Abstract

This paper explores the application of Graph Neural Networks (GNNs) to power flow problems, comparing several spectral and spatial methods. The research reveals that spatial methods generally outperform their spectral counterparts, which do not rely on spectral theory, eigenvalues, or eigenvectors. GraphSAGE [9] demonstrates the best performance among the spatial methods tested, achieving a Mean Absolute Percentage Error (MAPE) of 0.79% on the test set in an experiment with 14-buses and 0.53% in the experiment with 30-buses. These findings suggest that for power flow problems, it is beneficial to consider at least hybrid or predominantly spatial models that leverage information from non-immediate neighbors. This research highlights the potential of spatial GNN methods in accurately capturing the complexities of power systems, paving the way for more robust and efficient solutions in the domain. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.