Empirical Assessment of Graph Neural Network Convolution Operators for AC-OPF Learning

The AC Optimal Power Flow (AC-OPF) problem plays a crucial role in optimizing power generation dispatch to meet customer demand and also serves as a foundation for several downstream applications. However, the complexity and non-convex nature of the problem makes it a challenge for traditional physics-based methods to solve the AC-OPF problem in a timely manner. Machine learning models, particularly Graph Neural Networks (GNNs), have emerged as a promising solution, demonstrating superior performance across varying electricity transmission network topologies. Despite the availability of many GNN convolution operators, there is limited research comparing their effectiveness in solving the AC-OPF problem. This paper conducts an empirical evaluation of seven homogeneous GNN convolution operators, spanning a variety of graph data processing techniques. The operators are compared on the basis of losses (mean squared error and constraint violation loss), convergence rate, and computational cost (training time). The findings reveal that GINConv strikes the best balance between losses and computational cost, while the inclusion of edge features in the convolution operation generally improves model convergence behavior.