A widely linear least mean phase algorithm for adaptive frequency estimation of unbalanced power systems

•A robust frequency estimation method is proposed for unbalanced power systems.•It is achieved by using a widely linear model and a phase only cost function.•It eliminates the estimation oscillation encountered by the linear estimator.•The robustness of the proposed method is verified in real world case studies. A robust technique for online estimation of the fundamental frequency of both balanced and unbalanced three-phase power systems is proposed. This is achieved by introducing a widely linear least mean phase (WL-LMP) frequency estimator, based on Clarke’s transformation and widely linear complex domain modelling. The proposed method makes use of the full second-order information within the complex-valued system voltage, making it possible to eliminate otherwise unavoidable oscillations in frequency estimation. In this way, the WL-LMP inherits the advantages of the phase-only approach, such as its high angle estimation accuracy and immunity to voltage and harmonics variations, while accounting for the noncircularity of Clarke’s voltage in unbalanced conditions. Simulations over a range of unbalanced conditions, including those caused by voltage sags and higher order harmonics, and case studies for real-world unbalanced power systems support the analysis.