Optimal Reactive Power Dispatch Using Quasi-Oppositional Biogeography-Based Optimization

In this paper, quasi-oppositional biogeography based-optimization (QOBBO) for optimal reactive power dispatch (ORPD) is presented. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions of the regulating transformer and the Var injection of the shunts compensator, for real power loss minimization in the transmission system. The algorithm’s performance is studied with comparisons of canonical genetic algorithm (CGA), five versions of particle swarm optimization (PSO), local search based self-adaptive differential evolution (L-SADE), seeker optimization algorithm (SOA), biogeography based optimization (BBO) on the IEEE 30-bus and IEEE 57-bus power systems. The simulation results show that the proposed QOBBO approach performed better than the other listed algorithms and can be efficiently used for the ORPD problem. DOI: 10.4018/ijeoe.2012100103 International Journal of Energy Optimization and Engineering, 1(4), 38-55, October-December 2012 39 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. problem, including conventional approaches such as linear programming (LP) (Aoki, Fan, & Nishikor, 1988), interior point methods (Granville, 1994; Yan, Yu, Yu, & Bhattarai, 2006) and dynamic programming (DP) (Lu & Hsu, 1995). These methods are local optimizers in nature, i.e., they might converge to local solutions instead of global ones if the initial guess happens to be in the neighborhood of a local solution. DP method may cause the dimensions of the problem to become extremely large, thus requiring enormous computational efforts. Nonlinear optimization problems with complex constraints may be solved by many meta-heuristics methods such as evolutionary programming (EP) (Ma & Lai, 1996; Wu & Ma, 1995), genetic algorithm (GA) (Iba, 1994; Lee & Park, 1995; Swarup, Yoshimi, & Izui, 1994), particle swarm optimization (PSO) (Kawata, Fukuyama, Takayama, & Nakanish, 2000; Li, Cao, Liu, Liu, & Jiang, 2009; Zhao, Guo, & Cao, 2005), Tabu search (TS) (Yiqin, 2010), differential evolution (DE) (Liang, Chung, Wong, & Dual, 2007; Varadarajan & Swarup, 2008; Zhang, Chen, Dai, & Cai 2010), SOA (Dai, Chen, Zhu, & Zhang, 2009a; Dai, Chen, Zhu, & Zhang, 2009b), BBO (Bhattacharya & Chattopadhyay, 2010). Each of these methods has its own characteristics, strengths and weaknesses; but long computational time is a common drawback for most of them, especially when the solution space is hard to explore. Many efforts have been made to accelerate convergence of these methods. In this paper, opposition-based learning (OBL) (Tizhoosh, 2005) is applied on BBO to make it faster and achieve better optimal solution. The concept of OBL is earlier applied to accelerate PSO (Zhang, Ni, Wu, & Gu, 2009), DE (Rahnamayan, Tizhoosh, & Salama, 2007) and ant colony optimization (ACO) (Haiping, Xieyon, & Baogen, 2010). The main idea behind the OBL is considering the estimate and opposite estimate (guess and opposite guess) at the same time in order to achieve a better approximation for current candidate solution. Purely random selection of solutions from a given population has the chance of visiting or even revisiting unproductive regions of the search space. The chance of this occurring is lower for opposite numbers than it is for purely random ones. A mathematical proof has been proposed (Haiping, Xieyong, & Baogen, 2010) to show that, in general, opposite numbers are more likely to be closer to the optimal solution than purely random ones. The effectiveness of the proposed QOBBO based ORPD algorithm is tested on IEEE 30bus and IEEE 57-bus systems. The results of QOBBO are compared to those of PSO, comprehensive learning PSO (CLPSO), CGA, real standard version of PSO (SPSO-07), PSO with constriction factor (PSO-cf), PSO with adaptive inertia weight (PSO-w), local search based self-adaptive differential evolution (L-SADE), seeker optimization algorithm (SOA), and BBO to make it clear that the proposed method is powerful and reliable. This paper is organized as follows. Section 2 formulates ORPD problems, Section 3 and Section 4 describes the basic theory and algorithm respectively of the BBO technique. Opposition-based learning and quasi-oppositional based BBO applied to the ORPD are addressed in Section 5 and Section 6, respectively. Input parameter and test results are presented in Section 7 and Section 8, respectively. Section 9 provides the conclusion of this paper. 2. PROBLEM DESCRIPTION The general ORPD problem under normal operating condition may be formulated as follows: Minimize f u v ( , ) (1)