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Journal of Electrical and Computer Engineering
Volume 2014, Article ID 124136, 12 pages
Research Article

Application of Hybrid MOPSO Algorithm to Optimal Reactive Power Dispatch Problem Considering Voltage Stability

State Key Laboratory of Hybrid Process Industry Automation System and Equipment Technology, China Iron & Steel Research Institute Group, Beijing 100081, China

Received 20 March 2014; Revised 26 May 2014; Accepted 29 May 2014; Published 18 June 2014

Academic Editor: John N. Sahalos

Copyright © 2014 Yujiao Zeng and Yanguang Sun. 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.


This study presents a novel hybrid multiobjective particle swarm optimization (HMOPSO) algorithm to solve the optimal reactive power dispatch (ORPD) problem. This problem is formulated as a challenging nonlinear constrained multiobjective optimization problem considering three objectives, that is, power losses minimization, voltage profile improvement, and voltage stability enhancement simultaneously. In order to attain better convergence and diversity, this work presents the use of combing the classical MOPSO with Gaussian probability distribution, chaotic sequences, dynamic crowding distance, and self-adaptive mutation operator. Moreover, multiple effective strategies, such as mixed-variable handling approach, constraint handling technique, and stopping criteria, are employed. The effectiveness of the proposed algorithm for solving the ORPD problem is validated on the standard IEEE 30-bus and IEEE 118-bus systems under nominal and contingency states. The obtained results are compared with classical MOPSO, nondominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), and other methods recently reported in the literature from the point of view of Pareto fronts, extreme, solutions and multiobjective performance metrics. The numerical results demonstrate the superiority of the proposed HMOPSO in solving the ORPD problem while strictly satisfying all the constraints.