A Hybrid GNN-LSE Method for Fast, Robust, and Physically-Consistent AC Power Flow

Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a Physics-Informed Graph Neural Network (GNN) with a robust, iterative Linear State Estimation (LSE) refinement step to produce fast and physically-consistent solutions. The GNN, trained with a physics-informed loss function featuring an efficient dynamic weighting scheme, rapidly predicts a high-quality initial system state. This prediction is then refined using an iterative, direct linear solver inspired by state estimation techniques. This LSE refinement step solves a series of linear equations to enforce physical laws, effectively bypassing the non-linearities and convergence issues of traditional solvers. The proposed GNN-LSE framework is comprehensively validated on systems ranging from small radial distribution networks (IEEE 33-bus, 69-bus) to a large, meshed transmission system (IEEE 118-bus). Results show that our GNN variants are up to $8.4 \times 10^3$ times faster than NR. The LSE refinement provides a fast route to a physically-consistent solution, while heavy-loading stress tests (120%-150% of nominal) and N-1 contingencies demonstrate the method's reliability and generalization. This work presents a powerful and flexible framework for bridging fast, data-driven models with the rigorous constraints of power system physics, offering a practical tool for real-time operations and analysis.