Impedance-Informed and Self-Adaptive Graph Neural Networks for Short-Term Load Forecasting in Industrial Distribution Networks

Graph neural networks are often applied to load forecasting on the assumption that electrically related meter points should be modeled jointly, but this is rarely tested against a graph-free control, and building the graph usually requires a network model that is not always available. We ask whether an impedance-informed graph—estimated directly from PT/CT voltage and current, with no topology model—improves short-term load forecasting beyond what the forecasting architecture achieves alone. We compare an impedance-informed ST-GCN against binary and correlation-based graphs, a self-adaptive learned graph, a graph-free (identity-adjacency) ST-GCN control, an LSTM baseline, and a persistence baseline, at two industrial facilities (six and nine buses), using chronological splits, five seeds, and Bonferroni-corrected significance testing. The result is conditional and architecture-dependent. At one site, LSTM significantly beat every ST-GCN variant, including the graph-free control, so the shortfall is architectural, not graph-specific. At the other, every ST-GCN variant beat LSTM at the conventional level (not after Bonferroni correction), and the impedance graph gave among the lowest RMSE (20.2% below an untuned LSTM, 13.1% below a tuned LSTM); however, the graph-free control alone captured most of this gain, and impedance’s further improvement over it was not significant. Lagged cross-correlation, Granger-causality, and input-perturbation analyses corroborate this: the trained ST-GCN’s sensitivity tracks the impedance graph more closely than that of LSTM does, and a self-adaptive graph converges toward the impedance graph’s structure, with seed-to-seed variability, only where graph structure helps. Graph-based load forecasting is therefore not universally beneficial; most of its benefit traces to the sequence-modeling architecture rather than to any specific graph, and both claims should be checked against a graph-free control and corrected significance tests before deployment.