Estimation of Amplitude, Phase and Unbalance Parameters in Three-phase Systems: Analytical Solutions, Efficient Implementation and Performance Analysis

This paper focuses on the estimation of the instantaneous amplitude, phase, and unbalance parameters in three-phase power systems. Due to the particular structure of three-phase systems, we demonstrate that the maximum-likelihood estimates (MLEs) of the unknown parameters have simple closed-form expressions and can be easily implemented without matrix algebra libraries. We also derive and analyze the Cramer-Rao Bounds (CRBs) for the considered estimation problem. The performance of the proposed approach is evaluated using synthetic signals compliant with the IEEE Standard C37.118. Simulation results show that the proposed estimators outperform other techniques and reach the CRB under certain conditions.