Scaling Graph Neural Networks for Large-Scale Power Systems Analysis: Empirical Laws for Emergent Abilities

The scale-up of AI models for analyzing large-scale power systems necessitates a thorough understanding of their scaling properties. Existing studies on these properties provide only partial insights, showing predictable decreases in loss function with increased model scales; yet no scaling law for power system AI models has been established, resulting in unpredictable performance. This letter introduces and explores the concept of "emergent abilities" in graph neural networks (GNN) used for analyzing large-scale power systems-a phenomenon where model performance improves dramatically once its scale exceeds a threshold. We further introduce an empirical power-law formula to quantify the relationship between this threshold and the power system size. Our theory precisely predicts the threshold for the emergence of these abilities in large-scale power systems, including both a synthetic 10,000-bus and a real-world 19,402-bus system.