Data-Driven Priors for Robust PSSE via Gauss-Newton Unrolled Neural Networks

Renewable energy sources, elastic loads, and purposeful manipulation of meter readings challenge the monitoring and control of today's power systems (PS). In this context, fast and robust state estimation (SE) is timely and of major importance to maintaining a comprehensive view of the system in real-time. Conventional PSSE solvers typically entail minimizing a nonlinear and nonconvex least-squares cost using e.g., the Gauss-Newton method. Those iterative solvers however, are sensitive to initialization and may converge to local minima. To overcome these hurdles, the present paper draws recent advances on image denoising to put forth a novel PSSE formulation with a data-driven regularization term capturing a deep neural network (DNN) prior. For the resultant regularized PSSE objective, a "Gauss-Newton-type" alternating minimization solver is developed first. To accommodate real-time monitoring, a novel end-to-end DNN is constructed subsequently by unrolling the proposed alternating minimization solver. The deep PSSE architecture can further account for the power network topology through a graph neural network (GNN) based prior. To further endow the physics-based DNN with robustness against bad data, an adversarial DNN training method is put forth. Numerical tests using real load data on the IEEE 118-bus benchmark system showcase the improved estimation and robustness performance of the proposed scheme compared with several state-of-the-art alternatives.