Value-oriented probabilistic predict-and-optimize for stochastic scheduling of hydrogen-electric coupled microgrids

Probabilistic forecasting is increasingly used to support uncertainty-aware microgrid scheduling, but many forecasting methods are still trained for generic statistical accuracy rather than the downstream operational value of forecast errors. This mismatch becomes more severe in hydrogen-electric coupled microgrids, where hybrid storage makes the operating consequence of forecast errors strongly dependent on their source and timing. To bridge this gap, this paper proposes Cost-Sensitive Probabilistic Learning (CSPL), a value-oriented probabilistic predict-and-optimize framework for hydrogen-electric coupled microgrids under multi-source uncertainty. The novelty of CSPL lies in jointly learning a task-time importance tensor for source- and horizon-dependent operational value, constructing an importance-aware probabilistic forecasting interface with physical feasibility and dependence preservation, and using a surrogate-assisted bilevel search to keep importance learning tractable under two-stage stochastic scheduling. Experiments on the Rye microgrid show that, relative to a strong uniform-weight stochastic baseline, CSPL reduces the hindsight value-oriented prediction loss (H-VOPL) by 37.4% and the realized total cost by 4.4%, while maintaining calibration and operational reliability. These results show that, in hydrogen-electric coupled microgrids, aligning probabilistic forecasting with downstream operational value can improve scenario-based stochastic scheduling.