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Doctoral Thesis

Use of FACTS Devices for Power Flow Control and Damping ofOscillations in Power Systems

Author(s): Sadikovic, Rusejla

Publication Date: 2006

Permanent Link: https://doi.org/10.3929/ethz-a-005274771

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Diss. ETII No. 16707

Use of FACTS Devices for

Power Flow Control and

Damping of Oscillations in

Power Systems

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY

ZURICH

for the degree of

Doctor of Technical Sciences

presented byRUSE.)LA SADIKOVIC

Master of Science, Faculty of Electrical Engineering,

University of Tuzla

bom October 144\ 1969

in Tuzla, Bosna and Hercegovina

accepted on the recommendation of

Prof. Dr. Goran Andersson, examiner

Prof. Dr. Caludio A. Cahizares, co-cxaminer

2006

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Acknowledgments

This dissertation presents the results of my research done at the Power

system Laboratory of the Swiss Federal Institute of Technology (ETH)

during the years 2002 - 2004.

First of all I would like to express my deep gratitude to my advLsoi

Prof. Goran Andersson for giving me the opportunity to work on this

project. His valuable suggestions and his encouragement and patiencehave boon a big help for me over the last for years,

I am very grateful to Dr. Petr Korba four his skilled guidance, valuable

comments, stimulating discussions and support throughout this project.

Special thanks go to Prof. Claudio A. Cahizares for accepting to co-

referee this thesis.

I also would like to thank my colleagues at the laboratory for the en¬

joyable discussions and friendly atmosphere. I particularly thank my

oflice-mates Dr. Andrei Karpatchev and Mirjana Milosevic for the re¬

laxed work afmospheie in our ollice. I am very giatetul as well to Maria

Lourdes Steiner-Igcasenza for proofreading this thesis.

Finally, I would like to extend my deepest gratitude and personal thanks

to those closest to me. In particular, I would like to thank my husband

Adrian, my son Berin and my parents for their support, encouragement

and understanding.

Rusejla Sadikovic

3

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Abstract

Due to the deregulation of the electrical market, difficulty in acquiring

rights-of-way to build new transmission lines, and steady increase in

power demand, maintaining power system stability becomes a difficult

and very challenging problem. In large, interconnected power systems,

power system damping is often reduced, leading to lightly damped elec¬

tromechanical modes of oscillations. Implementation of new equipment

consisting high power electronics based technologies such as Flexible

Alternating Current Transmission Systems (FACTS) and proper con¬

troller design become essential for improvement of operation and con¬

trol of power systems.

The aim of this dissertation is to examine the ability of FACTS de-

vkes. such as Thyristor Controlled Series Capacitor (TCSC). Unified

Power Flow Controller (UPFC) and Static VAr Compensator (SVC)for power flow control and damping of electromechanical oscillations in

a power system. A power flow control strategy is based on linearization

of active and reactive power flows around an operating point. A control

strategy for damping of oscillations, including several FACTS devices

and PSSs, is based on different approaches, both off-line and on-line,

e.g. residue based method, pole shifting method and genetic algorithms.The robustness of each approach is discussed. One part of this disser¬

tation deals with location of FACTS devices considering multiple tasks,

powei flow control and damping of oscillations.

The results of the case studies demonstrate advantages and disadvan¬

tages of the considered control approaches.

5

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Kurzfassung

Als Folge der Liberalisierung vieler Elektrizitätsmärkte ergeben sich für

den Netzbelrieb zusätzliche anspruchsvolle Aufgaben. Die Erschwer¬

nis des Baus zusätzlicher Uberfragungsleitungen aufgrund langwieriger

Bewilligungsverfahrcn sowie ein starkes Wachstum der Nachfrage nach

elektrischer Energie stellen an die Netzbetreiber hohe Ansprüche bezü¬

glich der Gewährleistung der Systemstabilität. In grossen, stark ver¬

machten Nefzstrukturen werden Leistungspendelungen nur bedingt ge¬

dämpft und können zu erheblichen elektromechanischen Schwingungeiiführen. Aus diesem Grund ist die Anwendung neuer Kontrollmecha-

nismen basierend auf leisUuigselektronisehen Technologien wie Flexible

Alternating Current Transmission Systems (FACTS) hinsichtlich eines

sicheren Netzbefriebs notwendig.

Das Ziel dieser Dissertation ist die Untersuchung der Eignung von FACTS

Geräten, wie Thyristor Controlled Series Capacitor (TCSC), Unified

Power Flow Controller (UPFC) sowie Static VAr Compensator (SVC) in

Bezug auf Lastfiuss-Steuerung sowie Dämpfung von Leistungspendehui-

gen. Es wird ein auf der Lincarisicrung des Wirk- und Blindleistungs-

11 usses basierendes Verfahren zur Lastfluss-Regehmg vorgestellt, welches

die Dämpfung von Leistuiigspendelungen mittels FACTS Geräten und

PSS's beinhaltet. Dabei setzt sich dieses Verfahren aus den folgendenoff- und on-line Methoden zusammen: Der Residuen basierten Meth¬

ode, der Pol-Verschiebuiigsmethode und den genetischen Algorithmen.

Eiläuterungen bezüglich der Robustheit dieser Methoden werden eben¬

falls diskutiert. Ein weiterer Bestandteil dieser Dissertation setzt sich

mit der Bestimmung des Einsatzortes von FACTS-Geräten auseinander.

Als Resultat der untersuchten Fallstudien werden sowohl Vor- als auch

7

8 Kurzfassung

Nachteile der betrachteten Methoden zur Lastftuss-Steuerung aufgezeigt.

Contents

1 Introduction 13

1.1 Thesis outline 17

1.2 Contributions 17

1.3 List of Publications 18

2 Modeling of FACTS devices 10

2.1 Thyiistoi Controlled Series Capacitor 19

2.2 Unified Power Flow Controller 23

2.3 Static VAr Compensator 30

3 Use of FACTS Devices for Damping of Power System

Oscillations 33

3.1 Introduction 33

3.2 Modal Analysis 34

3.3 FACTS POD Controller Design 38

3.4 Case Studies 40

3.4.1 Design of TCSC POD Controller 41

3.4.2 Design of UPFC POD Controller 45

3.4.3 Design of SVC POD Controller 5J

3.5 Summary 53

9

10 Contents

4 On the Location of the TSCS 55

4.1 Dynamic Criterion 56

4.2 Static Criterion 56

4.3 Case Study 58

4.4 Summary 62

5 Self-Tuning Controllers 65

5.1 Adaptive Model Identification 66

5.2 Residue Based Adaptive Control 69

5.3 Pole Shifting Adaptive Control 76

5.4 Summary 85

6 Coordinated Tuning of PSS and FACTS POD

Controllers 87

6.1 Genetic Algorithms 88

6.1.1 Selection 88

6.1.2 Crossover 89

6.1.3 Mutation 89

6.2 PSS and FACTS POD Controller design 90

6.3 Case study 91

6.3.1 Case Study with the TCSC - Case Study I. . .

94

6.3.2 Case Study with the SVC -Case Study II. . .

101

6.3.3 Case Study with the TCSC and the SVC - Case

Study III 106

6.4 Summary Ill

Contents 11

7 Concluding Remarks 113

A IEEE 39 Bus Test System Data 117

B IEEE 68 Bus Test System Data 123

C IEEE Sensitivity Analysis 131

Bibliography 135

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v^XlcLpTJGr X

Introduction

Modern bulk power systems cover large geographic areas, e.g. the Eu¬

ropean UCTE system and the North American svstems. antf have a

large number of load buses and generators. Additionally, available gen¬

erating plants are often not situated near load centers and powei must

consequently be transmitted ovei long distances. To meet the load and

electiic maiket demands, new lines should be added to the system, but

due to environmental reasons, the installation of electric power tians-

mission lines must often be restricted. Hence, the utilities are forced to

rely on alreadv existing infra-structure instead of building new trans¬

mission lines. In order to maximize the efficiency of generation, trans¬

mission and distribution of electric power, the transmission netwoiks

are very often pushed to their physical limits, where outage of lines or

other equipment could result in the rapid failure of the entire system.

With such increasing stress on the existing transmission lines the use

of Flexible AC Transmission Systems (FACTS) devices becomes an im¬

portant and effective option.

FACTS technologies offer competitive solutions to today's power sys¬

tems in terms of increased power flow transfer capability, enhancingcontinuous control over the voltage profile, improving system damping,

minimizing losses, etc. FACTS technology consists of high power elec¬

tronics based equipment with its real-time operating control [1, 2, 6].There are two groups of FACT'S controllers based on different techni¬

cal approaches, both lesulting in controllers able to solve transmission

13

14 Chapter 1. Introduction

problems.

The first group employs reactive impedances or tap-changing trans¬

formers with thyristor switches as controlled elements; the second group

employs self-commutated voltage-sourced switching converters. The so¬

phisticate control and fast response are common for both groups. The

Static VAr Compensator (SVC), Thyristor Controlled Series Capacitor

(TCSC) and Phase Shifter belong to the first group of controllers while

Static Synchronous Compensators (STATCOM), Static SynchronousSeries Compensators (SSSC), Unified Power Flow Controllers (UPFC)and Interline Power Flow Controllers (IPFC) belong to the other group.

The power system may be thought of as a large, interconnected non¬

linear system with many lightly damped electromechanical modes of

oscillation. If the damping of these modes becomes too small, or even

positive, it can impose severe constraints on the system's operation. It

is thus important to bo able to determine the nature of those modes,

find stability limits and in many cases use controls to prevent insta¬

bility The poorly damped low frequency electromechanical oscillations

occur due to inadequate damping torque in some generators, causing

both local-mode oscillations (1 Hz to 2 Hz) and inter-area oscillations

(0.1 Hz to 1 Hz) [19]. The traditional approach employs power sys¬

tem stabilizers (PSS) on generator excitation control systems in order

to damp those oscillations. PSSs are effective but they aie usuall) de¬

signed for damping local modes and in large power systems they may

not provide enough damping for inter-area modes. Hence, in order to

improve damping of these modes, it is of interest to study FACTS power

oscillation damping (POD) controllers [17]. In large power systems the

number of inter-area modes is usually larger than the number of control

devices available [3]. Generally, damping of power system oscillations

is not the primary reason of placing FACTS devices in the power sys¬

tem, but rather power flow control [6, 7]. However, when installed,

supplementary control lows can be applied to existing devices in order

to improve damping, as well as satisfy the primary requirements of the

device.

One of the very important questions in the practical application of con¬

troller installation is whether to use local or remote input signals (oftenreferred to as global signals) as feedback signals. There are different

approaches, [3, 13, 15, 17]. The advantages of the local signals are their

15

simplicity and reliability. On the other hand, they might not give ade¬

quate observability of some of the significant inter-area modes [4]. The

advantage of the global signals is that they contain infoimation about

the overall network dynamics in contrast to the local signals. But from

an economic viewpoint, the implementation of a control scheme using

global signals may be more cost effective than installing new contiol

devices [3]. Since remote signals are often transmitted by the exist¬

ing communication channels, time delay is involved, which could be an

impediment. In this thesis, the local signal is used as the controller's

feedback signal.

A conventional damping control design considers a single operating con¬

dition of the system. In this kind of controller the feedback is fixed and

amplifies the control erroi, which in turn determines the value of the

input signal v (controller output) to the system. The way in which the

error is processed is the same for all operating conditions. In Chaptei 3.

a conventional lead-lag controller designed for nominal operating point

is piesonted and applied ou three different types of FACTS devices

This conti oiler is simple, but works often only within a limited opeiat-

ing range. In case of contingencies, changed operating conditions can

cause poorly damped or even unstable oscillations since the controller

parameters yielding satisfactory damping for one operating condition

may no longer provide sufficient damping for another one. In order

to address this issue, reseaicheis, over the years, have proposed différ¬

ent approaches for adaptive control structures for PSSs as well as for

FACTS devices. Some of them are reviewed in Chaptei 5.

The primary idea is to oveicome the problems that might be encoun¬

tered by conventionally tuned controllers with the changing of operating

conditions. Dealing with an adaptive on-line tuning, the identification

of the static and dynamic characteristics of the system plays an impor¬

tant role togethei with the control strategy itself. In Chaptei 5, on-line

identification based on the automatic detection of oscillations in power

systems using dynamic data such as currents, voltages and angle dif¬

ferences measured across transmission lines, provided on-line by phasormeasurement units, is presented [5]. The on-line collected measured

data are subjected to a further evaluation with the objective to esti¬

mate dominant modes (frequencies and damping) dining any operation

of the power system or to give reduced transfer function of the unknown

power system.


Based on two approaches of on-line identification of the power system, a

control strategy for on-line tuning of the POD controllers is developed.

The first approach is based on modal analysis, i.e. residue method,

and the second employs self-tuning controllers (STC) based on the pole

shifting method. The self-tuning controller is based on the idea of sep¬

arating the estimation of unknown parameters from the design of the

optimal controller, [29].

Although controllers tuned by the conventional design approach aie

simple, lack of robustness of that kind of controllers is not the only

problem encountered. Conventional procedures become time consum¬

ing and difficult to implement for cases in which:

• there is a significant number of PSSs and FACTS POD controllers

t.o be coordinated,

• coordination must be conducted for a variety of operating conditions

and

• certain performance specifications have to be satisfied.

As a consequence of the presence of different types of the stabilizers in

the system, e.g. the PSSs and FACTS POD controllers, the undesired

and detrimental interactions between them may occur [34]. To avoid

this a simultaneous optimization and coordination of the parameter set¬

tings of both stabilizers is required in order to enhance overall system

stability and minimizing possible adverse interactions. A solution to

this problem is the use1 of Genetic Algorithms (GA) methodology, and

this has been investigated in Chapter 6.

In [38] and [39]. PSS tuning by means of GA is presented. These papers

investigate the use of genetic algorithms to design robust PSS, in which

several operating conditions and system configurations are simultane¬

ously considered in the design process. In [38], simultaneous tuning of

nine PSSs in 14 operating conditions for the New England power sys¬

tem was performed. The objective function used for GA optimization

was the sum of the damping ratios for all eigenvalues in all operating

conditions. Two additional objective functions that allowed some eigen¬

values to be shifted to the left-hand side of the complex plane or to a

1.1. Thesis outline 17

wedge-shape sector in the complex plane were further investigated in

[39]. In [40], the authors propose the use of advanced techniques in

GA for the optimal tuning of PSSs again for different operating condi¬

tions. The results obtained in these papers proved that GA could be

a powerful tool for robust PSS damping controller design. Considering

FACTS POD tuning, the GA approach is used in [36] in order to design

SVC and TCSC clamping controllers to enhance damping of inter-area

modes in a three-area six-machine system. In Chapter 6 of this thesis,

the GA approach is used as well, as a tool for design of multiple! POD

controllers in a large, realistic system.

1.1 Thesis outline

Following the Introduction, Chapter 2 describes the injection models of

the FACTS devices, and their use in power flow control.

Chapter 3 gives an overview of the conventional POD controller de¬

sign and their application on the TCSC. UPFC and SVC.

In Chapter 4. an approach for the optimal location of FACTS devices

combining the static (for optimal location of the power flow controller)and the dynamic criteria (for optimal location of the damping controller)

is presented.

The concept of one-line tuning of the FACTS POD controllers is pre¬

sented in Chapter 5.

In Chapter 6 a method for simultaneous coordinated tuning of the

FACTS POD controller and the PSS controllers is presented.

Chapter 7 summarizes the findings in this work with some suggestions

for future; research directions.

1.2 Contributions

The main contributions of this thesis can be summarized as:


• Application of POD controller to Unified Power Flow Controllers

(UPFC') based on residue approach, considering different local sig¬

nals as feedback signals.

• Proposal of an approach for location of FACTS devices for multi¬

ple control objectives, considering static and dynamic criteria.

• Application of self-tuning controllers based on residue method and

on pole shifting method.

• Application of genetic algorithm methodology to coordination of

power system controllers for robust damping of electromechanical

oscillations.

1.3 List of publications

The work presented in this thesis has been reported by the following

publications:

1. R. Sadikovic and G. Andersson, Power Flow Control by SensitivityBased Facts Controllers, IPEC 2003, Singapore, November 2003.

2. R. Sadikovic, G. Andersson and P. Korba. A Power Flow Control

Strategy for FACTS Devices, WAV, 2004, Spain, June 2004.

3. R. Sadikovic, P. Korba and O. Andersson, Application of FACTS

Devices for Damping of Power System Oscillations, IEEE Pow-

erTech 2005, Russia, June 2005.

4. R. Sadikovic, G. Andersson and P. Korba, Method for Location ofFACTS for Multiple Control Objectives, X SEPOPE, Brasil, May

2006.

5. R. Sadikovic, P. Korba and G. Andersson, Self-tuning Controller

for Damping of Power System Oscillations with FACTS Devices,

IEEE PES General Meeting. Canada, .lune 2006.

6. R. Sadikovic, G. Andersson and P. Korba, Damping Controller

Design for Power System Oscillations, Intelligent Automation &

Soft Computing Journal. Vol. 12, No. 1, pp: 51-62, 2006.

Chapter 2

Modelling of FACTS

Devices

Flexible AC transmission systems (FACTS) devices are installed in

power systems to increase the power flow transfer capability of the trans¬

mission systems, to enhance continuous control over the voltage profile

and/or to damp power system oscillations [6, 7]. The ability to control

power rapidly can increase stability margins as well as the damping of

the power system, to minimize losses, to work within the thermal limits

range, etc.

In this chapter, injection models of the Thyristor Controlled Series Ca¬

pacitor (TCSC), Unified Power Flow Controller (UPFC) and Static Var

Condensât or (SVC), used in this dissertation, with appropriate controls,

are presented.

2.1 Thyristor Controlled Series Capacitor

Model

A Thyristor Controlled Series Capacitor (TCSC) configuration consists

of a series capacitor bank, C, in parallel with a fhyristor-controlled re¬

actor, L, as shown in Figure 2.1. This simple model utilizes the' concept

19

20 Chapter 2. Modelling of FACTS Devices

of a variable series reactance. The series reactance is adjusted automat¬

ically, within limits, to keep the specified amount of active power flow

across the line. There aie the certain values of inductive and capacitivereactance which cause steady-state resonance. The TCSC can be con¬

tinuously controlled either in capacitive or in inductive area, avoiding

the steady-state resonant region. The details about the modelling of

the TCSC can be found in [6, 7].

The control action of the TCSC is usually expressed in terms of its

percentage of the compensation, kc, defined as:

k,3";

100% (2.1)

where, 2'/ is the line reactance and x(. is the effective capacitive reac¬

tance provided by TCSC.

c

L -^

Figure 2.1: Basic TCSC topology

The TCSC is assumed to be connected between buses i and j in a trans¬

mission line as shown in Figure 2.2, whore the TCSC is presented sim¬

plified like a continuously controllable reactance (capacitive) [11].

V,

-if-n+Jxi

v,

-V.+

Figure 2.2: TCSC located in a transmission line

2.1. Thyristor Controlled Series Capacitor Model 21

From Figure 2.2 the line current /,„, is given by :

ti+j{ti-jc)

The influence of the capacitor is equivalent to a voltage source

depends on voltages V, and Vr The; current injection model

TCSC is obtained by replacing the voltage across the TCSC

equivalent current source J, as seen in Figure 2.3. In Figure 2.2,

—jxrl^- and from Figure 2.3 follows

IsVf jXi 1

Hl,

ri+jx, ri+jxi

Current injections into nodes i and j are

(2.2)

which

of the

by an

Vs =

(2.3)

/„n + à/

y

Figure 2.3: Replacement of a voltage source by a current source

V:rfrjxi

Vi

© -•« 'y ©

Figure 2.4: Current injection model for a TCSC

/äS3

-J?l v, - v,

'7 t j-Ti n + j(x, ~xr)

Isi — ~F$j

(2.4)

(2.5)


and therefore; the appropriate current injection model of the TCSC can

be presented as shown in Figure 2.4.

max âamp

Figure 2.5: General form of the TCSC control system

The general form of the TCSC control system used in this thesis is

shown in Figure 2.5, where the Control Strategy block represents the

design method for power flow controller based on linearization of power

flow equations around an operating point. The output of the block is

the change of the compensation degiee given by:

AAv. = AP(rf + (a-, - xc)'2)/{2(V? - V%V, cos0„)(l - kc)...

-rf(V,Vj coxO.j)- + VtV, hin0„(l " Ml

whore AP = Prfj - P is the input in the block.

(2.0)

K,,i is the proportional part and Trd is the integral time constant of

the TCSC PI controller. The time constant T approximates delay due

to the main circuit characteristics and control systems. C,],ul,p is the

signal from TCSC damping controller, explained in next chaptei. P is

the TCSC line active power and Prf,f is the line active power to be main¬

tained bv TCSC AA;m,n and AAâr are the limits on the compensation

degree changes.

2.2. Unified Power Flow Controller 23

2.2 Unified Power Flow Controller

The UPFC can provide simultaneous control of all basic power system

parameters (transmission voltage, impedance and phase angle). The

controller can fulfill functions of reactive shunt compensation, series

compensation and phase shifting, meeting multiple control objectives.From a functional perspective, the objectives are met by applying a DC

capacitor, shunt connected transformer and voltage source conveiter in

parallel branch and dc capacitor, voltage source convenor and series

injected transformer in the series branch.

The two voltage source converters are a so called "back to back" AC

to DC voltage source converters operated from a common DC link ca¬

pacitor, Figure 2.6. The shunt converter is primarily used to provideactive power demand of the series converter through the common DC

link. Converter 1 can also generate or absorb reactive power, if it is

desired, and thereby provides independent shunt reactive compensation

for the line. Converter 2 provides the main function of the UPFC' by in¬

jecting a voltage with controllable magnitude and phase angle in series

with the line, Figure 2.7. The reactance .ï,s describes the reactance seen

from terminals of the series transformer and is equal to (in p.u. base on

system voltage and base power)

./;,- = Tkrl„T(SB/Ss) (2.7)

where j> denotes the series transformer reactance, r,naj- the maximum

per unit value of injected voltage magnitude, Sß the system base power,

and Ss the nominal rating power of the series converter.

The UPFC injection mode1! is derived enabling three parameters to be si¬

multaneously controlled [8], They are namely the shunt reactive power,

Qmnvi jand the magnitude, r, and the angle, 7, of injected series voltage

Vse. Figure 2,7 shows the circuit representation of a UPFC. where the

series connected voltage source is modelled by an ideal series voltagewhich is controllable in magnitude and phase, and the shunt converter

is modelled as an ideal shunt current source. In Figure 2.7,

7,,t = 7, + 7,= Vt+Jlç)*'0' (2.h)

where It is the current, in phase with V, and Iq is the current in quadra¬

ture with V,. In Figure 2.8 the voltage source V„(, is replaced by the


shunt side

COr-

series

transformer

shunt

transformer

series side

1fj}

Converter 1

I[ X

Figure 2.6; Implementation of the UPFC by back-to-back voltage

source converters

A-A

7 "se Jxs

Qsh

Psc Qse

Figure 2.7. The UPFC electric eiicuit airangement

current source /",„, = - jb„V/.,, in parallel with x,. The active power

VJ

Figure 2.8: Transformed series voltage source

supplied by the shunt current source can be calculated from

2.2. Unified Powei Flow Controller 25

= -VJt (2 9)

With the UPFC losses neglected,

P(. ONVl = PCGN\1 (<2 HO

The appaicnt powei supplied by the series voltage source converter is

c ale ulated from

Sconvi = V*tlsf

Vl' Vj| (2 11)

Active and re.utive powei supplied by Conveitei 2 àrQ distinguished as

Pconvz = 'KVlVl biu(0, - Ô, + 7) - rb,V,2 sin 7 (2 U)

Q< ONV2= rb,VlV)iob(9l - 9, + 7) + ;^V;2cos7 (2 13)

Substitution of (2 9) and (2 12) into (2 10) gives

I,- ib^V^miO, - 0j + -)) + rb,V, sm 7 (2 14)

rl he c lurent of the shunt source is then given by

/,,, = {It+jlq)t>°>= (-r6sV;sin(0,7 I 7) 1 rfc,V,sin7 I jl,)e3°' (2 lr0

Fiom Tiguie 2 8 the bus <unent mjeetions <an be defined as

(2 16)

(2 17)

wheie

(2 18)

/, = J <*h"

*inj

h =*m?

1trl'i

= -jbsV,c

= -)b,rV,eJ1

Substituting (2 15) and (2 18) into (2 16) and (2 17) give-s

7t = {-eb,Vq sm(0„ + 7) + 1 b<yt sm.7 + jP,)cje t

+jrb,VlC(ô'i'l)(2 19)


I, jbsV,e'i0'+^ (2.20)

where Iq is an independently controlled variable;, representing a shunt

reactive source. Based on (2.19) and (2.19), the cuirent injection model

can be presented as in Figure 2.9. Besides the expressions for current

V,-

© ',«

JxsJ

7 ©

Figure 2.9: UPFC current injection model

bus injection, due to the control purposes, it is very useful to have

expressions for power flows from both sides of the UPFC injection model

defined. At the UPFC shunt side;, the active and reactive power flows

are given as

Ptl = -rb!V,Vjùn(9,j+f)-bf,V,Vlsm(017) (2.21)

Q,i - -rb.y* cos 1+Qwlivl- bX + WVjL-mO,, (2.22)

whereas at the series side they are;

Pyi - rb„V,Vj t,m{6,j + 7) + b,VtV, sin0,7 (2.23)

Q,2 - rbMV, ca»(0,j + y) <\V? + b„V,V} cos0,3 (2.24)

As can be seen from previous equations, the UPFC current injectionmodel is defined by the constant series branch susccptance, hs. which

is included in the; system bus admittance matrix, and the bus current

injections. 1, and lj. If there is a control objective to be achieved, the

bus current injection are modified through changes of the UPFC con¬

trol parameters r, 7 and lq. In the case of power flow control, i.e. the

third control variable;, Iq, is inactive, so the UPFC performs the func¬

tion of the series compensation, the control objective is to niaintain the

power of controlled line at the expected value. That means the UPFC

should operate in the automatic power flow control mode keeping the

active and reactive line power flow at the specified values Prej and QTrj-


The control objective can be achieved by linearizing the line power flow

equations, (2.23) and (2.24), around an operating point [10]. Figure 2.10

shows the general form of the UPFC control system used in this thesis.

The linearization results with the Control Strategy block in Figure 2.10.

The outputs of the block are the changes of the control variables Ar

and A7, given by

A)—:

A7 =

APsm(0%3 + 7) + A<3cos(fl,7 + 7)__

APcos(9,j +7) - AQsm{9,3 +7)

rbKV,V]

(2.25)

(2.2G)

where AP = P,Ff ~ P and AQ = Qref — Q are the inputs in the block.

In this thesis it is assumed that the third control variable J.q is inactive,

so the UPFC performs the function of the series compensation. K^ and

Kr are the proportional parts and T7 and Tr are the integral time con¬

stants of the UPFC PI controllers. Cciampj and Cdr,mpr are the signalsfrom the UPFC damping controllers, explained in the next chapter.

^darnpy I

+ jhi -\ r

UPFC

. \

hjr \_

Power

network 1Qi

P \ / Q

Fref Qref

AP

J«LControl

strategy

Ay

Ar

Figure 2.10: General form of the UPFC control system

Operation of the UPFC demands proper power rating of the series and

shunt branches. The rating should enable the UPFC to archive pre¬

defined power flow objective. The flow chart of Figure 2.11 shows an

algorithm for UPFC rating [8],


The algorithm starts with definition of the series transformer short cir¬

cuit reactance, xj., and the system base power, Sb- Then, the; initial

estimation is given for the series converter rating power, A'.<j, and the

maximum magnitude of the injected series voltage, r,nilJ. In the next

step can be determined the effective reactance of the UPFC seen fioin

the terminals of the series transformer. (x$).

Load flows are; compute«! by changing the angle 7 between 0° and 360°

in steps of 10°, with the magnitude r kept at its maximum value1 rmnr.

Such rotational change of the UPFC parameter influences active and

reactive1 power flows in the system. The largest impact is given to the

power flowing though the line with UPFC installed. The control objec¬tive is to maintain the active and reactive; power flow whose prescribedvalue's should be achieved within the UPFC steady state operation.

Then, the power flow procedure is performed to check whether the pre¬

defined objective is achieved satisfactory with estimated parameters, If

the load flow requirements are not satisfied at any operating points, it is

necessary to go one stop back, estimate1 again Ss and rmar, and performnew rotational change; of the UPFC within the power flow procedure.This loop is performed until the load flow requirements are completelyfulfilled. In addition, the active, reactive and apparent power of the

series converter are calculated for each step change in the; angle 7.

With the power flow requirements fulfilled and the series converter pow¬

ers calculated, it lias to be checked whether the maximum value of the;

series converter apparent power max Sri,„„2. is larger than the initially

estimated power Ss, If max SconU2 is not larger than the power 65, it is

necessary to check whether the power S$ is at an acceptable1 minimum

level. If not, the value of Ss is reduced and the loop starts again. The

acceptable minimum is achieved when two consecutive iterations do not

diifer more than the pre-established tolerance

When the power S$ is minimized, the load flow proceelure is performeelwith smaller step of rotational change of the angle; 7(1°), in order to

get maximum absolute value of the series/shunt converter active power,

max !-P,-„„„i |. The value given by max \PCOnv\ \ is considered to be min¬

imum criterion for dimensioning shunt converter rating power, whereas

the power Ss represents series converter rating power as a function of

the maximum magnitude rmaj.


[ ÜLHNE xj., SB|

[ 'mu,lnl1'»1 SS J

CALCULATE

PhKl-OKM LOAU 1-LÜW

V [0". 10°. 360"]

ULMLLEU?/ (INCRfcASfc Ss)

CALCULAIL

^conv2> ^t.unv2 Stortv2

DECREASE is

(INCREASE S,)

I'ERhORM LOADhLOW

7 " [0".10° 360"]

CAl-CUlAll- max Hconv|

tMJTPUT SS, SCOnvl,'ma*

Figure 2.11: Algorithm for optimal rating of the UPFC, [8]


2.3 Static VAr Compensator

The Static VAr Compensator (SVC) is a shunt connected device whose

main functionality is to regulate the; voltage at a chosen bus by suit¬

able control of its equivalent reactance. A basic topology consists of a

series capacitor bank, C, in parallel with a thyristor-controlled reactor,

L, as shown in Figure 2.12. In practice the SVC can be seen as an

adjustable reactance [1]. that can perform both inductive and capaci¬

tive compensation. The dc;tails about the modelling of the SVC can be

found in [fi, 7]. The; SVC connected at node j is shown in Figure 2.13.

c^z

Figure 2.12: Basic SVC topology

Figure 2.14 shows the injection model of the SVC, where IJiUC is the

complex SVC injected current at node j, V\ and V3 are the complex

voltages at nodes i and j. The reactive power injection in node j is

given bv:

Q:, = -VfDsvc (2.27)

where, Bayc = Be Bj„ Br and Bl are the susceptance of the fixed

capacitor and thyristor controlled reactor, respectively. The reactive

power can be transferred into injected current at bus j given by

jVjBs (2.28)

Figure 2.15 shows the SVC control block diagram where V) is the voltage

magnitude at the SVC terminal, V,,,; is the voltage to be maintained by

SVC. K is the1 gain of the controller, T is the time constant associated

2.3. Static VAr Compensator 31

with the SVC control action, Aß,„m and ABHla, denote the limits to

the change of the; SVC susceptance and C,ia„ip is the signal from the

damping controller.

n +Piv,j

ßsvcwc =z£/

Figure 2.13: Representation of a SVC

V;'1 + /*/

V;

1®

Figure 2,14: Current injection model of a SVC


_n J'j

SVC ryi[Ui

' ' \Power

networkA-"min

V,'iS AK> K AB

J *

1+sT

Vn-V

Figure 2.15: General form of the SVC control system

Chapter 3

Use of FACTS Devices

for Damping of Power

System Oscillations

3.1 Introduction

The power system may be thought of as a large, interconnected non¬

linear system with many lightly damped electromechanical modes of

oscillation. If the damping of these modes becomes too small or nega¬

tive, it can impose severe constraints on the system's operation. It is

thus important to be able to determine their nature, find stability limits

and in many cases use controls to prevent their instability. Electrome¬

chanical oscillations can be1 broadly classified into two main groups:

• Tnter — area oscillations

• Local oscillations

Inter-area oscillations are observed when a group of machines in one1

area swings against another group in another area normally with a fre¬

quency below 1 H'/,. The study the inter-area modes is quite complicatedsince it requires detailed representation of the entire interconnected sys-

33

31 Chapter 3. Use of FACTS Devices for Damping...

tem and inter-area modes are influenced by several states of larger areas

of the power network.

Local oscillations are observed when one particular plant swings against

the rest of the system or several generators at frequencies of typically 1

ITz to 2 Hz [12].

With the power industry moving toward deregulation, long-distance

power transfers are1 steadily increasing, outpacing the addition of new

transmission facilities and causing the inter-area oscillations to become

more lightly damped [11]. During the last decade, FACTS devices have

been employed to damp power system oscillations [13. 14, 15. 16]. Some¬

times, these controllers are placed in the power system for some other

reasons (to improve the voltage stability or to control power flow) [fi, 7],then to damp power oscillations. However, when installed, supplemen¬

tary control can be applied to existing controllers in order to improve

damping, as well as satisfy the primary requirements of the device. POD

contiol can be applied as well through the power system stabilizer (PSS)on generator excitation control systems. PSSs are effective1 but they are

usually designed for damping of local electromechanical oscillations and

in large power systems timing all of them might be very difficult. In

this chapter. POD control has been applied to three FACTS devices,

TCSC, UPFC and SVC in order to damp inter-area oscillations. The

main focus is on the TCSC, UPFC and SVC influence on powei os¬

cillation damping when a large disturbance is applied. The controller

design method utilizes the residue approach [15. 16. 17]. The presented

approach solves the optimal location of the FACTS devices, as well as

the selection of the propel feedback signals.

3.2 Modal Analysis

In order to identify oscillatory modes of a multi-machine system, the

linearized system model including PSS and FACTS devices system can

be used by

A.f = AA:r -I- BAv

Ay = CAx + DAv (3.1)

where

Ax is the; state vector of length equal to the; numbers of states n

3.2. Modal Analysis 35

Ay is the output vector of length m

Au is the input vector of length r

A is the n by n state matrix

B is the control or input matrix of size; n by r

C is the; output matrix of size; m by n

D is the; feed forward matrix of dimensions m by r.

The; eciuation

det(XI - A) = 0 (3.2)

is referred to as the; characteristic equation of matrix A and the values

of A, which satisfy the; eliaracteristic equation, are the eigenvalues of

matrix A. Because the matrix A is a n by 7i matrix, it ha« n solutions

of eigenvalues

A = AL,A2,...An (3.3)

with assumption that A£ =/= \j, i =/= j.

For every eigenvalue A,, there is an eigenvector <j>t which satisfies Equa-t ion

M = A,0, (3.4)

é, is called the right eigenvector of the state matrix A associated with

the eigenvalue A,. Each right eigenvector is a column vector with the

length equal to the number of the states.

Left eigenvector associated with the eigenvalue A, is the1 n-row vector

which satisfies

ipiA = \,il), (3.5)

The right eigenvector describes how each mode of oscillation is dis¬

tributed among the system states. In other words, it indicates on which

system variables the mode is more observable1. The right eigenvector is

called mode shape.

The left eigenvector, together with the system's initial state, eietennines

the amplitude of the mode. A left eigenvector carries mode controlla¬

bility information.

Numerous indices, such as participation factors, transfer function residues

and mode sensitivities can be calculated from eigenvectors. Those; in¬

dices are very useful in system analysis and controller design.


Foi a paitkulai eigenvalue A, = er, | ju,, the leal part of the eigen¬

value gives the damping, and the imaginary part gives the fiequenty of

oscillation I he lelative damping ratio is given by

£ - ^^ (3 0)

The oscillatoiy modes having damping ratio less than 3% aie said to

be critical [18] When designing damping controls one has to take caie

about margin due to uncertainties oi disturbances Hence the damp¬

ing îatio of at least 5% should be the objective of the contiol design [19]

Participation factors

J he sensitivity of a paiticular eigenvalue A, to the changes m the diag¬

onal elements oi the state matiix A is given [18], by

r)A,Pk,

4'h,4>k, (-Î 7)

wheie 4>hi ^ 'he A"1 element m the ;"' row of the the left tigeuvec toi </>,,

and 0i,i ^ the klh element in the ?"' eolunin of the right eigenvtctoi <j>,

Ihe paitie lpation fatten p*, is a measure of the relative participation of

the kth state vanable in the ith mode, and vice veisa Ihe paiticipation

faetoi is used in this thesis foi purpose of conventional tuning of PSSs

in Chaptei 6

Controllability and observability

In order to modify a selected oscillatoiy mode by a feedback contiollei

the chosen input of the controller must influence the behavioi of that

mode and the1 mode must also be visible m the chosen feedback sig

nal l e the behavior of that mode should be leffected m the feedback

signal The mevisuies foi those two piopeities aie the modal conti ol-

labihty and observability lespertivt ly The modal eontiollabihty and

modal observability matiices aie defined, [181 by

B' - * XB

C = C* (is)

Ihe mode is not controllable if the corresponding low oi the matnx B'

is a /eio vet toi, and the mode is not observable il the eoiuspouelmg

3.2. Modal Analysis 37

column of the matrix C" is a zero vc;ctor. If a mode is either not con¬

trollable or not observable, feedback between the output and the input

will have- no effect on the mode.

Residues

Considering (3.1) with single input, and single output (SISO) and as¬

suming D = 0. the open loop transfer function of the system can be

obtained by

v '

Au{s)

- C(hI - A)~lB (3.9)

The transfer function G(s) can be expanded in partial fractions of the1

Laplace transform of y in terms of C and B matrices and the1 light and

left eigenvectors as

*w - tv^N

£R'

(3.10)A,)

Each term in the denominator, R,, of the summation is a scalar called

residue. The residue R{ of a particular mode i gives the measure of

that mode's sensitivity to a feedback between the output y and the

input u: it is the product of the mode's observability and controllability.

Figure 3.1 shows a system C(s) equipped with a feedback control Il(s).

When applying the feedback control, eigenvalues of the initial system

C(s) are changed. It can be proven, [17], that when the; feedback control

is applied, the shift of an eigenvalue can be; calculated by

A\l = R,H(\,) (3.11)

It can be observed from (3.11) that the shift of the eigenvalue caused

by the controller is proportional to the; magnitude of the conespondingresidue. For a certain mode, the same type of feedback contiol jTA(.s-),

regardless of its structure and parameters, can be; tested at different

locations. For the mode of the interest, residues at all locations have

to be calculated. The largest residue then indicates the most effective

location to apply the feedback control.


3.3 FACTS POD Controller Design

Supplementary control action applied to FACTS devices to inciease

the system clamping is called Power Oscillation Damping (POD). Since

FACTS controllers are located in transmission systems, local input sig¬

nals are always preferred, usually the active; or reactive power flow

through FACTS device or FACTS terminal voltages. Figure 3.1 shows

the considered closed-loop system where G(s) represents the power sys¬

tem including FACTS devices and 11(,s) FACTS POD controller.

Yref+^c ^ H(s)u-— G(s)

\/(s)

k

Figure 3,1: Closed-loop system with POD control

Input -->| K-p |-1+Slr

Sl\u

1+ilu

1+5'lead

1+s.Tlag

1+8-1 lead

1+sTi.

ag

mc stages

Output

Figure 3.2: POD controller structure

The POD controller consists of an amplification block, a wash-out and

low-pass filters and me stages of lead-lag blocks as depicted in Figure1 3.2

(usually in,, = 2). The transfer function, /7(.s), of the POD controllei

is given by

/,(.,) K1

1 + sT„

KlIAs)

sT, 1 + hi Irnri

1 t- sTwJ \ i -I sTinq

'3.121

where K is a positive constant gain and H\{s) is the transfer function

of the wash-out filter, low pass filter and lead-lag blocks. Tm is a mea-

suiomeul time constant and T„, is the washout time constant. Ti(ua aud

Tia!J are the lead and lag time constant, respectively. Changes of an

eigenvalue A, can be described by (3.11). The objective of the FACTS

damping controller is to improve the damping ratio of the selected oscil¬

lation mode ?. Therefore, AA, must be a real negative value in order to

3.3. FACTS POD Controller Design 39

move; the real part of the eigenvalue to the left half complex plane. Fig¬

ure 3.3 shows the displacement of the eigenvalue after FACTS damping

control action.

jw

Direction c/Rj

Direction of AX,- -AX Hj (X,-)Vc,- AX,- /"*

y»W

V JO)

(K=AK) (K=0)

Figure 3.3: Shift of eigenvalues with the POD controller

From (3.11), it can be clearly seen that with the same gain of the

feedback loop, a larger residue will result in a larger change of the

corresponding oscillatory mode. Therefore, the best feedback signal for

the FACTS damping controller is the one with the largest residue for

the considered mode of oscillation. The same is true for the optimal lo¬

cation of the POD controller, which also automatically means the best

location for the FACTS device in order to damp oscillations. In Fig¬

ure 3.3, the phase angle shows the compensation angle;, which is needed

to move the eigenvalue direct to the left parallel with the real axis. This

angle will be achieved by the lead-lag function and the parameters T/f,ufj

and Tiag, [17], determined by

Prow = 180° - arg{Rt)

I otnrtl '

'Pi end1 sm{J

Pini)

Tlead

Tint)

1

(XcXluy

1 + bin( -

m,.

(3.13)


where arg(R,) denotes the phase angle of the residue /?,, w, is the

frequency of the mode of oscillation in rad/sec. The controller gain K

is computed as a function of the desired eigenvalue location according

to (3.11):

A,,rfrs '"- A,K

/?,//i (A,(3.14)

3.4 Case Studies

The FACTS POD controller location and the feedback signal should be

selected in a such a way that the residues corresponding to each of the

critical modt;s are as high as possible [20]. Anyhow, it might not be

cost effective to place; the FACTS device at a particular location just to

damp oscillations. In order to satisfy the primarily requirements of the

FACTS device as well as the damping of oscillations, a compromise has

to be made for each individual case. In this chapter, only damping is

considered, i.e. the primary aim is to damp oscillations.

Since the FACTS devices arc; located in transmission lines, local input

signals like power deviation, bus voltages or bus currents, are preferably

used. To find the best location and the most appropriate feedback sig¬

nal for FACTS POD controller, different lines in the system are tested.

A 10 machine, 39 bus test, system, known as New England system,

shown in Figure 3.1. [21]. is considered here for the case studies. The

static and dynamic; data are given in Appendix A.

3.4.1 Design of TCSC POD Controller

The; uncontrolled system has one critical oscillatory interarea mode

characterized with eigenvalue A = —0.0517 + ,?2.35, and with low damp¬

ing ratio, £ —. 0.022, i.e. less than 3%. Table 3.1 shows the numerical

results of the residue values associated with critical mode calculated

using the transfer functions AP/Akr. AP is active power deviation,

chosen as a feedback signal, AAv- represent TCSC input, characterized

by the compensation degree, i.e. the compensation in p.u. of the line

reactance. According to Table 3.1, the line 37-38 has the largest residue

for the transfer function, having k, as the TCSC control variable1 and,

3.4. Case Studies 41

Figure 3.4: System configuration for the case study

therefore, the most effective location to apply the feedback control. Us¬

ing the; method presented above, the POD controller parameters a\~Q

calculated in order to shift the real part of the oscillatory mode, to the

left half complex plane. The gain K is calculated in order to reach the;

relative damping ratio of the oscillatory mode at least 5%.

The root-locus, when the gain of TCSC controller K varies horn 0 to

10, is shown in Figure 3.5. It is clear that TCSC POD controller has

minor influence on local modes, like on mode #4. The; local modes can

be successfully damped by PSSs, which are not used in this test system.

It is also obvious that POD controller affects the oscillatory mode the

most (mode; #!), but another inter-area mode, mode #2, might become

critical, if the POD gain K is too high. Some other modes are affected

as well. In order to have good damping of inter-area modes, and as less

as possible negative influence on the other modes, compromise; foi the

POD gain has to be found for each individual application. With the

chosen gain in this case;, all modes affected remains well damped, see


Mode residues of the tiansfer function AP/Akc

TCSC location mline 37-38 0.0814

line 39-31 0.0753

line 16-19 0.0715

line 26-29 0.0357

line 31-32 0.0349

line 21-22 0.0254

line 31-25 0.0243

line 23-24 0.0177

line 35-36 0 0129

line 16-17 0.0123

line 16-21 0.0115

line 25-26 0.0018

Table1 3.1: Location indices of TCSC

Figure 3.6.

The obtained transfer function for the TCSC POD controllei is:

//(,)_ ££ _ , 1749

(^_\ (J^\ (MXtoL+i)2 (3,5)w

Akr \0As + iJ V.10.S fiy voooiis + \) v '

in order to check controller ability to stabilize the system, a three-

phase fault is applied in the line 33-11 closed to the bus 33. The; lault is

cleared after 50 ms by opening the faulted line. In Figuie 3.7, a eliiect

compaiison between the power flow lesponse of the system with the

fault with and without damping contiol is given. The reference value

for the active power flow is calculated from the steady state calculation

foi the faulted line out of service.


jco

Damping ratio 0.05

Figure 3.5: Root-locus of the TCSC POD controller

when A' varies from 0(*) to !()()

Figure 3.6: Displacement of eigenvalues without (*) and with (°) pro¬

posed POD controller

M Chapter 3. Use of FACTS Devices for Damping...

Fault at bus 33 with line 33-14 out

With control

Without control

30 40

Time [s]

Mgure 3 7 Ac tive powei flow with and without damping c ontrol in e on-

trolled hue 37-38


3.4.2 Design of UPFC POD Controller

The same procedure as for the TCSC is here repeated for the UPFC.

The UPFC has two control parameters, r and 7, the magnitude and

the angle of the series injected voltage, respectively. The third vari¬

able, shunt reactive power. Qrnl,v\ is inactive;, so the UPFC perforinsthe function of the series compensation. Therefore, it is theoretically

possible to consider four possible POD control loops, as indicated in

Table 3.2. However, from Table 3.2. where the critical mode residues

of the resulting four transfer functions are calculated, one can see that.

AQ is not a good choice for the POD controller as an input signal, since

the residues of AP/Ar and AP/A7 have almost always larger values

than AQ/Ar and AQ/A7. Basexl on this fact, AP is considered to be;

a better input signal than AQ. Hence, there; are two suitable loops re¬

maining: the first one based on the feedback signal Ar and the second

one based on the signal A7. From Table 3.2, the line 25-26 has the

largest residue for the transfer function AP/Ar and therefore would be

the most effective location to apply the feedback control on Ar variable;.

The corresponding transfer functions employed here are given by (3.16)and (3.17) where the lead-lag parameters were obtained according to

(3.13).

H (s)^4^

- 0.0933 ( -1 ^w

A?- \{)As -J IJ

H (,S) _. ^__ _-, 7.8998( !

)

However, the residue of the other transfer function, AP/A7, is not large.This means, the contribution of the damping controller applied to that

control variable in this chosen line will be rather small, see Figure 3.8.

The contribution to the damping of oscillations with two applied POD

controllers does not differ much, compared to the results when the onlyone POD controller, given by (3.16), is applied. That could be expected,due to small residue value of AP/A7. According to this observation,

another line should be; selected for the UPFC location. Good candidate's

for UPFC location might also be the lines 37-38, 16-19 and 28-29, see

Table 3.2.

lO.s A /0.2776.S + 1_____

1 _________

i().s A /0.3104.S F f

lO.s + 1/1 0.5705.S + 1

(3.16)2

3.17)


Mode residues, |7?,|, of the different transfer functions

UPFC location AP/Ar(7 = 7o )

_p/A7

(r =- r„)

AQ/Ar(7 = 7o )

AQ/A7

line 25-26 3.0329 0.0286 1.0916 0.0070

line 37-38 2.6801 0.1725 1.5417 0.1212

line; 26-28 2.0020 0.0455 0.2111 0.0334

line 26-29 1.8797 0.0660 0.1868 0.0492

line 31-25 1.8479 0.0531 0.3506 0.0273

line 16-19 1.7738 0.2545 0.0787 0.1055

line 31-32 1.7178 0.0277 0.3357 0.0257

line 28-29 1.7080 0.3657 0.5652 0.2784

line 39-31 1.5249 0.0007 0.1400 0.0019

line; 17-27 1.0282 0.0320 0.4294 0.0362

line 21-22 0.7048 0.2192 0.3736 0.1905

line L6-21 0.6422 0.0829 0.3361 0.0769

line 23-24 0.4436 0.0324 0.3310 0.0316

Table; 3.2: Location indices of UPFC

Figures 3.9 and 3.10 show the root, locus for the UPFC located in line 37-

38 and with two POD controllers obtained by transfer functions AP/Arand AP/A-), when the gain of UPFC POD controller, A", varies from 0

to 10. As in the case with the TC'SC, the oscillatory mode #1 is moved

to the; left half complex plane, but another inter-area mode, mode -//2, is

moved towards the right direction. Local modes, mode //3 and ff4. are

slightly affected as well. Howewer, with the chosen gain, in Figures 3.9

and 3.10 marked with (V), affected modes remain well damped, sec

Figure 3.11. Note that with two POD controllers added to the UPFC.

stability performance does not change.

The ability of the UPFC POD controller with UPFC location in the;

line 37-38 is shown in Figures 3.12 and 3.13. The fault is applied to the

line 36-37 close to the bus 36 and cleared after 50 ins by opening the;

faulted line. The corresponding transfer functions employed in this line1

are given by (3.18) and (3.19). The reference values for the active and

reactive power flows are calculated from the steady state calculations,



j \» |Both POD controller

Controller on gamma

Controller on r

Without controller

Time [s]

Both POD controller

Controller on gamma

— Controller on r

- Without controller

Time [s]

Figure 3.8: Active and reactive powei flow with damping control m con¬

trolled line 25-26

for the case when the faulted line is out of service

AP

Ar

AP

A7

0.09

1.35

1

0.1«+1

Ols-r-

10s \ /"0.3118.S- + 1

0.5752.S + 1

0.3071.S 1-1

lO.s + 1

lO.s

lO.s -1- 1 0.5831 s + 1

(3 18)

(3.19)

48 Chapter 3. Use of FACTS Devices for Damping..

jeo

Mode 4

Damping ratio 0.05-

Figure 3.9: Root-locus of the UPFC POD controller (f£)K varies from ()(*) to 10(D)

jeo Damping ratio 0.05

Figure 3.10: Root-locus of the LTFC POD controller (f^)A' varies from ()(*) to 10(D)


-0 8

Figuie 3 11: Deaninant eigenvalues without eontioller (*) and with both

controllers (D), foi chosen gains

Fault at bus 36 with line 3S-37 out

Time [si

Figuie 3.12: Active and îeactive powei flow without damping control

in controlled line 37-38


0

5-0 5

i'

t -»t

g -2 5-

1 -3-

(_

IX -3 5-

2


—.1 5

J 05

1 °

ft AWith both POD controliftrs

With controller on r

With controlleron gamma.

in U^_ :5- -0 5

i "1

-1 5

11,11

15

Time [s]

A f\ f\ f\^\s/l/VV^^

With both POD controllers

With controller Orl (

With controller on gamma

15 20

Time [s]

Figuie 3 13 Active &m\ reactive powei flow with damping tontiol in

controlled line 37-38


3.4.3 Design of SVC POD Controller

In order to find a suitable location lor the SVC to damp an oscilla-

toiv mode, the SVC is located in different buses of the test system

Table 3.3 shows the numerical results of the residues for the transiei

function AV/ABsvc- where AV denotes SVC bus terminal voltage

and ABsvc susceptance of the SVC. According to Table 3.3, bus 28

has the biggest residue; value associated with critical mode and therefore1

the1 most effective location to apply the feedback control.

Mode residues oi the tiansfer function AV/ABS,„.

SVC location \P,\bus 28 0.0388

bus 29 0.0385

bus 20 0.0219

bus 20 0.0243

bus 23 0.02 ft)

bus 19 0.0199

bus 27 0.0189

bus 22 0.0183

bus 24 0.0173

bus 21 0.0172

bus lfi 0.01G8

bus 17 0 0100

Table 3.3: Location indices of SVC1

The corresponding transfer Junction employed as POD controller in bus

28 is given by

H(s)AV

ABsvc2.5471

1 10 s

O.l.s + 1 J V KJ.s + 1 / V 0 61335 +

0.2871« f 1

(3.20)

The root-locus, when the gain of SVC POD controller, A", varies from

0 to 10, is shewn in Figure 3.14. Like in the case of TCSC and UPFC,

SVC1 POD controller has little influence on local modes Heie. it has

to be pointed out that the first shift into the left half complex plane

m Figure 3.14 is influenced by the SVC voltage contioller. POD SVC


11

10

9

8

7

1« 6

5

4

3

2

1

0

Damping ratio 0 05

-1

Mode 2* ->i

Mode 1

[jnvn*

D 00 Q

momipo— .o-osaa—a—a o

-0 6 -0 4

Figure 3.14. Root-locus of the SVC POD controller

K vanes iiom ()(*) to J0(O)


CO 0 95

S) 09

|> 0 85

08

0 75

With control

Without control

10 15 20 25 30 35 40

Time [s]

Figuie 3.15: Voltage magnitude of SVC bus

3.5. Summary 53

-a 06

» 0 4


—i'—

—i ,___—j—,—

With control

Without control

5 10 15 20 25 30 35 40

Time [s]

Figure 3.10: Voltage magnitude of the faulted bus

controller itself has a small influence on the damping of the oscillatorymode in this case. Figures 3.15 and 3.16 show the response of the SVC"

with and without a POD controller to the fault applied in line 23-24

close to the bus 23. The fault is cleaied after 50 ms by opening the

faulted line.

3.5 Summary

In this chapter the residue contiollei design method has been presented

It is a conventional, linear approach and requires the linearized system

model at a particular operating point. The controllers obtained from

conventional approach are simple but often work oulv within a limited

operating range. In case of contingencies, changed operating conditions

can cause poorly clamped oi even unstable oscillations since the1 set

oi existing controller parameters yielding satisfactory damping foi one

operating condition may no longer be valid for another one.

Seite Leer /Blank leaf

Chapter 4

On the Location of the

Provided optimal locations, FACTS devices are capable of performing

multiple tasks; for example power flow control, voltage; control, minimiz¬

ing the losses, damping of oscillations etc. The location of the FACTS

device has a large impact on its performance witli regard to the objec¬

tives to be: fulfilled. A location being the best for one objective1 may be

less suitable for another objective.

If the objective of the Thyristor Controlled Series Capacitor (TC'SC),for example, is the power flow control, the most effective location is of¬

ten in highly loaded linos [11]. Applying the power flow control or any

other objective of FACTS devices in general, it is often desirable to have

a control design which enables the operation of the controlled transmis¬

sion path without affeîcting the rest of the system. So far there is no

FACTS controller that is able to satisfy the control objective without af¬

fecting the rest of the system, but it is possible to minimize: its influence.

In this chapter a proceduie for placing a TCSC considering both power

flow control and damping of power oscillations is presented. A method¬

ology used to give the insight into the influence of the TCSC location in

the system, on the rest of the system, is power flow sensitivity analysis.

Sensitivity analysis gives a direct measure of t he eontrollabilit y of t he ac¬

tive power flow in the specified line by the chosen location of the TC'SC1.

55

56 Chapter 4. On the Location of the TCSC

Besides power flow control, satisfactory damping of power oscillations

is an important issue as well. In Chapter 3 damping control utilizes the

residue method and the presented approach solves the optimal location

of the TCSC device regarding damping of the oscillatory modes.

In this chapter both methodologies are used in order to find the suit¬

able location for both tasks, power fiejw control and damping control.

The proposed algorithm has been demonstrated on the same test as in

previous chapter.

4.1 Dynamic Criterion

Dynamic criteria is based em the residue method. This part is presentedin Chapter 3. According to this criteria, the1 most effective location

means the1 best location ol the POD controller, while the compromisehas to be found foi the location of both the powei flow controller and

POD controller. In general, the optimal location of the TCSC controller

obtained from a dynamic criterion is not the same as that with a static

criterion.

4.2 Static Criterion

The static criteria used for optimal location of the TC'SC controller

is based on the sensitivity of the line flows with respect to the series

compensation in a line. The sensitivity of the line flows determines the

influence of an output variable to a control variable In this case, it is a

direct measure of the controllability of the active power flow in specified

line by the TCSC located m the same, or in another line.

A power system in the steady state is modelled by the load flow equa¬

tions:

F(X,Z,D)={) (4.1)

where X is the (vT x 1) vector of state variables, Z is the (ri-, x 1)vector of control variables, i.e. input form FACTS devices, D is the

vector of parameters, i.e. line reactances, loads. The first order Taylor

4.2. Static Criterion 57

expansion of (4.1) in the neighborhood of the nominal operating point

(Xa,Z",D") gives

0 _. F(X° + AX, Zl) + AZ, D{) + AD) «

F(X°.Z°, D°) + FTAX + FZAZ + FDAD (4.2)

with .lacobian matrices F,,Fz,Fo that are computed at the1 nominal

operating point {X°,Z{>,D0). Fiom (4.2) follows that

FrAX + FZAZ + FDAD = 0 (4.3)

since F(X°, Z°, O0) = 0. Assuming that Fr is non-singular,

AX = -F;lF,AZ- F-[FDAD

= &\ZAZ + S,DAD (4.4)

with

Srz = —F~ Fz

Srp = -F-lFD (4 5)

At the operating point, the power flow vector M'° is dotenniued bv a

function //,WQ ^ H(X°,Z°.Dn) (4 0)

With a perturbation by AZ it becomes

W{) - AW - H(X{) + AX, Z" + AZ, D° 4 AP) (4.7)

Linearization yields

AH' « W, AX t WZAZ + WDAD (4.8)

Substituting (4.4) into (4 8) gives

AW - [~WTF-*FZ + WZ]AZ 4- [-W, F;'FD\AD (4.9)

Assuming AD --- 0 leads to

AW = [W,,Sit + WZ}AZ (4.10)

where

SWZ=WTSTZ + WZ (4.11)


Equation (4.11) represents the power flow sensitivities of output vari¬

ables with respect to control variables, i.e. it gives the direct measure

of the controllability of the active1 power in the specified line / by the

chosen location of the TCSC, w. In the line flow compensation system.

U' is the active line How vector and Z is the vector of control variables,

degree of compensation, F., is the .lacobian matrix used in standard

Newton-Raphson load flow computations. The .lacobian matrices F,.

Wz and Wx are derived in Appendix C.

4.3 Case Study

According to the dynamic criterion, i.e. the residue method, line 37-38

has the largest residue value, and therefore: the most effective location

to apply the feedback control. Due to clarity, Table 4.1 presented in

Chapter 3 is repeated here, with the lines that have the largest residue

values.

Mode residues, of the transfer function AP/Akr

TCSC location \K\line 37-38 0.0814

line 39-31 0.0753

line 10-19 0.0715

line: 20-29 0.0357

line: 31-32 0.0349

line 21-22 0.0254

line 31-25 0.0243

Table 4.1: Location indices of TCSC according to dynamic criterion

Applying the power flow control or the damping of oscillations control,

it is often desirable to have a control design which enables the operation

of the: controlled transmission path without affecting the rest of the sys¬

tem; e g. changed active power value in one line has minimum influence

on active power flows in the other lines. In order to see: whether there

is a suitable location of the TC'SC that would give us that minimum

influence, active power flow sensitivities are calculated for each TCSC

location. To present all sensitivities would be quite unreadable, so the

4.3. Case Study 59

Table 4.2 shows the sum of the absolute values of all line sensitivities

(number of line. 1 = 46), for those TCSC' locations (w), that have the

laigest residue values according to Table 4 1 Power flow sensitivitie-s

are piesentod in noimahzed form, i.e. power flow sensitivity has value

one in the line where the TC'SC' located, and calculated for a few dif¬

ferent opeiating points. Note that heie it is not impoitant whethei the

sensitivities have a positive or negative sign. The optimal location of

the TCSC utilizing the static cnteiion results with the minimum influ¬

ence on the active1 powei flows in the other lines

TCSC

location

E|6'„«lBase1 case1

(all lines)

Line 23-24

outage

y\swjLine 13-14

outage

^|6'lllE|Line 33-14

outage

hue 20-29 2.9785 2.9791 2.9752 2.9786

hue 20-28 3.0108 3 0114 3.0105 3.0106

line 31-32 7.9969 7.9977 7.8947 7.6942

line 31-25 8.4293 8.4339 7.5489 8.7549

line 39-31 11.0626 11.0558 10.3349 11.0744

line 37-38 11.2313 11.3853 10 3954 12.4894

hue 10-19 14.3080 14.2161 14.1640 14.1025

Table 4.2' Sum of normalized power How sensitivities for diileient TCSC

locations (Base case and line outage cases for 39-bus test

svstem)

The powei flow sensitivities are valid only foi the operating points for

which they are computed. The value of the active power flow through

the1 lines is not of interest and consequently not the specific power flow

sensitivity value foi each line. As can be observed iroin Table1 4.2,

the actual power flow sensitivity values for dilfeient lines outages differ

slightly fioin the1 base case. In that sense, the powei flow sensitivity

matrix calculated foi the base case gives proper insight into the influ¬

ence of the TCSC location on the rest of the system.

Figuie 4.1 shows the relation between the residue and the powei flow

sensitivity foi different locations of the TCSC. There aie three groups.

The first group presents the lines with the biggest residue values, i e

they give the best location in order to satisfy the dynamic criteiion, but


with very high power flow sensitivities. Considering the: static: criterion,

the lines from the first group are not appropriate locations for the TCSC.

The lines from the second group have lower values of the residues but

lower values of the power flow sensitivities as well. In the third group

there is just one1 line, 20-29, with the minimal value of the power flow

sensitivity, i.e. that line gives the best location in order to satisfy the

static criterion, and the residue value is in the middle of the sorting list

in Table 4.1, i.e. it is big enough.

•

Line 16-19-^*

(Line 39-31—

Group II

Line 31-26 ^—^. Line 37-38

Une 31-32

Group III

(~*~*)— Line 26-29

)l I I—, ,—,1 1

"0 0 02 0 04 0 06 0 06 0 1

Residue

Figure 4.1: Functionality of two different criteria

Considering both criteria, line 20-29 is found to be the optimal loca¬

tion for the TCSC. The obtained transfer function for the- TCSC POD

controller in line 20-29 is given by:

H(s) - $£. -= 0.7 (-J-) (-^L.) (° ' 'Y (4.12)

In order to investigate whether the: TCSC' located in the line 26-29 can

successfully damp the oscillation, the fault is applied in the line 33-14

close to the bus 33 and cleared after 50 ms by opening the faulted line.

The TCSC is located subsequently in the lines 26-29 and 37-38, since

the line 37-38 has the maximum residue value and hence, it is the best

location to damp oscillations in the: system. For both locations, TC'SC

4.3. Case Study 01

has the same level of compensation. The dynamical response of active

power flow in Figure 4.2, shows that the TCSC located in line 26-29 can

successfully damp oscillations.

Figure 4.2: Active power flow in the line 10-19 for two different TCSC's

locations

For the next case, the TSCS is located subsequently again in lines 26-29

and 37-38 respectively and the loads in the TCSC's terminal buses 26

and 37 respectively, are increased for 10%, followed by the fault in the:

line 13-14 closed to the bus 13. cleared after 50 ms without changing

the system topology. Due to the load increase, the active power refer¬

ence values through TCSC's are changed. Dynamical lespouse of active-

power flow for this case is shown in Figure 5.13. Oscillatory mode is

successfully damped for both locations, but active power flow change1 in

the line 26-29 affects less (less than 1%) the: base case value of the act ive

power flow in observed line 31-32, which validates line 26-29 again as

the optimal TCSC location for the tested system.

One1 other scenario is studied. The loads on buses 15, 18 and 27 are:

increased for 10% but the reference values of the active power through

the controlled lines are kept constant. Figure 4.4 shows the active power

flow response and the variation of the percentage compensation of the:

TCSC located in line 37-38. For this case the available controllability

is lost, i.e. it is not possible to reach the specified reference value of the


„45

__

TCSC in line 37-38

TCSC In Una 26-29

1/ A A A A ftAAAA^11/ V vv«vvvvw^

0 10 20 30 40 50 ÊÛ 70

tima [s]

Figure 4.3: Active power flow in the line 31-32 for two different TCSC's

locat ions

active power flow, while for TCSC located in line 26-29, controllability

is still flexible. Figure1 4.5.

Figuie 4.4: Active power flow and compensâtion of TCSC m the con¬

trolled line 37-38 for the case of multiple load increase1

4.4. Summary 63

40 60

time [s]

Figure 4.5: Active power flow and compensation of TCSC in the con¬

trolled line 26-29 for the case of load increase

4.4 Summary

In this chapter, an approach for the optimal location of a FACTS device

combining the static (for optimal location of the power flow controller)and the dynamic criterion (for optimal location of the damping con¬

troller) has been presented. In general, the optimal location of the

TC'SC controller obtained according to the dynamic: criterion is not the

same as that one obtained according to the static: criterion. In this

chapter the static criterion ancl the dynamic criterion were combiner! in

such a way that the resulting location of the FACTS device could be

optimally selected with respect to both control objectives.

Chapter 5

Self-Tuning Controllers

A conventional damping control design consideis a single1 operating con¬

dition of tile system. In this kind of controllers, feedback is fixed and

amplifies the error, which in turn determines the value of the input sig¬

nal v (eontrollei output) for the system The way in which the error is

processed is the same for all operating conditions. The basis of the adap¬

tive system is that it influences the way in which the c'iror is pioc;csse<i,

There are three basic approaches to the pioblem of adaptive control;

heuiistic approach, self-tuning controllers (STC) and model adaptive

reieieuee systems (MRAS), [28].

The sell-tuning eontrollei is based on the idea ol separating the estima¬

tion of unknown parameters fiom the design of the optimal conti oiler,

[29]. The unknown parameters are estimated on-line, using recursive es¬

timation of the chataetetistics of the system and its distuibances. The

approach used in STCs was first mentioned in the work of Kaiman in

1958. [30] and then revived in the eaily 1970s bv the work of Astrom

and Wittenmark, [31], and others. Researchers, over the years, have

been developing this approach. A self-tuning eontrollei for power sys¬

tem stabilizers (PSSs) has been reported in [22] wheie Piony analysis

extracts oscillation modes from sequential data and estimates oscillation

frequency, damping, amplitude and phase of each mode The authois

in [24. 25, 20] have done the work on PSS self-tuning eontrollei based

on pole assignment where the amount of pole shifting is adjusted ex¬

pending upon the changes of system operating conditions.

65

06 Chapter 5. Self-Tuning Controllers

In Chapter 3, a conventional lead-lag controller designed usually for one

particular operating point, usually the nominal one, has been presented.This controller is simple, but works satisfactorily often only within a

limited operating range. In case of contingencies, changed operating-

conditions can cause poorly damped or even unstable oscillations since:

the; set of controller parameters yielding satisfactory damping for one

operating condition may no longer be valid for another one. A more

sophisticated controller which can maintain good damping over a wide

range of operating conditions, is therefore needed. To reach this goal,

the identification of the static and dynamic characteristics of the system

plays an important role: together with the control strategy itself.

5.1 Adaptive Model Identification

As mentioned, on-line identification of process parameters is an impor¬

tant part of a self-tuning controller. Figure 5.1 shows the adaptive

control scheme for the self-tuning controller for FACTS POD parame¬

ters. While it is necessary to work with derivatives of measured signal

Figure 5.1: Adaptive control scheme for FACTS, general form

when describing a continuous-time dynamic system, like power system,

it is considerably simpler to construct discrete models. They rely on

5.1. Adaptive Model Identification 07

signal values taken at sampling periods, T„. In the case of controlling a

continuous-time1 system one considers a continuous-time control object

and a discrete controller. An interface between differently operating dy¬

namic: systems, like sample and hold units, is essential. It is necessary

to use a suitable mathematical description to express behavior of the

discretized control loop.

The1 considered system model is linear, having single-input single-output

(SISO) and time-varying parameters. The theoretical assumption is

that the power system is working around a certain operating point for

a certain period of time, which enables the estimated coefficients of

the time varying linear model to converge to the actual values. The

considered model has in time domain the form given by

n a" b

1-1 1 -1

where y(k) is the value of the measured output variable at time k, u(k)is the value of the measured input variable at time k (controller output)

and c(A;) is the random nonmeasurable component (white noice). This

model is called AutoRegrcssive with an eXternal input (ARX model)or regression model. If is more convenient to describe ARX mode1!

employing backward time-shift operator z~\ i.e z~ly{k) — y(k ~ 1),

A{z~l)y{k) = B{z~l)u{k) + e{k) (5.2)

where the individual polynomials of equation (5.2) take the form

A(z"1) =--. 1 -\-OiZ~1 +a,2z~'2 + ... +ori„z""

B(z-i) = blz~l+b2z-2+ „ +bnbz-n> (5.3)

The quality of the regression model used is valuator] by the estimation

error given by

e(k) = y(k) i)(k) (5.4)

where i/(k) is the model output at time k with c(k) — 0. The goal of

the parameter estimation is t.o identify (n„ +7)/,) coefficients n,(k) and

b,(k) oi the1 model (5.1) in a way that the sum of the1 squared prediction

errors (5.5) is minimized.

J = min£"(A') = min[?/(A') Jj(k)}" (5.5)


For the: model to be optimal for VA:, its parameters must be updated

recursively once per sampling period T, for each new measurements u(k)and y(A). The method used for identification of the values of the model

parameters is based on Kaiman Filtering technique (KF). Moie details

legarding the KF theory can be found in [33]. The set of standard KF

equations in a recursive form to bo solved once per sampling period 1\

is given by (5.6)-(5.10) and the variables are described in Table 5.1.

g(k) == K(k - IMA-) [y' (k)K(k - l)^(A) + Q,„]"'

(5 6)

y(k) -= ¥>''(»/>(* 1) (5.7)

E(k) -= y(k)-y (5.8)

p(k) -- P(k l) + e(A-)e;(A) (!) 9)

K(k) -- K{k - 1) - g(k)ipT{k)K(k - 1) + Qp (5 10)

Variable Description

y(k) output measurement (desired response1 of model at time A')

a{k) input measurement (eontrollei output at time k)

m model output (response of model at time A*)

<p(k) buffered measurements <p(k) e Tl(n" * "b)xl

cp(A-) = [-y(k - 1) y(k - na)u{k - 1)... u(k - m)]T

e(k) estimation error at time k

p(k) vector of estimated parameters p{k) £ 'K(""'+"6)xl

p(Ä)-[ai(A),---.u„„(n7),t1(Ä),.. bllb(k)}

ff(*) Kalman-gain. g(k) Tluxl

K(k) correlation of estimation error. K(k) C TV x"

Q,n correlation of measurement noise, Qm fe 7JlxI

LJp correlation of process noise, Qv 'R,nyv

Table 5.1: Variables of the algorithm for parameter estimation

To ensure numerical robustness, the above standard adaptive filtering

algorithm has been enhanced by (5.11) and (5.12) The covariance

matrix K(k) is enforced by (5.11) to remain symmetrical. For a better

paiameter tracking, a regularized constant trace1 algorithm (5.12) has

5.2. Residue Based Adaptive Control 69

been employed with experimentally obtained c\/c-2 = 104 and I being

the unitiy matrix of the same dimension as A'(A;) [5].

m . manpä ,5,,)

*<*> - mm+>> (512>

As a result of the described adaptive model identification technique, the

power system model required for the controller design becomes available

at any time k.

5.2 Residue Based Adaptive Control

For the residue based adaptive controller, adaptive model identification

part differs from above described procedure in mode1! used for the1 es¬

timation. The estimation method chosen here is autoregressive (AR)

model, given by (5.13), which presents the; counterpart of the: ARX

mode1!. (5.1), for a single output signal.

I«

y (A)- -- J] aty(k - i) + c(k) (5.13)i = i

rewritten in z' domain

A{z-l)y{z) ^ e{k) (5.f4)

Figure 5.2 shows adaptive control scheme for this method. The result of

this adaptive model identification is detection of the dominant oscilla¬

tory mode in the system. The estimated linear discrete-time AR model

(5.13) of power system is given by

C(z) =_i_

=J (5.15)

A(z-i + J2a'z~

l=-l

The detected oscillations are characterized by the solution of the char¬

acteristic polynomial equation. The characteristic equation results from

(5 15) and has the form

A(z~y) = 1+tnjr1...+a„2-°" =0 (5.16)


Figure 5 2 Geneial form of residue based adaptive control scheme toi

FACTS

ancl the n solutions-

X'! - nf ± jW, (5.17)

The estimated discrete-time1 model of the system has to be converted

lo a continuous one. Ileie, Tustm's appioximation is employed. The

relationship between z~v and .s to be substituted into (5 10) to obtain

A, is foi Tustin's appioximation given by

T,

14 i

T,(5 18)

The next step is to calculate the eigenvalues, A,, of the1 continuous-time

model The most mipoitant oscillations that should be detected regaicl¬

ing stability are the dominant ones. They are characterised by complex

eigenvalues having the biggest real part among the others. Finally, the

parameters characterizing the oscillations of interest, such as frequency

/" and relative damping Ç, aie directly calculated from the dominant


eigenvalue pair A, — a, ±jw, as follows:

o,100

>i

2tt

(5.19)

(5 20)

APl,i

Adaptive

algorithm based

on Kaiman filter

.KK, f,!

G(s)

ls+1

IwS

r^b+i

'I leadO + 1

Tla"g(f|)8 + 1

*rei

AkP

Figure 5.3: Residue based adaptive conti oiler, using Kaiman filtering

Figuie 5.3 shows the closed loop control system with a residue1 based

POD contioller This kind of the controller is presented in detail in

Chapter 3 With an oscillatory mode known from identification part,

POD parameteis aie obtained from the equations below, pi osent ed in

Chaptei 3 by

ficamp - 180°-ar<?(J?,) (5.21)

=

r1 -

' lend

s in

in,L)

(5.22)Ptan 1 -\ sin

in,

Plaq =

1(5.23)

wt\/~ar

Pend = ("cPloq (5 24)

K .=.

R,Ih(K)(5.25)

Since no information about the angle of compensation is available foi an

update it has to be assumed that the mode residue remains unchanged.

Hence, the system model has to be available in older to find optimal


location for FACTS devices, in this case TCSC. and consequently to cal¬

culate the values of residues for the controller design. From Figure 5.3,

one can see that 7),,„,y, Tlnq and the gain K are updated online at every

sampling period, Ts, according to (5.23)-(5.25). A relatively simple and

powerful adaptive controller tuning has been achieved in considered test

system using this approach.

The1 test system used for applying the residue based controller is the

New England 39 bus system, shown in Figure 3.4, Chapter 3. For this

case: study the dynamic data of some generators were modified in or¬

der to get illustrative results. The modified system has one oscillatory,

inter-area mode characterized by A = -0.0784 ± J5.3677 with damping

ratio £ = 1.40%. Performed residue and sensitivity analysis show that

the lino 20-29 is, again, the most suitable location for TCSC in order to

satisfy both, i.e. a power flow and damping control.

As mentioned, the problem with a set of fixen! controller parameters

i.e. tuned by conventional method, arises when the system topology is

changed. In such cases, the re-tuning of POD parameters is required.

One solution of this problem is to re-tune the controller parameters for

every new operating condition based on a complete set of the model

parameters. In following Figures, dynamic responses obtained by this

approach are denoted as "re-tuned POD", i.e. POD is re-tuned for ap¬

propriate operating condition, e.g. with the line out of service, whereas

"fixed POD" means POD controller tuned as well by residue based

method, but for nominal condition.

In order to compare all approaches, the following disturbances are con¬

sidered for simulation with a fault for 100 ms close to the buses:

1 bus # 16 followed by outage of the line f 6-17 and with line 25-26

out of service

2. bus # 25 followed by outage of the line 25-26 ancl with lines 23-24

and 32-18 out of service

Figures 5.4 and 5.5 show the active power How dynamic response for

the first disturbance, with comparison of the results obtained for fixed

tuned POD, re-tuned POD, and proposed adaptive tuned POD. It can

be noted that "re-tuned" POD, tuned for system's opeiating condition


when line 25-20 is out of service, is not able to damp oscillations af¬

ter the applied disturbance, i.e. when the system topology is changed

again. Figures 5.0 and 5.7 show the dynamic response for the second

disturbance. The "re-tuned" POD is able: in this case to damp oscil¬

lations as well as the fixed POD. The disadvantage of this approach is

the: necessity of knowing all power system's data and performing on-line

linearization for the each new operating condition.

However, all figures show that the adaptive tuned POD in both cases

has the best peiformance ancl shows the robustness compare to conven¬

tional tuned POD Figure 5.7 shows the comparison between fixed POD

and adaptive tuned POD, ior the second disturbance». Figure 5.8 shows

the results of detection of oscillations for case in Figure 5.4; relative

damping of the dominant oscillatory mode, frequency of the dominant

oscillatory mode1 and predictive error, which is the erroi between the

filtered measured signal and its prediction.

Fault at bus 16 with line 16-17 out and line 25-26 out of service

I' 1 1 '

' 1II ,

Adaptive tun«d POD

Fixed POD

;~iiIMk^^

if1

0 10 20 30 40 50 60 70 80 90

Time [s]

Figure 5.4: Active power flow in the controlled line 2G-29


Fault at bus 16 with line 16-17 out and Una 25-26 out of sen/ice

Figure 5.5' Active power flow in the controlled line 26-29

Fault at bus 26 with Una 25-26 out and lines 23-24 and 32-16 out of service

F'igure 5.6' Active powei flow in the controlled line 26-29


Fault at bus 25 with line 25-26 out and lines 23-24 and 32-18 out of service

70 80 90

Figmo 5,7; Active power flow in the controlled line 26-29

Dominant relative damping [%]

°[îrvVW-^-

0 10 20 30 40 SO 60 70 80

Dominant frequency [Hz]

Figuie 5.8: Results of detection of oscillations for the case in Figuie 5 1


5.3 Pole Shifting Adaptive Control

In order to apply residue based adaptive control method, the system

mode1! has to be available in order to find optimal location for FACTS

devices and consequently to calculate the values of residues for the1 con¬

troller design. For the self-tuning controller design technique proposed

in this section, no system model is required. An adaptive control based

on pole-shifting is employed as a self-tuning controller.

The pole shifting method is based on pole assignment method [26]. A

controller based on the: pole assignment method is designed to achieve

the: pre-defined poles of the characteristic1 polynomial [28]. Like1 the1 pole-

assignment method, pole shifting method deals with closed loop poles.

The: poles of the open loop system are first obtained from characteristic

polynomial and then shifted toward the origin of the1 unit z circle by a

pole shifting factor rv.

r +

Ô H (z-l) S(z-l)

Figure 5.9: Considered closed loop control system

Figure 5.1 shows the considered adaptive control scheme. Employed

controller design comes from the general closed loop diagram shown in

Figure 5.9. The uncontrolled system is identified by a discrete model of

the ARX form, (5,2), or by a transfer function

S(z~Y(z~

U(z A(z •)

with polynomials

A(z-') =

B{z~v) =

1 + a{{k)z1+a2(k)z~

6i(fc)2_1 \-b2{k)z~2 +

+ ... (•• anii(k)z~

+ b„,{k)z-T"

(5.26)

(5.27)

(5.28)

where the system parameters a, and &,, are known from a real-time1

parameter identification method for any time k. The poles of the open-

loop system are first obtained by solving the open-loop characteristic:

5.3. Pole Shifting Adaptive Control 77

expiation from (5.27) frozen for the actual time k;

A{z~[) --- 1 + e-jiz-1 + a2z~2 + ... + c7„„ j""" -= 0 (5.29)

The discrete transfer function of the considered controller is given by

ff(*-i)_^>=ÇU(5 30)1 '

E(z-i) F(z'x)[ '

where

F(«-l)-l + /i2-l + . • + ./>-' + . - f fr,,z"" (5.31)

G(z-i)^g0 + giz-'1 + . -. + 9.Z-' 1 . + 9n,Z-"f (5.32)

and ri/- = nc, — 1, n,, — n„ — 1.

The transfer function of the: closed loop system, illustrated in the block

diagiam in Figure 5.9, then takes the form

Y(z-])_

B(z-l)Gjz-])

Riz-')~

A(z-l)F{z~i) + Biz-])Giz~l)l''" " '

The transfer function of the closed loop system has to be suitably ad¬

justed by choosing a controller transfer function to guarantee the over¬

all stability of the closed loop system. According to pole: assignment

method, by choosing the characteristic polynomial

«„

(5.34)P{z~^11 = 1

n the polynomial equation

P(z-J) =- A(z -l)F{z- ') rB( l)Ciz~l) (5.35)

where nv -- rn<i,x{ii,„ \-iij.h\, + n„), one should achieve the pre-set

poles. As mentioned, the open loop poles of the system are obtained by

solving (5.29). If all the roots of (5.29) are: within the unit circle in the:

2-domahi, the system is stable. If is clear, the system is more stable as

the closer the poles are to the origin of the unit circle. The function of

the pole shifting self-tuning control is to shift all roots of (5.29) towards

the origin of the unit circle by a factor r\. This implies that P{z~l)takes the form of a polynomial .4(2_1) multiplied with an array of n.

iir, np

Piz-1) = i -t Y.P'^'= ! + J2a'aiZ" (5-36)


where 0 < a < 1 and the prescribed coefficients p, — t) for , > n„.

Hence, the resulting close-loop poles will be the roots of the character¬

istic equation given by

P(z~l) - 0 (5.37)

Substituting (5.27), (5.28), (5.31). (5.32) ancl (5.36) into (5.35) and

comparing the coefficients at the same power of z"'on the both sides,

gives:M H - L (5.38)

M

f 0 0 bi 0

ai 1

ai

0 l>2 bi

b-2

an„ 1 K0

0

ai 0 b„,0

0 0 <*/.a 0 0

0

0

&i(5.39)

H =Jrif

90

9nq

(5.40)

ui(ev - 1)a2(«2 - f)

^,,K"-i)0

0

5,11)

If the variable a in matrix L is fixed, one has a special c a se of the pole

assignment control algorithm where the coefficients of the controller


II(z- ') (5.44)

transfer function, f,(i = l,...n/) and g,(i = l,...nq), can be calculated

at every sample: from (5.38) by

H = M lL (5.42)

and the control u can be calculated, as shown in Fig. 5.9. by

or with zero reference value r

U(z ') Gjz ')

Y(z- M F{z-*)

Fi'om (5.44) follows

Uiz~[)Fiz-1) = Yiz-')Ciz~l) (5.45)

rewritten in time domain

u(k) + fiu(t 1) I ... + f„}u{t-nf) = goy(t) \ g\y{t-l) + ...+yn,y{t-nq)(5.46)

or

u(k) = ipT(k)H(k) (5.47)

with fik) = [-u(k - 1),..., -u(k -«,/), y (/,-),. ..,y(k - vq)\ and H given

by (5.40).

Proper value of the pole shifting factor depends on the operating condi-

tions. For that reason it is desirable to adapt the parameter a on line.

From (5.47), it is obvious that the control at time k, u.(k). is a function

of pole shifting factor at that, time, with constraint h,„,„ < u < vmilT-

Sensitivity function can be calculated from (5.47) as

dit ... dll.. „„.

— = ip1 • — (5.48)da da

Substituting (5.42) into (5.48) gives

ÈL=(pr.M-.M (5/19)da da

p- - f M"1 • [a,, 2a2a,.... «„«„„n""-1] (5.50)da


With the approximation

^.= £! (5.51)

dn Aa

the modification factor a is given by

Aa = K-\~\-1 -Au (5.52)da

where Au is the contiol margin defined as

Au = f """" ~ U U~ Ü (5.53)

[ u - u,„,„ u < 0

and A" is a positive constant chosen to avoid excessive variation in e».

The variable pole: shifting factor, <\{k), can be calculated by

aik) = aih) + Aa (5.54)

where: a(/r()) is any value between 0 and 1.

Figure 5.10 and Figure 5.13 show the direct comparison between the

active power flow response of the system to the: fault with fixed POD

parameters and adaptive tuned parameters of the POD controller, for

two different cases. The simulations arc carried out for two disturbances

for fOO ins. The faults arc1 created 1.0 s after the start of the simulations

ancl they are applied close to the following buses:

1. bus #16 followed by outage of the line 16-17

2. bus #21 followed by outage of the line 21-22 and with line 32-18

and 33-14 out of service

The fixed POD parameters are tuned using the residue1 method. The

results given in this Figures show that the oscillations of the system

are1 damped out efficiency and demonstrates the ability of the: system

to adapt to a new operating conditions. Figure 5.12 shows the compar¬

ison of the active power How for the case on Figure1 5.10. with lixed and

variable polo shifting factor, a.

Variation of the pole shifting factor for two studied cases is shown in

Figure 5.11 and Figure 5.14. It can be seen lhat pole shifting factor

adapts itself to the dynamic of the system and it can converge either to


some landom value or to its staitmg value, [32], in older to achieve the

desired closed-loop poles.

One moie result of the adaptive model identification is shown on Fig¬

ure 5.15 and Figuie 5.16 Figure 5 15 shows the poles of the closed loop

system with the POD paramoteis tuned using the residue method, in

the ca.se with the fault applied in the line 29-30 ancl with the lines 12-26

and 13-22 out of service, frozen for actual time k. Figure 5 16 shows,

foi the same case, the poles of the characteristic polynomial equation

of the svstem closed with an adaptive tuned POD conti oiler, frozen a,s

well foi actual time k.


- Adaptive tuned POD

Fixed tuned POD

10 20 30 40 50 60 70 80 90

Time [s]

Figuie 5 10 Active power flow in contioiled line 26-29


Figure 5.11: Variation of the pole shifting factor, a, for case in Fig¬

ure 5.10


Figure: 5.12: Comparison of active power flow in controlled line 26-29

with fixed and variable pole shifting factor, a


Fault at bus 29 with 29-30 out and with lines 12-26 and 13-22 out of service

Or

s. -a

1-25

' .

Fixed tuned POD

Adaptive tuned POO

0 10 20 30 40 50 60 70 80 90

Time Is]

Figure 5.13- Active powei flow in controlled line 26-29

Figuie 5.14: Variation of the pc)le shifting factoi, a, foi case1 in Fig¬

ure 5.13


1 ——t r— 1 ,

#

#

:.. |i —^—. „

*'

*

*

-0 5 0 0 5

Real axis

Figure 5.15: Polos of the closed loop system with fixed tuned POD con¬

troller for case in Figure 5.13

• **

>

m * ,, - —-

* * »

**

-0 5 0 0 5

Real axis

Figuie 5.16: Poles of the closed loop system with adaptive tuned POD

controller for case in Figure 5.13

5.4. Summary 85

5.4 Summary

In the first part of this chapter, a simple adaptive tuning method based

on residue approach has been elaborated and applied to the TCSC. It

has been shown that in some cases the set of TCSC POD controller

tuned by conventional methodology, can not stabilize (he power system

under all admissible operating conditions. In this case, a re1-! lining is

necessary. An algorithm for detection of oscillation luis been utilized to

automate1 this procedure. For this approach, the system model has to be

available in order to find optimal location for FACTS devices and con¬

sequently to calculate the values of residues for the controller design.

That has been motivation for applying more flexible self-tuning con¬

troller based on pole shifting approach, elaborated in the second part of

the chapter. Using the proposed indirect adaptive control scheme1, there

is no need to know a priori the actual parameters of the power system

model in order to design the controller. This is a practical advantage of

the presented method. Simulations showed that the proposed method

led automatically to an improvement of the damping characteristic un¬

der different operating conditions.

Seite Leer /

Blank leaf

i

Chapter 6

Coordinated Tuning of

PSS and FACTS POD

Controllers

With a conventional design approach, it might be very dilficult to prop¬

erly handle a coordinated design for multiple controllers and for a va¬

riety of operating conditions. Power oscillation damping controllers of

FACTS devices (FACTS POD) are effective in contribution to the damp¬

ing of poorly damped inter-area modes while power system stabilizers

(PSSs) are an efficient tool for clamping of the local modes, but they

can damp the inter-area modes as well [19]. The aim of* tuning both

stabilizers is the same as for tuning the individual ones; to ensure that

the power system operates with adequate damping ewer a wide range1 of

operating conditions and system configurations.

As a consequence of the action of both stabilizers in the system, the

PSSs and FACTS POD, undesired interactions between them may oc¬

cur [34]. This requires a simultaneous optimization and coordination

of the parameter settings of both stabilizers in order to enhance overall

system stability and minimizing possible adverse interactions between

stabilizers.

This chapter presents a method used for the cooidinalod tuning of POD

87

88 Chapter 6. Coordinated Tuning...

FACTS eontrollei s and PSSs using Genetic Algorithms (GA). For GA

technique it suffices to specify the objective function ancl to place finite

bounds on the optimized parameters. It provides greater flexibility re¬

garding controller structure and objective function considered [39], than

conventional optimization techniques. The use of GA helps to obtain an

optimal tuning for all PSS and FACTS POD parameters simultaneously,

which thereby takes care of undesired interaction between controllers.

6.1 Genetic Algorithms

Genetic Algorithms (GAs) are optimization methods based on concepts

of natural selections and genetics. They work with a population of so¬

lutions, each representing a possible solutions to given problem. One of

the: advantages of genetic algorithms is that they do not require any prior

knowledge or special properties of the objective function [37]. There1 are

some1 disadvantages of GAs as well, like long computing time's, paramo-

tin- tuning, e.g. some parameters have: to be adjusted by the user (mu¬tation and crossover probabilities, population size etc.). GAs are bet¬

ter suited for unconstrained optimization problems than to constrained

problems [37].

The main component of GA is a string which represents one parameloi

or one chromosome of an individual. Each individual represents a possi¬

ble solutions within a search space. A number of individuals constitute

a population. The initial population consist of N randomly generated

individuals, where N is the size of population. At every iteration of

the algorithm, the fitness of each individual in the current population

is oomput<:d. The genetic operators, selection, crossover and mutation

are then applied in order to create new population that is closer to the

optimal solution as described below.

6.1.1 Selection

After the individuals have received their fitness value, the selection

mechanism copy them according to their fitness. The individuals with

high fitness value have better possibility for reproduction into the next

generation. There are several schemes for the selection process: roulette

6.1. Genetic Algorithms 89

Parent 1 1 0 1 1 1 0 0 t 0 0 Crossover 10 1110 1110 Offspring 1

i J; :

Parent 2 10 0 10 0 1110 100100 0 100 Offspring 2

Figure 6.1: One-point crossover example

wheel selection, tournament selection and rank-based selection are com¬

mon selection methods. Stochastic uniform selection is used in GA

simulations in this chapter.

6.1.2 Crossover

In the next stage, two individuals (parent) are chosen ancl combined

to create offsprings. The: combination is done with a given probability,

typically in the range of 0.6-1.0, otherwise parents are unchanged. The

simplest crossover operator is on-point crossover. It does the combina¬

tion by choosing at random a cutting point at which each of the parents

is divided into two parts in order to create two offsprings which contain

information from each of the parent string. Figure 6.1 shows one-point

crossover example.

6.1.3 Mutation

The1 mutation operator is applied to change the value:s in a randomly

chosen location on an individual. This enables the search of some re¬

gions of the search space which would be otherwise unieachable. There

are many forms for different types of presentation. Figure 6.2 shows the

single mutation operation.

Mutation

Offspring i o I 1 1 0 1 I I 0 i [V- 10 110 0 1110 ^^

Figure: 6.2: Mutation example

The described operators are used when the individuals are encoded with

binary alphabet. Binary encoding is a standard GA representation that

can be: applied to many problems.


The GA requires an initial population to begin the search process. The

most common method is to randomly generate solutions for the entire

population. The GA moves from generation to generation selecting and

reproducing the parents until a stopping criterion is met. The: simplest

stopping criterion is a specified maximum number of generations.

6.2 PSS and FACTS POD Controller De¬

sign

PSS acts through the excitation system in order to produce an addi¬

tional damping torque proportional to speed change of the generator,

[19], used as input signal for PSS for simulations in this chapter, ft

involves transfer function consisting of an amplification block, a wash¬

out block and two lead-lag blocks. The following equation describes the

structure of the PSS used in this thesis.

*-«-"-(i^)(SS)(i^) «">

The: lead-lag blocks provide the appropriate phase-lead characteristics

to compensate the phase lag between the exciter input and the generator

electrical torque.

As discussed in Chapter 3, the structure of FACTS POD controller has

a similar structure to that of the PSS controllers.

""<">-*"(ïfk)(îT^)' (6'2)

The time constant Tw is usually considered a.s a known parameter wiUi

some1 predefined values.

The objective of the parameter tuning by the GA optimization pro-

ceduie is to achieve the minimum 5% damping for all oscillatoiy modes

over all operating conditions under consideration, i.e. when all t\, > 5%,

the optimization procedure is stopped. Parameters to be determined by

the GA procedure are Kpss,, Tu, T2;, TA, and T4l for PSS controllers,

and K[,'ACrSi, P\j and T-2, for FACTS POD controllers, where i and j

are the numbers of PSS and FACTS POD controllers, respectively.

6.3. Case Study 91

Let Q represent the set of selected operating points. For a ceitain

operating point, the power system is linearized around the operating

point, the eigenvalues of the closed loop system are computed, and the1

objective1 function is evaluated using the eigenvalues whose have1 damp¬

ing ratio less than 5%. The optimization problem to be solved by the

GA is formulated as a max-min optimization problem, where the ob¬

jective function maximues the minimum damping latio in all scenarios

in Q [35] Hence the pioblem can be mathematically described as the

optimization problem

F = max mm Ç (0"'5)p n

subject to

Kpasi, jriLYi< Kfss r

< ^Vs'.S't, m

Tu mm< T, < T

-1 11, mai

'P*,, min< Ph < * 2i, mai

n,, 77) 17)< TS( < -t,h, mur

Tit m in< Ta, < T

1 47, 77H7 r

KFACTS), 777 7 77,< K-fatc'à, < KrAcrsj

Pit 77U7Î< Pi, < T

1 1 /, mai

T,1 it ,

777 7 77< P'i, < ^2], mar

wheio p is total numbei of operating conditions under consideration, n

is the number of eigenvalues with damping ratio less than 5% and ( is

the closed-loop damping ratio

6.3 Case Study

A 16-machine, 68 bus test system, shown in Figure 6.3, is considered

for the case studies. This is a reduced order equivalent of the inte'i-

counected New England test system (NKTS) and New Yotk powei sys¬

tem (NYPS). The static and dynamic data are adopted fiorn [19], and

can be found in Appendix B, but the buses are renumbered keeping the1

topology and data the same. All generators exeept the slack generator

G13 are equipped with slatie excitation system and powei system stabi¬

lizer (PSS), to ensuie appropriate damping loi its local modes. FACTS


devices used in case studies are the TCSC and the SVG. For the test

system with all devices installed, the active power flow and bus voltage

were chosen as feedback signal for the TCSC POD and the SVC POD,

respectively, and generator speed for PSSs. Figure 6.4 shows the domi¬

nant eigenvalues of the linearized system model, without any controller.

It is found that the system has four inter-area modes which are lightly

damped, shown in Table 6.1.

Eigenvalue

a ± juj

Damping ratio Frequency (Hz)u>

2xje+^Mode 1 -0.0347 + J2.4208 0.0143 0.3853

Mode 2 -O.0G62 1 ;/3.7208 0.0178 0.5922

Mode 3 -0.1020 t. ./4.3I34 0.0236 0.6865

Mode 4 - 0.1390 ±./4.9806 0.0279 0.7927

Table 6.1: Inter-area modes of the test system

To find the best location for TCSC, the following tie-lines have been

investigated: 41 - 42, 42 • 52, 47 - 53, 53 - 54, 53 - 27, 49 - 46, 60 - 61,

50 - 51. Table 6.2 shows the normalized residues in the system for dif¬

ferent TCSC's locations. The results reveal that the line 50-51 is the

most suitable TCSC's location for mode #1, mode #2 and mode #4,

whereas the lino 42-41 is the most suitable location for mode #2. mode

//3 and mode #4.

To find the best location for SVC, the following load buses have been

investigated: 27, 41. 42. 50. 51, 52, 53, 60, 01. Table fi.3 shows the

normalized residues in the system for proposed SVC's locations. It, can

bo seen that the bus 50 is the most suitable location for SVC! in order

to influence damping of all intor-area modes

The GA methodology used in this thesis is provided by MATLAB 7.1,

[41]. The population size is set to 100, the maximum number of gener¬

ation is 30.

6.3. Case Study 93

-$[-©4f® ^©

l_^,_©

©-f-

@-f-

©4t

î_©

^

*

^f©

^H®

$f®

^h®

>

V\/

©H-^

^f®

-©

Figuie 6.3 16-marhine test system


jeo 6

Damping ratio 0.05

* <-^Mode 4

* -< Mode 3

•< Mode 2

* -<- -Mode 1

Figure 6.4: Dominant open-loop eigenvalue's of the test system

Normalized residues

Line Mode 1 Mode 2 Mode 3 Mode 4

52 -- 42 0.0475 0.0120 0.0305 0.0146

42 41 0.0023 1 0.9573 0.9551

53 - 47 0.0184 0.0002 0.001 0.0004

53 - 54 0.1288 0.0358 0.7726 0.0055

53 - 27 0.0086 0.0024 0.0515 0.0004

40 - 49 0.043 0.0249 0.0079 0.0367

60 - 61 0.1210 0.0556 1 0.0111

50 - 51 1 0.3699 0.5525 1

Table: 6.2: Location indices of TCSC

6.3.1 Case Study with the TCSC - Case Study I

Case study I considers the GA methodology for the simultaneous tuning

of 15 PSSs and TCSC" POD controller, in a way that the closed loop

system is stable and sufficiently damped for the specified system config¬

urations. The TCSC" is located in line 50 — 51. To design the proposed

controllers, linearized models for the1 following four different operating

6.3. Case Study 95

Normalized residues

Bus Mode f Mode 2 Mode 3 Mode 4

27 0.0163 0.0194 0.1527 0.0035

41 0.0090 0.0090 0.0071 0.0020

42 0.0004 0.001 0.0015 0.0026

50 0.4064 1 0.4937 1

51 0.0585 0.8669 0.1369 0.9643

52 0.0304 0.0916 0.0088 0.2786

53 0.0383 0.3695 0.4296 0.0811

60 0.0065 0.0263 0.2069 0.0132

61 1 0.0524 1 0 6080

Table 6.3: Location indices of SVC'

conditions for uncontrolled system are considered:

• Ba.se case

• Line 52 — 42 out of service

• Line 53 - 47 out of service

• Line: 42 — 41 out of service

The considered operating conditions are chosen as not desirable scenar¬

ios, since an outage of one of the lines in the inter-connection between

two part of the test system, NETS and NYPS, weakens that connection

considerably. During the optimization, each PSS is set up with bounds

ranging from 0 to 40 for the gain and from 0 to 1 seconds for the time

constants, the same as for TCSC POD lead and lag time constants. The

bound for TCSC POD gain is set from 0 to ft).

Figure 6.5 shows the dominant eigenvalues of the test system where

the controllers are tuned by conventional approach, based on residue

method, and by GA methodology.

Remark: Tuning by conventional approach is done just for the base:

case. The change of operating conditions for the system lead to the

new system topology and hence, the new residue values ancl lead and

lag time constants. Therefore it would be: very difficult to find the op-


jca

* GA tuning

o Conventional tuning 0 k

o

« p * \° * V,

o iäS8*

Darning0.05

ratio °A

* o \* V

* ö\* \

o \* \

0 \

o ana»« m» * * ******* ttw nnawna»» «—>—eßsm—

Figure 6.5: Dominant closed-loop eigenvalues with the TCSC installed

in the system (for nominal operating conditions)

limal parameters for all considered operating conditions by the residue

method.

The final values of the: optimized parameters for PSSs and TCSC POD

controller are given in Table 6.4 and Table 6.5 respectively, obtained byGA approach, Tables 6.6 and 6.7 show the same parameters obtained

by conventional approach.

To evaluate the performance of the designed controllers, the simula¬

tions are carried out for two disturbances for 80 ms. The faults are1

created 1.0 s after the start of the simulations and they are appliedclose to the following buses:

1. bus # 42 followed by outage of the line 42-41

2. bus # 60 followed by outage of the line 60-61 and with line 53-27

out of service

The dynamic responses of the hystem following the elescriebed distur¬

bances are shown in Figure 6.9 and 6.10, respectively. The angular

separation between machines Gl and G16 are chosen to display since

6.3. Case Study 97

they are located in different areas. In order to examine the robustness

of the proposed controllers, a second disturbance, shown in Figure 6.7,

which does not belong to the group of the considered operating condi¬

tions when damping the controller.

Fault at bus 42 with bus 42-41 out

GA tuning

Conventional tuning

10 20 30 40

Time [s]

60

Figure 6,6: Relative angle between generators Gl and G16 for operating

condition mentioned on the top of plot - Case study I

Nonlinear simulations of the two previously described contingencies for

the system controlled by the designed PSSs and TCSC' POD confirm the

result shown in Figure 6.5. Although the controller* are tuned, using

conventional and G A methodology, aimed at achieving same mininmm

clamping, the controllers tuned by the GA methodology provide better

damping compared to the1 controllers tuned by conventional methodol-

CR.V-



CDI -50

« -60

-70

.,,,.,,, , ,

*-. .

Conventional tuning

L .

\w

20 30 40

Time [s]

Figuie 6.7- Relative angle between geneiators G l and G16 for operating

condition mentioned on the top of plot - Case study I

6.3. Case Study 99

PSS number + V) Kpss Pi T2 TA 'i\

Gl 10 22.2085 0.0908 0.5953 0.9584 0.3501

G2 10 11.7805 0.0349 0.2291 0.8014 0.5889

G3 10 37 7845 0.8869 0.1574 0.6691 0.6452

G4 10 38.3255 0.4376 0.9192 0.8552 0.5144

G 5 10 13.8715 0.2788 0.8789 0.2990 0.4032

G6 10 0.6275 0.0322 0.9801 0.0224 0.2799

G 7 10 18.9483 0.4391 0.7087 0.6754 0.0140

08 10 4.2650 0.4639 0.9662 0.4519 0.8767

G9 10 23.5469 0.3073 0.1616 0.9874 0.6020

G10 10 16.5584 0.8783 0.7659 0.6242 0.8721

Gil 10 33.1221 0.7248 0.1394 0.5936 0.8328

G12 10 39.6903 0.5653 0.0709 0 0889 0.8833

G13 - - - - - -

G14 10 39.2158 0.9117 0.0488 0.9381 0.8997

G15 10 16.0124 0.2167 0.6825 0.3896 0 4715

G16 10 29.8229 0.7304 0.1906 0.3278 0.6659

Table 6.4: Parameters lor PSSs controllers obtained by GA approach in

case study 1

FACTS controller T Kfacts Tlenà Pia a

TCSC 10 3.9740 0.1521 0.8118

Table 6 5: Parameters for for FACTS POD controllers obtained by OA

approach in case study I


PSS number • îJJ Kpss T\ T2 ra n

Gl 10 10 0.093 0.1695 0.0930 0.1695

02 10 15 0.0871 0.1179 0.0871 0.1179

G3 10 20 0.1326 0.1405 0.1320 0.1405

04 10 20 0.0947 0.2214 0.0947 0.2214

G 5 10 20 0.0989 0.2121 0.0989 0.2121

G6 10 20 0.1210 0.1734 0.1210 0.1734

07 10 25 0.0687 0.1492 0.0687 0.1492

G8 10 20 0.0848 0.1859 0.0848 0.1859

09 10 28 0.1063 0.1483 0.1063 0.1483

G10 10 20 0.1196 0.1275 0.1196 0.1275

Gil 10 10 0.0839 0.0892 0.0839 0.0892

012 10 10 0.1221 0.1348 0.1221 0.1348

G13 - - - - - -

GJ4 10 40 0.2613 0.2766 0.2613 0.2766

G15 10 40 0.2145 0.2498 0.2145 0.2498

G16 10 40 0.1951 0.2062 0.1951 0.2062

Table 6.6: Parameters for PSSs controllers obtained by conventional ap¬

proach in case study 1

FACTS controller T KFACTS Tit ad J Inq

TCSC 10 2 0.1470 0.9395

Table 6.7: Parameteis for for FACTS POD controllers obtained by con¬

ventional approach in case study I

6.3. Case Study 101

6.3.2 Case Study with the SVC - Case Study II

lu the case study II. the aim is the simultaneous tuning of all PSSs

and SVC POD controller. The SVC is located on bus 50. The same

linearized models as in Case Study 1 are, used for uncontrolled system

in order to design the proposed controllers. Figure 6.8 shows the dean¬

inant eigenvalues with the SVC installed in the system. Again, the

tuning with OA provides better damping compare to conventional tun¬

ing based on modal analysis. Considering damping of inter-area modes.

Figures 6.5 and 6.8 show that the system with the TCSC installed pro¬

vides better damping for inter-area modes compare to the system with

the SVC.

jeo

'

0 Conventional tuning

2 * GA tuning0 *\

0 \ .0

0*

o

e

6 "

*

Damping ratio

0.05

0* V

^ „ >\* \

* V4 * 2

2

*

0— -1 -0 5\ -3.5 -3 -2.5 -2 -1.5 0

Figure 6.8: Dominant closed-loop eigenvalues with the SVC" installed in

the system (for nominal operating condition)

The following disturbances are considered for simulation with a fault

for 80 ms close to the following buses:

f. bus # 53 followed by outage of the: line 53-47

2. bus if 60 followed by outage of the line 60-61 and with line 53-27

out of service


The dynamic iespouses of the system following described disturbances

are shown in Figure 6.9 and 6.10, respectively.


t\i

c -70<

GA tuning

Conventional tuning

Figure1 6.9: Relative angle between generators G 1 and G16 ior operating

condition mentioned on the top of plot - Case study II

In both oases, the controllers tuned by GA methodology provide better

damping compared with conventional approach. The final values of the

optimized parameters for PSSs and SVC POD controllers are given in

Table 6.10 and Table 6.11.

Comparing Figures 6.10 and 6.7, since they show dynamical response

for the same operating condition, it is obvious that the PSSs and the

TCSC", tuned by the GA, are: able to damp the oscillations within about

25 s, whereas the PSSs and the SVC need about 35 s for the same.

6.3. Case Study 103


13

I -55

54) -60O)C

<-65

1 *

^.. ,

-

Conventional tuning

- L

/\AAA/w-•

yvvvv^

30

Time [s]

Figure 6 10 Relative angle between geneialois Gl and Clfi loi oper¬

ating condition montioned on the top oi plot - Case study

II

104 Chapter 6. Coordinated Tuning.

PSS number * W Kpss n r2 Vj Pa

Gl 10 10.2653 0.4424 0.8189 0.7508 0.2351

G2 10 7.6746 0.2703 0.2072 0.1832 0.5312

03 10 36.9950 0.4360 0.6476 0.6372 0.4.812

04 10 31.0307 0.2924 0.0048 0.9534 0.9431

G 5 10 32.8585 0.1354 0.3087 0.8306 0.2327

GO 10 33.9995 0.2272 0.2861 0.2747 0.9942

07 10 19.5452 0.2215 0.1830 0.9778 0.3111

08 10 37.9839 0.6944 0.2559 0.5545 0.0437

G9 10 26.4172 0.0150 0.0533 0.9972 0.9212

G10 10 14.9597 0.8245 0.1457 0.2640 0.7141

Gil 10 12.7762 0.8742 0.4090 0.0697 0.3345

G12 10 39.6353 0.8836 0.6029 0.9424 0.5495

013 - - - - - -

G14 to 37.2248 0.6760 0.2154 0.7316 0.5303

Gl 5 10 21.4287 0.8316 0.4252 0.9441 0.7204

016 10 22.0855 0.1195 0.1746 0.9431 0.6054

Table 6.8: Controller parameters for PSSs controllers obtained by GA

approach in case study II

FACTS controller Pi, KFACTS Tu<i±\ Tin qSVC 10 7.09 0.930t 0.8319

Table 6.9: Controller parameters for FACTS POD controllers obtained

by GA approach in case study II

6.3. Case Study 105

PSS number T1 'W Kpss 1\ T2 73 T4

Gl 10 10 0.0976 0.1580 0.0976 0.1580

G2 10 10 0.1083 0.1250 0.1083 0.1250

G3 10 10 0.1329 0.1391 0.1329 0.1391

G4 10 5 0.0980 0.1040 0.0980 0.1040

05 10 20 0.1130 0.1861 0.1130 0.1801

GO 10 40 0.1179 0.1783 0.1179 0.1783

G7 10 30 0.0687 0.4205 0.0687 0.4205

G8 10 40 0.0367 0.1426 0.1106 0.1426

G9 10 30 0.1314 0.1417 0.1314 0.1417

G10 10 20 0.1198 0.1274 0.1198 0.1274

Gil 10 10 0.0839 0.0892 0.0839 0.0892

012 10 10 0.1220 0.1349 0.1220 0.1349

013 - - - - - -

G14 10 40 0.2615 0.2758 0.2015 0.2758

Gl 5 10 40 0.1997 0.2014 0.1997 0.2014

G10 10 40 0.1950 0.2064 0.1950 0.2064

Table 6.10: Controller parameters for PSSs controllers obtained by con¬

ventional approach in case study II

FACTS controller T KFACTS * 11" a (7 PlanSVC 10 5 0.1529 0.4717

Table: 6.11: Controller parameters for FACTS POD controllers obtained

by conventional approach in case study II

106 Chapter 6. Coordinated Tuning'...

6.3.3 Case Study with the TCSC and the SVC -

Case Study III

This case study presents the results after applying GA methodology

to the simultaneous tuning of all PSSs, the SVC and the TCSC POD

controllers in test system. Since there are: two FACTS POD controllers,

the aim is to achieve 7% damping for all oscillatory modes ove:r all op¬

erating conditions under consideration. According to the results shown

in Table 6.2 and Table 6.3, line 41 -- 42 is chosen for TC'SC location,

whereas bus 50 is chosen for SVC location. To design the proposed

controllers, linearized models for the following four different operating

conditions for uncontrolled system are considered;

• Base: case

• Line 53 - 47 and line 60 - 61 out, of service

• Line 53 - 54 and line 39 45 out of service

• Line 46 - 49 and line 53 - 47 out, of service1

The following disturbances are considered for simulation with a fault

for 80 ms close to the following buses:

1. bus # 46 followed by outage of the line 46-49 and with line 53-47

out of service

2. bus # 60 followed by outage of the line 60-61 ancl with line 53-27

out of service1

Dynamic responses for above disturbances are shown in Figures 6.12

and 6.13, respectively. These figures exhibit the relative angular sepa¬

ration between the generators located in separate geographical regions.

The final values of the optimized parameters for PSSs and SVC POD

controllers are given in Table 6.14 and Table 6.15.

As in case studies I and II, the GA methodology provides better damp¬

ing compared with conventional damping. To evaluate1 the performance

6.3. Case Study 107

* GA tuningVi o Conventional tuning o

\

1000

0 \** o 0 \

s

6

o

*

*

**

*»

Damping ratio 0.07——»A* a

4

* \

2o A

n

0i atcon »t »i toi ma«

0

sm ' «••»

-2.5 -2 -1 5 -1

O

Figure 6.11: Dominant closed-loop eigenvalues with the TCSC and the

SVC installed in the system (for nominal operating condi¬

tion)

and robustness of the designed controllers, the second disturbance is

chosen to be: the1 same as for the previous cases.

108 Chapter G. Coordinated Tuning...


-70

GA tuning

Conventional tuning

20 30 40

Time [s]

Figuie 6.12 Relative angle between generators Gl and G16 for operat¬

ing condition mentioned on the top of plot


-30 i r- , i 1— 1

< -6

GA tuning

Conventional tuning

20 30 40 50 60

Time [s]

Figure 6 13- Relative angle between geneiatois Gl and 016 foi opeiat

ing condition mentioned cm the top of plot

6.3. Case Study 109

PSS number Ta Kpss ïi Pz Ti Fa

Gl 10 31.3586 0.7606 0.3331 0.0848 0.4809

G2 10 38.2932 0.9468 0.1699 0 6002 0.9106

03 10 34.5484 0.5244 0.2125 0.2413 0.2052

CM 10 36.4488 0.9070 0.4036 0.4063 0.3791

G5 10 31.8271 0.3701 0.2870 0.4896 0.8186

06 10 27.4265 0.4169 0.7222 0.6956 0.1588

G7 10 32.2473 0.9946 0.8566 0.3700 0.4241

G8 10 38.9045 0.4319 0.7723 0.5000 0.3217

09 10 32.7795 0.8846 0.3527 0.6502 0.7449

G10 10 36.9588 0.8781 0.2445 0.6507 0.3935

Gil 10 35.5656 0.2881 0.4313 0.0605 0.0462

012 10 35.0717 0.9287 0.1631 0.2421 0.5010

013 - - - - - -

014 10 38.0251 0.9202 0.4881 0.9249 0.3011

G15 10 36.7685 0.9485 0.0903 0.0250 0.3818

G16 10 35.3055 0.8335 0.4210 0.9522 0.4564

Table 6.12: Controller parameters for PSSs controllers obtained by GA

approach in case study III

FACTS controller T,, XFACTS J lend Pirn,

SVC 10 0.4397 0.5247 0.6396

TCSC 10 0.3272 0.0519 0.9687

Table 6.13: Ccmtroller parameters for FACTS POD controllers obtained

by GA approach in case study III


PSS number T,„ P'pss P Pi T, Ta

Gl 10 40 0.0929 0.1096 0.0929 0.1696

02 10 25 0.1083 0.1250 0.1083 0.1250

G 3 10 25 0.1118 0.1212 0.1118 0.1212

G4 10 40 0.0947 0.2214 0,0947 0.2214

G5 JO 40 0.0989 0 2121 0.0989 0.2121

GO 10 35 0.1210 0.1734 0.1210 0.1734

G7 10 40 0.0687 0.1492 0.0687 0.1492

08 10 40 0.0850 0.1856 0 0850 0.1856

09 10 40 0.1065 0.1481 0,1065 0.1481

G10 10 30 0.1198 0,1277 0.1198 0.1274

OU 10 15 0.0839 0.0892 0.0839 0.0892

G12 10 25 0.1220 0.1349 0,1220 0.1349

G13 - - - - - _

G14 10 40 0.4018 0.4174 0,4018 0.4174

Gl 5 10 40 0.1254 0,1412 0.1254 0.1412

G10 10 40 0.2110 0.2124 0.2116 0.2124

Table: 6.14: Controller parameters for PSSs controllers obtained by con¬

ventional approach in case study III

FACTS controller '/;, KFACTS Pifad Finn

SVC 10 2 0.1137 0.3954

TCSC 10 0.5 0.0737 0.6098

Table 6.15: Controller parameters for FACTS POD controllers obtained

by conventional approach in case study III

6.4. Summary 111

6.4 Summary

In this chapter, simultaneous tuning of multiple PSSs and FACTS POD

controllers has been illustrated using GA methodology. The1 control

design methodology was illustrated by throe case studies. In the first

two cases, the POD controllers were designed for 15 PSSs and a different,

single FACTS POD controller. In the third case, the aim was to tune 15

PSSs and two FACTS POD controllers. The performance of the design

was validate using non-linear simulations. Furthermore, comparison

with the conventional tuning procedure showed that the performance is

more robust when damping controllers were designed by GA procedure.

Seite Leer /

Blank leaf

Chapter 7

Concluding Remarks

In this thesis, different control design methodologies for designing FACTS

power flow controllers and power oscillations damping controllers in

power systems have been illustrated.

The injection models of the Thyristor Controlled Series Capacitor (TC'SC).Unified Power Flow Controllers (UPFC) and Static VAR Compensator

(SVC) with their power flow controllers have been demonstrated. The

injection models are very simple to implement and they have been ap¬

preciate for the kind of investigation carried out in this thesis. The

software for both steady-state study and dynamic study of large power

systems embedded with FACTS devices have been developed.

The application of FACTS damping controllers, using conventional ap¬

proach based on the residue method turned out to lack robustness under

changed operating conditions. Poorly damped or even unstable oscilla¬

tions can result in instability, since the controller parameters yielding

satisfactory clamping for one operating condition may no longer be valid

for another one. In those cases, a re-tuning is necessary. That provided

the motivation for developing an adaptive control strategy.

A simple adaptive tuning method based on the residue approach has

been developed and applied to the TCSC. The disadvantage of this sim¬

ple approach is that the system model has to be available in order to

find optimal location for FACTS devices and consequently to calculate

113

114 Chapter 7. Concluding Remarks

the values of residues for the controller design. This is the reason for the1

implementation of a more flexible self-tuning controller. The pole: shift¬

ing method was applied in the control design. As the system dynamics

are identified on-line, based on the automatic detection of oscillations in

power systems using dynamic data from the system, the most dominant

oscillation mode: present at any time: is identified. Hence, the control

provides maximum damping of the identified frequency all the time,

under different, operating conditions, leading to an improvement of the

damping characteristic.

In general, the optimal location of the FACTS controller obtained ac¬

cording to the dynamic criteria is not the same as the one obtained

according to the static criteria. A compromise has to bo found for each

particular case, considering multiple tasks, for example powei flow con-

trol and damping of oscillations. The procedure for considering the

TCSC location in order to satisfy the mentioned requirements has been

presented. As the static criteria (for optimal location of the power flow

controller), power flow sensitivity analysis has boon used; as the dy¬

namic criteria (for optimal location of the damping controller), residue

analysis has been used. Verification by simulation matched predictedlocation as optimally selected TC'SC location with respect to both con¬

trol objectives.

The concept of simultaneous coordination of multiple controllers in the

svstem, like PSS and FACTS POD controllers, has been applied. The

concept has been based on Genetic Algorithm (GA) methodology, in

which an optimization problem to be solved is to determine the con¬

ti oiler parameters so that they provide required damping of the closed-

loop system, under different operating conditions. Furthermore:, com¬

parison with the: conventional based tuning procedure showed that the

performance is more: robust when damping controllers were designed by

GAs proceelure.

In this thesis, on-line tuning was applied just on the TCSC. It would be

desirable to apply all proposed on-line approaches to FACTS devices,

e.g. SVC and UPFC". This task could bo the subject of future research.

Designing POD controllers, local signals as a feedback signals were used

in this work. In general, the use of phasor measurement units (PMU)ensures transmission of remote signals in almost real time. Allowing the

115

controller to use multiple input signals, some of which might be remote,

could prove as more effective in damping of oscillations. Moreover, it

might be possible to build a hierarchical control scheme in order to

achieve better control of oscillations ancl, for example, optimization of

power flow, especially in case of multiple contingencies. Future1 reseaich

in this direction would provide more insight into these1 possibilities.

Se/teBlank

Leer

Appendix A

IEEE 39 Bus Test

System Data

The topology of the system is .shown in Figuie 6,3. All data here are in

pu with a base power of 100 MVA

Bus Nr. Voltage Power generation Real load Reactive load

1 1.03 10 00 11 04 2.50

2 0.982 - 0.092 0.046

3 0.983 6.50 0.00 0.00

4 0.997 6 32 0 00 0.00

5 1.011 5.08 0.00 0.00

6 1.050 6.50 0.00 0.00

7 1.063 5.60 0.00 0.00

8 1.0278 5.40 0.00 0.00

9 1 0265 8 30 0.00 0.00

10 1.015 2 50 0 00 0.00

Table A.T Machine bus data

117

118 Appendix A. IEEE 39 Bus Test System Data

Bus Nr. Real load Reactive load

11 0.00 0.00

12 0.075 0.88

13 0.00 0.00

14 0.00 0.00

15 3.20 1.53

16 3.29 0.32

17 0.00 0.00

18 1.58 0.30

19 0.00 0.00

20 6.28 1.03

21 2.74 1.15

22 0.00 0.00

23 2.47 0.846

24 3.086 -0.92

25 2.24 0.472

26 1.39 0.17

27 2.81 0.755

28 2.06 0.276

29 2.835 0.269

30 0.00 0.00

31 0.00 0.00

32 3.22 0.024

33 5.00 1.84

34 0.00 0.00

35 0.00 0.00

36 2.338 0.84

37 5.22 1.76

38 0.00 0.00

39 0.00 0.00

Table A.2: Load bus data

119

From To Resistance Reactance Line charging Tap latio

39 31 0.0035 0.0411 0.6987 0.00

39 1 0.0010 0.0250 0.7500 0.00

31 32 0.0013 0.0151 0.2572 0.00

31 25 0.0070 0.0086 0.1460 0.00

32 33 0.0013 0.0213 0.2214 0.00

32 18 0.0011 0.0133 0 2138 0.00

33 34 0.0008 0.0128 0.1312 0.00

33 14 0.0008 0.0129 0.1382 0.00

34 35 0.0002 0.0026 0.0434 0.00

34 37 0.0008 0.0112 0.1476 0.00

35 36 0.0006 0.0092 0.1130 0.00

35 11 0.0007 0.0082 0.1389 0.00

36 37 0.0004 0.0040 0.0780 0.00

37 38 0.0023 0.0363 0.3804 0.00

38 1 0.0010 0.0250 1.2000 0.00

30 11 0.0004 0.0043 0.0729 0.00

30 13 0.0004 0.0043 0.0729 0.00

13 14 0.0009 0.0101 0.1723 0.00

14 15 0.0018 0.0217 0.3660 0.00

15 16 0.0009 0.0094 0.1710 0.00

16 17 0.0007 0.0089 0.1342 0.00

16 19 0.0016 0.0195 0,3040 0.00

16 21 0.0008 0.0135 0.2548 0.00

16 24 0.0003 0.0059 0.0680 0.00

17 18 0.0007 0.0082 0.1319 0.00

17 27 0.0013 0.0173 0.3210 0.00

21 22 0.0008 0.0140 0.2565 0.00

22 23 0.0006 0.0096 0.1846 0.00

23 24 0.0022 0.0350 0.3610 0.00

25 26 0.0032 0.0323 0.5130 0.00

26 27 0.0014 0.0147 0.2396 0.00

26 28 0.0043 0.0474 0.7802 0.00

26 29 0.0057 0.0625 1.0290 0.00

28 29 0.0014 0.0151 0.2490 0.00

12 11 0.0016 0.0435 0.0000 1.006

12 13 0.00 J 6 0.0435 0.0000 1.006

Continued on next page

120 Appendix A. IEEE 39 Bus Test System Data

Continued iiom pievious page

From To Resistance Reactance Line charging Tap ratio

35 2 0.0000 0.0250 0.0000 1 070

30 3 0.0000 0.0200 0.0000 1.070

19 4 0.0007 0.0142 0.0000 1.070

20 5 0 0009 0.0180 0.0000 1.009

22 6 0.0000 0.0143 0.0000 1.025

23 7 0.0005 0.0272 0 0000 0.00

25 8 0.0006 0.0232 0.0000 1.025

31 10 0.0000 0.0181 0 0000 1.025

29 9 0.0008 0.0156 0 0000 1.025

19 20 0.0007 0.0138 0.0000 1 000

Table A.3: Line data

Machine

Xi

Ra

xA

KT'

x,

K'^

HD

Gl

0.003

0.00

0.02

0.006

7.0

0.019

0.008

0.7

500

0

G2

0.035

0.00

0.295

0.0697

6.56

0.282

0.170

1.5

30.3

0

G3

0.0304

0.00

0.2495

0.0531

5.7

0.237

0.0876

1.5

35.8

0

G4

0.0295

0.00

0.262

0.0436

5.69

0.258

0.166

1.5

28.6

0

G5

0.054

0.00

0.67

0.132

5.4

0.62

0.166

0.44

26.0

0

G6

0.0224

0.00

0.254

0.05

7.3

0.241

0.0814

0.4

34.8

0

G7

0.0322

Ü.00

0.295

0.049

5.66

0.292

0.186

1.5

26.4

0

G8

0.028

0.00

0.29

0.057

6.7

0.280

0.0911

0.41

24.3

0

G9

0.0298

0.00

0.2106

0.057

4.79

0.205

0.0587

1.96

34.5

0

G10

0.0125

0.00

0.1

0.031

10.2

0.069

0.008

0.0

42.0

0

Table

A.4:Machinedvnamicdata

ei

Qseu

+^

enen

3ffl

OHBXa<D

aa<

Machineno

A',!Ta

Yfimm

VRma-c

KE

Te

-êx

B,,

AV

Tf

10

00

00

00

00

0

26.2

0.05

-1.0

1.0

00.405

0.1175

2.0252

0.057

0.5

35.0

0.06

-1.0

10

00.5

0.0031

1.6988

0.08

1.0

45.0

0.06

-1.0

1.0

00.5

0.0006

2.0787

0.08

1.0

540.0

0.02

-10.0

10.0

00.785

0.0000

1.0384

0.03

1.0

650

0.02

-1.0

1.0

00.471

0.0004

1.6608

0.0754

1.246

740.0

0.02

-6.5

6.5

00.73

0.0821

0.2830

0.03

1.0

85.0

0.02

-1.0

1.0

00.528

0.0005

1.8645

0.0854

1.26

940.0

0.02

-10.5

10.5

01.4

0.1015

0.1953

0.03

1.0

10

5.0

0.06

-1.0

1.0

00.25

0.0010

1.5249

0.04

1.0

Table

A.5:DC

excitationsvstemdata

Appendix B

IEEE 68 Bus Test

System Data

The topology of the system is shown in Figuie 6.3. All data here are1 in

pu with a base1 powei of 100 MVA.

Table B.l. Machine bus data

Bus Nr. Voltage Powei generation

1 1.045 2.5

2 0.98 5.45

3 0.983 6.50

4 0.997 6.32

5 1.011 5.052

6 1.050 7 00

7 1.063 5.60

8 1.03 5.40

9 1.025 8.00

10 1.010 5 00

11 1.000 10.00

12 1.0156 13 50

13 1.011 35.91


123

124 Appendix B. IEEE 68 Bus Test System Data

Table B.l: Machine bus data (continued)Bus Nr. Volt age Power generation

14 1.00 17.85

15 1.00 10.00

16 1.00 40.00

Table B.2: Load bus data

Bus Nr. Real load Reactive load

17 0.00 0.00

18 1.58 0.30

19 0.00 0.00

20 6.80 1.03

21 1.740 1.15

22 0.00 0.00

23 1.48 0.85

24 3.09 -0.92

25 2.24 0.47

26 1.39 0.17

27 2.81 0.76

28 2.06 0.28

29 2.84 0.27

30 0.00 0.00

31 0.00 0.00

32 0.00 0.00

33 1.12 0.00

34 0.00 0.00

35 0.00 0.00

36 1.02 -0.1946

37 60.00 3.00

38 0.00 0.00

39 2.67 0.126

40 0.6563 0.2353

41 10.00 2.50

42 11.50 2.50


Table B.2: Load bus data (continued)Bus Nr. Real load Reactive load

43 0.00 0.00

44 2.6755 0.0484

45 2.08 0.21

46 1.507 0.285

47 2.0312 0.3259

48 2.4120 0.022

49 1.64 0.29

50 2.00 -1.47

51 4.37 -1.22

52 24.7 1.23

53 2.527 1.1856

54 0.00 0.00

55 3.22 0.02

56 5.00 1.84

57 0.00 0.00

58 0.00 0 00

59 2.31 0.84

60 5.221 WM

61 1.04 1.25

62 0.00 0.00

63 0.00 0.00

64 0.09 0.88

65 0.00 0.00

66 0.00 0.00

67 3.20 1.53

68 3.29 0.32

Table B.3: Line data

From lb Resistance Reactance Line charging Tap ratio

53 54 0.0070 0.0822 0 3493 0

53 30 0.0008 0.0074 0.48 0

54 55 0 0013 0.0151 0.2572 0



Taille B.3: Line data (continued)From To Resistance Reactance Line charging Tap ratio

54 25 0.007 0.0086 0.146 0

54 1 0.00 0.0181 0.00 1.025

55 56 0.0013 0.0213 0.2214 0

55 18 0.0011 0.0133 0.2138 0

56 57 0.0008 0.0128 0.1342 0

56 66 0.0008 0.0129 0.1382 0

57 58 0.0002 0.0026 0.0434 0

57 60 0.0008 0.0112 0.1476 0

58 59 0.0006 0.0092 0.1130 0

58 63 0.0007 0.0082 0.1389 0

58 2 0 0.0250 0 1.07

59 60 0.0004 0.0046 0.078 0

60 61 0.0023 0.0363 0.3804 0

61 30 0.0019 0.0183 0.29 0

62 03 0.0004 0.0043 0.0729 0

62 65 0.0004 0.0043 0.0729 0

62 3 0 0.02 0 1.07

64 63 0.0016 0.0435 0 1.06

64 65 0.0016 0.0435 0 1.06

65 66 0.0009 0.0101 0.1723 0

66 67 0.0018 0.0217 0.3C6 0

67 68 0.0009 0.0094 0.171 0

68 17 0.0007 0.0089 0.1342 0

68 19 0.0016 0.0195 0.3040 0

68 21 0.0008 0.0135 0.2548 0

68 24 0.0003 0.0059 0.0680 0

17 18 0.0007 0.0082 0.1319 0

17 27 0.0013 0.0173 0.3216 0

19 20 0.0007 0.0138 0 1.06

19 4 0.0007 0.0142 0 1.07

20 5 0.0009 0.0180 0 1.009

21 22 0.0008 0.0140 0.2565 0

22 23 0.0006 0.0096 0.1846 0

22 6 0 0.0143 0 1.025

23 24 0.0022 0.0350 0.3610 0


Table B.3: Line data (continued)From To Resistance Reactance | Line: charging Taj) îatio

23 7 0.0005 0.0272 0 0

25 20 0.0032 0.0323 0.5310 0

25 8 0.0006 0.0232 0 1.025

26 27 0.0014 0.0147 0.2396 0

26 28 0.0043 0.0474 0.7802 0

26 29 0.0057 0.0625 1.0290 0

28 29 0.0014 0.0151 0.2490 0

29 9 0.0008 0.0156 0 1.025

61 30 0.0019 0.0183 0.29 0

61 36 0.0022 0.0196 0.34 0

61 36 0.0022 0.0196 0.34 0

36 37 0.0005 0.0045 0.32 0

34 36 0.0033 0.0111 1.45 0

35 34 0.0001 0.0074 0 0.946

33 34 0.0011 0.0157 0.202 0

32 33 0.0008 0.0099 0.168 0

30 31 0.0013 0.0187 0.333 0

30 32 0.0024 0.0288 0.488 0

53 31 0.0016 0.0163 0.25 0

31 38 0.0011 0.0147 0.247 0

33 38 0.0036 0.0444 0.693 0

38 46 0.0022 0,0284 0.43 0

46 49 0.0018 0.0274 0.27 0

53 47 0.0013 0.0188 1.31 0

47 48 0.0025 0.0208 0.40 0

47 48 0.0025 0 0268 0.40 0

48 40 0.0020 0.022 1.28 0

35 45 0.0007 0.0175 1.39 0

37 43 0.0005 0.0276 0 0

43 44 0.0001 0.0011 0 0

44 45 0.0025 0.073 0 0

39 44 0 0.0411 0 1.00

39 45 0 0.0839 0 0

45 5L 0.0004 0.0105 0.72 0

50 52 0.0012 0.0288 2.06 0



Table B.3: Line data (continued)From To Resistance Reactance Line charging Tap ratio

50 51 0.0009 0.0221 1.62 0

49 52 0.0070 0.1141 1.16 0

52 42 0.0040 0.0600 2.25 0

42 41 0.0040 0.0600 2.25 0

41 40 0.0060 0.0840 3.15 0

31 10 0 0.026 0 1.04

32 11 0 0.013 0 1.04

36 12 0 0.0075 0 1.04

37 13 0 0.0033 0 1.04

41 14 0 0.0015 0 1.00

42 15 0 0.0015 0 1.00

52 16 0 0.0030 0 1.00

53 27 0.032 0.32 0.41 0

Machine no. AV TA v Urn 7 r\ Vrima.1-

1 200 0.05 -5 5

2 200 0.05 -5 5

3 200 0.05 -5 5

4 200 0.05 -5 5

5 200 0.05 -5 5

6 200 0.05 -5 5

j 200 0.05 -5 5

8 200 0.05 -5 5

9 200 0.05 -5 5

10 200 0.05 -5 5

Table: B.4: Static excitation system data

Machine

Xi

Ra

xA

K7"'1d

xq

*;

VH

D

Gl

0.0125

0.00

0.1

0.031

10.2

0.069

0.028

1.5

42

0

G2

0.035

0.00

0.295

0.0697

6.56

0282

0.060

1.5

30.2

0

G3

0.0304

0.00

0.2495

0.0531

5.7

0.237

0.050

1.5

35.8

0

G4

0.0295

0.00

0.262

0.0436

5.69

0.258

0.040

1.5

28.6

0

G5

0.027

0.00

0.33

0.066

5.4

0.31

0.060

0.44

26.0

0

G6

0.0224

0.00

0.254

0.05

7.3

0.241

0.045

0.4

34.8

0

G7

0.0322

0.00

0.295

0.049

5.66

0.292

0.045

1.5

26.4

0

GS

0.028

0.00

0.29

0.057

6.7

0.280

0.05

0.41

24.3

0

G9

0.0298

0.00

0.2106

0.057

4.79

0.205

0.050

1.96

34.5

0

G10

0.0199

0.00

0.169

0.0457

9.37

0.115

0.045

1.5

31.0

0

Gil

0.0103

0.00

0.128

0.018

4.1

0.123

0.015

1.5

28.2

0

G12

0.022

0.00

0.101

0.031

7.4

0.095

0.028

1.5

92.3

0

G13

0.0030

0.00

0.0296

0.0055

5.9

0.0286

0.005

1.5

248.0

0

G14

0.0017

0.00

0.018

0.00285

4.1

0.0173

0.0025

1.5

300.0

0

G15

0.0017

0.00

0.018

0.00285

4.1

0.0173

0.0025

1.5

300.0

0

G16

0.0041

j0.00

0.0356

0.0071

7.8

0.0334

0.006

1.5

225.0

0

Table

B.5:Machinedvnamicdata


Appendix C

Sensitivity Analysis

Notation

In this part, the following notations and definitions are used:

• ne' number of transmission lines

• f, (' : indices for transmission lines

• Z( --- V( \ .;'(./> J'ct) ; series impedance of line ('

• Vf = 9t +" jbf ' series admittance of line C

• Zc = fad}' • vec'ôi' of series capacitive resistances

• P : vector of active power injections at all nodes except slack node

• Q : vector of reactive power injections at PQ-nodes

• W : vector of active power line flows

• SL^ : seM of linos connected to bus i

• Spv : set of PV nodes

• Sr(* : set of PQ -nodes

• SLK : slack node

131

132 Appendix C. Sensitivity Analysis

d(f( 2rt(xp - Xtt)• li =

• fit

ütc, (r= + (r,-ir/)2)2

8bf ~(k -x,f)2 + 7'|Oxa (,f + (A/- rifyy

Jacobian Matrix F,

F,Pz,

Que

dp

UZce

OQ,

àZCf'

ldV? - KV, cosö,,) - ßtVtV, hinö,, ? + SLK,* e- S7'"'

0 ot her wise1

(Cl)

/M-V/* + V,Vr,cos0„)-7fV,V';bin0,J 7 f S"'«,? S''(,)

0 otherwise

(C 2)

Jacobian Matrix Wr

OW't__

d\Vt

~rJÖ7~~

1 0

wT = [ w0 wv ]

«/«V.VjSiiiöy-^VjCosÖ,, //SLK, ijff(c;j)

0 otherwise

- ge V, V, sin 0,7 + be V, V, cos 0,, 7 / SLK, yefotheiwise

(C.4)

i)Wf_

2*7/V, - e;^V? cos 0,7 - beVt sin 0„ ? e 5/>Q ',.; £ ^

0 otherwise

t)V, { 0

-<7fV, oos{V,7 - bfV, hhi0(/ i G 6"J'Q i,jCôtherwise

(0-5)

(C 6)

133

Jacobian Matrix W.

W* ~ [Wzt ]

9W(_

f 1((V;2 - V,V, cos 0„) - /9,V, V, sm0„ t ~ f

(0 7)


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Curriculum vitae

EDUCATION

2002 - 2006 Swiss Federal Institute of Technology (ETII),Zürich, Switzerland, PhD studies in Electric

Power Systems1998 - 2001 Faculty of Electrical Engineering, Tuzla, Bosna

and Hercogovina, MSc studies in Electric Power

Engineering1988 1995 Faculty of Electrical Engineering. Tuzla, Bosna

and Hercegovina, BSc studies in Electric Power

Engineering1984 - 1988 Secondary school: Gymnasium "Mesa Se-

limovic", Tuzla, Bosna and Hercegovina

EXPERIENCE

2002 - 2006

1997 -- 2002

1996 - 1997

1993 - 1995

Research Assistant at the Power Systems Lab¬

oratory, Swiss Federal Institute of Technology

(ETII), Zurich, Switzerland

Research Assistant at Faculty of Electrical Engi¬

neering, Tuzla, Bosna and Hercegovina

ICS, Italian Nongovernmental Humanitarian Or¬

ganization, Tuzla, Bosna and HercegovinaLocal Center for Refugees, Tuzla, Bosna and

Hercegovina

.1.39

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