Covariance Analysis of LAV Robust Dynamic State Estimation in Power Systems

In power system state estimation, the robust least absolute value robust dynamic estimator is well known. However, the covariance of the state estimation error cannot be obtained easily. In this article, an analytical equation is derived using influence function approximation to analyze the covariance of the robust least absolute value dynamic state estimator. The equation gives insights into the precision of the estimation and can be used to express the variances of the state estimates as functions of measurement noise variances, enabling the selection of sensors for specified estimator precision. Simulations on the IEEE 14-bus, 30-bus, and 118-bus systems are given to illustrate the usefulness of the equation. Monte Carlo experiments can also be used to determine the covariance, but many data points are needed and hence many runs are required to achieve convergence. Our result shows that to obtain the covariance of the state estimation error, the analytical equation proposed in this article is four orders of magnitude faster than a 10 000-run Monte Carlo experiment on both the IEEE 14-bus and 30-bus systems.