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

TL;DR

The paper addresses the slow and sometimes unstable NR-based AC Power Flow solutions in large grids by introducing a two-stage hybrid method: a physics-informed GNN (GNN-PINN) rapidly predicts an initial state, which is then refined by an iterative linear state estimation (LSE) step to enforce physical laws. The GNN is trained with a dynamic weighting PINN loss that balances data fidelity with physics residuals, and a partitioned linear refinement (LSE) provides a fast, robust path to a physically-consistent solution, bypassing non-linear NR convergence issues. Empirical evaluation on IEEE 33-, 69-, and 118-bus systems demonstrates up to 8.4e3x speedups over NR, substantial improvements in physical consistency after refinement, and strong generalization under heavy loading and N-1 contingencies; the LSE step acts as a safety net for brittle outliers and ill-conditioned cases. The approach offers a practical, real-time capable tool for grid analysis and operation, bridging data-driven speed with physics-based reliability, while noting tendencies under distribution shift and pointing to future work in sim-to-real transfer and AC-OPF extensions.

Abstract

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.

Figures (8)

• Figure 1: DeeperEdgeGNN architecture. The model uses three sequential NNConv layers without residual connections.
• Figure 2: Flowchart of the proposed hybrid GNN-LSE methodology. Stage 1 involves training the GNN-PINN to produce a fast initial prediction. Stage 2 refines this prediction using a robust, iterative linear solver to yield a physically-consistent solution.
• Figure 3: Training performance on the IEEE 33-bus system.
• Figure 4: Distribution of active power mismatches across the distribution test systems. The boxplots clearly show the significant reduction in both median error and outlier magnitude achieved by the PINN approach and LSE refinement compared to the data-only model.
• Figure 5: Distribution of active power mismatches for the IEEE 118-bus system.