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Journal of Applied Mathematics
Volume 2012, Article ID 104952, 18 pages
Research Article

Modeling Electromechanical Overcurrent Relays Using Singular Value Decomposition

1Department of Electrical Engineering, National Taipei University of Technology, Taipei 10608, Taiwan
2Department of Computer and Communication Engineering, St. John’s University, Tamsui District, New Taipei City 25135, Taiwan
3Department of Power Supply, Taiwan Power Company, Zhongzheng District, Taipei City 10016, Taiwan

Received 17 August 2012; Accepted 5 November 2012

Academic Editor: Ricardo Perera

Copyright © 2012 Feng-Jih Wu 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 presents a practical and effective novel approach to curve fit electromechanical (EM) overcurrent (OC) relay characteristics. Based on singular value decomposition (SVD), the curves are fitted with equation in state space under modal coordinates. The relationships between transfer function and Markov parameters are adopted in this research to represent the characteristic curves of EM OC relays. This study applies the proposed method to two EM OC relays: the GE IAC51 relay with moderately inverse-time characteristic and the ABB CO-8 relay with inverse-time characteristic. The maximum absolute values of errors of hundreds of sample points taken from four time dial settings (TDS) for each relay between the actual characteristic curves and the corresponding values from the curve-fitting equations are within the range of 10 milliseconds. Finally, this study compares the SVD with the adaptive network and fuzzy inference system (ANFIS) to demonstrate its accuracy and identification robustness.