International Journal of Electrical and Computer Engineering 2:9 2007
Thyristor Controlled Series Compensator-based
Controller Design Employing Genetic
Algorithm: A Comparative Study
Sidhartha Panda and N. P. Padhy
resonance (SSR); damping the power oscillation; and
enhancing transient stability [4]-[11].
Most of the literatures on TCSC are based on small
disturbance analysis that requires linearization of the system
involved. However, liner methods cannot properly capture
complex dynamics of the system, especially during major
disturbances. This presents difficulties for tuning the TCSC
controller in that, the controllers tuned to provide desired
performance at small signal condition do not guarantee
acceptable performance in the event of major disturbances.
Despite significant strides in the development of advanced
control schemes over the past two decades, the conventional
lead-lag (LL) structure controller as well as the classical
proportional-integral-derivative (PID) controller and its
variants, remain the controllers of choice in many industrial
applications. These controller structures remain an engineer’s
preferred choice because of their structural simplicity,
reliability, and the favorable ratio between performance and
cost. Beyond these benefits, these controllers also offer
simplified dynamic modeling, lower user-skill requirements,
and minimal development effort, which are issues of
substantial importance to engineering practice [12]-[13].
The problem of FACTS controller parameter tuning is a
complex exercise. A number of conventional techniques have
been reported in the literature pertaining to design problems of
conventional power system stabilizers namely: the eigenvalue
assignment, mathematical programming, gradient procedure
for optimization and also the modern control theory.
Unfortunately, the conventional techniques are time
consuming as they are iterative and require heavy computation
burden and slow convergence. In addition, the search process
is susceptible to be trapped in local minima and the solution
obtained may not be optimal [14].
Genetic algorithm (GA) is becoming popular for solving
the optimization problems in different fields of application,
mainly because of its robustness in finding an optimal solution
and ability to provide a near-optimal solution close to a global
minimum. Unlike strict mathematical methods, the GA does
not require the condition that the variables in the optimization
problem be continuous and different; it only requires that the
problem to be solved can be computed. GA employs search
procedures based on the mechanics of natural selection and
survival of the fittest. The GAs, which use a multiple-point
instead of a single-point search and work with the coded
structure of variables instead of the actual variables, require
Abstract—In this paper, genetic algorithm (GA) opmization
technique is applied to design a Thyristor Controlled Series
Compensator (TCSC)-based controller to enhance the power system
stability. Two types of controller structures, namely a lead-lag (LL)
and a proportional-integral-derivative (PID) are considered. Further,
for the optimization of proposed controller parameters, two objective
functions namely Integral Square Error (ISE) and Integral of Timemultiplied Absolute value of the Error (ITAE) are considered. The
design problem of the proposed controller is formulated as an
optimization problem and GA is employed to search for optimal
controller parameters. A detailed analysis on the selection of
objective function and controller structure on the effectiveness of the
TCSC controller is carried out and simulation results are presented.
The dynamic performances of both the LL and PID structured TCSCcontroller are analyzed and compared under various disturbance
conditions. It is observed that lead-lag structured TCSC controller
where the controller parameters are optimized using ITAE as
objective function, gives the best system response compared to all
other alternatives.
Keywords—Genetic algorithm, ISE, ITAE, lead-lag controller,
PID controller, power system stability, thyristor controlled series
compensator.
R
I. INTRODUCTION
ECENT development of power electronics introduces the
use of flexible ac transmission system (FACTS) devices
in power systems. FACTS devices 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 power
system [1]. The detailed explanations about the FACTS
controllers are well documented in the literature and can be
found in [2]–[3]. 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
components; reducing net loss; providing voltage support;
limiting short-circuit currents; mitigating subsynchronous
Sidhartha Panda is a research scholar in the Department of Electrical
Engineering, Indian Institute of Technology, Roorkee, Uttaranchal, 247667,
India. (e-mail: speeddee@iitr.ernet.in, panda_sidhartha@rediffmail.com).
N.P.Padhy is Associate professor in the Department of Electrical
Engineering, IIT, Roorkee India.(e-mail:, nppeefee@iitr.ernet.in)
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International Journal of Electrical and Computer Engineering 2:9 2007
only the objective function, thereby making searching for a
global optimum simple [15]. The GA as an optimization
technique has advantage as it adapts to irregular search space
unlike other conventional techniques. The advantage of using
GA is evident, as it finds its application in a number of papers
for optimization problems. Therefore, in the present work GA
is employed to search the optimal controller parameters.
In this paper, a comprehensive assessment of the effects of
TCSC-based damping controller has been carried out. Two
types of TCSC-based controller structure namely a lead-lag
(LL) and a proportional-integral-derivative (PID) structure are
considered. The design problem of the proposed controllers is
transformed into an optimization problem. The design
objective is to improve the stability of a single-machineinfinite-bus (SMIB) power system, subjected to severe
disturbances. Further, for the optimization purpose, two
objective functions namely Integral Square Error (ISE) and
Integral of Time-multiplied Absolute value of the Error
(ITAE) are considered. GA-based optimal tuning algorithm is
used to optimally tune the parameters of these controllers for
minimizations of ISE and ITAE. The proposed controllers
have been applied, tested and compared on a weakly
connected power system. The dynamic performances of both
the LL and PID structured TCSC-controller are analyzed at
different loading conditions and under various disturbance
condition.
This paper is organized as follows. In Section II, the
modeling of power system under study, which is a SMIB
power system with a TCSC, is presented. The proposed
controller structures and problem formulation are described in
Section III. A short overview of GA is presented in Section
IV. Simulation results are provided and discussed in Section V
and conclusions are given in Section VI
normally in response to some system parameter variations.
According to the variation of the thyristor firing angle ( α ) or
conduction angle ( σ ), this process can be modelled as a fast
switch between corresponding reactance offered to the power
system.
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.
There exists a steady-state relationship between α and the
reactance XTCSC. This relationship can be described by the
following equation [3]:
X TCSC ( α ) =
+
C
4 X C2
(XC −XP )
π
cos 2 ( σ / 2 ) [ k tan( kσ / 2 ) − tan( σ / 2 )
π
( k 2 −1)
X C = Nominal reactance of the fixed capacitor C.
X P = Inductive reactance of inductor L connected in
parallel with C.
σ = 2( π − α ) , the conduction angle of TCSC controller.
k=
X C / X P , the compensation ratio.
Since the relationship between α and the equivalent
fundamental frequency reactance offered by TCSC,
X TCSC ( α ) is a unique-valued function, the TCSC is
modeled here as a variable capacitive reactance within the
operating region defined by the limits imposed by α. Thus
XTCSCmin ≤ XTCSC ≤ XTCSCmax, with XTCSCmax = XTCSC (αmin) and
XTCSCmin = XTCSC(1800) = XC. In this paper, the controller is
assumed to operate only in the capacitive region, i.e., αmin > αr
where αr corresponds to the resonant point, as the inductive
region associated with 900 < α < αr induces high harmonics
that cannot be properly modeled in stability studies.
B. Power System Under Study
The SMIB power system with TCSC (shown in Fig. 2), is
considered in this study. The generator has a local load of
admittance Y = G + jB and the transmission line has
impedance of Z = R + jX.
iS
VB
VT
T1
iL
( σ + sin σ )
( XC − X P )
(1)
A. Thyristor Controlled Series Compensator (TCSC)
TCSC is one of the most important and best known series
FACTS controllers. It has been in use for many years to
increase line power transfer as well as to enhance system
stability. The basic module of a TCSC is shown in Fig.1. It
consists of three components: capacitor banks C, bypass
inductor L and bidirectional thyristors T1 and T2. The firing
angles of the thyristors are controlled to adjust the TCSC
reactance in accordance with a system control algorithm,
iC
X C2
where,
II. MODELING THE POWER SYSTEM WITH TCSC
iS
XC −
Z=R+jX
TCSC
I
L
G
T2
Y=G+jB
V
Fig. 1 Basic module of a TCSC
Fig. 2 Single-machine infinite-bus power system with TCSC
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International Journal of Electrical and Computer Engineering 2:9 2007
•
In the figure VT and VB are the generator terminal and
infinite bus voltage respectively. The generator is represented
by the third-order model comprising of the electromechanical
swing equation and the generator internal voltage equation.
The state equations may be written as [16]:
•
ω = [Pm − Pe − D( ω − 1 )] M
Pe = E q' i q + ( X q − X d ' ) i d i q
(2)
•
δ = ωb ( ω − 1 )
(3)
VT = v d + jv q
(4)
I = i d + ji q
(5)
[
•
]
E q' = E fd − E q' − ( X d − X d ' i d Tdo'
(17)
VT = ( X q i q ) 2 + ( E q' − X d i d ) 2
(18)
Here, E fd is the field voltage; T do' is the open circuit
field time constant; X d and X d ' are the d-axis reactance and
the d-axis transient reactance of the generator respectively.
The IEEE Type-ST1 excitation system is considered in this
work. It can be described as:
where, Pm and Pe are the input and output powers of the
generator respectively; M and D are the inertia constant and
damping coefficient respectively; ωb is the synchronous speed;
VT is the terminal voltage; I is the current, δ and ω are the
rotor angle and speed respectively.
•
[
E fd = K A ( V ref − VT ) − E fd
]
(19)
TA
where, KA and TA are the gain and time constant of the
excitation system; V ref is the reference voltage.
The d- and q-axis components of armature current, I can be
calculated as:
⎡i d ⎤ ⎡Yd ⎤ ' V B
⎢ ⎥ = ⎢ ⎥ Eq − 2
Ze
⎣⎢i q ⎦⎥ ⎣⎢Yq ⎦⎥
(16)
III. THE PROPOSED APPROACH
X 1 ⎤ ⎡ sin δ ⎤
⎡ R2
⎢
⎥⎢
⎥
⎣− X 2 R1 ⎦ ⎣cos δ ⎦
A. Structure of the LL and PID Controller
(6)
Max.
σ0
with,
Yd = ( C1 X 1 − C 2 R 2 ) Z e2
(7)
Yq = ( C1 R1 + C 2 X 2 ) Z e2
(8)
C1 = 1 + RG − XB
(9)
C 2 = RB + XG
(10)
Z e2 = R1 R2 + X 1 X 2
(11)
+
σ 0 + Δσ
∑
+
1
1 + sTTCSC
(12)
X 1 = X Eff + C 1 X q
(13)
X 2 = X Eff + C1 X d '
(14)
X Eff = X − XTCSC ( α )
(15)
Output
Min.
Δσ
1 + sT 3
1 + sT 4
1 + sT 1
1 + sT 2
sT W
1 + sT W
KS
Δω
Input
Fig. 3 Lead-lag structure of TCSC-based controller
Proportional
KP
R1 = R − C 2 X d ' R 2 = R − C 2 X q
X TCSC ( α )
Δω
Input
Max.
+
1/sKi
Integral
KD
+
du
dt
∑
+
Δσ
+
∑
σ 0 + Δσ
1
1 + sTTCSC
X TCSC ( α )
Output
Min.
+
σ0
Derivative
Fig. 4 PID structure of TCSC-based controller
The LL and PID structures of TCSC-based damping
controller, to modulate the reactance offered by the TCSC,
X TCSC ( α ) are shown in Figs. 3 and 4 respectively. The
input signal of the proposed controllers is the speed deviation
(∆ω), and the output signal is the reactance offered by the
TCSC, X TCSC ( α ) .
•
The generator power Pe , the internal voltage E q' and the
terminal voltage VT can be expressed as:
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The LL controller consists of a gain block with gain KS, a
signal washout block and two-stage phase compensation
blocks. The signal washout block serves as a high-pass filter,
with the time constant TW, high enough to allow signals
associated with oscillations in input signal to pass unchanged.
From the viewpoint of the washout function, the value of TW is
not critical and may be in the range of 1 to 20 seconds [17].
The phase compensation block (time constants T1, T2 and T3,
T4) provides the appropriate phase-lead characteristics to
compensate for the phase lag between input and the output
signals. The proportional, integral and derivative parameters
of the PID controller are KP, Ki and KD respectively. In the
Figs. 3 and 4, σ 0 represents the initial conduction angle as
desired by the power flow control loop. The steady state
power flow loop acts quite slowly in practice and hence, in the
present study, σ 0 is assumed to be constant during large
disturbance transient period.
IV. OVERVIEW OF GENETIC ALGORITHM (GA)
GA has been used for optimizing the parameters of the
control system that are complex and difficult to solve by
conventional optimisation methods. GA maintains a set of
candidate solutions called population and repeatedly modifies
them. At each step, the GA selects individuals from the
current population to be parents and uses them to produce the
children for the next generation. Candidate solutions are
usually represented as strings of fixed length, called
chromosomes. A fitness or objective function is used to reflect
the goodness of each member of the 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.
• The population undergoes reproduction in a number of
iterations. 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, are
applied to parents to produce offspring.
• The offspring are inserted into the population and the
process is repeated.
The computational flow chart of the GA optimization
approach followed in the present paper is shown in Fig. 5.
B. Problem Formulation
In case of LL controller, the washout time constants TW and
the time constants T2 , T4 are usually prespecified. In the
present study, TW =10s and T2 = T4 = 0.1 s are used. The
controller gain KS and the time constants T1 and T3 are to be
determined. In case of PID controller, the parameters KP , Ki
and KD are to determined. During steady state conditions Δσ
and σ 0 are constant. During dynamic conditions, conduction
angle ( σ ) and hence X TCSC ( α ) is modulated to improve
power system stability. The desired value of compensation is
obtained through the change in the conduction angle ( Δσ ),
according to the variation in Δω . The effective conduction
angle σ during dynamic conditions is given by:
σ = σ 0 + Δσ
Start
Specify the parameters for GA
(20)
Generate initial population
C. Objective Function
In this paper, two different objective functions are
considered for optimization of LL and PID controller
parameters. First is ISE and second is ITAE. These are defined
as follows:
t sim
ISE = ∫ e 2 (t ) dt
Gen.=1
Time-domain simulation
Find the fittness of each individual
in the current population
Gen.=Gen.+1
(21)
Gen. > Max. Gen.?
0
Stop
Yes
t sim
ITAE = ∫ t | e (t )| dt
No
(22)
Apply GA operators:
selection,crossover and mutation
0
where, e is the error signal and t sim is the time range of
simulation.
In ISE, only error is considered and therefore no importance
is given to time. But for the power system stability problems,
it is required that settling time should be less and also
oscillations should die out soon. To this end in ITAE, while
performing integration, time is multiplied with error so that
oscillations die out sooner. In the present paper, speed
deviation Δω following a disturbance is taken as the error
signal
Fig. 5 Flowchart of the genetic algorithm
Tuning a controller parameter can be viewed as an
optimization problem in multi-modal space as many settings
of the controller could be yielding good performance.
Traditional method of tuning doesn’t guarantee optimal
parameters and in most cases the tuned parameters needs
improvement through trial and error. In GA based method, the
tuning process is associated with an optimality concept
through the defined objective function and the time domain
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simulation. The designer has the freedom to explicitly specify
the required performance objectives in terms of time domain
bounds on the closed loop responses. Hence the GA methods
yield optimal parameters and the method is free from the curse
of local optimality. In view of the above, the proposed
approach employs GA to solve this optimization problem and
search for optimal set of TCSC-based damping controller
parameters.
unknowns. For the very first execution of the programme, a
wider 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. Optimisation is
terminated by the prespecified number of generations. The
best individual of the final generation is the solution.
B. Lead-lag Controller
The lead-lag structure shown in Fig. 3 is first considered as
the TCSC-based controller. The controller parameters are
optimized considering both the objective functions ISE and
ITAE. The optimized parameters are shown in Table II. Figs.
6 and 7 show the convergence rate of ISE and ITAE
respectively with the number of generations. It may be noted
that the higher converged values of ITAE is due to
multiplication of time factor as indicated in equations (21)
and (22), and it doesn’t in any way ascertain a poor response.
The actual response must be observed through the plots, as
discussed later.
V. RESULTS AND DISCUSSIONS
A. Application of GA Optimization Technique
In order to optimally tune the parameters of the TCSCbased controller, as well as to assess its performance and
robustness under wide range of operating conditions with
various fault disturbances and fault clearing sequences, the
MATLAB/SIMULINK model of the example power system
shown in Fig. 2 is developed using equations (2)–(19). For
objective function calculation nominal operating condition is
0
considered with P = 0.9 pu and δ = 51.8 . The objective
e
0
function is evaluated for each individual by simulating the
system dynamic model considering a three-phase fault at the
generator terminal busbar at t = 1.0 sec.
For the purpose of optimisation of equations (21) and (22),
routines from GA toolbox were used. The fitness function
comes from time-domain simulation of power system model.
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. Although the chances of GA giving a local optimal
solution are very few, sometimes getting a suboptimal solution
is also possible. While applying GA, a number of parameters
are required to be specified. An appropriate choice of these
parameters affects the speed of convergence of the algorithm.
For different problems, it is possible that the same parameters
for GA do not give the best solution, and so these can be
changed according to the situation.
4
200
Population size
50
Type of selection
Normal geometric [0 0.08]
Type of crossover
Arithmetic [2]
Type of mutation
Nonuniform [2 200 3]
Termination method
Maximum generation
Convergence of ISE
3.7
3.6
3.5
3.4
3.2
0
50
100
150
200
Generations
Fig. 6 Convergence rate of ISE (lead-lag)
0.055
Convergence of ITAE
Maximum generations
3.8
3.3
PARAMETERS USED IN GENETIC ALGORITHM
Value/Type
-7
3.9
TABLE I
Parameter
x 10
0.05
0.045
0.04
0.035
0.03
0
50
100
150
200
Generations
Fig. 7 Convergence rate of ITAE (lead-lag)
In Table I the parameters for GA optimization routines are
given. The description of these operators and their properties
can be found in reference [18]. One more important point that
affects the optimal solution more or less is the range for
The electromechanical eigenvalues without and with the
lead-lag structured TCSC controller for the two obtained
optimized parameters settings (for ISE & ITAE) are shown in
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Table III. It is clear that the open loop system without TCSC
controller is just stable and power system oscillations are
poorly damped as electromechanical mode of the eigenvalues
lie just left of the line in s-plane (s = -0.0795). System stability
and the damping characteristics are greatly improved as the
electromechanical mode eigenvalue significantly shift to the
left of the line in s-plane by application of lead-structured
TCSC controller, optimized for ISE and ITAE. It is also clear
that ITAE outperform the ISE as the shift in electromechanical
mode eigenvalue to the left of the line in the s-plane is more (s
= - 5.9189) for ITAE than that (s = - 4.4279) for ISE.
75
δ (deg)
55
50
45
40
OPTIMIZED LEAD- LAG CONTROLLER PARAMETERS USING ISE AND ITAE
30
T1
0.1135
T3
0.0146
ISE
86.621
0.1556
0.0392
IT AE
60
35
KS
115.6823
ISE
65
TABLE II
Parameters/
Objective function
ITAE
NC
70
0
1
2
3
4
5
6
Time (sec)
Fig. 8 Power angle response without and with control (ISE & ITAE)
under 100 ms three-phase fault disturbance (lead-lag)
TABLE III
0.01
ELECTROMECHANICAL EIGENVALUES WITH LEAD-LAG STRUCTURED TCSC
CONTROLLER OPTIMIZED USING ISE AND ITAE
-0.0795 ±
7.6831i
With lead-lad structured TCSC
controller
ISE
ITAE
-4.4279 ±
1.6382i
ISE
IT AE
0.005
Δ ω (pu)
Without
controller
NC
-5.9189 ±
13.6873i
0
-0.005
In order to verify the effectiveness of the proposed TCSC
controller optimized using ISE and ITAE, simulation studies
are carried out. A three-phase, self-clearing fault of 100 ms
duration is applied at the generator terminal busbar at t = 1 s.
The original system is restored upon the fault clearance. The
system power angle response for the above contingency is
shown in Fig. 8. In the Fig. 8, the response without the
controller is shown with the dotted line with the legend NC;
and the responses with TCSC controller optimized using ISE
and ITAE are shown with dotted line and solid line with
legends ISE and ITAE respectively. It is clear from the Fig. 8
that, without controller even though the system is stable,
power system oscillations are poorly damped. It is also clear
that, proposed TCSC controller significantly suppresses the
first swing in the power angle and provides good damping
characteristics to low frequency oscillations by stabilizing the
system much faster. Further, it is also obvious from Fig. 8 that,
the performance of TCSC controller is better when the
objective function used is ITAE as compared with ISE.
Figs. 9-12 show the responses of speed deviation, terminal
voltage, electrical power output of generator and the reactance
offered by the TCSC response for the above contingency. It
can be observed from these results that, when ISE is used as
objective function oscillations remain for longer time. In
ITAE, however, we get improved damping with lower settling
time.
-0.01
0
1
2
3
4
5
6
Time (sec.)
Fig. 9 Speed deviation response without and with control (ISE &
ITAE) under 100 ms three-phase fault disturbance (lead-lag)
VT (pu)
1.005
1
0.995
NC
ISE
IT AE
0.99
0
1
2
3
4
5
6
Time (sec)
Fig. 10 Terminal voltage response without and with control (ISE &
ITAE) under 100 ms three-phase fault disturbance (lead-lag)
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x 10
1.6
NC
1.4
2
ISE
IT AE
1.2
1
Δ ω (pu)
Pe (pu)
1
0.8
0.6
0
-1
0.4
NC
0.2
0
-3
ISE
-2
0
1
2
3
4
5
IT AE
0
6
1
2
4
5
0.48
0.46
NC
1.5
ISE
1
IT AE
0.44
x 10
-3
0.5
Δ VT (pu)
0.42
0.4
0.38
0.36
0
-0.5
-1
-1.5
0.34
NC
ISE
IT AE
-2
0.32
-2.5
1
0.3
0
1
2
3
4
5
2
3
4
5
6
Time (sec)
6
Time (sec)
Fig. 15 Terminal voltage response without and with control (ISE &
ITAE) for 1 pu step increase in mechanical power input (lead-lag)
Fig. 12 Variation of reactance offered by TCSC without and with
control (ISE & ITAE) under 100 ms three-phase fault disturbance
(lead-lag)
1.1
NC
ISE
60
IT AE
1.05
Pe (pu)
58
δ (deg)
6
Fig. 14 Speed deviation response without and with control (ISE &
ITAE) for 1 pu step increase in mechanical power input (lead-lag)
Fig. 11 Generator electrical power output without and with control
(ISE & ITAE) under 100 ms three-phase fault disturbance (lead-lag)
XTCSC (pu)
3
Time (sec)
Time (sec)
56
1
0.95
54
NC
0.9
ISE
52
IT AE
0
1
2
3
4
5
0
1
2
3
4
5
6
Time (sec)
6
Time (sec)
Fig. 13 Power angle response without and with control (ISE & ITAE)
for 1 pu step increase in mechanical power input (lead-lag)
Fig. 16 Generator electrical power output response without and with
control (ISE & ITAE) for 1 pu step increase in mechanical power
input (lead-lag)
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0.38
OPTIMIZED PID CONTROLLER PARAMETERS USING ITAE
ISE
0.37
XTCSC (pu)
TABLE IV
NC
Parameters/
Objective function
ITAE
IT AE
0.36
0.34
0.33
1
2
3
4
5
Ki
0.6627
KD
0.0364
The performance of PID and lead-lag structured TCSC
controller optimized using ITAE as objective function, are
compared by applying a severe disturbance. A three-phase
fault is applied at the generator terminal busbar at t =1 s. and
removed after 100 ms. The original system is restored upon
the fault clearance. Figs. 19-23 show the system response for
the above contingency with PID and lead-lag structured TCSC
controller. In the Figs.19-23, the response with PID structured
TCSC controller are shown in dotted line with legend ‘PID’
and the response with lead-lad structured TCSC controller are
shown in solid line with legend ‘Lead-lag’.
0.35
0
KP
72.8996
6
Time (sec)
Fig. 17 Variation of reactance offered by TCSC without and with
control (ISE & ITAE) for 1 pu step increase in mechanical power
input (lead-lag)
The effectiveness of the proposed controllers is also tested
for a disturbance in mechanical power input. The input
mechanical power is increased by a step of 0.1 pu at t=1 sec.
Figs. 13-17 show the responses of power angle, speed
deviation, terminal voltage deviation, generator electrical
power output and reactance offered by the TCSC respectively
for the above contingency. The figure illustrates the advantage
of using ITAE over ISE as the objective function.
PID
65
Lead-lag
δ (deg)
60
C. PID Controller
As we have seen that ITAE is better objective function than
ISE; therefore the parameters of the PID controller (shown in
Fig. 4) are optimized using ITAE as objective function. The
optimized parameters are shown in Table IV. Fig. 18 shows
the convergence rate of ITAE with the number of generations
for a PID structured TCSC controller. Comparison of
converged values of ITAE for lead-lag and PID (shown in
Figs. 7 and 18) shows that, in case of lead-lag structured
TCSC controller, ITAE converges to a lower value than that of
PID structure. So lead-lad structure should give a better
response compared to the PID structure.
55
50
45
40
0
1
2
3
4
5
6
Time (sec)
Fig. 19 Power angle response with PID and Lead-lag structure TCSC
controller under 100 ms three-phase fault disturbance (ITAE)
x 10
-3
PID
10
Lead-lag
0.088
5
0.084
Δ ω (pu)
Convergence of ITAE
0.086
0.082
0.08
0
0.078
-5
0.076
0.074
0.072
0
0
50
100
150
1
2
3
4
5
6
Time (sec)
Fig. 20 Speed deviation response with PID and Lead-lag structure
TCSC controller under 100 ms three-phase fault disturbance (ITAE)
200
Generations
Fig. 18. Convergence rate of ITAE (PID)
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International Journal of Electrical and Computer Engineering 2:9 2007
For completeness, the performance of PID and lead-lag
structured TCSC controller optimized using objective function
ITAE are compared for a step disturbance in mechanical
power input. The input mechanical power is decreased by a
step of 0.1 pu at t=1 sec. Figs. 24-27 show the responses of
power angle, speed deviation, terminal voltage deviation,
generator electrical power output respectively for the above
contingency. These Figs. confirm that lead-lag structured
TCSC controller provides better response than PID structured
TCSC controller.
1.006
PID
1.004
Lead-lag
1.002
VT (pu)
1
0.998
0.996
0.994
52
0.992
0
1
2
3
4
5
6
49
δ (deg)
Fig. 21 Terminal voltage response with PID and Lead-lag structure
TCSC controller under 100 ms three-phase fault disturbance (ITAE)
1.6
PID
1.4
Lead-lag
50
Time (sec)
Pe (pu)
PID
51
0.99
48
47
46
Lead-lag
1.2
45
1
44
0
4
6
8
Time (sec)
Fig. 24 Power angle response with PID and Lead-lag structure TCSC
controller for 1 pu step decrease in mechanical power input (ITAE)
0.8
0.6
0.4
x 10
0.2
0
2
-3
PID
1
0
1
2
3
4
5
Lead-lag
0.5
6
Time (sec)
Δ ω (pu)
Fig. 22 Generator electrical power output with PID and Lead-lag
structure TCSC controller under 100 ms three-phase fault disturbance
(ITAE)
0
-0.5
-1
PID
-1.5
Lead-lag
0.45
-2
XTCSC (pu)
0
2
4
6
8
Time (sec)
0.4
Fig. 25 Speed deviation response with PID and Lead-lag structure
TCSC controller for 1 pu step decrease in mechanical power input
(ITAE)
0.35
VI. CONCLUSION
In this study, a comparative study of TCSC controller
design by genetic algorithm for power system stability
enhancement is presented and discussed. Different controller
structures, namely a lead-lag (LL) and a proportional-integralderivative (PID) and objective functions namely Integral
Square Error (ISE) and Integral of Time-multiplied Absolute
value of the Error (ITAE) are considered and the performance
of the proposed controllers are compared and analysed. The
0.3
0
1
2
3
4
5
6
Time (sec)
Fig. 23 Variation of reactance offered by TCSC with PID and Leadlag structure TCSC controller under 100 ms three-phase fault
disturbance (ITAE)
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International Journal of Electrical and Computer Engineering 2:9 2007
controllers are tested on the example power system under
various large and small disturbances. Simulation results reveal
that ITAE is a better objective function than ISE for
optimization problems concerning TCSC controller design.
Further, it is observed that lead-lag structured TCSC controller
where the controller parameters are optimized using ITAE as
objective function, gives the best system response compared to
all other alternatives.
x 10
REFERENCES
[1]
[2]
[3]
[4]
[5]
-4
PID
12
[6]
Lead-lag
Δ VT (pu)
10
[7]
8
6
[8]
4
[9]
2
[10]
0
[11]
1
2
3
4
5
6
7
8
Time (sec)
[12]
[13]
Fig. 26 Terminal voltage deviation response with PID and Lead-lag
structure TCSC controller for 1 pu step decrease in mechanical power
input (ITAE)
[14]
0.9
PID
Lead-lag
0.88
[15]
Pe (pu)
0.86
0.84
[16]
0.82
[17]
0.8
[18]
0.78
0.76
Sidhartha Panda received the M.E. degree in Power Systems Engineering
from University College of Engineering, Burla, Sambalpur University, India
in 2001. Currently, he is a Research Scholar in Electrical Engineering
Department of Indian Institute of Technology Roorkee, India. He was an
Associate Professor in the Department of Electrical and Electronics
Engineering, VITAM College of Engineering, Andhra Pradesh, India and
Lecturer in the Department of Electrical Engineering, SMIT, Orissa, India.
His areas of research include power system transient stability, power system
dynamic stability, FACTS, optimization techniques, distributed generation
and wind energy.
0.74
0
2
4
6
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Available: http://www.control-innovation.com/
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8
Time (sec)
Fig. 27 Generator electrical power output with PID and Lead-lag
structure TCSC controller for 1 pu step decrease in mechanical power
input (ITAE)
APPENDIX
Narayana Prasad Padhy was born in India and received his Degree
(Electrical Engineering), Masters Degree (Power Systems Engineering) with
Distinction and Ph.D., Degree (Power Systems Engineering) in the year 1990,
1993 and 1997 respectively in India. Then he has joined the Department of
Electrical Engineering, Indian Institute of Technology (IIT) India, as a
Lecturer, Assistant Professor and Associate Professor during 1998, 2001 and
2006 respectively. Presently he is working as a Associate Professor in the
Department of Electrical Engineering, Indian Institute of Technology (IIT)
India. He has visited the Department of Electronics and Electrical
Engineering, University of Bath, UK under Boyscast Fellowship during 200506 . His area of research interest is mainly Power System Privatization,
Restructuring and Deregulation, Transmission and Distribution network
charging, Artificial Intelligence Applications to Power System and FACTS.
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, δ0=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, α0=156.040, XC=0.21,
XP=0.0525
617