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The optimal reactive power dispatch problem plays an important key in electrical power systems, especially in local distribution power companies. The objective of the optimal reactive power dispatch (ORPD) problem is to determine controlling variables related to the reactive power to minimize the power loss, voltage deviation, etc. The security constraint ORPD is an upgraded version, which considers outage lines in contingency cases. As the definition pointed out by Carpentier (Carpentier, 1962), a secure system is the one that will continue to operate satisfactorily after the loss of one or more components. In the other words, the security-constrained ORPD (SCORPD) problem satisfies all of operating constraints in both normal and contingency cases.
Several conventional and artificial intelligent-based methods have been implemented for solving the optimal reactive power dispatch problems. In the past, some classical methods such as linear programming (Aoki, Fan & Nishikori, 1988), quadratic programming (Quintana & Santos-Nieto, 1989), Lagrange approach (de Sousa, Baptista & da Costa, 2012) have been applied for this problem. However, the disadvantages of these techniques are difficult to handle large systems, easy convergence to local optima. Some of them only calculate on continuous and differential objective functions. In recent years, despite the development of computers, stochastic search methods have been widely employed for the ORPD. For example, El Ela et al. applied differential evolution (DE) for ORPD in the IEEE 30-bus system (El Ela, Abido & Spea, 2011). Khazali and Kalantar proposed harmony search (HS) algorithm for the IEEE 30-bus and 57-bus systems (Khazali & Kalantar, 2011). On the other hand, Vlachogiannis and Lee applied evolutionary algorithm (EA) to solve the optimal real and reactive power for the IEEE 118-bus system (Vlachogiannis & Lee, 2008). Other modern algorithms have been employed to improve the global solution such as particle swarm optimization (PSO) (Singh, Mukherjee & Ghoshal, 2015), teaching-learning-based optimization (TLBO) (Mandal & Roy, 2013). The development of stochastic methods gives the challenge to find an effective method while increasing the number of variables and constraints of power systems.
Among effective stochastic methods, PSO is a well-known optimizer evaluated on diverse applications. The main idea of PSO is based on the behavior of birds when they make their immigration every year. Each particle has a position and a velocity. After each iteration, a new velocity is randomly generated from the global and local positions. Due to its simplicity, the PSO developed rapidly in order to solve optimization problems in various fields (Zhang, Wang & Ji, 2015). The PSO method is a robust method for searching the global solution. However, the quality of its solution is not so good. Therefore, a hybridization of PSO with DE is a favorable approach to enhance the performance of the PSO. For example, Esmin et al. proposed a mutation particle swarm optimizer to minimize the power loss for the IEEE 118-bus system (Esmin, Lambert-Torres & De Souza, 2005) while Sayah and Hamouda proposed a combination with the DE for solving economic dispatch problems (Sayah & Hamouda, 2013).
In this paper, the authors proposed a hybrid particle swarm optimization and differential evolutionary (HPSO-DE) (Sayah & Hamouda, 2013) for solving the SCORPD problem with three various objective functions of minimizing the power loss, voltage deviation, and stability index. The proposed method is a combination of DE and PSO, where PSO places the memory information for DE to create the promising solution for complex optimization problems. The proposed approach has utilized the advantage of PSO on the speed of convergence and the advantage of DE on the quality of obtained solutions. The proposed method has been evaluated on the IEEE 30-bus system considering five outage lines and the obtained results are compared to those from the conventional PSO and DE methods.