Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 501893, 14 pages
Research Article

Optimal PMU Placement with Uncertainty Using Pareto Method

Electrical Engineering Department, University of Kashan, Kashan 87317-51167, Iran

Received 16 December 2011; Revised 30 March 2012; Accepted 4 April 2012

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2012 A. Ketabi et al. 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 paper proposes a method for optimal placement of Phasor Measurement Units (PMUs) in state estimation considering uncertainty. State estimation has first been turned into an optimization exercise in which the objective function is selected to be the number of unobservable buses which is determined based on Singular Value Decomposition (SVD). For the normal condition, Differential Evolution (DE) algorithm is used to find the optimal placement of PMUs. By considering uncertainty, a multiobjective optimization exercise is hence formulated. To achieve this, DE algorithm based on Pareto optimum method has been proposed here. The suggested strategy is applied on the IEEE 30-bus test system in several case studies to evaluate the optimal PMUs placement.