Applied Computational Intelligence and Soft Computing

Volume 2016 (2016), Article ID 8546108, 22 pages

http://dx.doi.org/10.1155/2016/8546108

## Design of Optimal Proportional Integral Derivative Based Power System Stabilizer Using Bat Algorithm

^{1}Department of Electrical Engineering, Rajasthan Technical University, Kota, Rajasthan 324010, India^{2}Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttaranchal 247667, India

Received 7 November 2015; Accepted 1 February 2016

Academic Editor: Meng J. Er

Copyright © 2016 Dhanesh K. Sambariya and Rajendra Prasad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The design of a proportional, derivative, and integral (PID) based power system stabilizer (PSS) is carried out using the bat algorithm (BA). The design of proposed PID controller is considered with an objective function based on square error minimization to enhance the small signal stability of nonlinear power system for a wide range of operating conditions. Three benchmark power system models as single-machine infinite-bus (SMIB) power system, two-area four-machine ten-bus power system, and IEEE New England ten-machine thirty-nine-bus power system are considered to examine the effectiveness of the designed controller. The BA optimized PID based PSS (BA-PID-PSS) controller is applied to these benchmark systems, and the performance is compared with controllers reported in literature. The robustness is tested by considering eight plant conditions of each system, representing the wide range of operating conditions. It includes unlike loading conditions and system configurations to establish the superior performance with BA-PID-PSS over-the-counter controllers.

#### 1. Introduction

Power system stability is an ability to regain synchronism on occurrence of disturbance. In general, an electric power system (EPS) is large, complex in nature, and interconnected and prone to small signal oscillation on occurrence of disturbances. These low-frequency electromechanical oscillations (EMOs) persist because of insufficient damping torque caused by high/adverse operating conditions. In the absence of sufficient damping, the EMOs may persist for longer time resulting in limitations on power transfer capability of EPSs. In multimachine EPS model, two distinct types of EMOs are recognized [1]. The oscillations associated with generators at a generating station, swinging with respect to the rest of the power system, are called intra-area mode oscillations.

Similarly, the swinging of many machines in an area of EPS against machines in another area is called interarea oscillations. Thus, a supplementary control signal is added to the excitation system to damp out these oscillations, and the system is called the power system stabilizer (PSS) [2]. The widely used PSS is conventional PSS, which is designed by phase compensation in the frequency domain and is introduced as lead lag compensator. It is necessary to have a linearized model of EPS to design CPSS parameters by using modern control techniques, such as to provide well damping for both types of oscillations. The CPSS parameters are tuned to an operating point which may fail to give satisfactory damping to other operating conditions within the power system. The use of adaptive control techniques to design CPSS may eliminate this limitation but is complex in nature and costly [3, 4].

In recent years, many optimization methods based on random search are suitable for solving complex problems, which are impossible to be solved by mathematical methods such as the gradient. Application of new optimization methods and fuzzy and intelligent method is the focus of researchers to design a good quality controller for enhancement of small signal stability of a power system [5, 6].

In [7], the fuzzy logic based power system stabilizer is designed for single-machine infinite-bus power system model and extended it to multimachine power system. To mitigate the shortcomings of conventional methods many optimization based algorithms have been proposed. The methods available in literature are Tabu search [8], evolutionary algorithm [9], the differential evolution (DE) algorithm [2], simulated annealing [10], genetic algorithm [11], fuzzy logic with genetic algorithm [12], fuzzy logic with harmony search algorithm [13], interval type-2 fuzzy logic controller, different membership function based fuzzy controller, artificial bee colony (ABC) [14], particle swarm optimization [15, 16], robust fast output sampling feedback [17], and an iterative linear matrix inequalities algorithm [18].

The different controller structures are always the field of interest for researchers. The proportional integral derivative (PID) type PSS is used for improving damping of EPSs. This is generally accepted in the industries for various applications. In literature several PID based PSSs are designed for SMIB power system such as using genetic algorithm (GA) [19, 20], harmony search algorithm (HSA) [19, 21], bacterial foraging algorithm (BFA) [22, 23], real coded genetic algorithm (RCGA) [24], Ziegler-Nichols (ZN) [25], hybrid particle swarm-bacteria foraging optimization (PSO-BFA) [25], artificial bee colony (ABC) [26], and biogeographical based optimization (BBO) [27] and for two-area four-machine ten-bus power system such as iterative linear matrix inequality (ILMI) [18] based PID based PSS which is successfully employed. The application of GA has been reported to tune the PI and PID based PSS design for multimachine power systems [20, 28].

To mitigate the drawbacks of above optimization methods for PSS design, a relatively new optimization scheme known as the bat algorithm (BA) is used for the PID type PSS parameter design. It appeared as a promising one for handling the optimization problems even with epistatic objective functions as in ten-machine power systems where the number of variables is ranging up to 27. It is not largely affected by the size and nonlinearity of the problem and can converge to the optimal solution in many cases where many analytical methods fail to converge. Considering the strength of this algorithm, it is employed in the present work for the optimal PID tuning for stability enhancement in SMIB, four-machine, and ten-machine power systems.

In the organization of the paper, the problem is formulated in Section 2 with information about power system models, on PID and about the objective function used in optimization. Section 3 includes the detail on bat algorithm. The PID parameters tuning scheme and results are included for three power systems in Section 4. The simulation results and eigenvalue analysis is carried out with proposed BA-PID-PSS for SMIB, four-machine, and ten-machine power systems in Sections 4.1, 4.2, and 4.3, respectively. Lastly, the analysis is concluded in Section 5.

#### 2. Problem Formulation

The aim of the paper is to utilize the bat algorithm for tuning the PID parameters in the power system; therefore, the EPS elements such as generators, excitation system, and PSS must be modeled. To complete the tuning process, an objective function to obtain satisfactory results is necessary and should be defined. Therefore, the system model and an objective function used in PSS parameter tuning in a multimachine power system are elaborated.

##### 2.1. Test System Configuration

The systems under consideration are single-machine connected to infinite-bus (SMIB) power system, two-area four-machine ten-bus power system, and IEEE New England 10-machine 39-bus power system. The general representation of a power system using nonlinear differential equations can be given as in the following equation:where and represent the vector of state variables and the vector of input variables, respectively. As in [29], the power system stabilizers can be designed by use of the linearized incremental models of the power system around an operating point. The general representation of a power system can be written in terms of state equations as in Moreover, a brief introduction of the considered systems is given in the next sections.

###### 2.1.1. SMIB Power System

The single line diagram representation of single-machine connected to infinite-bus power system is shown in Figure 1. The connection of transmission line to generator, automatic voltage regulator, excitation system, and power system stabilizer is shown in this figure [29–31]. The linearized model called Heffron-Phillip model is presented in Figure 2. The scheme of sensing signals and the optimization scheme are also shown in this figure. The considered synchronous machines of SMIB and multimachine power systems are of model 1.0 type as discussed in [2]. To cover all operating conditions, the power system with generators, stabilizers, and excitation systems can be modeled by a set of nonlinear differential equations as in (1) [32].