Probabilistic Residual Load Modelling with Spatio-Temporal Graph Neural Networks and Mondrian Conformal Calibration

Accurate probabilistic load forecasting (PLF) is critical for grid security under increasing renewable-driven volatility. However, achieving both computational efficiency and well-calibrated nodal uncertainty remains challenging for spatio-
temporal PLF models. This paper introduces a lightweight hybrid framework that models load residuals relative to operational day-ahead forecasts. We employ a frozen, reservoir-style spatio-temporal graph neural network (STGNN) to extract topological embeddings, which serve as context for an XGBoost-based quantile
regressor. These predictions are further calibrated using Mondrian conformalized quantile regression (M-CQR) to target reliable coverage across node–horizon segments. Evaluated on a 12-country ENTSO-E system, the proposed framework outperforms competing baselines at the operationally critical 1-hour and 24-hour horizons, while remaining competitive at intermediate horizons. Ablation results show that the frozen encoder matches or
exceeds the accuracy of fully trained alternatives while achieving
an ∼82× reduction in training time. Furthermore, the M-CQR calibration enables the identification of localized risks that aggregate calibration metrics may obscure. The resulting sharp and well-calibrated prediction intervals offer a computationally efficient and reliable solution for risk-aware decision support in
real-world grid operations.