Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow

We present PINCO, an unsupervised learning framework that integrates Graph Neural Networks with physics-informed neural networks for AC optimal power flow (AC-OPF) solutions. Unlike state-of-the-art unsupervised methods that require prescreened datasets containing only feasible instances, our approach operates on unfiltered data, including ill-conditioned cases. The framework addresses two critical gaps in the literature: (1) robustness to topology changes up to N-2 contingencies, and (2) detecting optimal power flow instances that are infeasible without relying on traditional solvers for data filtering. PINCO embeds physical laws into the learning process via augmented Lagrangian multipliers. In addition, it introduces a clustering branch with learnable centroids that automatically separate feasible from infeasible solutions based on constraint-violation patterns. We evaluate the framework across systems of varying complexity, including the IEEE 30-bus, IEEE 57-bus, and Swiss transmission networks, demonstrating scalability and robustness under diverse loading conditions and topology variations. Benchmarking against DeepOPF-FT and the IPOPT solver shows that PINCO achieves comparable constraint satisfaction while delivering two to three orders of magnitude computational speedup compared to IPOPT and lower operational costs across all configurations.