Hybrid Algorithm for Coordinated Design of PSSs and SVC

1Electrical Engineering Department, Faculty of Engineering, Jazan University, KSA.

2Computer Science Department, Faculty of Computer Science and Information Technology, Jazan University,

KSA.

Abstract- The evaluation of novel coordinated design of Power System Stabilizers (PSSs) and Static Var

Compensator (SVC) in a multimachine system by statistical method is presented in this study. The coordinated

design process of PSSs and SVC above a great range of loading is formed as an optimization task. The Bacterial

Swarming Optimization (BSO), which couples synergistically the Bacterial Foraging (BF) with the Particle

Swarm Optimization (PSO), is used to seek for optimum controllers elements. By reducing the suggested

objective function, in which the speed variations among generators are engaged; stability investigation of the

system is enhanced. To compare the ability of PSS and SVC, both are independently designed, and then in a

coordinated way. Simultaneous setting of the BSO based on coordinated controller gives robust damping

characteristics over a great range of operating conditions and wide disturbance compared with optimized PSS

based on BSO (BSOPSS) and optimized SVC based on BSO (BSOSVC). Also, a statistical T test is done to

assure the robustness of coordinated controller contra uncoordinated one.

Keywords: PSSs; SVC; Power System; Coordinated design; BSO; Statistical T test.

Received: April 26, 2021. Revised: June 20, 2022. Accepted: July 16, 2022. Published: September 2, 2022.

1. Introduction

The power transfer in an integrated power system

is obliged by transient stability, voltage stability and

small stability. These constraints define a full

utilization of obtainable transmission corridors.

Flexible AC Transmission System (FACTS) is the

technology that supplies the necessary corrections of

the transmission functionality to fully use the existing

transmission facilities and then, reducing the gap

among the stability and thermal limits [1].

Latterly, there has been an interest in the

development and use of FACTS controllers in

transmission systems [2 – 6]. These controllers use

power electronics circuits to supply more flexibility

to AC power systems. The most popular type of

FACTS in terms of application is the SVC. This

device is known to enhance system properties like

stability limits, voltage regulation and var

compensation, dynamic over and under voltage

control, and damp system oscillations. The SVC is an

electronic circuit that controls dynamically the flow

of power through a variable admittance to the

transmission system.

Eventually, various researchers have presented

many techniques for planning SVC to improve the

damping of oscillations of power systems and

enhance systems stability. A robust control opinion

in planning SVC controller to decay swing modes is

presented in [7]. An adaptive network based fuzzy

system for SVC is discussed in [8] to enhance the

alleviation of oscillations. A multi input, single

output fuzzy neural network is introduced in [9] for

voltage stability assessment of the power systems

with SVC. A technique of determining the position

of a SVC to improve the stability of power system is

presented in [10]. A systematic approach for planning

SVC controller, based on wide area signals, to

enhance the damping of power system oscillations is

suggested in [11]. Genetic Algorithm technique is

employed for simultaneous tuning of a PSS and a

SVC based controller in [12]. A state estimation task

of power systems incorporating many FACTS circuit

is developed in [13]. A fresh hybrid method for

simulation of power systems equipped with SVC is

addressed in [14]. The design of SVC with delayed

input signal using a state space model based on Pade

approximation method is introduced in [15].

Bacterial Foraging Optimization Algorithm (BFOA)

for planning SVC to damp system oscillations for

single machine infinite bus system and multimachine

system is presented in [16]. Flower pollination

algorithm is introduced in [17] for SVC design. An

enforcement of probabilistic theory to the

coordinated plan of PSSs and SVC is used in [18].

The implementation of the decentralized modal

control style for pole placement in power system

using FACTS circuits is displayed in [19]. The

parameter setting of a PID controller for a FACTS

based stabilizer using multi-objective evolutionary

algorithm is discussed in [20]. A comprehensive

evaluation of the effects of the PSS and FACT circuit

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1E. S. ALI, 2S. M. ABD ELAZIM

when independently applied and also via coordinated

application is performed in [21].

Many optimization algorithms have been

adopted to resolve a variety of engineering process in

the past decade. GA has engaged the attention in the

scope of controller parameter optimization. Although

GA is satisfactory in detecting global or near global

optimal result of the task; it requires a very long run

time that may be various minutes or even many hours

depending on the measure of the system under study.

Also, swarming strategies in bird flocking and fish

schooling are utilized in the PSO and offered in [22].

However, PSO pains from the partial optimism,

which produces the less exact at the regulation of its

speed and the direction. Furthermore, the algorithm

cannot work out the problems of scattering and

optimization [23-24]. Moreover, the algorithm

suffers from slow convergence in refined search

stage, low local search ability and algorithm may lead

to possible entrapment in local minimum solutions.

A newer evolutionary computation algorithm, called

BF scheme has been presented by [25-27] and further

established by [28-29]. The BF algorithm depends on

random search directions which may lead to protract

in finding the global solution. A novel algorithm BF

oriented by PSO is evolved that combine the above

mentioned optimization algorithms [30-31]. This

combination pursues to make use of PSO capability

to exchange social information and BF ability in

detecting a new solution by elimination and dispersal.

This new hybrid technique called Bacterial Swarm

Optimization (BSO) is used in this study to resolve

the above aforesaid problems and drawbacks.

In this study, a comprehensive evaluation of the

effects of the PSSs and SVC based control when

independently applied and also via coordinated

application has been performed. The design task of

PSS and SVC based controller to evolve power

system stability is transformed into an optimization

task. The design objective is to enhance the stability

of a multimachine power system, subjected to a

disturbance. BSO technique is used to find the

optimal PSS and SVC controller elements. BSO

based SVC controller (BSOSVC) and BSO based

PSS (BSOPSS) are discussed and their performances

are compared with the coordinated design of

BSOPSS and BSOSVC. Simulation results are

introduced to ensure the robustness of the suggested

controller to develop the power system dynamic

stability. Also, a statistical T test is proceed to

support the robustness of coordinated controller

against uncoordinated one.

2. Problem Statement

A. Power System Model

A power system can be stated by a set of nonlinear

differential equations as:

),( UXfX 



(1)

Where

X

is the vector of the state variables and U

is the vector of input variables. In this study

T

f

V

fd

E

q

E X ],,,,[ 





and

U

is the PSS and

SVC output signals. Here,



and



are the rotor

angle and speed, respectively. Also, q

E



,fd

E and

f

V are the internal, the field, and excitation voltages

respectively.

In the planning of PSS and SVC, the linearized

models around a balance point are used. Therefore,

the state equation of a power system with

n

generators and

m

PSS and SVC can be stated as:

BuAXX 

 (2)

Where

A

is a

n

55



matrix and equalizes

Xf



/ while

B

is a

m

n



5 matrix and equals

Uf



/.

Both

A

and

B

are estimated at a certain

operating point.

X

is a

15



n

state vector and

U

is

an 1



m

input vector.

B. PSS Modelling and Damping Controller Design

The operating task of a PSS is to create an

appropriate torque on the rotor of the generator

involved in such a way that the phase lag among the

exciter and the generator electrical torque is

compensated. The extra stabilizing signal is

proportional to speed [32]. The block diagram of the

th

i PSS with exciter is shown in Fig. 1.

Where

i



 is the deviation in speed from the

synchronous speed. This kind of stabilizer composes

of a washout filter, a dynamic compensator. The

output signal is fed as an extra input signal,

i

U to the

regulator of the excitation system. The washout filter

is applied to reset the steady state offset in the output

of the PSS. The value of the time constant

W

T is

usually not critical and it may range from 0.5 to 20 s.

The dynamic compensator is composed of two lead

lag circuits and an extra gain. The adaptable PSS

elements are the gain of the PSS,

i

K and the time

constants,

i

T

1

–

i

T

4

. The lead lag block in the system

reserves phase lead compensation for the phase lag

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that is presented in the circuit between the exciter

input and the electrical torque. The desired phase lead

can be derived from the lead lag circuit even if the

denominator portion composing of i

T2 and i

T4

allows a fixed lag angle.

C. SVC Modelling and Damping Controller Design

The thyristor controlled reactor in parallel with a

fixed capacitor bank given in Fig. 2, is utilized in this

work to develop the SVC model. Then, the system is

shunt connected to the AC system via a set up

transformer to get the voltages up to the desired

transmission levels [8].

It is clear from (3) and Fig. 3, if the firing angle



of the thyristors is planned; SVC is capable to control

the bus voltage magnitude. Time constant ( r

T) and

gain ( r

K) represent the thyristors firing control

system. The SVC parameters are presented in

Appendix.











 )(

1

.

s

V

t

V

ref

V

r

K

e

B

r

T

e

B (3)

The variable effective susceptance of the TCR is

given by







/2

L

X

V

B



 )2sin22( (4)

Where L

X is the reactance of the fixed inductor of

SVC. The effective reactance is

)/12(22sin

/

x

r

x

r

C

X

e

X







(5)

Where e

X=-1/ e

B and x

rL

X

e

X/.

An extra stabilizing signal from speed can be

required on the SVC control loop. The block diagram

of a SVC with extra stabilizing signal is displayed in

Fig. 3. This controller may be seen as a lead lag

compensator. It includes gain block, limiter, signal

washout circuit and two phases of lead lag

compensator. The elements of the damping

controllers for the aim of simultaneous coordinated

design are gained using the BSO algorithm.

D. System under Study and SVC Location

Fig. 4 displays the single diagram of the used

system. Details of system data are given in [33]. The

participation matrix can be utilized in mode identity.

Table (1) indicates the eigenvalues, and frequencies

of the rotor modes. Examining Table (1) shows that

the 0.2371 Hz mode is the interarea mode with G1

swinging versus G2 and G3. The 1.2955 Hz mode is

the intermachine oscillation local to G2. Moreover,

the 1.8493 Hz mode is the intermachine mode local

X

T

SVC

B

C

B

L

AC Transmission System

Fig. 2. SVC equivalent circuit.

Fig. 3. Block diagram of SVC.

Fig. 1. Block diagram of PSS with exciter.

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to G3. The positive real part of eigenvalue of G1

points instability of the system. The loading levels

are shown in Table (2).

To determine the convenient placement of the SVC

in the system, two designing will be given below. The

first one is based on studying the impact of loading

percentage while the second is interested with the line

outage on voltages [34]. Tables (3, 4) show the effect

of loading and line outage on node voltages of the

system. It can be observed that the voltages are

significantly affected at buses 5, and 6 respectively

which are load buses. The reasons that rise the

considerable voltage change are the relation of these

buses with the longest lines in the system which has

larger resistances and reactances than the others.

Thus, the option of buses number 5 or 6 for installing

the SVC controller is predicted to be the most

compatible choice. Because both of them are near to

generator number 1 which causes the system

insecurity due to its unstable mode. Also, bus number

5 is the worst bus and will be taken as the best

position for composing the SVC controller in this

paper.

3. Objective function

The elements of the PSSs and SVC can be elected

to diminish the following objective function:

J=

 





0132312 dtwwwt (6)

Where 2112 www  , 3223 www  ,

and 3113 www  .

This index is relied on the Integral of Time multiple

Absolute Error (ITAE). The merit of this elected

performance indicator is that minimal dynamic plant

information is required. To diminish the

computational load in this work, the value of the

wash out time constant

W

T is specified to 10

second, the amounts of i

T2 and i

T4 are kept fixed at

a sensible value of 0.05 second and setting of i

T

1 and

i

T3 are undertaken to acquire the net phase lead

required by the system. Based on the objective

function Joptimization task can be modelled as:

reduce J subjected to:

Table (2) Loading of the system (in p.u)

Light

Normal case

Heavy

Generator

G1

G2

G3

P Q

0.965 0.22

1.0 -0.193

0.45 -0.267

P Q

1.716 0.6205

1.63 0.0665

0.85 -.1086

P Q

3.57 1.81

2.2 0.713

1.35 0.43

Load

A

B

C

P Q

0.7 0.35

0.5 0.3

0.6 0.2

P Q

1.25 0.5

0.9 0.3

1.00 0.35

P

Q

2.0 0.9

1.8 0.6

1.6 0.65

at G1 0.6 0.2 1.00 0.35 1.6 0.65

Generator

Eigenvalues

Frequencies

Damping

ratio

G1

G2

G3

+0.15 1.49j

-0.35 8.14j

-0.67 11.62j

0.2371

1.2295

1.8493

-

0.1002

0.0430

0.0576

Table (1) The eigenvalues, and frequencies of

the rotor modes.

~~

~

1

6

4

8

load A

2

5

7load C 9

3

load B

Local load

Created with the Trial Edition of SmartDraw 3.

Fig. 4. System under study.

Table (3) Effect of load percentage on load bus voltages

% Load .25 .5 .75 1 1.25 1.5 1.75

Bus 4 1.06 1.05 1.04 1.03 1.01 0.99 0.98

Bus 5 1.06 1.04 1.02 0.99 0.96 0.94 0.9

Bus 6 1.06 1.05 1.03 1.01 0.99 0.97 0.94

Bus 7 1.05 1.04 1.04 1.03 1.01 1.00 0.98

Bus 8 1.05 1.04 1.03 1.02 0.99 0.98 0.96

Bus 9 1.05 1.05 1.04 1.03 1.02 1.01 1.0

line

4

-

5

4

-

6

5

-

7

6

-

9

7

-

8

-

9

Bus 4 1.039 1.028 0.996 1.005 1.016 1.022

Bus 5

0.839

0.998

0.938

0.968

0.974

0.989

Bus 6 1.020 0.942 0.975 0.964 0.999 1.009

Bus 7

0.988

1.022

1.017

1.016

1.019

1.010

Bus 8 0.989 1.006 1.001 1.005 0.969 0.978

Bus 9 1.024 1.017 1.019 1.023 1.013 1.034

Table (4) Effect of line outage on load bus voltages

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,[35]. Specially, the effect are presented

in Table

(3) and Table (4).

max

i

K

i

K

i

K

min

max

i

T

i

T

i

T

1

min

1



max

i

T

i

T

i

T

3

min

3

 (7)

Typical ranges of the optimized values are [1- 100]

for

i

K and [0.06-1.0] for

i

T

1

and

i

T

3

.

This work focuses on coordinated plan of PSSs and

SVC using BSO algorithm. The target of the

optimization is to find for the optimum controller

parameters setting that improve the damping

characteristics of the system. Also, all controllers are

planned simultaneously, taking into account the

interaction among them.

4. Hybrid BF-PSO Optimization

Algorithm

PSO is a stochastic optimization technique that

draws inspiration from the behaviour of a flock of

birds or a group of social insects with limited

individual capabilities. In PSO a population of

particles is initialized with random positions



i

Xand

velocities



i

V, and a fitness function using the

particle’s positional coordinates as input values.

Positions and velocities are detected, and the function

is evaluated with the new coordinates at each time

step [22-23]. The velocity and position equations for

the d-th dimension of the i-th particle in the swarm

may be stated as follows:

))(.(

2

.

2

))(.(

1

.

1

)(.)1(

t

id

X

gd

XC

t

id

X

lid

XCt

id

Vt

id

V









(8)

)1()()1(  t

id

Vt

id

Xt

id

X (9)

Where

lid

X is the best position of every bacterial

and gd

Xis the global best bacterial.

Furthermore, the BF is based upon search and

optimum foraging decision making abilities of the

Escherichia coli bacteria [30]. The coordinates of a

bacterium represent an individual solution of the

optimization problem. Such a set of trial solutions

converges towards the optimum solution following

the foraging group dynamics of the bacteria

population. Chemotactic movement is remained until

a bacterium goes in the direction of positive nutrient

gradient. After a certain number of complete swims

the best half of the population undergoes

reproduction, eliminating the rest of the population.

To escape local optima, an elimination dispersion

event is performed where, some bacteria are

liquidated at random with a small probability and the

novel replacements are launched at random positions

of the search space. A detailed description of the

algorithm can be traced in [30-31]. Moreover, the

flow chart of BSO is given in Fig. 5.

[Step 1] Initialize parameters

,

n

,S,

C

N,

S

N,

re

N

,

ed

N,

ed

P.),,.......,2,1)(( i

NiiC





Where,

:

n

Dimension of the search space,

:

S

The number of bacteria in population,

:

re

N The number of reproduction steps,

:

C

N The number of chemotactic steps,

:

S

N Swimming length after which tumbling of

bacteria is performed in a chemotaxis loop,

:

ed

N The number of elimination-dispersal

events to be imposed over the bacteria,

:

ed

P The probability with which the

elimination and dispersal will continue,

:)(iC The size of the step taken in the random

direction specified by the tumble,

:



The inertia weight,

:

2

,

1

CC The swarm confidence,

:),,( kji





Position vector of the i-th bacterium,

in j-th chemotactic step and k-th reproduction,

:



i

V Velocity vector of the i-th bacterium.

[Step 2] Update the following

:),,( kjiJ Cost or fitness value of the i-th

bacterium in the j-th chemotaxis, and the k-th

reproduction loop.

:

_bestg





Position vector of the best position

found by all bacteria.

:),,( kji

best

J Fitness value of the best position

found so far.

[Step 3] Reproduction loop: 1





k

[Step 4] Chemotaxis loop: 1





jj

[Sub step a] For i=1, 2,…, S, take a chemotaxis

step for bacterium i as follows.

[Sub step b] Compute fitness function, ),,(

k

j

i

J

.

[Sub step c] Let ),,( kjiJ

last

J to save this

value since one may find a better cost via a run.

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[Sub step d] Tumble: generate a random vector

n

Ri  )( with each element

n,.,1,2,......m i

m

 ),( a random number on 1] 1,[



.

[Sub step e] Move: Let

)()(

)(

)(),,(),1,(

ii

T

i

iCkjikji









.

[Sub step f] Compute ),1,(

k

j

i

J



.

[Sub step g] Swim: one considers only the i-th

bacterium is swimming while the others are not

moving then

i) Let 0



m(counter for swim length).

ii) While S

Nm



(have not climbed down too

long)

 Let 1





mm

 If

last

JkjiJ  ),1,( (if doing better),

Let ),1,( kjiJ

last

J and let

)()(

)(

)(),,(),1,(

ii

T

i

iCkjikji









and

use this ),1,(

k

j

i





to compute the new

),1,(

k

j

i

J



as shown in new [sub step f]

 Else, let

S

Nm . This is the end of the while

statement.

[Step 5] Mutation with PSO operator

For i=1, 2,……,S

 Update the bestg _





and ),,( kji

best

J

 Update the position and velocity of the d-th

coordinate of the i-th bacterium according to

the following rule:











 ),1,(

_

.

1

.

1kji

old

d

bestg

C

new

id

V

new

id

V



new

id

Vkji

old

d

kji

new

d

 ),1,(),1,(



[Step 6] Let 2/_

S

r

S



The

r

S

_bacteria with highest cost function )( J

values die and other half bacteria population with

the best values split.

[Step 7] If

re

Nk , go to [step 3]. One has not

reached the number of specified reproduction steps,

so one starts the next generation in the chemotaxis

loop.

More details of BF and PSO parameters are

presented in Appendix.

5. Results and Simulations

Fig. 6. shows the change of objective function with

various techniques. The algorithm is run keeping

limiting value of cost function at 6

10. It was found

that the BSO gives faster convergence than PSO and

j˃

k˃

i ˃ S

Initialize all variables. Set all loop

counter and

bacterium index i to 0

Increase elimination and dispersal loop

counter l = l + 1

Start

l˃

Increase reproduction loop counter k = k + 1

Yes

No

Increase chemotaxis loop counter j= j + 1

Yes

Perform

elimination

and dispersal for all

bacteria

No

Yes

Perform

reproduction

Increase bacterium index i = i + 1

No

Yes

Compute the cost function value for

i

th

bacterium as J (

i, j, k, l ) and set Jlast = J ( i, j, k, l )

Update the direction and position of

i

th

bacterium by PSO

Compute the cost function value J ( i, j+1, k, l )

Set swim counter m = 0

m˃

Yes

m = m + 1

No

J ( i, j+1, k, l ) < Jlast

Yes

No

Set Jlast = J ( i, j, k, l )

Swim

Fig. 5. Flow chart of BSO algorithm.

Tamble

Print the

results and

stop

Set m =

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BF. Furthermore, BSO converges at a faster rate (44

iterations) compared with that for PSO (68 iterations)

and BFOA (88 iterations). Also, computational time

(CPU) of both algorithms is compared based on the

average CPU time taken to converge the solution.

The average CPU for BSO is 43.4 second while it is

68.3 and 79.2 second for PSO and BF respectively.

Table (5), gives the system eigenvalues, and

damping ratio of mechanical mode with several

loading conditions. It is clear that, the system with

BSOSVC has small damping factors (



=-0.65,-

0.69,-1.06) for light, normal, and heavy loading

respectively. Also, the suggested coordinated

controller shifts substantially the electromechanical

eigenvalues to the left of the S-plane and the values

of the damping factors with the suggested

coordinated controller are improved significantly to

be (



=-1.13,-1.17,-1.57) for light, normal, and

heavy loading respectively. Moreover, the damping

ratios corresponding to coordinated controller are

better than that corresponding to individual ones.

Thus, compared with the BSOSVC and BSOPSS, the

suggested coordinated controller greatly improves

the system stability and enhances the damping

behaviour of electromechanical modes. Results of

various controllers parameters set values based on the

time domain objective function using BF are

displayed in Table (6).

A. Response under normal loading

Fig. 7 and Fig. 8, give the response for normal

loading. The results of these studies show that

the suggested coordinated controller has an

excellent ability in damping power oscillations and

greatly improves the dynamic stability of the

system. Also, the settling

times of oscillations are Ts =1.7, 2.0, and 2.2

second for coordinated controller, BSOPSS, and

BSOSVC respectively so the suggested controller

is able of supplying enough damping to the system

oscillatory modes. Thus, the coordinated controller

extends the system stability limit and the power

transfer ability.

Table (5) Mechanical modes and under various loading.

Uncoordinated

Coordinated BSOPSS BSOSVC

-3.32 9.42j,

0.3324

-1.13 6.72j,

0.1658

-0.44 0.75j,

0.50

-4.74 7.39j,

0.54

-4.98 6.09j,

0.633

-1.13 0.72j,

0.8434

-3.76 6.1j,

0.5247

-4.88 6.37j,

0.6081

-0.97 0.67j,

0.8228

-3.1 9.87j,

0.2997

-3.83 7.45j,

0.4572

-0.65 0.79j,

0.6354

Light

load

-3.01 8.85j,

0.322

-1.21 6.63j,

0.1795

-0.38 0.74j,

0.4568

-3.98 8.14j,

0.4392

-4.51 6.34j,

0.5797

-1.17 0.63j,

0.8805

-3.95 8.29j,

0.4301

-4.24 6.32j,

0.5571

-0.95 0.74j,

0.7889

-3.27 11.3j,

0.277

-2.76 9.0j,

0.2932

-0.69 0.78j,

0.6626

Normal

load

-3.04 8.96j,

0.3213

-1.24 6.76j,

0.1804

-0.45 0.87j,

0.4594

-3.93 8.27j,

0.4292

-4.13 5.9j,

0.5735

-1.57 0.73j,

0.9068

-3.67 8.42j,

0.398

-3.97 6.55j,

0.5183

-1.08 0.83j,

0.7929

-2.9 11.38j,

0.2461

-1.97 8.78j,

0.2189

-1.06 .83j,

0.7873

Heavy

load

Table (6) Optimal PSSs and SVC parameters for different controllers.

Coordinated Design Uncoordinated Design

PSS1 PSS2 PSS3 SVC PSS1 PSS2 PSS3 SVC

49.51 1.4931 1.7437 0.9158 31.24 8.4379 6.3887 63.721

0.4652 0.5827 0.3716 0.3712 0.6839 0.3462 0.2479 0.7423

0.2684 0.2119 0.1052 0.2882 0.5165 0.1385 0.3253 0.5978

Fig. 6. Change in objec

tive function.

Fig. 7. Change of under normal loading.

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B. Response under heavy load condition

Fig. 9 and Fig. 10, show the system response

at heavy loading with fixing the controllers

parameters. It can be seen that the response

with the suggested coordinated controller

gives good damping behaviour to low

frequency oscillations and the system is more

quickly stabilized than BSOPSS and BSOSVC.

Also, the settling times of these

oscillations are Ts =1.7, 2.0, and 2.2 second for

coordinated controller, BSOPSS, and BSOSVC

respectively. Thus, the simulations results reveal that

the simultaneous coordinated planning of the

BSOSVC damping controller and the BSOPSS

explains its notability to both the uncoordinated

designed controller of the BSOSVC and the

BSOPSS. Moreover, this controller has a soft

architecture and the potentiality of application in real

time environment.

C. Statistical T test

To assess the robustness of the suggested

coordinated controller, the performance of the system

with the suggested coordinated controller is

compared to uncoordinated one. A statistical T test is

performed between the coordinated controller and

uncoordinated one to assess the robustness of the

suggested coordinated controller. The damping ratios

of mechanical modes for the coordinated and

uncoordinated controller under various loading

conditions are elected as input to statistical T test.

This test determines that, is there a specific different

between two controllers or not?

Let the null hypothesis: 0

2

1

0





H

Let the alternative hypothesis: 0

2

1





H

Where

2

,

1



are the mean values of damping ratios

of coordinated and uncoordinated controller

respectively. The significance level 05.0





is

established. Table (7) gives the output parameters of

the statistical T test. The input to the T test is the

damping ratios of the rotor modes for various

controllers and operating conditions. The result

concludes to reject

0

H. Moreover, one can decide

from this test that there is a respectable moral

difference between the two controllers. Also, the

output of

12





for coordinated and uncoordinated

controller is indicated in Fig. 11. This Figure shows

the superiority of the suggested coordinated

controller in decreasing the settling time and

damping power oscillations versus uncoordinated

one.

Fig. 8. Change of under normal loading.

Fig. 9. Change of under heavy loading.

Fig. 10. Change of under heavy loading.

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6. Conclusions

The statistical evaluation of the robust coordinated

design of PSSs and SVC damping controller in a

power system is proposed in this paper. The design

task of the suggested controller is established as an

optimization process and BSO is used to search for

optimal controller parameters. Simulations results

assure the robustness of the suggested coordinated

controller in supplying good damping characteristic

to system oscillations for a wide range of loading

conditions and large disturbance. Also, it is supreme

to uncoordinated controller through the statistical

evaluation. Coordination between various devices

via fresh optimization algorithms is the future work

of this paper.

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Variance 0.03409811 0.016694377

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t Critical two-tail 2.306004133

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Appendix

The system data are as shown below:

a) Excitation system: 400;

A

K

second; 0.05

A

T 0.025;

f

K .second 1

f

T

b) SVC Controller: msecod 15

r

T



; α0 =140;

r

K

=50.

c) Bacteria parameters: Number of bacteria =10;

number of chemotatic steps =10; number of

elimination and dispersal events = 2; number of

reproduction steps = 4; probability of elimination and

dispersal = 0.25; the values of attract

d=0.01; the

values of attract



=0.04; the values of repelent

h=0.01;

the values of

repelent



=10.

d) PSO parameters:

1

C=

2

C=2.0,



=0.9.

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Conflicts of Interest

The author(s) declare no potential conflicts of

interest concerning the research, authorship, or

publication of this article.

Contribution of individual authors to

the creation of a scientific article

(ghostwriting policy)

The author(s) contributed in the present

research, at all stages from the formulation

of the problem to the final findings

and solution.

Sources of funding for research

presented in a scientific article or

scientific article itself

No funding was received for conducting this

study.

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4.0 (Attribution 4.0 Int

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BY 4.0))

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