Widely linear adaptive frequency estimation in three-phase power systems under unbalanced voltage sag conditions

A new framework for the estimation of the instantaneous frequency in a three-phase power system is proposed. It is first illustrated that the complex-valued signal, obtained by the αβ transformation of three-phase power signals under unbalanced voltage sag conditions, is second order noncircular, for which standard complex adaptive estimators are suboptimal. To cater for second order noncircularity, an adaptive widely linear estimator based on the augmented complex least mean square (ACLMS) algorithm is proposed, and the analysis shows that this allows for optimal linear adaptive estimation for the generality of system conditions (both balanced and unbalanced). The enhanced robustness over the standard CLMS is illustrated by simulations on both synthetic and real-world voltage sags.