Journal of Applied Mathematics
Volume 2013 (2013), Article ID 879078, 9 pages
Research Article

Applying Hybrid PSO to Optimize Directional Overcurrent Relay Coordination in Variable Network Topologies

1Department of Electrical Engineering, St. John’s University, 499, Section 4, Tam King Road, Tamsui District, New Taipei 25135, Taiwan
2Department of Computer Science and Information Engineering, St. John’s University, 499, Section 4, Tam King Road, Tamsui District, New Taipei 25135, Taiwan
3Graduate Institute of Computer and Communication Engineering, National Taipei University of Technology, No. 1, Section 3, Chunghsiao E. Road, Taipei 10608, Taiwan

Received 4 December 2012; Revised 20 January 2013; Accepted 25 January 2013

Academic Editor: Frank Werner

Copyright © 2013 Ming-Ta Yang and An Liu. 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.


In power systems, determining the values of time dial setting (TDS) and the plug setting (PS) for directional overcurrent relays (DOCRs) is an extremely constrained optimization problem that has been previously described and solved as a nonlinear programming problem. Optimization coordination problems of near-end faults and far-end faults occurring simultaneously in circuits with various topologies, including fixed and variable network topologies, are considered in this study. The aim of this study was to apply the Nelder-Mead (NM) simplex search method and particle swarm optimization (PSO) to solve this optimization problem. The proposed NM-PSO method has the advantage of NM algorithm, with a quicker movement toward optimal solution, as well as the advantage of PSO algorithm in the ability to obtain globally optimal solution. Neither a conventional PSO nor the proposed NM-PSO method is capable of dealing with constrained optimization problems. Therefore, we use the gradient-based repair method embedded in a conventional PSO and the proposed NM-PSO. This study used an IEEE 8-bus test system as a case study to compare the convergence performance of the proposed NM-PSO method and a conventional PSO approach. The results demonstrate that a robust and optimal solution can be obtained efficiently by implementing the proposal.