load following in a deregulated power system with thyristor controlled series compensator

Electrical Power and Energy Systems 65 (2015) 136–145

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Load following in a deregulated power system with Thyristor ControlledSeries Compensator

http://dx.doi.org/10.1016/j.ijepes.2014.09.0380142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (R.J. Abraham).

M. Deepak, Rajesh Joseph Abraham ⇑Department of Avionics, Indian Institute of Space Science and Technology, Thiruvananthapuram 695 547, India

a r t i c l e i n f o

Article history:Received 27 August 2014Received in revised form 19 September2014Accepted 23 September 2014

Keywords:DeregulationGenetic AlgorithmThyristor Controlled Series Compensator

a b s t r a c t

Load following is considered to be an ancillary service in a deregulated power system. This paper inves-tigates the effect of a Thyristor Controlled Series Compensator (TCSC) for load following in a deregulatedtwo area interconnected thermal system with two GENCOs and two DISCOs in either areas. Optimalgain settings of the integral controllers in the control areas are obtained using Genetic Algorithm byminimizing a quadratic performance index. Simulation studies carried out in MATLAB validates that aThyristor Controlled Series Compensator in series with tie-line can effectively improve the load followingperformance of the power system in a deregulated environment.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Conventionally, the electricity supply industry has been a natu-ral monopoly wherein electricity was considered as merely energysupply sector. In this monopolistic market, same agency is respon-sible for power generation, transmission, distribution and control.Since few decades, electric power industry has undergone rapidchanges from the conventional, monopolistic Vertically IntegratedUtility (VIU) configuration to Horizontally Integrated Utility con-figuration with distinct entities namely GENCOs, TRANSCOs andDISCOs [1–5]. This has introduced an open power market and com-petition among different market players where customers/DISCOscan buy power from different suppliers/GENCOs at competitiveprices. Since power generation, transportation, distribution andcontrol tasks are segregated, they have to be separately paid for,by the transacting parties [2]. In the new competitive electricitymarket, maintaining the physical flow of electricity, satisfyingconsumer’s demand at proper voltage and frequency level, main-taining security, economy and reliability of the system, ensuringproper protection, control and all measures for the proper func-tioning of the system are treated as separate ancillary services [4].

Load following is one among such ancillary services. In a powersystem, changes in power supply or demand affect the operatingconditions. Hence, a power system must be kept very tightlycontrolled in two ways. First, power coming into the system mustbe exactly balanced against power flowing out, at every moment.

Second, the system frequency must be held constant as far aspossible [3]. It too, can wander as power flow changes, and as aresult, the system can become unstable. Instant adjustment ofthe generation to track the fluctuations between the power supplyand demand so that the system is in perfect balance is called speedregulation or load following.

Literature survey shows that several researchers have proposeddifferent methods to tackle the load frequency control problem inderegulated environment [5–16]. Donde et al. [5] has proposed anintroductory idea of LFC control in deregulated power systemconsidering bilateral contract, contract violation, etc. A PID tuningtechnique using internal mode control for decentralized load fre-quency control in deregulated environment has been investigatedin [6].

The authors of [7] has proposed a decentralized robust LFCdesign technique through mixed H2/H1 for three area powersystem under bilateral policy scheme. A new robust controller forload frequency control in a deregulated electricity environmentbased on H1 norm and structured singular values of each controlarea has been reported in [8]. In practical environment, access toall state variables of a system is limited and measuring them iseither difficult or impossible. Rakhshani and Sadesh [9] hassuggested some practical viewpoints on load frequency controlproblem in deregulated power system. A decentralized neural net-work based controller for load frequency control in a deregulatedpower system has been explored in [10]. The impact of interlinepower flow controller and Redox flow batteries on a two areamultiple unit thermal reheat power system in restructuredenvironment has been investigated in [11].

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Nomenclature

f nominal system frequencyPri rated power in the ith areaH inertia constantDPDi incremental load change in area iDPGi incremental generation change in ith GENCOT12 synchronizing coefficientTGi steam turbine time constantTRi reheat unit time constantTTi turbine time constantBi frequency bias constantKI integral gain

KRi steam turbine reheat constantJ cost indexTTCSC TCSC time constantKTCSC TCSC gain constantRi self-regulation parameters for the governor of the ith

areaDi load damping coefficient in ith areaGENCO generation companyTRANSCO transmission companyDISCO distribution companyISO independent system operator

M. Deepak, R.J. Abraham / Electrical Power and Energy Systems 65 (2015) 136–145 137

The effect of Superconducting Magnetic Energy Storage in loadfrequency control of a deregulated system with decentralizedcontroller based on mixed H2/H1 technique has been explored in[12]. Load frequency control for an interconnected system withmulti-source power generation under deregulated environmenthas been presented in [13]. A new robust strategy to adapt classicalautomatic generation control system to changing environment ofpower system operation based on bilateral AGC scheme hasbeen proposed in [14]. A robust decentralized approach based onl-synthesis for load frequency controller design of a restructuredmulti-area power system under possible contract has beenreported in [15]. An intelligent solution for load frequency controlin a restructured power system using extended classifier systemhas been explored in [16].

In the mean time, several studies have investigated the poten-tial of using Flexible AC Transmission Systems (FACTS) devicesfor better power system control since it provides more flexibility.Not only the power transfer capability of transmission lines canbe increased [17–24], but also, the dynamic stability can beenhanced using TCSC [25]. However, a literature survey showsthat, the effect of a TCSC on oscillations in area frequencies andtie-line power following a load perturbation has not yet beenstudied. Hence this work aims to

1. Develop the linear incremental mathematical model of TCSCsuitable for AGC applications.

2. Optimize the integral gain settings of control areas usingGenetic Algorithm.

3. Study and compare the effect on AGC in deregulated environ-ment of a thermal power system without and with TCSC.

Deregulated environment

In a restructured power market, there are distinct and separateentities namely GENCOs, TRANSCOs and DISCOs exclusively forgeneration, transmission and distribution of electric power. In sucha scenario, any DISCO can have individual and independent powercontracts with any GENCO either in the same area (UnilateralContract) or in other areas (Bilateral Contract) but under thesupervision of ISO [5]. Since the DISCOs are free to choose anyGENCOs for power contract based on prices, various combinationsof GENCO–DISCO contracts are possible in practice which can bevisualized through DISCO Participation Matrix (DPM). Number ofrows of the DPM is equal to number of GENCOs whereas numberof DISCOs determine the number of columns of DPM. Each entryin this matrix called contract participation factor (cpf), correspondsto the fraction of the total load contracted by a DISCO (column)towards a GENCO (row). Thus the ijth entry of the DPM corre-sponds to the fraction of the total power contracted by DISCOj fromGENCOi. Thus for a two area system with two GENCOs (GENCO1,

GENCO2) and two DISCOs (DISCO1;DISCO2) in area-1 and twoGENCOs (GENCO3, GENCO4) and two DISCOs (DISCO3;DISCO4) inarea-2, DPM is given by

DPM ¼

cpf11 cpf12 cpf13 cpf14




26664

37775 ð1Þ

The sum of all the entries in a column in this matrix is unity. i.e.,

XNGENCO

i¼1

cpfij ¼ 1; for j ¼ 1;2; . . . ;NDISCO ð2Þ

where NGENCO is the total number of GENCOs and NDISCO is thetotal number of DISCOs. The expression for contracted power ofith GENCO with DISCOs is given as

DPgci ¼XNDISCO

j¼1

cpfijDPLj; for i ¼ 1;2; . . . ;NGENCO ð3Þ

where DPgci is the contracted power of ith GENCO and DPLj is thetotal load demand of jth DISCO. The scheduled steady state powerflow on the tie-line is given as:

DPtie12;scheduled = (Demand of DISCOs in area-2 from GENCOs inarea-1)-(Demand of DISCOs in area-1 from GENCOs in area-2).

The scheduled steady state power flow on the tie-line is givenas:

DPtie12;scheduled ¼X2

i¼1

X4

j¼3

cpfijDPLj �X4

i¼3

X2

j¼1

cpfijDPLj ð4Þ

¼ cpf13DPL3 þ cpf14DPL4 þ cpf23DPL3 þ cpf24DPL4ð Þ ð5Þ� cpf31DPL1 þ cpf32DPL2 þ cpf41DPL1 þ cpf42DPL2ð Þ

The tie-line power error is defined as:

DPtie12;error ¼ DPtie12;actual � DPtie12;scheduled ð6Þ

At steady state, the tie-line power error, DPtie12;error , vanishes asthe actual tie-line power flow reaches the scheduled power flow.This error signal is used to generate the respective Area ControlError (ACE) signal as in the traditional scenario. i.e.,

ACE1 ¼ B1Df 1 þ DPtie12;error ð7Þ

ACE2 ¼ B2Df 2 þ a12DPtie12;error ð8Þ

where a12 ¼ � Pr1Pr2

with Pr1 and Pr2 being the rated area capacities ofarea-1 and area-2 respectively.

It is noted that the total load of the ith control area (DPDi) isthe sum of the contracted and uncontracted load demand of theDISCOs of the ith control area.

138 M. Deepak, R.J. Abraham / Electrical Power and Energy Systems 65 (2015) 136–145

Linearized model of TCSC

Thyristor Controlled Series Compensator (TCSC) is a series com-pensating device to govern the power flow by compensating for

Fig. 1. Schematic diagram of the interconnected power system with T

Fig. 2. Linearized model of an interconnected th

the reactance of transmission line. It consists of a series capacitorshunted by a Thyristor controlled inductive reactor whose reac-tance is varied according to the firing angle, a of the thyristor[26]. Both capacitive and inductive reactance compensation are

CSC in series with tie-line near to area-1 in deregulated scenario.

ermal–thermal system under deregulation.


possible by proper selection of capacitor and inductor values of theTCSC device. The variable reactance XTCSC represents the net equiv-alent reactance of the TCSC, when operating in either the inductiveor the capacitive mode.

Fig. 1 shows the schematic diagram of a two area intercon-nected thermal–thermal power system with TCSC connected inseries with the tie-line under deregulated environment. For analy-sis, it is assumed that TCSC is connected near to the Area 1. Thereactance to resistance ratio in a practically interconnected powersystem is quite high and hence tie-line resistance is neglected. Theincremental tie-line power flow without TCSC is given by [3],

DPtie12ðsÞ ¼2pT0

12

s½Df 1ðsÞ � Df 2ðsÞ� ð9Þ

where T012 is the synchronizing coefficient without TCSC and Df 1

and Df 2 are the frequency deviations in areas 1 and 2 respectively.When TCSC is connected in series with the tie-line, the current flowfrom area-1 to area-2 can be written as,

i12 ¼j V1 j \ðd1Þ� j V2 j \ðd2Þ

jðX12 � XTCSCÞð10Þ

where X12 and XTCSC are the tie-line reactance and TCSC reactancerespectively.

From Fig. 1,

Ptie12 � jQtie12 ¼ V�1I12 ¼j V1 j \ð�d1Þj V1 j \ðd1Þ� j V2 j \ðd2Þ

jðX12 � XTCSCÞ

� �

ð11Þ

Separating the real part of Eq. (11),

Ptie12 ¼j V1 jj V2 jðX12 � XTCSCÞ

sinðd1 � d2Þ ð12Þ

Let kc be the percentage of compensation offered by the TCSCkc ¼ XTCSC

X12. The tie-line flow can be represented in terms of kc as

Ptie12 ¼j V1 jj V2 jX12ð1� kcÞ

sinðd1 � d2Þ ð13Þ

To obtain the linear incremental model, d1; d2 and kc areperturbed by Dd1; Dd2; Dkc from their respective nominal valuesd0

1; d02 and k0

c , so that, from Eq. (13)

DPtie12 ¼j V1 jj V2 j

X12ð1� k0c Þ

2 sinðd01 � d0

2ÞDkc

þ j V1 jj V2 jX12ð1� k0

c Þcosðd0

1 � d02ÞðDd1 � Dd2Þ ð14Þ

If J012 ¼

jV1 jjV2 jX12

sinðd01 � d0

2Þ, and T012 ¼

jV1 jjV2 jX12

cosðd01 � d0

2Þ, then Eq. (14)becomes

DPtie12 ¼J0

12

ð1� k0c Þ

2 Dkc þT0

12

ð1� k0c ÞðDd1 � Dd2Þ ð15Þ

Since Dd1 ¼ 2pR

Df 1dt and Dd2 ¼ 2pR

Df 2dt and taking Laplacetransform, Eq. (15) yields

DPtie12ðsÞ ¼J0

12

ð1� k0c Þ

2 DkcðsÞ þ2pT0

12

sð1� k0c Þ½Df 1ðsÞ � Df 2ðsÞ� ð16Þ

Eq. (16) reveals that the tie-line power flow can be regulated bycontrolling DkcðsÞ, the percentage compensation of TCSC. If thecontrol input signal to TCSC damping controller is assumed to beDErrorðsÞ and the transfer function of the signal conditioning circuitis KTCSC

1þsTTCSC, then

DkcðsÞ ¼KTCSC

1þ sTTCSCDErrorðsÞ ð17Þ

where KTCSC is the gain of the TCSC controller and TTCSC is the timeconstant of the TCSC. Since TCSC is kept near to area-1, frequencydeviation Df 1 may be suitably used as the control signal DErrorðsÞ,to the TCSC unit to control the percentage incremental change inthe system compensation level. Hence,

DkcðsÞ ¼KTCSC

1þ sTTCSCDf 1ðsÞ ð18Þ

Thus the deviation in the tie-line power flow after the perturbationbecomes,

DPtie12 ¼2pT0

12

sð1� k0c Þ½Df 1ðsÞ � Df 2ðsÞ�

þ J012

ð1� k0c Þ

2

24

35 KTCSC

1þ sTTCSCDf 1ðsÞ ð19Þ

State space model of the two-area deregulated system withTCSC

The block schematic shown in Fig. 2 represents the detailedblock diagram model of a two area multi-unit thermal system inderegulated environment. The LFC in a deregulated power marketshould be designed to accommodate all possible transactions, suchas unilateral based transactions, bilateral transactions, and a com-bination of these two transactions. The AGC system on whichinvestigations have been carried out comprises a two area inter-connected thermal system as shown in Fig. 2. Area 1 consists oftwo GENCOs (GENCO1 and GENCO2) of reheat thermal power gener-ation units and Area 2 comprises two GENCOs (GENCO3 andGENCO4) of non reheat thermal units. KI1 and KI2 are the integralgain settings in area 1 and area 2 respectively. The state spacemodel of the two area system is characterized by the state spaceform as

_X ¼ AX þ BU þ Cp ð20Þ

where X; U and p are the state, control and load disturbance inputvectors respectively whereas A; B and C are the respective matricesof appropriate dimensions. The vectors X; U and p are given by

X ¼

Df 1

DPG1

DPG2

DPR1

DPR2

DPT1

DPT2

Df 2

DPG3

DPG4

DPT3

DPT4

DP0tieDkc

2666666666666666666666666666664

3777777777777777777777777777775

; U ¼u1

u2

� �; p ¼

DPD1

DPD2

� �

Total load demand of ith Area, DPDi ¼PN

i¼1DPLi + Uncontracted loaddemands of DISCOs in ith area where DPLi denotes the contractdemand ith DISCO, N is the number of DISCOs in ith area. The statesare chosen as deviations in frequencies (Df 1;Df 2) in area-1 andarea-2 respectively, the deviations in the power outputs of DISCOsin area-1 (DPG1;DPG2) and (DPG3;DPG4) in area-2, the deviations inreheat outputs in area-1 ðDPR1;DPR2), the deviations in turbine out-puts in area-1 (DPT1;DPT2) and (DPT3;DPT4) in area-2 and the

Table 1GA parameters.

Population size 100Cross over 0.8Elite count 2Mutation 0.2No. of generations 100Initial penalty 10Penalty factor 100


deviations in tie-line power flow (DPtie12) and are also shown inFig. 2.

Objective function formulation for AGC

The ultimate objective of AGC is to maintain frequency andinter-area tie-line power within their respective scheduled valuesfollowing a sudden load perturbation at the earliest. To do so, theintegral gains of the control areas (KI1;KI2) are tuned optimally toobtain the area frequencies and power exchange with minimum

Table 2Optimized gain settings of control areas.

Unilateral contract Bi

KI1 KI2 KI

Without TCSC 0.0246 0.009 0.0With TCSC 0.243 0.0097 0.0

0 10 20 30 40 50 60 70 80 90 100−1.74

−1.735−1.73

−1.725−1.72

−1.715−1.71

−1.705−1.7

x 10−4

Generation

Fitn

ess

valu

e

Best fitness

J= −0.000173774 K

I1=0.0246

KI2

=0.009

(a) Case-1:Unilateral Contract Without TCSC

0 10 20 30 40 50 60 70 80 90 1009.7

9.72

9.74

9.76

9.78

9.8

9.82

9.84x 10

−3

Generation

Fitn

ess

valu

e

Best fitness

J= 0.00971741K

I1=0.024

KI2

=0.0101

(c) Case-2:Bilateral Contract Without TCSC

0 10 20 30 40 50 60 70 80 90 1009.762

9.764

9.766

9.768

9.77

9.772

9.774x 10

−3

Generation

Fitn

ess

valu

e

Best fitness

J=0.00976314K

I1=0.071

KI2

=0.022

(e) Case-3:Contract Violation Without TCSC

Fig. 3. Generation vs fitness values

overshoot and lower settling time. A quadratic performance indexdefined by,

J ¼Z t

0ðDf 2

1 þ Df 22 þ DP2

tie12;errorÞdt ð21Þ

is minimized for 10% load demand on each DISCO to obtain the opti-mum values of KI1 and KI2 using Genetic Algorithm.

Genetic Algorithm (GA)

GA is a directed random search technique that uses ’’the sur-vival of the fittest’’ concept in search of better solutions. Normallythe parameters to be optimized are represented as individualstrings in a GA population which are reproduced as in nature[27]. To start the optimization, GA uses randomly produced initialpopulation and then, each individual string in the population isevaluated by their fitness, normally represented by the value ofobjective function. Individuals with higher fitness values areselected and are then modified through selection, crossover andmutation to obtain the next generation of individuals strings. Thenew generation on average, will be ’’better’’ than the current

lateral contract Contract violation

1 KI2 KI1 KI2

24 0.0101 0.071 0.022248 0.01 0.0712 0.0222

0 10 20 30 40 50 60 70 80 90 100−1.715

−1.71

−1.705

−1.7x 10

−4

Generation

Fitn

ess

valu

e

Best fitness

J= −0.000171202K

I1=0.243

KI2

=0.0097

(b) Case-1:Unilateral Contract With TCSC

0 10 20 30 40 50 60 70 80 90 1009.6

9.659.7

9.759.8

9.859.9

9.95

x 10−3

Generation

Fitn

ess

valu

e

Best fitness

J=0.00972048K

I1=0.0248

KI2

=0.01

(d) Case-2:Bilateral Contract With TCSC

0 10 20 30 40 50 60 70 80 90 1009.76

9.77

9.78

9.79

9.8

9.81

9.82x 10

−3

Generation

Fitn

ess

valu

e

Best fitness

J=0.00976722K

I1=0.0712

KI2

=0.0222

(f) Case-3:Contract Violation With TCSC

obtained from GA optimization.

0 2 4 6 8 10 12 14 16 18−0.4

−0.3

−0.2

−0.1

0

0.1

Time (s)

Δ f 1 (

Hz)

Without TCSCWith TCSC

(a) Deviation in frequency of area-1

0 2 4 6 8 10 12 14 16 18−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Time (s)

Δ f 2

(H

z)


(b) Deviation in frequency of area-2

0 2 4 6 8 10 12 14 16 18−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

Time (s)

Δ Ptie

12

actu

al (p

u M

W)


(c) Deviation in tie-line power flow

Fig. 4. Variations in area frequencies (Df 1 and Df 2) and tie-line power (DPtie12) incase-1.

0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (s)

GE

NC

O−

1 (p

u M

W)


(a) Deviation in power output of GENCO-1

0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

0.1

Time (s)

GE

NC

O−

2 (p

u M

W) Without TCSC

With TCSC

(b) Deviation in power output of GENCO-2

Fig. 5. Deviation in generation (DPG1 and DPG2) of GENCOs in area-1 for case-1.

0 2 4 6 8 10 12 14 16 18−0.02

0

0.02

0.04

0.06

0.08

Time (s)

GE

NC

O−

3 (p

u M

W) Without TCSC

With TCSC


0 2 4 6 8 10 12 14 16 18−0.02

0

0.02

0.04

0.06

0.08

Time (s)

GE

NC

O−

4 (p

u M

W) Without TCSC

With TCSC




population [28]. In this way, the above process is repeated to createthe subsequent new generations until some termination conditionis reached.

In this work, GA is used to tune the integral gain settings(Ki1;Ki2) of area-1 and area-2 respectively with and without TCSC.

An initial generation of 100 individual strings representing Ki1 andKi2 is chosen randomly. The performance index (J) given by Eq. (21)is evaluated for each individual string in the population andindividuals strings with higher fitness values are selected for crossover and mutation to obtain the next generation. The GA parame-ters used are given in Table 1. The algorithm is repeated for 100number of generations and computation is terminated until for aparticular generation, average fitness is within 1% of best fitnessvalue in the generations. This indicates convergence in the popula-tion. The gain settings based on the best fittest value from the cur-rent generation is chosen as optimal gain settings.

The optimized gain settings for (1) Unilateral Contract (2) Bilat-eral Contract and (3) Contract violation for areas 1 and 2 are givenin Table 2. Presented in Fig. 3 are plots showing the generation ver-sus fitness function for different cases.

Simulation results and discussion

Time domain simulations using MATLAB have been carried outfor the AGC system with 10% load demand on each DISCO, ieDPL1 ¼ DPL2 ¼ DPL3 ¼ DPL4 ¼ 0:1 pu. TCSC is placed near area-1considering 50% compensation. Fourth-order Runge–Kutta methodwith an integration step size of 0.01 s is used for simulations. Stud-ies are carried out on AGC in deregulated environment, for threedifferent possibilities as given below.

� Case 1: Unilateral contract.� Case 2: Bilateral contract.� Case 3: With contract violation.

Case 1-unilateral contract

In unilateral contract, DISCOs in an area can have power con-tract with GENCOs in the same area only. Assume that each DISCOhas a total load demand of 0.1 pu MW. Let DISCO1 and DISCO2 inarea-1 have power contract with GENCO1 and GENCO2 in area-1as per the following DPM,

DPM ¼

0:6 0:7 0 00:4 0:3 0 00 0 0 00 0 0 0

26664

37775 ð22Þ

0.1

0.12

W) Without TCSC

With TCSC


The dynamic responses without and with TCSC are plotted inFig. 4. It can be observed that, with TCSC, the transient responsehas been improved in terms of ripples as well as settling time. Inunilateral contract, GENCOs in area-1 are having power contractswith DISCOs in area-1 only. Hence as per the DPM given by Eq.(22), DPtie12scheduled using Eq. (5) becomes zero and is depicted inFig. 4(c). It may be noted that as per Eq. (3), at steady state,power output of GENCO-1 = ðcpf11 � DPL1Þ + ðcpf12 � DPL2Þ +ðcpf13 � DPL3Þ + ðcpf14 � DPL4Þ = (0.6 � 0.1) + (0.7 � 0.1) + (0 � 0.1) +(0 � 0.1) = 0.13 pu MW and power output of GENCO-2 at steadystate = ðcpf21�DPL1Þ + ðcpf22�DPL2Þ + ðcpf23�DPL3Þ + ðcpf24�DPL4Þ =(0.4 � 0.1) + (0.3 � 0.1) + (0 � 0.1) + (0 � 0.1) = 0.07 pu MW. Simi-larly at steady state, power output of GENCO-3 = ðcpf31 � DPL1Þ +ðcpf32�DPL2Þ + ðcpf33�DPL3Þ + ðcpf34�DPL4Þ = (0 � 0.1) + (0 � 0.1) +(0 � 0.1) + (0 � 0.1) = 0 pu MW and GENCO-4 has a steady statepower output of ðcpf41�DPL1Þ + ðcpf42�DPL2Þ + ðcpf43�DPL3Þ +ðcpf44�DPL4Þ = 0 pu MW. The power outputs of various GENCOSare plotted without and with TCSC in Figs. 5 and 6 and simulationresults matches with calculated values. It can be seen from Figs. 5and 6 that a TCSC improves the power outputs in terms ofovershoots and the responses are more smooth.

0 2 4 6 8 10 12 14 16 18−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Time (s)

Δ f 1

(Hz)



0 2 4 6 8 10 12 14 16 18−0.4

−0.3

−0.2

−0.1

0

0.1

Time (s)

Δ f 2

(H

z)



0 2 4 6 8 10 12 14 16 18−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

Time (s)

Δ Ptie

12

actu

al (pu

MW

)



0 2 4 6 8 10 12 14 16 18−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

Time (s)

Δ Ptie

12

erro

r (pu

MW

) Without TCSCWith TCSC

(d) Deviation in tie-line power flow error

Fig. 7. Variations in area frequencies (Df 1 and Df 2) actual tie-line power (DPtie12)and tie-line power error (DPtie12error).

Case 2-bilateral transactions

In this scenario a DISCO in an area has freedom to have powercontract with any GENCOs in other control areas. The bilateral con-tracts between DISCOs and various GENCOs are simulated based onthe following DPM, given by

DPM ¼

0:1 0:24 0:33 0:180:2 0:16 0:17 0:22

0:27 0:4 0:5 00:43 0:2 0 0:6

26664

37775 ð23Þ

Figs. 7–9 depict the corresponding simulation results withoutand with TCSC. It may be noted that with TCSC, the transient oscil-lations and settling times have been reduced. It is clear fromFig. 7(d) that with TCSC, DPtie12;error vanishes faster. In this case, cal-culated value of DPtie12;scheduled ¼ �0:04 pu MW, as given by Eq. (5)

0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

Time (s)

GE

NC

O−

1 (p

u M


0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

0.1

0.12

Time (s)

GE

NC

O−

2 (p

u M

W) Without TCSC

With TCSC



0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Time (s)

GE

NC

O−

3 (p

u M

W) Without TCSC

With TCSC


0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Time (s)

GE

NC

O−

4 (p

u M

W) Without TCSC

With TCSC



0 2 4 6 8 10 12 14 16 18−0.8

−0.6

−0.4

−0.2

0

0.2

Time (s)

Δ f 1

(HZ

)



0 2 4 6 8 10 12 14 16 18−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Time (s)

Δ f 2

(H

z)



0 2 4 6 8 10 12 14 16 18−0.2

−0.15

−0.1

−0.05

0

Time (s)

Δ Ptie

12

actu

al (pu

MW

)



0 2 4 6 8 10 12 14 16 18−0.15

−0.1

−0.05

0

0.05

Time (s)

Δ Ptie

12

erro

r (pu

MW

) Without TCSCWith TCSC

(d) Deviation in tie-line power flow error

Fig. 10. Variations in area frequencies (Df 1 and Df 2) and actual tie-line power(DPtie12) and (DPtie12error) for case-3.

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

Time (s)

GE

NC

O−

1 (p

u M

W)



0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

Time (s)

GE

NC

O−

2 (p

u M

W) Without TCSC

With TCSC



0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Time (s)

GE

NC

O−

3 (p

u M

W) Without TCSC

With TCSC

(a) Deviation in power output of GENCO-3.

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Time (s)

GE

NC

O−

4 (p

u M

W) Without TCSC

With TCSC




matches with simulation result. At steady state, power output ofGENCO-1 = DPG1 = (0.1 � 0.1) + (0.24 � 0.1) + (0.33 � 0.1) + (0.18� 0.1) = 0.085 pu MW. Similarly DPG2 = (0.2 � 0.1) + (0.16 � 0.1) +(0.17 � 0.1) + (0.22 � 0.1) = 0.075 pu MW, at steady state. Further,at steady state, DPG3 = (0.27 � 0.1) + (0.4 � 0.1) + (0.5 � 0.1) +(0 � 0.1) = 0.117 pu MW and DPG4 = (0.43 � 0.1) + (0.2 � 0.1) +(0 � 0.1) + (0.6 � 0.1) = 0.123 pu MW. The corresponding plots arepresented in Figs. 8 and 9. TCSC has improved the transientbehaviour of the response.

Case 3-contract violation

In this scenario, DISCOs in an area may have an excess uncon-tracted power demand. As per industrial practice, this uncon-tracted load must be supplied by the GENCOs in the same areaaccording to their respective ACE participation factor. Consider acase where DISCO-1 demands 0.1 pu MW uncontracted excesspower.

The total load in area I (DPD1) = Contracted Load of DISCO1 +Contracted Load of DISCO2 + Uncontracted power = (0.1 + 0.1) +0.1 = 0.3 pu MW.

Similarly for area II (DPD2) = Contracted Load of DISCO3 +Contracted Load of DISCO4 = (0.1 + 0.1) = 0.2 pu MW.

With the DPM given by Eq. (23), at steady state, GENCO-1 gen-erates, DPG1 = ðcpf11 � DPL1Þ + ðcpf12�DPL2Þ + ðcpf13�DPL3Þ + ðcpf14�DPL4Þ + ðapf11 � uncontractedpowerÞ = (0.1 � 0.1) + (0.24 � 0.1) +(0.33 � 0.1) + (0.18 � 0.1) + ð0:5� 0:1:Þ = 0.135 pu MW. Similarlyat steady state, DPG2 = 0.125 pu MW. Further, DPG3 = 0.117 pu MWand DPG4 = 0.123 pu MW which are same as in previous case. Theuncontracted load of DISCO-1 is reflected in generations ofGENCO-1 and GENCO-2 in its area. The responses obtained for thiscase are shown in Figs. 10–12 and clearly reveal the superiority ofTCSC over those without TCSC. The uncontracted load of DISCO-1 isreflected in DPG1 DPG2 at steady state as shown in Fig. 11 andmatches with calculated (desired) value. As shown in Fig. 12, thegeneration of GENCOs-3 and 4 is not affected by the excessuncontracted load of DISCO-1.

In deregulated environment the contract affects not only theload demand of an area but also the exchanged tie-line power flow.

0 2 4 6 8 10 12 14 16 18 20−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Time (S)

Δ kc

Unilateral contractWith bilateral contractWith contract violation

Fig. 13. Variation in the incremental change of the percentage compensation (Dkc)of TCSC for case-1, case-2 and case-3.


Inclusion of TCSC in the existing system enables better perfor-mance in terms of settling time and faster response.

Fig. 13 shows the variation in incremental change of the per-centage compensation (Dkc) of TCSC for the deregulated power sys-tem with unilateral, bilateral and contract violation cases. It maybe noted that, the TCSC reactance varies in accordance with tie-linepower flow deviations.

Conclusion

An attempt has been made to damp out the area frequencyoscillations and tie-line power flow after a sudden load demandusing TCSC. A linearized model of the TCSC has been proposedand used to study its effect in load following. Extensive analysisis done for AGC scheme considering unilateral transactions, bilat-eral transactions, and contract violation. Genetic Algorithm hasbeen used to tune the integral gain settings of both areas withand without TCSC considering a quadratic performance index forthe above three scenarios. It is found that in all the cases, the areafrequency error becomes zero at the steady state. Performance ofAGC has been improved in terms of settling time, peak overshoot,damping, etc., with the use of TCSC in all the three cases. It is foundthat actual values of generations and tie-line power exchanges ofGENCOs obtained from simulations are matching with the corre-sponding calculated (desired) values. Hence a Thyristor ControlledSeries Compensator (TCSC) can be used effectively for load follow-ing in a deregulated power system.

Appendix A

1. System Data [29]

KP1 ¼ KP2 ¼ 120 Hz=pu MWTP1 ¼ TP2 ¼ 20 sR1 ¼ R2 ¼ R3 ¼ R4 ¼ 2:4 Hz=pu MWB1 ¼ B2 ¼ B3 ¼ B4 ¼ 0:42249TG1 ¼ TG2 ¼ TG3 ¼ TG4 ¼ 0:08 sTT1 ¼ TT2 ¼ TT3 ¼ TT4 ¼ 0:42 sTR1 ¼ TR2 ¼ 10 s;KR1 ¼ KR2 ¼ 0:5Pr1 ¼ Pr2 ¼ 1200 MWX12 ¼ 10 X

T12 ¼ 0:0866

d0 ¼ 300

2. TCSC Data [22]

KTCSC ¼ 2TTCSC ¼ 0:02 s

Appendix B

State space equations of the two area system

_Df 1ðtÞ ¼1

TP1�Df 1ðtÞ þ KP1 � DPG1ðtÞ þ KP1 � DPG2ðtÞ½

�KP1DPD1ðtÞ � KP1DPtieðtÞ�

_DPG1ðtÞ ¼�1TR1

�DPG1ðtÞ þ1

TR1� KR1

TT1

� �DPR1ðtÞ þ

KR1

TT1DPT1ðtÞ

� �

_DPG2ðtÞ ¼�1TR2

�DPG2ðtÞ þ1

TR2� KR2

TT2

� �DPR2ðtÞ þ

KR2

TT2DPT2ðtÞ

� �

_DPR1ðtÞ ¼1

TT1½DPT1ðtÞ � DPR1ðtÞ�

_DPR2ðtÞ ¼1

TT2½DPT2ðtÞ � DPR2ðtÞ�

_DPT1ðtÞ ¼1

TG1� 1

R1� Df 1ðtÞ � DPT1ðtÞ þ apf11 � u1ðtÞ

�

þcpf11DPL1 þ cpf12DPL2 þ cpf13DPL3 þ cpf14DPL4

�

_DPT2ðtÞ ¼1

TG2� 1

R2� Df 1ðtÞ � DPT2ðtÞ þ apf12 � u1ðtÞ

�

þcpf21DPL1 þ cpf22DPL2 þ cpf23DPL3 þ cpf24DPL4

�

_Df 2ðtÞ ¼1

TP2½�Df 2ðtÞ þ KP2 � DPG3ðtÞ þ KP2 � DPG4ðtÞ � KP2DPD2ðtÞ

� a12 � KP2DPtieðtÞ�

_DPG3ðtÞ ¼1

TT3½DPT3ðtÞ � DPG3ðtÞ�

_DPG4ðtÞ ¼1

TT4½DPT4ðtÞ � DPG4ðtÞ�

_DPT3ðtÞ ¼1

TG3� 1

R3� Df 2ðtÞ � DPT3ðtÞ þ apf21u2ðtÞ þ cpf31DPL1

�

þcpf32DPL2 þ cpf33DPL3 þ cpf34DPL4

�

_DPT4ðtÞ ¼1

TG4� 1

R4� Df 2ðtÞ � DPT4ðtÞ þ apf22 � u2ðtÞ þ cpf41DPL1

�

þcpf42DPL2 þ cpf43DPL3 þ cpf44DPL4

�

_DP0tieðtÞ ¼2pT12

ð1� kcÞ½Df 1ðtÞ � Df 2ðtÞ�

_DkcðtÞ ¼KTCSC

TTCSCDf 1ðtÞ �

1TTCSC

DkcðtÞ

DPtieðtÞ ¼J0

ð1� kcÞ2DP0tieðtÞ þ DkcðtÞ

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load following in a deregulated power system with thyristor controlled series compensator

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