Probabilistic Forecasting of Multi-Energy Loads in Integrated Energy Systems via Condition-Aware Dynamic Coupling Routing and Conformal Quantile Calibration

Abstract

Accurate probabilistic forecasting of multi-energy loads is essential for risk-aware dispatch in integrated energy systems (IES), yet existing methods rely on static task-sharing structures, decouple long-term dependency modeling from cross-task interaction, and produce probabilistic outputs with limited structural regularity and calibration stability. This paper proposes DCR-PatchTST-CQ, a unified multi-task probabilistic forecasting framework. A patch-based backbone encodes long input windows while preserving local temporal structure; an operating-condition-aware dynamic coupling routing module adaptively regulates cross-task information flow according to the operating state and forecast horizon; and a calibrated quantile head integrates monotonicity constraints, reliability regularization, and task- and horizon-wise conformal calibration to jointly improve quantile ordering, interval sharpness, and coverage reliability. The framework is evaluated on a four-year IES dataset from Arizona State University’s Tempe campus (2020–2023), with all results averaged over five random seeds. Relative to the strongest baseline for each metric, DCR-PatchTST-CQ attains the lowest point-forecasting error, reducing the cooling-load MAE, RMSE, and MAPE by 4.9%, 9.5%, and 20.6% and the electrical-load MAE and RMSE by 7.5% and 9.9%; the largest gain reflects the dominant electricity–cooling coupling under a desert climate. After conformal calibration, the empirical coverage of all three loads approaches the 90% nominal level while the intervals remain sharper, reducing the normalized weighted interval score (nWIS) by 12.9%–27.3%. Paired tests confirm that the nWIS reductions are statistically significant for all three loads. Condition-aware dynamic routing combined with stratified conformal calibration is therefore promising for probabilistic multi-energy load forecasting in campus-scale IES.