Complex-Variable Weighted Least Modulus State Estimation

The use of the Weighted Least Absolute Value (WLAV) state estimator is especially advantageous in systems that utilize Phasor Measurement Units (PMUs). Although PMU measurements and the phasor state vector are complex-valued, traditional WLAV methods operate solely in the real domain. This paper introduces the Weighted Least Modulus (WLM) state estimator, which is the counterpart of the WLAV method in complex variables. The WLM state estimator exploits the coupling of real and imaginary measurement components for noise filtering and bad data elimination. The paper demonstrates that the WLM state estimator replaces the WLAV linear programs with conic programs. An efficient implementation in complex variables is also derived through the Iteratively Reweighted Least Squares (IRLS) technique within the Wirtinger calculus framework. The WLM state estimator is tested on networks with up to 6495 nodes in PMU-only and hybrid measurement scenarios. The results were compared to the IRLS solution using real variables and a traditional linear programming formulation. They show that the IRLS-based WLM state estimator achieves a significant speedup compared to WLAV implementations and, at the same time, gives overall better estimation results.