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The Scientific World Journal
Volume 2014, Article ID 539420, 8 pages
Research Article

Accurate Parameter Estimation for Unbalanced Three-Phase System

Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong

Received 20 February 2014; Revised 11 July 2014; Accepted 17 July 2014; Published 4 August 2014

Academic Editor: Gordana Jovanovic Dolecek

Copyright © 2014 Yuan Chen and Hing Cheung So. 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.


Smart grid is an intelligent power generation and control console in modern electricity networks, where the unbalanced three-phase power system is the commonly used model. Here, parameter estimation for this system is addressed. After converting the three-phase waveforms into a pair of orthogonal signals via the αβ-transformation, the nonlinear least squares (NLS) estimator is developed for accurately finding the frequency, phase, and voltage parameters. The estimator is realized by the Newton-Raphson scheme, whose global convergence is studied in this paper. Computer simulations show that the mean square error performance of NLS method can attain the Cramér-Rao lower bound. Moreover, our proposal provides more accurate frequency estimation when compared with the complex least mean square (CLMS) and augmented CLMS.