Advancing the MILP-based Load Restoration with Graph Neural Networks

The evolution of power systems into sophisticated cyber-physical systems calls for an urgent need for reliable load restoration methods, especially in the face of increasing system complexities and the demand for rapid recovery. This paper formulates the optimal load restoration problem as a binary integer problem and introduces a customized problem-specific optimization framework employing a Graph Neural Network for faster distributed optimal load restoration decisions. The proposed framework extracts restoration environment-specific attributes and offers an adaptive heuristic tailored to handle similar restoration scenarios. This approach leverages the learned policy imitating the optimal choices of actions by the system operator to facilitate faster, more effective smart grid responses, thereby allowing local controllers with optimal decisions under varying network constraints. We validate our framework through two case studies on distribution systems, comparing its performance against the traditional, generalized approach. Our findings highlight the potential of ML-driven solutions in transforming load restoration processes, contributing to the development of self-healing and adaptive smart grids.