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Top1. Introduction
Optimal reactive power dispatch (ORPD) has a growing impact on secure and economical operation of power systems. It is an effective method to minimize the transmission losses and maintain the power system running under normal conditions. All controllable variables, such as voltage of generators, tap ratio of transformers, Var injection of shunt compensators, are determined which minimizes real power losses, satisfying a given set of operational constraints. It is an effective method to improve voltage level, decrease power losses and maintain the power system running under normal conditions.
Different classical techniques have been reported in the literature pertaining to ORPD 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.