Bayesian state estimation for partially observable distribution networks via power flow-informed neural networks

The performance of existing distribution network state estimation (SE) methods is unsatisfactory due to limited real-time measurements. In this paper, a Bayesian SE method is proposed for partially observable distribution networks using a novel power flow-informed neural network (PFINN). The Bayesian SE model is first established with the goal of directly minimizing the SE error and obtaining the expectation of states conditional on measurements. The conditional expectation is then viewed as a nonparametric regression that can be parameterized by a PFINN where a physics loss penalty is introduced into the loss function to constrain the neural network outputs to be consistent with power network operating constraints. Test results on balanced and unbalanced distribution networks using field data show that the proposed method can achieve better estimation accuracy than the Bayesian SE method without power flow informing. For a fixed neural network, it is always possible to enhance its performance by adding a physics loss term to the original loss function, along with a suitable weight which can be obtained using existing automatic hyperparameter tunning methods.