An adaptive Clarke transform based estimator for the frequency of balanced and unbalanced three-phase power systems

Abstract

Abstract-In this paper we examine the general problem of estimating the frequency of a balanced or unbalanced three-phase power system. The Clarke transform is commonly employed to transform the three real voltages to in-phase and quadrature components that are combined to form a complex exponential, the frequency of which can then be estimated. The imbalance between the voltages in an unbalanced system results in significant performance degradation. We address this problem by generalising the Clarke transformation to the case where the voltages are not equal. We then propose a new simple yet accurate algorithm for the estimation of the frequency. We simulate the algorithm and show that it achieves the performance that is obtained in the balanced case, practically sitting on the Cramér-Rao Bound.