A Fast Convergence Geometric–Statistical Approach for the Estimation of Three-Phase Electrical Signal Parameters

The characterization of real-time electrical signals is paramount in electrical engineering for applications, such as synchronization and fault detection. However, signal distortion poses significant challenges to parameter estimation, which must be accurate and fast. This study presents a novel approach to the estimation of electrical signal parameters that combines a new geometric–statistical framework with rapid convergence and good precision. The proposed open-loop approach is based on the recursive covariance and the elliptical representation of unbalanced three-phase signals. Its mathematical formulation facilitates a substantial acceleration of the approximation process, culminating in the fastest convergence time documented to date. In addition, the proposed method consistently outperforms other estimators in terms of settling time, remaining within one cycle of the fundamental signal. The resulting errors in frequency or phase estimation and TVE were lower than or comparable to those of relevant alternatives.