• available transfer capability;
  • multi-objective evolutionary optimization;
  • multi-objective particle swarm optimization;
  • reactive power planning;
  • strength Pareto evolutionary algorithm;
  • voltage collapse


This paper presents a new approach to treat reactive power (VAr) planning problem using multi-objective evolutionary algorithms (EAs). Specifically, strength Pareto EA (SPEA) and multi-objective particle swarm optimization (MOPSO) approaches have been developed and successfully applied. The overall problem is formulated as a nonlinear constrained multi-objective optimization problem. Minimizing the total incurred cost of the VAr planning problem and maximizing the amount of available transfer capability (ATC) are defined as the main objective functions. The aim is to find the optimal allocation of VAr devices in such a way that investment and operating costs are minimized and at the same time the amount of ATC is maximized. The proposed approaches have been successfully tested on IEEE 14 buses system. As a result a wide set of optimal solutions known as Pareto set is obtained and encouraging results show the superiority of the proposed approaches and confirm their potential to solve such a large-scale multi-objective optimization problem. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.