Power System State Estimation Using Gauss-Newton Unrolled Neural Networks with Trainable Priors

Power system state estimation (PSSE) aims at finding the voltage magnitudes and angles at all generation and load buses, using meter readings and other available information. PSSE is often formulated as a nonconvex and nonlinear least-squares (NLS) cost function, which is traditionally solved by the Gauss-Newton method. However, Gauss-Newton iterations for minimizing nonconvex problems are sensitive to the initialization, and they can diverge. In this context, we advocate a deep neural network (DNN) based "trainable regularizer" to incorporate prior information for accurate and reliable state estimation. The resulting regularized NLS does not admit a neat closed form solution. To handle this, a novel end-to-end DNN is constructed subsequently by unrolling a Gauss-Newton-type solver which alternates between least-squares loss and the regularization term. Our DNN architecture can further offer a suite of advantages, e.g., accommodating network topology via graph neural networks based prior. Numerical tests using real load data on the IEEE 118-bus benchmark system showcase the improved estimation performance of the proposed scheme compared with state-of-the-art alternatives. Interestingly, our results suggest that a simple feed forward network based prior implicitly exploits the topology information hidden in data.