Benchmarking Graph Neural Networks for AC Power Flow: The Role of Inductive Biases and Physical Constraints

Fast and accurate models for AC power flow (ACPF) are increasingly important as modern electrical grids require more frequent system analyses. Graph neural networks (GNNs) naturally exploit electrical grid topology, yet the effects of architectural design choices on predictive performance remain poorly understood given differences in graph representations and evaluation settings across studies. We present a unified benchmark of representative GNN architectures for ACPF prediction under a common experimental framework. All models use identical preprocessing and training procedures and comparable parameter budgets, isolating the impact of message-passing mechanisms and inductive biases. We also analyze errors by distance from the slack bus and systematically ablate key design components. We evaluate predictive accuracy and physical consistency on the IEEE 14-bus and IEEE 118-bus systems. Results indicate that anisotropic message-passing architectures offer the most favorable trade-off between predictive accuracy and physical consistency under the studied parameter and topology constraints. Explicit edge features encoding line impedances and global context aggregation are particularly important for representing electrical interactions and system-wide dependencies, especially for voltage-angle predictions on the topologically bottlenecked IEEE-118 grid. Under a budget with approximately fixed parameters, two or three message-passing layers generally provide the best balance between depth and representation width, while additional depth offers no consistent improvement. Ablations also show that standard residual and root connections are not necessarily beneficial in shallow models, and that aggregation operators involve trade-offs between statistical accuracy and physical consistency. These results provide practical guidelines for designing graph-based power system models.