Multi objective-optimization-with-fuzzy-based-ranking-for-tcsc-supplementary-controller-to improve-rotor-angle-and-voltage-stability

World Academy of Science, Engineering and Technology
International Journal of Electrical, Electronic Science and Engineering Vol:3 No:4, 2009

Multi-objective Optimization with Fuzzy Based
Ranking for TCSC Supplementary Controller to
Improve Rotor Angle and Voltage Stability
S. Panda, S. C. Swain, A. K. Baliarsingh, A. K. Mohanty and C. Ardil

International Science Index 28, 2009 waset.org/publications/10255

Abstract—Many real-world optimization problems involve
multiple conflicting objectives and the use of evolutionary algorithms
to solve the problems has attracted much attention recently. This
paper investigates the application of multi-objective optimization
technique for the design of a Thyristor Controlled Series
Compensator (TCSC)-based controller to enhance the performance of
a power system. The design objective is to improve both rotor angle
stability and system voltage profile. A Genetic Algorithm (GA) based
solution technique is applied to generate a Pareto set of global
optimal solutions to the given multi-objective optimisation problem.
Further, a fuzzy-based membership value assignment method is
employed to choose the best compromise solution from the obtained
Pareto solution set. Simulation results are presented to show the
effectiveness and robustness of the proposed approach.

Keywords—Multi-objective Optimisation, Thyristor Controlled
Series Compensator, Power System Stability, Genetic Algorithm,
Pareto Solution Set, Fuzzy Ranking.
I. INTRODUCTION

P

OWER system oscillations and system voltage profile are
the two important criteria which define the performance of
a power system subjected to a disturbance [1]. There has been
much research interest in developing new control
methodologies for increasing the performance of the power
system. Recent development of power electronics introduces
the use of Flexible AC Transmission Systems (FACTS)
controllers in power systems. 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 [28]. The majority of the control methodologies presented in
literature concerns improvement of only one type of stability

S. Panda is working as a Professor in the Department of Electrical and
Electronics Engineering, NIST, Berhampur, Orissa, India, Pin: 761008.
(e-mail: panda_sidhartha@rediffmail.com ).
S. Swain is working as an Assistant Professor in the Electrical Engineering
Department, School of Technology, KIIT University, Bhubaneswar, Orissa,
India (e mail:scs_132@rediffmail.com).
A.K.Baliarsingh is a Research Scholar in the Electrical Engineering
Department, School of Technology, KIIT University, Bhubaneswar, Orissa,
India (e-mail:scs_132@rediffmail.com).
A. K. Mohanty is an Ex-Professor in N. I. T. Rourkela. now working as a
Professor in Electrical Engg. Deptt. at KIIT UNIVERSITY Bhubaneswar
C. Ardil is with National Academy of Aviation, AZ1045, Baku,
Azerbaijan, Bina, 25th km, NAA (e-mail: cemalardil@gmail.com).

performance; either improving the oscillatory stability
performance (reflected in the deviation in generator speed) or
the system voltage profile and minimization of a single
objective function is employed to get the desired performance.
Multi-objective genetic algorithm approach has been applied
to design a TCSC controller [9], where the three objectives are
closely related and the voltage deviations are not taken into
account. Further, the procedure to obtain the best compromise
solution from the obtained Pareto set is not addressed.
Obviously, the main purpose of design of any controller is to
enable it to improve both oscillatory stability and system
voltage profile. Design of such kind of controller is inherently
a multi-objective optimisation problem.
There are two general approaches to multiple objective
optimisations. One approach to solve multi-objective
optimisation problems is by combining the multiple objectives
into a scalar cost function, ultimately making the problem
single-objective prior to optimisation. However, in practice, it
can be very difficult to precisely and accurately select these
weights as small perturbations in the weights can lead to very
different solutions. Further, if the final solution found cannot
be accepted as a good compromise, new runs of the optimiser
on modified objective function using different weights may be
needed, until a suitable solution is found. These methods also
have the disadvantage of requiring new runs of the optimiser
every time the preferences or weights of the objectives in the
multi-objective function change [10]. The second general
approach is to determine an entire Pareto optimal solution set
or a representative subset. Pareto optimal solution sets are
often preferred to single solutions because they can be
practical when considering real-life problems, since the final
solution of the decision maker is always a trade-off between
crucial parameters [11].
The main motivation for using Genetic Algorithm (GA) to
solve multi-objective optimisation problems is because GAs
deal simultaneously with a set of possible solutions (the socalled population) which allows the user to find several
members of the Pareto optimal set in a single run of the
algorithm, instead of having to perform a series of separate
runs as in the case of the traditional mathematical
programming techniques. The Pareto optimal solutions are
ones within the search space whose corresponding objective
vector components cannot be improved simultaneously.
Additionally, GAs are less susceptible to the shape or
continuity of the Pareto front as they can easily deal with

11



A. Non-Linear Equations

discontinuous and concave Pareto fronts, whereas these two
issues are known problems with mathematical programming
[12].
In this paper, the design problem of a TCSC is formulated
as a multi-objective optimisation problem. GA based multiobjective optimisation method is adapted for generating Pareto
solutions in designing a TCSC-based controller. The design
objective is to improve the oscillatory stability and system
voltage profile of a power system following a disturbance.
Further a fuzzy based membership function value assignment
method is employed to choose the best compromise solution
from the obtained Pareto set. Simulation results are presented
at various loading conditions to show the effectiveness and
robustness of the proposed approach.
The reminder of the paper is organized in five major
sections. Power system modeling with the proposed TCSCbased supplementary damping controller is presented in
Section II. The proposed design approach and the objective
function are presented in section III. In Section IV, an
overview of multi-objective optimization gas been presented.
The results are presented and discussed in Section V. Finally,
in Section VI conclusions are given.

The non-linear differential equations of the SMIB system
with TCSC are derived by neglecting the resistances of all
components of the system (generator, transformer and
transmission lines) and the transients of the transmission lines
and transformer. The non-linear differential equations are
[13]:

1
[ Pm
M

C

(3)

VT ]

(4)

2

Xd

E' q

Xd
Xq

Xd

Xd

V B cos

'

sin
VB X ' d
cos
Xd '

'

VT

( VTd 2

X Eff

XT

VTq 2 )

X TL

X TCSC ( )

X 'd

X Eff , X ' q

Xd

'

X 'd )

sin 2

'

'

X Eff E ' q

VTq

Xd

(X q

'

X q VB

VTd

X 'd )

2X d ' X q

'

Xd

Eq

VB ( X q

sin

X Eff

'

Xq

X Eff
(5)

XL
T1

L

Infinite bus

VR +

T2

XP

KA
[V R
1 sT A
E ' q VB

Pe

VB

XT

E fd ]

where,

X 'd

Generator

(2)

[ Eq

T ' do

E ' fd

The single-machine infinite-bus (SMIB) power system
installed with a TCSC, shown in Figure 1 is considered in this
study. In the figure, XT and XL represent the reactance of the
transformer and the transmission line respectively; VT and VB
are the generator terminal and infinite bus voltage
respectively.
TCSC is one of the most important and best known FACTS
devices, which has been in use for many years to increase line
power transfer as well as to enhance system stability.
Basically, a TCSC consists of three main components:
capacitor bank C, bypass inductor L and bidirectional
thyristors SCR1 and SCR2. The firing angles of the thyristors
are controlled to adjust the TCSC reactance in accordance
with a system control algorithm, normally in response to some
system parameter variations. According to the variation of the
thyristor firing angle or conduction angle, this process can be
modeled as a fast switch between corresponding reactance
offered to the power system.

XC

Pe ]

1

E 'q

II. MODELING THE POWER SYSTEM WITH TCSC

VT

(1)

b

X TCSC

_

E max
fd

VT

KA
1 sTA

E fd

E min
fd

Fig. 1 Single machine infinite bus power system with TCSC
Fig. 2 Simplified IEEE type ST 1A excitation system

12


The simplified IEEE Type-ST1A excitation system is
considered in this work. The diagram of the IEEE Type-ST1A
excitation system is shown in Fig. 2. The inputs to the
excitation system are the terminal voltage VT and reference
voltage VR. The gain and time constants of the excitation
system are represented by KA and TA respectively.
B. Linearized Equations
In the design of electromechanical mode damping stabilizer,
a linearized incremental model around an operating point is
usually employed. The Phillips-Heffron model of the power
system with FACTS devices is obtained by linearizing the set
of equations (1) – (5) around an operating condition of the
power system. The linearized expressions are as follows:

[ K1

A. Structure of Proposed TCSC-based Supplementary
Damping Controller
The commonly used lead–lag structure is chosen in this
study as TCSC-based supplementary damping controller as
shown in Fig. 4. The structure consists of a gain block; a
signal washout block and two-stage phase compensation
block. The phase compensation block provides the appropriate
phase-lead characteristics to compensate for the phase lag
between input and the output signals. The signal washout
block serves as a high-pass filter which allows signals
associated with oscillations in input signal to pass unchanged.
Without it steady changes in input would modify the output.

(6)

b

Eq '

III. THE PROPOSED APPROACH

K 2 Eq

[ K 3 Eq

'

'

KP

K4

D

KQ

] / M (7)

E fd ] / Td 0

sT
WT
1 sT
WT

KT

Input

Gain
Block

'

1 sT3
1 sT4

1 sT1
1 sT2

Output

Two stage
lead-lag Block

Washout
Block
GTCSC ( s )

(8)

E fd '

[ K A (K 5
KV

K 6 Eq

Fig. 4. Structure of the proposed TCSC-based supplementary
damping controller

'

(9)

E fd ] / T A

)

where,

K1

Pe

K3

Eq

K5

VT

, K2

Pe

E'q , K 4
, K6

E 'q , K P
Eq

VT

Pe

, KQ

Eq

E 'q , KV

The damping torque contributed by the TCSC can be
considered to be in to two parts. The first part KP, which is
referred as the direct damping torque, is directly applied to the
electromechanical oscillation loop of the generator. The
second part KQ and KV, named as the indirect damping torque,
applies through the field channel of the generator. The
damping torque contributed by TCSC controller to the
electromechanical oscillation loop of the generator is:

VT

TD

The modified Phillips-Heffron model of the singlemachine infinite-bus (SMIB) power system with TCSC-based
damping controller is obtained using linearized equations (6)(9) as shown in Fig. 3.

TD

K P KT K D

0

(10)

The transfer functions of the TCSC controller is:

uTCSC

KT

sTwT
1 sTwT

1 sT1
1 sT2

1 sT3
y (11)
1 sT4

K1
_

Pm +
_

_

1
Ms D

Where, uTCSC is the output signal of TCSC controller and y
is the input signal. The input signal of the proposed TCSCand the output is
based controller is the speed deviation
the change in conduction angle
. During steady state
conditions
= 0 and so the effective reactance X Eff is

0

s

GTCSC(s)

K4
K2

Eq '

KP
1

KV

KQ

K5

_

_

K 3 sT ' do

+

E fd

KA
1 sTA

given by: X Eff
_

_
_

XT

X TL

X TCSC (

0)

. During dynamic

VS conditions the series compensation is modulated for damping
+

K6
Fig. 3 Modified Phillips-Heffron model of SMIB with TCSC-based
supplementary damping controller

system oscillations. The effective reactance in dynamic
conditions is given by: X Eff X T X TL X TCSC ( ) , where

and
2(
) , 0 and 0 being initial
0
value of firing and conduction angle respectively.
From the viewpoint of the washout function the value of
washout time constant is not critical in lead-lag structured

13


controllers and may be in the range 1 to 20 seconds [1]. In the
present study, washout time constant of TWT 10 s is used. The
controller gains KT ; and the time constants T1, T2, T3 and T4
are to be determined.
B. Objective Function
It is worth mentioning that the TCSC controller is designed
to damp power system oscillations and improve the system
voltage profile after a disturbance. A multi-objective function
based on
and VT is used as an objective function in the
present study. The objective can be formulated as the
minimisation of function F given by:

several objectives that require optimization. In case of single
objective optimization problems, the best single design
solution is the goal. But for multi-objective problems, with
several and possibly conflicting objectives, there is usually no
single optimal solution. Therefore, the decision maker is
required to select a solution from a finite set by making
compromises. A suitable solution should provide for
acceptable performance over all objectives.
A general formulation of a MOP consists of a number of
objectives with a number of inequality and equality
constraints. Mathematically, the problem can be written as
[14]:
for i =1, 2,…,n.

minimise/maximise fi(x)

F

F1 , F2

(12)

Subject to constraints:
gj (x)

| . t . dt

|

(13)

0

| VT | . t . dt

(14)


| and | VT | denote the
In the above equations, |
absolute values of rotor speed and terminal voltage deviations
following a disturbance and t1 is the time range of the
simulation. For the objective function calculation, the timedomain simulation of the power system model is carried out
for the simulation period.
C. Optimization Problem
In this study, it is aimed to minimize the proposed objective
functions F. The problem constraints are the TCSC Controller
parameter bounds. Therefore, the design problem can be
formulated as the following optimization problem:
Minimize F

(15)

Subject to
min

KT

KT

min

T1

T1

T2

min

T2

T2

T3

min

T3

T3

T4

min

T4

T4

T1

0

k = 1, 2,…, K

fi(x) = { f1(x),…fn(x)}

0

KT

j = 1, 2, …, J

Where

t1

F2

and

0

hk (x)

t1

F1

Where,

(21)

max

max

max

max

max

n = number of objectives or criteria to be optimized
x = {x1, …, xp} is a vector of decision variables
p = number of decision variables
There are two approaches to solve the MOP. One approach
is the classical weighted-sum approach where the objective
function is formulated as a weighted sum of the objectives.
But the problem lies in the correct selection of the weights or
utility functions to characterise the decision-makers
preferences. In order to solve this problem, the second
approach called Pareto-optimal solution can be adapted. The
MOPs usually have no unique or perfect solution, but a set of
non-dominated, alternative solutions, known as the Paretooptimal set. Assuming a minimisation problem, dominance is
defined as follows:
A vector u = (u1,….,un) is said to dominate v = ( v1,…..,vn)
if and only if u is partially less than v ( u p< v),
i

(16)

{1,…,n}, ui

vi

i

{1,…,n}; ui < vi (21)

(17)

U is said to be Pareto-optimal if and only
A solution xu
if there is no xv U for which v = f(xv) = (v1,…,vn) dominates
u = f(xu) = ( u1,…,un).

(18)

B. Pareto-optimal solutions

(19)
(20)

The proposed approach employs genetic algorithm to solve
this optimization problem and search for optimal set of the
TCSC Controller parameters.
IV. MULTI-OBJECTIVE OPTIMIZATION
A. Multi-objective optimization
A multi-objective optimization problem (MOP) differs from
a single-objective optimization problem because it contains

Pareto-optimal solutions are also called efficient, nondominated, and non-inferior solutions. The corresponding
objective vectors are simply called non-dominated. The set of
all non-dominated vectors is known as the non-dominated set,
or the trade-off surface, of the problem. A Pareto optimal set is
a set of solutions that are non-dominated with respect to each
other. While moving from one Pareto solution to another,
there is always a certain amount of sacrifice in one objective
to achieve a certain amount of gain in the other. The elements
in the Pareto set has the property that it is impossible to further
reduce any of the objective functions, without increasing, at
least, one of the other objective functions.

14


Pareto-optimal solutions are also called efficient, nondominated, and non-inferior solutions. The corresponding
objective vectors are simply called non-dominated. The set of
all non-dominated vectors is known as the non-dominated set,
or the trade-off surface, of the problem. A Pareto optimal set is
a set of solutions that are non-dominated with respect to each
other. While moving from one Pareto solution to another,
there is always a certain amount of sacrifice in one objective
to achieve a certain amount of gain in the other. The elements
in the Pareto set has the property that it is impossible to further
reduce any of the objective functions, without increasing, at
least, one of the other objective functions.


C. GA method for generating Pareto solutions
The ability to handle complex problems, involving features
such as discontinuities, multimodality, disjoint feasible spaces
and noisy function evaluations reinforces the potential
effectiveness of GA in optimisation problems. Although, the
conventional GA is also suited for some kinds of multiobjective optimisation problems, it is still difficult to solve
those multi-objective optimisation problems in which the
individual objective functions are in the conflict condition.

crossover operator of GA exploits structures of good solutions
with respect to different objectives to create new nondominated solutions in unexplored parts of the Pareto front. In
addition, most multi-objective GA does not require the user to
prioritise, scale, or weigh objectives. Therefore, GA has been
the most popular heuristic approach to multi-objective design
and optimization problems.
Pareto-based fitness assignment was first proposed by
Goldberg [15], the idea being to assign equal probability of
reproduction to all non-dominated individuals in the
population. The method consisted of assigning rank 1 to the
non-dominated individuals and removing them from
contention, then finding a new set of non-dominated
individuals, ranked 2, and so forth. In the present study, before
finding the Pareto-optimal individuals for the current
generation, the Pareto-optimal individuals from the previous
generation are added. The computational flow chart of the
proposed multi-objective optimization algorithm is shown in
Fig. 5.
V. RESULTS AND DISCUSSIONS
A. Application of Genetic Algorithm
The objective function given by equation (12) is evaluated
by simulating the system dynamic model considering a 10 %
step increase in mechanical power input ( Pm ) at t = 1.0 sec.
Optimization is terminated by the prespecified number of
generations. While applying GA, a number of parameters are
required to be specified. An appropriate choice of the
parameters affects the speed of convergence of the algorithm.
Table I shows the specified parameters for the GA algorithm.
One more important factor that affects the optimal solution
more or less is the range for unknowns.

Start
Initialize population and
Pareto optimal set
Gen. = 0
Time-domain simulation of
power system model

Objective function evaluation

TABLE I PARAMETERS USED IN MULTI-OBJECTIVE GENETIC ALGORITHM
Obtain Pareto solution set

Apply GA opterators
(selection, crossover and
mutation)

Value/Type

Maximum generations
Gen. = Gen. +1

Parameter

100

No
Yes
Gen. >
max. Gen. ?

0.01
Pareto-optimal sorting
Blending

Type of selection

Reduce Pareto
optimal set size

50

Mutation rate
Selection operator

Yes

Population size

Recombination operator

Pareto size >
max. size ?

Pareto optimal selection

Stop

No

Fig. 5 Flowchart of the multi-objective genetic algorithm
optimization algorithm to generate Pareto solutions

Being a population based approach; GA is well suited to
solve MOPs. A generic single-objective GA can be easily
modified to find a set of multiple non-dominated solutions in a
single run. The ability of GA to simultaneously search
different regions of a solution space makes it possible to find a
diverse set of solutions for difficult problems with nonconvex, discontinuous, and multi-modal solutions spaces. The

For the very first execution of the program, 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. The final Pareto solution surface is shown
in Fig. 6 where the Pareto solutions are shown with the marker
‘o’.
B. Best Compromise Solution
In the present paper, a Fuzzy-based approach is applied to
select the best compromise solution from the obtained Pareto
set. The j-th objective function of a solution in a Pareto set fj

15


It is clear from Table III that the open loop system is
unstable at all the loading conditions because of negative
damping of electromechanical mode (s = 0.2655, 0.0278,
0.4864 for nominal, light and heavy loading respectively).
Without optimized TCSC controller parameters the system
stability is maintained as the electromechanical mode
eigenvalue shift to the left of the line in s-plane (s = -0.0081, 1.1828, -0.0088 for nominal, light and heavy loading
respectively) for all loading conditions. It is also clear that
MOGA optimized TCSC controller shifts substantially the
electromechanical mode eigenvalue to the left of the line (s = 3.6835, -3.8535, -2.3982 for nominal, light and heavy loading
respectively) in the s-plane, which enhances the system
stability and improves the damping characteristics of
electromechanical mode.

Fitness of F2

8.56
8.55
8.54
8.53
8.52
8.51

10

15

20

25

30

35

Fintess of F1

Fig. 6 Pareto solution surface

is represented by a membership function

j

TABLE II LOADING CONDITIONS CONSIDERED

defined as [16]:

fj


1,

f jmax
j

f

f

max
j

f

j

min
j

,

f jmin
fj

0,
max

where f j

min

and f j

Loading

fj

f jmax

(22)

f jmax

i

m

n

i 1

j 1

0.4652
0.1286
0.777

68.51
30.06
87.81

0

Without
control
0.2655
4.9846i
0.0278
5.5445i
0.4864
3.9793i

Without
optimized
TCSC
-0.0081
0.0283i
-1.1828
4.1526i
-0.0088
0.0209i

With MOGA
optimized
TCSC
-3.6835
1.8176i
-3.8535
3.3751i
-2.3982
1.5389i

(23)
i
j

where, n is the number of objectives functions and m is the
number of solutions. The solution having the maximum value
i

is the best compromise solution.
Using the above approach the best compromise solution is
obtained as:
of

0.9
0.4
1.1

Nominal
loading
Light
loading
Heavy
loading

is

i
j

j 1

i

(deg.)

TABLE III SYSTEM ELECTROMECHANICAL MODE EIGENVALUES

values of the j-th objective function, respectively.

n

(pu)

Loading
Conditions

are the maximum and minimum

For each solution i, the membership function
calculated as:

Q

(pu)

Nominal loading
Light loading
Heavy loading

f jmin

P

conditions

KT =55.8577, T1 = 0.1684 s, T2 = 0.0637 s, T3 = 0.3126 s
and T4 = 0.3126 s
C. Eigenvalue Analysis
To assess the effectiveness and robustness of the proposed
stabilizers, three different loading conditions given in Table II
are considered. The system electromechanical mode
eigenvalues without and with the proposed controllers are
shown in Table III. Table III also shows the system
electromechanical eigenvalues without optimized TCSC
controller parameters. In this case the values are randomly
chosen as:

D. Simulation Results
In order to verify the effectiveness of the proposed
approach, the performance of the MOGA optimized TCSC
controller is tested for different loading conditions and
compared with the case where the TCSC-based controller
parameters are not optimized (i.e. using the randomly chosen
values as the TCSC-based controller parameters). A 10 % step
increase in mechanical power input at t =1.0 sec is considered.
The response with TCSC without optimization are shown in
dotted lines (with legend NO); and the responses with MOGA
optimized TCSC controllers are shown with solid lines (with
legend MOGA). The system is unstable without control for the
above contingency and the responses are not shown in figures.
The system speed deviation and terminal voltage response for
the above contingency at all the loading condition are shown
in Figs. 7 and 8 respectively. These simulation results
illustrate the effectiveness and robustness of proposed design
approach. It is clear that the proposed TCSC controller has
good damping characteristics to low frequency oscillations
and stabilizes the system quickly for all loading conditions.

KT =40, T1 =0.2 s, T2 =0.05 s, T3 =0.25 s and T4 =0.05 s.

16


-4

-3

x 10

10

NO
MOGA

8

4

VT (pu)

(pu)

NO
MOGA

15

6

2

10

5

0
-2
-4

x 10

20

0

0

1

2

3

4

5
6
Time (sec)

7

8

9

0

10

1

2

3

4

5
6
Time (sec)

7

8

9

10

(a) Nominal loading

(a) Nominal loading
-3

-4

10

5

x 10

NO
MOGA

NO
MOGA

(pu)

VT (pu)

5

0

0

-5

0

1

2

3

4

5
6
Time (sec)

7

8

9

-5

10

0

1

2

3

4

5
6
Time (sec)

7

8

9

10

(b) Light loading

(b) Light loading
-4

10

x 10

NO
MOGA

8

NO
MOGA

0.03

6
4

VT (pu)

(pu)


x 10

2

0.02

0.01

0
-2
-4

0

0

1

2

3

4

5
6
Time (sec)

7

8

9

10

0

(c) Heavy loading
Fig. 7 Speed deviation responses for a 10 % step increase in
mechanical power input (a) nominal loading (b) light loading
(c) heavy loading.

1

2

3

4

5
6
Time (sec)

7

8

9

(c) Heavy loading
Fig. 8 Terminal voltage responses for a 10 % step increase in
mechanical power input (a) nominal loading (b) light loading
(c) heavy loading.

VI. CONCLUSIONS
In this study, the performance improvement of a power
system by optimal design of a TCSC-based controller is
presented and discussed. The design objective is to improve
both rotor angle stability and system voltage profile. A
Genetic Algorithm (GA) based solution technique is applied to
generate a Pareto set of global optimal solutions to the given
multi-objective optimisation problem. Further, a fuzzy-based
membership value assignment method is employed to choose
the best compromise solution from the obtained Pareto
solution set. Eigenvalue analysis and simulation results are

presented under various loading conditions to show the
effectiveness and robustness of the proposed approach.The
proposed method is valuable for the design of the interactive
decision making. The decision makers can choose from the
solutions in the Pareto-optimal set to find out the best solution
according to the requirement and needs as the desired
parameters of their controllers. The results show that
evolutionary algorithms are effective tools for handling multiobjective optimization where multiple Pareto-optimal
solutions can be found in one simulation run.

17

10


REFERENCES
[1]
[2]

[3]

[4]

[5]

[6]

[7]

[8]


[9]

[10]

[11]
[12]

[13]

[14]
[15]
[16]

P. Kundur, Power System Stability and Control, McGraw-Hill, 1994
A. D Del Rosso, C. A Canizares and V.M. Dona, “A study of TCSC
controller design for power system stability improvement,” IEEE Trans.
Power Systs., vol-18, pp. 1487-1496. 2003.
S. Panda, N. P. Padhy, R. N. Patel “Modeling, simulation and optimal
tuning of TCSC controller”, International Journal ofSimulation
Modelling. Vol. 6, No. 1, pp. 7-48, 2007.
S. Panda, and N. P. Padhy “Comparison of Particle Swarm Optimization
and Genetic Algorithm for FACTS-based Controller Design”, Applied
Soft Computing. Vol. 8, pp. 1418-1427, 2008.
S. Panda, S. C. Swain, A. K. Baliarsingh, C. Ardil, “Optimal
Supplementary Damping Controller Design for TCSC Employing
RCGA”, International Journal of Computational Intelligence, Vol. 5,
No. 1, pp. 36-45, 2009.
Sidhartha Panda and Narayana Prasad Padhy, “Application of Genetic
Algorithm for PSS and FACTS based Controller Design”, International
Journal of Computational Methods, Vol. 5, Issue 4, pp. 607-620, 2008.
S. Panda and R.N.Patel, “Damping Power System Oscillations by
Genetically Optimized PSS and TCSC Controller” International Journal
of Energy Technology and Policy, Vol. 5, No. 4, pp. 457-474, 2007.
S. Panda, N.P.Padhy and R.N.Patel, “Robust Coordinated Design of PSS
and TCSC using PSO Technique for Power System Stability
Enhancement”, Journal of Electrical Systems, Vol. 3, No. 2, pp. 109123, 2007.
Sidhartha Panda, N.P.Padhy, “Thyristor Controlled Series Compensatorbased Controller Design Employing Genetic algorithm: A Comparative
Study” International Journal of Electronics, Circuits and Systems, Vol.
1, No. 1, pp. 38-47, 2007.
C. A .C. Coello, “A comprehensive survey of evolutionary-based
multiobjective optimization techniques”, Knowledge and Information
Systems, Vol. 1, No. 3, pp. 269-308. , 1999.
V. Chankong and Y. Haimes, Multiobjective Decision Making Theory
and Methodology, New York: North-Holland. 1983.
C. M Fonseca, and P. J. Fleming, ‘Genetic algorithms for multiobjective
optimization: formulation, discussion and generalization, Proceedings of
the Fifth International Conference on Genetic Algorithms, San Mateo
California. pp. 416-423, 1993.
H. F. Wang, F. J. Swift, A Unified Model of FACTS Devices in
Damping Power System Oscillations Part-1: Single-machine Infinite-bus
Power Systems, IEEE Trans. Power Delivery, Vol. 12, No. 2, pp. 941946, 1997.
S. S. Rao, Optimization Theory and Application,New Delhi: Wiley
Eastern Limited, 1991.
D. E. Goldberg, Genetic Algorithms in Search, Optimization, and
Machine Learning, Addison-Wesley, 1989.
Sidhartha Panda “Multi-objective evolutionary algorithm for SSSCbased controller design”, Electric Power System Research., Vol. 79,
Issue 6, pp. 937-944, 2009.

India. He is working towards his PhD in KIIT University in the area of
Application of Computational Intelligent Techniques to Power System
Stability Problems and Flexible AC Transmission Systems controller design.
Dr. A. K. Mohanty is an Ex-Professor in N.I.T.Rourkela.Now he is working
as a Professor in Electrical Engg. Deptt. at KIIT UNIVERSITY Bhubaneswar.
Cemal Ardil is with National Academy of Aviation, AZ1045, Baku,
Azerbaijan, Bina, 25th km, NAA

Sidhartha Panda is a Professor at National
Institute of Science and Technology, Berhampur,
Orissa, India. He received the Ph.D. degree from
Indian Institute of Technology, Roorkee, India in
2008, M.E. degree in Power Systems Engineering
in 2001 and B.E. degree in Electrical Engineering
in 1991. Earlier he worked as Associate Professor
in KIIT University, Bhubaneswar, India and
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.
S. C. Swain received his M.E. degree from UCE Burla in 2001. Presently he
is working as an Assistant Professor in the Department of Electrical
Engineering, School of technology, KIIT,University, Bhubaneswar, Orissa,
India. He is working towards his PhD in KIIT
University in the area of Application of Computational Intelligent Techniques
to Power System.
A. K. Baliarsingh is working as an Assistant Professor in the Department of
Electrical Engineering, Orissa Engineering College, Bhubaneswar, Orissa,

18

Multi objective-optimization-with-fuzzy-based-ranking-for-tcsc-supplementary-controller-to improve-rotor-angle-and-voltage-stability

More Related Content

What's hot (20)

Viewers also liked (16)

Similar to Multi objective-optimization-with-fuzzy-based-ranking-for-tcsc-supplementary-controller-to improve-rotor-angle-and-voltage-stability (20)

More from Cemal Ardil (20)

Recently uploaded (20)

Multi objective-optimization-with-fuzzy-based-ranking-for-tcsc-supplementary-controller-to improve-rotor-angle-and-voltage-stability