international journal of pure and applied mathematics volume … · 2018-03-15 · analyzing the...

A HYBRID KRILL HERD-GENETIC ALGORITHM BASED TRANSIENT STABILITY

ENHANCEMENT OF COORDINATED PSS AND SSSC CONTROLLER

IN MULTI-MACHINE POWER SYSTEM

1A. Kathiravan,

2Alamelu Nachiappan

1Research Scholar

Department of Electrical and Electronics Engineering

Pondicherry Engineering College, Puducherry, India. 2Department of EEE, Pondicherry Engineering College, India

[email protected], [email protected]

Abstract: Power system oscillations are the major

crises in a large interconnected network. It certainly

affects the power system stability and remains a

challenge for scheduling and planning of the power

demand in a deregulated market. This paper represents

the Hybrid Krill Herd-Genetic Algorithm (KH-GA)

optimization method based on global optimization for

analyzing the stability of multi-machine power system.

The two algorithms are inspired by biological and

environmental characterization. A typical three

generator nine bus benchmark power system is

considered for small signal stability analysis using

MATLAB/Simulink. The angular frequency in a power

system is affected by deviation in power generation,

variation in load, and faults. The angular frequency

deviation causes fluctuation in generator speed and rotor

angle leading to electromechanical oscillations ina

power system. So, the deviation in angular frequency is

considered as a reliable parameter for the stability study

of the system. Several optimization techniques such as

Firefly, Cuckoo and Krill Herd (KH)algorithms are

employed for the coordinated tuning of power system

stabilizer (PSS) and Static Synchronous Series

Compensator (SSSC) along with proposed Hybrid

KH-GA algorithm to improve transient stability of the

power system. The capability of the suggested Hybrid

KH-GA algorithm is validated with the other

optimization techniques taken into consideration. The

simulated results show higher convergence rate and

better low frequency oscillation (LFO) damping

capability.

Index Terms: Multi- machine, Krill Herd algorithm,

Genetic Algorithm, Hybrid KH-GA, PSS, SSSC, low

frequency Oscillation.

1. Introduction

According to power systems, the electrical utilities often

encounter a stability problem. Power system inter

connection imposes a different kind of oscillations to the

power system. To ensure better stability, the frequency

and terminal voltage of the power system needs to be

maintained at their rated values [1]. In order to minimize

these oscillations and increase the system dynamic

stability, the most convincing and reliable solution is to

install a PSS in the generator excitation system.

However, the application of PSSs has limitations for

damping of inter-area oscillations and nonlinear systems

[2- 4].

A Flexible AC Transmission System (FACTS)

has numerous advantages in comparison with

conventional PSS. FACTS controllers use the

application of high power solid state devices for

Sub-synchronous Resonance (SSR) mitigation, voltage

regulation, real power flow enhancement, and Low

Frequency Oscillation (LFO) damping [5]. The wide

application of the voltage source converter (VSC)based

FACTS controllers are better choices for improving the

power systems stability. SSSC finds an important part

for its robustness and capability to vary the reactance

characteristics between capacitive region to inductive

region which gives the strength to improve the real

power flow and damp the LFOs. Apart from its

robustness and reliability, SSSC can also perform

various tasks in stability studies, schedule power flow,

minimize net power loss, and enhance overall stability

[6].

Heuristic and meta-heuristic optimization

algorithms are the two major classifications of stochastic

optimization technique. Heuristic algorithms reach the

solution in quick time but no guarantee for best solution

is reached [7]. A meta-heuristic algorithm uses the

randomization and local search makes it convenient for

global search. The best examples of Meta- heuristic

techniques are Genetic Algorithm (GA),Particle Swarm

Optimization (PSO), Firefly Algorithm (FA), Cuckoo

Algorithm (CA) and Bat Algorithm (BA) [8]. Optimal

settings of rule-based PSS using PSO search have been

discussed in [9]. Multi-machine PSS with a Multi-

objective design using PSO is considered in [10]. The

International Journal of Pure and Applied MathematicsVolume 118 No. 20 2018, 1043-1057ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

1043

integrated design of FACTS and PSS is investigated

stability enhancement [11]. In [12], the authors

real-coded GA for optimize the system damping using

Eigen value based objective function. However,

authors claimed that PSO outperformed GA and it

reaches the best solution in less iteration than GA.

authors have also tested various stabilizers like PSS,

SVC, TCSC, STATCOM and TCPS individually to

enhance system damping.

In brief literature, many researchers come out

with combined PSS and FACTS based stabilizers have

enhanced dynamic stability in a power syste

parameter-constrained nonlinear algorithm is developed

using global tuning procedure. The power system

stability is enhanced by considering the Eigen values as

an objective function for an integrated PSS and FACTS

based stabilizer using GA is investigated

SSSC is a VSC based series compensator which

manageable voltage quadrature to the line current

The SSSC has the ability to provide compensation

between capacitive reactance to inductive reactance

independent of line current. Moreover, SSSC

damp the LFOs with help of external damping controller

[16].

The FA is a biologically inspired meta

optimization algorithm characterized by

habit of fireflies [17]. In fact, the FA

resemblances of other swarm intelligence

algorithms like PSO, BA, Bacterial Foraging

(BFA), Cuckoo Optimization Algorithm (COA)

Artificial Bee Colony Optimization (ABC).

searches the best solution globally and

quickly [18]. The Krill Herd Algorithm (KHA)

recent optimization technique connected with

nature of krill herds. The krill swarm searches the area

of maximum food density based on

environmental and biological behaviors [21

In this study, a new Hybrid KH-GA

purposed for single objective function. The aim of

Hybrid KH-GA is to produce the faster

rate. The proposed Hybrid KH-GA algorithm is verified

on three generator nine bus standard test system for

location of integrated SSSC and PSS stabilizer

the integrated PSS and FACTS stabilizers

placement obtained by hybrid KH-GA can

damping effect and strengthen the overall stability. The

time-domain simulations with different loading

situations are carried out for analyzing the

proposed controllers individually and also

simultaneously.

The rest of the paper is coordinated as follows:

Section II describes the complete dynamical modelling

of a synchronous machine, Excitation system,

SSSC and AVR are discussed. Section III

complete methodology of a proposed Hybrid KH

algorithm. Section IV briefly explains the

function and implementation. Section V

simulation results and discusses the efficiency of

is investigated for

, the authors uses

damping using

. However, the

PSO outperformed GA and it

than GA. The

stabilizers like PSS,

and TCPS individually to

many researchers come out

stabilizers have

power system. In [13], a

constrained nonlinear algorithm is developed

power system

is enhanced by considering the Eigen values as

PSS and FACTS

is investigated [14]. The

is a VSC based series compensator which injects a

line current[15].

compensation

between capacitive reactance to inductive reactance

ver, SSSC effectively

damping controller

meta-heuristic

the flashing

the FA has many

swarm intelligence based

Bacterial Foraging algorithms

Cuckoo Optimization Algorithm (COA)and

ptimization (ABC). The COA

and converge it

l Herd Algorithm (KHA) is a

connected with swarm

rill swarm searches the area

of maximum food density based on distinct

[21, 22].

GA technique is

. The aim of

faster convergence

GA algorithm is verified

test system for best

stabilizer. Hence,

with optimal

can fetch best

the overall stability. The

with different loading

arried out for analyzing the potency of

individually and also

paper is coordinated as follows:

mplete dynamical modelling

machine, Excitation system, PSS,

ection III presents a

Hybrid KH-GA

explains the objective

validates the

discusses the efficiency of the

proposed algorithm. Finally, Section VI deals with the

summary and conclusion.

2. Power System Modelling

A. Synchronous Generator Modelling

A benchmark three-machine nine

shown in Fig. 1. Data for generators, line

loads are found in [4]. The generators

modeled by specified third order

as in [3].The generator dynamic equations are given

equations (1)-(3), which consist of q

voltage equation and electromechanical swing equation.

��

��

� �� Where, ��is the variation in internal rotor angle or

load angle in degrees, �� is change

generator speed deviation in rad/sec

synchronous speed in rad/sec, �speed in rad/sec,��is the generator�� is the generator inertia constant

power input to the rotor in p.u, �� power in p.u.

�� ΄

�� ΄ !"�� Where, �� is the variation

voltage in volts, #�$�΄ is the transient open circuit time

constant, �� is thep.u field voltage

axis synchronous reactance, ��΄transient reactance, "��is the direct axis sta

p.u, and ��΄ is the generator internal voltage

Figure 1. Three-machine nine-

B. Exciter Modelling

The excitation system is designed to produce the control

the excitation voltage with the aid

regulator (AVR) and damping voltage can be obtained

from PSS is displayed in Fig. 2.PSS comprises

Section VI deals with the

Power System Modelling

Modelling

machine nine-bus test system is

ata for generators, lines, buses and

The generators and PSSs are

differential equations

The generator dynamic equations are given in

(3), which consist of q-axis generator

voltage equation and electromechanical swing equation.

(1)

�� (2)

in internal rotor angle or

is change in rotor speed or

generator speed deviation in rad/sec, ��is the generator �� is the internal rotor

generator damping coefficient,

inertia constant, �� is mechanical

is the electromagnetic

! � ��΄ % (3)

is the variation in effective internal

is the transient open circuit time

field voltage , �� is the direct

��΄ is the direct axis

rect axis stator current in

internal voltage in p.u.

-bus power system

is designed to produce the control

excitation voltage with the aid of automatic voltage

regulator (AVR) and damping voltage can be obtained

.PSS comprises of gain,

International Journal of Pure and Applied Mathematics Special Issue

1044

wash-out filter, and two stage lead lag compensator.

Wash-out filter attenuates low frequencies and allows

the high frequencies, whereas the lead-lag compensator

provides a necessary phase lead to compensate the phase

lag between excitation and the synchronous machine

electrical torque. The dynamic equation is given [3] by:

�� & �'(�)*�� )+ � ,-..% � ��% (4)

Where, Vref is the reference generator terminal

voltage,)+is the generator terminal voltage, TA and KA is

the AVR time constant and gain respectively, ��is the

excitation voltage in volts, �� is the deviation in

excitation voltage in p.u, and UPSS is the output of the

PSS.

Figure 2. AVR and PSS based generic excitation system

C. SSSC Modelling

The SSSC is a series based FACTS device providing

series compensation to a transmission line is displayed

in Fig. 3. The important functional elements of SSSC are

three-phase controlled voltage source inverter (VINV), a

boosting series coupling transformer with a leakage

reactance of XSCT and a DC link capacitor (CDC). Two

input signals m and ψ are controlling the performance of

the SSSC [16].The signal m refers amplitude

modulation ratios of Pulse Width Modulated

(PWM)VSI pulses that manipulate the inserted voltage,

and the signal ψrefers phase angle between injected

voltage and line current ignoring the inverter losses[18,

25]. The stability study of SSSC by considering the

dynamic model is as follows [25]: "+./// � "+.� � 0"+.� � "�1∠∅ (5)

Where, "+./// is series injected current, "+.� is

direct axis series current, 0"+.� is the quadrature axis

series current, ∅ refers phase angle between direct and

quadrature axis series currents. )456////// � 78)9:;<=> � 0=?@>A � 78)9∠> (6)

Where: > � ∅ ± 90 (7)

�6EF�+ � 4EF

9EF � �GHEF :"+.�;<=> � "+.�=?@>A (8)

Where,)9 indicates DC link voltage,"9 indicates

DC link current, m is the modulation ratio defined by

PWM pulses, k refers fixed ratio between AC voltage

and DC voltage of VSI[16].

Figure 3. Power system model with SSSC

3. Hybrid KH-GA Technique

A. KHA

The KHA is a biologically inspired meta-heuristic

optimization algorithm inspired by herding nature of the

krill swarm. Krill swarm has a tendency to find a place

where highest food density is available with minimum

distance. In a two-dimensional surface, the time stamped

movements of an individual krill is identified by three

important activity [21]; (1) Movement induced by other

krill individuals, (2) Foraging activity and (3) Random

diffusion.

The KHA uses Lagrangian model to expand the

search area to an n-dimensional decision space as: �I�+ � J� � K� � �� (9)

Where, Ni indicates the movement of ith krill

induced by neighbors, Fi represents the foraging

behavior of ith krill individual and Di denotes the

physical diffusion of ith krill individual[22].

Description of basic KHA technique as discussed

below:

(1) Motion induced by other krill individuals According to krill nature of living, individual krill

attracted by other krills mutually to form a large krill

swarm. The direction of motion induced ( L� ), is

estimated from local swarm density (local effect), target

swarm density (target effect), and repulsive swarm

density (repulsive effect). The motion of the krill

individual can be estimated as:

J�M�N � J�OPL� � �MJ�$Q� (10)

Where:

L� � L�Q$HOQ � L�+O*R�+ (11)


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Where, J�M�N is the new induced speed of ith krill,

Nmax is the maximum induced speed, ωn refers inertia

weight of motion induced (between 0 to 1 second), J�$Q�

is the last motion induced, L�Q$HOQ refers local effect

contributed by neighbors, and L�+O*R�+ indicates target

direction effect contributed by best individual krill.

The sensing distance S. between krill individuals and

neighbors is found by their behavior.

S.,� � �U5 ∑ W � � XW5XY� (12)

Where,S.,� denotes the sensing distance for the ith

krill and N refers number of krill and Xi indicates the

related positions of ith krill. If the distance of (Xi-Xj)

<S.,� then Xjis the neighbor of Xi.

(2) Foraging motion

The krill neighbors are induced and attracted towards

best food location and also possess previous knowledge

about the food location. This activity of krills is referred

as Foraging Motion.

The foraging activity of the ith krill is expressed as:

K� � )�Z� � ��K�$Q� (13)

Where:

Z� � Z��$$� � Z�[�.+ (14)

Where,Vf denotes foraging speed, ωf denotes

inertia weight of the motion induced (between 0 to

1),Fiold is the last foraging motion value,Z��$$�

is the

attractive food, and Z�[�.+ denotes the optimal fitness of

an ith krill so far.

The core of the food density is found by the fitness

distribution for every iteration is expressed as:

�$$� � ∑ \]I_\

∑ \]_\

(15)

Where, �$$� denotes the core region of food

density, Ki refers fitness value of ith krill individual.

(3) Physical diffusion

Every krill individuals physically diffuse

themselves randomly. The ith krill motion depends on

maximum diffusion speed and a random directional

vector. The expression of Di is as follows:

�� OP `1 � 44bcde � (16)

Where, Dmax is the maximum diffusion speed, � is the

random directional vector, I refers the actual iteration

number and Imax indicates the maximum iteration

number.

(4) Motion process of KHA The movements of the individual krills are always

approaches towards best fitness value. This algorithm

utilizes local and global conditions makes it most

efficient one. The positional vector during the interval t

to t+∆g can be denoted as:

�:g � ∆gA � �:gA � ∆g �I�+ (17)

Where, �:g � ∆gA denotes the updated krill

individual position, and �:gA represents the current

position of the krills. The ∆gis an important operator in

tuning the optimization problem. The ∆g constant is

considered as a scaling parameter for the speed vector. It

is expressed as:

∆g � h+ ∑ �,ij � kiX!56XY� (18)

Where, NV refers total count of variables, kiXand

,ijare the lower bound and upper bound of jth variables

(j = 1, 2….NV). A constant number Ct is carefully

chosen between the values 0 and 2. The low values of

Ctdirect the krills to search the space more carefully.

The KHA has been analyzed for so many

non-linear multi-objective systems in end result it

cannot always produce optimal solutions in global

search space [21-23]. Since the KHA applies random

search and it cannot rapidly finds the optimal solution.

B.GA

The GA is an efficient heuristic technique which finds

best solution for the complex non-linear problems [24].

It effectively searches the various regions of a solution

space and finds a numerous set of solutions even for

complex problems [21-24]. The important aspect of this

algorithm is the genetic operators. They are (i)

Selection, (ii) Crossover, and (iii) Mutation. These

operators are intending to produce the best child by

random selection of best mates (studs) [23].

The reproduction steps are as follows,

(i) Rearrange two stud particles (Random selection)

(ii) Check the divergence according to Hamming

interval between the rearranged stud and current mate:

1. If the diversity is greater than the set threshold,

perform crossover to generate one offspring.

2. If the diversity is less than the set threshold, mutate

the current mate to generate the new child.

The conventional GA is customized by choosing

the best mate (stud) to produce the best child is framed

as Stud Genetic Algorithm (SGA). The selected stud is

combining genetically with other stud individuals

through the genetic operators like crossover and

mutation to produce new population [23].

(1) Function of Genetic operators The crossover operation is based on binomial crossover

method to update the mth components of ith krill by the

following expression:

�,� � l *,�mn@S�,� < h* �,� qr=q s (19)

Where: h* � 0.2'v�,[�.+ (20)

Where, h* is the crossover probability, which is

randomly selected between 0 and 1.

The Mutation operation is depends on the principle of

adaptive mutation scheme. It is expressed as:

�,� � w R[�.+,� � x� -,� � �,�!mn@S�,� < �y �,� qr=q s

(21)


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Where:

�z � 0.005 'v�,[�.+| (22)

Where, �z isa mutation probability and µ is a

constant number chosen between 0 and 1.

C. Proposed Hybrid KH–GA Algorithm

The purposed Hybrid KH-GA optimization algorithm is

a novel hybrid technique combining the KHA and GA.

Since KHA cannot find optimal solution always in

global search area but the existence of genetic operators

certainly helps to refine the search locally in a global

search space and quickly converges the ideal solution.

Hence, the hybrid KH-GA optimization technique

definitely accelerates convergence speed.

Flowchart of proposed Hybrid KH-GA algorithm

is displayed in Fig. 4.

Figure 4. Flowchart of Hybrid KH-GA algorithm


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D. Implementation of objective Function

An objective function (Fitness function) is a

mathematical expression which is taken as an input

parameter for an optimization algorithm. The objective

function for a standard three generator nine bus system

with an integrated PSS and SSSC stabilizer is designed.

In this research, Objective function is formulated on the

basis of two performance indices namely Integral of a

Time-multiplied Absolute value of Error (ITAE) and

Integral Square Error (ISE).The ISE index minimizes

the overshoot and ITAE reduces the steady state error.

The performance indices are intended to achieve the

quick settling time and to minimize the LFOs. However,

the overall stability of a test system can be improved by

minimizing the speed deviations of generators. Hence

the integration of speed variations of the generators is

considered as an objective function. The objective

function is given by,

} � ~ g�|�2 � �1| � |�3 � �1| Sg+� (23)

Where, J indicates objective function, t is the total

simulation time, ω1, ω2, and ω3 are speeds of generators

G1, G2, and G3 respectively.

In this research, an objective function is provided

in Eq. (23) is taken as an input parameter for the

purposed Hybrid KH-GA Algorithm for optimal

location of SSSC and to boost the damping effect tand

also system stability.

4. Results and Discussion

The three generator nine bus system is designed for the

stability analysis. The generators G2 and G3 are

installed with PSS and generator G1 connected with a

simple exciter. The efficiency of the test system is

analyzed under different load settings given in Table

1.1. The non-linear time zone simulation is executed

using Matlab/Simulink programming for a three phase

fault.

Let us consider, If a three phase to ground fault

occurs at bus 7 at t = 0.5 sec. The element Y77 is

increased 1000 times to represent very high admittance

to ground in order to simulate this fault . The fault is

cleared at t = 0.6 sec. The fault clearance is simulated by

restoring the value of Y77 to its pre-fault value at t = 0.6

sec

Table 1.1 Test system with different load settings

Nominal Loading Heavy Loading Lightly Loading

P Q P Q P Q

Generator

G1 71.64 27.04 134.91 43.30 9.11 17.64

G2 163.00 6.65 163.00 17.87 163.00 -2.83

G3 85.00 -10.85 85.00 -0.90 85.00 -19.17

Load

L1 0 0 0 0 0 0

L2 0 0 0 0 0 0

L3 0 0 0 0 0 0

L4 0 0 0 0 0 0

L5 125 50 150 60 100 40

L6 90 30 108 36 72 24

L7 0 0 0 0 0 0

L8 100 35 120 42 80 28

L9 0 0 0 0 0 0

A. Nominal Loading Condition

The efficiency of proposed optimization technique for

the integrated controller is validated with the test system

under nominal loading. The Fig. 5.1(a), (b) & (c)

represents the rotor angle deviations of Generator 1, 2

and 3 with respect to synchronous angular speed. Due to

the large disturbance, the sustained oscillations start

grows and cause stability issue if the system may not

install a controller. Whereas, the test system with

optimally located SSSC show better damping effect to

the LFO’s when correlated with other optimization

algorithms. The time taken to attain steady state

condition of these oscillations is also very good for the

system optimized by Hybrid KH-GA. Power flow

results after installing SSSC is listed in Table 1.2.

Injected SSSC Series Voltage with proposed

Hybrid KH-GA technique at line 8:Vse (pu) = 0.1634@

3.000


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Table 1.2 Power flow after SSSC installed - Normal load

Bus V Angle Injection Generation Load

No pu Deg MW MVar MW Mvar MW MVar

1.00 1.04 0.00 60.46 26.96 62.46 26.96 0.00 0.00

2.00 1.02 9.88 163.00 6.62 163.00 6.62 0.00 0.00

3.00 1.02 5.30 85.00 -10.99 85.00 -10.99 0.00 0.00

4.00 1.02 -1.87 7.42 0.00 -0.00 0.00 -7.42 0.00

5.00 0.99 -3.55 -125.00 -50.00 -0.00 0.00 125.00 50.00

6.00 1.01 -3.23 -90.00 -30.00 -0.00 0.00 90.00 30.00

7.00 1.02 4.32 0.26 0.00 0.00 0.00 -0.26 0.00

8.00 1.01 1.39 -98.00 -35.00 1.99 0.00 100.00 35.00

9.00 1.03 2.60 1.63 0.00 0.00 0.00 -1.63 0.00

Total

4.78 -92.40 310.46 22.59 305.67 115.00

Figure 5.1 (a) Generator 1 frequency

Figure 5.1 (b) Generator 2 frequency

Figure 5.1 (c) Generator 3 frequency

B.Heavy Loading Condition

The proposed optimization technique is utilized for the

test system with coordinated controller under heavy

loading condition to check its effectiveness. The Fig.

5.1(a), (b) & (c) represents the rotor angle deviations of

Generator 1, 2 and 3 with respect to synchronous

angular speed. The system without controller will cause

power oscillations due to the large disturbance since it

may not adequately damped. Whereas, the test system

with optimally located SSSC show better damping effect

to the LFO’s when correlated with other optimization

algorithms. The time taken to attain steady state

condition of these oscillations is also very good for the

system optimized by Hybrid KH-GA. Power flow


Injected SSSC Series Voltage with proposed Hybrid

KH-GA technique at line 9:Vse (pu) = 0.2607 @ 3.000


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Table 1.3 Power flow after SSSC installed - Heavy load



1 1.04 0.00 125.39 43.01 125.39 43.01 0.00 0.00

2 1.02 5.72 163.00 17.32 163.00 17.32 0.00 0.00

3 1.02 1.16 85.00 -1.45 85.00 -1.45 0.00 0.00

4 1.01 -3.90 -0.00 0.00 -0.00 0.00 0.00 0.00

5 0.98 -7.13 -149.05 -60.00 0.00 0.00 149.05 60.00

6 0.99 -6.63 -108.00 -36.00 0.00 0.00 108.00 36.00

7 1.01 0.12 0.00 0.00 0.00 0.00 0.00 0.00

8 1.00 -3.11 -111.28 -42.00 3.26 0.00 114.54 42.00

9 1.02 -1.55 0.00 0.00 0.00 0.00 0.00 0.00

Total 5.05 -79.11 376.66 58.86 371.60 138.00

Figure 5.2 (a)Generator 1 frequency



C. Light Loading Condition

The proposed optimization technique is utilized for the

test system with coordinated controller under light

loading condition to check its effectiveness. The Fig.

5.1(a), (b) & (c) represents the rotor angle deviations of

Generator 1, 2 and 3 with respect to synchronous

angular speed. Due to the large disturbance, the

sustained oscillations start grows and cause stability

issue if the system may not install a controller. Whereas,

the test system with optimally located SSSC show better

damping effect to the LFO’s when related with other

optimization algorithms. The time taken to attain steady

state condition of these oscillations is also very good for

the system optimized by Hybrid KH-GA. Power flow


Injected SSSC Series Voltage with proposed

Hybrid KH-GA technique at line 2: Vse (pu) = 0.2715 @

4.000


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Table 1.4 Power flow after SSSC installed - Light load



1 1.04 0.00 -1.06 17.77 -1.06 17.77 0.00 0.00

2 1.02 14.05 163.00 -2.86 163.00 -2.86 0.00 0.00

3 1.02 9.31 85.00 -19.16 85.00 -19.16 0.00 0.00

4 1.03 0.03 -98.84 -0.00 6.16 -0.00 -2.17 0.00

5 1.00 -0.04 -72.00 -40.00 -0.00 0.00 98.84 40.00

6 1.02 -0.01 -72.00 -24.00 -0.00 0.00 72.00 24.00

7 1.03 8.52 0.00 0.00 0.00 0.00 0.00 0.00

8 1.02 5.96 -79.27 -28.00 -0.00 0.00 79.27 28.00

9 1.03 6.63 0.00 0.00 0.00 0.00 0.00 0.00

Total 5.14 -96.25 253.09 -4.25 247.95 92

Figure 5.3 (a) Generator 1 frequency



The objective function (J) is effectively minimized

by adopting proposed optimization technique. The

convergence rate of the different optimization

techniques are displayed in Fig.5.3 (d). It is clearly

evident that proposed Hybrid KH-GA algorithm

converges in fewer iterations and the objective function

(Fitness function) is also minimized effectively. Hence

the purposed algorithm finds the best location of SSSC,

and also reduces the electro mechanical oscillations

effectively.


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Figure 5.3 (d) The Convergence for Objective function minimization using

FA, COA, KH and Hybrid KH-GA.

5. Conclusions

In this research, a coordinated control of PSS and SSSC

is discussed. An objective function is effectively

minimized using Hybrid KH-GA technique for finding

best location of SSSC so as to minimize the power

oscillation. The non-linear system with a coordinated

controller is simulated through MATLAB/Simulink to

assess the influence of the purposed algorithm. The

soundness of the purposed coordinated controller is

investigated by testing its performance under normal,

heavy and light load settings. The simulated results

reveal that the dynamic performance and LFO damping

capability are significantly enhanced by optimal

placement of SSSC. Therefore, the purposed algorithm

provides a better power oscillation damping effect to the

integrated PSS and SSSC controller and improves the

overall stability.

6. Acknowledgment

The authors wish to thank the authorities of Electrical

and Electronics Engineering department, Pondicherry

Engineering College for the facilities provided to the

research work.

References

[1] M. Farahani and S. Ganjefar (2017),“Intelligent

power system stabilizer design using adaptive fuzzy

sliding mode controller,” Neurocomputing, vol. 226, pp.

135-144.

[2] BehrouzMohammadzadeh, Reza Gholizadeh-

Roshanagh, and SajadNajaravadanegh (2014),“Optimal

designing of SSSC Based Supplementary Controller for

LFO Damping of Power System Using COA,” ECTI

Transactions on Electrical Eng., Electronics, and

Communications, vol. 12, pp. 64-72.

[3] P. Kundur, Power System Stability and Control.

New York: McGraw-Hill, 1994.

[4] P. M. Anderson and A. A. Fouad, Power system

control and stability. Piscataway, N.J.: Wiley-

Interscience, 2003.

[5] G. Hingorani and L. Gyugyi, “Understanding

FACTS-Concepts and Technology of Flexible AC

Transmission Systems” New York: IEEE Press, 2000.

[6] Gyugyi L., Schauder C. D. &Sen K. K

(1997),“Static synchronous series compensator: A

solid-state approach to the series compensation of

transmission lines” Power Delivery, IEEE Transactions

on, vol. 12(1), pp. 406 -417.

[7] X. S. Yang, “Engineering Optimization: An

Introduction with Metaheuristic Applications”. Wiley &

Sons, New Jersey, 2010.

[8] SankalapArora, Satvir Singh (2013),“The

Firefly Optimization Algorithm: Convergence analysis

and parameter selection” Int. J. of Comp. Appl.

(0975-8887), vol. 69, no.3, pp. 48-52.

[9] M. A. Abido (2002), “Optimal Design of

Power-System Stabilizers Using Particle Swarm

Optimization” IEEE Trans. Energy Conv., vol. 17, no. 3,

pp. 406-413.

[10] H. Shayeghi, H.A. Shayanfar, A. Safari, and R.

Aghmasheh (2010), “A robust PSSs design using PSO in


1055

a multi-machine environment” Energy Conversion

&Management, vol. 51, pp. 696-702.

[11] M. A. Abido (2004), “Analysis of Power

System Stability Enhancement via Excitation and

Facts-Based Stabilizers” Electrical Power Components

and Systems, vol. 32, no. 1, pp. 75-91.

[12] SidharthaPanda, and Narayana Prasad Padhy

(2008), “Comparison of particle swarm optimization

and genetic algorithm for FACTS-based controller

design” Applied Soft Computing, vol.8, pp.1418-1427.

[13] Xianzhang Lei, Edwin N. Lerch, and

DusanPovh (2001), “Optimization and Coordination of

Damping Controls for Improving System Dynamic

Performance” IEEE Trans. Power Syst., vol. 16, no. 3,

pp. 473-480.

[14] Y.L. Abdel-Magid, M.A. Abido (2004),

“Robust coordinated design of excitation and

TCSC-based stabilizers using genetic algorithms”

Electric Power Syst. Res., vol. 69, pp.129-141.

[15] E.S. Ali, S.M. Abd-Elazim (2012),

“Coordinated design of PSSs and TCSC via bacterial

swarm optimization algorithm in a multimachine power

system” Int. J. Elect. Power and Energy Syst., vol. 36,

pp. 84-92.

[16] PeymanFarhang, KazemMazlumi, and

JavadGholinezhad (2012),“Design of Output feedback

SSSC and PSS Controllers to Enhance the Stability of

Power System Using PSO” ELECO 2011 7th Int. conf.

on Elect. & Elec. Eng. pp. 194-198.

[17] Luke Jebaraj, Charles ChristoberAsirRajan, and

Kumar Sriram (2014),“Application of Firefly Algorithm

in Voltage Stability Environment Incorporating Circuit

Element Model of SSSC with Variable Susceptance

model of SVC” Advances in elect. Eng., vol., pp. 1-12.

[18] H.F. Wang (1999), “Design of SSSC Damping

Controller to Improve Power System Oscillation

Stability”, IEEE conference, pp.495-500.

[19] X. S. Yang (2010), “Firefly algorithm,

stochastic test functions and design optimisation,” Int. J.

of Bio-Inspired Computation, vol. 2, no. 2, pp. 78–84.

[20] BehrouzMohammadzadeh, Reza Gholizadeh-

Roshanagh, and SajadNajaravadanegh and Seyed Reza

SeyedNouri (2016),“COA Based SSSC and STATCOM

Optimal Controllers designing with The Aim Better

Damping of Oscillations: A Comparative Study”

Int.Journal of Elect. Eng. & Informatics, vol.8, no.3,

pp.697-710.

[21] HosseinShayeghi, AbdollahYounesi, and

YasharHashemi (2015),“Simultaneous Tuning of

Multi-Band Power System Stabilizer and Various

IPFC-based Damping Controllers: An Effective method

for Mitigation of Low frequency Oscillations”, Int.

Journal of Mechatronics, Elect. And Comp. Tech., vol.

5(17), pp. 2443- 2454.

[22] Qin Li, and Bo Liu2017,“Clustering using an

Improved Krill Herd algorithm” Algorithms 2017,

10,56, pp. 1-12.

[23] Gai-Gewang, Amir H. Gandomi, and Amir H.

Alavi,“Stud Krill Herd Algorithm” Neurocomputing,

128(2014), pp. 363-370.

[24] YahyaNaderi, TohidRahimi, BabakYousefi,

and SeyedHossainHosseini,“Assessment Power

Frequency Oscillation Damping using POD Controller

and Proposed FOD Controller”, Int. J. of Elect., comp.,

Energetic, Electronic and Comm., Eng., vol.8, no.11, pp.

1794-1800, 2014.

[25] S. Khani, M. Sadeghi, S.H. Hosseini, “Optimal

Design of SSSC Damping Controller to Improve Power

System Dynamic Stability Using Modified Intelligent

Algorithms”, IEEE conference on power electronics and

drive systems and technologies, pp.393-397, 2010.

[26] S Nazeer Hussain, K Hari Kishore

"Computational Optimization of Placement and Routing

using Genetic Algorithm” Indian Journal of Science and

Technology, ISSN No: 0974-6846, Vol No.9, Issue

No.47, page: 1-4, December 2016.

[27] T. Padmapriya and V. Saminadan, “Priority

based fair resource allocation and Admission Control

Technique for Multi-user Multi-class downlink Traffic

in LTE-Advanced Networks”, International Journal of

Advanced Research, vol.5, no.1, pp.1633-1641, January

2017.

[28] Rajesh, M., and J. M. Gnanasekar. "

GCCover Heterogeneous Wireless Ad hoc Networks.&

quot; Journal of Chemical and Pharmaceutical Sciences

(2015): 195-200.

[29] S.V.Manikanthan and K.Baskaran “Low Cost

VLSI Design Implementation of Sorting Network for

ACSFD in Wireless Sensor Network”, CiiT

International Journal of Programmable Device Circuits

and Systems, Print: ISSN 0974 – 973X & Online: ISSN

0974 – 9624, Issue : November 2011, PDCS112011008.


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