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AbstractThis paper presents a multi-objective GeneticAlgorithm (GA) approach to tune the parameters of a Thyristor

Controlled Series Compensator (TCSC), for power system stability

improvement. Pareto method type of selection is used in the present

multi-objective GA approach, which gives a set of solutions from

which the best one can be chosen according to the requirements and

needs. The design problem of TCSC controller is formulated as a

parameter-constrained, multi objective optimization problem, and the

parameters of the TCSC controller are optimally tuned. By

minimizing the time-domain based multi objective function, in which

the deviations in the oscillatory rotor angle, rotor speed and

accelerating power of the generator are involved, stability

performance of the system is improved. The proposed controllers are

tested on a weakly connected power system subjected to a

disturbance. Simulations are executed for an example power system

to analyze the effectiveness and robustness of the proposed

controllers.

KeywordsMulti-objective genetic algorithm, Phillips-Heffronmodel, power system stability, TCSC.

I. INTRODUCTION

HEN large power systems are interconnected by

relatively weak tie lines, low frequency oscillations are

observed. These oscillations may sustain and grow to cause

system separation if no adequate damping is available [1].

Recent development of power electronics introduces the use

of flexible ac transmission system (FACTS) controllers in

power systems. FACTS controllers are capable of controlling

the network condition in a very fast manner and this feature of

FACTS can be exploited to improve the stability of a powersystem [2]. Thyristor Controlled Series Compensator (TCSC)

is one of the important members of FACTS family that is

increasingly applied with long transmission lines by the

utilities in modern power systems. It can have various roles in

the operation and control of power systems, such as

scheduling power flow; decreasing unsymmetrical

Manuscript received August 1, 2006.

Sidhartha Panda is a research scholar in the Department of Electrical

Engineering, Indian Institute of Technology, Roorkee, Uttaranchal, 247667,

India. (e-mail: [email protected]).

R.N.Patel and N.P.Padhy are faculty in the Department of Electrical

Engineering, Indian Institute of Technology, Roorkee, Uttaranchal, 247667,

India.(e-mail: [email protected], [email protected])

components; reducing net loss; providing voltage support;

limiting short-circuit currents; mitigating subsynchronous

resonance (SSR); damping the power oscillation; and

enhancing transient stability [3]-[6]. The problem of FACTS

controller parameter tuning is a complex exercise as

uncoordinated local control of FACTS controller may cause

destabilizing interactions [7]-[8].

The Phillips-Heffron model is a well-known model for

synchronous generators [9]. Traditionally, for the small signal

stability studies of a single-machine infinite-bus (SMIB)

power system, the linear model of Phillips-Heffron has been

used for years, providing reliable results.Although the model

is a linear model, it is quite accurate for studying low

frequency oscillations and stability of power systems. It has

also been successfully used for designing and tuning the

classical Power System Stabilizers.

Recently Genetic algorithms (GA) are becoming popular to

solve the optimization problems in different fields of

application, mainly because of their robustness in finding an

optimal solution and ability to provide a near optimal solution

close to a global minimum [10]. As the GA has an apparent

benefit to adapt to irregular search space of an optimization

problem, many researchers have employed GA for

optimization problems in power systems [11]-[13]. Most of

the authors adapted a single objective function, or converted

the multi objective function into a single objective function

using appropriate weights, in the GA optimization problem.

However, a problem that arises is how to normalize, prioritize

and weight the contributions of the various objectives in

arriving at a suitable measure. Further, one of the primary

difficulties presented by the weighted sum type multi-

objective problems is that normally there is no single solution

to such problems which is optimum in the sense traditionally

expected. Instead there is a large family of alternative

solutions according to various objectives, which have the

same global fitness.

This paper adapts Pareto method type selection in the GA

algorithm to solve the multi objective optimization problem.

In this method, instead of selecting and breeding just the best

overall solution, a set of solutions are maintained based upon

the values of all the separate objectives. These set of solutions

are such that any of the objective functions can not be

improved further without at the same time worsening another.

Power System Stability Improvement by TCSC

Controller Employing a Multi-ObjectiveGenetic Algorithm Approach

Sidhartha Panda, R.N.Patel, N.P.Padhy

W

International Journal of Intelligent Systems and Technologies 1;4 www.waset.org Fall 2006

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In such a case all the other lesser solutions are said to be

dominated by these better ones and are discarded.

In this study the design problem of TCSC controller to

improve power system stability is transformed into a multi-

objective optimization problem where the multi-objective GA

approach is employed to search for the optimal TCSCcontroller parameters. By Pareto method type of selection, a

set of non-dominated solution is obtained, from which the user

could choose the one that best suits the requirements and

needs. The simulation results have been carried out to

demonstrate the effectiveness and robustness of the proposed

approach to enhance the power system stability.

II. THYRISTORCONTROLLED SERIES COMPENSATOR(TCSC)

TCSC is one of the most important and best known FACTS

devices, which has been in use for many years to increase line

power transfer as well as to enhance system stability. The

main circuit of a TCSC is shown in Fig. 1. The TCSC consists

of three main components: capacitor bank C, bypass inductorL and bidirectional thyristors SCR1 and SCR2. The firing

angles of the thyristors are controlled to adjust the TCSC

reactance in accordance with a system control algorithm,

normally in response to some system parameter variations.

According to the variation of the thyristor firing angle or

conduction angle, this process can be modeled as a fast switch

between corresponding reactance offered to the power system.

When the thyristors are fired, the TCSC can be

mathematically described as follows:

dt

dvCiC = (1)

dt

diLv L= (2)

LCS iii += (3)

where iC and iL are the instantaneous values of the currents in

the capacitor banks and inductor, respectively; iS the

instantaneous current of the controlled transmission line; v is

the instantaneous voltage across the TCSC. Assuming that the

total current passing through the TCSC is sinusoidal; the

equivalent reactance at the fundamental frequency can be

represented as a variable reactance XTCSC. The TCSC can be

controlled to work either in the capacitive or the inductive

zones avoiding steady state resonance. This mode is calledvenire control mode. There exists a steady-state relationship

between the firing angle and the reactance XTCSC. Thisrelationship can be described by the following equation [14]:

+

+

=

))2/tan()2/ktan(k(

)1k(

)2/(cos

)XX(

X4

sin

)XX(

XX)(X

2

2

PC

2C

PC

2C

CTCSC

(4)

where,

=CX Nominal reactance of the fixed capacitor C.

=PX Inductive reactance of inductor L connected in

parallel with C.

== )(2 Conduction angle of TCSC controller

P

C

X

Xk= = Compensation ratio

SCR1

L

C

iL

iC

v

is

SCR2

Fig. 1 Configuration of a TCSC

T1

T2

L

XC

XL

VB

XTCSC

XP

CXTGVT

Fig. 2 Single machine infinite bus power system with TCSC

III. MODELING THE POWERSYSTEM WITH TCSC

The single-machine infinite-bus power system shown in

Fig. 2 is considered in this study. The system has a TCSC

installed in the transmission line. In the figure XT and XL

represent the reactance of the transformer and the transmission

line respectively, VT and VB are the generator terminal voltage

and infinite bus voltage respectively.

A. The Non-Linear equations

The non-linear differential equations of the single machine

infinite bus power system with TCSC are [1, 9]:

=

b

]PP[M

1em =

]EE[

'T

1'E fdq

doq +=

]VV[sT1

K'E TR

A

Afd

+=

where,

=

2sinX'X2

)'XX(Vsin

X

V'EP

'qd

dq2

B

'd

Bqe

=

cosV

'X

)'XX(

X

'EXE B

d

dd

'd

qdq


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ysT1

sT1

sT1

sT1

sT1

sTKu

4

3

2

1

w

wT

+

+

+

+

+=

(8)

where, u and y are the TCSC controller output and input

signals, respectively. In this structure, Tw is usually

prespecified and is taken as 10 s. Also, two similar lag-lead

compensators are assumed so that T1=T3 and T2=T4. The

controller gain KT and time constants T1 and T2 are to be

determined. In this study, the input signal of the proposed

TCSC controller is the speed deviation and the output is

change in conduction angle . During steady state conditions

= 0 and XEff = XT+XL-XTCSC(0). During dynamic

conditions the series compensation is modulated for damping

system oscillations. The effective reactance in dynamic

conditions is: XEff = XT+XL-XTCSC(), where = 0+ and

=2(-), 0 and 0 being initial value of firing & conduction

angle respectively.

B. Objective Function

It is worth mentioning that the TCSC controller is designed

to minimize the power system oscillations after a disturbance

so as to improve the stability. These oscillations are reflected

in the deviations in the generator rotor angle (), rotor speed

() and accelerating power (Pa). A multi-objective

function based on , and Pa is used as an objective

function in the present study. The objective can be formulated

as the minimization of:

)F,F,F(J 321= (9)

where,

= 1t0 21 dt)]X,t([F , = 1t0 22 dt)]X,t([F and =

1t

0

2a3 dt)]X,t(P[F

In the above equations, (t, X), (t, X) and Pa (t, X)

denote the rotor angle, speed and accelerating power

deviations for a set of controller parameters X (note that here

X represents the parameters to be optimized; i.e. KT, T1, T2,

the parameters of TCSC controller), and t1 is the time range of

the simulation. With the variation of the parameters X, the

(t, X),

(t, X) and

Pa (t, X) will also be changed. Forobjective function calculation, the time-domain simulation of

the power system model is carried out for the simulation

period. It is aimed to minimize this objective function in order

to improve the system response in terms of the settling time

and overshoots.

C. Optimization Problem

In this study, it is aimed to minimize the proposed objective

functions J. The problem constraints are the TCSC Controller

parameter bounds. Therefore, the design problem can be

formulated as the following optimization problem:

Minimize J (10)

subject to

maxTT

minT KKK

max11

min1 TTT

max22

min2 TTT (11)

The proposed approach employs genetic algorithm to solve

this optimization problem and search for optimal set of the

TCSC Controller parameters.

D. Multi-Objective Genetic Algorithm (MOGA)

GA has been used as optimizing the parameters of control

system that are complex and difficult to solve by conventional

optimization methods. GA maintains a set of candidate

solutions called population and repeatedly modifies them. A

fitness or objective function is used to reflect the goodness of

each member of population. Given a random initial population

GA operates in cycles called generations, as follows: Each member of the population is evaluated using a

fitness function.

Time Domain Simulation ofPower System Model

Objective Function Evaluation

Yes

Gen.=Gen.+1

GA Operators

AlgorithmEnd?

Generate InitialPopulation

Gen.=0

Start

End

No

Fig. 6 Flowchart of the GA optimization algorithm

The population undergoes reproduction in a number ofiterations. One or more parents are chosen stochastically,

but strings with higher fitness values have higher

probability of contributing an offspring.

Genetic operators, such as crossover and mutation areapplied to parents to produce offspring.

The offspring are inserted into the population and theprocess is repeated.

The designer has the freedom to explicitly specify the

required performance objectives in terms of time domain

bounds on the closed loop responses. The fitness function

comes from time domain simulations, which is the power

system stability program. Using each set of controllers

parameters the time domain simulation is performed and the

fitness value is determined. Good solutions are selected and

by means of the GA operators new and better solutions are

achieved. This procedure continues until a desired termination

criterion is achieved.


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In case of multi objective optimization, there are several

criterions that need to be simultaneously satisfied. Often those

criterions are contradicting and cannot have optimum at the

same time, thus improving the value of one-criterion means

getting worse values for another. This arises the question how

to use those criterions to find the optimal solution and how tosearch the parameter space. One of the solutions for

optimizing a multi objective problem is by selecting weights

and aggregating the functions to a single objective. The other

type of solution is by using Pareto method type of selection

which is used in the present study. By this method a set of

non-dominated solution is obtained, from which the user

could chose the one that best suits the requirements. The

advantage of this method is that the decision is taken after the

optimization; and one can see the obtained results and choose

amongst them, instead of selecting weights and aggregating

the functions to a single one and getting a single solution [17].

This is very useful, when there is no detailed information

about the functions optimized and the weights giving goodresults are unknown. In the present study MOGA approach is

employed for the optimal tuning of TCSC parameters X so as

to minimize the objective function J. The computational flow

chart of the GA optimization algorithm is shown in Fig. 6.

TABLEI

PARAMETERS USED IN GAALGORITHM

Parameter Value/Type

Maximum generations 50

Population size 50

Mutation rate 0.3

Selection operator Pareto-optimal sorting

No. of Pareto-surface individuals 3

Recombination operator Blending

Type of selection Pareto optimal selection

TABLEII

BOUNDS OF UNKNOWN VARIABLES

ParametersGain

KT

Time constants

T1 T2

Minimum range 30 0.1 0.02

Maximum range 80 0.6 0.4

V. RESULTS

To evaluate the capability of the TCSC controller on

damping electromechanical oscillations of the electric power

system, simulations on the SMIB system (shown in Fig. 2) are

performed. The relevant parameters are given in the

Appendix. For the purpose of optimization of (10), routines

from GA toolbox are used. While applying GA, a number of

parameters are required to be specified. An appropriate choice

of the parameters affects the speed of convergence of the

algorithm. Table I shows the specified parameters for the GA

algorithm. One more important point that affects the optimal

solution more or less is the range for unknowns. For the very

first execution of the program, more wide solution space can

be given and after getting the solution one can shorten the

solution space nearer to the values obtained in the previous

iteration. Bounds for unknown parameters of gains and time

constants used in the present study are shown in Table II,

where T1 and T2 are the numerator and denominator time

constants of the lead/lag blocks of TCSC Controller.

Optimization is terminated by the prespecified number ofgenerations. The best individual of the final generation is the

solution.

The objective function is evaluated for each individual by

simulating the system dynamic model considering a 10% step

increase in mechanical power input (Pm ) at t = 1.0 sec. The

objective functions F1, F2 and F3 attain a finite value since the

deviations in rotor angle, speed and accelerating power are

regulated to zero in steady state. The optimization was

performed with the total number of generations set to 50. As

the three number of Pareto-surface individuals are specified in

the GA algorithm, three solutions are obtained in the GA run.

The convergence of objective functions F1, F2 and F3 are

shown in Figs. 7 (a)-(c). Table III shows the values of thethree Pareto solutions obtained by the MOGA.

The three obtained solutions are tested by applying a step

disturbance of 10% increase in Pm. Fig. 8 shows the response

of rotor angle, for the above contingency for all the three

obtained Pareto solutions. As the mechanical power input is

increased by a step of 10% at t=1 sec, the power angle also

increases so that electrical power becomes equal

0 10 20 30 40 503.535

3.54

3.545

3.55

3.555

3.56

3.565

3.57

3.575

3.58

Generation

ConvergenceofobjectivefunctionF1

(a)

0 10 20 30 40 502

2.5

3

3.5

4

4.5

5x 10

-6

Generation

ConvergenceofobjectivefunctionF2

(b)


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0 10 20 30 40 500.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

Generation

Convergenceofobject

ivefunctionF3

(c)

Fig. 7 Convergence of objective functions (a) F1, (b) F2 and (c) F3

TABLEIIITHREE PARETO SET OF OPTIMIZED TCSCPARAMETERS OBTAINED BY

MULTI-OBJECTIVE GENETIC ALGORITHM

Parameters Solution-1 Solution-2 Solution-3

KT 68.6880 69.7589 42.1656

T1=T3 0.0534 0.4445 0.1967

T2=T4 0.0982 0.1693 0.1262

0 2 4 6 8

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (sec)

Deviationin(rad)

Solution-1

Solution-2

Solution-3

Fig. 8 Response of rotor angle for three Pareto-surface solutions

to mechanical power. Further, it can be observed from Fig. 8

that, the response of power angle when Solution-1 parameters

are used for the TCSC controller (shown in Fig.8, with legend

Solution-1), there is no overshoot and the deviation in power

angle becomes stable at about 3 sec after the initial

oscillations.

0 2 4 6 8-4

-2

0

2

4

6

8

10

12x 10

-4

Time (sec)

Deviationin(p

u)

Solution-1

Solution-2

Solution-3

Fig. 9 Response of speed for three Pareto-surface solutions

The response of power angle when Solution-2 parameters are

used for the TCSC controller is shown in Fig. 8 with legendSolution-2. In this case both overshoot and oscillations are

present and the settling time is 6.5 sec. With, Solution-3

parameters used for TCSC controller, the oscillations in the

power angle response are minimized (as shown in Fig.8 with

legend Solution-3). From the above analysis one can

conclude that Solution-3 parameters give the best power angle

response in terms of overshoot and settling time.

Fig. 9 shows the speed response for all the three Pareto

solution parameters for TCSC controller. It can be seen from

the figure that for Solution-1, both overshoot and oscillation

are present. For the case of Solution-2, though overshoot is

less, settling time is more. The best response in terms of

overshoot and settling time is obtained with Solution-3parameters. Fig. 10 shows the response of accelerating power

for the above disturbance. In this case, Solution-2 gives better

response in terms of overshoot and settling time.

The system eigenvalues without and with TCSC controller

is shown in Table IV, for all the three Pareto solutions. It is

also clear from the Tables that, the system loses stability

0 1 2 3 4 5-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time (sec)

DeviationinP

a(pu)

Solution-1

Solution-2

Solution-3

Fig. 10 Response of accelerating power for three Pareto-surface

solutions


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TABLEIV

SYSTEM EIGENVALUES WITHOUT AND WITH TCSCCONTROLLER FORTHREE

PARETO SOLUTIONS

With TCSC ControllerWithout

TCSCcontroller Solution-1 Solution-2 Solution-3

0.54916.4386i

-1.9987 9.3375i

-0.7636 2.0511i

-2.2561 3.9195i

-10.59963.8708i

-11.4768 5.4086i

-9.6266 7.7772i

-7.9520 6.8104i

_ -13.6599 -74.4628 -23.4994

_ -2.6686 -3.3 -6.2253

_ -0.1031 -0.1029 -0.1018

without the TCSC controller. The system stability is

maintained with TCSC controller with all three obtained

solutions.

In order to verify the effectiveness of the optimized

controllers, the performance of the TCSC controller is also

tested for a disturbance in reference voltage setting. The

reference voltage is increased by a step of 5% at t=1 sec. Fig.

11 shows the variation in power angle for the above

disturbance for all the three Pareto solutions. As the reference

voltage setting is increased by a step of 5% at t=1 sec, thepower angle decreases so as to decrease electrical power for

all the solutions. Further, it can be observed from Fig. 11 that

the response of power angle when Solution-1 parameters are

used for the TCSC controller, there is no overshoot and the

deviation in power angle becomes stable at about 3 sec after

the initial oscillations. For the case of Solution-2 parameters,

both overshoot and oscillations are present and the settling

time is about 7 sec. With Solution-3 parameters used for

TCSC controller, the oscillations are absent in the power angle

response. It is clear from above analysis that Solution-3

parameters give the best power angle response in terms of

overshoot and settling time.

The responses of speed and accelerating power for the abovedisturbance are shown in Figs. 12 & 13 for the three Pareto

solution parameters for TCSC controller. It can be seen from

Fig. 12 that, both overshoot and oscillation are present for

Solution-1. For the case of Solution-2, though overshoot is

less, settling time is more. Solution-3 gives the best response

in terms of overshoot and settling time. Further, it is clear

from Fig. 13 that the best response in terms of overshoot and

settling time is obtained for Solution-2.

0 2 4 6 8-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Time (sec)

Deviationin(rad)

Solution-1

Solution-2

Solution-3

Fig. 11 Response of rotor angle for 5% step change in reference

voltage

0 2 4 6 8-7

-6

-5

-4

-3

-2

-1

0

1

2x 10

-4

Time (sec)

Deviationin(pu)

Solution-1

Solution-2Solution-3

Fig. 12 Response of speed for 5% step change in reference voltage

0 1 2 3 4 5 6-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Time (sec)

DeviationinPa(pu)

Solution-1

Solution-2

Solution-3

Fig. 13 Response of accelerating power for 5% step change in

reference voltage


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0 1 2 3 4 5-4

-2

0

2

4

6

8

10x 10

-4

Time (sec)

Deviationin(pu)

Pe=0.4, =25.98

Pe=0.8, =49.69

Pe=1.0, =60.62

Pe

=1.1, =65.94

Fig. 14 Response of speed for 10% set increase in mechanical power

input at different operating conditions

Different operating conditions are also considered to verify

the robustness of TCSC controller. The parameters obtained

by the Solution-3 are used for the TCSC controller. The

disturbance applied is a 10% step increase in mechanical

power input at t=1 sec. Fig. 14 shows the response of speed

variation at different loading conditions. The results clearly

show that the dynamic performance of the system with TCSC

controller, genetically optimized at nominal loading condition,

is robust to wide variation in loading conditions.

VI. CONCLUSION

In this study, the power system stability enhancement by aTCSC controller is presented and discussed. A parameter-

constrained, time-domain based, multi objective function is

developed to damp the power system oscillations. Then a

multi-objective genetic algorithm approach is employed to

search for the set of TCSC controller parameters. Pareto

method type of selection technique, which gives a set of

solutions, is used in the present study. The controllers are

tested on weakly connected power system subjected to

different disturbances. The simulation results are presented

and analyzed for all the three obtained Pareto solutions.

Further, the results also show that the dynamic performance of

the system with TCSC controllers, genetically optimized at

nominal loading condition, is quite robust to wide variation inloading conditions. However, the limitation is that the

dynamic performance deteriorates somewhat at light loading

conditions.

APPENDIX

System data: All data are in pu unless specified otherwise.

Generator: H = 4.0 s., D = 0, Xd=1.0, Xq=0.6, Xd =0.3, Tdo = 5.044, f=50,

Ra=0, Pe= 1.0, Qe=0.303, 0=60.620.

Exciter :( IEEE Type ST1): KA=200, TA=0.04 s.

Transmission line and Transformer: (XL = 0.7, XT = 0.1) = 0. 0 + j0.7

TCSC Controller: XTCSC0 = 0. 245, 0=156.040

, XC=0.21, XP=0.0525

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