Widely Linear Modeling for Frequency Estimation in Unbalanced Three-Phase Power Systems

Real-time frequency estimation in three-phase power systems is revisited from the state space point of view, in order to provide a unified framework for frequency tracking in both balanced and unbalanced system conditions. This is achieved by using a novel class of widely linear complex valued Kalman filters, which provide unbiased frequency estimation and are faster converging and more robust to noise and harmonic artifacts than the existing methods. It is shown that the Clarke´s transformed three-phase voltage is circular for balanced systems and noncircular for unbalanced ones, making the proposed widely linear estimation perfectly suited both to identify the fault and to provide accurate estimation in unbalanced conditions, critical issues where standard models typically fail. The analysis and simulations show that the proposed model outperforms the recently introduced widely linear stochastic gradient-based frequency estimators, based on the augmented complex least mean square. Comprehensive simulations on synthetic and real-world power system data, in both balanced and unbalanced conditions, support the approach.