PaperLoad following in a deregulated power system with Thyristor Controlled Series Compensator

Load following in a deregulated power system with Thyristor Controlled
Series Compensator
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 2014
Received in revised form 19 September
2014
Accepted 23 September 2014
Available online 17 October 2014
Keywords:
Deregulation
Genetic Algorithm
Thyristor 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 deregulated
two area interconnected thermal system with two GENCOs and two DISCOs in either areas. Optimal
gain settings of the integral controllers in the control areas are obtained using Genetic Algorithm by
minimizing a quadratic performance index. Simulation studies carried out in MATLAB validates that a
Thyristor Controlled Series Compensator in series with tie-line can effectively improve the load following
performance of the power system in a deregulated environment.
Ó 2014 Elsevier Ltd. All rights reserved.
Introduction
Conventionally, the electricity supply industry has been a natu-
ral monopoly wherein electricity was considered as merely energy
supply 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 rapid
changes from the conventional, monopolistic Vertically Integrated
Utility (VIU) configuration to Horizontally Integrated Utility con-
figuration with distinct entities namely GENCOs, TRANSCOs and
DISCOs [1–5]. This has introduced an open power market and com-
petition among different market players where customers/DISCOs
can buy power from different suppliers/GENCOs at competitive
prices. Since power generation, transportation, distribution and
control tasks are segregated, they have to be separately paid for,
by the transacting parties [2]. In the new competitive electricity
market, maintaining the physical flow of electricity, satisfying
consumer’s demand at proper voltage and frequency level, main-
taining security, economy and reliability of the system, ensuring
proper 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 power
system, changes in power supply or demand affect the operating
conditions. Hence, a power system must be kept very tightly
controlled in two ways. First, power coming into the system must
be exactly balanced against power flowing out, at every moment.
Second, the system frequency must be held constant as far as
possible [3]. It too, can wander as power flow changes, and as a
result, the system can become unstable. Instant adjustment of
the generation to track the fluctuations between the power supply
and demand so that the system is in perfect balance is called speed
regulation or load following.
Literature survey shows that several researchers have proposed
different methods to tackle the load frequency control problem in
deregulated environment [5–16]. Donde et al. [5] has proposed an
introductory idea of LFC control in deregulated power system
considering bilateral contract, contract violation, etc. A PID tuning
technique using internal mode control for decentralized load fre-
quency control in deregulated environment has been investigated
in [6].
The authors of [7] has proposed a decentralized robust LFC
design technique through mixed H2/H1 for three area power
system under bilateral policy scheme. A new robust controller for
load frequency control in a deregulated electricity environment
based on H1 norm and structured singular values of each control
area has been reported in [8]. In practical environment, access to
all state variables of a system is limited and measuring them is
either difficult or impossible. Rakhshani and Sadesh [9] has
suggested some practical viewpoints on load frequency control
problem in deregulated power system. A decentralized neural net-
work based controller for load frequency control in a deregulated
power system has been explored in [10]. The impact of interline
power flow controller and Redox flow batteries on a two area
multiple unit thermal reheat power system in restructured
environment has been investigated in [11].
http://dx.doi.org/10.1016/j.ijepes.2014.09.038
0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.
E-mail address: rajeshja@gmail.com (R.J. Abraham).
Electrical Power and Energy Systems 65 (2015) 136–145
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes

The effect of Superconducting Magnetic Energy Storage in load
frequency control of a deregulated system with decentralized
controller based on mixed H2/H1 technique has been explored in
[12]. Load frequency control for an interconnected system with
multi-source power generation under deregulated environment
has been presented in [13]. A new robust strategy to adapt classical
automatic generation control system to changing environment of
power system operation based on bilateral AGC scheme has
been proposed in [14]. A robust decentralized approach based on
l-synthesis for load frequency controller design of a restructured
multi-area power system under possible contract has been
reported in [15]. An intelligent solution for load frequency control
in a restructured power system using extended classifier system
has been explored in [16].
In the mean time, several studies have investigated the poten-
tial of using Flexible AC Transmission Systems (FACTS) devices
for better power system control since it provides more flexibility.
Not only the power transfer capability of transmission lines can
be increased [17–24], but also, the dynamic stability can be
enhanced using TCSC [25]. However, a literature survey shows
that, the effect of a TCSC on oscillations in area frequencies and
tie-line power following a load perturbation has not yet been
studied. Hence this work aims to
1. Develop the linear incremental mathematical model of TCSC
suitable for AGC applications.
2. Optimize the integral gain settings of control areas using
Genetic 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 separate
entities namely GENCOs, TRANSCOs and DISCOs exclusively for
generation, transmission and distribution of electric power. In such
a scenario, any DISCO can have individual and independent power
contracts with any GENCO either in the same area (Unilateral
Contract) or in other areas (Bilateral Contract) but under the
supervision of ISO [5]. Since the DISCOs are free to choose any
GENCOs for power contract based on prices, various combinations
of GENCO–DISCO contracts are possible in practice which can be
visualized through DISCO Participation Matrix (DPM). Number of
rows of the DPM is equal to number of GENCOs whereas number
of DISCOs determine the number of columns of DPM. Each entry
in this matrix called contract participation factor (cpf), corresponds
to 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 from
GENCOi. Thus for a two area system with two GENCOs (GENCO1,
GENCO2) and two DISCOs (DISCO1; DISCO2) in area-1 and two
GENCOs (GENCO3, GENCO4) and two DISCOs (DISCO3; DISCO4) in
area-2, DPM is given by
DPM ¼
cpf11 cpf12 cpf13 cpf14
2
6
6
6
4
3
7
7
7
5
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 the
total number of DISCOs. The expression for contracted power of
ith GENCO with DISCOs is given as
DPgci ¼
XNDISCO
j¼1
cpfijDPLj; for i ¼ 1; 2; . . . ; NGENCO ð3Þ
where DPgci is the contracted power of ith GENCO and DPLj is the
total load demand of jth DISCO. The scheduled steady state power
flow on the tie-line is given as:
DPtie12;scheduled = (Demand of DISCOs in area-2 from GENCOs in
area-1)-(Demand of DISCOs in area-1 from GENCOs in area-2).
The scheduled steady state power flow on the tie-line is given
as:
DPtie12;scheduled ¼
X2
i¼1
X4
j¼3
cpfijDPLj À
X4
i¼3
X2
j¼1
cpfijDPLj ð4Þ
¼ cpf13DPL3 þ cpf14DPL4 þ cpf23DPL3 þ cpf24DPL4ð Þ ð5Þ
À cpf31DPL1 þ cpf32DPL2 þ cpf41DPL1 þ cpf42DPL2ð Þ
The tie-line power error is defined as:
DPtie12;error ¼ DPtie12;actual À DPtie12;scheduled ð6Þ
At steady state, the tie-line power error, DPtie12;error, vanishes as
the actual tie-line power flow reaches the scheduled power flow.
This error signal is used to generate the respective Area Control
Error (ACE) signal as in the traditional scenario. i.e.,
ACE1 ¼ B1Df1 þ DPtie12;error ð7Þ
ACE2 ¼ B2Df2 þ a12DPtie12;error ð8Þ
where a12 ¼ À Pr1
Pr2
with Pr1 and Pr2 being the rated area capacities of
area-1 and area-2 respectively.
It is noted that the total load of the ith control area (DPDi) is
the sum of the contracted and uncontracted load demand of the
DISCOs of the ith control area.
Nomenclature
f nominal system frequency
Pri rated power in the ith area
H inertia constant
DPDi incremental load change in area i
DPGi incremental generation change in ith GENCO
T12 synchronizing coefficient
TGi steam turbine time constant
TRi reheat unit time constant
TTi turbine time constant
Bi frequency bias constant
KI integral gain
KRi steam turbine reheat constant
J cost index
TTCSC TCSC time constant
KTCSC TCSC gain constant
Ri self-regulation parameters for the governor of the ith
area
Di load damping coefficient in ith area
GENCO generation company
TRANSCO transmission company
DISCO distribution company
ISO independent system operator
M. Deepak, R.J. Abraham / Electrical Power and Energy Systems 65 (2015) 136–145 137

Linearized model of TCSC
Thyristor Controlled Series Compensator (TCSC) is a series com-
pensating device to govern the power ﬂow by compensating for
the reactance of transmission line. It consists of a series capacitor
shunted 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
Fig. 1. Schematic diagram of the interconnected power system with TCSC in series with tie-line near to area-1 in deregulated scenario.
Fig. 2. Linearized model of an interconnected thermal–thermal system under deregulation.
138 M. Deepak, R.J. Abraham / Electrical Power and Energy Systems 65 (2015) 136–145

possible by proper selection of capacitor and inductor values of the
TCSC device. The variable reactance XTCSC represents the net equiv-
alent reactance of the TCSC, when operating in either the inductive
or the capacitive mode.
Fig. 1 shows the schematic diagram of a two area intercon-
nected thermal–thermal power system with TCSC connected in
series with the tie-line under deregulated environment. For analy-
sis, it is assumed that TCSC is connected near to the Area 1. The
reactance to resistance ratio in a practically interconnected power
system is quite high and hence tie-line resistance is neglected. The
incremental tie-line power flow without TCSC is given by [3],
DPtie12ðsÞ ¼
2pT0
12
s
½Df1ðsÞ À Df2ðsÞŠ ð9Þ
where T0
12 is the synchronizing coefficient without TCSC and Df1
and Df2 are the frequency deviations in areas 1 and 2 respectively.
When TCSC is connected in series with the tie-line, the current flow
from area-1 to area-2 can be written as,
i12 ¼
j V1 j ðd1ÞÀ j V2 j ðd2Þ
jðX12 À XTCSCÞ
ð10Þ
where X12 and XTCSC are the tie-line reactance and TCSC reactance
respectively.
From Fig. 1,
Ptie12 À jQtie12 ¼ VÃ
1I12 ¼j V1 j ðÀd1Þ
j V1 j ðd1ÞÀ j V2 j ðd2Þ
jðX12 À XTCSCÞ

ð11Þ
Separating the real part of Eq. (11),
Ptie12 ¼
j V1 jj V2 j
ðX12 À XTCSCÞ
sinðd1 À d2Þ ð12Þ
Let kc be the percentage of compensation offered by the TCSC
kc ¼ XTCSC
X12
. The tie-line flow can be represented in terms of kc as
Ptie12 ¼
j V1 jj V2 j
X12ð1 À kcÞ
sinðd1 À d2Þ ð13Þ
To obtain the linear incremental model, d1; d2 and kc are
perturbed by Dd1; Dd2; Dkc from their respective nominal values
d0
1; d0
2 and k
0
c , so that, from Eq. (13)
DPtie12 ¼
j V1 jj V2 j
X12ð1 À k
0
c Þ
2
sinðd0
1 À d0
2ÞDkc
þ
j V1 jj V2 j
X12ð1 À k
0
c Þ
cosðd0
1 À d0
2ÞðDd1 À Dd2Þ ð14Þ
If J0
12 ¼ jV1jjV2j
X12
sinðd0
1 À d0
2Þ, and T0
12 ¼ jV1jjV2j
X12
cosðd0
1 À d0
2Þ, then Eq. (14)
becomes
DPtie12 ¼
J0
12
ð1 À k
0
c Þ
2
Dkc þ
T0
12
ð1 À k
0
c Þ
ðDd1 À Dd2Þ ð15Þ
Since Dd1 ¼ 2p
R
Df1dt and Dd2 ¼ 2p
R
Df2dt and taking Laplace
transform, Eq. (15) yields
DPtie12ðsÞ ¼
J0
12
ð1 À k
0
c Þ
2
DkcðsÞ þ
2pT0
12
sð1 À k
0
c Þ
½Df1ðsÞ À Df2ðsÞŠ ð16Þ
Eq. (16) reveals that the tie-line power flow can be regulated by
controlling DkcðsÞ, the percentage compensation of TCSC. If the
control input signal to TCSC damping controller is assumed to be
DErrorðsÞ and the transfer function of the signal conditioning circuit
is KTCSC
1þsTTCSC
, then
DkcðsÞ ¼
KTCSC
1 þ sTTCSC
DErrorðsÞ ð17Þ
where KTCSC is the gain of the TCSC controller and TTCSC is the time
constant of the TCSC. Since TCSC is kept near to area-1, frequency
deviation Df1 may be suitably used as the control signal DErrorðsÞ,
to the TCSC unit to control the percentage incremental change in
the system compensation level. Hence,
DkcðsÞ ¼
KTCSC
1 þ sTTCSC
Df1ðsÞ ð18Þ
Thus the deviation in the tie-line power flow after the perturbation
becomes,
DPtie12 ¼
2pT0
12
sð1 À k
0
c Þ
½Df1ðsÞ À Df2ðsÞŠ
þ
J0
12
ð1 À k
0
c Þ
2
2
4
3
5 KTCSC
1 þ sTTCSC
Df1ðsÞ ð19Þ
State space model of the two-area deregulated system with
TCSC
The block schematic shown in Fig. 2 represents the detailed
block diagram model of a two area multi-unit thermal system in
deregulated environment. The LFC in a deregulated power market
should be designed to accommodate all possible transactions, such
as unilateral based transactions, bilateral transactions, and a com-
bination of these two transactions. The AGC system on which
investigations have been carried out comprises a two area inter-
connected thermal system as shown in Fig. 2. Area 1 consists of
two GENCOs (GENCO1 and GENCO2) of reheat thermal power gener-
ation units and Area 2 comprises two GENCOs (GENCO3 and
GENCO4) of non reheat thermal units. KI1 and KI2 are the integral
gain settings in area 1 and area 2 respectively. The state space
model of the two area system is characterized by the state space
form as
_X ¼ AX þ BU þ Cp ð20Þ
where X; U and p are the state, control and load disturbance input
vectors respectively whereas A; B and C are the respective matrices
of appropriate dimensions. The vectors X; U and p are given by
X ¼
Df1
DPG1
DPG2
DPR1
DPR2
DPT1
DPT2
Df2
DPG3
DPG4
DPT3
DPT4
DP0
tie
Dkc
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
; U ¼
u1
u2

; p ¼
DPD1
DPD2

Total load demand of ith Area, DPDi ¼
PN
i¼1DPLi + Uncontracted load
demands of DISCOs in ith area where DPLi denotes the contract
demand ith DISCO, N is the number of DISCOs in ith area. The states
are chosen as deviations in frequencies (Df1; Df2) in area-1 and
area-2 respectively, the deviations in the power outputs of DISCOs
in area-1 (DPG1; DPG2) and (DPG3; DPG4) in area-2, the deviations in
reheat 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

deviations in tie-line power flow (DPtie12) and are also shown in
Fig. 2.
Objective function formulation for AGC
The ultimate objective of AGC is to maintain frequency and
inter-area tie-line power within their respective scheduled values
following a sudden load perturbation at the earliest. To do so, the
integral gains of the control areas (KI1; KI2) are tuned optimally to
obtain the area frequencies and power exchange with minimum
overshoot and lower settling time. A quadratic performance index
defined by,
J ¼
Z t
0
ðDf
2
1 þ Df
2
2 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. Normally
the parameters to be optimized are represented as individual
strings in a GA population which are reproduced as in nature
[27]. To start the optimization, GA uses randomly produced initial
population and then, each individual string in the population is
evaluated by their fitness, normally represented by the value of
objective function. Individuals with higher fitness values are
selected and are then modified through selection, crossover and
mutation to obtain the next generation of individuals strings. The
new generation on average, will be ’’better’’ than the current
Table 1
GA parameters.
Population size 100
Cross over 0.8
Elite count 2
Mutation 0.2
No. of generations 100
Initial penalty 10
Penalty factor 100
Table 2
Optimized gain settings of control areas.
Unilateral contract Bilateral contract Contract violation
KI1 KI2 KI1 KI2 KI1 KI2
Without TCSC 0.0246 0.009 0.024 0.0101 0.071 0.022
With TCSC 0.243 0.0097 0.0248 0.01 0.0712 0.0222
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
Fitnessvalue
Best fitness
J= −0.000173774
KI1
=0.0246
KI2
=0.009
(a) Case-1:Unilateral Contract Without TCSC
0 10 20 30 40 50 60 70 80 90 100
−1.715
−1.71
−1.705
−1.7
x 10
−4
Generation
Fitnessvalue
Best fitness
J= −0.000171202
KI1
=0.243
KI2
=0.0097
(b) Case-1:Unilateral Contract With TCSC
0 10 20 30 40 50 60 70 80 90 100
9.7
9.72
9.74
9.76
9.78
9.8
9.82
9.84
x 10
−3
Generation
Fitnessvalue
Best fitness
J= 0.00971741
KI1
=0.024
KI2
=0.0101
(c) Case-2:Bilateral Contract Without TCSC
0 10 20 30 40 50 60 70 80 90 100
9.6
9.65
9.7
9.75
9.8
9.85
9.9
9.95
x 10
−3
Generation
Fitnessvalue
Best fitness
J=0.00972048
KI1
=0.0248
KI2
=0.01
(d) Case-2:Bilateral Contract With TCSC
0 10 20 30 40 50 60 70 80 90 100
9.762
9.764
9.766
9.768
9.77
9.772
9.774
x 10
−3
Generation
Fitnessvalue
Best fitness
J=0.00976314
KI1
=0.071
KI2
=0.022
(e) Case-3:Contract Violation Without TCSC
0 10 20 30 40 50 60 70 80 90 100
9.76
9.77
9.78
9.79
9.8
9.81
9.82
x 10
−3
Generation
Fitnessvalue
Best fitness
J=0.00976722
KI1
=0.0712
KI2
=0.0222
(f) Case-3:Contract Violation With TCSC
Fig. 3. Generation vs fitness values obtained from GA optimization.

population [28]. In this way, the above process is repeated to create
the subsequent new generations until some termination condition
is 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 and
Ki2 is chosen randomly. The performance index (J) given by Eq. (21)
is evaluated for each individual string in the population and
individuals strings with higher fitness values are selected for cross
over and mutation to obtain the next generation. The GA parame-
ters used are given in Table 1. The algorithm is repeated for 100
number of generations and computation is terminated until for a
particular generation, average fitness is within 1% of best fitness
value 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 given
in 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 out
for the AGC system with 10% load demand on each DISCO, ie
DPL1 ¼ DPL2 ¼ DPL3 ¼ DPL4 ¼ 0:1 pu. TCSC is placed near area-1
considering 50% compensation. Fourth-order Runge–Kutta method
with an integration step size of 0.01 s is used for simulations. Stud-
ies are carried out on AGC in deregulated environment, for three
different 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 DISCO
has a total load demand of 0.1 pu MW. Let DISCO1 and DISCO2 in
area-1 have power contract with GENCO1 and GENCO2 in area-1
as per the following DPM,
DPM ¼
0:6 0:7 0 0
0:4 0:3 0 0
0 0 0 0
0 0 0 0
2
6
6
6
4
3
7
7
7
5
ð22Þ
0 2 4 6 8 10 12 14 16 18
−0.4
−0.3
−0.2
−0.1
0
0.1
Time (s)
Δf1
(Hz)
Without TCSC
With 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)
Δf2(Hz)
Without TCSC
With TCSC
(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)
ΔPtie12actual
(puMW)
Without TCSC
With TCSC
(c) Deviation in tie-line power flow
Fig. 4. Variations in area frequencies (Df1 and Df 2) and tie-line power (DPtie12) in
case-1.
0 2 4 6 8 10 12 14 16 18
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Time (s)
GENCO−1(puMW)
Without TCSC
With TCSC
(a) Deviation in power output of GENCO-1
0 2 4 6 8 10 12 14 16 18
0
0.02
0.04
0.06
0.08
0.1
Time (s)
GENCO−2(puMW)
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)
GENCO−3(puMW)
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)
GENCO−4(puMW)
Without TCSC
With TCSC

The dynamic responses without and with TCSC are plotted in
Fig. 4. It can be observed that, with TCSC, the transient response
has been improved in terms of ripples as well as settling time. In
unilateral contract, GENCOs in area-1 are having power contracts
with DISCOs in area-1 only. Hence as per the DPM given by Eq.
(22), DPtie12scheduled using Eq. (5) becomes zero and is depicted in
Fig. 4(c). It may be noted that as per Eq. (3), at steady state,
power output of GENCO-1 = ðcpf11 Â DPL1Þ + ðcpf12 Â DPL2Þ +
ðcpf13 Â DPL3Þ + ðcpf14 Â DPL4Þ = (0.6 Â 0.1) + (0.7 Â 0.1) + (0 Â 0.1) +
(0 Â 0.1) = 0.13 pu MW and power output of GENCO-2 at steady
state = ðcpf21 ÂDPL1Þ + ðcpf22 ÂDPL2Þ + ðcpf23 ÂDPL3Þ + ðcpf24 ÂDPL4Þ =
(0.4 Â 0.1) + (0.3 Â 0.1) + (0 Â 0.1) + (0 Â 0.1) = 0.07 pu MW. Simi-
larly at steady state, power output of GENCO-3 = ðcpf31 Â DPL1Þ +
ðcpf32 ÂDPL2Þ + ðcpf33 ÂDPL3Þ + ðcpf34 ÂDPL4Þ = (0 Â 0.1) + (0 Â 0.1) +
(0 Â 0.1) + (0 Â 0.1) = 0 pu MW and GENCO-4 has a steady state
power output of ðcpf41 ÂDPL1Þ + ðcpf42 ÂDPL2Þ + ðcpf43 ÂDPL3Þ +
ðcpf44 ÂDPL4Þ = 0 pu MW. The power outputs of various GENCOS
are plotted without and with TCSC in Figs. 5 and 6 and simulation
results matches with calculated values. It can be seen from Figs. 5
and 6 that a TCSC improves the power outputs in terms of
overshoots and the responses are more smooth.
Case 2-bilateral transactions
In this scenario a DISCO in an area has freedom to have power
contract with any GENCOs in other control areas. The bilateral con-
tracts between DISCOs and various GENCOs are simulated based on
the following DPM, given by
DPM ¼
0:1 0:24 0:33 0:18
0:2 0:16 0:17 0:22
0:27 0:4 0:5 0
0:43 0:2 0 0:6
2
6
6
6
4
3
7
7
7
5
ð23Þ
Figs. 7–9 depict the corresponding simulation results without
and with TCSC. It may be noted that with TCSC, the transient oscil-
lations and settling times have been reduced. It is clear from
Fig. 7(d) that with TCSC, DPtie12;error vanishes faster. In this case, cal-
culated value of DPtie12;scheduled ¼ À0:04 pu MW, as given by Eq. (5)
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)
Δf1(Hz)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
−0.4
−0.3
−0.2
−0.1
0
0.1
Time (s)
Δf2(Hz)
Without TCSC
With TCSC
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)
ΔPtie12actual
(puMW)
Without TCSC
With TCSC
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)
ΔPtie12error(puMW)
Without TCSC
With 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 ).
0 2 4 6 8 10 12 14 16 18
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
GENCO−1(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
GENCO−2(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
Time (s)
GENCO−3(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
Time (s)
GENCO−4(puMW)
Without TCSC
With TCSC

matches with simulation result. At steady state, power output of
GENCO-1 = DPG1 = (0.1 Â 0.1) + (0.24 Â 0.1) + (0.33 Â 0.1) + (0.18
Â 0.1) = 0.085 pu MW. Similarly DPG2 = (0.2 Â 0.1) + (0.16 Â 0.1) +
(0.17 Â 0.1) + (0.22 Â 0.1) = 0.075 pu MW, at steady state. Further,
at steady state, DPG3 = (0.27 Â 0.1) + (0.4 Â 0.1) + (0.5 Â 0.1) +
(0 Â 0.1) = 0.117 pu MW and DPG4 = (0.43 Â 0.1) + (0.2 Â 0.1) +
(0 Â 0.1) + (0.6 Â 0.1) = 0.123 pu MW. The corresponding plots are
presented in Figs. 8 and 9. TCSC has improved the transient
behaviour 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 area
according to their respective ACE participation factor. Consider a
case where DISCO-1 demands 0.1 pu MW uncontracted excess
power.
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 Â DPL1Þ + ðcpf12 ÂDPL2Þ + ðcpf13 ÂDPL3Þ + ðcpf14Â
DPL4Þ + ðapf11 Â uncontractedpowerÞ = (0.1 Â 0.1) + (0.24 Â 0.1) +
(0.33 Â 0.1) + (0.18 Â 0.1) + ð0:5 Â 0:1:Þ = 0.135 pu MW. Similarly
at steady state, DPG2 = 0.125 pu MW. Further, DPG3 = 0.117 pu MW
and DPG4 = 0.123 pu MW which are same as in previous case. The
uncontracted load of DISCO-1 is reflected in generations of
GENCO-1 and GENCO-2 in its area. The responses obtained for this
case are shown in Figs. 10–12 and clearly reveal the superiority of
TCSC over those without TCSC. The uncontracted load of DISCO-1 is
reflected in DPG1 DPG2 at steady state as shown in Fig. 11 and
matches with calculated (desired) value. As shown in Fig. 12, the
generation of GENCOs-3 and 4 is not affected by the excess
uncontracted load of DISCO-1.
In deregulated environment the contract affects not only the
load demand of an area but also the exchanged tie-line power flow.
0 2 4 6 8 10 12 14 16 18
−0.8
−0.6
−0.4
−0.2
0
0.2
Time (s)
Δf1(HZ)
Without TCSC
With TCSC
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)
Δf2(Hz)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
−0.2
−0.15
−0.1
−0.05
0
Time (s)
ΔPtie12actual
(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
−0.15
−0.1
−0.05
0
0.05
Time (s)
ΔPtie12error(puMW)
Without TCSC
With TCSC
(d) Deviation in tie-line power flow error
Fig. 10. Variations in area frequencies (Df1 and Df 2) and actual tie-line power
(DPtie12) and (DPtie12error ) for case-3.
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
Time (s)
GENCO−1(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
Time (s)
GENCO−2(puMW)
Without TCSC
With TCSC
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
Time (s)
GENCO−3(puMW)
Without TCSC
With TCSC
(a) Deviation in power output of GENCO-3.
0 2 4 6 8 10 12 14 16 18
0
0.05
0.1
0.15
0.2
0.25
Time (s)
GENCO−4(puMW)
Without TCSC
With TCSC

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 may
be noted that, the TCSC reactance varies in accordance with tie-line
power flow deviations.
Conclusion
An attempt has been made to damp out the area frequency
oscillations and tie-line power flow after a sudden load demand
using TCSC. A linearized model of the TCSC has been proposed
and used to study its effect in load following. Extensive analysis
is done for AGC scheme considering unilateral transactions, bilat-
eral transactions, and contract violation. Genetic Algorithm has
been used to tune the integral gain settings of both areas with
and without TCSC considering a quadratic performance index for
the above three scenarios. It is found that in all the cases, the area
frequency error becomes zero at the steady state. Performance of
AGC has been improved in terms of settling time, peak overshoot,
damping, etc., with the use of TCSC in all the three cases. It is found
that actual values of generations and tie-line power exchanges of
GENCOs obtained from simulations are matching with the corre-
sponding calculated (desired) values. Hence a Thyristor Controlled
Series 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 MW
TP1 ¼ TP2 ¼ 20 s
R1 ¼ R2 ¼ R3 ¼ R4 ¼ 2:4 Hz=pu MW
B1 ¼ B2 ¼ B3 ¼ B4 ¼ 0:42249
TG1 ¼ TG2 ¼ TG3 ¼ TG4 ¼ 0:08 s
TT1 ¼ TT2 ¼ TT3 ¼ TT4 ¼ 0:42 s
TR1 ¼ TR2 ¼ 10 s;
KR1 ¼ KR2 ¼ 0:5
Pr1 ¼ Pr2 ¼ 1200 MW
X12 ¼ 10 X
T12 ¼ 0:0866
d0 ¼ 300
2. TCSC Data [22]
KTCSC ¼ 2
TTCSC ¼ 0:02 s
Appendix B
State space equations of the two area system
_Df1ðtÞ ¼
1
TP1
ÀDf1ðtÞ þ KP1 Á DPG1ðtÞ þ KP1 Á DPG2ðtÞ½
ÀKP1DPD1ðtÞ À KP1DPtieðtÞŠ
_DPG1ðtÞ ¼
À1
TR1
ÀDPG1ðtÞ þ
1
TR1
À
KR1
TT1

DPR1ðtÞ þ
KR1
TT1
DPT1ðtÞ

_DPG2ðtÞ ¼
À1
TR2
ÀDPG2ðtÞ þ
1
TR2
À
KR2
TT2

DPR2ðtÞ þ
KR2
TT2
DPT2ðtÞ

_DPR1ðtÞ ¼
1
TT1
½DPT1ðtÞ À DPR1ðtÞŠ
_DPR2ðtÞ ¼
1
TT2
½DPT2ðtÞ À DPR2ðtÞŠ
_DPT1ðtÞ ¼
1
TG1
À
1
R1
Á Df1ðtÞ À DPT1ðtÞ þ apf11 Á u1ðtÞ

þcpf11DPL1 þ cpf12DPL2 þ cpf13DPL3 þ cpf14DPL4

_DPT2ðtÞ ¼
1
TG2
À
1
R2
Á Df1ðtÞ À DPT2ðtÞ þ apf12 Á u1ðtÞ

þcpf21DPL1 þ cpf22DPL2 þ cpf23DPL3 þ cpf24DPL4

_Df2ðtÞ ¼
1
TP2
½ÀDf2ðtÞ þ KP2 Á DPG3ðtÞ þ KP2 Á DPG4ðtÞ À KP2DPD2ðtÞ
À a12 Á KP2DPtieðtÞŠ
_DPG3ðtÞ ¼
1
TT3
½DPT3ðtÞ À DPG3ðtÞŠ
_DPG4ðtÞ ¼
1
TT4
½DPT4ðtÞ À DPG4ðtÞŠ
_DPT3ðtÞ ¼
1
TG3
À
1
R3
Á Df2ðtÞ À DPT3ðtÞ þ apf21u2ðtÞ þ cpf31DPL1

þcpf32DPL2 þ cpf33DPL3 þ cpf34DPL4

_DPT4ðtÞ ¼
1
TG4
À
1
R4
Á Df2ðtÞ À DPT4ðtÞ þ apf22 Á u2ðtÞ þ cpf41DPL1

þcpf42DPL2 þ cpf43DPL3 þ cpf44DPL4

_DP0
tieðtÞ ¼
2pT12
ð1 À kcÞ
½Df1ðtÞ À Df2ðtÞŠ
_DkcðtÞ ¼
KTCSC
TTCSC
Df1ðtÞ À
1
TTCSC
DkcðtÞ
DPtieðtÞ ¼
J0
ð1 À kcÞ
2
DP0
tieðtÞ þ DkcðtÞ
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