GRAPH NEURAL NETWORKS FOR POWER FLOW APPROXIMATION ON DISTRIBUTION GRIDS

Abstract

Context. The growing integration of distributed energy resources (DERs) into power distribution networks demands fast and accurate power flow (PF) analysis for real-time monitoring, state estimation, and optimal dispatch. The Newton-Raphson (NR) method, while robust, becomes computationally expensive when invoked repeatedly in optimization loops and probabilistic analyses. Graph neural networks (GNNs) have emerged as promising surrogate models, yet existing benchmarks focus exclusively on IEEE transmission test cases with fewer than 300 buses. Distribution networks – characterized by radial topologies, high R/X ratios, and heterogeneous load profiles – remain largely unexplored.Objective. The goal of this work is to systematically evaluate four GNN architectures (GCN, GAT, GraphSAGE, MPNN) and an MLP baseline for AC power flow approximation on medium-voltage (MV) and low-voltage (LV) distribution networks, quantifying the value of graph-based message passing and identifying the topological factors that govern prediction accuracy.Method. Five architectures are benchmarked on ten SimBench distribution grids (15–144 buses, rural to commercial topologies). For each grid, power flow scenarios with ±30% load variation are solved using Newton-Raphson. All models share identical hyperparameters and three random seeds (150 experiments total). Metrics: mean absolute error for voltage magnitude and angle, and inference speedup.Results. All GNNs reduce voltage magnitude error by 62–75% over the topology-agnostic MLP. GraphSAGE achieves the best speed-accuracy trade-off (22× speedup). LV grids are significantly harder than MV (Mann-Whitney p = 0.002), with error correlated to network diameter and bridge fraction. MPNN underperforms with 2 layers but reaches competitive accuracy with 4 layers.Conclusions. For the first time, a systematic GNN benchmark for distribution-level power flow is presented, demonstrating thatgraph structure reduces prediction error by 62–75% over a topology-agnostic baseline. A statistically significant MV/LV performance gap is identified and traced to network diameter and bridge fraction, revealing a fundamental limitation of shallow GNNs on radial networks. GraphSAGE is recommended as the default architecture for real-time applications