Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

Accurate detection of the system parameters in unbalanced three-phase power systems is a prerequisite for the optimal operation and control of future smart grids. However, theoretical and practical performance bounds of various estimators for unbalanced systems are only just being established. To this end, we introduce the appropriate Cramer- Rao lower bounds (CRLBs) for frequency estimation, based on the αβ-transformed unbalanced voltage contaminated with noise. Next, for rigor, the maximum likelihood estimation (MLE) method for frequency estimation is introduced as a maximizer of an “augmented periodogram.” The underlying augmented complex statistics is shown to cater for all the available secondorder information, including the noncircularity associated with unbalanced systems. To find the ML solution, Newton's iterative method is employed and its initialization is implemented by a discrete Fourier transform-based dichotomous search technique. We show that the MLE of phases and amplitudes of both the positive and negative phase-sequence components within the αβ-transformed voltage can be generically derived based on the ML frequency estimates. In this way, a unified framework is provided to accurately detect voltage characteristics of the positive and negative phase-sequence components within an unbalanced three-phase power system when its frequency experiences off-nominal conditions. Simulations verify that the proposed MLE approaches theoretical CRLBs for all parameters under consideration.