Power System Stabilizers Design Using BAT Algorithm

E. S. ALI

Electrical Department, Faculty of Engineering, Jazan University, Jazan, KINGDOM OF SAUDI ARABIA

Abstract: - A new metaheuristic method, the BAT algorithm based on the echolocation behaviour of bats is

proposed in this paper for optimal design of Power System Stabilizers (PSSs) in a multimachine environment.

The PSSs parameter tuning problem is converted to an optimization problem which is solved by the BAT

search Algorithm. An eigenvalues based objective function involving the damping factor, and the damping ratio

of the lightly damped electromechanical modes is considered for the PSSs design problem. The performance of

Key-Words: Power System Stabilizers; BAT Algorithm; Genetic Algorithm; Multimachine System; Power

System Stability; Low Frequency Oscillations.

Received: October 12, 2021. Revised: September 16, 2022. Accepted: October 14, 2022. Published: November 23, 2022.

1. Introduction

One problem that faces power systems is the

low frequency oscillations arising due to

disturbances. These oscillations may sustain and

grow to cause system separation if no adequate

generators existing in one area against each other

and is known as local mode [2-3]. Power System

Stabilizer (PSS) is used to generate supplementary

control signals for the excitation system in order to

mitigate both types of oscillations [4].

In the last few years, Artificial Intelligence (AI)

techniques have been discussed in literature to solve

problems related to PSS design. Artificial Neural

Network (ANN) for designing PSS is addressed in

[5-8]. The ANN approach has its own merits and

techniques, FLC formulates the control action of a

plant in terms of linguistic rules drawn from the

behaviour of a human operator rather than in terms

of an algorithm synthesized from a model of the

plant [9-15]. It does not require an accurate model

of the plant; it can be designed on the basis of

linguistic information obtained from the previous

knowledge of the control system and gives better

performance results than the conventional

controllers. However, hard work is inevitable to get

-synthesis [23] have been also used for PSS design.

However, these methods are iterative, sophisticated

and the system uncertainties should be carried out in

a special format. On the other hand, the order of the

stabilizers is as high as that of the plant. This gives

rise to the complex structure of such stabilizers and

design approach assumes full state availability.

been applied to PSS design problems. Simulated

Annealing (SA) is presented in [26] for optimal

tuning of PSS but this technique might fail by

getting trapped in one of the local optimal. Another

heuristic technique like Tabu Search (TS) is

introduced in [27-28] to design PSS. Despite this

optimization method seems to be effective for the

design problem, the efficiency is reduced by the use

long run time depending on the size of the system

under study. Also, it suffers from settings of

algorithm parameters and gives rise to repeat

revisiting of the same suboptimal solutions. A

Particle Swarm Optimization (PSO) for the design

of the PSS parameters is illustrated in [31].

weak local search ability and algorithm may lead to

possible entrapment in local minimum solutions. A

relatively newer evolutionary computation

algorithm, called Bacteria Foraging (BF) scheme

has been developed by [32] and further established

recently by [33–47]. The BF algorithm depends on

random search directions which may lead to delay in

reaching the global solution. In order to overcome

these drawbacks, a BAT search optimization

algorithm is proposed in this paper.

electromechanical modes to a prescribed zone in the

s-plane in such a way that the relative stability is

confirmed. The effectiveness of the proposed

BATPSS is tested on a multimachine power system

under various operating conditions in comparison

with GAPSS and CPSS through time domain

analysis, eigenvalues and performance indices.

Results evaluation show that the proposed algorithm

attains good performance for suppressing the low

frequency oscillations under various operating

machines interconnected power system, can be

formalized by a set of nonlinear differential

equations as:

(1)

where

is the vector of the state variables and

(3)

This structure consists of a gain, washout filter, a

dynamic compensator and a limiter as it is shown in

Fig. 1. The output signal is fed as a supplementary

input signal,

to the regulator of the excitation

gain

is used to determine the amount of damping

to be injected. Then, a washout filter makes it just

act against oscillations in the input signal to avoid

steady state error in the terminal voltage. Also, two

lead-lag circuits are included to eliminate any delay

between the excitation and the electric torque. The

limiter is included to prevent the output signal of the

constants

and

are fixed at a reasonable

value of 0.05 second. The stabilizer gain

time constants

2.3 Test System

robust PSS. The generator and loading level are

given in Table (1) for these loading conditions.

algorithm inspired by the echolocation behaviour of

natural bats in locating their foods. It is introduced

by Yang [50-53] and is used for solving various

optimization problems. Each virtual bat in the initial

population employs a homologous manner by

performing echolocation to update its position. Bat

echolocation is a perceptual system in which a series

of loud ultrasound waves are released to create

to classify between prey and barrier.

at

position

with a fixed frequency

seek for prey. It regulates the frequency of its

release

in the range of [0, 1], relying on the

closeness of its aim.

The position

and velocity

of each bat should

be defined and updated during the optimization

process. The new solutions

and velocities

at

search, once a solution is chosen among the current

Assuming

means that a bat has just found

where,

is constant in the range of [0, 1] and

positive constant. As time reaches infinity, the

loudness tends to be zero, and

flow chart of the BAT algorithm is shown in Fig. 3,

and the parameters are given in appendix.

4. Objective Function

damping to low frequency of oscillations, the

parameters of the PSSs may be picked to minimize

the following objective function:

This will place the system closed loop eigenvalues

in the D-shape sector characterized by

as shown in Fig. 4.

the real part and the damping ratio of the eigenvalue

of the operating point. In this paper,

problem based on the objective function

stated as: minimize

5.2 Response under light load condition

Figs. 8-9, show the system response under light

loading condition with fixing the controller

parameters. It is clear from these figures, that the

proposed BATPSS has good damping

characteristics to system oscillatory modes and

second for BATPSS, GAPSS, and CPSS

respectively. Hence, the proposed BATPSS outlasts

GAPSS and CPSS controllers in attenuating

oscillations effectively and minifying settling time.

Consequently, the proposed BATPSS extend the

power system stability limit.

5.3 Response under heavy load condition

BATPSS, GAPSS, and CPSS respectively. Hence,

BATPSS controller greatly enhances the damping

characteristics of power system. Furthermore, the

settling time of the proposed controller is smaller

than that in [37-39].

that the BAT based PSSs using the proposed

objective function introduces superior damping and

attains better robust performance in comparison

(ITAE), are being used as:

It is noteworthy that the lower the value of these

indices is, the better the system response in terms of

time domain characteristics [62-68]. Numerical

listed in Table (4). It can be seen that the values of

these system performance with the BATPSS are

smaller compared with those of GAPSS and CPSS.

This demonstrates that the overshoot, settling time

decreased by applying the proposed BAT based

tuned PSSs. Eventually; values of these indices are

smaller than those obtained in [69].

6. Conclusions

[3] J. Machowski, J. Bialek, and J. Bumby, “Power

[7] R. Segal, A. Sharma, and M. L. Kothari, “A Self-

[9] H. A. Toliyat, J. Sadeh, and R. Ghazi, “Design

[10] Z. S. El-Razaz, and E. S. Ali, “Design of An

[12] A. M. El-Zonkoly, A. A. Khalil and N.M.