As long as the voltage is in phase quadrature with the line current, the series

Controller only supplies or consumes variable reactive power. Any other phase

relationship will involve handling of real power as well.

Shunt Controllers

As in the case of series Controllers, the shunt Controllers may be variable

impedance, variable source, or a combination of these. In principle, all shunt

Controllers inject current into the system at the point of connection.

Even variable shunt impedance connected to the line voltage causes a variable

current flow and hence represents injection of current into the line.

As long as the injected current is in phase quadrature with the line voltage, the

shunt Controller only supplies or consumes variable reactive power. Any other

phase relationship will involve handling of real power as well.

Combined series-series Controllers

29 | P a g e

This could be a combination of separate series controllers, which are controlled

in a coordinated manner, in a multiline transmission system. Or it could be a

unified Controller, in which series Controllers provide independent series

reactive compensation for each line but also transfer real power among the lines

via the power link.

The real power transfer capability of the unified series-series Controller,

referred to as Interline Power Flow Controller, makes it possible to balance

both the real and reactive power flow in the lines and thereby maximize the

utilization of the transmission system.

Note that the term "unified" here means that the de terminals of all Controller

converters are all connected together for real power transfer.

Combined series-shunt Controllers

This could be a combination of separate shunt and series Controllers, which are

controlled in a coordinated manner, or a Unified Power Flow Controller with

series and shunt elements.

30 | P a g e

In principle, combined shunt and series Controllers inject current into the

system with the shunt part of the Controller and voltage in series in the line

with the series part of the Controller.

However, when the shunt and series Controllers are unified, there can be a real

power exchange between the series and shunt Controllers via the power link.

Depending on the power electronic devices used in the control, the FACTS controllers

can be classified as

(A) Variable impedance type.

(B) Voltage Source Converter (VSC) type.

The variable impedance type controllers include:

(i) Static Var Compensator (SVC), (shunt connected)

(ii) Thyrister Controlled Series Capacitor or compensator (TCSC), (series

connected)

(iii) Thyristor Controlled Phase Shifting Transformer (TCPST) of Static PST

(combined shunt and series)

The VSC based FACTS controllers are

(i) Static synchronous Compensator (STATCOM) (shunt connected)

(ii) Static Synchronous Series Compensator (SSSC) (series connected)

(iii) Interline Power Flow Controller (IPFC) (combined series-series)

(iv) Unified Power Flow Controller (UPFC) (combined shunt-series)

Some of the special purpose FACTS controllers are

(a) Thyristor Controller Braking Resistor (TCBR)

(b) Thyristor Controlled Voltage Limiter (TCVL)

(c) Thyristor Controlled Voltage Regulator (TCVR)

(d) Inter-phase Power Controller (IPC)

(e) NGH-SSR damping

31 | P a g e

The FACTS controllers based on VSC have several advantages over the

variable impedance type. For example, a STATCOM is much more compact

than a SVC for similar rating and is technically superior.

It can supply required reactive current even at low values of the bus voltage and

can be designed to have in built short term overload capability.

Also, a STATCOM can supply active power if it has an energy source or large

energy storage at its DC terminals.

*********************

32 | P a g e

EE6004 FLEXIBLE AC TRANSMISSION SYSTEMS

UNIT 2

STATIC VAR COMPENSATORS AND APPLICATIONS

2 MARKS

1. Write the application of SVC.

SVC’s are installed to solve a variety of power system problems

Voltage regulation

Reduce voltage flicker caused by varying loads like arc furnace, etc.

Increase power transfer capacity of transmission systems.

Increase transient stability limits of a power system

Increase damping of power oscillations

2. Define the term static VAR compensator (SVC).

Static VAR Compensator is an electrical device, commonly known as SVCs, or

shunt connected devices, varies the reactive power output by controlling or switching

the reactive impedance components by means of power electronics devices. The SVC

regulates voltage at its terminals by controlling the amount of reactive power injected

into or absorb from the power system. The term ―Static‖ refers to the fact that the

SVC has no moving parts. Hence it requires low maintenance.

3. What are advantages of slope in the dynamic characteristics of SVC?

Substantially reduces the reactive power rating of the SVC for achieving nearly

the same control objectives.

Prevents the SVC from reaching its reactive power limits too frequently

Facilitates the sharing of reactive power among multiple compensators

operating in parallel

33 | P a g e

4. What is the best location for SVC? Justify.

It has been proven that the midpoint of the transmission line is the optimal

location of SVC. This proof is based on the linear load which is not valid

practically

For nonlinear load model it was found that the best location for advanced Static

VAR compensator close to the receiving end where the wide range of reactive

power could be controlled.

5. What are the general characteristics of SVCs?

The lowering of maintenance requirements due to the absence of rotating parts

The very fast control response time

The feasibility of individual phase control

Reduced losses

Highly reliable

6. List the Advantages of SVC.

Cheaper

Higher capacity

Faster and more reliable

Simple operation

Improves steady state stability and transient stability

7. Define voltage stability.

It is the ability of a power system to maintain steady acceptable voltages at all

buses in the system under normal operating conditions and after being subjected to a

disturbance.

8. What are the two basic modes of SVC?

Voltage regulation mode

VAR mode (SVC susceptance kept constant)

34 | P a g e

9. List out the prevention of voltage instability in transmission lines

Placement of series and shunt capacitors

Installation of synchronous condensers

Placement of FACTS controllers

Coordination of multiple FACTS controllers

Under Voltage load Shedding

10. What are the symptoms of voltage collapse?

Low voltage profiles

Heavy reactive power flows

Inadequate reactive support

Heavily loaded system

11. What are the general characteristics of SVC?

Lowering maintenance requirement from the absence of rotating parts

Very fast control response time

Feasibility of individual phase control

Diminished losses

High reliability

Lack of contribution to system short circuit capacity

Generation of harmonics by SVCs except thyristor switched capacitor

Variation of SVC reactive power generation as the square of terminal voltage

when it is operating outside the linear controllable range, leading to a

substantial in reactive power support at a lower voltage

12. What are the advantages of the slope in the SVC dynamic characteristics?

Substantially reduces the reactive power rating of the SVC for achieving nearly

the same control objectives

35 | P a g e

Prevents the SVC from reaching its reactive power limits too frequency

Facilitates the sharing of reactive power among multiple compensators

operating in parallel

13. What are the different cases involved in power angle curves of a SMIB

system?

Uncompensated case

Ideal midpoint SVC unlimited rating (Qsvc > 4Pmax)

Fixed capacitor connected at its midpoint

Midpoint SVC with limited rating (Qsvc = 2Pmax)

14. What is the objective of SVC enhancement in transient stability?

An SVC significantly enhances the ability to maintain synchronism of a power

system that is controlled and co-ordinated system, even when the system is subjected

to large sudden disturbances. So the SVC enhancement in transient stability provides

steady power transfer in transmission lines.

15. Write down the equation for SVC bus voltage.

VS = VSVC + ISVC XS

16. Give the advantages of the slope in the SVC dynamic characteristics.

The reactive power rating is reduced

SVC is prevented from reaching its reactive power limit too frequently

It provides effective parallel operation of two parallel connected SVC’s

17. What is SVC slope in the dynamic characteristics?

To improve the power system operating performance 2.5% voltage de-regulation

will be provided in SVC operation. So this voltage de-regulation results in 5% slope in

the SVC dynamic characteristics.

36 | P a g e

18. How the SVC prevents the reactive power rating, reaching its limit too

frequently?

Due to slope in the SVC dynamic characteristics the no load to change in load

variation limit will be increased, so the SVC is prevented from reaching its reactive

power limit too frequently. Thus the total reactive power needed is reduced to certain

limit.

19. Explain the load sharing of two parallel connected SVC‟s.

Without slope in the SVC dynamic characteristics there is a discontinuous gap

between capacitive and inductive region. This gap will be reduced by operating two

parallel connected SVC’s with slope (2.5% voltage de-regulation) in the SVC dynamic

characteristics.

20. What are the conditions involved for influence of the SVC on system voltage?

Coupling transformer ignored

With coupling transformer

System gain

*********************

16 MARKS

1. Discuss in detail about the static and dynamic V-I characteristics of SVC (16)

V-I Characteristics of the SVC

The steady-state and dynamic characteristics of SVCs describe the variation of

SVC bus voltage with SVC current or reactive power.

Two alternative representations of these characteristics are shown in Fig. Part

(a) illustrates the terminal voltage–SVC current characteristic and part (b)

depicts the terminal voltage–SVC reactive-power relationship.

37 | P a g e

(a) The voltage–current characteristic of the SVC and (b) The voltage– reactive-power

characteristic of the SVC.

Dynamic Characteristics

Reference Voltage, Vref : This is the voltage at the terminals of the SVC during the

floating condition, that is, when the SVC is neither absorbing nor generating any

reactive power.

The reference voltage can be varied between the maximum and minimum limits

as Vref max

and Vref min

either by the SVC control system, in case of thyristor-

controlled compensators, or by the taps of the coupling transformer, in the case

of saturated reactor compensators.

Typical values of Vref max

and Vref min

are 1.05 p.u and 0.95 p.u, respectively.

38 | P a g e

Linear Range of SVC Control: This is the control range over which SVC terminal

voltage varies linearly with SVC current or reactive power, as the latter is varied over

its entire capacitive-to-inductive range.

Slope or Current Droop: The slope or droop of the V-I characteristic is defined as the

ratio of voltage-magnitude change to current-magnitude change over the linear-

controlled range of the compensator. Thus slope KSL is given by

𝑲𝑺𝑳 =∆𝑽

∆𝑰 𝜴

where ΔV = the change in voltage magnitude (V)

ΔI = the change in current magnitude (A)

The per-unit value of the slope is obtained as

𝑲𝑺𝑳 =∆𝑽/𝑽𝒓

∆𝑰/𝑽𝒓

𝒑. 𝒖

where Vr and Ir represent the rated values of SVC voltage and current, respectively.

For ΔI= Ir ,

𝑲𝑺𝑳 =∆𝑽(𝒂𝒕 𝑰𝒓𝒐𝒓𝑸𝒓)

𝑽𝒓

𝒑. 𝒖

where Qr represents the rated reactive power of SVC.

Thus the slope can be defined alternatively as the voltage change in percent of

the rated voltage measured at the larger of the two maximum inductive or

maximum capacitive-reactive-power outputs, as the larger output usually

corresponds to the base reactive power of the SVC.

In some literature, the reactive power rating of the SVC is defined as the sum of

its inductive and capacitive rating.

The slope is often expressed as an equivalent reactance:

𝑿𝑺𝑳 = 𝑲𝑺𝑳 𝒊𝒏 𝒑.𝒖

39 | P a g e

The slope can be changed by the control system in thyristor-controlled

compensators, whereas in the case of saturated reactor compensators, the slope

is adjusted by the series slope-correction capacitors.

The slope is usually kept within 1–10%, with a typical value of 3–5%.

Although the SVC is expected to regulate bus voltage, that is, maintain a flat

voltage-current profile with a zero slope, it becomes desirable to incorporate a

finite slope in the V-I characteristics.

Steady-State Characteristics

The steady-state V-I characteristic of the SVC is very similar to the dynamic V-I

characteristic except for a dead band in voltage, as depicted in Figures (a) and

(b).

In the absence of this dead band, in the steady state the SVC will tend to drift

toward its reactive-power limits to provide voltage regulation. It is not desirable

to leave the SVC with very little reactive-power margin for future voltage

control or stabilization excursions in the event of a system disturbance.

To prevent this drift, a dead band about Vref holds the ISVC at or near zero value,

depending on the location of the dead band.

Thus the reactive power is kept constant at a set point, typically equal to the

MVA output of the filters.

This output is quite small; hence the total operating losses are minimized. A

slow susceptance regulator is employed to implement the voltage dead band,

which has a time constant of several minutes.

Hence the susceptance regulator is rendered virtually ineffective during fast

transient phenomena, and it does not interfere with the operation of the voltage

controller.

40 | P a g e

2. Explain how SVC can be used to enhance the power transfer capacity of a

transmission line. (16)

Increase In Steady-State Power-Transfer Capacity

An SVC can be used to enhance the power-transfer capacity of a transmission

line, which is also characterized as the steady-state power limit.

Consider a single-machine infinite-bus (SMIB) system with an interconnecting

lossless tie line having reactance X shown in Figure (a) and (b).

The single-machine infinite-bus (SMIB) system: (a) an uncompensated system and (b) an SVC-

compensated system.

Let the voltages of the synchronous generator and infinite bus is V1∟δ and

V2∟00 respectively.

The power transferred from the synchronous machine to the infinite bus is

expressed as

𝑷 =𝑽𝟏𝑽𝟐

𝑿𝒔𝒊𝒏𝜹

For simplicity, if V1 = V2 = V, then,

𝑷 =𝑽𝟐

𝑿𝒔𝒊𝒏𝜹

The power thus varies as a sinusoidal function of the angular difference of the

voltages at the synchronous machine and infinite bus, as depicted in Figure (c)

41 | P a g e

(c) The variation of line real-power flow and SVC reactive-power flow in a SMIB system

The maximum steady-state power that can be transferred across the

uncompensated line without SVC corresponds to 𝛿 - 900; it is given by

𝑷𝒎𝒂𝒙 =𝑽𝟐

𝑿

Let the transmission line be compensated at its midpoint by an ideal SVC. The

term ideal corresponds to an SVC with an unlimited reactive-power rating that

can maintain the magnitude of the midpoint voltage constant for all real power

flows across the transmission line.

The SVC bus voltage is then given by Vm∟δ/2. The electrical power flow

across the half-line section connecting the generator and the SVC is expressed

as

𝑷𝑪 =𝑽𝟏𝑽𝟐

𝑿/𝟐𝒔𝒊𝒏

𝜹

𝟐

The power transfer in the other half-line section interconnecting the SVC, and

the infinite bus is also described by a similar equation. Assuming further that

Vm = V1 = V2 = V, the equation can be rewritten as

42 | P a g e

𝑷𝑪 =𝟐𝑽𝟐

𝑿𝒔𝒊𝒏

𝜹

𝟐

which is depicted graphically in Figure (c). The maximum transmittable power across

the line is then given by

𝑷𝑪 =𝟐𝑽𝟐

𝑿

The midpoint-located ideal SVC doubles the steady-state power limit and

increases the stable angular difference between the synchronous machine and

the infinite bus from 900 to 180

0.

If the transmission line is divided into n equal sections, with an ideal SVC at

each junction of these sections maintaining a constant-voltage magnitude (V),

then the power transfer (𝑃𝐶′ ) of this line can be expressed theoretically by

𝑷𝑪′ =

𝑽𝟐

𝑿/𝒏𝒔𝒊𝒏

𝜹

𝒏

The maximum power, 𝑃𝐶𝑚𝑎𝑥′ , that can be transmitted along this line is nV

2/ X.

In other words, with n sections the power transfer can be increased n times that

of the uncompensated line.

It may be understood that this is only a theoretical limit, as the actual maximum

power flow is restricted by the thermal limit of the transmission line.

It can be shown that the reactive-power requirement, QSVC, of the midpoint

SVC for the voltage stabilization is given by,

𝑸𝑺𝑽𝑪 =𝟒𝑽𝟐

𝑿 𝟏 − 𝒄𝒐𝒔

𝜹

𝟐

Figure (c) also depicts the variation of QSVC with 𝛿. It is seen that to double the

power transfer to 2Pmax, the required reactive-power rating of the SVC is four

times the maximum power transfer in an uncompensated case, that is, 4Pmax.

Such high-rated SVCs may not be economically feasible.

43 | P a g e

The power-transfer increase achievable with realistic SVCs of limited ratings is

depicted in Figure (d). Curve (a) shows the power-angle relationship for the

uncompensated case.

Power-angle curves of a SMIB system: curve (a) for an uncompensated case; curve (b) for an

ideal midpoint SVC with unlimited rating (QSVC > 4Pmax); curve(c) for a fixed capacitor

connected at its midpoint; and curve (d) for a midpoint SVC with limited rating (QSVC ≈ 2Pmax).

Curve (b) shows the same relationship for an ideal SVC of a large reactive-

power rating QSVC in excess of 4Pmax. Curve (c) represents the power-angle

curve for a midline-located fixed capacitor.

This curve is based on the corresponding equivalent reactance between the

synchronous generator and the infinite bus. If an SVC incorporating a limited-

rating capacitor as in the preceding text (QSVC ≈ 2Pmax) is connected at the line

midpoint, it ensures voltage regulation until its capacitive output reaches its

limit.

In case the system voltage declines further, the SVC cannot provide any voltage

support, and behaves as a fixed capacitor.

Curve (d) represents the power-angle curve that shows this fixed-capacitor

behavior and demonstrates that the realistic maximum power transfer will be

much lower than the theoretical limit of 2Pmax if the SVC has a limited reactive-

power rating.

44 | P a g e

3. Draw and discuss in detail about the advantages of slope in dynamic

characteristics of SVC (16)

Advantages of the Slope in the SVC Dynamic Characteristics

Although the SVC is a controller for voltage regulation, that is, for maintaining

constant voltage at a bus, a finite slope is incorporated in the SVC’s dynamic

characteristic and provides the following advantages despite a slight deregulation of

the bus voltage. The SVC slope

Substantially reduces the reactive-power rating of the SVC for achieving nearly

the same control objectives

Prevents the SVC from reaching its reactive-power limits too frequently

Facilitates the sharing of reactive power among multiple compensators

operating in parallel

Reduction of the SVC Rating

Figure illustrates two dynamic V-I characteristics of an SVC. Characteristic

OA′B′C’ incorporates a finite slope, whereas characteristic OABC does not.

The slope has been deliberately exaggerated to demonstrate its effect.

Assuming that the system load line varies between L1 and L2, the reactive-

power rating of the SVC needed for providing flat voltage regulation is QCm

capacitive to QLm inductive, as determined from the characteristic OABC.

However, if a small deregulation in the SVC bus voltage is considered

acceptable, the maximum reactive-power rating of the SVC required for

performing the voltage control corresponding to the same variation in the

system load line is Q′Cm capacitive to Q′Lm inductive. Evidently, Q′Cm < QCm

and Q′Lm <QLm.

Thus a much lower SVC reactive-power rating and, hence, a much lower cost is

required for nearly the same control objective.

45 | P a g e

It has been shown for an example system that the SVC rating can be reduced to

half, with a 5% slope in the V-I characteristic.

Reduction in the SVC reactive-power rating by the current slope

Prevention of Frequent Operation at Reactive-Power Limits

Figure also shows that if there is no slope in the dynamic characteristic, even a

small change in the system load line (from a small variation, E2 − E1, in the no-

load equivalent system voltage, as viewed from the SVC bus) may cause the

SVC to traverse from one end of the reactive-power range to the other end to

maintain constant voltage.

The reactive-power limits of the SVC are reached more frequently if the ac

system tends to be strong, that is, when the slope of the system load line is quite

small. The effectiveness of the SVC as a voltage-control device therefore

becomes limited.

With a finite slope in the V-I characteristic, the SVC continues to operate in the

linear-controllable range for a much larger variation in the load line of the

external ac system.

For instance, the SVC can exercise voltage control for a significantly larger

variation, E4 − E3, in the equivalent ac system no-load voltage.

46 | P a g e

When the external ac system is subjected to a disturbance, both the slope of the

load line (indicative of the equivalent system reactance) and the system no-load

voltage are influenced. However, the feature discussed here has been explained

in terms of changes in the no-load voltage only.

Load Sharing Between Parallel-Connected SVC:

Consider two SVCs, SVC1 and SVC2, connected at a system bus as depicted in

Figure (a). The two SVCs have the same ratings but the reference voltages, Vref,

of the two control characteristics differ by a small amount, ε.

In practice ε is small and is not zero. Two cases are examined: one in which

both the SVCs have a zero slope, as shown in Figure (b), and the other in which

the two SVCs have a finite slope, as illustrated in Figure(c).

The composite V-I control characteristic of the two SVCs is derived by

summing up the individual currents of both SVCs for the same bus-voltage

magnitude—procedure that is repeated over the entire range of SVC bus

voltage.

The composite characteristic is indicated by the thicker line. In the case of zero

current slope, the composite operating characteristic is beset with a

discontinuity around point A.

(a)

47 | P a g e

(b)

(c)

(a) Two parallel-connected SVCs at a system bus; (b) two SVCs in parallel with difference ε in

the reference-voltage set points without current droop; and (c) two SVCs in parallel with

current droop and with difference ε in the reference-voltage set points

When the system load line intersects the V-I characteristic at A, a quiescent

operating point results that corresponds to full reactive-power production on

SVC1 (point B) and full inductive-reactive power absorption on SVC2 (point C).

Thus one SVC partially compensates the output of the other, which is

uneconomical because the losses are high. On the left of point A, SVC2 controls

the bus voltage, whereas SVC1 remains at full production.

However, on the right of point A, it is SVC1 that controls the bus voltage and

SVC2 that is at full absorption. This operation clearly demonstrates that the two

SVCs are not well coordinated. The current droop ensures that the composite V-

I control characteristic of both SVCs is continuous despite the difference in the

voltage-reference set points.

48 | P a g e

If the two SVCs and the power system achieve a stable-operating point at A,

SVC1 operates at B and SVC2 at C. The reactive-load sharing of the two

compensators is improved, and the losses are minimized.

4. Explain the role of SVC in the enhancement of stability under sudden changes

in the operating conditions of power system (or) Discuss the method of

improving transient stability with SVC (16)

Transient Stability Enhancement and Power Oscillation Damping

Transient stability enhancement and power oscillation damping require the

appropriate variation of the transmission line (terminal) voltage in order to control the

transmitted power so as to counteract the prevailing acceleration or deceleration of the

disturbed machine(s).

Transient Stability Enhancement

The transient stability indicates the capability of the power system to recover

following a major disturbance.

A major disturbance, for example a severe fault on a heavily loaded line, can

result in a large step-like decrease in the transmitted electric power while the

generators feeding the line receive constant mechanical input power.

The difference between mechanical input and electrical output power causes the

machines to accelerate.

Transient stability at a given power level and fault clearing time is primarily

determined by the P versus δ characteristic of the post-fault system that controls

the electric power transmission and thereby the rate of energy absorption from

the machine

The voltage increased above its nominal value will increase the electric power

transmitted and thus will increase also the deceleration of the machine.

49 | P a g e

Reactive shunt compensation can significantly increase the maximum

transmittable power. Thus, it is reasonable to expect that, with suitable and fast

controls, shunt compensation will be able to change the power flow in the

system during and following dynamic disturbances so as to increase the

transient stability limit and provide effective power oscillation damping.

(a)

(b)

Illustration of the equal area criterion for transient stability of a two machine,

Two-line power system

The potential effectiveness of shunt (as well as other compensation and flow

control techniques) on transient stability improvement can be conveniently

evaluated by the equal area criterion.

The meaning of the equal area criterion is explained with the aid of the simple

two machines (the receiving end is an infinite bus), two line system shown in

Figure (a) and the corresponding P versus δ curves shown in Figure (b).

Assume that the complete system is characterized by the P versus δ curve ―a‖

and is operating at angle δ1 to transmit power P1 when a fault occurs at line

segment ―1‖.

50 | P a g e

During the fault the system is characterized by the P versus δ curve "b" and

thus, over this period, the transmitted electric power decreases significantly

while mechanical input power to the sending-end generator remains

substantially constant corresponding to P1.

As a result, the generator accelerates and the transmission angle increases from

δ1 to δ2 at which the protective breakers disconnect the faulted line segment ―1‖

and the sending-end generator 'absorbs accelerating energy, represented by area

―A1.‖

After fault clearing, without line segment ―1‖ the degraded system is

characterized by the P versus δ curve ―c.‖

At angle δ2 on curve ―c‖ the transmitted power exceeds the mechanical input

power P1 and the sending end generator starts to decelerate; however, angle δ

further increases due to the kinetic energy stored in the machine.

The maximum angle reached at δ3, where the decelerating energy, represented

by area ―A2‖ becomes equal to the accelerating energy represented by area

―A1‖.

The limit of transient stability is reached at δ3 = δcrit, beyond which the

decelerating energy would not balance the accelerating energy and synchronism

between the sending end and receiving end could not be restored. The area

―Amargin,‖ between δ3 and δcrit represent the transient stability margin of the

system.

Power Oscillation Damping

In the case of an under-damped power system, any minor disturbance can cause

the machine angle to oscillate around its steady-state value at the natural

frequency of the total electromechanical system.

The angle oscillation, of course, results in a corresponding power oscillation

around the steady-state power transmitted.

51 | P a g e

Waveforms illustrating power oscillation damping by reactive shunt compensation:

(a) generator angle, (b) transmitted power, and (c) var output of the shunt compensator.

The lack of sufficient damping can be a major problem in some power systems

and, in some cases; it may be the limiting factor for the transmittable power.

Since power oscillation is a sustained dynamic event, it is necessary to vary the

applied shunt compensation, and thereby the (midpoint) voltage of the

transmission line, to counteract the accelerating and decelerating swings of the

disturbed machine(s).

The requirements of var output control, and the process of power oscillation

damping, is illustrated by the waveforms in Figure.

Waveforms in Figure (a) show the undamped and damped oscillations of angle

δ around the steady-state value δ0. Waveforms in Figure (b) show the undamped

and damped oscillations of the electric power P around the steady-state value

Po.

Waveform c shows the reactive power output Qp of the shunt-connected var

compensator.

52 | P a g e

The capacitive (positive) output of the compensator increases the midpoint

voltage and hence the transmitted power when dδ/dt > 0, and it decreases those

when dδ/dt < 0.

5. With a case study explain how an SVC can be used to prevent voltage

instability in a power system. (16)

Prevention of Voltage Instability

Voltage instability is caused by the inadequacy of the power system to supply

the reactive-power demand of certain loads, such as induction motors.

A drop in the load voltage leads to an increased demand for reactive power that,

if not met by the power system, leads to a further decline in the bus voltage.

This decline eventually leads to a progressive yet rapid decline of voltage at

that location, which may have a cascading effect on neighboring regions that

causes a system voltage collapse.

Principles of SVC Control

(a)

(b)

53 | P a g e

(a) An SVC connected at the load bus by a radial transmission line supplying a load and (b) the

voltage profile at the receiving end of a loaded line with a varying power factor load.

The voltage at a load bus supplied by a transmission line is dependent on the

magnitude of the load, the load-power factor, and the impedance of the

transmission line. Consider an SVC connected to a load bus, as shown in Figure

(a).

The load has a varying power factor and is fed by a lossless radial transmission

line. The voltage profile at the load bus, which is situated at the receiver end of

the transmission line, is depicted in Figure (b).

For a given load-power factor, as the transmitted power is gradually increased,

a maximum power limit is reached beyond which the voltage collapse takes

place.

In this typical system, if the combined power factor of the load and SVC is

appropriately controlled through the reactive-power support from the SVC, a

constant voltage of the receiving-end bus can be maintained with increasing

magnitude of transmitted power, and voltage instability can be avoided.

A Case Study

An SVC can be used successfully to prevent voltage instability. The case study

presented here demonstrates the application of SVC to mitigate voltage

instability in a radial system loaded by a large composite load of induction

motors and static loads, all under steady-state and transient conditions.

The 400-kV radial case-study system shown in Figure (c) involves power

supply over a double-circuit transmission line to a load center that comprises a

50% large induction motors (IM) and 50% static loads.

An FC–TCR SVC is connected to the tertiary of a 3-winding load transformer,

and the SVC voltage controller is of the PI type.

54 | P a g e

The instability is caused by tripping one of the transmission lines and is

detected from eigenvalue analysis

(c) A case-study system.

55 | P a g e

(d) The system transient response for opening one circuit (50% IM load without a SVC).

The post-disturbance response for 1 s period is shown in Figure (d). In the

absence of the SVC, the load voltage falls to a level of 0.8 p.u in 80 mS after

the initial transients and falls further to a magnitude of 0.57 p.u in less than 1S.

The onset of induction-motor instability occurs at a voltage of 0.8 p.u. With

falling terminal voltage, the induction-motor load reactive power starts

increasing rapidly, leading to eventual voltage collapse.

If the induction motor loads are completely replaced by static loads of same

value, voltage instability does not occur. After the damping of fast initial

transients, the load voltage stabilizes in about 50 mS.

56 | P a g e

The final value of the stabilized load voltage is a function of the capacitive

reactive- power rating of the SVC, which can be improved further by additional

steady-state voltage-regulating devices.

It is evident that this voltage stabilization is achieved only from the rapid

response offered by the SVC.

A breaker switched shunt capacitor of equivalent rating as the SVC is unable to

prevent voltage collapse.

5. Explain the methods of voltage control by SVC (16)

Voltage Control by the SVC

The voltage-control action of the SVC can be explained through a simplified

block representation of the SVC and power system, as shown in Figure. The power

system is modeled as an equivalent voltage source, VS, behind equivalent system

impedance, XS, as viewed from the SVC terminals. The system impedance XS indeed

corresponds to the short-circuit MVA at the SVC bus and is obtained as

𝑿𝑺 =𝑽𝒃

𝟐

𝑺𝑪

. 𝑴𝑽𝑨𝒃 𝒊𝒏 𝒑.𝒖 (𝟏)

where

Sc = the 3-phase short circuit MVA at the SVC bus

Vb = the base line-to-line voltage

MVAb = the base MVA of the system

If the SVC draws a reactive current ISVC, then in the absence of the SVC voltage

regulator, the SVC bus voltage is given by

𝑽𝑺 = 𝑽𝑺𝑽𝑪 + 𝑰𝑺𝑽𝑪𝑿𝑺 (𝟐)

Or

57 | P a g e

𝑽𝑺 = 𝑽𝑺𝑽𝑪∠𝟎𝟎 + 𝑰𝑺𝑽𝑪∠ − 𝟗𝟎𝟎𝑿𝑺∠𝟗𝟎𝟎 (𝟑)

Or

𝑽𝑺 = (𝑽𝑺𝑽𝑪 + 𝑰𝑺𝑽𝑪𝑿𝑺) ∠𝟎𝟎 (𝟒)

system voltage VS. The SVC bus voltage decreases with the inductive SVC

current and increases with the capacitive current.

Equation (2) represents the power-system characteristic or the system load line.

An implication of Eq. (2) is that the SVC is more effective in controlling

voltage in weak ac systems (high XS) and less effective in strong ac systems

(low XS).

The voltage-control action in the linear range is described as

𝑽𝑺𝑽𝑪 = 𝑽𝒓𝒆𝒇 + 𝑿𝑺𝑳𝑰𝑺𝑽𝑪 (𝟓)

where ISVC is positive if inductive, negative if capacitive.

It is emphasized that the V-I characteristics described here relate SVC current

reactive power to the voltage on the high-voltage side of the coupling

transformer.

58 | P a g e

(a) A simplified block diagram of the power system and SVC control system;

(b) a phasor diagram of the ac system for the inductive SVC current; and

(c) characteristics of the simplified power system and the SVC.

Influence of the SVC on the System Voltage

The constant-equivalent-source voltage Vs is given by,

∆𝑽𝑺𝑽𝑪 = −𝑿𝑺∆𝑰𝑺𝑽𝑪

The VSVC is also related to ISVC through the SVC reactance, BSVC, as follows:

𝑰𝑺𝑽𝑪 = 𝑩𝑺𝑽𝑪𝑽𝑺𝑽𝑪

For incremental changes, the above equation is linearized to give

𝑰𝑺𝑽𝑪 = 𝑩𝑺𝑽𝑪𝟎∆𝑽𝑺𝑽𝑪 + ∆𝑩𝑺𝑽𝑪𝑽𝑺𝑽𝑪𝟎

Substituting ∆ISVC from the above equations we get,

∆𝑽𝑺𝑽𝑪

∆𝑩𝑺𝑽𝑪

=−𝑽𝑺𝑽𝑪𝟎

𝑬𝑺𝑪𝑹 + 𝑩𝑺𝑽𝑪𝟎

59 | P a g e

where the effective short-circuit ratio (ESCR) is defined as

𝑬𝑺𝑪𝑹 =𝟏

(−∆𝑽𝑺𝑽𝑪/∆𝑰𝑺𝑽𝑪)=

𝟏

𝑿𝑺

= 𝑩𝑺

where 𝐵𝑆= the equivalent system susceptance

*******************************

60 | P a g e

EE6004 FLEXIBLE AC TRANSMISSION SYSTEMS

UNIT 3

THYRISTOR CONTROLLED SERIES CAPACITOR

AND APPLICATIONS

2 MARKS

1. What is TCSC?

TCSC is a capacitive reactance compensator, which consists of a series capacitor

bank shunted by a thyristor controlled reactor. The basic conceptual TCSC module

comprises a series capacitor, C, in parallel with a thyristor controlled reactor, Ls, in

order to provide a smoothly variable series capacitive reactance.

2. What is the basic principle of TCSC?

The basic operating principle behind the TCSC is that, it can provide a

continuously variable capacitor by means of partially cancelling the effective

compensating capacitance of the thyristor controlled reactor.

3. List the advantages of TCSC

Rapid , continuous control of transmission-line, series-compensation level

Dynamic control of power flow in selected transmission lines within the

network to enable optimal power flow conditions and prevent the loop flow of

power

Damping of the power swings from local and inter area oscillations

Suppression of synchronous oscillations

Decreasing DC offset voltages.

61 | P a g e

4. What are the applications of TCSC?

Mitigation of sub synchronous resonance

Enhancement of system damping

Power system stability improvement

To increase power transfer capability

5. What is meant by bypassed thyristor mode?

In this bypassed mode, the thyristor are made to fully conduct with the conduction

angle of 180 degree. The TCSC module behaves like a parallel capacitor-inductor

combination. However the net current through the module is inductive, for the

susceptance of the reactor is chosen to be greater than that of the capacitor. Also

known as the thyristor switched reactor (TSR) mode

6. What are different modes of operation of TCSC?

Bypassed thyristor mode

Blocked thyristor mode

Partially conducting thyristor(Capacitive-Vernier) mode

Partially conducting thyristor(inductive-Vernier) mode

7. What is the indication of voltage collapse points?

The Collapse points are indicative of the maximum load ability of the transmission

lines or the available transfer capability (ATC)

8. What is the need for variable-series compensation?

Enhanced base power flow and load ability of series compensator line

Additional losses in the compensator line from the enhanced power flow

Increased responsiveness of the power flow in the series compensated line from

the outage of other lines in the system

62 | P a g e

9. List the models of TCSC.

Modeling for sub-synchronous resonance SSR studies

Variable reactance model

Transient stability model

Long term stability model

10. What is the effect of TCSC in SSR problem?

At sub synchronous frequency the TCSC presents an inherently resistive-inductive

reactance. The sub-synchronous oscillations cannot be sustained in the situations and

consequently get damped.

11. How is the variation of capacitive reactance achieved in TCSC?

By varying the firing angle of the anti-parallel thyristor connected in series with

the reactor in the TCR, the fundamental frequency inductive reactance of the TCR can

be changed. This affects a change in the reactance of TCSC and it can be controlled to

produce either inductive or capacitive reactance.

12. What are the causes of series compensation in long transmission lines?

Sub-synchronous oscillations, caused by interaction between the electrical

network and the generator torsional system.

Low frequency (1Hz-10Hz) oscillations caused by interaction between the

series capacitors and the shunt inductors, especially during line switching and

faults. These oscillations have large magnitudesand last for long periods

because of high shunt reactor Q factors.

Switching oscillations, caused by the switching of lines.

13. Define sub synchronous resonance (SSR)

It is an electric power system condition, where the electric network exchanges

energy with the turbine generator at one or more of the natural frequencies of the

combined system below the synchronous frequency of the system.

63 | P a g e

14. What are the different modes of operation of TCSC?

Bypassed- thyristor mode

Blocked - thyristor mode

Partially conducting thyristor or Vernier mode

15. What are symptoms of voltage collapse?

The main symptoms of voltage collapse are low voltage profiles, heavy reactive

power flows, inadequate reactive support, and heavily loaded systems.

16. How is voltage instability identified in the power system?

Voltage instability problem is mainly because of insufficient reactive capacity

of power systems during disturbances like line outage contingencies.

Voltage collapse is mathematically indicated when the system Jacobian

becomes singular.

17. What does voltage collapse means?

Voltage collapse is a loss of stability in large scale electric power systems which

causes blackout when voltages decrease terribly.

18. What are the needs of the damping control of a TCSC?

Stabilize both post disturbance oscillations and spontaneously growing

oscillations during normal operations

Obviate the adverse interactions with high frequency phenomena in power

system such as network resonance

Preclude local instabilities within the controller bandwidth

Be robust in that it imparts the desired damping over a wide range of system

operating conditions

Be reliable

64 | P a g e

19. What are the locations to place TCSC in a power system?

The TCSC should be located in lines that experience limiting power oscillations

The swing of voltage on each side of the TCSC must be within acceptable

limits otherwise multiple sides may be necessary

The control action of the TCSC in one transmission path should not cause

undue power swing in a parallel path

Sometimes it may be advisable to distribute the control action among multiple

TCSCs rather than confining the control action to one large rating TCSC

20. What are the needs for variable series compensation?

Enhance base power flow and load ability of the series compensated line

Additional losses in the compensated line from the enhanced power flow

Increase responsiveness of power flow in the series compensated line from the

outage of other lines in the system

21. How is system voltage stability limit improved?

Voltage stability is primarily associated with the reactive power support.

FACTS devices can regulate the active and reactive power control as well as

adaptive to voltage magnitude control simultaneously because of their

flexibility and fast control characteristics.

Placement of these devices in suitable location and proper coordination between

FACTS controllers can leads to control in line flow and maintain bus voltages

in desired level and so improve voltage stability margins and of the power

systems.

22. What is Bang Bang control?

Bang Bang control is a discrete control form in which the thyristor are either

fully switched on (α=90) or fully switched off (α=180)

65 | P a g e

Thus, TCSC alternates between a fixed inductor and a fixed capacitor,

respectively, and it is advantageous that such control is used not only for

minimizing first swings but for damping any subsequent swings as well.

Bang bang control is employed in face of large disturbances to improve the

transient stability.

*********************

16 MARKS

1. Explain the working and characteristics of TCSC (16)

Thyristor-Controlled Series Capacitor (TCSC)

Working Principle

The basic Thyristor-Controlled Series Capacitor scheme consists of the series

compensating capacitor shunted by a Thyristor-Controlled Reactor.

In a practical TCSC implementation, several such basic compensators may be

connected in series to obtain the desired voltage rating and operating

characteristics.

Basic Thyristor-Controlled Series Capacitor scheme

66 | P a g e

This arrangement is similar in structure to the TSSC and, if the impedance of

the reactor, XL, is sufficiently smaller than that of the capacitor, XC, it can be

operated in an on-off manner like the TSSC.

However, the basic idea behind the TCSC scheme is to provide a continuously

variable capacitor by means of partially canceling the effective compensating

capacitance by the TCR.

The TCR at the fundamental system frequency is a continuously variable

reactive impedance, controllable by delay angle a, the steady-state impedance

of the TCSC is that of a parallel LC circuit, consisting of a fixed capacitive

impedance, Xc, and a variable inductive impedance, XL(α), that is,

𝑿𝑻𝑪𝑺𝑪(𝜶) =𝑿𝑪𝑿𝑳 (𝜶)

𝑿𝑳 𝜶 − 𝑿𝑪

𝑿𝑳 𝜶 = 𝑿𝑳 𝜶 𝝅

𝝅 − 𝟐𝜶 − 𝒔𝒊𝒏𝜶 𝜶 , 𝑿𝑳 ≤ 𝑿𝑳(𝜶) ≤ ∞

where XL = ωL, and α is the delay angle measured from the crest of the capacitor

voltage.

The TCSC thus presents a tunable parallel LC circuit to the line current that is

substantially a constant alternating current source.

Characteristics

As the impedance of the controlled reactor, XL(α), is varied from its maximum

(infinity) toward its minimum (ωL), the TCSC increases its minimum

capacitive impedance, XTCSC.min

= XC = 1/ωC, (and thereby the degree of series

capacitive compensation) until parallel resonance at Xc = XL(α) is established

and XTCSC.max

theoretically becomes infinite.

Decreasing XL(α) further, the impedance of the TCSC, XTCSC(α) becomes

inductive, reaching its minimum value of XLXC /(XL – XC) at a = 0, where the

capacitor is in effect bypassed by the TCR.

67 | P a g e

Therefore, with the usual TCSC arrangement in which the impedance of the

TCR reactor, XL, is smaller than that of the capacitor, XC, the TCSC has two

operating ranges around its internal circuit resonance: one is the αClim ≤ α ≤ π/2

range, where XTCSC(α) is capacitive, and the other is the 0 ≤ α ≤ αLlim range,

where XTCSC(α) is inductive, as illustrated in Figure.

The impedance vs. delay angle α characteristic of the TCSC.

The steady-state model of the TCSC described above is based on the

characteristics of the TCR established in an SVC environment, where the TCR

is supplied from a constant voltage source.

This model is useful to attain a basic understanding of the functional behavior

of the TCSC.

However, in the TCSC scheme the TCR is connected in shunt with a capacitor,

instead of a fixed voltage source.

The dynamic interaction between the capacitor and reactor changes the

operating voltage from that of the basic sine wave established by the constant

line current.

68 | P a g e

A deeper insight into this interaction is essential to the understanding of the

actual physical operation and dynamic behavior of the TCSC, particularly

regarding its impedance characteristic at sub-synchronous frequencies.

2. Explain the variable reactance modeling of TCSC (or) with neat diagram,

explain the variable reactance model of TCSC and derive transient stability

and long term stability models (16)

Modeling of the TCSC

A TCSC involves continuous-time dynamics, relating to voltages and currents

in the capacitor and reactor, and nonlinear, discrete switching behavior of thyristors.

Deriving an appropriate model for such a controller is a complicated task.

Variable-Reactance Model

A TCSC model for transient- and oscillatory-stability studies, used widely for

its simplicity, is the variable-reactance model depicted in Figure.

In this quasi-static approximation model, the TCSC dynamics during power-

swing frequencies are modeled by a variable reactance at fundamental

frequency.

A block diagram of the variable-reactance model of the TCSC

69 | P a g e

It is assumed that the transmission system operates in a sinusoidal steady state,

with the only dynamics associated with generators and PSS.

This assumption is valid, because the line dynamics are much faster than the

generator dynamics in the frequency range of 0.1–2 Hz that are associated with

angular stability studies.

The variable-reactance TCSC model assumes the availability of a continuous-

reactance range and is therefore applicable for multi module TCSC

configurations.

This model is generally used for inter-area mode analysis, and it provides high

accuracy when the reactance-boost factor is less than 1.5.

(i) Transient-Stability Model

In the variable-reactance model for stability studies, a reference value of TCSC

reactance, Xref, is generated from a power-scheduling controller based on the

power-flow specification in the transmission line.

The reference Xref value may also be set directly by manual control in response

to an order from an energy-control center, and it essentially represents the

initial operating point of the TCSC; it does not include the reactance of fixed

capacitors (FC).

The reference value is modified by an additional input, Xmod, from a modulation

controller for such purposes as damping enhancement.

Another input signal, this applied at the summing junction, is the open-loop

auxiliary signal, Xaux, which can be obtained from an external power-flow

controller.

A desired magnitude of TCSC reactance, Xdes, is obtained that is implemented

after a finite delay caused by the firing controls and the natural response of the

TCSC.

70 | P a g e

This delay is modeled by a lag circuit having a time constant, TTCSC, of typically

15–20 ms.

The resulting XTCSC is added to the Xfixed, which is the reactance of the TCSC

installation’s FC component. To obtain per-unit values, the TCSC reactance is

divided by the TCSC base reactance, Zbase, given as

𝒁𝒃𝒂𝒔𝒆 =(𝒌𝑽𝑻𝑪𝑺𝑪)𝟐

𝑴𝑽𝑨𝒔𝒚𝒔

where

kVTCSC = the rms line–line voltage of the TCSC in kilovolts (kV)

MVAsys = the 3-phase MVA base of the power system

(ii) Long-Term-Stability Model

The capability curves of the TCSC depend on the duration for which the

voltage- and current-operating conditions persist on the TCSC.

In general, two time-limited regions of TCSC operation exist: the transient-

overload region, lasting 3–10 s, and the temporary-overload region, lasting 30

min; both are followed by the continuous region.

This function keeps track of the TCSC variables and their duration of

application, and it also determines the appropriate TCSC overload range, for

which it modifies the Xmax limit and Xmin limit. It then applies the same

modifications to the controller.

The variable-reactance model does not account for the inherent dependence of

TCSC response time on the operating conduction angle.

Therefore, entirely incorrect results may be obtained for the high-conduction-

angle operation of the TCSC or for whenever the power-swing frequency is

high.

71 | P a g e

However, the model is used widely in commercial stability programs because of

its simplicity, and it is also used for system-planning studies as well as for

initial investigations of the effects of the TCSC in damping-power oscillations.

A reason for the model’s widespread use lies in the assumption that controls

designed to compensate the TCSC response delay are always embedded in the

control system by the manufacturer and are therefore ideal.

Hence the response predicted by the model is a true replica of actual

performance. In situations where this assumption is not satisfied, a more

detailed stability model is required that accurately represents the inherent slow

response of the TCSC.

3. Explain the basic principle and different modes of operation in TCSC. What

are the advantages of TCSC? (16)

Modes of TCSC Operation

There are essentially three modes of TCSC operation; these are illustrated in Figure

and described in the following text.

Bypassed-Thyristor Mode

In this bypassed mode, the thyristors are made to fully conduct with a

conduction angle of 1800.

Gate pulses are applied as soon as the voltage across the thyristors reaches zero

and becomes positive, resulting in a continuous sinusoidal of flow current

through the thyristor valves.

The TCSC module behaves like a parallel capacitor–inductor combination.

However, the net current through the module is inductive, for the susceptance

of the reactor is chosen to be greater than that of the capacitor.

72 | P a g e

Also known as the thyristor-switched-reactor (TSR) mode, the bypassed

thyristor mode is distinct from the bypassed-breaker mode, in which the circuit

breaker provided across the series capacitor is closed to remove the capacitor or

the TCSC module in the event of TCSC faults or transient over voltages across

the TCSC.

Different operating modes of a TCSC: (a) the bypassed-thyristor mode; (b) the blocked-

thyristor mode; (c) the partially conducting thyristor (capacitive-vernier) mode; and (d)

the partially conducting thyristor (inductive-vernier) mode.

This mode is employed for control purposes and also for initiating certain

protective functions.

73 | P a g e

Whenever a TCSC module is bypassed from the violation of the current limit, a

finite-time delay, Tdelay must elapse before the module can be reinserted after

the line current falls below the specified limit.

Blocked-Thyristor Mode

In this mode, also known as the waiting mode, the firing pulses to the thyristor

valves are blocked.

If the thyristors are conducting and a blocking command is given, the thyristors

turn off as soon as the current through them reaches a zero crossing.

The TCSC module is thus reduced to a fixed-series capacitor, and the net TCSC

reactance is capacitive.

In this mode, the dc-offset voltages of the capacitors are monitored and quickly

discharged using a dc-offset control without causing any harm to the

transmission-system transformers.

Partially Conducting Thyristor, or Vernier, Mode

This mode allows the TCSC to behave either as a continuously controllable

capacitive reactance or as a continuously controllable inductive reactance.

It is achieved by varying the thyristor-pair firing angle in an appropriate range.

However, a smooth transition from the capacitive to inductive mode is not

permitted because of the resonant region between the two modes.

A variant of this mode is the capacitive-vernier-control mode, in which the

thyristors are fired when the capacitor voltage and capacitor current have

opposite polarity.

This condition causes a TCR current that has a direction opposite that of the

capacitor current, thereby resulting in a loop-current flow in the TCSC

controller.

74 | P a g e

The loop current increases the voltage across the fixed capacitor FC, effectively

enhancing the equivalent-capacitive reactance and the series-compensation

level for the same value of line current.

To preclude resonance, the firing angle a of the forward-facing thyristor, as

measured from the positive reaching a zero crossing of the capacitor voltage, is

constrained in the range αmin ≤ α ≤1800.

This constraint provides a continuous vernier control of the TCSC module

reactance. The loop current increases as α is decreased from 1800 to αmin.

The maximum TCSC reactance permissible with a αmin is typically two-and-a-

half to three times the capacitor reactance at fundamental frequency.

Advantages of the TCSC

Use of thyristor control in series capacitors potentially offers the following little-

mentioned advantages:

Rapid, continuous control of the transmission-line series-compensation level.

Dynamic control of power flow in selected transmission lines within the

network to enable optimal power-flow conditions and prevent the loop flow of

power.

Damping of the power swings from local and inter-area oscillations.

Suppression of sub-synchronous oscillations. At sub-synchronous frequencies,

the TCSC presents an inherently resistive–inductive reactance. The sub-

synchronous oscillations cannot be sustained in this situation and consequently

get damped.

Decreasing dc-offset voltages. The dc-offset voltages, invariably resulting from

the insertion of series capacitors, can be made to decay very quickly (within a

few cycles) from the firing control of the TCSC thyristors.

75 | P a g e

Enhanced level of protection for series capacitors. A fast bypass of the series

capacitors can be achieved through thyristor control when large over voltages

develop across capacitors following faults. Likewise, the capacitors can be

quickly reinserted by thyristor action after fault clearing to aid in system

stabilization.

Voltage support. The TCSC, in conjunction with series capacitors, can generate

reactive power that increases with line loading, thereby aiding the regulation of

local network voltages and, in addition, the alleviation of any voltage

instability.

Reduction of the short-circuit current. During events of high short-circuit

current, the TCSC can switch from the controllable-capacitance to the

controllable-inductance mode, thereby restricting the short-circuit currents.

4. Analyze the capability of TCSC in damping the oscillations of power system

(or) discuss the role of TCSC in the enhancement of system damping (16)

Capability Characteristics

Although TCSC design is based on the application requirements, the

operational limits are determined by the characteristics of different TCSC components.

The important limits are described in the following list:

Voltage limits, of which the maximum amount across any operating equipment

(including series capacitors) is determined by the equipment’s insulation level.

The constraint on voltage may vary with the duration of voltage application.

For short durations (typically less than 2 s), the overvoltage limit is more

critical than that of the capacitor.

Current limits, which may need to be imposed on the currents in the thyristor

valve, fixed capacitor, and surge inductor to prevent overheating. Harmonics

76 | P a g e

also cause heating and therefore have a constraining effect on the TCSC

operation.

Firing-angle limits of the thyristors, which must be carefully restricted so that

the TCSC does not venture into the resonant region (even temporarily).

Principle of Damping

The concept of damping enhancement by line-power modulation can be

illustrated with the two-machine system depicted in Figure.

The machine SM1 supplies power to the other machine, SM2, over a lossless

transmission line.

Let the speed and rotor angle of machine SM1 be denoted by η1 and φ1,

respectively; of machine SM2, denoted by η2 and φ2, respectively.

The TCSC line-power modulation for damping enhancement

During a power swing, the machines oscillate at a relative angle Δφ = (φ2 - φ1).

If the line power is modulated by the TCSC to create an additional machine

torque that is opposite in sign to the derivative of the rotor-angle deviation, the

oscillations will get damped.

77 | P a g e

This control strategy translates into the following actions: When the receiving

end–machine speed is lower than the sending end–machine speed, that is, Δη =

(η2 - η1) is negative, the TCSC should increase power flow in the line.

In other words, while the sending-end machine accelerates, the TCSC control

should attempt to draw more power from the machine, thereby reducing the

kinetic energy responsible for its acceleration.

On the other hand, when Δη is positive, the TCSC must decrease the power

transmission in the line. This damping control strategy is depicted in Figure

through plots of the relative machine angle Δφ, the relative machine speed Δη,

and the incremental power variation ΔPmod.

TCSC Power-Oscillation Damping (POD) Control

The main objective of the TCSC installation is the damping of N–S inter-area

mode. Power-flow control is not considered, nor is SSR damping, as the

generators are mainly hydroelectric.

The control input to the POD controller is selected as the active power flow in

the line. However, the line-current signal is found to be almost equally

effective.

It may be noted that the amount of line active-power variation caused by the

TCSC is a function of both the change in TCSC reactance as well as the line

current loading.

Thus if the TCSC control operates with a constant gain, the TCSC will be most

effective in damping power oscillations during high line loadings and least

effective during low line loadings.

To maintain a near-uniform damping contribution over a wide range of line

loadings, a gain-scheduling scheme is adopted, as shown in Figure.

78 | P a g e

A gain-scheduling scheme

In the figure, the input, IN, to the gain controller is derived from the control

signal input, I(P) to the POD controller by passing it through a low-pass filter

having a time constant Tav2, which is large enough to not interact with the

power-oscillation frequency .

A low value of line-power flow, INL, provides a high gain, KGL; a high line

loading, INF, provides a low gain, KGF.

Any intermediate level of power-flow IN results in an interpolated gain KG,

which is then used for power-oscillation damping

Enhancement of System Damping

The TCSC can be made to vary the series-compensation level dynamically in

response to controller-input signals so that the resulting changes in the power

flow enhance the system damping.

The power modulation results in a corresponding variation in the torques of the

connected synchronous generators—particularly if the generators operate on

constant torque and if passive bus loads are not installed.

The damping control of a TCSC or any other FACTS controller should generally

do the following:

Stabilize both post disturbance oscillations and spontaneously growing

oscillations during normal operation; obviate the adverse interaction with high-

79 | P a g e

frequency phenomena in power systems, such as network resonances; and

preclude local instabilities within the controller bandwidth.

In addition, the damping control should be robust in that it imparts the desired

damping over a wide range of system operating conditions, and be reliable.

**************************

80 | P a g e

EE6004 FLEXIBLE AC TRANSMISSION SYSTEMS

UNIT 4

VOLTAGE SOURCE CONVERTER BASED FACTS

CONTROLLERS

2 MARKS

1. What is STATCOM?

The STATCOM (or SSC) is a shunt-connected reactive power compensation

device that is capable of generating and/or absorbing reactive power and in which the

output can be varied to control the specific parameters of an electric power system.

2. State the salient features of STATCOM features.

Compact size

System voltage support and stabilization by smooth control over a wide range

of operating conditions

Dynamic response following system contingencies

High reliability with redundant parallel converter design and modular

construction

Flexibility of future reconstruction to Back to Back (BTB) power transmission

3. List the applications of STATCOM.

Damping of power system oscillations

Damping of sub synchronous oscillations

Balanced loading of individual phases

Reactive compensation of AC-DC converters and HVDC links

Improvement of steady state power transfer capacity

81 | P a g e

4. Compare the V-I Characteristic of STATCOM & SVC.

5. How the reactive power compensation is done using STATCOM?

A STATCOM is a controlled reactive power source. It provides the desired

reactive power generation and absorption entirely by means of electronic processing of

the voltage and current waveforms in a voltage source converter

6. List the modes of operation of STATCOM.

The STATCOM can be operated in two different modes:

Voltage regulation mode under this mode it has 3 sub divisions. There are,

Over excited mode of operation

Under excited mode of operation

Normal(floating) excited mode of operation

Var control mode

7. Compare STATCOM and SVC.

The STATCOM has the ability to provide more capacitive reactive power

during faults, or when the system voltage drops abnormally, compared to

ordinary static var compensator.

This is because the maximum capacitive reactive power generated by a

STATCOM deceases linearly with system voltage, while that of the SVC is

proportional to the square of the voltage.

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Also, the STATCOM has a faster response as it has no time delay associated

with thyristor firing. Nevertheless, these advantages come at a higher price

(about 20% more)

8. What are the functions of STATCOM?

Dynamic voltage control in transmission and distribution systems

Power oscillation damping in power transmission systems

Transient stability improvement

Ability to control not only reactive power but, if needed, also active power

(with a DC energy source available)

9. Define STATCOM.

The STATCOM has been defined as per CIGRE/IEEE with following three operating

scenarios.

First component is static: based on solid state switching devices with no

rotating components;

Second component is Synchronous: Analogous to an ideal synchronous

machine with three sinusoidal phase voltages at fundamental frequency;

Third component is compensator: rendered with reactive compensation.

10. List the advantages/benefits of STATCOM.

The STATCOM offers following advantages:

Superior voltage supporting capability

Fast response

Large reactive power generation under low system voltage condition

Less harmonics generation

Smaller filter capacity

Less space requirement

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11. What is UPFC?

The UPFC is a device which can control simultaneously all three parameters of

line power flow (line impedence, voltage and phase angle).Such ―new‖ FACTS device

combines together the features of two ―old‖ FACTS devices‖ the Static Synchronous

Compensator (STATCOM) and the Static Synchronous Series Compensator (SSSC). It

is proposed by Gyugyi in 1991.

12. List the application of UPFC.

Power flow control

Power swing damping

Voltage dips compensation

Fault Current Limiting

13. State the salient features of UPFC.

The UPFC is versatile and multifunction power flow controller with capabilities

of terminal voltage regulation, series line compensation and phase angle

regulation

Minimization of power losses without generator rescheduling

Regulating power flow through a transmission line

More reliable

Provides dynamic security

Acts as harmonic isolator

14. What are the parameters that can be improved using STATCOM in power

system?

The dynamic voltage control in transmission and distribution system

The power oscillation damping in power transmission system

84 | P a g e

The transient stability

The voltage flicker control

The control of not only reactive power but also active power in the connected

line, requiring a Dc energy source

15. What are the different constraints for operating UPFC?

The series injected voltage magnitude

The line current through series converter

The shunt converter current

The minimum line side voltage of the UPFC

The maximum line side voltage of the UPFC

The real power transfer between the series converter and the shunt converter

16. What are the operating modes of UPFC?

VAR Control Mode

Automatic Voltage Control Mode

Direct Voltage Injection Mode

Phase Angle Shifter Emulation Mode

Line Impedance Emulation Mode

Automatic Power Flow Control Mode

17. What are the functions of series converter in the UPFC?

A UPFC series converter exchanges both real and reactive power with the

transmission line. Although the reactive power is internally generated or absorbed by

the series converter, the real power generation or absorption is made feasible by the dc

energy storage device.

85 | P a g e

18. What are the functions of shunt converter in the UPFC?

In a UPFC shunt converter mainly used to supply the real power demand of series

converter, which it derives from the transmission line itself. The shunt converter

maintains constant voltage of the dc bus. In addition, the shunt converter functions like

a STATCOM and independently regulate the terminal voltage of the interconnected

bus by generating or absorbing a requisite amount of reactive power

19. What is SSSC?

Static Synchronous Series Compensator (SSSC) is a modern power quality FACTS

device that employs a voltage source converter connected in series to a transmission

line through a transformer. The SSSC operates like a controllable series capacitor and

series inductor. The primary difference is that its injected voltage is not related to the

line intensity and can be managed independently. This feature allows the SSSC to

work satisfactorily with high loads as well as with lower loads.

20. What are the basic components of SSSC?

The Static Synchronous Series Compensator has three basic components:

Voltage Source Converter (VSC) – main component

Transformer – couples the SSSC to the transmission line

Energy Source – provides voltage across the DC capacitor and compensate

for device losses

21. What is the role of SSSC?

The SSSC injects a compensating voltage in series with the line irrespective of the

line current. From the phasor diagram, it can be stated that at a given line current, the

voltage injected by the SSSC forces the opposite polarity voltage across the series line

reactance. It works by increasing the voltage across the transmission line and thus

increases the corresponding line current and transmitted power

86 | P a g e

22. Give the expression about power transfer characteristics of SSSC with line

compensation

𝑷 =𝑽𝑺𝑽𝑹

𝑿𝑳 −𝑽𝑪

𝑰

𝒔𝒊𝒏𝜹

23. What is the power transfer characteristic of SSSC with line compensation

The compensating reactance is defined to be negative when the SSSC is operated

in an inductive mode and positive when operated in capacitive mode. The voltage

source converter can be controlled in such a way that the output voltage can either lead

or lag the line current by 90o during normal capacitive compensation, the output

voltage lags the line current by 90o. The SSSC can increase or decrease the power flow

to the same degree in either direction simply by changing the polarity of the injected

ac voltage.

24. What are the control parameters attained by the SSSC?

The active power flow of the transmission line

The reactive power flow of the transmission line

The bus voltage

The impedance of the transmission line

25. List the different operating modes of SSSC

Active power flow control

Reactive power flow control

Bus voltage control

Reactance control

26. What are the applications and advantages of SSSC?

The SSSC is typically applied to correct the voltage during a fault in the

power system. However, it also has several advantages during normal

conditions:

87 | P a g e

Power factor correction through continuous voltage injection and in

combination with a properly structured controller

Load balancing in interconnected distribution networks.

It can also help to cover the capacitive and reactive power demand.

Power flow control

Reduces harmonic distortion by active filtering

*********************

16 MARKS

1. Explain the basic construction, principle of operation and V-I characteristics

of STATCOM (16)

Construction of STATCOM

The STATCOM (or SSC) is a shunt-connected reactive-power compensation

device that is capable of generating and or absorbing reactive power and in

which the output can be varied to control the specific parameters of an electric

power system.

It is in general a solid-state switching converter capable of generating or

absorbing independently controllable real and reactive power at its output

terminals when it is fed from an energy source or energy-storage device at its

input terminals.

A STATCOM is analogous to an ideal synchronous machine, which generates a

balanced set of three sinusoidal voltages—at the fundamental frequency—with

controllable amplitude and phase angle.

88 | P a g e

A STATCOM is a controlled reactive-power source. It provides the desired

reactive-power generation and absorption entirely by means of electronic

processing of the voltage and current waveforms in a voltage-source converter

(VSC).

The STATCOM principle diagram: (a) a power circuit; (b) an equivalent circuit; and (c) a

power exchange

A single-line STATCOM power circuit is shown in Figure (a), where a VSC is

connected to a utility bus through magnetic coupling.

In Figure (b), a STATCOM is seen as an adjustable voltage source behind a

reactance—meaning that capacitor banks and shunt reactors are not needed for

reactive-power generation and absorption, thereby giving a STATCOM a

compact design, or small footprint, as well as low noise and low magnetic

impact.

Principle of Operation

A dc capacitor bank is used to support (stabilize) the controlled dc voltage

needed for the operation of the VSC.

89 | P a g e

The reactive power of a STATCOM is produced by means of power-electronic

equipment of the voltage-source-converter type.

The VSC may be a 2- level or 3-level type, depending on the required output

power and voltage.

A number of VSCs are combined in a multi-pulse connection to form the

STATCOM. In the steady state, the VSCs operate with fundamental-frequency

switching to minimize converter losses.

The exchange of reactive power between the converter and the ac system can be

controlled by varying the amplitude of the 3-phase output voltage, Es, of the

converter, as illustrated in Figure(c).

That is, if the amplitude of the output voltage is increased above that of the

utility bus voltage, Et, then a current flows through the reactance from the

converter to the ac system and the converter generates capacitive-reactive

power for the ac system.

If the amplitude of the output voltage is decreased below the utility bus voltage,

then the current flows from the ac system to the converter and the converter

absorbs inductive-reactive power from the ac system.

If the output voltage equals the ac system voltage, the reactive-power exchange

becomes zero, in which case the STATCOM is said to be in a floating state.

Adjusting the phase shift between the converter-output voltage and the ac

system voltage can similarly control real-power exchange between the

converter and the ac system.

However, the real power that the converter exchanges at its ac terminals with

the ac system must, of course, be supplied to or absorbed from its dc terminals

by the dc capacitor.

90 | P a g e

Although reactive power is generated internally by the action of converter

switches, a dc capacitor must still be connected across the input terminals of the

converter.

The primary need for the capacitor is to provide a circulating-current path as

well as a voltage source.

Depending on the converter configuration employed, it is possible to calculate

the minimum capacitance required to meet the system requirements, such as

ripple limits on the dc voltage and the rated-reactive power support needed by

the ac system.

V-I Characteristics

A typical V-I characteristic of a STATCOM is depicted in Figure. The

STATCOM can supply both the capacitive and the inductive compensation and

is able to independently control its output current over the rated maximum

capacitive or inductive range irrespective of the amount of ac-system voltage.

That is, the STATCOM can provide full capacitive-reactive power at any

system voltage—even as low as 0.15 pu.

The characteristic of a STATCOM reveals strength of this technology: that it is

capable of yielding the full output of capacitive generation almost

independently of the system voltage (constant-current output at lower voltages).

This capability is particularly useful for situations in which the STATCOM is

needed to support the system voltage during and after faults where voltage

collapse would otherwise be a limiting factor.

Figure also illustrates that the STATCOM has an increased transient rating in

both the capacitive- and the inductive-operating regions.

The maximum attainable transient over current in the capacitive region is

determined by the maximum current turn-off capability of the converter

switches.

91 | P a g e

In the inductive region, the converter switches are naturally commutated;

therefore, the transient-current rating of the STATCOM is limited by the

maximum allowable junction temperature of the converter switches.

The V-I characteristic of the STATCOM

In practice, the semiconductor switches of the converter are not lossless, so the

energy stored in the dc capacitor is eventually used to meet the internal losses

of the converter, and the dc capacitor voltage diminishes.

However, when the STATCOM is used for reactive-power generation, the

converter itself can keep the capacitor charged to the required voltage level.

This task is accomplished by making the output voltages of the converter lag

behind the ac-system voltages by a small angle (usually in the 0.18–0.28 range).

In this way, the converter absorbs a small amount of real power from the ac

system to meet its internal losses and keep the capacitor voltage at the desired

level.

The same mechanism can be used to increase or decrease the capacitor voltage

and thus, the amplitude of the converter-output voltage to control the var

generation or absorption.

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2. Explain in detail about the implementation of UPFC (16)

The Unified Power Flow Controller

The UPFC was devised for the real-time control and dynamic compensation of

ac transmission systems, providing multifunctional flexibility required to solve

many of the problems facing the power delivery industry.

Within the framework of traditional power transmission concepts, the UPFC is

able to control, simultaneously or selectively, all the parameters affecting power

flow in the transmission line, and this unique capability is signified by the

adjective "unified" in its name.

Alternatively, it can independently control both the real and .reactive power

flow in the line.

Basic Operating Principle

From the conceptual viewpoint, the UPFC is a generalized synchronous voltage

source (SVS), represented at the fundamental (power system) frequency by

voltage phasor Vpq with controllable magnitude Vpq (0 ≤ Vpq ≤ Vpqmax) and angle

ρ (0 ≤ ρ ≤ 2π), in series with the transmission line, as illustrated for the usual

elementary twomachine system .

(a) Conceptual representation of the UPFC in a two-machine power system.

93 | P a g e

In this functionally unrestricted operation, which clearly includes voltage and

angle regulation, the SVS generally exchanges both reactive and real power

with the transmission system.

Since, as established previously, an SVS is able to generate only the reactive

power exchanged, the real power must be supplied to it, or absorbed from it, by

a suitable power supply or sink.

In the UPFC arrangement the real power exchanged is provided by one of the

end buses (e.g., the sending-end bus), as indicated in Figure (a) .

Implementation of the UPFC

In the presently used practical implementation, the UPFC consists of two

voltage-sourced converters, as illustrated in Figure(b).

(b) Implementation of the UPFC by two back-to-back voltage-sourced converters

Theseback-to-back converters, labeled "Converter 1" and "Converter 2" in the

figure, are operated from a common de link provided by a de storage capacitor.

As indicated before, this arrangement functions as an ideal ac-to-ac power

converter in which the real power can freely flow in either direction between

94 | P a g e

the ac terminals of the two converters, and each converter can independently

generate (or absorb) reactive power at its own ac output terminal.

Converter 2 provides the main function of the UPFC by injecting a voltage Vpq

with controllable magnitude Vpq and phase angle p in series with the line via an

insertion transformer. This injected voltage acts essentially as a synchronous ac

voltage source.

The transmission line current flows through this voltage source resulting in

reactive and real power exchange between it and the ac system. The reactive

power exchanged at the ac terminal is generated internally by the converter.

The real power exchanged at the ac terminal is converted into de power which

appears at the de link as a positive or negative real power demand.

The basic function of Converter 1 is to supply or absorb the real power

demanded by Converter 2 at the common de link to support the real power

exchange resulting from the series voltage injection.

This de link power demand of Converter 2 is converted back to ac by

Converter 1 and coupled to the transmission line bus via a shuntconnected

transformer.

In addition to the real power need of Converter 2, Converter 1 can also

generate or absorb controllable reactive power, if it is desired, and thereby

provide independent shunt reactive compensation for the line.

It is important to note that whereas there is a closed direct path for the real

power negotiated by the action of series voltage injection through Converters 1

and 2 back to the line, the corresponding reactive power exchanged is supplied

or absorbed locally by Converter 2 and therefore does not have to be

transmitted by the line.

Thus, Converter 1 can be operated at a unity power factor or be controlled to

have a reactive power exchange with the line independent of the reactive power

95 | P a g e

exchanged by Converter 2. Obviously, there can be no reactive power flow

through the UPFC de link.

3. Explain the steady state UPFC model for power flow studies (16)

Modeling of UPFC for Power Flow Studies

It follows from that discussion that an equivalent circuit consisting of two

coordinated synchronous voltage sources should represent the UPFC adequately

for the purpose of fundamental frequency steady-state analysis. Such an

equivalent circuit is shown in Figure.

UPFC Equivalent circuit

The synchronous voltage sources represent the fundamental Fourier series

component of the switched voltage waveforms at the AC converter terminals of

the UPFC. The UPFC voltage sources are:

𝑬𝒗𝒓 = 𝑽𝒗𝒓 𝒄𝒐𝒔𝜹𝒗𝒓 + 𝒋𝒔𝒊𝒏𝜹𝒗𝒓 (𝟏)

𝑬𝒄𝒓 = 𝑽𝒄𝒓 𝒄𝒐𝒔𝜹𝒄𝒓 + 𝒋𝒔𝒊𝒏𝜹𝒄𝒓 (𝟐)

96 | P a g e

Where 𝑽𝒗𝒓 and 𝜹𝒗𝒓are the controllable magnitude (Vvr min ≤ Vvr ≤ Vvr max) and phase

angle (0 ≤ 𝜹𝒗𝒓 ≤2π) of the voltage source representing the shunt converter. The

magnitude 𝑽𝒄𝒓 and phase angle 𝜹𝒄𝒓 of the voltage source representing the series

converter are controlled between limits (Vcr min ≤ Vcr ≤ Vcr max) and (0 ≤𝜹𝒄𝒓 ≤ 2π),

respectively.

The phase angle of the series-injected voltage determines the mode of power

flow control.

If 𝜹𝒄𝒓 is in phase with the nodal voltage angle θk, the UPFC regulates the

terminal voltage.

If 𝜹𝒄𝒓is in quadrature with respect to θk, it controls active power flow, acting as

a phase shifter.

If 𝜹𝒄𝒓 is in quadrature with the line current angle then, it controls active power

flow acting as a variable series compensator.

At any other value of 𝜹𝒄𝒓 , the UPFC operates as a combination of voltage

regulator, variable series compensator, and phase shifter.

The magnitude of the series-injected voltage determines the amount of power

flow to be controlled. Based on the equivalent circuit shown in Figure, the

active and reactive power equations are

At bus „k‟:

𝑷𝒌 = 𝑽𝒌𝟐𝑮𝒌𝒌 + 𝑽𝒌𝑽𝒎[𝑮𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒎) + 𝑩𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒎)]

+𝑽𝒌𝑽𝒄𝒓[𝑮𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒄𝒓) + 𝑩𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒄𝒓)]

+𝑽𝒌𝑽𝒗𝒓[𝑮𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒗𝒓) + 𝑩𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒗𝒓)] (𝟑)

𝑸𝒌 = −𝑽𝒌𝟐𝑮𝝔𝒌 + 𝑽𝒌𝑽𝒎[𝑮𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒎) + 𝑩𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒎)]

+𝑽𝒌𝑽𝒄𝒓[𝑮𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒄𝒓) + 𝑩𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒄𝒓)]

+𝑽𝒌𝑽𝒗𝒓[𝑮𝒌𝒎𝒔𝒊𝒏(𝜽𝒌 − 𝜽𝒗𝒓) + 𝑩𝒌𝒎𝒄𝒐𝒔(𝜽𝒌 − 𝜽𝒗𝒓)] (𝟒)

97 | P a g e

At bus „m‟:

𝑷𝒎 = 𝑽𝒎𝟐 𝑮𝒎𝒎 + 𝑽𝒎𝑽𝒌[𝑮𝒎𝒌𝒄𝒐𝒔(𝜽𝒎 − 𝜽𝒌) + 𝑩𝒎𝒌𝒔𝒊𝒏(𝜽𝒎 − 𝜽𝒌)]

+𝑽𝒎𝑽𝒄𝒓[𝑮𝒎𝒎𝒄𝒐𝒔(𝜽𝒎 − 𝜽𝒄𝒓) + 𝑩𝒎𝒎𝒔𝒊𝒏(𝜽𝒎 − 𝜽𝒄𝒓)] (𝟓)

𝑸𝒎 = −𝑽𝒎𝟐 𝑩𝒎𝒎 + 𝑽𝒎𝑽𝒌[𝑮𝒎𝒌𝒔𝒊𝒏(𝜽𝒎 − 𝜽𝒌) + 𝑩𝒎𝒌𝒄𝒐𝒔(𝜽𝒎 − 𝜽𝒌)]

+𝑽𝒎𝑽𝒄𝒓[𝑮𝒎𝒎𝒔𝒊𝒏(𝜽𝒎 − 𝜽𝒄𝒓) + 𝑩𝒎𝒎𝒄𝒐𝒔(𝜽𝒎 − 𝜽𝒄𝒓)] (𝟔)

At Series Converter:

𝑷𝒄𝒓 = 𝑽𝒄𝒓𝟐 𝑮𝒎𝒎 + 𝑽𝒄𝒓𝑽𝒌[𝑮𝒌𝒎𝒄𝒐𝒔(𝜹𝒄𝒓 − 𝜽𝒌) + 𝑩𝝔𝒎𝒔𝒊𝒏(𝜹𝒄𝒓 − 𝜽𝒌)]

+𝑽𝒄𝒓𝑽𝒎[𝑮𝒎𝒎𝒄𝒐𝒔(𝜹𝒄𝒓 − 𝜽𝒎) + 𝑩𝒎𝒎𝒔𝒊𝒏(𝜹𝒄𝒓 − 𝜽𝒎)] (𝟕)

𝑸𝒄𝒓 = −𝑽𝒄𝒓𝟐 𝑩𝒎𝒎 + 𝑽𝒄𝒓𝑽𝒌[𝑮𝒌𝒎𝒔𝒊𝒏(𝜹𝒄𝒓 − 𝜽𝒌) + 𝑩𝒌𝒎𝒄𝒐𝒔(𝜹𝒄𝒓 − 𝜽𝒌)]

+𝑽𝒄𝒓𝑽𝒎[𝑮𝒎𝒎𝒔𝒊𝒏(𝜹𝒄𝒓 − 𝜽𝒎) + 𝑩𝒎𝒎𝒄𝒐𝒔(𝜹𝒄𝒓 − 𝜽𝒎)] (𝟖)

At Shunt Converter:

𝑷𝒗𝒓 = −𝑽𝒗𝒓𝟐 𝑮𝒗𝒓 + 𝑽𝒗𝒓𝑽𝒌[𝑮𝒗𝒓𝒄𝒐𝒔(𝜹𝒗𝒓 − 𝜽𝒌) + 𝑩𝒗𝒓𝒔𝒊𝒏(𝜹𝒗𝒓 − 𝜽𝒌)] (𝟗)

𝑸𝒗𝒓 = −𝑽𝒗𝒓𝟐 𝑩𝒗𝒓 + 𝑽𝒗𝒓𝑽𝒌[𝑮𝒗𝒓𝒔𝒊𝒏(𝜹𝒗𝒓 − 𝜽𝒌) + 𝑩𝒗𝒓𝒄𝒐𝒔(𝜹𝒗𝒓 − 𝜽𝒌)] (𝟏𝟎)

Assuming loss-less converter valves, the active power supplied to the shunt converter,

Pvr, equals the active power demanded by the series converter, Pcr; that is,

𝑷𝒄𝒓 + 𝑷𝒗𝒓 = 𝟎 (𝟏𝟏)

Furthermore, if the coupling transformers are assumed to contain no resistance then

the active power at bus k matches the active power at bus m. accordingly,

𝑷𝒄𝒓 + 𝑷𝒗𝒓 = 𝑷𝒌 + 𝑷𝒎 = 𝟎 (𝟏𝟐)

The UPFC power equations, in linearised form, are combined with those of the AC

network. For the case when the UPFC controls the following parameters:

a. voltage magnitude at the shunt converter terminal (bus k)

b. active power flow from bus m to bus k

98 | P a g e

c. reactive power injected at bus m, and taking bus m to be a PQ bus.

The linearised system of equations is given by equation (13), where ΔPbb is the

power mismatch.

∆𝑷𝒌

∆𝑷𝒎

∆𝑸𝒌

∆𝑸𝒎

∆𝑷𝒎𝒌

∆𝑸𝒎𝒌

∆𝑷𝒃𝒃

=

𝝏𝑷𝒌

𝝏𝜽𝒌

𝝏𝑷𝒌

𝝏𝜽𝒎

𝝏𝑷𝒌

𝝏𝑽𝒌𝑽𝒌

𝝏𝑷𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒌

𝝏𝜹𝒄𝒓

𝝏𝑷𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒌

𝝏𝜹𝒗𝒓

𝝏𝑷𝒎

𝝏𝜽𝒌

𝝏𝑷𝒎

𝝏𝜽𝒎

𝝏𝑷𝒎

𝝏𝑽𝒌𝑽𝒌

𝝏𝑷𝒎

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒎

𝝏𝜹𝒄𝒓

𝝏𝑷𝒎

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒎

𝝏𝜹𝒗𝒓

𝝏𝑸𝒌

𝝏𝜽𝒌

𝝏𝑸𝒌

𝝏𝜽𝒎

𝝏𝑸𝒌

𝝏𝑽𝒌𝑽𝒌

𝝏𝑸𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒌

𝝏𝜹𝒄𝒓

𝝏𝑸𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒌

𝝏𝜹𝒗𝒓

𝝏𝑸𝒎

𝝏𝜽𝒌

𝝏𝑸𝒎

𝝏𝜽𝒎

𝝏𝑸𝒎

𝝏𝑽𝒌𝑽𝒌

𝝏𝑸𝒎

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒎

𝝏𝜹𝒄𝒓

𝝏𝑸𝒎

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒎

𝝏𝜹𝒗𝒓

𝝏𝑷𝒎𝒌

𝝏𝜽𝒌

𝝏𝑷𝒎𝒌

𝝏𝜽𝒎

𝝏𝑷𝒎𝒌

𝝏𝑽𝒌𝑽桜

𝝏𝑷𝒎𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒎𝒌

𝝏𝜹𝒄𝒓

𝝏𝑷𝒎𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒎𝒌

𝝏𝜹𝒗𝒓

𝝏𝑸𝒎𝒌

𝝏𝜽𝒌

𝝏𝑸𝒎𝒌

𝝏𝜽𝒎

𝝏𝑸𝒎𝒌

𝝏𝑽𝒌𝑽𝒌

𝝏𝑸𝒎𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒎𝒌

𝝏𝜹𝒄𝒓

𝝏𝑸𝒎𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒎𝒌

𝝏𝜹𝒗𝒓

𝝏𝑷𝒃𝒃

𝝏𝜽𝒌

𝝏𝑷𝒃𝒃

𝝏𝜽𝒎

𝝏𝑷𝒃𝒃

𝝏𝑽𝒌𝑽𝒌

𝝏𝑷𝒃𝒃

𝝏𝑽𝒎𝑽𝒎

獲𝑷𝒃𝒃

𝝏𝜹𝒄𝒓

𝝏𝑷𝒃𝒃

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒃𝒃

𝝏𝜹𝒗𝒓

∆𝜽𝒌

∆𝜽𝒎

∆𝑽𝒌

𝑽𝒌

∆𝑽𝒎

𝑽𝒎

∆𝜹𝒄𝒓

∆𝑽𝒄𝒓

𝑽𝒄𝒓

∆𝜹𝒗𝒓

(𝟏𝟑)

∆𝑷𝒌

∆𝑷𝒎

∆𝑸𝒌

∆𝑸𝒎

∆𝑷𝒎𝒌

∆𝑸𝒎𝒌

∆𝑷𝒃𝒃

=

𝝏𝑷𝒌

𝝏𝜽𝒌

𝝏𝑷𝒌

𝝏𝜽𝒎

𝝏𝑷𝒌

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑷𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒌

𝝏𝜹𝒄𝒓

𝝏𝑷𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝑷𝒌

𝝏𝜹𝒗𝒓

𝝏𝑷𝒎

𝝏𝜽𝒌

𝝏𝑷𝒎

𝝏𝜽𝒎

𝝏𝑷𝒎

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑷𝒎

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒎

𝝏𝜹𝒄𝒓

𝝏𝑷𝒎

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒎

𝝏𝜹𝒗𝒓

𝝏𝑸𝒌

𝝏𝜽𝒌

𝝏𝑸𝒌

𝝏𝜽𝒎

𝝏𝑸𝒌

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑸𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒌

𝝏𝜹𝒄𝒓

𝝏𝑸𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒌

𝝏𝜹𝒗𝒓

𝝏𝑸𝒎

𝝏𝜽𝒌

𝝏𝑸𝒎

𝝏𝜽𝒎

𝝏𝑸𝒎

‵𝑽𝒌𝑽𝒗𝒓

𝝏𝑸𝒎

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒎

𝝏𝜹𝒄𝒓

𝝏𝑸𝒎

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒎

𝝏𝜹𝒗𝒓

𝝏𝑷𝒎𝒌

𝝏𝜽𝒌

𝝏𝑷𝒎𝒌

𝝏𝜽𝒎

𝝏𝑷𝒎𝒌

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑷𝒎𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒎𝒌

𝝏𝜹𝒄𝒓

𝝏𝑷𝒎𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒎𝒌

𝝏𝜹𝒗𝒓

𝝏𝑸𝒎𝒌

𝝏𝜽𝒌

𝝏𝑸𝒎𝒌

𝝏𝜽𝒎

𝝏𝑸𝒎𝒌

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑸𝒎𝒌

𝝏𝑽𝒎𝑽𝒎

𝝏𝑸𝒎𝒌

𝝏𝜹𝒄𝒓

𝝏𝑸𝒎𝒌

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑸𝒎𝒌

𝝏𝜹𝒗𝒓

𝝏𝑷𝒃𝒃

𝝏𝜽𝒌

𝝏𝑷𝒃𝒃

𝝏𝜽𝒎

𝝏𝑷𝒃𝒃

𝝏𝑽𝒌𝑽𝒗𝒓

𝝏𝑷𝒃𝒃

𝝏𝑽𝒎𝑽𝒎

𝝏𝑷𝒃𝒃

𝝏𝜹𝒄𝒓

𝝏𝑷𝒃𝒃

𝝏𝑽𝒄𝒓𝑽𝒄𝒓

𝝏𝑷𝒃𝒃

𝝏𝜹𝒗𝒓

∆𝜽𝒌

∆𝜽𝒎

∆𝑽𝒗𝒓

𝑽𝒗𝒓

∆𝑽𝒎

𝑽𝒎

∆𝜹𝒄𝒓

∆𝑽𝒄𝒓

𝑽𝒄𝒓

∆𝜹𝒗𝒓

(𝟏𝟒)

If voltage control at bus k is deactivated, the third column of Equation (13) is

replaced by partial derivatives of the bus and UPFC mismatch powers with

respect to the bus voltage magnitude Vk.

Moreover, the voltage magnitude increment of the shunt source, ΔVvr/Vvr is

replaced by the voltage magnitude increment at bus k, ΔVk/Vk. If both buses, k

and m, are PQ the linearised system of equations is given by equation (14).

99 | P a g e

4. Explain the operation and control of power flow by SSSC (16)

SSSC Definition

A static synchronous generator operated without an external electric energy

source as a series compensator whose output voltage is in quadrature with, and

controllable independently of, the line current for the purpose of increasing or

decreasing the overall reactive voltage drop across the line and thereby controlling the

transmitted electric power. The SSSC may include transiently rated energy storage or

energy absorbing devices to enhance the dynamic behavior of the power system by

additional temporary real power compensation, to increase or decrease momentarily,

the overall real (resistive) voltage drop across the line.

Principle of Operation

A series capacitor compensates the transmission-line inductance by presenting a

lagging quadrature voltage with respect to the transmission-line current. This voltage

acts in opposition to the leading quadrature voltage appearing across the transmission-

line inductance, which has a net effect of reducing the line inductance. Similar is the

operation of an SSSC that also injects a quadrature voltage, VC, in proportion to the

line current but is lagging in phase:

𝑽𝑪 = −𝒋𝒌𝑿𝑰𝑳 (𝟏)

Where

𝑉𝐶 = the injected compensating voltage

I𝐿 = the line current

𝑋 = the series reactance of the transmission line

𝑘 = the degree of series compensation

The current in a line compensated at its midpoint by the SSSC is expressed as

𝑰𝑳 =𝟐𝑽𝒔𝒊𝒏𝜹/𝟐

𝑿+

𝑽𝑪

𝑿 (𝟐)

100 | P a g e

Where

V = the magnitude of voltage (assumed to be the same) at the two ends of the

transmission line

δ = the angular difference across the line

The corresponding line-power flow is then expressed as

𝑷 = 𝑽𝑰𝑳𝒄𝒐𝒔(𝜹/𝟐) (𝟑)

𝑷 =𝑽𝟐𝒔𝒊𝒏𝜹

𝑿+

𝑽𝑽𝑪

𝑿 𝒄𝒐𝒔(𝜹/𝟐) (𝟒)

Figure 1: Series-compensation scheme using the SSSC

Figure 2: (a) Generalized series connected synchronous voltage source employing a multi phase

converter with an energy storage device, (b) the different operating modes for real and reactive

power exchange

(a)

(b)

101 | P a g e

A series-compensation scheme using the SSSC is depicted in Figure 1. Normally,

the SSSC-output voltage lags behind the line current by 900 to provide effective

series compensation.

In addition, the SSSC can be gated to produce an output voltage that leads the line

current by 900, which provides additional inductive reactance in the line.

This feature can be used for damping power swings and, if the converter has

adequate rating, for limiting short-circuit currents.

A typical SSSC controller connected in a transmission line is shown in Figure 2.

This controller comprises a VSC in which its coupling transformer is connected in

series with the transmission line.

The valve-side voltage rating is higher than the line-side voltage rating of the

coupling transformer to reduce the required current rating of the gate turn-off

(GTO) thyristor valves.

The valve-side winding is delta-connected to provide a path for 3rd harmonics to

flow. Solid-state switches are provided on the valve side to bypass the VSC during

periods of very large current flow in the transmission line or when the VSC is

inoperative.

The basic dc voltage for conversion to ac is provided by the capacitor, and the dc to

ac conversion is achieved by pulse width–modulation techniques. The dc-capacitor

rating is chosen to minimize the ripple in the dc voltage.

Control of Power Flow

The schematic of a SSSC is shown in Figure 3(a). The equivalent circuit of the

SSSC is shown in Figure 3(b). The magnitude of VC can be controlled to regulate

power flow.

The winding resistance and leakage reactance of the connecting transformer appear

is series with the voltage source VC. If there is no energy source on the DC side,

102 | P a g e

neglecting losses in the converter and DC capacitor, the power balance in steady

state leads to

Re VCI* =0 (5)

Figure 3: Schematic of SSSC

The above equation shows that VC is in quadrature with I. If VC lags I by 900, the

operating mode is capacitive and the current (magnitude) in the line is increased

with resultant increase in power flow.

On the other hand, if VC leads I by 900, the operating mode is inductive, and the

line current is decreased. Note that we are assuming the injected voltage is

sinusoidal (neglecting harmonics). Since the losses are always present, the phase

shift between I and VC is less than 900 (in steady state). In general, we can write

VC=VC cosγ-jsinγ ejφ= VCp-jVCr ejφ (6)

where φ is the phase angle of the line current, γ is the angle by which VC lags the

current. VCp and VCr are the in-phase and quadrature components of the injected

voltage (with reference to the line current).

VSC

I

(a) Schematic of SSSC

(b) Equivalent Circuit

+

I

VC r Xl

103 | P a g e

We can also term them as active (or real) and reactive components. The real

component is required to meet the losses in the converter and the DC capacitor.

We use the convention that the reactive voltage lagging the current by 900 as

positive (Note that for a SVC or STATCOM, we used the convention of lagging

reactive current as positive.)

According to this convention, the positive reactive voltage implies capacitive mode

of operation while negative reactive voltage implies inductive mode of operation.

Since γ is close to ±900, we can write

γ = sgn VCr −90𝟎 +α𝟎 (7)

where sgn(.) indicates the signum function whose value is +1 if the argument is

positive and -1 if the argument is negative. Substituting Equation (3.33) in (3.32) we

can write,

VCp=VC sinα , VCr=VC cosα (8)

Since the losses are expected to be small (typically below 1%) the magnitude of VCp

is very small and may be neglected to simplify the analysis. VCp will vary during a

transient to increase or decrease the voltage across the DC capacitor (particularly in

the case of type 2 converter where the ratio between the AC voltage and the DC

capacitor voltage is constant, with no modulation).

3. Discuss about the modeling of SSSC in load flow and transient stability studies

(16)

Modelling of SSSC

For stability studies involving phenomena of frequency below 5 Hz, it is adequate

to express the network equations using Phasor by neglecting network transients.

However, for phenomena involving higher frequencies, one cannot ignore network

transients (even for studies involving sub-synchronous frequency oscillations).

104 | P a g e

Figure 1: Representation of SSSC in a transmission line

We can illustrate the derivation of the network equations by considering the single

line containing a SSSC shown in Figure 1.

Neglecting harmonics, we can express the system equations (including SSSC) in

D-Q variables (referred to a synchronously rotating axis).

The advantage of using these variables is that in steady state, the D-Q components

are constants and can be expressed as rectangular coordinates of Phasor.

Neglecting zero sequence components, we can express the network equations

(using two phase variables, α and β) in the complex form given below.

Ldi

dt+Ri=VS − VC

− VR (1)

where

i= iβ+jiα , VS=VSβ+jVSα ,

VC= VCβ+jVCα, VR=VRβ+jVRα

Transforming from α, β to D - Q components which are related as,

iαiβ =

cosθ sinθ

-sinθ cosθ

iDiQ

(2)

where θ = ω0t+θ0. There is no loss of generality in assuming θ0 = 0. Similar

transformation as given above applies to the variables vSα, vSβ and vSD, vSQ and so on.

QS -QR

I

VR∠-δ/2

P

VS∠δ/2

+ δ/2

δ/2

VR

VS

I

(a) Single Line Diagram

(b) Phasor Diagram

105 | P a g e

We can also express Equation (2) as a complex equation given below.

iβ+jiα =(iQ+ji

D)e

jω𝟎 t=Iejω𝟎 t (3)

Utilizing Equation (2) and similar equations for other variables in Equation (1), the

latter can be expressed as

Ld(Iejω𝟎 t)

dt+R Iejω𝟎 t = VS − VC

− VR ejω𝟎 t (4)

Simplifying, we get,

𝑳dI

dt+jω𝟎 LI+RI=VS − VC

− VR (5)

where

I=IQ+jID, VS=VSQ+jVSD, VC=VCQ

+jVCD , VR=VRQ

+jVRD

In steady state, I is a constant and dI /dt = 0. Hence, we get (in steady state),

R+jωoL I=VS − VC

− VR (6)

The advantages of writing a complex equation such as Equation (4) for a network

element (such as a transmission line) are two fold

The extension to a complex network consisting of inductors, capacitors, resistors etc is

straightforward.

The derivation of phasor equations in steady state (such as Equation (5)) is, again,

simplified.

Both lower case and upper case letters are used for D-Q components as they are both

instantaneous quantities as well as components of phasors (in steady state).

106 | P a g e

Actually, the term `dynamic phasors' can be used when the derivatives are not zero.

(under dynamic conditions). The voltage injected by SSSC can be expressed as

VCQ+jVCD= VCp

− jVCr

ejφ (7)

Where,

tanφ=ID

IQ

(8)

The equation for the DC capacitor voltage is

Cdvdc

dt+Gvdc=Idc (9)

Figure 2: Operating region of SSSC in VC - I plane

From the power balance considerations,

Re VCI =vdcidc (10)

The L.H.S is expressed as

IVCp=IVCsinα=IkVdcsinα (11)

From the above, we get

idc=kIsinα (12)

where I= ID2 +IQ

2 ,

VC

o I

o

VCmin

XCmax

D

(a) Voltage control mode

XCmin

VC

B

C

I

A

(b) Reactance control mode

Imax Imax

VCmax

VCmin

VCmax A

B

107 | P a g e

In steady state, we can express VC as

VC=k2I

Gsinα (13)

Note that α > 0 in steady state. The operating region in the VC - I plane is shown in

Figure 2, where SSSC is operated in voltage control.

This figure also shows the operating region when the SSSC is operated in the

reactance control mode. However, as discussed earlier, the voltage control model is

more advantageous than the reactance control mode.

The operating region in the voltage control mode is OABCD. The slope of OA and

OD are obtained from Equation as

dVC

dI= ±

k2

G (14)

Corresponding to α = 900. VC is assumed to be positive when it is capacitive and

negative when it is inductive.

Note that VC min = -VC max. Similarly XC is assumed to be positive (when capacitive)

and negative (when inductive). Also XC min = -XC max. The operating region in the

reactance control mode is OAB.

======================

108 | P a g e

EE6004 FLEXIBLE AC TRANSMISSION SYSTEMS

UNIT 5

CO-ORDINATION OF FACTS CONTROLLERS

2 MARKS

1. What do you understand by coordination of FACTS controllers?

The term coordinated implies that the controllers have been tuned simultaneously

to effect an overall positive improvement of the control scheme

2. Define the term “Co-ordination”

The term coordinated implies that the controllers have been tuned simultaneously

to effect an overall positive improvement of the control scheme

3. How is coordination of FACTS controllers carried out?

Controller interactions can occur in the following combinations:

Multiple FACTS controllers of a similar kind

Multiple FACTS controllers of a dissimilar kind

Multiple FACTS controllers and HVDC converter controllers

4. What is the need for coordination of different FACTS controllers?

109 | P a g e

Adverse interaction due to fast controls

Usually controls are tuned optimally assuming the remaining power system to

be passive

Above parameters not optimal when dynamics of other controller are existent

( Power System Stabilizers(PSS), HVDC, FACTS)

5. Give The frequency range of the different control interactions

0 Hz for steady state interactions

0-3Hz for electromechanical oscillations

2-15Hz for small signal or control oscillations

>15 Hz sub synchronous resonance interactions

>15 Hz for electromagnetic transient high frequency resonance or harmonic

resonance interactions, and network resonance interactions

6. What are the basics procedures of the controller design?

Derivation of the system model

Enumeration of the system performance specifications

Selection of the measurement and control signals

Coordination of the controller design

Validation of the design performance evaluation

7. Write the assumptions of control coordination for damping enhancement?

All controllers in the system including FACTS have the transfer function of the

type kjGj (S)

The component Gj(S) in the transfer function is responsible for causing the left

shift in the electromechanical mode

110 | P a g e

The gain Kj in the transfer function decides the magnitude of left shift in the

mode of interest

8. What is meant by controller interactions?

If two or more FACTS devices are connected in same transmission line then the

operating variables between them must have better co-ordinated, that is called

controller interaction. If FACTS devices are not co-ordinated, it creates unwanted

oscillation in the transmission lines.

9. What is meant by steady state interaction?

Steady-state interactions between different controllers (FACTS-FACTS or

FACTS- HVDC) occur between their system related controls.

They are steady state in nature and do not involve any controller dynamics.

These interactions are related to issues such as the stability limits of steady

state- state voltage and steady-state power, included are evaluations of the

adequacy of reactive-power support at buses, system strength and so on.

10. What is the analysis method used to determine the steady state interaction?

Load-Flow and Stability programs are used to determine the steady state

interaction.

11. What is meant by electromechanical oscillation interaction?

Electromechanical oscillation interaction between FACTS controllers involve

synchronous generators, compensator machines and associated power system stabilizer

control. The oscillations include local mode oscillations typically in the range of 0.8 -

2 Hz, and interarea mode oscillations, typically in the range of 0.2 - 0.8 Hz.

12. What is the analysis methods used to determine the electromechanical

oscillation interaction?

Eigen value analysis programs are used to determine this interaction.

111 | P a g e

13. What is meant by control or small signal oscillation interactions?

Controller interactions between individual FACTS controllers and the network or

between FACTS controllers and HVDC links may lead to the onset of oscillations in

the range of 2 - 15 Hz. These oscillations are largely dependent on the network

strength and the choice of FACTS controller parameters, and they are known to result

from the interaction between voltage controllers of multiple SVC’s, the series

resonance between series capacitors and shunt reactors in the frequency range of 4 - 15

Hz and so forth. The emergence of these oscillations significantly influences the

tuning of controller gain.

14. What are the analysis methods used to determine the control or small signal

oscillation interaction?

These high frequency oscillation interactions are determined by frequency

scanning programs, electromagnetic transient programs (EMTP’s), Physical simulators

and eigen value analysis programs.

15. What is meant by sub synchronous resonance interactions?

Sub synchronous oscillations may be caused by the interaction between the

generator torsional system and the series compensated transmission lines, the HVDC

converters, the generator excitation control or even the SVC’s. Theses oscillations

usually in the frequency range of 10 - 50/60 Hz, can potentially damage generator

shafts.

16. What are the analysis methods used to determine the sub synchronous

resonanceinteractions?

These SSR oscillation interactions are determined by frequency scanning

programs, electromagnetic transient programs (EMTP’s), Physical simulators and

eigen value analysis programs.

17. What is meant by high frequency interaction?

112 | P a g e

High-frequency oscillations in excess of 15 Hz are caused by large nonlinear

disturbances, such as the switching of capacitors, reactors, or transformers for which

reason they are classified as electromagnetic transients. FACTS controllers need to be

co-ordinated to minimize such interactions.

*********************

16 MARKS

1. Discuss the different classification of controller interactions. (16)

Controller Interactions

Controller interactions can occur in the following combinations:

Multiple FACTS controllers of a similar kind.

Multiple FACTS controllers of a dissimilar kind.

Multiple FACTS controllers and HVDC converter controllers.

Because of the many combinations that are possible, an urgent need arises for

power systems to have the controls of their various dynamic devices

coordinated.

The term coordinated implies that the controllers have been tuned

simultaneously to effect an overall positive improvement of the control scheme.

The frequency ranges of the different control interactions have been classified as

follows:

0 Hz for steady-state interactions

0–3/5 Hz for electromechanical oscillations

2–15 Hz for small-signal or control oscillations

10–50/60 Hz for sub-synchronous resonance (SSR) interactions

113 | P a g e

>15 Hz for electromagnetic transients, high-frequency resonance or harmonic

resonance interactions, and network-resonance interactions

Steady-State Interactions

Steady-state interactions between different controllers (FACTS–FACTS or

FACTS–HVDC) occur between their system-related controls.

They are steady state in nature and do not involve any controller dynamics.

These interactions are related to issues such as the stability limits of steady-state

voltage and steady-state power; included are evaluations of the adequacy of

reactive-power support at buses, system strength, and so on.

An example of such control coordination may be that which occurs between the

steady-state voltage control of FACTS equipment and the HVDC

supplementary control for ac voltage regulation.

Load-flow and stability programs with appropriate models of FACTS

equipment and HVDC links are generally employed to investigate the foregoing

control interactions.

Steady-state indices, such as voltage-stability factors (VSF), are commonly

used.

Centralized controls and a combination of local and centralized controls of

participating controllers are recommended for ensuring the desired coordinated

performance.

Electromechanical-Oscillation Interactions

Electromechanical-oscillation interactions between FACTS controllers also

involve synchronous generators, compensator machines, and associated power

system stabilizer controls.

114 | P a g e

The oscillations include local mode oscillations, typically in the range of 0.8–2

Hz, and inter-area mode oscillations, typically in the range of 0.2–0.8 Hz.

The local mode is contributed by synchronous generators in a plant or several

generators located in close vicinity; the inter-area mode results from the power

exchange between tightly coupled generators in two areas linked by weak

transmission lines.

Although FACTS controllers are used primarily for other objectives, such as

voltage regulation, they can be used gainfully for the damping of

electromechanical oscillations.

In a coordinated operation of different FACTS controllers, the task of damping

different electromechanical modes may be assumed by separate controllers.

Alternatively, the FACTS controllers can act concertedly to damp the critical

modes without any adverse interaction. Eigenvalue analysis programs are

employed for determining the frequency and damping of sensitive modes.

Control or Small-Signal Oscillation interactions

Control interactions between individual FACTS controllers and the network or

between FACTS controllers and HVDC links may lead to the onset of

oscillations in the range of 2–15 Hz (the range may even extend to 30 Hz).

These oscillations are largely dependent on the network strength and the choice

of FACTS controller parameters, and they are known to result from the

interaction between voltage controllers of multiple SVCs, the resonance

between series capacitors and shunt reactors in the frequency range of 4–15 Hz,

and so forth.

The emergence of these oscillations significantly influences the tuning of

controller gains. Analysis of these relatively higher frequency oscillations is

made possible by frequency-scanning programs, electromagnetic-transient

programs (EMTPs), and physical simulators (analog or digital).

115 | P a g e

Eigenvalue analysis programs with modeling capabilities extended to analyze

higher-frequency modes as well may be used.

Subsynchronous Resonance (SSR) Interactions

Sub-synchronous oscillations may be caused by the interaction between the

generator torsional system and the series-compensated-transmission lines, the

HVDC converter controls, the generator excitation controls, or even the SVCs.

These oscillations, usually in the frequency range of 10–50/60 Hz, can

potentially damage generator shafts. Sub-synchronous damping controls have

been designed for individual SVCs and HVDC links.

In power systems with multiple FACTS controllers together with HVDC

converters, a coordinated control can be more effective in curbing these

torsional oscillations.

High-Frequency Interactions

High-frequency oscillations in excess of 15 Hz are caused by large nonlinear

disturbances, such as the switching of capacitors, reactors, or transformers, for

which reason they are classified as electromagnetic transients.

Control coordination for obviating such interactions may be necessary if the

FACTS and HVDC controllers are located within a distance of about three

major buses.

Instabilities of harmonics (those ranging from the 2nd to the 5th) are likely to

occur in power systems because of the amplification of harmonics in FACTS

controller loops.

Harmonic instabilities may also occur from synchronization or voltage-

measurement systems, transformer energization or transformer saturation

caused by geo-magnetically induced currents (GICs).

116 | P a g e

2. Explain the various kinds of control interactions occurring between different

FACTS controllers using their frequency response characteristics. (16)

The Frequency Response of FACTS Controllers

The composite-frequency response of a FACTS controller, together with its

associated ac system, provides a good indication of the control-system stability,

especially while an attempt is made to coordinate several FACTS or HVDC

controllers.

A time domain–based frequency-scanning method (FSM) is used for obtaining

the frequency responses of individual and coordinated FACTS controllers.

A current source is used to inject a spectrum of frequencies at the FACTS

controller bus. The local voltage developed at the bus is measured, and its

harmonic content is evaluated through the use of Fourier analysis.

The simulations are performed with an EMTP that has detailed models of

FACTS controllers.

To avoid the operation of any system component in its nonlinear region, the

magnitudes of injected harmonic currents are chosen to be quite small, thereby

ensuring linearized system behavior around the operating point.

In HVDC converters, an injected-current magnitude is considered sufficiently

small if it does not cause a firing-angle oscillation in excess of 0.58. Two

frequency response examples of FACTS controllers, one for the SVC, the other

for the TCSC—are presented in the following.

The Frequency Response of the SVC

The study system considered is shown in Figure (a). A ±50 MVAR SVC is

connected at the midpoint of the network that connects systems 1 and 2.

The frequency response is obtained for two operating points. At the first

operating point, the SVC maintains a bus voltage of 1.02 pu, with a firing angle

117 | P a g e

α = 1020 corresponding to a reactive-power absorption of 22.5 MVAR

(inductive).

Small-magnitude harmonic currents, Ih, are injected at discrete frequencies

ranging from 5 to 45 Hz.

The corresponding impedances are computed as the ratio of the developed

voltage and the injected-harmonic disturbance- current components.

Figure (a): A study system for frequency scanning of the SVC.

Figure (b): The impedance magnitude of the SVC frequency response.

118 | P a g e

Figure (c): The impedance angle of the SVC frequency response.

The impedance magnitude and angle-frequency responses are plotted in Figures

(b) and (c), respectively.

The SVC presents a parallel resonance at 33 Hz and behaves inductively from 5

to 33 Hz, becoming capacitive at resonance and tending to resume inductive

behavior as the frequency is increased beyond 33 Hz.

The frequency response is obtained for the second steady state–operating point.

The bus voltage is now regulated at 1.10 pu, with a thyristor firing angle α =

1470 corresponding to a reactive-power injection of 50 MVAR (capacitive).

The corresponding magnitude and angle-frequency responses are, again, plotted

in Figures (b) and (c), respectively.

It is seen that the resonant frequency modifies to 19 Hz and the impedance peak

becomes three times that of the inductive SVC operation.

The phase plot indicates that the higher the firing angle, the smaller the

frequency ranges of inductive operation.

The Frequency Response of the TCSC

119 | P a g e

Figure (d): A study system for the TCSC frequency response.

The 60-Hz test system used for evaluating the TCSC frequency response is depicted in

Figure (d).

Figure (e): The impedance-magnitude plot of the TCSC frequency response

Figure (f): The impedance-angle plot of the TCSC frequency response.

120 | P a g e

The frequency response is obtained for two conduction angles: 800 and 86

0. The

impedance magnitude and angle plots are illustrated in Figure (e) and Figure

(f), respectively.

It is evident that the TCSC-compensated system presents an inductive behavior

until it reaches 45–50 Hz; thereafter, its behavior tends to become capacitive,

resembling that of a pure capacitor.

3. Analyze in detail about SVC-SVC interaction (or) discuss in detail about

different factors for SVC-SVC interaction. (16)

SVC–SVC Interaction

1. The Effect of Electrical Coupling and Short-Circuit Levels

The interaction phenomena are investigated as functions of electrical distance

(electrical coupling) between the SVCs and the short-circuit level at the SVC buses.

(a) Uncoupled SVC Buses

A simplified test system shown in Figure (a) is considered for the interaction analysis

performed through eigenvalue analyses and root-loci plots.

121 | P a g e

Figure (a): An SVC interaction-analysis network.

All the generating units are represented by infinite buses. If the transfer

reactance between buses 1 and 2 is high, making the buses electrically

uncoupled, then the SVCs connected to those buses do not interact adversely.

Increasing the proportional gain of SVC 1 connected to bus 1, even to the

extent of making the SVC unstable, does not affect the eigenvalues of SVC 2

implying that the controller designs of SVCs can be done independently for

multiple SVCs in a power system if the transfer reactance between their

connecting buses is high.

(b) Coupled SVC Buses

If, however, the reactance between the two SVC buses is low, it constitutes a

case of high electrical coupling between the SVCs.

Here again, two possibilities exist with respect to short-circuit capacity of the

region where the SVCs are installed: the SVC region with a high short circuit

capacity and the SVC region with a low short-circuit capacity.

122 | P a g e

For high short-circuit capacity conditions in the same system as reveal that by

increasing the proportional gain of one SVC, the eigenvalues of the other SVC

are impacted very slightly.

Almost no control interaction exists between the two SVCs irrespective of their

electrical coupling, as long as they are in a high short-circuit-level region, that

is, when the ac system is stiff.

The reason for this condition is that the interlinking variable between the two

SVCs is the bus voltage.

Thus the controls of both SVCs can be independently designed and optimized,

but if the short-circuit capacity of the SVC region is low, varying the

proportional gain of SVC 1 will strongly influence the eigenvalues associated

with SVC 2.

It is therefore imperative that a coordinated control design be undertaken for

both SVCs. Despite simplifications in the study system and in the analysis

approach, the aforementioned interaction results are general, for the phenomena

investigated are independent of the number of buses, transmission lines, or

generators.

2. High-Frequency Interactions

To analyze the control interaction, one SVC is modeled in detail using the

generalized-switching-functions approach, while the second SVC is represented

by a passive equivalent network with same reactive power consumption at the

operating point under consideration.

In Figure (b), the equivalent system used for the control design of SVC 1 is

shown. The SVC controller is designed to give an acceptable rise, overshoot,

and settling times.

123 | P a g e

Figure (b): An equivalent system for the control design of SVC 1.

Eigenvalue analysis reveals that the dominant oscillation mode has an

eigenvalue of λSVC1 = −19 ± j119.7. This mode constitutes an oscillation of

frequency 19.1 Hz in SVC 1’s response to a 2% step in the reference-voltage

input, as shown in Figure (c). The system simulation is performed using a

nonlinear switching function based EMTP-type simulation.

Figure (c): An equivalent system for the control design of SVC 2.

The dominant mode of oscillation has an eigenvalue of λSVC2 = −19.7 ± j118.5

and constitutes an oscillation of 18.9 Hz in SVC 2’s response to a 2% step in

the reference-voltage input, as depicted in Figure (d).

124 | P a g e

Figure (d): The response of SVC 2 to a step input in the reference voltage.

The dominant oscillation mode has an associated eigenvalue of λ= +3.2 ±

j129.9, leading to an unstable oscillation of frequency 20.7 Hz in both SVCs’

responses when a 2% step input is applied to the reference voltage of SVC 2, as

depicted in Figure (e).

Figure (e): The response of independently designed SVCs to a step input in the reference voltage

of SVC 2.

This phenomenon clearly illustrates the adverse high-frequency interaction

between the two independently designed SVC controllers, and brings out the

need for a coordinated control design of the two SVCs.

125 | P a g e

A high-frequency eigenvalue analysis program is employed, and the gains of

both SVC controllers are adjusted simultaneously to stabilize the unstable

mode.

The response of both SVCs to a 2% reference step in SVC 2 is presented in

Figure (f). This response is rapid as well as stable.

Figure (f): The response of coordinately designed SVCs to a step input in the SVC

2 reference voltage.

The frequency response is then obtained for the transfer function relating the

controlled bus voltage with the reference voltage of SVC 1.

The resonant peak of the original SVC transfer function is enhanced

substantially during the independent design of SVC controllers, leading to

instability. A coordinated design significantly reduces the resonant peak,

thereby stabilizing the overall system.

4. Discuss the control coordination of multiple controllers using linear control

126 | P a g e

techniques. (16)

Coordination of Multiple Controllers using Linear-Control Techniques

The term coordination does not imply centralized control; rather, it implies the

simultaneous tuning of the controllers to attain an effective, positive improvement of

the overall control scheme. It is understood that each controller relies primarily on

measurements of locally available quantities and acts independently on the local

FACTS equipment.

The Basic Procedure for Controller Design

The controller-design procedure involves the following steps:

Derivation of the system model;

Enumeration of the system-performance specifications;

Selection of the measurement and control signals;

Coordination of the controller design; and

Validation of the design and performance evaluation.

Linear Quadratic Regulator (LQR)–Based Technique

The LQR technique is one of optimal control that can be used to coordinate the

controllers with the overall objective of damping low-frequency inter-area

modes during highly stressed power-system operations.

The system model is first linearized and later reduced to retain the modal

features of the main system over the frequency range of interest.

The control-system specifications are laid out as described previously.

Appropriate measurement and control signals are selected, based on

observability and controllability considerations, to have only a minimal

interaction with other system modes.

127 | P a g e

Using a projective-controls approach, the control-coordination method involves

formulating an LQR problem to determine a full-state-feedback controller in

which a quadratic performance index is minimized.

An output-feedback controller is then obtained, based on the reduced

eigenspace of the full-state solution.

The dominant modes of the full-state-feedback system are retained in the

closed-loop system with output feedback.

The order of the controller and the number of independent measurements

influence the number of modes to be retained.

The output-feedback solution results in the desired coordinated control. The

performance of coordinated controls is later tested and evaluated through time-

domain simulation of the most detailed model of the nonlinear system.

Global Coordination Using Nonlinear-Constrained Optimization

In the global-coordination technique, the parameters (both gain and time

constants) of the damping controllers of multiple FACTS controllers are

coordinated globally by using nonlinear-constrained optimization.

It is usually observed in power systems that if the FACTS controllers have large

ratings, their damping action on the real-power oscillations causes substantial

reactive power oscillations.

To restrict oscillations—in both the real and the reactive power—the

optimization problem is stated as follows:

Minimize

𝑭 = ∆𝑷𝑻𝑰∆𝑷 + 𝑲𝑸∆𝑸𝑻𝑰∆𝑸

∞

𝟎

𝒅𝒕 (𝟏)

Subject to

128 | P a g e

𝑽𝒎𝒊𝒏 ≤ 𝑽𝒃𝒖𝒔𝒌 ≤ 𝑽𝒎𝒂𝒙, 𝒌 = 𝟏, 𝟐, 𝒎 (𝟐)

where for n FACTS controllers,

∆𝑃 = [∆𝑃1, ∆𝑃2, ..., ∆𝑃n]T

= the n locally measured real-power-flow oscillations

∆𝑄 = [∆𝑄1, ∆𝑄2, ..., ∆𝑄n]T

= the n locally measured reactive-power oscillations

V bus k = the voltage magnitude of the kth

bus

KQ = the weighting factor

Vmax, Vmin = the upper and lower limits of the bus-voltage magnitude, respectively

If the primary control objective is to damp active-power oscillations, the

weighting factor KQ is assigned a small value, typically 0.2.

However, if reactive-power swings must also be restricted, KQ is assigned a

higher magnitude.

The foregoing optimization scheme results in robust controllers having a

significant damping influence on both large and small disturbances.

The transfer function, FD(s), of both damping controllers is assumed to be of the form

𝑭𝑫 𝑺 = 𝑲.𝒔𝑻𝟏

𝟏 + 𝒔𝑻𝟐

.𝟏 + 𝒔𝑻𝟑

𝟏 + 𝒔𝑻𝟒

(𝟑)

Although T2 and T4 are chosen a priori, parameters K, T1, and T3 are determined

for both controllers through the optimization procedure.

Control Coordination Using Genetic Algorithms

129 | P a g e

Genetic algorithms are optimization techniques based on the laws of natural

selection and natural genetics that recently have been applied to the control

design of power systems.

These techniques provide robust, decentralized control design and are not

restricted by problems of non-differentiability, nonlinearity, and non-convexity,

all of which are often limiting in optimization exercises.

Genetic-algorithm techniques use the linearized state-space model of the power

system.

The objective function is defined as the sum of the damping ratios of all the

modes of interest.

This sum is evaluated over several likely operating conditions to introduce

robustness. A minimum damping level is specified for all the modes; the other

constraints include limits on the gain and time constants of the damping

controllers assumed to be from a fixed structure.

The optimization problem is therefore stated as follows:

Maximize

𝑭 = 𝝃𝒊

𝒏

𝒋=𝟏

𝒎

𝒊=𝟏

(𝟒)

Subject to the following constraints:

𝑲𝒋 𝒎𝒊𝒏 ≤ 𝑲𝒋 ≤ 𝑲𝒋 𝒎𝒂𝒙,

𝝉𝟏 𝒎𝒊𝒏 ≤ 𝝉𝟏 ≤ 𝝉𝟏 𝒎𝒂𝒙,

𝝉𝟐 𝒎𝒊𝒏 ≤ 𝝉𝟐 ≤ 𝝉𝟐 𝒎𝒂𝒙,

𝝃 𝒎𝒊𝒏 ≤ (𝝃𝒋)𝒊 (𝟓)

where

n = the number of modes to be damped

m = the number of different possible operating conditions

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kj = the gain of the controller

𝝉 1, 𝝉 2 = the time constants of the lead-lag blocks

𝝃 = the damping ratio of the closed-loop eigenvalue

This maximization yields the gain kj and the time constants 𝝉1, 𝝉2 for all the

controllers for a pre-specified order p of the lead-lag blocks.

The time constant TW of the washout filter is assumed to be adequately large.

Likewise, the time constants 𝑻 1, 𝑻 2, 𝑻n of the low-pass filters are selected

beforehand.

The foregoing optimization problem involves a computation of eigenvalues of a

large system matrix, which is usually difficult to solve with conventional

techniques.

An advantage of genetic-algorithm techniques is that the parameter limits can

be varied during the optimization, making the techniques computationally

efficient.

Coordination of Multiple Controllers using Nonlinear-Control Techniques

Even though rotor-angle stability is essentially a nonlinear-control problem, the

theoretical concepts of linear-control theory can be applied to solve many issues

related to this stability problem.

Recently, however, several nonlinear-control techniques have been applied for

the design of FACTS controllers.

These techniques are likely to yield greatly improved controllers, as they

include the effects of system nonlinearities.

One nonlinear-control technique in which the system nonlinearities are

expressed as system changes constituting a function of time is the adaptive

control.

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If the number of controller parameters to be optimized is not too large, a cost-

penalty function technique can be used, which is based on nonlinear simulation.

An effective technique commonly used for enhancing transient stability during

large disturbances is the discontinuous control or bang-bang control.

Another nonlinear-control technique is the normal forms, which includes the

effects of higher-order terms in Taylor’s series to represent power systems—

especially during high-power transfers.

For damping low-frequency oscillations, FACTS controllers can be designed

using the dissipation technique, which is based on the concept that passive

systems always absorb energy.

For designing the controls of FACTS controllers in large power systems, the

energy, or Lyapunov, technique can be used.

For stability enhancement, nonlinear fuzzy and neural net techniques are

presently being researched.

In the future, these techniques may be extended for coordination of FACTS

controllers. One possible approach could be to first do a ―coarse‖ coordination

using linear-control techniques, followed by a ―fine‖ coordination employing

the nonlinear-control methods.

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