Algorithms for least median of squares state estimation of power systems

The least median of squares (LMS) estimator minimizes the vth ordered squared residual. The authors derived a general expression of the optimal v for which the breakdown point of the LMS attains the highest possible fraction of outliers that any regression equivariant estimator can handle. This fraction is equal to half of the minimum surplus divided by the number of measurements in the network. The surplus of a fundamental set is defined as the smallest number of measurements whose removal from that fundamental set turns at least one measurement in the network into a critical one. Based on the surplus concept, a system decomposition scheme that significantly increases the number of outliers that can be identified by the LMS is developed. In addition, it dramatically reduces the computing time of the LMS, opening the door to real-time applications of that estimator to large-scale systems. Finally, outlier diagnostics based on robust Mahalanobis distances are proposed.<>