NEO-Grid: A Neural Approximation Framework for Optimization and Control in Distribution Grids

Abstract: The rise of distributed energy resources (DERs) is reshaping modern distribution grids, introducing new challenges in attaining voltage stability under dynamic and decentralized operating conditions. This paper presents NEO-Grid, a unified learning-based framework for volt-var optimization (VVO) and volt-var control (VVC) that leverages neural network surrogates for power flow and deep equilibrium models (DEQs) for closed-loop control. Our method replaces traditional linear approximations with piecewise-linear ReLU networks trained to capture the nonlinear relationship between power injections and voltage magnitudes. For control, we model the recursive interaction between voltage and inverter response using DEQs, allowing direct fixed-point computation and efficient training via implicit differentiation. We evaluated NEO-Grid on the IEEE 33-bus system, demonstrating that it significantly improves voltage regulation performance compared to standard linear and heuristic baselines in both optimization and control settings. Our results establish NEO-Grid as a scalable, accurate, and interpretable solution for learning-based voltage regulation in distribution grids.