Empirical Study of Robust State Estimation for Power Systems

This paper provides insights into the existence of spurious local optima for the nonlinear `1-norm state estimator in power system applications. The linear least-absolute-value (LAV) estimator has attracted considerable attentions over the past few years, especially in the machine learning community, mainly due to its convexity and robustness with respect to sparse noise. Due to these properties, recent studies have attempted to apply the nonlinear version of the LAV to problems such as topological error detection in power systems. However, there has been no study so far that provides theoretical guarantees for finding the global solution of the nonlinear least-absolute-value (NLAV) estimator. In this study, we analyze the performance of NLAV on different real-world scenarios and compare it with the nonlinear least-squares (NLS), which is the common practice in power industry. In our study, we consider various factors, such as the number of measurements, available prior information, and the presence of bad data, on the performance of these estimators by performing more than 260000 simulations on several IEEE benchmark systems. Additionally, we use a recent result on robust principal component analysis and low-rank matrix completion to justify our observations and provide recommendations for realworld applications of these estimators.