Widely linear adaptive frequency estimation of unbalanced three-phase power systems

Abstract—A novel technique for online estimation of the fun-damental frequency of unbalanced three-phase power systems is proposed. Based on Clarke’s transformation and widely linear complex domain modeling, the proposed method makes use of the full second-order information within three-phase signals, thus promising enhanced and robust frequency estimation. The struc-ture, mathematical formulation, and theoretical stability and sta-tistical performance analysis of the proposed technique illustrate that, in contrast to conventional linear adaptive estimators, the proposed method is well matched to unbalanced system conditions and also provides unbiased frequency estimation. The proposed method is also less sensitive to the variations of the three-phase voltage amplitudes over time and in the presence of higher order harmonics. Simulations on both synthetic and real-world unbal-anced power systems support the analysis. Index Terms—Augmented complex least mean square (CLMS) (ACLMS), complex noncircularity, frequency estimation, unbal-anced three-phase voltage, widely linear modeling. I