design and implementation of a thyristor controlled …

(EXAMINER'S COPY)

DESIGN AND IMPLEMENTATION OF A THYRISTOR

CONTROLLED SERIES CAPACITOR FOR

RESEARCH LABORATORY APPLICATION

By

Ronnie Happy-Boy Mazibuko

BScEng

Submitted in fulfillment of the academic requirements for the degree of Master of

Science in Engineering, in the Department of Electrical Engineering, University of

Natal, Durban, South Africa.

September 2003

I hereby declare that all the material incorporated into this thesis is my own original

and unaided work except where specific reference is made by name or in the form

of a numbered reference. The work contained herein has not been submitted for a

degree at any other university.

Signed:

R H Mazibuko

ABSTRACT

The power transfer capability of a transmission line is determined by the magnitude of

the voltage at each end of the line, angle difference of these voltages and the

impedance of the line. This impedance is mainly inductive. Traditionally, fixed series

capacitor banks have been used for series comp~nsation. However, due to instability

problems associated with loading transmission line close to their thermal limits,

researchers have looked at other alternatives to line compensation by static devices

such as fixed series capacitors. Flexible AC Transmission Systems (FACTS) has

allowed power utilities to use existing transmission line networks close to their

thermal limits without compromising stability of the power system. A FACTS series

compensator is capable of influencing the transmission of power in a transmission line

by dynamic control of the series compensating reactance inserted in the line. There are

several different devices under the FACTS family, however, in this thesis only the

Thyristor-Controlled Series Capacitor (TCSC) was considered. A TCSC comprises a

fixed capacitor in parallel with a thyristor-controlled reactor (TCR). By varying the

firing angle ex:. of the thyristors, the TCSC can be made to act in variable inductive or

capacitive reactance mode. The thesis' overall objective was to design a practical

TCSC for use in a research laboratory for further research initiatives.

This thesis looks at different issues that need to be considered when designing and

rating a TCSC compensator. In particular, the thesis examines the effects of different

sizes of TCSC components on the rating of the device, the effects of harmonics on the

TCSC ratings, sizing of TCSC's variable reactance, and the response time of TCSC to

a step change in the firing angle.

A mathematical model of a TCSC in a single-machine infinite bus (SMIB) system was

developed and subsequently used in the initial design of the TCSC. Studies that were

done using mathematical model of the TCSC module confirmed the ability of the

Abstract

TCSC controller to dynamically control the capacitive compensating reactance in the

transmission line. The thesis then describes the development of a laboratory-scale

TCSC for research investigations. Measured results from the laboratory demonstrate

the ability of the TCSC series compensator to provide rapid control of series reactance

of a transmission line. A detailed mathematical model of the SMIB equipped with

TCSC module was developed, using parameter values of the laboratory scale

prototype, to investigate power oscillation damping. Time-domain simulation results

are presented in this thesis to demonstrate its ability to damp power swings in an

electrical network.

Abstract

Page jji

ACKNOWLEDGEMENTS

The work presented in this thesis was carried out under the supervision of Dr. Bruce

S. Rigby and Professor Ronald G. Harley both of the Department of Electrical

Engineering, University of Natal, Durban. I would like to thank Dr. Rigby for his

support, guidance throughout the course of this thesis, and for his efforts during the

correction of this thesis. I would also like to thank Professor Harley for affording me

the opporttmity to carry out this research work.

In addition, I would like to thank the following people:

The workshop staff for their input during TCSC circuit design

My family for their support, patience and their best wishes

My friends for their support

Eskom and University of Natal for providing much needed financial support

The staff and postgraduate students of Electrical and Electronic Engineering,

unfortunately too many to mention by name.

God for making everything possible

Table ofContents

TABLE OF CONTENTS

Abstract _

Acknowledgements, lll

List of Figures and Tables 1x

List of Symbols, XlV

CHAPTER ONE INTRODUCTION

1.1 Background 1.1

1.2 FACTS Series Compensators 1.3

1.3 Thyristor-Controlled Series Capacitor 1.3

1.4 Objectives Of The Thesis 1.4

1.5 Thesis Layout 1.6

1.6 Research Publications 1.7

CHAPTER TWO GENERAL OPERATION OF THE TCSC

2.1 Introduction 2.1

2.2 The world's first multi-module TCSC system [2] 2.2

2.3 Operating principles of a TCSC 2.4

2.4 Factors considered when selecting the inductor of the reactor loop 2.9

2.4.1 Introduction 2 9------------------- .

Table a/Contents

Page v

2.4.2 Firing region 2.10

2.4.3 The Reactance Order 2.13

2.4.4 Operating Capability of the TCSC 2.14

2.4.5 Rating the TCSC Components 2.16

2.4.6 Harmonic Performance of the TCSC 2.17

2.4.7 Transient Response of the TCSC 2.19

2.4.8 Frequency Response of the TCSC 2.23

2.5 Some common applications of the TCSC 2.24

2.5.1 Power Swing Damping 2.24

2.5.2 Mitigation of Subsynchronous Resonance 2.26

2.6 Conclusion 2.6

CHAPTER 3 MATHEMATICAL MODELING FOR

COMPUTER SIMULATION OF TCSC


3.2 Trigger circuit for the TCR 3.2

..., ...,Sizing of TCSC Variable Reactance Range 3.6.J . .J

3.4 TCSC Design and Rating 3.7

3.4.1 Sizing the TCSC's Internal Capacitor 3.7

3.4.2 Determining the TCSC's Maximum Reactance Order 3.8

3.4.3 Sizing the TCSC Inductor 3.8

3.4.4 Rating the TCSC's Circuit Components 3.18

3.5 Harmonic Analysis of the TCSC 3.20

Table ofContents

4.1 Introduction

Page vi

3.5.1 TCSC Ham10nic Voltage, 3.20

3.5.2 Ham10nic Analysis of the Line Current, 3.22

3.6 Conclusion 3.24'---------------------

4. DEVELOPMENT OF A LABORATORY PROTOTYPE TCSC

4.1--------

4.2 Practical Implementation, 4.2

4.2.1 Hardware Description 4.2

4.3 Practical Results 4.1 0

4.3.1 Practical TCSC Characteristics 4.10

4.3.2 Comparison of Simulated and Measured Results 4.12

4.4 Conclusion 4.24

5. APPLICATION OF THE TCSC TO DAMP POWER SYSTEM

OSCILLATIONS ON A SMIB SYSTEM

5.1 Introduction, 5.1

5.2 Application of the TCSC in Power System Oscillation Damping 5.2

5.3 Results of the Power Oscillation Damping Study 5.3

5.3.1 Trigger Circuit Control Strategy 5.3

5.4 Conclusion 5 9-------------------'

Table ofContents

Pag~ \:i.:

6. CONCLUSION


6.2 Factors that Influence the Design of the TCSC 6.1

6.3 Mathematical Models to Study the Performance of the TCSC 6.2

6.4 Development ofthe Laboratory-Scale TCSC 6.3

6.5 Power Oscillation Damping using the TCSC 6.4

6.6 Suggestions for Further Work 6.4

APPENDICES

APPENDIX A PARAMETERS OF A SIMPLE EMTDC CIRCUIT

USED DURING THE TCSC DESIGN STAGE

A.I Parameters of a Simple Circuit with a TCSC Device A.I-------

A.I.l Derivation of the Per-Unit System A.l

A.l.2 Transmission Line Impedance A.l

A.I.3 TCSC Device A.l

Table a/Contents

Page viU

APPENDIX B MODIFIED TRIGGER CIRCUIT FOR THE

CONTROL OF A THYRISTOR CONTROLLED SERIES CAPACITOR

APPENDIX C ADDITIONAL SIMULATION DETAILS AND

RESULTS FROM CHAPTER FOUR

APPENDIX D EMTDC SIMULATION MODEL FOR POWER

OSCILLATION DAMPING STUDY

D.1 Parameters of a Detailed EMTDC Circuit D.l

D 1.1 Generator Parameters (per unit unless stated) D.1

D 1.2 Turbine Model D.2

D 1.3 Transmission Line and TCSC Parameters (per phase) D.2

D 1.4 Infinite Bus-Bar D '). .J

REFERENCES R 1-----------------_..

Table a/Contents

Page ix

LIST OF FIGURES AND TABLES

FIGURES PAGE

Fig. 1.1 Two-machine power system diagram 1.1

Fig. 1.2 Two-machine power system diagram with series compensating

capacitors 1.2

Fig. 1.3 Diagram of a TCSC module 1.4

Fig. 2.1 One-line diagram of Slatt TCSC 2.1

Fig. 2.2 TCSC Module in series with a conventional capacitor. 2.4

Fig. 2.3 The reactance vs delay firing angle characteristic of the TCSC ........2.4

Fig. 2.4 TCSC diagram operating under thyristor blocked mode .2.5

Fig. 2.5 TCSC diagram operating under thyristor bypassed mode 2.6

Fig. 2.6 TCSC module under capacitive vernier operation mode .2.7

Fig. 2.7 Current waveforms during the vernier operating mode 2.8

Fig. 2.8 TCSC characteristic curves' variations with three sizes of the

reactor. ,,2.9

Fig. 2.9 Figure 2.9: Typical simulation results of the current and voltage

wavefOlIDs of the TCSC for different reactor sizes at the same firing

angle 2.10

Fig.2.10 Characteristics of the TCSC showing resonance region and Umin .....2.11

Fig. 2.11 TCSC characteristic curve showing the reactance range of the

device ,,2.12

Fig.2.12 Typical TCSC V-I capability characteristic 2.13

List ofFigures and Tables

Page x

Fig.2.13 Typical TCSC X-I capability characteristics 2.14

Fig. 2.14 3rd Harmonic voltage of the TCSC capacitor in pu of fundamental as a

function of the firing angle .2.17

Fig. 2.15 5th, 7th and 9th TCSC capacitor voltage harmonics in pu of fundamental

as a function of the firing angle 2.18

Fig. 2.16 Transient response of VTCSC to a step change of cc 2.19

Fig. 2.17 Transient response of VTCSC to a step change of cc 2.20

Fig. 2.18 Transient response of VTCSC to a step-down and step-up action of

cc 2.21

Fig. 2.19 Typical frequency response of a transmission line compensated with a

TCSC 2.22

Fig. 2.20 Power system oscillation damping: conventional capacitor vs bang-

bang controlled TCSC 2.24

Fig. 3.1 TCR trigger circuit and the TCSC 3.3

Fig. 3.2 Trigger pulses and the illustration of the firing delay time 3.4

Fig. 3.3 Time-domain results of the TCR trigger circuit 3.5

Fig. 3.4 TCSC characteristic curves' variations with three sizes of the

reactor 3.9

Fig. 3.5

Fig. 3.6

EMTDC/PSCAD time-domain simulation results of the TCSC with the

XTCR = 0.8 Q. The simulation was done at XORDER of 1 (A), XORDER of 2

(B) and XORDER of 3 (C) 3.11


XTCR = 1.2 Q .The simulation was done at XORDER of 1 (A), XORDER of 2

(B) andXoRDERof3 (C) 3.12


Fig. 3.7

Fig. 3.8

Page xi


XTCR = 1.6 O. The simulation was done at XORDER of 1 (A), XORDER of 2

(B) and XORDER of 3 (C) 3.13


XTCR = 0.8 a (A), 1.2 a (B) and 1.6 a (C). The simulation was done at

XORDER of 1 3.15

Fig. 3.9 EMTDC/PSCAD time-domain simulation results of the TCSC with the


XORDER of2 3.16

Fig. 3.10 EMTDC/PSCAD time-domain simulation results of the TCSC with the


XORDER of 3 3.17

Fig. 3.11 Harmonic generated in pu of fundamental as a function of alpha 3.20

Fig. 4.1 Diagram of the laboratory-scale TCSC .4.4

Fig. 4.2 The three-phase TCSC circuit .4.5

Fig. 4.3 The transmission line simulator. .4.6

Fig. 4.4 Relationship between the variable pot resistance and the firing

angle 4.7

Fig. 4.5 Original and modified synchronizing stage circuit. .4.8

Fig. 4.6 TCSC characteristic curve for a TCR = 0.8 ohms .4.10



Fig. 4.9 Comparison of phase A time-domain results at reactance order of 1:

Xtcr = 0.80 4.13


Page Xii

Fig. 4.10 Comparison of phase A time-domain results at reactance order of 1.5:

Xtcr =0.8Q 4.14

Fig. 4.11 Comparison of phase A time-domain results at reactance order of 2:

Xtcr = 0.8Q 4.15

Fig. 4.12 TCSC response to a 1 Hz modulation ofreactance order between 1 and

2. Xtcr = 0.8 Q 4.17

Fig. 4.13 TCSC response to a two level modulation of reactance order between

1.5 and 2. Xtcr = 0.8 Q .4.18

Fig. 4.14 TCSC response to a two level modulation of reactance order between 1

and 1.5. Xtcr = 0.8 Q .4.19

Fig. 4.15 TCSC response to a two level modulation of reactance order between 1

and 2. Xtcr = 0.8 Q 4.20

Fig. 4.16 TCSC transient response as the reactance order is changed from 1 to

3 4.22

Fig. 4.17 TCSC transient response as the reactance order is changed from 3 to

1 4.22

Fig. 4.18 TCSC transient response as the reactance order is changed from 3 to 1

back to 3 4.23

Fig. 5.1 SMIB transmission system with TCSC module used to investigate

power oscillation damping 5.4

Fig. 5.2 Relationship between the input to the controller and the firing

angle 5.5

Fig. 5.3 Time-domain simulation results ofthe SMIB system in Figure 5.1 with

and without the TCSC 5.7

Fig. 5.4 Complete Time-domain simulation results of the SMIB system in

Figure 5.1 with and without the TCSC 5.8


Page xiii

TABLE

Table 3.1 Summary of TCSC variable reactance ranges for typical applications in

the literature.

Table 3.2 The relationship of XTCR size and the resonant point for a given value

ofn and Xc = -j2 Q.

Table 3.3 TCSC component ratings at XTCSC = -j6 Q with XTCR = jO.8 Q

Table 3.4 TCSC component ratings at XTCSC = -j6 Q with XTCR =j 1.2 Q

Table 3.5 TCSC component ratings at XTCSC = -j6 Q with XTCR = j 1.6 Q

Table 3.6 Harmonics ofTCSC voltage at XTCR = 0.8 Q

Table 3.7 Harmonics of the Line Current at XTCR = 0.8 Q


LIST OF SYMBOLS

The commonly used symbols and notations adopted in this thesis are listed below.

Other symbols used in the text are explained where they first occur.

Acronyms

AC

AVR

BPA

DC

EMTDC

FACTS

POD

SMIB

SSR

TCR

TCSC

Alternating Current

Automatic Voltage Regulator

Bonneville Power Administration

Direct Current

Electro-Magnetic Transient Direct Current

Flexible AC Transmission System

Power Oscillation Damping

Single Machine Infinite Bus

Sub-Synchronous Resonance

Thyristor Controlled Reactor

Thyristor Controlled Series Capacitor

Synchronous generator symbols

Armature resistance

Stator leakage reactance

D-axis unsaturated magnetizing reactance

Field resistance

List ofSymbols

Pagp. xv

XF Field leakage reactance

RD D-axis damper resistance

XKD D-axis damper leakage reactance

XMFQ Field - damp mutual leakage reactance

XMQ Q-axis magnetizing reactance

RKQ Q-axis damper resistance

XKQ Q-axis damper leakage reactance

EF Synchronous generator field voltage

H Inertia constant

PE Electrical power output

PM Mechanical power output

QE Reactive power output

TE Electrical torque output

TM Mechanical torque output

VTO Terminal voltage magnitude at t = 0

0) Generator speed

0)0 Generator synchronous speed

eTO Terminal voltage phase at t = 0

System symbols

C

L

R

Capacitor

Inductor

Resistance

List ofSymbols

RL Transmission line resistor

XL Transmission line reactance

XORDER Reactance order

X TCSC TCSC reactance

XTcsc (MIN) TCSC minimum reactance

XTCSC (MAX) TCSC maximum reactance

U Firing delay angle

UMAX Maximum firing angle

UMIN Minimum firing angle

URES Resonant point firing angle

List a/Symbols

Page I. l

CHAPTER ONE

INTRODUCTION

1.1 Background

Despite the fact that bulk power transfers are increasing due to an ever-growing

number of consumers, the growth of electric power transmission facilities is

restricted by several factors such as difficulties in obtaining servitude, cost required

to build new transmission networks and the environmental impact of building new

networks. The steady-state power transfer capability of an AC transmission line can

be explained using the simple two-machine power system diagram of Figure 1.1.

PTR )

VS*VRPm = SinS

XL

Figure 1.1. Two-machine power system diagram

Figure 1.1 illustrates that the active power PTR transferred from sending bus to the

receiving bus is determined by the magnitude of IVs Iand IVRI, the phase

difference of the sending end to receiving end voltages as well as the transmission

line reactance XL. Figure 1.2 illustrates capacitive line compensation using a series

capacitor. The power transfer capability of the line is increased by inserting

Introduction

" Chapter One p ".,, age :.,'

capacitive reactance, Xc, in series with the line inductive reactance, XL. Equation

1.1 quantifies the magnitude of active power transferred from the sending bus to

the receiving bus for a line that has series capacitors.

PTR )

Figure 1.2: Two-machine power system diagram with series compensating

capacitors

VS*VRFTR = SinS 1.1

XL-XC

Historically, several conventional techniques have been studied and used to

influence these factors, namely line impedance and the load angle (8), and hence

transmit higher levels of active power over the transmission lines. Transformer tap

changing schemes and mechanical switching of conventional series and shunt

capacitors are some of the techniques that have traditionally been used to maximise

power transfer capabilities of high voltage AC transmission lines. However, since

these methods of influencing transmission line characteristics involve mechanical

operation of equipment such as circuit breakers, their use is limited for transient

and dynamic control of the power system. Another problem associated with the use

of conventional series capacitors is that they may lead to system instabilities and

sub-harmonic oscillations known as sub synchronous resonance (SSR) [14], [29].

Introduction

Chapter fIne Page 1.3

Sub synchronous resonance is described in [29] as the unstable interaction between

the electrical resonance(s) of a series capacitor compensated system and

mechanical resonance of the flexible distributed mass turbo-generator shaft.

1.2 FACTS Series Compensators

In recent years, power system researchers have been working on alternatives to

conventional methods of influencing the factors that determine power transfer

capability of the transmission line. These research works by numerous reputable

research institutes such as Electrical Power Research Institute (EPRI) coupled with

advancements in the field of power-electronics, both have led to the integration of

devices such as thyristors into existing methods of power systems control [3], [5].

There are several different types of FACTS devices and they all share, in different

degrees, a common aim of enabling long AC transmission lines to be loaded

closely to their thermal limits without causing any system instability.

Under steady-state conditions, a FACTS device can be used as a normal

conventional compensating device to compensate the transmission line reactance

and hence increase power transfer capability of the line. Over and above steady

state compensation, a FACTS device is capable of providing dynamic control of the

line's parameters and hence improving system security under fault and post-fault

conditions.

1.3 Thyristor-Controlled Series Capacitor

One of the first FACTS compensators to be designed and implemented is the

thyristor-controlled series capacitor (TCSC) [5]. As shown in Figure 1.3, a TCSC

consists of a conventional capacitor in parallel with thyristor controlled reactor

Introduction

4

(TCR). The TCR comprises an inductor in series with a paIr of back-to-back

thyristors.

~ ... a

-jXc

Figure 1.3: Diagram ora TCSC module

~XTCSC = f(a)

The net value of the TCSC reactance can be varied by changing the firing angle, a,

of the TCR. The TCSC reactance XTCSC can either be inductive or capacitive

depending on the value of the firing angle a.

1.4 Objectives Of The Thesis

The overall objective of this research work was to design and build a three phase

TCSC suitable for use in a research laboratory at Natal University. Extensive work

has been done on general operation of a TCSC and its ability to damp power

system oscillation [22], [27], [34]. However, not so much has been written on

techniques that need to be followed when designing a TCSC [19], [28], [36]. The

following points are key research topics that are addressed in this thesis.

Introduction

5

(a) Operating Region

One of the tasks that was conducted was to identify the range of the firing angles.

The firing angle not only determines whether the TCSC reactance is capacitive or

inductive, but also determines the magnitude of this reactance.

(b) Rating of TCSC components

Another topic that was investigated was the rating of the TCSC components.

(c) Harmonic analysis

Since the operation of the TCSC involves chopping the current AC waveform, it

was expected that harmonics would be generated. Hence, harmonic analysis was

conducted to substantiate harmonic contribution by the TCSC to the power system.

(d) Dynamic response of the TCSC

A step change in the firing angle was applied to investigate the transient response

of the device.

(e) Practical TCSC module

A three-phase TCSC laboratory scale model was built and tested. The objective in

constructing a TCSC was to obtain practical results of the TCSC and hence verify

theoretical results from the simulations.

(f) Power swing damping

The last objective was to demonstrate the designed TCSC in a typical application:

power oscillation damping was chosen for this research work.

Introduction

Page .1.6

1.5 Thesis Layout

This thesis is made up of six chapters and appendices. A technical literature review,

on the subject of series compensation using TCSC, was conducted and it can be

found in Chapter Two. Chapter Two also covers background theory on how the

TCSC operates. Chapter Two also provides literature review on approaches and

implications of selecting capacitor and reactor sizes. Most common applications of

the TCSC are also mentioned in Chapter Two.

Chapter Three contains the details on the development of a TCSC's mathematical

model for computer simulations. This model also includes the firing angle control

scheme, which provides firing pulses for the TCR's thyristors. Time-domain

simulations are investigated in this chapter and are also compared in later chapters

with the measured results obtained from the laboratory scaled TCSC. Chapter

Three also contains the details of the investigation of topics such as rating of the

TCSC components, harmonics generated by the TCSC and behavior of TCSC

impedance as the firing angle is subjected to a step change.

Chapter Four deals with the development of a laboratory scaled TCSC for practical

implementation. The chapter begins by describing different components that were

used to construct the hardware TCSC. Subsequent sections of Chapter Four,

contain measured results of the performance of the hardware TCSC, which are then

compared with results from the mathematical model developed in Chapter Three.

These comparisons were performed to ensure that a laboratory scaled TCSC was

operating as expected.

A mathematical model, developed in Chapter Three, is expended in Chapter Five

with the inclusion of multi-mass model representing turbine shafts as found in the

Introduction

Ch;'lplei~ One Page j '7

machine laboratory of the Natal University. The results of this model prove that the

TCSC can significantly improve damping of the network, when the network is

subjected to a short three-phase fault. Finally, Chapter Six summarises the results

of this work and suggests further research that could be undertaken in future

1.6 Research Publication

Some of the findings of this thesis have been presented at a national conference

[28].

Introduction

Chapter Two

CHAPTER TWO

Page 2. I

GENERAL OPERATION OF THE TCSC

2.1 Introduction

Chapter One of this thesis has briefly outlined the constraints that power utilities

need to overcome when transmitting power in AC transmission lines. The benefits

of using FACTS devices, such as Thyristor-Controlled Series Capacitor, were also

described. One of the main objectives of this thesis work is to determine the

methodology which needs to be followed when designing a TCSC device for an

AC transmission network, and to demonstrate the capability of the TCSC to damp

power oscillations after an occurrence of a major disturbance in a transmission

network.

The successful development of the design methodology reqUIres a thorough

literature review on the subject of TCSC design. Hence, a comprehensive literature

survey was conducted to evaluate some of the considerations and constraints that

have been encountered by other researchers in the field of TCSC design. This

chapter initially presents a historical experience on the first TCSC modules to be

commissioned. The chapter then outlines the operating principle of the TCSC

device. This chapter also describes several considerations that need to be addressed

when a TCSC is designed. Such considerations include the so-called reactance

order (XORDER), firing region, resonance point and rating of the TCSC components.

X ORDER can be defined as the ratio of TCSC effective reactance to that of the

internal capacitor reactance.

General Operation ofthe TCSC

Chapter Two Page 2.2

Another topic that is covered in this chapter is the issue of harmonics. Any

switching of an AC waveform will result in the generation of harmonics, hence the

effects of this phenomenon on the rating of the different components of the TCSC

had to be investigated. The last section of this chapter will outline some common

applications of the device. These applications are Power Oscillation Damping

(POD) and Sub-Synchronous Resonance (SSR). The literature survey will then

form the basis of the design approach that will be followed in the subsequent

design methodology covered in latter chapters of the thesis.

2.2 The World's First Multi-Module TCSC System [2]

The Bonneville Power Administration (BPA) thyristor-controlled series capacitor

installation was the first of its kind in the world [2]. The pilot site of the TCSC

project is Slatt substation on the Slatt-Buckley 500 kV transmission line owned by

BPA in Northern Oregon. At the Cl Slatt substation, six identical thyristor

controlled series capacitor modules were applied to each of the three phases. Each

phase of the line consisted of the capacitors, current limiting reactors, thyristor

switches and protective varistors all at potential of 500 kV (as shown by Figure 2.1

below). Three platforms, for each phase of the line, were specially designed to

mount the TCSC system. Communication between platform and ground was

achieved by fiber optics. All modules receive continuous signals from the control

unit, and these signals establish the operating mode and vernier control for each

individual module.



To B1UCkleY~ "''- '''IT"c..,.,sc TF

Series ModuleCapacitor t '

IsolationDisconnect

Reactor Thtistorvalves

i ..............•.......•.•....:

Figure 2.1: One-line diagram ofSlatt TCSC [27

The above Figure 2.1 shows an elementary one-line diagram of a Slatt TCSC on

one of the phases of the line. Each TCSC module consists of a back-to-back

thyristor in series with a reactor (TCR), and in parallel with a capacitor and a

varistor. A bypass switch is connected in parallel with an entire device for use in

protective functions. There are also two other isolation switches for TCSC isolation

purposes.

Performance Results

•

•

•

•

•

The test results demonstrated TCSC capability of high speed switching for

controlling power flow, which in turn allows increased loading of existing

transmission lines close to their thermal limits.

The system damping was also improved after the network was subjected to

extreme contingencies.

It was also shown that the fast-acting TCSC could provide the means of rapidly

increasing power transfer upon detection of the critical contingencies, resulting

in increased transient stability.

Sub-Synchronous Resonance (SSR) tests were also performed to demonstrate

the ability of the TCSC to greatly reduce a potential SSR problem.

The Slatt TCSC test also revealed that nearly all harmonic currents are

contained within the TCSC loop.

General Operation a/the TCSC


In conclusion, it is the objective of this work to develop a laboratory-scale TCSC in

order to carry out research into these and other issues.

2.3 Operating Principles of a TCSC

The basic thyristor-controlled senes capacitor scheme consists of the senes

compensating capacitor shunted by a thyristor-controlled reactor. In practice,

several TCSC. modules may be connected in series to obtain the desired voltage

rating and operating characteristic [2], [5], as shown in Figure 2.1. Another

common configuration, as shown in Figure 2.2 below, is to use a hybrid of a

conventional series capacitor and TCSC module, connected in series [3].

TCSC Module

~._--._---_._._----.-.------------

.-------------------------._-----,~ .. ;

I •

I ~I I

I ; ar ••Fixed Capj--------_._-------;; I. ;

+-1~1~I I._--._--------------

Figure 2.2: TCSC Module in series with a conventional capacitor

Under this arrangement, the conventional series capacitor is used for line

compensation and the TCSC is only utilized during contingencies.

The variable reactance of the TCSC is achieved by varying the firing delay angle

(ex) of the thyristor-controUed reactor.


<X (deg)

Inductive

90

180

-2 -1

Chapter Two

· .· .· .· .. . . . .· .· .· .· .· .· .· .· .· .· .· .· .

· .· .· .· .· . . . . .· . . . . .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· .· . . . . .· .....· . . . . .· . . . . .· .· .· .· .· .· .· .· .· . . . . .· .· .· .· .

o 1

XTese (pu)

Page 2.5

Resonance Region

Capacitive

2

Figure 2.3: The reactance vs delay firing angle characteristic ofthe TCSC

Figure 2.3 shows the characteristic of the TCSC reactance as a function of the

firing angle <x.

The TCSC has three basic modes of operation:

• Thyristor blocked,

• Thyristor bypassed and

• Vernier operation.

Thyristor blocked

Under this mode of operation, the thyristors valves are not conducting any current

(hence, the term blocked). The TCSC net reactance is effectively the capacitive

reactance of the capacitor, -jXe. This mode occurs when the firing angle is 1800•

Figure 2.4 shows that no current passes through the thyristors, hence IUNE = hese

and ITeR = O.


_.~

IUNE

Chapter Two

_.~

hese

~ ... a

Page 2.6

Figure 2.4: TCSC diagram operating under thyristor blocked mode

Thyristor bypassed

Under this mode of operation, the thyristor valves are gated for full conduction.

The resulting net TCSC reactance is effectively the parallel combination of -jXe

and jXTeR. This mode occurs when the firing delay angle, a, is equal to 90°. In

practice, some current also flows through the capacitor during bypassed operation,

but most flows through the thyristor valves and reactor because it is a much lower

impedance path.

IUNE~

~ ... a

.............j~ILnNE

Figure 2.5: TCSC diagram operating under thyristor bypassed mode

Figure 2.5 shows the flow of current under this mode. Depending on the design of

the TCSC, most of the line current flows through the TCR branch and hence IUNE ~

heR and le ~ O.


Vernier operation


This is the most common mode of operation. The vernier operation mode is sub

divided into two categories, namely: inductive vernier mode and capacitive vernier

mode. However, only capacitive vernier operation mode will be considered in this

thesis.

Under vernier mode, the TCSC reactance can be calculated for each firing angle

based on the equation below [23], equation 2.1, that defines the TCSC circuit

reactance as a function of the firing angle:

. 1lXrcRXrcsc = (0- _ sin 0-)+ 7rXrc~c (2.1)

where cr = 2n - 2a (conduction: angle)

XTCR = TCR reactance

Xc = fixed capacitor bank reactance

In this mode, the thyristor valves are gated near the end of each half cycle in a

manner that can circulate a controlled amount of inductive current through the

capacitor, thereby increasing the effective capacitive reactance of the module.


hCRt

-~IUNE

Chapter Two

hcsc

I

I

I

~ ... a

Page 2.8

Figure 2.6: TCSC module under capacitive vernier operation mode

Figure 2.6 shows the distribution of currents under capacitive vernier operation

mode. From the same figure above, the circuit appears somewhat like that of a

parallel L-C tank circuit with variable inductance, such a circuit has a reactance as

seen by the AC system at the TCSC terminals:

jXn.:R(a) * }XCXrcsc(a) = (2.2)

jXc - jXrcR(a)

Both, equations 2.1 and 2.2, show the relationship of the TCSC impedance with the

firing delay angle.



Line current - Vernier capacitive mode

~ /"~ /" i'..."-./ '-V "-+

Thyristor current - Vernier capacitive mode

timetime

Capacitor current - vernier capacitive mode

l'csc

time

Figure 2. 7 : Current wavefOrms during the vernier operating mode

The above figure 2.7, graphically, shows how the steady-state magnitude of the

TCSC current becomes larger than the nominal capacitor current when there is no

vernier operation.

2.4 Factors Considered when Selecting the Inductance of the Reactor Loop

2.4.1 Introduction

Section 2.3 has outlined the operating principles of the TCSC device. Different

operating modes were explained in this section, and the circuit diagrams showing



the current distribution, including current and voltage waveforms, in the loop were

included.

In this section, the intention is to discuss some important design issues that need to

be considered when designing a TCSC. These issues include the ftring region for

vernier capacitive mode, TCSC resonance point, rating of the TCSC components

and the ratio of the TCSC maximum reactance to the capacitive reactance of its

internal capacitor (XoRDER).

2.4.2 Firing Region

The component sizes of the LC circuit determine the range of the ftring region. The

bigger the TCR reactance, hence inductor, the more range available for vernier

capacitive operation (assuming the same capacitive compensation). Figure 2.8

illustrates this point:

TCSC Characteristic curves for different reactor sizes

180170160120 130 140 150

Firing Delay Angle ( Degrees )

11010090

I ·~ ···9 ·I ···! ·

8~·, ··

~ ···7 ., ··, ···6 ,"TCR = 0.6 tm

XTCR FO.BIlI ··\ · I \5

~\.

\.~TCR = 0.4 u

4. /

\ .Y...

\ ..3 '\ \++

" ++ f\-..2

+'." ...,. ....~........ t- ..:::-.:._..~1

0

XTCSC(PU)

Figure 2.8: TCSC characteristic curves' variations with three sizes ofthe reactor



The reactors are in per unit values of the internal capacitor of the TCSC. Ideally,

the control range should be as large as possible to achieve smoother operating

range. However, other factors such as TCSC components' rating (XTCR in

particular), hence economics there of, prevents this from being implemented in a

practical design [18]. Figure 2.8 also shows that the TCSC reactance increases, as

the firing delay angle is decreased from 180 degrees. At a given firing angle, the

current flow through the TCR-Capacitor loop decreases as the inductance of the

parallel reactor is increased. Figure 2.9 illustrates this point:

Circuit responses for different reactor sizes

21.00Hffi1.00

-- -----------.,.------· .· .· .· .1.9751.971.$1.£65

Vc

: /:-i:~~~~-::::::;:::::::::::~::::::.·~·i~~~·::::T:::::::: :;::.:::::42~fS:~': ../ : : : Id :o ; ~-------·· ..: ·VL: -:---.-. ~----···--·r··i/; ..··.. -·-·-:·· - ,

:: ::::'::::i:::::::::.:>~~:i ..:::::::::::::::;::::::::.:~~':.::t::::::::L::::::. '1.£6 1.97 1.975 1.00 Ha; 1.00 2

.~ ••~m •••••I·•••••··,••••••••••l.~ ••••••,.~·.·:· ••·•••••1.!Ii 1.!ffi 1.00 Hffi 1.97 1.975 1.00 1.gf) tOO tm5 2

Time (seconds)

Figure 2.9: Typical simulation results ofthe current and voltage waveforms ofthe

TCSC for different reactor sizes at the same firing angle


Resonance point


The operating range of the TCSC's firing angles in the capacitive region is from

180 degrees to Umin, UTCSC = [180°, Umin). If the TCSC is operated at the firing

delay angle of 180 degrees, no current flows through the TCR branch, and hence

the effective TCSC reactance is equal to the internal capacitive reactance, XTCSC =-

jXc.

However, if the firing angle is any angle within the firing range, [1800, Umin], the

TCSC reactance is greater than Xc. The actual value of this reactance can be

determined by equation 2.1. The exact resonance point of the TCSC is reached

when the capacitive reactance equals the inductive reactance of the TCR. At this

point, the TCSC reactance becomes infinitely large; hence the TCSC is always

operated well below this point. The following figure shows the location of Umin and

the resonance region where U approaches the resonant point and the TCSC

reactance becomes unacceptably large.

TCSC Characteristic curve

Resonanceregion \------------+XrCSC(MAX)

--- -1 XrCSC(MIN)

Umin

Figure 2.10: Characteristics ofthe TCSC showing resonance region and amin

As the figure above shows, the operating range of the TCSC is determined once the

minimum firing angle is set. For the TCSC with the above characteristics, Figure

2.10, the TCSC reactance range is [XTCSC(MIN), XTCSCCMAX)).


2.4.3 The Reactance Order


,The reactance order (XoRDER) of the TCSC is defined as the ratio of its capacitive

reactance to the capacitive reactance of its internal capacitor, with XoRDER ~ 3

typically [28]. The following figure illustrates how the XoRDER is determined:

TCSC Characteristic curve

XTCSC(MAXj

XTCSC(MINj

amin

Figure 2.11: TCSC characteristic curve showing the reactance range ofthe device

Since the minimum reactance of the TCSC is the same as the reactance of the

internal capacitor, XTCSC (MIN) = -jXc;

I XORDFJ< = :;;:~) (23)

One of the limiting factors in choosing a larger value of XoRDER is the resonant

region. The higher the maximum value of XoRDER is, the more OCMIN approaches

OCRES, with OCRES occurring when IXTCR I = 1Xc I.


Chapter Two

2.4.4 Operating Capability of the TCSC

Page 214

The operating range of the TCSC is dictated by a number of application

requirements. This section describes these limits in terms of typical capability

curves. One of these limiting factors is the voltage that appears across the TCSC at

the minimum firing delay angle, aMIN. An important consideration of this voltage

constraint is the duration. The maximum voltage constraint is typically given for

three duration: continuous, 30-minutes and a few seconds, as illustrated in Figure

2.12.

Capacitive Continuous

Inductive

O-t--------------------+o-

Figure 2.12: Typical TCSC X-I capability characteristic.

Figure 2.12 shows the operating capability characteristics of the TCSC in terms of

module voltage versus line current. Given that the control system can operate the

TCSC in any combination bypassed or vernier modes, the TCSC can vary its total

effective reactance anywhere within the region of the plot. Short-term overload

operation is possible at higher levels of line currents. Separate regions are shown



for 30-minutes and seconds overload capabilities. The capability can also be

illustrated in terms of reactance versus line current, as shown in Figure 2.13.

VTCSC

VTCSCCMAX)

Capacitive

contin~ a ~ 180'

o~~ ~ _

Inductive

Figure 2.13: Tvpical TCSC V-I capability characteristics

Figure 2.13 shows the gap in control range between capacitive and inductive

operation, as well as the reduction in dynamic range with increasing line current.

Other TCSC applications require a relatively smooth control of the reactance. Such

a characteristic can be achieved by connecting several TCSC modules III senes

instead of a single module.


Chapter Two

2.4.5 Rating the TCSC Components

Page 2.16

One of the critical design factors that needs to be considered when designing a

TCSC device is the rating of its components, namely, capacitor, thyristors and the

inductor. When designing a TCSC, the added dimension of thyristor control

increases the number of factors to be considered, as compared to conventional

series compensation. The voltage that appears across the TCSC (hence Vc) and the

current through the TCSC set the limits on the operating range of the device.

In the capacitive vernier mode, the circulating loop current adds to the line current

and produces higher capacitor currents. This increases voltage drop across the

series capacitor, and thus increases the net series compensation as seen from the

line. The following are some of the TCSC rating requirements, for both steady-state

and transient operation, that need to be considered:

• Current rating,

• Voltage rating and

• MVAR rating

Current rating

The TCSC current ratings are similar to those used for conventional capacitor

banks:

IRATED = Continuous line current.

hEMP = Temporary line current.

tTEMP = Duration OfITEMP (typically 30 minutes).

hRANs = Capacitor transient current.

Typical values for the temporary and the transient capacitor currents are hEMP =

1.35*IRATED and hRANs = 2*IRATED [36].



Voltage rating

The voltage rating of the TCSC is established based on the steady-state and

transient performance requirements.

VRATED = Continuous voltage across the TCSC (typically, ~ Xc*IRATED

because of capacitive vernier operating mode).

VTEMP = Maximum temporary voltage across the TCSC (typically, ~ Xc*ITEMP).

VTRANS = Voltage developed across the TCSC during the transient swmgs

(Typically 2:: XC*hEMP).

MVArRating

Another important rating parameter, for both capacitor and TCR inductor, is the

MYAI. The following MVAr ratings are considered:

Continuous rating:

MVAr = 3*IRATED*VRATED

Short-time transient rating:

MVArtrans = 3*hRANS*VTRANS

2.4.6 Harmonic Performance of the TCSC

The TCSC operation with partial conduction of the TCR causes harmonic currents

to circulate inside the TCSC loop. These harmonic currents are caused by the TCR

harmonic currents that circulate through the series compensation capacitor. The

TCR generates all odd harmonics, the magnitudes of which are a function of the

delay angle u, as illustrated in Figure 2.14 and Figure 2.15 below.


Chapter Two· Page 2.18

whereV3 is 3rd harmonic voltageV I is the fundamental voltage

0.02

0.06

0.04

0.08

0.10

0.12

O.+---,-----r--..---,---r--=:;==---

Degrees

Figure 2.14: 3rd

Harmonic voltage ofthe TCSC capacitor in pu offundamental as a

function o[the firing angle

Figure 2.14 shows the per unit magnitude of the 3rd harmonic voltage as a function

of the firing delay angle. Harmonics greater than the 3rd are much smaller in

relation to the fundamental and have minimal effect on the power system as a

whole. This is mainly because the TCSC is usually applied to long, high impedance

lines, in which the generated line current harmonics is relatively low [36].

Another important fact about the harmonic currents is that they are confined within

the capacitor-TCR loop [16]. This implies that there are no special filters required

in the line. However, the TCSC capacitor has to be rated such that it can handle the

harmonics (3rd

in particular) voltages it will experience under normal operation.

Figure 2.15 shows harmonic currents greater than 3rd as a function of the firing

delay angle.


0.005

o

-0.005

-0.010

Chapter Two

7th

Page 2.19

WhereV . 5th 7th 0 9th

N - IS, rharmonic voltage.VI - is the fundamentalvoltage

Figure 2.15: 5th, i h and 9th TCSC capacitor voltage harmonics in pu of

fundamental as a function ofthe firing angle

The above results show the dominanCe of the third harmonic over the remaining

harmonics. As Figure 2.14 illustrates, the 3rd harmonic increases substantially as

the firing delay angle is decreased; hence attempts should be made, during design

stage, to maintain the magnitude of the 3rd harmonic at tolerable levels.

2.4.7 Transient Response of the TCSC

The transient response of the TCSC's reactance, due to the step change of the firing

delay angle, is another important characteristic of the device that need to be looked

at during design stages.



Figure 2.16 shows a typical transient response of the TCSC when its commanded

reactance is instantaneously changed from a lower reactance to a higher reactance.

This can be achieved by instantaneously changing the firing delay angle.

(;i' 8 ..-----------.:---------TI:--------.

~ : :~ I :

~ 6 ~-----------------------~'--------~,----------ig I

~ Io I

~ :~ 4 1------------:.-------------------------:- -- ------------ ---- ---- --

, II I, .I ,

I i2'--- ...l...- --1.... -'

15 2 25 3

3

,~ ~

30 ..------------y--.---------r---------,~

~ 20 r------------------------~---'"" ,o ,~ 10 :I)01~ 0o>u -10(f) I

~ -20 r------------------------f--AI 8: i-30 L- ...:......J.__....::..!... --I.. ---J

15 2 25

Time (seconds)

Figure 216: Transient response ofVTCSC to a step change of ex:

Figure 2.16 shows that a step change of the TCSC reactance was applied at t = 2

seconds. The reactance step change resulted to the increase ofthe voltage across the

TCSC. Two vertical lines, A and B, of Figure 2.16 show the duration required for

the TCSC voltage to reach the new level. This duration is approximately equal to 8

cycles.



Figure 2.17 shows the transient response of the TCSC voltage, as the commanded

reactance is instantaneously decreased. The voltage across the TCSC decreases in

response to a step change in TCSC reactance. However, the time duration required

for the TCSC voltage to reach a new voltage level is much shorter.

6.-----------r---------r----------,

------------------------!-,---------7-"----------j,,,,,,

,00 :E :~ I I

';,;' 4 1------------;'- - - - - - - - - - - - - - - - - - - - - - - - : - - - - - - - - - - - - - - - - - - - - - - -o ,c •~ ,o 'o '~ 2u(I)UI-

2 2.5 3

30,--------__r----------,----------,

';)20

*"o~ 104)Clli 0'0>u -10(I)uI- -20

, ,, ,-----------------------~------------------------~-----------------------, ,, ,

• II •r -- - -- - --- - -- - - -- - - - _.- -,- -- - --- - - - - --- - -- - --- ---I II •I

---- - - ----------------- -.- -- --- ------------------I,

I ,

------------------------~------------------------I------------------------

32.52

-30 L-- ---ll.....- ~ --'

1.5

Time (seconds)

Figure 2.17: Transient response ofVTCSC to a step change of oc

As can be observed from both Figure 2.16 and Figure 2.17, the response time of the

TCSC voltage is asymmetric. When the reactance is increased (as seen in Figure

2.16), the TCSC voltage response time is relatively slow compared to when the

reactance is decreased (as seen in Figure 2.17). This can be clearly seen when both

step-up and step-down cycles are shown on the same graph, as Figure 2.18

illustrates.



7.-------r----...--------;,----,-,------,II

"(f.;'- 6 ---- .. -------- ..~--------_ ... ----:--------------~----__..;_, -----I~ :: Ie 5 ~ -:-.. .. ~ -Q) I 1

g : :IS 4 1------..,..--------------.-------------- --------------.---------_----~ : :G • ~-- _~ 3 - ... ------------ ... -------------:-------------- I

u • :~ 2 L-- ~'------------~,--------------~--------------I- "

1 ,1'---_--i. ....L L..- --l... ---'

0.51 1.5 2 2.5 3

30 .....------....-----..,------,-------,--------,

32.521.5

Time (seconds)

.................... ............. -1-"" -,I ,

I I, 1

.................................................................. .. -I- -1-

-30 L- -L- ......J.. -'-- -L- ---'

0.5

, , I

1 , I

,....." 20 :- -:- -:-~ , I I

o "~ 10 - - - - - - - - - - - - - -:- - - - - - - - - - - - - - -,Q)

:il' 0'*'"o>v -10({)

vI- -20

Figure 2.18: Transient response ofVTCSC to a step-down and step-up action of er

This behavior is attributed to a physical nature of capacitors. Response time is

shorter when the reactance is decreased because the capacitor is simply bypassed

and discharges instantaneously. However, when the reactance is increased, the

response of the TCSC voltage will be slower because of the initial charge stored by

the capacitor [28].


Chapter Two Page 223

2.4.8 Frequency Response of the TCSC

Another important factor in the TCSC design is its frequency response. Frequency

response is a critical factor that needs to be considered, more especially if the

TCSC is being used in mitigation of Sub-Synchronous Resonance. Figure 2.19

illustrates a typical frequency response of a transmission line compensated with a

TCSC.

50. --,-------,-----,------,-----,

;--._-----.'--- -----_ ..:- .... _-_._--;-------- '!~

504540

. -:---- ·_·_--··~-_·_·---·-I

, ,•. ~ .,' • _. - •• - • - •• r - - - - - - -

3520 25 30

Frequency (Hz)

1510

ol..-. _

o 5

en 40"- ' ~ ~ : ~ ".""."E.co 30 ~ ~~~+_ ••• _:-.------- ••-.~ •• --.------~-----------:-(1)

~ 20 ;'"al'"-',-<: "Resonance:point

E 10 ~............ ........:---..>-:---:-~................ ,

--.............------.-----;--'----

100 c

;------------: _------ ---_ -en* 50~·OJ(1)"0

..Q2 0 f-- , : ,Clcro

~ -50 ~ .. : >.--:t£ -'-__-;---~-~_ --

.....~;/~~~~~.~..... ----;

-100 '------..--'---o 5 10 15 20 25 30

Frequency (Hz)35 40 45 50

Figure 2.19: Typical frequency response ora transmission line compensated with a

As Figure 2.19 shows, the frequency response of a transmission line compensated

with a TCSC shows similar behavior to a transmission line compensated with

conventional fixed capacitors. The figure shows that at the frequency of 30 Hz, the



capacitive reactance of the TCSC is equal to the inductive reactance of the

transmission line, hence the existence of a resonance point. However, in the case of

the TCSC there is extra resistance at this resonant frequency [32]. This is another

advantage of the TCSC, especially if the TCSC is used for power swing damping.

This resistive component of the TCSC impedance is usually exploited to provide

more positive damping torque when the power system experiences power

oscillations.

2.5 Some Common Applications Of The TCSC

The TCSC's high speed switching capability provides a mechanism for controlling

line power flow, which permits increased loading of existing transmission lines.

This allows for rapid readjustment of line power flow in response to various

contingencies, such as damping of power swings and Sub-synchronous resonance

(SSR).

The TCSC can also be used as a conventional series capacitor by regulating steady

state power flow within its design limits. This section summarizes some of these

typical benefits of the TCSC.

2.5.1 Power Swing Damping

One of the important applications of the TCSC is to damp power oscillations.

When damping power oscillations, it is necessary to vary the applied compensation

so as to counteract the accelerating or decelerating swings of the power system

[10]. When a transient fault occurs, the rotationally oscillating generator accelerates

and its rotor speed increases, so the electric power transmitted must be increased to

limit the excess kinetic energy picked up by the generator. Conversely, when the

generator decelerates, the electrical power transmitted must be decreased.



Figure 2.20 shows a typical machine's speed deviation, due to a transient fault. The

figure also shows the benefit of using the TCSC's variable reactance to damp

power swing oscillations. The blue curve shows the response of the system using a

conventional (fixed) capacitor to compensate for the line inductance. As the graph

illustrates, the oscillations are lightly damped. The red curve is the response of the

system using a TCSC with the same steady state degree of compensation.

As the figure indicates, the oscillation damping is greatly improved by using a

TCSC to vary the series compensation dynamically. In this particular illustration,

the TCSC was controlled by a bang-bang type of controller [10]. The bang-bang

controller can be defined as a controller with two states of capacitive reactance.

Firing delay angle (degrees)

54.43.532.521.50.5

'---

1300

190

180

170

160

150

140

-5

Machine's speed deviation ( rad/sec )

I~\ '\ 1\

11~1 /,

\ I1\ ! 1\ (' /\ /\ /\ /\I \

")1 \ ! \ j \ / V \) \j / l/ \.5

v

V \j v

5

o

2.5

-2

0.5 1.5 2 2.5 3 3.5 4 4. 5

Time

Figure 2.20: Power system oscillation damping: conventional capacitor vs bang-bang

controlled TCSC.

The waveforms of Figure 2.20 show the corresponding uncontrolled and controlled

oscillations of the machine's speed d~viation around its steady state, following an

assumed fault that initiated the oscillations. The first waveform, Figure 2.20, shows

the TCSC firing delay angle. As the figure shows, this firing angle can either be


·Chapter Two Page 2.26

180° or 138°. The level of compensation is at the maximum, a = 138°, when the

speed deviation is positive. Conversely, the compensation level is at the minimum,

a = 180°, when the speed deviation is negative.

As the figure shows, the bang-bang controller is effective for damping large

oscillations. However, damping relatively small power oscillations, continuous

variation of the firing delay angle may be a better alternative [10].

2.5.2 Mitigation of Subsynchronous Resonance

Subsynchronous resonance involves oscillatory exchange of energy between a

generator and the system below the fundamental system frequency, which is caused

by series capacitive compensation. This phenomenon can result in dangerously

large power oscillations (at subsynchronous frequencies) between the mechanical

system and electrical system.

Computer simulation studies can be used to identify subsynchronous modes of

oscillations. When the SSR contingency occurs, the TCSC can then be used to

operate at levels that would mitigate the dangers of SSR.

2.6 Conclusion

Designing a TCSC could prove to be complicated task, unless all issues involved

are clearly defined and addressed. This chapter has outlined these issues in detail

and discussed the design limits associated with them. The review has shown that

the choice of reactor and capacitor sizes of the TCSC, not only determines the

operating region of the device, but also its operating performance. Rating of the



TCSC components and harmonics contributions are major issues when designing a

TCSC. The dominance of the 3rd harmonic voltages was shown.

Chapter Two also discussed both the steady state and transient response of the

TCSC. Under steady state conditions, it was shown that when the TCSC (instead of

a conventional series capacitor) is fitted in a transmission line a similar resonant

condition occurs to conventionally compensated line. However, the additional

resistance introduced by the TCSC at resonance frequency, helps to produce

positive damping to suppress power swing oscillations as well as to mitigate SSR.

Under transient conditions, typical TCSC response curves were shown. The review

also discussed the asymmetric nature of the TCSC response due to a step change in

the firing delay angle.

Last section of Chapter Two discussed different applications of the TCSC, namely,

damping power swings oscillations and mitigation of SSR. A typical response of

the TCSC, controlled by a bang-bang type of controller, was shown and different

control strategies were also mentioned. The phenomenon of SSR was also

explained and the benefit of the TCSC to suppress it was also outlined.

The next chapter, Chapter Three, presents and develops the mathematical models of

the TCSC used in the analysis and simulation studies of this thesis.


Chap/er Three

CHAPTER THREE

Page 3.1

MATHEMATICAL MODELING FOR COMPUTERSIMULATION OF TCSC

3.1 Introduction

Chapter Two of this thesis has presented a literature survey that was carried out in

order to understand those issues of the TCSC needed to develop the first TCSC

hardware for the Machine's laboratory at Natal University. The first TCSC to be

developed and applied to a transmission line, at Slatt substation - USA, was briefly

discussed and the performance results of the pilot project were discussed.

Chapter Two then described different operating modes of the TCSC. However,

most attention was placed on the capacitive vernier mode because the entire design,

covered by this thesis, is based on this mode. Different factors, which need to be

considered when designing the device, were outlined. These factors include the

sizes of the TCSC components, the resonant point and the so-called reactance

order. Another important topic that was covered in Chapter Two was the rating of

the TCSC's components, namely, the internal capacitor and the reactor. The effect

of harmonics was also discussed and their behavior in a transmission line with a

TCSC was outlined.

Chapter Two then discussed both the time-domain and frequency responses of a

transmission line equipped with the TCSC. Lastly, some common applications of

the TCSC were discussed in Chapter Two.

Mathematical Modeling for Computer Simulation of TCSC

Chapter Three Page 3.2

Chapter Three outlines the work that was done during the development of a

mathematical simulation model of the TCSC. All simulations were done on the

EMTDC and MATLAB simulation platforms [37], [38]. Some issues that are

discussed in this chapter include the development of the thyristor trigger circuit,

choices of component sizes and some typical simulation results of the TCSC

circuit.

3.2 Trigger Circuit for the TCR

The pulses generated by the trigger circuit sequentially trigger the thyristors of the

TCR circuit. The firing sequence is the order the thyristors turn on (and off) during

operation. Figure 3.1 shows the trigger logic circuit connected to the TCSC. In

comparison, if the thyristors were replaced by diodes, then as soon as the voltage

across the valve 1 went positive, the diode will turn on. However, if the thyristor is

being used, a delay can be introduced on valve 1 by waiting for a period of time

before applying a firing pulse. The time from when the voltage goes positive to

when the firing pulse is applied is called the firing delay time, as Figure 3.2

illustrates. This delay angle is usually converted to a firing angle, OC, using the

system frequency.



TCR Control Scheme

Vc

Thyristor Controlled Series Capacitor

~IL

IIIIIIL _

Firing pulses

eve

Desired firingangle (a)

Reset

Integrator

Wo (rad/sec)

Zerocrossing

2n fa \_____ I

Vc

IIfIIIIIfIIIfIIfI

-------------------- I

1---------------------------------------------------------,II

Leveldetector

Wherefa =System frequency

in rad/s

Figure 3.1: TCR trigger circuit and the TCSC

Mathematical Modeling for Computer Simulation ofTCSC


The TCR trigger circuit was designed based on the detection of zero crossing of

the commutating capacitor voltage as shown in Figure 3.1. An integration of the

fundamental frequency (rad/sec) produces a ramp signal eve. A zero crossing

outputs a pulse whenever the reference, Ve, goes through zero from a negative

to a positive value. This pulse resets the integrator, so the output of the

integration block produces a saw-tooth signal, which starts at 0.0 and reaches n

radians before being reset.

The desired firing angle, ex, is then compared to this ramp signal eve. When the

ramp is equal or greater then the desired firing angle, the output of the level

detector changes its state from low to high (0 to 1). The resultant level is the

firing pulse sent to the thyristors. Figure 3.3 shows the EMTDC simulation

results of the TCR trigger circuit.

11

Radians

oTime (sec)

Firingpulses

o

Firing delaytime

yFiringpulse

Time (sec)

Figure 3. 2: Trigger pulses and the illustration ofthe firing delay time

Matherpatical Modeling for Computer Simulation of TCSC


Caplcitor voltaget:.£

n ,Ill I(~\ 11\ /1VcJ / \ \(Volts) {'

kJ\ I I-

\

J IU \

-51I~/ ~J IV

0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

1.Reset pulses .from zero crossing detector

1

Reset O.pulses

(l

-0.50.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

,t Integration eX.re systemfrequeocy and reseted at 2pi

/ / / / / / / / / /" I I / / / / / /~

1/ V 11 / / / 1/ ,/ I

1/Svcanda / / /! 1/I

(radians) // /

(

0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

')1CRtrigger pulses

:

1Fning

pulses (

-10.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

tiIre (sec<nls)

Figure 3.3: Time-domain results ofthe TCR trigger circuit



The full PSCAD/EMTDC circuit and the parameters of the components that

were used to generate the results of Figure 3.3 are found in Appendix A.

3.3 Sizing of TCSC Variable Reactance Range

Since the main function of a TCSC is to provide a controllable capacitive

compensating reactance in series with a transmission line, the design of any

TCSC installation begins by specifying the range of the compensating reactance

values that the device is required to provide for a specific application under

consideration.

A literature review [1-5, 23,32] was thus carried out to establish typical variable

reactance ranges for the common TCSC applications and results of this review

are summarised in Table 3.1. The table shows the typical range of TCSC

compensating reactance as a percentage of transmission line reactance in each

case.

", ",

.' VARIi\B~'E~' "• > ?". - ".-;'" , - ~':<i-:r·-,

,'REACT:~tDERA~N:G:E, " ';.'.' <.', < ~

Local Mode

Damping

Inter-Area Mode

Damping

Sub-Synchronous

Reactance

First Swing

Small Signal

Small Signal

SSR Damping

30%

10%

20%

Case-Specific

Table 3.1: Summary ofTCSC variable reactance ranges for typical applications

in the literature,



The literature study revealed that the first swing damping requires the TCSC to

provide a larger percentage of variable compensation than does small signal

damping, which only needs about 10% variable capacitive reactance. In the case

of inter-area modes, damping can be accomplished with only 20% variable

compensation. Selection of a TCSC suitable for SSR damping depends entirely

on the torsional modes of the system under investigation.

For the torsional modes in the Machine Research Laboratory, SSR is known to

manifest itself at compensation levels between 40% and 70% [39] and the base

impedance of this system is 160. Therefore, to study the SSR characteristics of

a TCSC in this laboratory, and to compare them with those of conventional

(fixed) series compensating capacitors, a minimum TCSC reactance of -j6.40

is desirable and it should be capable of varying up to -j 11.20. By contrast, if

the TCSC was to be used for power oscillation damping studies in the

laboratory, without any possibility of exciting SSR, one would require a TCSC

whose maximum reactance is below 40% of the line reactance.

Taking all these factors into account, it was decided to design a single-module

TCSC that would be capable of providing controllable compensation of -j20 to .

-j6Q (12.5% to 37.5% of system reactance). This compensation range is

suitable for a wide range of power oscillation damping studies but below the

level of compensation where SSR becomes a concern.

3.4 TCSC Design and Rating

The design procedure that was used in this study is based on that outlined in

[19]; briefly, the steps followed in designing the TCSC are as follows:


Chapter Three

3.4.1 Sizing the TCSC's Internal Capacitor

Page 3.8

The reactance of a TCSC's internal (fixed) capacitor sets the minimum value of

capacitive compensating reactance of the device; thus, based on the desired

compensation range of the TCSC described above, each phase of the TCSC

module required an internal capacitor of reactance -j2Q at 50Hz, or 1592 ~F.

3.4.2 Determining the TCSC's Maximum Reactance Order

(XORDER(M.AX»)

The reactance order of a TCSC is defined as a ratio of its effective capacitive

reactance to the capacitive reactance of its internal capacitor, with XORDER :s; 3

typical. Thus, in this application each TCSC required a XORDER(max) value of 3,

which is within typical range.

3.4.3 Sizing the TCSC Inductor

When sizing the inductor in the thyristor-controlled reactor (TCR) branch of a

TCSC, a number of issues are of concern, namely the current rating of both the

inductor itself and the thyristors in series with it, the range of delay angles over

which TCSC can be controlled, and the likely SSR characteristics of the TCSC

[32]. Also, the inductor must be chosen so as to ensure that there is only a single

resonant frequency in the TCSC's reactance versus firing angle characteristic

[3].

(. It ~ KrCR

a res = Jr 2 n - 1) 2 Xc··········

n=1,2,3 .......

.......... .......( 3.1)

Equation 3.1, from [3], was used to ensure that there was only one resonant

point in the TCSC firing region. In ensuring that only one resonant point occurs

in the firing region, Equation 3.1 was evaluated for several values of n for a

chosen ratio of XTCR/Xc, as shown in Table 3.2. The inductive reactance of the



TCR inductor is typically chosen as 0.1 to 0.3 times the TCSC's internal

capacitive reactance Xc, although higher ratios have been reported [23]. Briefly,

a lowering of the TCR inductance requires increased current rating of the circuit

elements in the TCR branch and decreases the range of delay angle over which

TCSC can be controlled; a higher TCR inductance reduces current rating of the

TCR branch's circuit elements and increases the range of angles over which the

TCSC can be controlled.

The TCR inductor values chosen were 2.55,3.83 and 5.10 mH (0.8, 1.2 and 1.6

Q at 50 Hz) allowing XTCRlXc ratios of 0.4, 0.6 and 0.8 to be selected for each

TCSC module. Three different sizes of the TCR inductor were chosen to have

more flexibility, since this is an experimental TCSC and having different sizes

would allow the TCSC to be used for investigating the impact of different

XTCR/Xc ratios on TCSC performance in later projects. The XTCR/Xc ratios were

chosen to be somewhat higher than the typical range of 0.1 to 0.3 so as to

reduce the current ratings of the inductors and thyristors in the TCR branch

whilst still maintaining a workable range of oolay angles and a single resonant

frequency in the TCSC's impedance versus firing angle characteristics.


Chapter Three

TCSC Characteristic curves for different reactor sizes

Page 3.10

9

8

7

6

Fo.8~ \TCX/=0.6 u

XYCR

5

~ ¥ \ f\.TCR =0.4 Iu/

4

'i\ \ Y3

"-"-.\'"2 ~.......... ~ ....

1

Xycsc(pu)

100 110 120 130 140 150 160 170 180

Firing Delay Angle (Degrees )

Figure 3.4: TCSC characteristic curves' variations with three sizes ofthe reactor

Figure 3.4 shows the TCSC characteristic curves for different TCR inductor

values. The figure shows that the firing range increases as the reactor size is

increased.

@50Hz

0.20

0.80

1.20

1.60

Resonant

,point (n=l),,', >"1">·, . ,,'., '

151.54 °

99.50°

Resonant'

point (n=2)

-29.14°

-61.50°

R~~9~t;;

point (n=3)",' .... ' .'

37.70°

-104.61°

-168.57°

-19.22°

-218.45°

-307.99°

-383.50°

Table 3.2: The relationship ofXTCR size and the resonant point for a given value

ofn andXc = -;2 n



Table 3.2 shows that, for the chosen values of reactors, only one resonant point

exists in the operating range of the firing delay angle (i.e. between firing 90° to

180°). However, if the reactor size were chosen to be 0.2 Ohms (as the table

shows), two resonant points would have occurred in the operating range of the

firing delay angle.

TCSC Simulation Results

The next step, after deciding on the TCSC's component sizes, in constructing

the laboratory-scaled TCSC was to simulate the circuit in order to verify its

operation and the effect of changing the reactor size. Another important

observation that was made from the simulations, was the response of the circuit

when the reactance order is changed.

There are two sets of results that were captured from this simulation study. The

first set of simulation results show the circuit response when the reactance order

was changed and the second set shows the circuit response when the reactor size

was increased.



A B I CIII

Xorder = 1 Xorder = 2 I Xorder = 350 50

I50I

II

/-- "", /' "'-" /'Line Current ~ ~, ~~ /--- /-~ /~ ~ ~I

0.-/ °_/ I

°L/(Amps) "-~V '-~V ~V '-"-V I

"~ / ",-,--VI

-50 -50 -50

° 0,01 0,02 0.Q3 0,04 0,05 ° 0,01 0,02 0,03 0,04 0,05 ° 0,01 0,02 0.Q3 0,04 0,05

100 I 100 100I I / 1\ /CapacitorI

/1"- /-1', _/ \° I °1/ °Current (Amps) I ',- ~"-- -\ if \ 1/I

-100 I -100 -100\

II

° 0,01 0,02 0,03 0,04 0,05 I ° 0,01 0,02 0.Q3 0,04 0,05 ° 0,01 0.Q2 0,03 0,04 0,05

200II 200 200I

/~\ r--\II

'~,Capacitor Voltage ° ~-

°/...--..........,.

°"

(Volts)~.~

~- ,~_/ ~/ .,--,/ "- / \J~--

-200 -200 -200

° 0,01 0.02 0.Q3 0,04 0,05 ° om 0.Q2 0,03 0,04 0,05 ° 0,01 0,02 0.Q3 0,04 0,05

100 100 100

(1\ "Thyristor

° ° ... /' /' °1\ / i \

Current (Amps) I ....~l-i ',,- J .... \ I1 1/II \,.,

-100 I -100 -100

° 0,01 0,02 0.Q3 0,04 0,05 I

° 0,01 0,02 0.Q3 0,04 0,05I

° 0,01 0,02 0,03 0,04 0,05I II I

200 I 200 I 200I I n ~\ n 1\I I

Thyristor I II /l ('. Vl f'. I

Voltage (Volts) ° I ON L. I'J V t'J v' I

°~J V I\J V ~f VI II II I

-200 I -200 I -200

° 0.01 0.Q2 0,03 0,04 0,05 I

° 0,01 0,02 0.Q3 0,04 0,05 I

° 0,01 0.Q2 0.Q3 0,04 0,05I I

Time (seconds) I Time (seconds) I Time (seconds)I II I

Figure 3.5: EMTDC/PSCAD time-domain simulation results ofthe TCSC with the XrCR = 0.8 Q.

The simulation was done at XoRDERofl (A). XoRDER of2 (B) andXoRDER of3 (C).



A B c'" t X"d". 1 '" Xo",,,· 2 : '" Xo",,,· 3

~~p:;n~I",O j'",fi"fl:t!'1:j,Ij 1.,:Ft,~tf;t4o 0.01 0.02 0.03 0.04 0.05 0 om 0.02 0.03 0.04 0.05 I 0 0.01 0.02 0.03 0.04 0.05

::+ J' i 1E j .::+/f~t t~l j

.::+ vC +vC ht vi

o 0.01 0.02 0.03 0.04 0.05

:]-~rf~~Fd

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.02 0.03Time (seconds)

0.02

0.02

0.02

0.01

0.01

0.01

om

o

o

o

.~:+ ~f ~~ ~ ~ ej

.:} 1It ~r (f ~

0.05

0.05

0.05

0.04

0.04

0.04

003

0.03

0.03

Time (seconds)

0.02

0.02

0.02

om

om

0.01

o

o

o

.:J +f +1--:

g=:7~:'~o [- ±1±1Jo 0.01 0.02 0.03 0.04 0.05

~:r~~:Cvo:)~LI-1 ~h[ J-200

o 0.01 0.02 0.03 0.04 0.05

~~;:~;~p:~,I I I I I I-100

o 0.01 0.02 0.03 0.04 0.05

~:~~'vOlu]l-----1 I I I !

o 0.01 0.02 0.03 0.04 0.05

Time (seconds)

.. Figure 3.6: FJvfTDC/PSCAD time-domain simulation results of the TCSC with the XTCR = 1.2 n.



A B cXorder = 2'"ET --, -,-,T,,-, ---", -"""".

o~...Cb"mL [:<mm~: ~--T "--(' iI I I I I-50 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

Xorder =3'"FTT 'TT-,","":", : ~, : ~

o 4m~~---;---/.----:---"'-~---+---"-----:, I I I ,

I . I II 1 I I !, I I , I-50 : : : : :

o 0.01 0.02 0.03 0.04 0.05

100 r---------,----------r----------I----------,----------I'~\ ' '(~\ ' ,

/ '\! Y i !Of•. ------;--j---------l--------t:---------\:-------/-:

\ ' ,,'!' , ,I I , I ,

, '\ / ' "/'-100 i '--../, ,~, ,'---- ,

o 0.01 0.02 0.03 0.04 0.05

':l3<I6T2, \ ,j-----j---\.j/ ,: ''---{' : ,~ , :

-100 : : : : :o 0.01 0.02 0.03 0.04 0.05

0.05

0.05

0.04

0.040.03

0.03

0.02

0.020.01

0.01

100 c--------T--------;---------T--------T--------i~ , ~ , ~

o L--../.+~~-+/--!--~,---~7~..-:'--iV : '--Y : '---:- :

I , I I ,I I , I ,

-100 I : : : : :

o100 r---- - - - - -;-- - --- -- - -:---- - -----i ------ ---:- ---------~

f:--., ! i /~" ! !

o f-. -------- :--------\i---------{------'\:--------), ,,/, '~''. .' ," ' , ,

'---~: : ~: : :-100I' ",

o

Xorder = 1

'"FTTT'Un. C=, ~,mL,~c::t~...""",:c:!(Amps) 0 --- -----~----~~: '~/ :

i i : : !-50 0 0.01 0.02 0.03 0.04 0.05

WOErTiT!C..""""C"~' ~_~,nn"'~"~~~~(Amps) 0 --- ---T- ~---r : : i

~ ! i : :-100 0 0.01 0.02 0.03 0.04 0.05

, WOfT'L~~TC..='"Vo'-m,n...V>",nnAmn",,,,,n,n__,(Volts) 0 _~: :-~-~_-: : _-...-/:

] ! i ! i-100 0 0.01 0.02 0.03 0.04 0.05

0.050.040.030.020.01

50c~--------lT-----[-----:'\---------I-:--~--------r---------i\ ' , ' , 0

o f-,\--.-J--- ---L i :\ :\ i j ---T-- ----j--L\---io : :/ : \:-50 I ' , , : '----:

o '

50 -- - - - - -- - -- - -- - - - -- -! ---------T---------1-- --------, I I I

'" : /:' : /""> :o --'---\--~-J----:-~---:--,,-I---~-L..\--:"---(' : "--i/ : -~

, I I ,, I I ,

-50 ""o 0.01 0.02 0.03 0.04 0.05

~:-.;:;C=.~ rnnnnmmrnnmrmmHn...

-5J---~--~---~--~---o 0.01 0.02 0.03 0.04 0.05

100 c------jU---r-----::--:---------T/U----\---r---------:

o Kn i 1n---l. -- -~--f1!, ,j, \ I.-100 ' . , , ' ,

o 0.01 0.02 0.03 0.04 0.05Time (seconds)

0.050.040.02 0.03

Time (seconds)

0.01

--nl-------:--u-----~r--------~~---~T--------l

Of.-,- ---,-- --".in--j-:--LL\i-rv---:\ I 1 , '\, I

, ! i j j i

100

-100o

wormnmrnm-immnTn ---'-rmnm:Thyristor Voltage : : ' : i(Volts) 0 ;! ;;

" "I I "I I "I I "

-100 " "o 0.01 0.02 0.03 0.04 0.05

Time (seconds)

Figure 3.7: EMTDC/PSCAD time-domain simulation results ofthe TCSC with the XTCR = 1.612The simulation was done at XORDER Of1 (A). XoRDER of2 (B) andXoRDERof3 (C),


Chapter Three

Observations from the simulation

Page 3.]5

• Figures 3.5 - 3.7 show that at reactance order of 1, there is no current

flowing through reactor and thyristor switches. This is because the thyristors are

gated at the angle of 1800.

• The figures also show that both the capacitor voltage and capacitor current

increase as the reactance order is changed from the value of 1 to the value of3.

• The figures also show that during capacitive firing mode, the capacitor

current is the sum of the line current and the TCR branch current.

The effe~t of changing the TCR branch reactor was investigated. Figures 3.8

3.10 show the time-domain simulations for different reactor sizes and the

following observations were made:

• At the firing delay angle of 1800, the TCR reactor has no effect on the

TCSC circuit because the thyristors are blocked (no conduction). Hence, the

line current is equal to the capacitor current and both the capacitor current and

capacitor voltage do not change with changes of the TCR reactor size.

• Figure 3.9 and 3.10, illustrate that both the magnitude of the TCR current

and capacitor current (hence reactor voltage magnitude and capacitor voltage

magnitude) decrease as the reactor size increases. This implies that to decrease

the current rating of the capacitor, reactor and thyristor valves, a larger reactor

should be used



A B c

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

- - - - - - - - - - 7- - - - - - - - - - .,. - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - .., • j , ,

, , , I I

i~~"\ 1 /:/--,,'\. i io ~- ---- -----A:': ------ ---"i\ ---- -- --- r--- - - - - - -"'h: ------ --;i

.... /: :'-- : :~ /:............~/ I ,"-..........., I -' I, , , ,

: : : :

XTCR =1.6 ohms

20 c----L------:----------r-I------~--------;-------)

: \: : \ : /:o V--- -----;----\-----:---- ------~----\----;----.I-----~, , , 1/': \.! / : ',: :: ,,~ : '\.., :

, , I , ,

-50o

-20 !L-__~ _"_ _'_ ~__~

o

'::A~\ iA1;/ i '-_i/ i \ ..-l,/ i

-20 ! : : : : :

o 0.01 0.02 0.03 0.04 0.05

50

0.050.040.030.020.01

XTCR =1.2 ohms

'" Rmuumu~uif----T"--------io ---- -----+----\------:-/--------~--_\-----~---- -----~: 1\: : : :

: ~ : : :, , , I ,

-20 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

'" k1~m----i-------;c~-------T/----------

o ---- -----:----'\----1/-:----------:---\-----:---- -----j, 1 1 ~, )

: ,,: : ,----L :, ) , , I

-20 ' , , : 'o

50 c----------j----------T---------T----------r---------1

:/_~,,: :/~i !o ~----------1--------~+--------y--------'i----------~'"' /: ''',. .//: ", //:

'-"-.~ : : ~: : '---.-/ :, , , J, , ,

-50 ! ' , ,

o 0.01 0.02 0.03 0.04 0.05

0.050.040.030.020.01

XTCR =0.8 ohms" kjummuum:;<uuu,umu)~~~~~;rent 0 - -----i.\ -----L--I----i---\----i-f--!

i'---'\,1/ ! .~ iI , I • ,

-20 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

20 c----------:----------r---------:-----------:----------1~. : /-~, : /:

~:"""~'c='o l~---/------L-\------J/---------i---\-----L-j-----!mps ::: \: :: "--..: : ~/ :J I , , I

-20 ' , , , ,

o50 . - --- -------- - - - - - - - -----.- -- ----- -- --- - - - - - ------ ------

I I "I I "I, "

~~~;:;or Voltage0 l--------)(~~<---------i~~>~--------_JG /, ",- ,/, ", / '"-~:. :~/: :,--/:

I , I I ,I , , , ,

-50 ! ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

Thy 0.'0' co=~0 tUuuuu uUTm uumumum ,

(Amps) -1: r i I ,o 0.01 0.02 0.03 0.04 0.05

Thyri"= vo".~o fUU ..U...;.u..m.u.mu .....uu:o ""

(Volts) i i : i

-10 "':o 0.01 0.02 0.03 0.04 0.05

Time (seconds)

.:: rmmumm"uumm uumu mmm :~: rmmruummmu mnm,nunm

o 0.01 0.02 0.03 0.04 0.05 I 0 0.01 0.02 0.03 0.04 0.05I

'" rmnnnnnumrnmrnmTmnm i '" [mnmn:m.nmim .. mnwno : i : : : : 0 I i ' I :

: : :: f :: :: : :: I :: :I I , , ",

-10 ! ' , " : -10 " :o 0.01 0.02 0.03 0.04 0.05 I 0 0.01 0.02 0.03 0.04 0.05

Time (seconds) : Time (seconds)

Figure 3.8: EMTDC/PSCAD time-domain simulation results ofthe TCSC with the XTCR = 0.8 Q (A). 1.2 Q (E) and 1.6 Q (C).The simulation was done at XORDER of1.



A B c

0.050.040.030.020.01

XTCR =1.6 ohms'0[5 , , ; .

: : ~' : /-0'\ ' , '/ 'I , , I ,

I I I I I

o=u\um"/__ ------~--\_----:--I------~i \ i i \ i i: ~ : ~' :

-20 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

50 ---fi-------:----------r----/----~--------T'----/l-----:

, \ ' '\ ' ,

o f -----;---''-,-----i--7-----~--~\--j-7'----j: \y : \....>' :

-50 : : : : :

o 0.01 0.02 0.03 0.04 0.05

100----------V\i----------T---------~T----------r---------i

, , , , ,o f- --- -- ---I; -- ------ --r:- --- -- -- -- ~ ---------,: ------- ---A

1\ /: :\ /: '\. /:'---...../ : :"---/ : : ,-----,/ :

-100 I : ': :o

XTCR = 1.2 ohms

"k····························,·~ : /~ : -:,:ui\mrm/m\·V:---------j

, \. '/ ' \, ,: '--.; : '--' :-20 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

" ~mui\yC---[-----------i-~~-------T--.----(

o --/---j--::'-<.:,----i---- ------~--:>_-:\----'V;--;/---it \' I , II , I I I, , , I I

I "~ I

-50 ' , : ' :o 0.01 0.02 0.03 0.04 0.05

100 '----------i~--r---------T/-~-~------T--------1

,l~;lum0muuuj, I I , I

-100 : : : : :

o 0.01 0.02 0.03 0.04 0.05

0.050.04

XTCR = 0.8 ohms

'l'TTT: : /;,\ : -:~~~:;=', 7---!1\\-----~----,!--L\d----j---------~, 1/' , ,, I , , I

t I , , ,I , , I I

-20 : , : , :

o 0.01 0.02 0.03 0.04 0.05" ~ , , ,..........•..........,

7:';:,'C==,:04'~c~-50 : ' : ' ,

o 0.01 V.VZ 0.03'"r·· TTi········)·······)%':,:;0' Vol,,,,,,,, _. --------p~~----7-----:_~\_-------)

-. //, ,\, ' ". /'~, J ........ I ,~,

I ) , , ,, I , I I

-100 ' , , , ,

o 0.01 0.02 0.03 0.04 0.05

"~uuumufmulmu'\u,.,:=:\V=J~JC:\,

"bii\'So -- ----:/----'---~--~--+-- ----;~---~." =J.uuium\r,um\j, I I 1 :

o 0.01 0.02 0.03 0.04 0.05 o 0.01 0.02 0.03 0.04 0.05 o 0.01 0.02 0.03 0.04 0.05

~~:;O<VOh.;:~]~~-50 ----------, -

;

50 ~----------ilr----r\-l----------t-i--l1----~\r-----/---1

o[l/)U'[JJ i .. \fl-50 - ---- --L---------i-\ ---- :w-----w~- w,

'T;u---~---:-----------:-----------!----------~

I \' , , ,I I , , ,

o -- --- ,-- --Sn\:--- --- ~-- -- (- ---;, I I I

.'0rLLumj~~.Jlo 0.01 0.02 0.03 0.04

Time (seconds)

0.05 o 0.01 0.02 0.03 0.04

Time (seconds)

0.05 o 0.01 0.02 0_03 0.04 0.05Time (seconds)

Figure 3.9: EAfTDC/PSCAD time-domain simulation results ofthe TCSC with the XrcR = 0.8 n (A), 1.2 n (B) and 1.6 n (C).

The simulation was done at XORDER Of2


A

XTCR =0.6 ohms'TUUTUUTuuuruuu;uu'~~:~~;rent 0~f ; i.~~.J/0..; ;

j , ,''' I ,, , ,I , I I I, , , , ,

-so : : : : :o 0.01 0.02 0.03 0.04 0.05

"Iuu'uuuruuruuu'uuuuCapacitorCurrento ..~.~[ /J.~.·····i··· j(Amps) ::::. :

, 'I I, , ,, , , , 1

-200 : : : : ;o 0.01 0.02 0.03 0.04 0.05

200 ··--······i··········r···--·----i.~ ;-- --1

~;;:,~tc:;or Voltageo -- .. ----. 1------.\--------.l----.\;---------I1: :\__Ji' \-.-! :-200 : : : : :

o 0.01 0.02 0.03 0.04 0.05

0.02 0.03

2°l~/\--Tr-tfU·····----T·······~··r······--·!Thy"",m Vol'.",0~(LJ ju .+ \i- r---o

J-- ~

(Volts) :,: \J l :: : : : I

-200 0 0.~1 0.~2 0.03 0.04 0.05

Time (seconds)

Chapter Three

B

XTCR =1.2 ohms

':Fr~-so : : : : :

o 0.01 0.02 0.03 0.04 0.05

200 i' --. -- T·········T""'" --';"""""1o --.~~.----.i--~~~.."_... i--. ~, 1/ ' ,:;r-._--;

1 • , • I, , , , ,1 , , , ,, , , , ,

-200 : : : : :o 0.01 0.02 0.03 0.04 0.05

":fuUAI~L)Ji------· :~r .. ·~, :-200 : : : : :

o 0.01 0.02 0.03 0.04 0.05

IOTuu;umuTUUUrmm!uuujo ~----t----.-;-- \j----:~.--·t-- --.~It' I I

, , I I I, ,, , I I I, I I , I

-100 : : : : :o 0.01 0.02 0.03 0.04 0.05

200 c·-- -- : r""'" -- ., ; j

o~--~--·{~L1\tn'PtJll~ vi ."" " I, I , , I

, I , I i

-200 ! : : : : :

o 0.01 0.02 0.03 0.04 0.05

Time (seconds)

Page 3.18

cXTCR =1.6 ohms

':tfJ;6JA-SO ' . . . .

o 0.01 0.02 0.03 0.04 0.05

:~:F~o 0.01 0.02 0.03 0.04 0.05

200 '------·/·--r--=···r······-~··i-·---·····r··--.. ···1, ''\ I I I ,

ot ,mum'\u; ,uuu t U/'--/1: :~: i'-- 1I , , I I

-200 . . . : .o 0.01 0.02 0.03 0.04 0.05

10: r=mIUUjUU;U]: : : "-..i, , , ,, , , I

-100 ::::o 0.01 0.02 0.03 0.04 0.05

200 ,-- ---- -. -'1' -- -- ----. r---- .. ----i -- ... -- --T--. ------1./u·" . /1 I"-- ' ,

o ~--rr--(l-- --';':';n;'--. :--.U--\i'n'j',\ / . , , " ." i i i l' i

-200 ! : : : : :

o 0.01 0.02 0.03 0.04 0.05Time (seconds)

Fgure 3.10: EMTDC/PSCAD time-domain simulation results ofthe TCSC with the XTCR = 0.8 n (A), 1.2 n (13) and 1.6 n (C).The simulation was done at XoRDERof3



3.4.4 Rating the TCSC's circuit components

The detailed EMTDC simulation model of a TCSC that was developed was

used to run a number of additional case studies in order to predict the actual

reactance versus firing angle characteristics of the designed TCSC and to decide

upon appropriate current and voltage ratings for its circuit components.

Tables 3.3 to 3.5 summarise the rating requirements obtained from the studies

done for each value of TCR inductor at two transmission line conditions: rated

line current and twice rated line current based on the parameters of the

Machine's Research Laboratory. In each case, the study was carried out with the

TCSC module providing its maximum capacitive reactance of -j6 Q, since this

is the condition under which its voltages and currents are at a maximum for a

given line current. The performance of the TCSC at higher than rated line

current is of interest since the device may be required to tolerate temporary

overcurrents during transient studies in the laboratory.

XTCR =0.8 Q

Line Current Capacitor Reactor

kVAr Voltage (rms) Current (rms)

1 pu (7.87 Arms) 6.63 53.89 29.69

2 pu (15.74 A rrns) 26.69 108.06 82.34

Table 3.3: TCSC component ratings at X TCSC = -j6 nwithXTcR = jO.8 n

XTCR = 1.2 Q



1 pu (7.87 Arms) 5.77 53.55 24.68

2 pu (15.74 Arms) 23.31 107.62 49.73

Table 3.4: TCSC component ratings at X TCSC = -j6 nwith X rcR = jI.2 n



XTCR = 1.6 Q



1 pu (7.87 Arms) 4.486 49.213 19.29

2 pu (15.74 Arms) 20.886 106.31 49.10

Table 3.5: TCSC component ratings at Xrcsc = -j6 QwithXrcR = ji.6 Q

The results of the studies confirmed that the required current rating of the

thyristors and the reactor within the TCSC decreases as the TCR inductance is

increased. Based on the results in the above Tables, air core inductors were built

for the laboratory TCSC using 3.15 mm diameter copper wire, resulting in a

worst-case current carrying requirement of 55 Amps.

The same current rating was applied when choosing the thyristors for the TCSC.

Finally, six 400V, 777 f.lF capacitors were purchased. These hardware

components were combined to form the first -j2 Q to -j6 Q module of the

laboratory-scale three-phase TCSC in order that testing and evaluation could be

done.


Chapter Three

3.5 Harmonic Analysis of the TCSC

Page 3.21

The EMTDC model of TCSC was used to investigate the impact of harmonics

on the transmission line and on the TCSC's loop current for the laboratory

TCSC design carried out in the previous section. The harmonics ofthe capacitor

voltage and their effects on the power system were studied. The component

sizes for the mathematical model are the same as those found in Appendix A,

however the results presented in this section are only those captured for XTCR =

0.8Q.

3.5.1 TCSC Harmonic Voltage

The measured 3fd, 5th and 7th TCSC harmonic voltages versus ftring angle are

shown in Table 3.6. These results were then plotted in Matlab to graphically

illustrate the characteristic of the magnitude of each harmonic voltage as the

ftring angle was varied. Figure 3.11 shows the characteristics of the harmonic

voltages as the ftring angle was varied. Each harmonic is expressed as a

percentage ratio with respect to the fundamental frequency voltage component.

20 ~::O-:--:------'----'-----;===::::C====::::;l: : ! + 3rdHarmonie

18 .: .........•.... ~ : ; -B- 5thHarmonie: :' --e- 7th Harm onie, ,

16 ...•......... ;.. . ~. -- : .....•........ ;._ __ ~._ .I • , , ,

: '\: : : :

V~~~ X :: ••••••••••••• ' •••••••~ •••••••• ·.···I••••••••••••••j.···••••••••• 1•••••••••••••

:•••••••••••••/·••••••••••••·r\·.I··••••••••••••)••••••••••·r···••••••••••, "

2' ~ ~ ~ ~ ~-------------

, : :

Firin!! Delav An!!le

Figure 3. JJ: Harmonic generated in pu offundamental as a function ofalpha



Firing Delay Angle (Angle) 50 Hz TCSC Voltage (Volts) 3RD Order TCSC Voltage 5TH Order TCSC Voltage 7TH Order TCSC Voltage

(% of fundamental) (% offundamental) (% of fundamental)

180 9.697 0.00 0.00 0.00

170 9.810 0.29 0.16 0.05

160 9.922 0.57 0.31 0.21

155 10.175 1.16 0.67 0.40

150 11.230 2.75 1.36 0.65

148 11.665 3.82 1.61 0.67

146 12.195 4.50 1.93 0.64

144 14.541 6.02 2.28 0.55

142 15.654 7.74 2.51 0.43

140 20.380 10.03 2.67 0.29

138 27.510 11.80 2.77 0.00

136 30.410 13.98 2.65 0.29

134 108.320 15.21 2.49 0.52

132 123.930 16.03 2.20 0.67

130 90.270 17.08 1.94 0.81

128 35.780 17.91 1.60 0.99

126 23.00 I 18.91 1.10 1.09

124 18.020 19.54 0.69 1.08

122 15.927 19.94 0.43 1.04

Table 3.6: Harmonics ofTCSC voltage at XTCR = 0.8 n


Chapter Three

3.5.2 Harmonic Analysis of the Line Current

Page 3.23

The Table 3.7 shows the results of the harmonic analysis of the line current at

XTCR = 0.8 Q. The resonant point of the TCSC circuit with reactor of 0.8 ohms

is approximately 123°, hence the operation range ofthe TCSC is [135°, 180°]. It

can be seen, from Table 3.7 that the worst-case harmonics are below 5% of the

fundamental frequency current. The same trend is found in the case of other

reactor values (XTCR = 1.2 Q and XTCR = 1.6 Q). It can therefore be seen that the

harmonics are indeed largely confined inside the TCSC loop and, moreover,

that the effect of the harmonics presents in the TCSC capacitor voltage on the

rest of the power system is also slight.

. Clearly though, the TCSC capacitor must itself be rated to handle the harmonics

present in its voltage under normal operating conditions (Figure 3.11). In the

case of the laboratory-scale TCSC, the 77hlF capacitors that were purchased

were rated to 400 V rms for normal fundamental frequency operation. It was

thus assumed that because the peak amplitudes of all the voltages in the

harmonic spectrum of the laboratory TCSC would be significantly below 400V,

and because the laboratory TCSC would not be in continuous service, the 400 V

capacitors would be acceptable for this application.



Firing Line Current 3RD 5TH Harmonic 7TH Harmonic Sum of the HarmonicDelay (Amps) Harmonic Line Current Line Current Harmonic currents as a %Angle

(Fundamental) Line Current(Amps) (Amps)

currents of the(Degrees) fundamental

(Amps) (Amps)component

180 2.424 0 0 0 0 0%

160 2.437 0.001 0.0004 0.0002 0.0016 0.065654 %

155 2.452 0.002 0.0008 0.0004 0.0032 0.130506 %

150 2.514 0.007 0.0019 0.0006 0.0095 0.377884 %

145 2.570 0.001 0.0028 0.0030 0.0068 0.264591 %

140 3.042 0.030 0.0069 0.0004 0.0373 1.226167 %

135 7.630 0.342 0.0325 0.0068 0.3813 4.997379 %

Table 3. 7: Harmonics ofthe Line Current at X rcR = 0.8 Q


3.6 Conclusion

Chapter Three•

Page 3.25

Chapter Three has presented the development of the mathematical model to

investigate the characteristics of the TCSC. As an important integral part of the

TCSC circuit design, the control circuit that generates the firing pulses for the

TCR thyristors was presented and its operation was also explained. The chapter

has outlined the methodology that was followed to determine the sizes of both

the capacitor and the reactor in the laboratory-scale TCSC to be constructed.

The effect of changing the size of reactor was investigated. Reactors of sizes 0.8

Q, 1.2 Q and 1.6 Q were chosen for the laboratory-scale TCSC. The

investigation confirmed that the ratings of the TCSC components are dependent

on the size of the TCSC reactor. The current and kVAr ratings of both the

capacitor and reactor decrease as the size of the reactor is increased.

This chapter has also discussed the impact of TCSC harmonics on the

transmission line currents. Several simulations were conducted to deduce the

effect of the TCSC harmonics on the power system. The simulation results

showed that:

• The TCSC 3rd

harmonic voltage is dominant and other orders of voltage

harmonics are negligible in magnitude. The results also show that the

magnitude of the harmonic voltages increases as the reactor size is

decreased;

• The harmonic currents were found to be largely confined within the

TCSC loop. Only a small magnitude of the harmonic currents ( 5% at most)

was found in the line currents.

Chapter Four considers the actual construction of the laboratory-scale TCSC.

Chapter Four also presents a comparison of the simulated and measured

performance of the laboratory-scale TCSC.


Chapter Four

CHAPTER FOUR

Page 4.1

DEVELOPMENT OF ALABORATORY

PROTOTYPE TCSC

4.1 Introduction

The earlier chapters of this thesis have dealt with the theoretical development of

the Thyristor-Controlled Series Capacitor (TCSC) and its associated trigger

circuit. Chapter Three has outlined the development of the TCSC's trigger

circuit and its capability to vary the capacitive magnitude of the TCSC. Chapter

Three has also outlined the methodology that was followed to determine the

components' sizes and their voltage I current ratings in the laboratory-scale

TCSC model.

The development of the mathematical model of the TCSC was also described in

Chapter Three. Time-domain simulations and frequency responses of the TCSC

mathematical model were also included in Chapter Three.

Chapter Four describes the development of a laboratory-scale TCSC for the

Machines Research Laboratory at Natal University. The purpose of this

laboratory-scale TCSC development is to confirm, using practical

measurements, those capabilities of the TCSC model, which were demonstrated

in the simulation studies of earlier chapters and, in so doing, to demonstrate the

practicality of the TCSC. However, the laboratory-scale model is also intended

to form the basis for possible future investigations into the use of the TCSC to

dynamically control the reactance of the transmission line as a means of

enhancing power system stability. Hence, the parameters of the TCSC have

been designed specifically for the Machines Research Laboratory system [39].

Development ofa Laboratory Prototype TCSC

Chapter Four Page 4.2

Finally, this chapter provides measured results of the performance of the

laboratory-scale TCSC; these measured results are compared with the

performance predicted using the simulation model of the TCSC developed in

Chapter Three.

4.2 Practical Implementation

The first section of this chapter begins by providing a description of different

equipment, which was used during the development and testing of the

laboratory-scale TCSC.

4.2.1 Hardware Description

Figure 4.1 shows the detailed diagram of the circuit used during the testing

phase of the TCSC. The measured results from the TCSC, which are presented

in this chapter, were captured using a data acquisition card mounted in a

personal computer. The hardware TCSC will eventually be fully integrated into

the Machines Research Laboratory that already exists at Natal University.

However, for the purpose of this project, the hardware TCSC was tested using a

combination of the transmission line simulator and AC voltage sources in the

. Machines Research Laboratory. Although not all the equipment in the

laboratory was used in the testing of the hardware TCSC, some of it is included

in the following description for completeness, since it is likely to form part of

future TCSC studies.

Voltage Source

A three-phase variac (variable voltage transformer) provided the variable

voltage supply. The input voltage to the variac was connected to the infinite bus

supply in the laboratory (220 V line).


TCSC Hardware


As discussed in earlier chapters, the TCSC is made up of a conventional

capacitor connected in parallel with a thyristor-controlled reactor (TCR). Figure

4.1 shows a single-line diagram of the TCSC together with other components of

the test circuit. The capacitance in each phase of the circuit in Figure 4.1 is 1554

~F (rated at 400 V per phase) corresponding to 2 n at 50 Hz.

As discussed in Chapter Three, three different TCR inductor sizes were chosen

for future flexibility. Thus, depending on the tests conducted, the TCR

inductors, in each phase in Figure 4.1, were either 2.55 mH, 3.83 mH or 5.10

mH air core devices (either 0.8 n, 1.2 n or 1.6 n at 50 Hz).



r·····················,···~····· ..···· ..···· ..··········· j

XTCR ! r---....!P i 1

RL

Xc ~ t--b-[ Xci 1- 2 I .0----I

y Vc

Transmission line simJlator Thyristor ControlI Series Capacitor

InfiniteBus

Desired angle

Trigger Circuit

Vc SynchronizationStage

0-

f ~ ,

Figure 4.1: Diagram ofthe laboratory-scale TCSC

T"\ ...... ~1~__............. # "../' .... T ,..J.. ..... _ ..... .f"'v-t. D .....,.+,...",~n rr\!r


Figure 4.2: The three-phase TCSC circuit

Transmission Line Simulator

The Micro-Machine Research Laboratory contains a transmission line simulator

that can model transmission networks of up to 1700 km in length. The

transmission line simulator is composed of a bank of lumped inductors and

capacitors that may be switched in or out as per requirement [39], [40]. The

inductors were specially designed with large air gaps in order to avoid

saturation.

• r r ,

Chapter Four

Figure 4.3: The transmission line simulator

Page 4.6

Micro-Alternator

Although the measurements carned out in this thesis did not make use of the

micro-alternators in the laboratory, it is assumed that the future TCSC

investigations will include these machines. Indeed, the ratings and impedance

range of the hardware TCSC that has been designed are ultimately related to the

parameters and ratings of the laboratory micro-alternators. The laboratory

micro-alternators are three-phase machines with a rated line-to-line voltage of

220 V and a rated per-phase current of 7.87 A, resulting in an overall three

phase power rating of3 kVA.


Trigger Circuit

For the laboratory testing, an existing three-phase trigger channel circuit was

adapted for the TCSC application. The need to adapt this trigger channel

circuitry arose because firing of the TCSC's thyristors is synchronized to the

TCSC capacitor voltage. The capacitor voltage in a TCSC application varies

significantly in amplitude as the transmission line current (and TCSC firing

condition) varies. As a result, the conventional synchronizing stage of the

existing analogue trigger channel was found to give inaccurate and inconsistent

performance when used to determine the required turn on pulses for the TCSC's

thyristors.

These inaccuracies are due to following reasons:

a). In the analogue synchronizing stage (zero crossing detector), the width

of the zero crossing pulses depends on the magnitude of AC voltage, as

shown in Appendix B. The amplitude of the TCSC capacitor voltage is

expected to vary by a significant amount (2-3 times) under normal

operating conditions.

b). The ramp stage of the analogue trigger channel can only be set up to

provide accurate generation of firing pulses for one amplitude of TCSC

capacitor voltage. At other values of TCSC capacitor voltage, the turn on

pulse occurs at incorrect points on the waveform, as clearly seen in

Appendix B.

To minimize the impact of variations in the amplitude of the capacitor voltage,

two design changes were made in the trigger channel. Extra gain was added in

the synchronization stage, as shown by Figure 4.5. This extra gain reduces (but

does not completely get rid of) the variation in width of the zero crossing pulses

as the capacitor voltage amplitude changes. Secondly, the value of resistor R

(Figure 4.5) was carefUlly chosen such that the trigger channel has its best

accuracy at a TCSC capacitor voltage in the middle of the expected operating



range. Clearly, these measures do not remove the errors, but there were found to

significantly reduce their impact on the overall operation of the trigger channel.

A set of diagrams that illustrates the impact of variations in the TCSC capacitor

voltage amplitude on the accuracy of the firing pulses is found in Appendix B.

Time delay(ms)

9 ~- ---------: --------- -:- -----. ---; -. -....---: --- ----.+.--------;----------~----...., , ,, , ,, , ,, , ,

8 ------ ..y--------t···----..i-'" ------j-----. -. --t--------- i---------- j-..-------(--------

: ••••••••t•••••••·.1••••••••Et••••••·.'·······••r••••J••••••••,••••••••: : : : : :: : : : : :

4 ---- ----..:-- ---- -.. -~ ---- -----..:---- ------ ~ -------- - ~- -- ------..:---------~ ~-- -- ------~--------, , 'I '"• I " '"I I r I I •

3 ----.--.~---- --- --.;-.--- -- --+.---·----i----- ..--+------ ).-·-------i----------~--. -- ..-

2 -.------.!.--.------l---.-----). -- -------i------ l ------: --- -_L __!. ., , , , , : ~ :

·-1-:" !~ .Q'-----'----L--.L--_---"-_---..l__.l..-_----L_----.l_---.J

Q 1000 2000 3000 4000 5000 6000 7000 8000 9000

Volts (mY)

Figure 4.4: Relationship between the variable pot resistance and the firing

angle

, r T ,


-12 V

IN4007

O.OOI/IOOV

IN4007-12 V

6 I ~

Original synchronizing stage

IOkQ lN4l48--KJIN4148

l~6 I \ rKJ-l~1148 I 11 R= 150 kQ

"olating """'fonne, ~ ~ ~V ll::U33", I l'F~8.2 kQ 2 _ 7 6(secondary) I10 kQ 35V

TIOkQ

rc:::::J 12 VIkOlkn

2

IN4148

-12 V

Modified synchronizing stage

Figure 4.5: Original and modified synchronizing stage circuit

n,.nJnlnra""oMf I'lln T rrhnvnfrlY·" P ....n;nMlno rr.<:r

4.3 Practical Results


This section of the thesis presents and discusses the measured results that were

obtained from the laboratory-scale TCSC. The measured results are also compared

to the results of the mathematical model developed and simulated on EMTDC. The

laboratory-scale TCSC has three phases (A, B, and C), however only phase A

results are shown in this chapter. The rest of the results can be found in Appendix

C.

4.3.1 Practical TCSC Characteristics

Figure 4.6 to Figure 4.8 show that for each value ofTCR inductor used, the TCSC's

capacitive reactance increases with decreasing thyristor delay angle as expected.

Hence, the TCSC that was designed and constructed is in fact capable ofacting as a

controllable series capacitive reactance in the expected manner.

6,--------r....------,---..,...------,----,--------,

5.5 ----------+~1~ -----------·+--------------:--------------t--~~~~~~~J-------------5 -------------~- ------------:---------------:------ ------~-EMTDC-~mUrafr6f'i- -

!~ ! ! + mathematical equati

4.5 -------- -- -- --f- ~ --- -------f---------------r-------------- -f- ---- -- -------r------------

TCSC~~(O~ ••••••••••••••,••••'~ ••·.1••.•••••••••f••••••••••••••r•••••••••••••• ,••••••••••••••, ", ", ", "

2.5 _.. ------- ~ ------- --- -- ~ - -:_ --------- --_~ --------- -__ --~ ---- ,. _, ,, ,

2 --------------l---------------l---------------.-------~---~---s--~~........._e_--Er__C>

1.5 -- --- ---------, ---- --- --------t-- -- ------ ----t- ------

Delay Angle

Figure 4. 6:TCSC characteristic curve for a TCR - 0.8 ohms

• r T , n. ,


6,---lrr---.-----,----,------=========l

4.5

4

TCSC reactance (Ohms)

1L- L- L-__---l ---l ----'- ---=-=--__---:-:110 120 130 140 150 160 170 180

Delay Angle (degrees)

Figure 4.7: TCSC characteristic curve for a TCR = 1.2 ohms

180170160150140130120110

6r---------n;~-,---..,..----,------,-_;========~* practical, , , , , -Er EMlDC simulation

5.5 -----------r- -- -------;------------:-----------'1"-----------1' - m~thematical :equation

5 -----------(' -- ---:---------- --:------------~------------r_---- -----t-- ---------r---------4.5 -r---------'1"---------T-----------j-------------:----- -- -----r---------

4 ----- ---.- _!. - - - - - - --- - - - - - - - - - --~- ---- - - ---- - ~- - - - --- - - - - - -:- - - ----- - - - - -:- - -- - - ---- - --~ - - -- - - - - - --I , • • I, , , . ,I, I,

" ", I I I J

3.5 ---------- - ~ ------ --- ---j- ----;--j------------i------------ ~-------------1------------~- ----- -----: : + : , : :

3 -----------t- -------.---;-------- ~ ",*- ----+---~------------~------.------~ ------- -----~-----------

2.5 ---------+-----------(---------+---- ~ *------------:------------r-----------t-----------• ,. I,• " I I

2 ----- ------;------- - --- -: ------------~- ----- ---- --~-- - ------ ---~------___ ___ _, . , , .I " II 'I I

• ., I

, '"

1.5 -----------:------------;-----------'1"---------'1"---------- r-----------r------------r----------1 L-__-..L..__...-.1 ...L.__----'- .L' .1..' .1.....-__-1

100

TCSC reactance (Ohms)

Delay Angle (degrees)

Figure 4.8: TCSC characteristic curve for a TCR = 1.6 ohms


Figure 4.6 to 4.8 illustrate that there are some discrepancies between the simulated

results, measured results and the behavior predicted usmg the

equation 2.1 found in Chapter Two. The approximate equation cited in Chapter

Two is known to understate the actual capacitive reactance obtained from a TCSC

at delay angles near the TCSC's resonant point. However, Figures 4.6 to 4.8 show

that in each case the measured TCSC reactance near the resonant point is not only

lower than that predicted by the accurate simulation model but also lower than that

predicted by the approximate equation.

It was also noted that the discrepancy between the curves increases with increasing

TCR inductor size; furthermore a number of studies that show significantly better

agreement, used a TCSC with a smaller TCR inductor than in any of three cases

shown in this section [3], [22] and [23].

4.3.2 Comparison of Simulated and Measured Results

Figures 4.6 to 4.8 have illustrated the operating range, in the capacitive-reactance

region, of the laboratory-scale TCSC that is obtained from the design procedure

described in the previous chapters. This section focuses on time-domain results that

were measured from the laboratory-scale TCSC. These results are compared to

those generated from the EMTDC mathematical model included in Appendix C.

Figures 4.9 to 4.11 show the time-domain response of laboratory-scale TCSC

compared to simulated results. Only phase-A results are presented in this chapter;

the rest of the results are found in Appendix C. The tests results presented in this

section were conducted for all TCR inductors (0.80, 1.20 and 1.60).



Measured Results Simulated Results

o

20 r,--~,_---..__---,----____r-------,

10,----------·---

-10

-20 Li --'- ----' L.- -'--__----'

0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02

-10 ,--------

20 ir-----r-----r------,----,-------,

-20' i i

o

CapacitorVoltage (volts)

10, '" 10 I i

ThyristorICurrent (Amps)

5 ~- --------------r- -------------- -:- ---- ---- ------i------- ------··f·--·· _. -------O~......r~r_v~~ .............~~ .......~~...-..v'o'~-

I , I II , , II , , ,

-5 ~-- -- .. _.-- .. ---r-- --- ---- --- ---1- ------ --- -- --. j------- ----- -- -;- --- -- ----- ---

-10! : : ; : I

o 0.02 0.04 0.06 0.08 0.1

:t - + T--- -------------------1

-5 --------------J--------------.!---------------i---------------;--------------, I I •, I , ,, , t II , , I

-10 I : i : :Q4 QG QM Q~ Q~ Q5

10, I

:~L\X\/\.lt\/-5e----JLV.L-\l.j••--\Il••----v---

-10 I i i i i I

0.4 0.42 O.M 0.46 0.48 0.5

Time (seconds)0.10.080.02 0.04 0.06

Time (seconds)

10 I I

-10 '----, -'- ..L..-__------' ----'- --'

o

Line Current(Amps)

Figure 4.9: Comparison ofphase A time-domain results at reactance order ofl: Xtcr = O.8Q.




20 i i i I I

-20' ,0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02

20, I i

10 I J' I. I r', I ) ~ I I' \, I ,I' \ I

Capacitor 0 I 1 11 I ~ , \' I 'j I 1Voltage (volts) ,I i I" i \

/ / r /1\ (\/ \/ \) \) \J

1\ 1\ r (\ t\J \J \J \J \/

10

5

Thyristor 0Current (Amps)

5

-10o 0.02 0.04 0.06 0.08 0.1

10

5

o

-5

-100.4 0.42 0.44 0.46 0.48 0.5

0.50.480.44 0.46

Time (seconds)

0.42

o

5

-5

10

-100.40.10.080.02 0.04 0.06

Time (seconds)

5 I lti/l,tl ']Ml ~Mtl' ~(jp! qi\lli~

5 ~ 1\'111, .,1\'1'11 ,AIVb, .A'fl\ fVY~

10 i i i

-10' I i ! I I

o

Line Current 0(Amps)

Figure 4.10: Comparison o(phase A time-domain results at reactance order 0(1.5: Xtcr =0.8.Q.



Measured Results Simulated results

0,90.880.860.840.82

-20 r -- .. -~ Y.: - -~ Y.: - - -- - - - - --- .:.Y.:. -- -" --:.:-=-:: -- --"" -- -~

0.80.10.080.06

Capacitor, Voltage (volts)

0.90.880.860.840.82

5 ~- -- -- -- -- --.~

o

10 I I

-10 I ::, J

0.80.10.080.060.040.02

10 rl---,---------,----,.----,--------,

-10 I :: Io

ThyristorCurrent (Amps)

0.90.880.84 0.86

Time (seconds)

0.82

10 I I I

5 t;· ..•••·.t·······1y··/;········i\·······/~fvJ\ti\JL\iLV

-10 I : : : i I

0.80.10.080.04 0.06

Time (seconds)

0.02

10 I I I

-10 I : I

o

Line Current(Amps)

Figure 4.11: Comparison o[phase A time-domain results at reactance order 0[2: Xtcr = O.8.f2


Chapter Four 'page 4.16

The results from the laboratory-scale TCSC, Figure 4.9 to Figure 4.11, demonstrate that

the TCSC is capable of producing a variable capacitive reactance. The practical results

presented are only for the TCSC operated at approximately 50% of rated transmission

line current. However, the results obtained are sufficient to conclude whether the TCSC

functions correctly or not.

As shown by Figure 4.9, virtually zero current was flowing through the TCR branch

when the firing angle was set to 1800• The TCSC is effectively acting as a conventional

capacitor. However, as the firing angle was decreased, the current flowing through the

TCR branch increased. As it was explained in Chapter Two, under capacitive mode, the

current that flows through the series capacitor is a sum of the line current and the TCR

branch current. Hence, as the figures show, the decrease of the firing angle causes the

increase of the capacitor voltage.

Figure 4.11 shows the discrepancy (mentioned in the previous section) between the

simulated results and the practical results that occurs at low firing angles. In particular,

Figure 4.11 shows that the amplitude of the TCR current pulses is lower in the

measured results than the simulated results.

Transient Response

The simulation results of the mathematical model of the TCSC, developed in Chapter

Three, demonstrated that the TCSC could be used to modulate reactance when required.

This characteristic was also investigated using the laboratory-scale TCSC, as shown by

Figures 4.12 to 4.15. This was achieved by continuously varying the firing angle and

observing the response of other TCSC variables. Only results for the TCR reactor of 0.8

ohms are shown in this chapter, the complete set of results is found in Appendix C.




Variable potvoltage (volts)

3E i : i ~2 --~\----------i--------A---------t-~--------'(-----------/

, '~----' I~t::::::::::::~L;::-::::::::r::::::::::::-\:t~!-:::::::

Firing angle(degrees)

200 rt-------,-----,---------.-----------,

, '

:~>?: :150~:------------ --:--------- '~ i~'~, : ----------r~~<=;/-r----------------', '

-10L1 -----l.- ----l...- ----l...- _

o 0.5 1 1.5 2

40~ , t , J-~~j ••••••:••••~•••••••~••••~

, , ,

-401 i i :o 0.5 1 1.5 2

21.50.5

, , ,

'20 ~- --------- ------ --).- --------------- --l-------------------i- ---- ---- ---------

0~1Wffl~~-·1~-~~~~~~"-20 ~- --- ----------- ---;- ------. ---- --- --- -f- ------- --- --------:- ------ --------- --

, , ,-40 I [ : i

o 0.5 1 1.5 2

TCRcurrent(amps)

-1 1 , , , I 1000 0.5 1 1.5 2 0 0.5 1 1.5 2

40t , , , , 40 , ,, ,?Ol .~. ~ -:~ •••~•••VO~..;::;~) ~~.~~: .••••••••••~.-40 1 , , , I -40

0 0.5 1 1.5 2 0 0.5 1 1.5 2

10I I ' , ,. , ,

Li~~:ent 0 ~1~~~I~~~I~~I\~~I~~~loolr~I~I~I~~~~M~II~\ijlll~lj~~ o.~il....1

Time (seconds) Time (seconds)

Figure 4.12: TCSC response to a 1 Hz modulation ofreaetanee order between 1 and 2. Xter = 0.8 n.




21,50,5

, ,, ,, ,, ,, ,

________________ ..1'-----------------,__________________ 1-----------------4

5

3

2o

40. I I

TCSCReactance

21,50,5

, ', ' ', ' ', ' '

~---------------r-----------------;------------------; -----------------

~-""" :

T~

4

1o

40 1 ill I

Variable pot 3

'voltage (volts) 2

Figure 4.13: TCSC response to a two level modulation ofreactance order between 1.5 and 2. Xtcr = 0.8 .0.




3e±! ! j4

Variable pot TCSC 3

1

voltage (volts) ~ ········IF=I1=Ifl Reactance I I2o-------- - ---------;--------""""" ---------, ,, ,

-1 I' ,1 I 1

0 0.5 1 1.5 2 0 0.5 1 1.5 2

2:1~~~1~~~~~~~~~ ~wd~~I~d~20

Capacitor0voltage (volts)

-20 r . i 'I •. " , I -20,

0 0.5 1 1.5 2 0 0.5 1 1.5 2

10 10

Line Current(Amps) 0 0

-100.5 1 1.5 2 0 0.5 1 1.5 2

10

TCRcurrento~~~m.~~mw. o~--!II(amps)

-10 I I -10 I ~I i

0 0.5 1 1.5 2 0 0.5 1 1.5 2


Figure 4.14: TCSC response to a two level modulation ofreaetanee order between 1 and 1.5. Xter = 0.8 Q.



Measured Results

2

2

1.5

0.5 1 1.5

0.5

f-----h----------! -hh-------------f-------------j

c- ------ ------- -- -i- --- --- ---- --- --- j- ------ - -- - --- - - --f ------- -- --------i

Simulated Results

-10 ,---I -----'- .L.- ---'- -----'

o 0.5 1 1.5 2

40 ,

20 --- --- ---- -------~- --------- --- ----.:.- ----h_ -- --- - - - -l- --__ h_ - - ---- ---

o ~W~I~~-~--1~~ua~",~--20 -----------------,------------------i------------------;----------------

, ,, ,40 "

o 0.5 1 1.5 2

Time (seconds)

5

TCSC 4

Reactance 3

2

10

40

20

0

-20

-400

10

0

2

2

1.5

1.5

; t....._:C=Jl--:Co =:-------------L:L__D:::-----------

-1 : : :o U5 1 1.5 2

40'-1-~-~~-_

-40 L!- -'-- --1.. -'- -----"

o 0.5 1 1.5 2

Time (seconds)


Capacitor 20

voltage (volts) 0

-20

-400 0.5

10

Line Current(Amps) 0

-100.5

40,JTCRcurrent

(amps)

Figure 4.15: TCSC response to a two level modulation ofreaetanee order between 1 and 2. Xter = 0.8 n.



Figures 4.12 to 4.15 continue with the comparison between the measured results and

those generated in EMTDC using the mathematical model of the TCSC. As the figures

demonstrate, the reactance of the TCSC can be modulated by changing the control

input signal (firing angle). The analysis of the simulated results and other similar cases

[24] suggest that the TCSC responds to reactance orders with a simple time constant of

from 10ms to ISms, quite satisfactory for aiding power system stability. This claim was

proved to be correct by performing the tests and obtaining the results in Figures 4.16 to

4.18.

The results of Figures 4.16 to 4.18 show the transient response of the TCSC voltage

when the firing angle is suddenly changed from one state to another. These results

agree with the findings made in Chapter Two that the TCSC responds faster when a

step-up change is made in the firing angle (Xorder decreased) compared to the step

down change (Xorder increased). The results of this study demonstrate the capability of

the laboratory scale TCSC for rapid dynamic response.

A comparison of the responses in Figures 4.18 to 4.20 shows that the practical TCSC

exhibits a damped response whereas the simulated TCSC shows a slightly

underdamped response to step changes in Xorder. This discrepancy is probably due to

the non-idealities in the practical TCSC system (resistance in the TCR inductors,

forward volt drops of the thyristors and the limitations of the thyristor firing circuitry

previously discussed).



2.5 ,....-----.-----,,---,-----r--,-----,---,-------,---~--

-D.5

Variable potvoltage (V)

, ., I, ., .2 ' " .... t"T'"" .. ... ~~ .. _

:~:,if[~~~~~~ ~~:~::::I::::IJl, "f'---i----------~---------t---------:--------- ---------:- -- -------l----------~ -- -------j------- --

-1 L_...1...-_-L_--.---l__..L-_...l.-_---l.._----:-L-_~-~-~

o 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2

TCSC voltage(volts)

30,....----.----.----.----,--,----,---,..---,---,------,

20

-20

-300L--L.---L--...l..--.........l--...l...----'---L.----:-'-:-----=-'"=-~2

0.2 0.4 0.6 0.8 1 1.2Time (Seconds)

Figure 4.16: TCSC measured transient response as the reactance order is changedfrom 1 to 3.

2.5 ,....---,------,,------,-----,-----,----.---,..----,--,--~: : : : : : :

2 --- -----; ---------~-- --------:- --- ---...:.....-- -- -r---------i---------i- ----.-.:.....---------- --

2

1.5. , , , , , , , ,

- -- ~ - - - - -- - --~ --- -- - - - - -: - -------:-- - - - - - - - -~ - - - - - - - - -~ ---- ----- ~ --- - ----~- ----- -- - -:- -- - - - ---I • , , , , I , ,, , I • , I , , ,

, , I , I I , I 1

1 ----- ---} -------- -{- ---------:- --------:- ----- ----~ ---------t - --- - - - - - ~ - - - - - - - - - -;- - - - - -- - - -:-- - - - - - --, I , , , , , I r, I , I , I , I I, , I I 1 I , I ,

0.5 --------; --..... --~ ----- ----~- --------:- --- ------; --------.: ---- -----~- ---- --- -~- ---------c- -------, I , , , , , , ,

, I , , , , I , I

, I , I I , I , I

.---- -- - ~ - ------ ---:- - - - - - - -- -:- -- -- ----:- - - - - - - - - - ~ - - - - --. --~ ---- - - - - - ~ - - - ------~-- ------ - -~ - - - - - ---I , I I , , I , ,, , .I I I , I , I , •

- - - - - - - - ~ - - - - -- ---~ ------ - - - -;- - - - - -- -- -;-. --- - - - - - ~ -- - - - --- -; ------ - - ~- - - - - - -- - -;- ---- -----;- - - - - - ---: : : : : : ; ; ;-1 L-._--L._--l__--L._---'-__--'---_--'-__-'----_---'-__-'--_--'

o 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8

o-0.5

Variablepot voltage(V)

21.81.61.41.20.80.60.40.2

30,....---,------,,------,-----,-----,----.---,..----,--,-----,

20

-20

-30 '----"-----'----L.---'__...l...-_----'-__--'---_--'-__-'--_-Jo

TCSCvoltage (V)

Time (seconds)

Figure 4.17: TCSC measured transient response as the reactance order is changed

from 3 t01.


2

2

i1.81.61.40.8 1 1.2

Time (Seconds)0.60.40.2

• I , r , • • , I----------: ----------".----------f----------:----------;-----------f---------- f------- ---~-------- ---r---------

.', , : , , , , 11, ,

- - - - - - - - -1-- - - - - - - - - -:- - - - - - - -- - -:- - - - - - - - - - - t ---- -- ----~- ------ --- -:-- ---------r----------~ -----------:- -- -------, , " ,,", I " ",', , " "", , " "

, , , , ," ", I ,-- --- -----:-------- -- -:-. _. -- - --- ----------~- ----------:- -- - - - - - - --~--- --- - --- ~-----------:-----_._--" ",. I" t I , • I

" '" I I------- ~ -:- ------- --~- --------- ----------;- ----------f- ---- --- ---~ ---------- i-_ ..-------;- ---------:: :::::, , , , , , , ,

----- -- - --:- ------- ---:--- - - - - - - - -:- - - - - - - - - -:- - - - - - - - - --:---- - - --- --: --------- -:- ----- - - - - -;- - - - - - - - --, , I I , • , I

I , I I I I , I

•.••••• TT .: •····....··1..••.•.-------------------T----------r ----------1------- --r---------T---------f----------1----------T---- -- --

Q2 Q4 Q6 Q8 1.2 1.4 1.6 1B

2.5

2

1.5

Variable 1pot voltage

0.5(volts)

0

-0.5

-10

30

20

TCSG 10

voltage 0(volts)

-10

-20

-300

Figure 4. 18: TCSC measured transient response as the reactance order is changed

from 3 tol back to 3.

4.4 Conclusion


Chapter Four has described the development and testing of the laboratory-scale TCSC

for Natal University's Machines Research Laboratory. The chapter began by presenting

the original trigger channel circuit that was eventually modified to better suit the

requirements of the TCSC circuit. The circuit diagrams that illustrate changes from the

original circuit are included and explained in this chapter

A companson of the predicted response of the TCSC simulation model, the

approximate TCSC reactance versus delay angle equation, and the actual laboratory

scale TCSC's performance was made. As discussed in the previous section, the

comparison of the results has shown some discrepancies between the measured results

and the simulation results, more visibly at lower firing angles. This is mainly due to

non-idealities in the practical system that are not in the simulation model, in particular

the thyristor volt-drops and the non-ideal performance ofthe practical trigger circuit.

Time-domain simulation results were compared to the practical results measured from

the TCSC. These results proved that the laboratory-scale TCSC could be used to vary

its capacitive reactance by changing the firing angle.

Transient response of the laboratory-scale TCSC was also investigated in this chapter.

This was achieved by modulating the firing angle of the trigger circuit and observing

the response of different TCSC variables, such as TCSC voltage and TCR current. It

was then concluded that the laboratory-scale TCSC could potentially be used for

applications such as power swing damping.

The last investigation of this thesis work was to demonstrate that the TCSC circuit

could in practice be used to damp a generator power swing caused by a system

disturbance. Chapter Five considers the development of an EMTDC simulation of a

system similar to the one found in the Machines Research Laboratory. A model of the

TCSC developed in this thesis would then be utilized to damp a power swing on that

system.


Chapter Five

CHAPTER FIVE

Page 5.1

APPLICATION OF THE TCSC TO DAMP POWER

SYSTEM OSCILLATIONS ON A SMIB SYSTEM

5.1 Introduction

Chapter Four has described the development and testing of the laboratory-scale

TCSC model for the Machines Research Laboratory at Natal University. Different

components of the TCSC hardware were described in Chapter Four. Chapter Four

has also described the modifications that needed to be made to the trigger channel

circuit of the TCSC.

The test results of the laboratory-scale TCSC circuit are also included in Chapter

Four. The results in Chapter Four showed that the TCSC circuit is indeed capable

of providing a variable capacitive reactance. Time-domain simulation results also

demonstrated that the laboratory-scale TCSC could be used to rapidly modulate

capacitive reactance; this characteristic of the TCSC can be put to use in power

oscillation damping applications. Chapter Five presents a simulation study to

demonstrate the application of a TCSC to power oscillation damping. The single

machine infinite bus system considered in the simulation study is based on the

parameters of the Machine Research Laboratory, and the parameters of the TCSC

are those of the laboratory-scale device designed in this thesis.

Application ofthe TCSC to Damp Power System Oscillations on a SMIB System

Chapter Five Page 5.2

5.2 Application of the TCSC in Power System Oscillation Damping

Damping of power system oscillations has been recognised as an important issue in

electric power system operation. Numerous techniques of damping power swings

have been studied and applied. Application of power system stabilisers has been

one of the first measures employed to improve damping of the power swings.

However, with increasing transmission line loading over long distances, the use of

conventional power system stabilisers is limited by its slow control of power flow

and its inability in providing sufficient damping for inter-area power swings [5].

Previous chapters have shown that, in principle, a TCSC can be used to damp

power swings because of its characteristic ability to rapidly vary its capacitive

reactance.

A question of great importance is the selection of the input signal to the trigger

circuit for the TCSC in order to damp power oscillations in an effective manner.

From control design and practical consideration, a desirable input signal should

have the following characteristics [41], [7]:

• The swing modes should be observable III the trigger circuit input

signal.

• A desirable level of damping should be achieved.

• The input signal should preferably be local.

• The damping effect should be robust with respect to different system

operating conditions.

The machine's speed deviation is usually used as an input signal to the trigger

circuit. However, not all the above characteristics could be achieved. As an

example, the TCSC could be stationed hundreds of kilometers away from the



alternator. This situation will result in difficulties in having the machine's speed

deviation as an input to the trigger circuit. However, studies in this subject have

shown that the input signal to the trigger circuit can be synthesized from locally

measured variables such as capacitor voltage and line current [7], [9] and [41].

5.3 Results of the Power Oscillation Damping Study

Previous chapters have shown that the TCSC circuit is capable of providing

variable capacitive reactance by simply varying its trigger circuit's firing angle.

The last stage of this thesis research work was to develop a detailed EMTDC model

of a SMIB system in the Machines Research Laboratory, and then use the designed

TCSC to damp its power oscillations. The power oscillations were initiated by

opening the circuit breaker, as shown in the system diagram in Figure 5.1.

The EMTDC model of the SMIB system in the Machines Research Laboratory

consists of the individual turbine stages, the synchronous machine with its control

circuits, two parallel transmission lines and the infinite bus-bar. One branch of the

transmission line is fitted with a circuit breaker and the other branch has a three

phase TCSC. The complete EMTDC circuit can be found in Appendix D.

5.3.1 Trigger Circuit Control Strategy

As Figure 5.1 shows, a bang-bang controller was used in this investigation to

generate the firing pulses for the thyristors of the TCSC. The idea of producing the

firing pulses using a bang-bang controller is based on either inserting or bypassing

the series capacitive reactance at appropriate instants in the transmission line during

transient power swings.


---+IL 1

Pm

Turbine andsynchronous machine

V~endjnll

Chapter Five

Line 1i - - - - - - - - - - - - - - - - - - - - - - - - - - i BreakerII

IItII----------------------------

Line 2

Page 5.4

Vreceivinl!

Infinitebus

---+IL2Wo

W

~W

IIII----------------------------

XrCSC(MAX)

TCSCModule

a

'Bang-bang'! I I I

controller

XTCSC(MIN)

Control circuit

Triggercircuit

Figure 5.1: SMIB Transmission system with TCSC module used to investigate power oscillation damping

Application o/the TCSC to Damp Power System Oscillations on a SMIB System


The bang-bang control strategy adopted was to insert and remove additional

series compensation based on the speed deviation (co - coo) between generator

shaft speed and synchronous speed. The bang-bang control algorithm can be

expressed as follows:

Increase XTcsc if co - COo > deadband

Reduce XTCSC if co - COo < deadband (5.1)

The deadband was introduced to prevent the controller from reacting to small

variations in shaft speed from the desired synchronous speed. Appendix D

contains the EMTDC model and the design values, which were used in

simulating the circuit ofFigure 5.1.

43.532.521.510.5

-1'---__L-...__L-...__'--__L-...__'--__'--__L-_---l

o

1

0.5 ISpeed Ot+------\-----f------l,----+---+----I-----+---l } Dead band

deviation (pu) t----\:---f----\---+---.lr---!----.lr---A-0.5

1

2Xorder

3

I

t- U U U J

I II

I

I Io 0.5 1 1.5 2 2.5

Time (seconds)

3 3.5 4

Figure 5.2: Relationship between the input to the controller and the firing angle


r

It is important to note that research in this subject has shown that bang-bang

controller is more effective mainly to damp large-signal power swings;

subsequent small-signal damping requires a more continuous controller [9] and

[41]. However, the objective of Chapter Five is to demonstrate, using an

EMTDC model of the Machines Research Laboratory system that the TCSC is

capable, in principle, of damping power oscillations.

EMTDC Simulation Results

The power system network of Figure 5.1 was modeled in EMTDC to

demonstrate TCSC's capability to damp power system oscillations. The actual

EMTDC model and its parameters can be found in Appendix D. The EMTDC

graphical representation of the system comprises, at the sending end, a

synchronous generator coupled to a multi-mass turbine unit. The transmission

network consists of two parallel lines (Line 1 and Line 2) of lumped impedance

RL + jXL. The TCSC is inserted into one of the lines, while the circuit breaker is

inserted to the second line.

The theory of operation of the TCSC control scheme, to ensure that the inserted

reactance to the transmission line is providing positive damping torque, has

been covered in previous sections of this chapter.

The power oscillation damping controller was designed and the following are its

operation parameters:

XORDER = 3 if <D - <Do > deadband

XORDER = 1 if <D - <Do < deadband

XORDER = 1.5 if <D - <Do is within the deadband

Where deadband = [-0.15,0.15].

Application o/the TCSC to Damp Power System Dscillations on a SMIB System


Figure 5.3 compares the time-domain simulation results of the system with no

TCSC control to the results of the system with TCSC control. Both results

clearly demonstrate the capability of the TCSC to provide positive damping

torque. The fault was induced by opening the breaker, as shown in Figure 5.1, at

t = 1 second.

Rad/s

1 ~ -~ -~ --- - -.:. ----------~ -----------~ ---_.- -----: ----------.:.. -----------:..------- -~ ---- -------~ -----------~ ---------

o :-----------i-~·---··j-VJ(~-··:--·~W' :7\0~~ : : l: : ~,. : ; { : ,, , , , • I I ,

, I "I, I

-1 ----f- - - - ---- - - -; - - - - - -- - -: - - - - - - - - - - -~- - - - --- - - -: - - - - - - - - - -;- - - - - - - - - - - ~-- -- - - - - - - -! ----- ------ ~ ------. ----: -----. ---

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Degrees:~••••••·I •••••••••• r•••~ ••·I•••••· ••• ;•••••••••••:·••••••••••,•••••••••

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

65.54.5 ·543.53

I " ,

I " I, , , , , ,-~ - -. ---- - - --. -- ---- - - - -..... - -- ---- - - . ..,-- - - ---- ---. -- -- - --- -.-. - - - - - - --.-... -- - - -- ---I , , , , , ,

I • , , , , ,, , , I , , I

I , , I I , I

I , I , I , I

2.521.51

0.5Amps

Time (s)

/

Figure 5.3: Time-domain simulation results ofthe SMIB system in Figure 5.1

with and without the TCSC.

The rest of the time-domain simulation results are shown in Figure 5.4. As the

figure shows, the results are divided into two columns, left column consists of

the results of the system with TCSC control and the right column illustrates the

results of the system with no TCSC control.


TCSC Control NO TCSC Control

)V \j\Jfv\n tJ\, 'I.A "1/\1\ hA

~VJV IVVI v~ vv vv

I-I

~\[\ A.Clener~tor Spee De~ iation

,A

"'nl\r !lJ~Radlsec 0

-I

p~umt~'_

654

Time(s)

32

/ \ V ~ ../v-------.-

"-..-/ r-~

1/ -~

----- ---f---

/.~ / ~ \.--.......-- I-------- h

I.,

/ ""'- Iir-'"'to.. --V ............. r--. -----I----f----

0 I~

/ \ / '", ../v- 1''"'---V -"'"

/ "--J

1 1---

oo

o

o

oO.

o

8

70

6

0.6

-0.2

6543

Time(s)

2

I,~~ .lIIJj.. L h I>llIh,

... :aehine!§- rea wer--.. t"

Ge Ilera or te min~l vo tage

c - .

'"o ( '-~-/' cenerator ~ad Ange _.-

o

Per unit

oPer unit 0

-0.2-0.4

1~'l.1I

0.8 '" -- '--,

Per unit 0.6 IbL .......If ((in, ge11i~lItor-cur enr- Io.1.

8

Per unit 7

6

Figure 5.4: Complete Time-domain simulation results ofthe SMIB system in Figure 5.1 with and without the TCSC

Application o/the TCSC to Damp Power System Oscillations on a SMIB System

5.4 Conclusion


Previous chapters of this thesis have demonstrated that the TCSC is capable of

providing variable capacitive reactance by varying the firing signal ofthe thyristors. In

concluding this research work, the thyristor controlled series capacitor was applied to a

simple single machine infinite bus system, similar to the Machines Research

Laboratory system, to demonstrate its capability to damp power system oscillations. A

detailed EMTDC model ofthe system was developed and is found in Appendix D.

The trigger circuit, discussed in Chapter Four, was modified to suit the TCSC's

application ofpower swing damping: a bang-bang controller was chosen because of its

simplicity and ease to implement. While the results of this chapter have shown that the

bang-bang controller can be used to produce the firing signals for the thyristors, it was

highlighted that some other form of controller may be more effective, especially to

damp small-signal power swings. The synchronous machine's speed deviation was

used as the input to the control circuit. It was also noted that it is not always practical

to use the speed deviation as the input signal to the controller mainly because the

TCSC might be located long distances away from a generator. Hence, some research

work in this field has shown that the controller's input signal can be synthesized from

the locally measured variables at the TCSC installation [41].

Although the power oscillation damping study presented in this chapter is limited to

simulations, the measured results in the previous chapter have shown that the hardware

TCSC that has been designed in this thesis could be used in such a scheme. The

measured results of the laboratory-scale TCSC have shown that the device is capable

of varying its capacitive reactance at a frequency of 1· Hz, as required in a typical

power oscillation damping application. Furthermore, the results of Chapter Four

confirmed that the laboratory-scale TCSC can provide this variable capacitive

. reactance in response to both sinusoidal or bang-bang type control input. Thus, on the

basis of the measured results in Chapter Four, and the simulation results in this

chapter, it can be concluded that the laboratory-scale TCSC designed in this thesis



could potentially be used for practical power oscillation damping studies m the

Machines Research Laboratory.

Much advancement, in the field of TCSC design, has happened since the start of this

research work. These advancements include the impact of the voltage across the

thyristor valves to the accuracy of the firing delay angle, and in this area there is

certainly scope of further work as will be discussed in the concluding chapter of the

thesis which now follows.


6.1 Introduction

Chapter Six

CHAPTER SIX

CONCLUSION

Page 6.1

This thesis has examined the specific issue of designing and implementing a

thyristor controlled series capacitor with parameters suitable for application

studies in the Machines Research Laboratory at Natal University. The

investigations have shown that the TCSC is capable of rapidly varying its

capacitive reactance when operated in vernier capacitive mode. The

investigation has also shown that the TCSC can be used, not only to increase the

power transfer capability of a transmission line, but it is also capable of being

used as another tool to damp power system oscillations due to system

disturbances. This chapter summarises and reviews the principal fmdings of this

thesis, chapter by chapter, and finally suggests further research work that could

be undertaken in this area.

6.2 Factors that Influence the Design of the TCSC

Chapter Two has shown that designing a TCSC could prove to be a complicated

task, unless all issues involved are clearly defined and addressed. Chapter Two

outlined these design issues in detail and discussed the design limits associated

with them. The review, of Chapter Two, has shown that the choice of reactor

and capacitor sizes of the TCSC not only determines the operating region of the

device, but also its operating performance. Rating of the TCSC components and

harmonics contributions are a major issues when designing a TCSC. The

dominance of the 3rd harmonic voltages was shown.

Conclusion

Chapter Six Page 6.2

Chapter Two also discussed both the steady state and transient response of the

TCSC. Under steady state conditions, it was shown that when the TCSC

(instead of a conventional series capacitor) is fitted in a transmission line a

similar resonant condition occurs to a conventionally compensated line.

However, the additional resistance introduced by the TCSC at the resonant

frequency helps to produce positive damping to suppress power swing

oscillations as well as to mitigate SSR. Typical transient response curves for the

TCSC were also shown. The literature review also discussed the asymmetric

nature of the TCSC's response to a step change in the firing delay angle.

The literature review in Chapter Two also discussed different applications of the

TCSC, namely, damping power swings and mitigation of SSR. A typical

response of the TCSC, controlled by a bang-bang controller, was shown and

different control strategies were also mentioned. The phenomenon of SSR was

also mentioned and the benefit of the TCSC to suppress it was also outlined.

6.3 Mathematical Models to Study the Performance of the TCSC

Chapter Three has presented the development of a mathematical model to

investigate the characteristics of the TCSC. As an important integral part of the

TCSC circuit design, the control circuit that generates the firing pulses for the

TCR thyristors was presented and its operation was explained. The chapter also

outlined the methodology that was followed to determine the sizes of both the

capacitor and the reactor in the laboratory-scale TCSC.

The effect of changing the size of reactor was investigated. Reactors of sizes 0.8

n, 1.2 nand 1.6 n were chosen for the laboratory-scale TCSC. The

investigation confirmed that the ratings of the TCSC components are dependent

on the size of the TCSC reactor. It was found that the current and kVAr ratings

ofboth the capacitor and reactor decrease as the size of the reactor is increased.

Conclusion


Chapter Three also discussed the impact of TCSC harmonics on the

transmission line currents. Several simulations were conducted to deduce the

effect of the TCSC harmonics on the power system. The simulation results

showed that:

• The TCSC 3rd harmonic voltage is dominant and other orders of voltage

harmonics are negligible in magnitude. The results also show that the

magnitude of the harmonic voltages increases as the reactor size is

decreased;

• The harmonic currents were found to be largely confmed within the TCSC

loop. Only a small magnitude of the harmonic currents (5% at most) was

found in the line currents.

6.4 Development of the Laboratory-Scale TCSC

The main objective of Chapter Four was to outline all major steps that were

followed when constructing and eventually testing the laboratory-scale TCSC.

The chapter covers the design and testing of the trigger circuit. Its shortcomings

were also discussed. The measured results taken from the laboratory-scale

TCSC have shown reasonable agreement with the predictions made usmg

various simulation models of the system. The measured results have thus

1. Confirmed the validity of the mathematical models which have been used

during analysis and design of the laboratory-scale TCSC, with its control

scheme, in this thesis;

11. Provided confirmation of the theoretical principles of operation;

111. Demonstrated the ability of the TCSC to rapidly vary its capacitive

reactance.

Conclusion

Chapter Six

6.5 Power Oscillation Damping using the TCSC

Page 6.4

A number of papers reviewed in the literature survey of Chapter Two have

suggested that one of the important applications of the TCSC is to damp power

swings. To determine whether the laboratory-scale TCSC could be used to study

this application in future, a detailed mathematical model of a single machine

infinite bus system was developed in EMTDC, based on the parameters of the

Machines Research Laboratory. The simulation model of the laboratory-scale

TCSC was inserted in the transmission line of this study system. The results of

this theoretical study, together with the laboratory-scale TCSC designed in this

thesis could be used for practical investigations of power oscillation damping.

6.6 Suggestions for Further Work

This thesis has presented the first practical implementation of a laboratory-scale

TCSC designed for the Machines Research Laboratory at the University of

Natal. The work that was undertaken, during the design and implementation

stages of this thesis, gave a good insight into issues that need to be considered to

produce a functional TCSC. However, as is often the case in such research, the

investigations that have been done have addressed some issues and uncovered

further questions. Therefore, the author suggests that scope exists for further

work in this area as outlined below.

(a) To test the hardware TCSC design of this thesis, an existing analogue

thyristor trigger channel was adapted to the TCSC application. As

discussed in the main body of the thesis, using an analogue trigger

channel synchronized to the TCSC capacitor vOltages is not ideal and

leads to inaccurate generation of the thyristor turn on signals under

some conditions. In practice, transmission line TCSCs use thyristor

Conclusion


fIring circuits that are synchronized to the transmission line currents;

however this approach requires digital phase-locked loop hardware to

be designed, and lay outside the scope of this investigation. It is

suggested that the next phase of this project consider the

implementation of a digital trigger channel for the laboratory-scale

TCSC, synchronized to the transmission line current.

(b) Another area that can benefIt from further work is the design of TCSC

components, particularly the size of the reactors. This thesis has shown

that the size of the reactor determines the kVAr rating of the whole

TCSC circuit. In the literature review conducted in the thesis, it was

discussed that the TCSC's reactor should fall within recommended

range of sizes; for the laboratory-scale TCSC a decision was taken to

use reactor sizes of the highest possible values within this range, in

order to reduce the required rating of the thyristors and the reactors

themselves. However, later research work has shown that this design

methodology could lead to under-performance of the TCSC, especially

in the lower fIring angle range. Hence, the author recommends that in

the next phase of the project, the laboratory-scale TCSC's performance

should be examined with smaller reactor sizes.

(c) The results of Chapter Four and Five have shown that the laboratory

scale TCSC could be used for practical studies of power oscillation

damping. It is recommended that future work consider the use of the

laboratory-scale TCSC for damping the power oscillations of the micro

alternators in the Machines Research Laboratory, both using the bang

bang and continuos control approaches.

Conclusion

Appendix A

APPENDIX A

PageA.l

PARAMETERS OF A SIMPLE EMTDC CIRCUIT USEDDURING THE TCSC DESIGN STAGE

This section covers the list of parameters used during the design phase of the project.

These parameters were also used during the harmonic investigation.

A.t Parameters of a Simple Circuit with a TCSC device

A.Lt Voltage Source and Infinite bus

Source Voltage = 127 V

System Frequency = 50 Hz

Initial Phase = 0° / 30°

Ramp up Time = 0.05 s

Source Resistance = 1 Ohm

A.L2 Transmission Line Impedance

LUNE = 0.0513434 H

R = 2.0 Ohms

A.L3 TCSC Device

C = 1591.55 JlF

L = 0.00255, 0.00383 and 0.0510 H

Thyristor ON resistance = 0.01 Ohms

Thyristor OFF resistance = 1.0E6 Ohms

Forward Volt Drop = 0.1 V

Forward Break Over Voltage = 1.0E5 V

Reverse Withstand Voltage = 1.0E5 V

Minimum Extinction Time = 0 s

Parameters ofa Simple EMTDC Circuit used during the TCSC Design Process

Appendix A PageA.2

TCSC CIRCUITr

II

VOlC,g. Sourcev. 127 V1.50 HzInlllal Phase" 30 d.grees

G~~ ~

lIinel Iter

~

le, 1591,5

~

0.0513434 2,0

InflnlleSu.V·127V1.50HzInHJaJ Ph,•• .. 0 d.gree.

~

."'~

= \- \I,,.\.,

,\

'~. ;

FI!~II'l<3c:IRc:,l!IL

-J.l.....,~ CI~ r,e...

:(t4~~~

Angle In IRadlans

" Qt,JTf>I,ITC;:t:tAI'lN~4$, "

I I' rij'j r'Ili :.ill [it] [~I L'6'J L..,,) ;,..,,~l,.,~

" C!>

I Iter le Vier SawToOlh Re.etI I

IIll"!

1·........1·

f:JjJ fIl'l'1/'~N..)N· ,Lg ..,~ "-

0 0IlJne Ve " ~ngle T

if'

".'

Figure Ai: A simple EMI'DC rcsc circuit

Parameters ofa Simple EMTDC Circuit us<!d during the TCSC Design Pr~cess

AppendixB

APPENDIXB

Page B.I

MODIFIED TRIGGER CIRCUIT FOR THE CONTROLOF A THYRISTOR CONTROLED SERIES CAPACITOR

AppendixB PageB.2

-12 V

IN4007

1 kQ

1 kQ IN4007

6

-12 V

Figure B.]: Original Synchronizing stage ofthe trigger circuit

lOkQ IN4148

6

150kQ

12 v8.2kQ

L---,"-'---=j2 7

IN4148

lkQ

6

-12 V

Figure B.2: Modified Synchronizing stage ofthe trigger circuit

AppendixB Page B.3

4.7 kn IN4148

0.22 I 100V

33kn

IN414812 V

2 7

7411- ...1.-_+----"13 +

4

-12 V

8.2 V/400mW

Figure B.3: The Ramp stage

8.2 V

lknSpeed Pot

IN4148-12 V

IN4148

33 kn

Figure BA: The Comparator stage

~.~,

AppendixB PageB.4

\

.,TRIGGER

-- 4MPLIFIER

OSCILLAT~

):f , IJ TP6

4001

" .I2V7 OV

!

TP!

31<3RII

SYNC-STAGE

RIl331< I!'",

'"'"

\1

~ RAMP SLOPEl TRrM

RVI2DDK

":~. '

.11V

Figure B.5: The initial trigger circuit for each phase o(the hardware TCSC

AppendixB PageB.5

B.2 The Impact of the Changing Capacitor Voltage to the Thyristor FiringPulses

Chapter Four has discussed the impact of variations in the magnitude of

capacitor voltage to the thyristor firing pulses. The objective of this section is to

expand the discussion developed in Chapter Four by including graphical results.

The problem that is discussed in Chapter Four (and subsequently, in this

section) was resolved by modifications in the conventional synchronizing stage

(as outlined in Chapter Four). However, it is important to note that the graphical

results presented in this section are those of the unmodified trigger channel.

Figure B.5 shows the rated capacitor voltage that was used as the input to the

trigger channel. The zero-crossing detector was then used to output the reset

pulse (for the ramp signal) each time capacitor voltage becomes zero. The

capacitor voltage was then decreased to a value just below 10 volts, as shown

by Figure B.6. The figure clearly shows the error in the reset pulses and the

ramp signal. This is undesired behavior and it leads to incorrect turn on pulses.

This problem is more visible by the results of Figure B.7, where the capacitor

voltage was reduced further. The ramp pulses have now been transformed to a

level shape.

AppendixB PageB.6

CapacitorvoltageVc (volts)

10

o

-10

/'- r--. !'"" .r-'- /"..

J ---~ / \1 -t~\ / ~ / \~ j; i\ /1 1\ If ;\

L4--- ; , ,,I ' I 1\ I II ' I

.~

I I ~

I I I II I I I ; I

I I I I I I I I

Reset pulses(Zero crossing ofVc)

I I I I I I II I I I

I

Ramp Signal(Angle of Vc)

o

f\ 1\ 1\ 1\ 1\I'\. '" i\ 1\ 1\ 1\ 1\ r\. 1'\'\ '\ \ \ \ '\ \ 1'\ '\

0.4 0.42 0.44 0.46 0.48 0.5

Time (s)

Figure B.5: Ideal capacitor voltage as an input to the zero crossing detector

10,-------,------,----,--------,__-,-__--,--__,--_-,-__--,--_---,

Capacitor 0 f----\-+--+-+--\--+----,H----'r-+---(r----r-----''r-r----i-t-----'r--t--iHVoltage Vc (volts)

Reset pulses(zero crossing of Vc) o

~I,

~I, , ,

,l-!, ,

r'- r-'-- r- ~ ,.-..!.I .-:- ,...-!-

! I;

! i

W- I I- r-- I-- +- t-- r-- - +- - '-I I I

0.50.480.460.440.420.4

OJ----------t-----j-------+---+---t-------t---t---t---+------j

Ramp Signal(angle of Vc)

Figure B.6: A small error introduced by the decreased in capacitor voltage

AppendixB PageB.7

10

CapacitorVoltage Vc (volts) 0

·10

Reset pulses 0

(zero crossing ofVc)

Ramp Signal(angle of Vc)

o

J~I

~ .........~ ____~ .r=::.t------ ~ .........~

----I-----"

I----

I-----" I ----f----..-'.

I

.---:-- .---:-- .------ r--'- ,...-'- r---

N N 1'\1 I\J "f N '\J "J N \I

0.4 0.42

Time (s)() <lh 0.48 0.5

Figure B.7: A larger error introduced by the decreased in capacitor voltage to

below 5 volts.

Appendix C

APPENDIXC

Page C.l

ADDITIONAL SIMULATION DETAILS AND RESULTSFROM CHAPTER FOUR

AppendixC PageC.2

.__....-=L._.__~~~L._..... _"_'1

'" ~

r--'~ ,~~~~~--_.:1 ....-2_.._~tJ._~.J I'

Ic2 '" ! .S····················) .~ ~, ... .. ' (

"~.._.._.- ~-- ;: l_ ,~ ._.~W---~----.---~,~'-'-I . .~~ j~ ~

I j_.~~.- IL_.__ - __ -; __ ,~ ..~.C.~_J

", ,~

~

C'o~o'')~

~

,1 1f:,

~····,·" ..·,·_·,_··'..'·l·

C:::Q;"Q:' ~ 11>-' ~r~ ~/_....... CO~r'. ~'t 12:';,;

....~'

,~ I..

VI"" I' "tQo;lI""'SU f

Figure C.l: The EMTDC circuit diagram ofthe TCSC with sinusoidal modulationofthe firing angle\

AppendixC PageC.3

....

j...._"-"....::Z..........""....G~ ..._.._......_"_..".. '

101 ~...

r------"' -,::' -. ~--'::i

}/ j·_-:;L"..._"..~J---: ....--'..l 11

,,;~ ~ . '''~

S··· ....··· ......··· ...... C '

"~ - -: -c ~---~'tPL~_~~_,','~--I ~e t!; r..........~

j_._._.._~~----_.J

--- ;;-;-~w-~j'.~, M

...I'tHREE I{RAse TRIGGER CIRCUIT I

,\I,

t:!

.."

IFIRiNG ANGLE· SQUARE I

Figure C.2: The EMTDC circuit diagram ofthe TCSC with sguaremodulation ofthe firing angle"\ .

Appendix C Page C.4


20, I

,~O' : I

0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02-20! I

o

20 r,-----,----~---~----~---...,


10 ,,-------,-------,----,----,-----, 10 i I


5 ~- ---- ------- -~---- ------ ---~ ----- -------~------- --- ---~- --------- ---, , I ,, t 1 ,, , I ,, , I ,

o~-~----,..~-_+__-..---~~--""~--t-~I , I ,, , , ,rI, ,

-5 ~-. ---- -------f--- ----------:-- ------------:- ------------~.. --------- --, , I ,, I , ,, I , I

-10 I : : : : I

o 0.02 0.04 0.06 0.08 0.1

5 ~- ------------~ ------------ ------------+------------ ~-------------, ", ", "

°t: :: I-5 -------------i--- ---------- ------------i------------+-------- ----

, "

-10,: :: I

0.4 0.42 0.44 0.46 0.48 0.5

0.50.480.460.440.42

10 I

Time (seconds)

-10 I I

0.4

10 r,----..,....----~----,_----.._---__,

L(~m J~'J0::_:V:ty>y~,---V ,----¥---\, I , I

-10' i : : : I

o 0.02 0.04 0.06 0.08 0.1

Time (seconds)

Figure C.3: Comparison ofphase B time-domain results at reactance order of1

AppendixC Page C.5


0.50.480.460.440.42

20 " ---,..----,----,----,-----,

-20 L! -'-__~'____-i... __'______'

0.40.10.080.060.040.02

CapacitorVoltage(volts)

0.50.480.460.440.42

10 1 I I I I I

~O' ,~4

10, I I

:~l\L~--5 ~- -------- --_: -- _;_ ---- --- :_ -----_. ---- ~ --__0_- •

, , ,, , ,, , ,-10' : :: I

o 0.02 0.04 0.06 0.08 0.1

ThyristorCurrent(Amps)

10 " -----,---..,----..,----,..---,

5LP~-'-'-----~--f-------~-------1£-~----------ff:---------o ----- ----- ~-----+l: -----:

-5 - - -.....-?. --.---)J"'-'-r .-------"1" - .-.-----

-10 I i : i : ,0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02

o

10 "----,----.-----r----r---........,

-10 '-,__---' ~__........... L........__--'

o

Line Current(Amps)


Figure C. 4: Comparison ofphase B time-domain results at reactance order of1. 5

AppendixC Page C.6


0.90.880.860.840.820.8

-20 f- --------""'- ~-- ------ --'-"

0.10.080.060.040.02o


10,r----r------.----.----~--___,

0.90.880.860.840.820.10.080.060.04

, .

5 ~---------$l-~-------J1----;---------- - ----------.-, ,, ,, ,

O~V- --: --- ---:- --- --- --- --- --- ~---. ., ,, ,

-5~--- ---.-.---f--- --------+-- --------- --- -------- -V------, ,, ,

_1QI i :o 0.02


10 rl-----r----,-----,------,----, 10 I I I I, ,, ,

5~-1------\--;------r---.L1J-------)----r-----fF;--------- --I , , ,

o ~-----------_\----- ----\----- ..i. ----..:.----- -----~,,,\··')T.'\;! .

-10 I : ; : i I

0.8 0.82 0.84 0.86 0.88 0.9

, , ,, , ,

5~---rl~--)r-- ·-----8:------·--f---f\-----i-----·-----oH------ ----j- -----\----;- ------ ----1- -----\---j-"------.----

-5 ~---------. -r{---------\i---------- :---------~----------_1QI i : ; : I

o 0.02 0.04 0.06 0.08 0.1

Line Current(Amps)


Figure C.5: Comparison ofphase B time-domain results at reactance order of2

AppendixC Page C.7


20 I,----,--------r---,----...,---~

-20 'L-__--'--__--'- '---__--'-__---'0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02

~O' :o

20 j ill

-10


10, , 10, I


5 ~---·-------·j-------------i-------------!-------------;------------

O~-~~i-~-·T--·T-~T-~~

-5 ~------------1------------·1-·-----------r------------;------------

.10 ' : i i : Io 0.02 0.04 0.06 0.08 0.1

5 ~------------ -------------j------------ ------------ ------------

o[: I

-5 ------------ .1 ------------:------------, ,. ,, ', '.10' i :

0.4 0.42 0.44 0.46 0.48 0.5

10,,----r----,----r----,----,

5~---A------jTSJ-----------:---(\:--1£-:------w----;----------QC!\!-!r--r -----,--5 ~--------\J---------- -:---------- -:---------- -: ----------,-

I , I I, , I ,, , I I

.10' i i i :0.4 0.42 0.44 0.46 0.48 0.50.10.080.060.040.02

10 rl---,-----,-----r----r------,

-10' ; ; ; :o

Line Current(Amps)


Figure C.6: Comparison ofphase C time-domain results at reactance order ofl

AppendixC Page C.B



0.02 0.04 0.06 0.08 0.1

20 " ----,----.,.------,----,-----,

-20 IL ---L ---L --'- --'- ..J

0.4 0.42 0.44 0.46 0.48 0.5


10, 1

::"~- •••]j···;JL·rilL·••·J[·5f\lT1f~IrJ[r

-10 I i : i : I

o 0.02 0.04 0.06 0.08 0.1

10 [ , , , , ]

5 --~--.-------L~...... --..l.. ..--------:..51·.. ···----:-·--·--------·

vf' , ,

I I , I, I • I, t , I

~~~+ ..++ .. +~:-10 I i i : ;

0.4 0.42 0.44 0.46 0.48 0.5

0.50.480.44 0.46

Time (seconds)0.42

10 i r I I

:lu·Ju····f\••·tnrl\··-5 v::·.--.\J : \~~----------\J \y ---\0

I , , •I , , ,I , , II , , ,

-10 t i i ; i t

0.40.10.080.02 0.04 0.06

Time (seconds)

10 j I I I I

-10 I ;; ; I

o

','

Figure C. 7: Comparison o(phase C time-domain results at reactance order 0(1.5

AppendixC Page C.9



·10

o 0.06 0.08 0.1 0.8 0.82 0.84 0.86 0.88 0.9

10 ri-----r----,------r----,---------,

0.90.880.860.840.82-10 Li -'-- -'-- -'- -'- ....J

0.80.10.080.060.040.02

, , I ,

:~rft¥!Fra·······+:Jtrj-5iV' , , \-J ' r

r----- ------i----- - ------f----- ---·--~-----\-------i·----V--·--, , I I, I , I, I , ,

-10 I i i ; : I

o


10 i i I

:tf\.I\.·I/\••J/\::o:.:.-sV--------J--------\J--------V---------J-------\

, , I I, , , I

-10 I : i ; i i

0.8 0.82 0.84 0.86 0.88 0.90.10.080.060.040.02

10 i i i I

~O! : I

o

Line Current(Amps)


Figure C.S: Comparison ofphase C time-domain results at reactance order of2

Appendix C Page C.lO


3 4, ,

Variable pot :~i::3:::]lj 3

1 I Ivoltage (volts)2

. ,-1 ' ,

10 0,5 1 1,5 2 0 0.5 1 1.5 2

20 20

Capacitor0 ~~~~~~~~~!~~.~~~~~~~~~~!~~~~WW 0voltage (volts)

-20 ! , I ·200 0.5 1 1.5 2 0 0.5 1 1.5

10 10

Line Current 0 0(Amps)

·100.5 1 1,5 2 0 0,5 1 1.5 2

10 , ,, ,, ,

TCRcurrento~~IMM-----~~_tlrJ: 0 -_._- ..--(amps)

i : 111 i, , ,

-10' , ,

·100 0.5 1 1.5 2 0 0.5 1 1.5 2


Figure C.9: TCSC response to a two level modulation ofreactance order between 1 and 1.5; Xtcr = 1.2 n.

Appendix C Page Cll


2

2

2

2

1.5

1.5

1.5

1.5

Time (seconds)

0.5

0.5

0.5

0.5

.-iIM

3 5

Variable pot 2·~··ff]I:···4

voltage (volts) 1 ... ------------- ------------ ____ c ___________ ----,------- ________ 3

o ------------ -------- ---T----------- i-- --------- --- 2

-1 10 0.5 1 1.5 2 0

40 40

20Capacitor

voltage (volts) 0

-20

-40 -400 0.5 1 1.5 2 0

10 [ I I I I 10

1IIII1I11I11111IIInlllllilllllnllllllallllllllllllllllllnllllllIIdIUlllll'I""'IflIIlIIOIIIlI"11

Line ClUTent(Amps)

o~mR1~~.!lM"I1.1I10

-100.5 1 1.5 2 0

10

ob. I JTCR clUTent~~OOI~,(amps) 0

-10 I : ! -100 0.5 1 1.5 2 0

Time (seconds)

Figure C.10: TCSC response to a two level modulation ofreactance order between 1 and 2; Xtcr = 1.2 n.

AppendixC Page C.l2


-10 I j 1

o 0.5 1 1.5 2

10': : i

o~~~~-10 1 i i

o 0.5 1 1.5 2

~: i :-----

150~-----------: : V ~--~ r---------------;- -<~/i----------------

100 1 i io 0.5 i1.5 2

200 , I

2

2

1.5

1.5

40

20

0

-20

-400.5 1 1.5 2 0 0.5 1 1.5 2

10

0

0.5

0.5

ll~~

-10 LI -----i '-- ---'---- ----J

o 0.5 1 1.5 2

TCR ClUTent(amps)


C

-10

40

Capacitor20

voltage (volts) 0

-20

-400

10

Line ClUTent(Amps) 0


Figure CII: TCSC response to a 1 Hz modulation ofreactance order between 1 and 2; Xtcr = 1.2 Q.

AppendixC Page Cl3


3 rl-------,-----__,r-----..,-----, 5 ri-----,----,..--------r------,

2

21,5

1,50.5

0.5

: ~-----u---n r---------m----[ +--I--------j

o

-10' i

o 0.5 1 1.5 2

......-10 I i i i I

o 0.5 1 1.5 2

Time (seconds)

2 ,'----~-----'------'-----'o

40 I I , I

20 ~iliiljiiljilji{liiliilj~-liiliiliiliii!iihiiliiil~ilijijj~-ljiljilji{liilj~iiliii-Iiilii~-!il~\iiliil~o

: r: :"::'.'::': :': :':: :': :'-1- --u - - - u - - - - - - -j": :::..'::'::': :': :':::'1" -- ------------jo

10ir----~----,----r----__,

2

2

2

1.5

1,5

1.5

0.5

0.5

0,5

---~----------.J.~-~------~---------------f:.~,ll>. : : : -- - - - - - - - - - - - --

"''''1 :, ' ,; ; ;,

o

Time (seconds)

o

20 iljiljiliiilii!ii~ji~ii i~iiiiiiiijii{!jij~ii~i f~U~!ifl iiliiilii~iili jl~j Ijji~~iiii{liiliil]iijj i~j ~o

~:r---------------r------n - - - -- - - -j ---n - - - - - - - - - - - r---:-------:-:-1o 0.5 1 1.5 2

10 I i

-10 LI ---'- -'- --'- -l

o10, I I

.10 i I

o

Line ClUTent(Amps)

TCR ClUTent(amps)


Capacitorvoltage (volts)

Figure C.12: TCSC response to a two level modulation ofreaetanee order between 1.5 and 2; Xter = 1.2 n.

AppendixC Page C.14


3 1 I I [ 4, I

2

2

2

2

1.5

1.5

1.5

1.50.5

0.5

0.5

0.5

o

o

3 [ ( __ mm ' ,-----------------,

2 ~-----------------L~------------------'-I----1

O~...'--~_::, - 'i i : -.--~~-

-51 1 i :o ' : :

1 ' ,o

20. I I I I

-20 L'-----'------~-------'---------'

o10 ,.--------,------,-----,--------.,

-10 L'-----'------~-------'---------'

o5 ,,---------r------,.------,..--------,

2

2

1.50.5

0.5 1 1.5

Time (seconds)

",..·..···_"'"'·lE: J,.",-"j! nTuummmfmmumrurmuuuumuuu~

1 ----- .. ----- ----i------------ ----l------------- ----l-----------------

o ---- ... ------: ---+------------ -r----"-----1 i i :

o 0.5 1 1.5 2

20, I I

'~~fl~i~i~, , ,, , ,, , ,, , ,, , ,

-51 ; i io

TCRcurrent(amps)


Capacitorvoltage (volts) 0

-200 0.5 1 1.5 2

10


Figure C.13: TCSC response to a two level modulation ofreaetanee order between 1 and 1.5; Xter = 1.6 n.

AppendixC Page C.15


21.51

Time (seconds)

----. .

0.5

o

o

5,--------r-----,-----,---------,

4 ----------------- ,------- .. ------

3 ----------------- --------.-------- ----------------- ----------------

2 -- -- -- -- -- -- ---- -, -- -- -- -- -- -- -- -- -1---------1

1 :o 0.5 1 1.5 2

20 r,-------,-----r------,------,

-10 Lf-------'------'------~-----'

o 0.5 1 1.5 2

-20 Lf -'- -'-- ---' --J

o 0.5 1 1.5 2

10 rl-----.,------,-------,-------,

2

2

2

1.5

1.5

1.5

0.5

0.5

0.5 1

Time (seconds)

3 r-----,-----,------r-----,

~~~;-1 : : :

o 0.5 1 1.5 2

20 ~I---.,-----r--------,------,


Capacitor0voltage (volts)

-200

10

Line Current 0(Amps)

-100

5

TCR current(amps) 0

-50

Figure C.14: TCSC response to a two level modulation ofreactance order between 1 and 2; Xtcr = 1.6 n.

Appendix C Page C.16


2

2

2

1.5

1,5

1.5

1,5 2

Time (seconds)

0.5

0,5

0.5

0.5

'------

~~~: : :

5' : : :- 0 ' , '

o

-20' ; i ; ,

o10 " -------,----,----___,_------,

o

-10 L'-------'----------'----------'--------'

o

200 " -------,~---,----___,_---___,

lOO' i , i !

o20 r,----,-------,-----..,--------,

150 ~------------/;------ ..... ------;,,---.---------/-------------------, ,, ,, ,, ,, ,, ,, ,, ,

2

2

2

1,5

1,5

1.5

0,5

0.5

0.5 1Time (seconds)

3 ~ ;~,

::E:SJZ?:I~-1 ' , ,

o 0.5 1 1.5 2


20


-200

10


-100

5

TCRcurrent(amps) 0

-50

Figure C.15: TCSC response to a 1 Hz modulation ofreaetanee order between 1 and 2: Xter = 1.6 n.

AppendixC Page en


3 rl-----,------,--------,------, 5

2

2

2

1.5

1.5

1.5

0.5

0.5

0.5

I ----------------- ----------------

i ..J 1-_---------------'1-------14

3

-51 ; i : I

o

2o

20 ir-------,-----......,------,-------,

2

2

1.5

1.5

0

-200.5 1 1.5 2 0 0.5 1 1.5 2

10

0

0.5

0.5

, ,

.A~ ! ~ _

15frT\;~r~21 : i io 0.5 1 1.5 2

TCR current(amps) 0


20


-200

10

Line Current0(Amps)

-100


Figure C.16: TCSC response to a two level modulation ofreactance order between 1.5 and 2; Xtcr = 1.6 n.

AppendixD

APPENDIXD

PageD.]

EMTDC SIMULATION MODEL FOR POWER

OSCILLATION DAMPING STUDY

This section introduces the parameters of the EMTDC circuit that was used to

investigate power swings damping in Chapter Five.

D.l Parameters of a Detailed EMTDC Circuit

D.l.l Generator Parameters (per unit unless stated)

Ra 0.006 VTO 1.0

Xl = 0.11 8TO 0.2233 rad

X d = 1.98

Rf = 0.002

Xf = 0.1

~ 0.0212

X kd = 0.125

X mfd 0.0

X mq 1.87

Rkq = 0.029

X kq 0.257

Base voltage 220 Vrrns (Line to line)

Line Current = 7.873 Arms

Frequency 50Hz

H = 5.68144

EMTDC Simulation Model for Power Oscillation Damping Study

AppendixD PageD.2

D.l.2 Turbine Model

Number of turbines = 4

Machine 3 phase MVA = 0.003 MVA

Electrical base frequency = 50Hz

Synchronous speed 1500 rpm

Machine initial electrical speed 1 per unit

Inertia constant - turbine 1 0.37

Inertia constant - turbine 2 = 1.195



Inertia constant - generator = 1.67

Inertia constant - exciter = 0.0344

Spring constant from turbine 1 to 2 = 3339.5

Spring constant from turbine 2 to 3 = 7960.8

Spring constant from turbine 3 to 4 7357.6

Spring constant from turbine to generator = 8460.3

Spring constant from generator to exciter 22148.2

D.l.3 Transmission Line and TCSC Parameters (per phase)

= -j 2 n=

=

0.397 n

j 11.93 n

-j 2 n

j 1.2 n

XTCSC(MAX)

XTCSCCMIN)

= -j 4 n


D.1.4 Infinite Bus-Bar

Base apparent power

Base voltage

Series resistance

AppendixD PageD.3

0.003 MVA

220 VRMs (1-1)

0.001 n


AppendixD PageD.4

~J

r-"" .-./IN-., - ".. -v.-v-""'" BRK..l! 0.19315 0.019 'x'" "",., '" "'

I !""~'_.~ B' . I·I _"'~.""... I

=L....."".. ",_ I li I~ 0.019 C ,."....." "'''''''''''j''-''''''1'a ...".. ,... '''I . I-7 I I~ ,_...,_"...,--_..... ,..1-1 i El~~~r I"" ..,,!I"""·~~~OOO1(

_____ : '" Logic ... .,,---tf """ · \ 1-~- 2. ,•L.....

l

,,\0. I~""'_""''''CA A A 0

I.."...... -./IN- ...._.. , -"AA"'"'''''' ' Vro ..- v v vv-

____ l 0.'''' .". ---- I T <3{4..1.o.e~~!i~ - "'-./IN--'--"""'-v.J..".."-' 3-Phl.1 I. 0.19315 0.019 J;fuye·'''''..··......"·· ..,·....,, I

del • + 0 -./IN-"..""." "..........".-....... . J'o W 0.19315 0019 """.".., "..""".. ,_J-

••.""_ ".._,,!!t,

..~;" , ,,,.,, l!

..~;,.,,, ..,,., -,,.,",,.,,C.V.,t,9

W

"~'

lbgo

.,I~·"'''··,,······,~~j T~···"···,,··"'~~.!Q."" ,!ic:], o...""""""...~k= IIb 'W "'"",,'

~=: ,~--J~deltaW .El La~i;"''''''···'i!:;::..JL...

",lE]

~~Il:I curee "" Machlna

GO.3SEC.

I 1~ !

E;

~-"'''''''fEJ-,:{i),~ t~ RELEASE MACHINE

GO.6SEC.

~(/

[21Plot.

" .

.'Figure DJ: A detailed EMTDC circuit used tor damping power swings

EMTDC Simulation Modelfor Power Oscillation Damping Study

r~J. j_.". ;: ···.. _·'1j.:I··_··..........···.. J

-7 ! -) ~11.00382 L.J.;\ Q

·e;;-";;---l~}:rl ~

" -2 ~J-._ -; 'lc2 ~...

• @....I ..... " ,~L ,0"112 Ilcr2 / ~j-l

.f::!

*"~@'._._". ~ • __._•.~ .6 __ ,; 1c3 I=! \

j ~ Io~L_ ~-~W--€J'

~j~ ~ \

.,r

AppendixD

~u'.:, .

PageD.S

\OiIU IJ .." ....'u :t\

"'\'00

Ci9.~:~~rx ..r·"·~·.-i m.. ·..ar.. I=!."'. ..11.:._...." CO~&!

('l~l!.~. i ~

" .

. ,

Figure D2: EMI'DC model tor a three-phase TCSCcircuito[F'igure DJ

EMTDC Simulation Modelfor Fower Oscillation Damping Study

Page R.I

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References

design and implementation of a thyristor controlled …

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