Frequency and Phasor Estimations in Three-Phase Systems: Maximum Likelihood Algorithms and Theoretical Performance

In this paper, the problem of frequency and phasor estimation in three-phase systems is considered. Three-phase electrical signals are composed of three components that can be jointly exploited to improve the estimation performance. To exploit this property, most of the existing estimation algorithms are based on a linear preprocessing called the Clarke transform. In this paper, we investigate a more general situation where the preprocessing is obtained from a semi-orthogonal transform. This situation encompasses several strategies such as the single-phase estimator, the optimal three-phase estimator, and the Clarke-based estimator. For this general situation, we derive the maximum likelihood estimator of the angular frequency and complex phasors. We also examine how the choice of a particular semi-orthogonal transform affects the estimation performance, and present a new technique that statistically outperforms the Clarke transform. Regarding the estimation performance under noisy environment, we also introduce and derive a new criterion called the probability of IEEE C37.118 Standard compliance.