Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning

Abstract--The problem of state estimation for unobservable distribution systems is considered. A Bayesian approach is proposed that implements Bayesian inference with a deep neural network to achieve the minimum mean squared error estimation of network states for real-time applications. The proposed technique consists of distribution learning for stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad data detection and cleansing algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors of power injection distributions and the presence of bad data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation with deep neural networks outperforms existing benchmarks. We consider the problem of state estimation for distribution systems that have limited measurements. This problem is motivated by the need of coping with the rising presence of distributed energy resources (DER) in distribution systems.