Abstract
Accurate multi-node renewable energy forecasting is increasingly critical as national grids approach high renewable penetration, yet the spatial correlation structure that governs forecast accuracy changes continuously with meteorological conditions—a non-stationarity that deployed models systematically ignore. The consequence is that existing spatio-temporal graph neural network (ST-GNN) architectures fail most severely during precisely those high-variability events that are most consequential for spinning-reserve procurement and grid stability. This paper addresses this structural limitation analytically rather than empirically, advancing three formally proved contributions: (i) a model-class impossibility result establishing that any node-local estimator incurs irreducible spatial bias growing with the spatial scale of the driving meteorological event, providing a theoretical rather than empirical basis for graph-based forecasting; (ii) a theorem establishing the precise condition under which dynamic adjacency strictly dominates static adjacency in expected forecast loss, together with a robustness extension under approximate sufficient statistics; (iii) a convergence result for per-head blending coefficients under explicit, empirically checkable conditions. No model has been trained or evaluated on any dataset. The formal conditions derived here provide a basis for determining, from reanalysis data alone and without training any model, whether dynamic graph adaptation is warranted for a given renewable corridor—a diagnostic applicable to grid operators evaluating the overhead of inference-time adjacency modulation.