Learning scheduling-relevant joint uncertainty: Decision-aware compound-risk forecasting for microgrid dispatch

This paper studies joint probabilistic forecasting for renewable-rich microgrid scheduling, where costly operating outcomes are often caused by simultaneous high load and low renewable generation rather than by a large error in any single variable. The main challenge is to preserve calibrated load, wind, and PV marginals while assigning appropriate probability mass to the joint tail states that matter for dispatch. We propose a Compound-Risk End-to-End (CoRisk-E2E) framework that combines physically feasible marginal forecasting, conditional rank-diffusion scenario generation, compound-stress supervision, and decision-aware training. It preserves non-crossing marginals, captures temporal and cross-variable dependence, and emphasizes high-load and low-renewable conditions through progressive training with a continuous scheduling surrogate. The differentiable scheduling surrogate is used only for training, while all reported operating results are evaluated with the original exact two-stage CVaR MILP. The framework is evaluated in three data settings: the complete Rye load–wind–PV microgrid benchmark, a reduced IEEE load–PV case, and a public load–wind–solar transfer case. The results show that CoRisk-E2E improves joint-tail representation and exact-MILP operating performance, although NoDecision remains competitive on marginal and global scenario metrics. The operational benefit persists in the reduced-source case and the mapped transfer setting under the fixed Rye scheduler, but decreases with stronger domain shift. These findings indicate that explicitly learning scheduling-critical joint tails can improve microgrid decisions, while broader validation on additional complete microgrid systems remains necessary.