Physics-Informed Graph-Based Learning to Enable Solving Optimal Distribution Switching Problem

This letter introduces a novel graph convolutional neural network (GCN) architecture for solving the optimal switching problem in distribution networks while integrating the underlying power flow equations in the learning process. The switching problem is formulated as a mixed-integer second-order cone program (MISOCP), recognized for its computational intensity making it impossible to solve in many real-world cases. Transforming the existing literature, the proposed learning algorithm is augmented with mathematical model information representing physical system constraints both during and post training stages to ensure the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasibility</i> of the rendered decisions. The findings highlight the significant potential of applying predictions from a linearized model to the MISOCP form.