Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 275129, 8 pages

http://dx.doi.org/10.1155/2015/275129

## A Fuzzy Based Evolutionary Algorithm for Solving Multiobjective Optimal Power Flow with FACTS Devices

^{1}Faculty of Electrical and Electronics, Sathyabama University, Chennai 600119, India^{2}Department of Electrical and Electronics Engineering, Adhiparasakthi Engineering College, Melmaruvathur 603319, India

Received 31 March 2015; Revised 12 July 2015; Accepted 15 July 2015

Academic Editor: Juan F. San-Juan

Copyright © 2015 R. Vanitha and J. Baskaran. 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

A new Fuzzy Differential Evolution (FDE) algorithm is proposed for solving multiobjective optimal power flow with FACTS devices. This new optimization technique combines the advantages of Weighted Additive Fuzzy Goal Programming (WAFGP) and Differential Evolution (DE) in enhancing the capacity, stability, and security of the power system. As the weights used in WAFGP would have a significant impact on the operational and economical enhancements achieved in the optimization, they are optimized using evolutionary DE algorithm. This provides a way for exploring a balanced solution for a multiobjective problem without sacrificing any individual objective’s uniqueness and priority. The multiple objectives considered are maximizing the loadability condition of the power system with minimum system real power loss and minimum installation cost of the FACTS devices. Indian utility Neyveli Thermal Power Station (NTPS) 23 bus system is used to test the proposed algorithm using multiple FACTS devices. The results compared with that of DE based fuzzy goal programming (FGP) demonstrates that DE based WAFGP algorithm not only provides a balanced optimal solution for all objectives but also provides the best economical solution.

#### 1. Introduction

The ever-increasing demand of electric power and deregulation norms followed in certain countries create a heavy traffic, and thereby straining an existing power network. Maintaining the stability and security of power network becomes the foremost challenge for the power suppliers.

FACTS devices are power electronic devices that can be inserted in existing power network at desired location without altering the existing network. They provide required transmission line impedance, real power, and reactive power, maintain the voltage levels at buses which in turn increases the load carrying capacity of transmission network, reduces real and reactive power losses, and maintains voltage stability in the overall power network [1].

The optimal location and sizing of FACTS controllers in a power network are done for better utilization of these devices in an economical way. Several conventional and intelligent natural inspired algorithms are available in obtaining a global optimal solution for a single objective optimization [2–6]. When more than one objective is considered for optimization, the problem turns out into a multiobjective optimization yielding Pareto optimal solutions. The fuzzy concept is one of the most popular methodology that can be combined with any conventional/intelligent techniques to bring out the best global optimal solution from pareto optimal solutions.

Zadeh was the first to introduce the concept of fuzzy set theory in the year 1965 [7]. Narasimhan has illustrated the application of fuzzy subsets concepts to fuzzy goal programming in 1980 [8]. Tiwari et al. have formulated an additive model to solve fuzzy goal programming in 1987 [9]. This model is mostly suited for multiobjective problems where objectives have different levels of importance. Many researchers have used fuzzy technique with other optimization methods to solve multiobjective optimal power flow problems in an effective manner.

Rosehart et al. have combined interior point methods with goal programming in optimizing active and reactive power dispatch while maximizing voltage security in power systems in 2003. In 2011, Hazra and Sinha have presented a multiobjective particle swarm optimization method for minimizing generation cost and environmental pollution simultaneously. Liang et al. (2011) have presented a fuzzy based hybrid particle swarm optimization (PSO) approach in minimizing fuel cost, total emission, and total real power loss [10–12].

In 2011, Sivasubramani and Swarup have proposed multiobjective harmony search (MOHS) algorithm and He et al., in 2013, have used Artificial Bee Colony (ABC) algorithm to solve multiobjective OPF. Azizipanah-Abarghooee et al. have presented modified Shuffled frog-leaping algorithm (SFLA) in solving multiobjectives like reducing generation cost, decreasing transmission loss, improving voltage stability index, and power system security in 2014 [13–15]. In all the above papers, fuzzy membership is used to choose a comprise solution from the set of Pareto optimal solutions. In this paper, maximization and minimization goals for each objective in multiobjective OPF are determined using DE algorithm and are converted to fuzzy goals using fuzzy membership values. Each fuzzy goal is assigned with a weight and all fuzzy goals are combined together to frame the Weighted Additive Fuzzy Goal model. Taking the importance of each individual objective into consideration, the weights for each objective in multiobjective OPF is optimized using DE algorithm.

This paper is organized into seven sections. Section 1 provides an introduction. Section 2 presents the implementation of mathematical modelling of FACTS devices in power system network. Section 3 formulates this study’s problem. Section 4 describes the proposed FDE approach in detail for optimal location of FACTS in a multiobjective optimization. Section 5 presents and discusses the results, and Section 6 concludes the benefits of this study.

#### 2. Implementation of Facts Devices in Power System Network

The generalized real and reactive power flow equations for a bus “” without any FACTS devices connected in a power system can be written as:where nbr is the total number of transmission line branches in a power system; and are the angle and magnitude of bus admittance elements; and are magnitude and phase angle of bus voltages; and are real and reactive powers of the buses.

The introduction of FACTS devices in the power systems makes a significant change in the power flow equations that depends on the mathematical model of FACTS devices.

##### 2.1. Thyristor Controlled Series Capacitor

TCSC is a series compensated thyristor controlled device that is comprised of a capacitor in parallel with a TCR. Figure 1 depicts the equivalent circuit of a TCSC. In this model, the desired transmission line impedance can be achieved for smoother reactive power control by controlling the TCSC both in inductive and capacitive modes.