Robust Power System State Estimation Using t-Distribution Noise Model

In this paper, we propose an optimal robust state estimator using maximum likelihood optimization with the t-distribution noise model. In robust statistics literature, the t-distribution is used to model Gaussian and non-Gaussian statistics. The influence function, an analytical tool in robust statistics, is employed to obtain the solution to the resulting maximum likelihood estimation optimization problem, so that the proposed estimator can be implemented within the framework of traditional robust estimators. Numerical results obtained from simulations of the IEEE 14-bus system, IEEE 118-bus system, and experiment on a microgrid demonstrated the effectiveness and robustness of the proposed estimator. The proposed estimator could suppress the influence of outliers with smaller average mean-squared errors (AMSE) than the traditional robust estimators, such as quadratic-linear, squareroot, Schweppe-Huber generalized-M, multiple-segment, and least absolute value estimators. A new approximate AMSE formula is also derived for the proposed estimator to predict and evaluate its precision.