Modularity-guided physics-informed heterogeneous graph neural network for power flow prediction

High penetration of renewable energy and dynami=c topology variations demand fast, accurate, and topology-adaptive power-flow (PF) prediction. Traditional iterative PF methods are computationally expensive and may have convergence difficulties under repeated scenario evaluation or topology changes. Purely data-driven models often fail to capture topological heterogeneity and physical constraints, which limits generalization and physical consistency. This study proposes PI-HeteroGNN, a modularity-guided physics-informed heterogeneous graph neural network for PF prediction. It models loads, generators, composite nodes, and slack buses as distinct node types; encodes branch conductance and susceptance as relation-dependent edge features; and introduces modularity Q mod to represent community structure and regional coupling. AC PF residuals are incorporated during training to promote nodal active- and reactive-power balance. Experiments on the IEEE 118-bus system and subgraphs show that, relative to GINE, PI-HeteroGNN reduces full-system MAEs by 5.7%, 6.2%, 6.2%, and 5.7% for load-bus voltage angle, load-bus voltage magnitude, generator-bus reactive power, and generator-bus voltage angle, respectively. After removal of ten lines, it retains a mean error of 0.947% and a 95th-percentile error of 1.883%, representing reductions of 10.2% and 10.8% relative to GINE. These results demonstrate improved accuracy, physical consistency, and topology generalization for the evaluated PF prediction tasks.