Impact of the non-Gaussian measurement noise on the performance of state-of-the-art state estimators for distribution systems

This paper aims to investigate the impact of non-Gaussian measurement noise on state estimation (SE) results in distribution systems. To this end, the measurement noise is assumed to be distributed according to Gaussian or one of the following non-Gaussian probability distribution functions: Uniform, Laplace, Weibull and Gaussian mixture of two Gaussian components. The influence is investigated on three different state-of-the-art SE methods: weighted least squares (WLS) based static SE method, and two Kalman filter based forecasting-aided SE methods, namely extended Kalman filter (EKF) and unscented Kalman filter (UKF). Analyses are conducted on modified IEEE 37-bus system under different operating conditions, including quasi-steady state, sudden state changes and bad data. Performance of the methods in the presence of non-Gaussian measurement noise is compared against their performance when measurement noise is Gaussian distributed. The main conclusions were drawn, summarizing the impacts non-Gaussian measurement noise has on SE and proposing the solutions for overcoming some of the negative impacts.