Multi-Stage Distributionally Robust Scheduling With Structured Mixture Ambiguity for Hydrogen-Based Integrated Energy Systems: Finite-Sample Guarantees and Equivalent Reformulations

Hydrogen serves as a pivotal intermediary in linking renewable energy integration with diverse energy demands. This coupling introduces multiple uncertainties into the system, posing challenges for effective scheduling. This paper proposes a novel mixed-integer multi-stage distributionally robust optimization (MIMS-DRO) framework for the adaptive scheduling of hydrogen-based integrated energy systems (H-IESs) under multiple uncertainties. To accurately depict high-dimensional uncertainties stemming from uncertainty-type multiplicity and scheduling-stage proliferation, we develop an innovative structured mixture ambiguity set, which fully exploits the statistical independence structure between low-dimensional uncertainty components while encoding the feature of multi-modality, thus substantially mitigating conservatism. Based on this ambiguity set, we formulate the MIMS-DRO scheduling problem, where variables related to hydrogen-to-ammonia are treated as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">here-and-now</i> decisions for stable production while the remaining dispatch variables serve as mixed-integer recourse decisions. Subsequently, we establish theoretical set-inclusion relationships for related ambiguity sets and prove the finite-sample guarantee for the proposed framework. To efficiently solve the resulting scheduling problem, we develop a tailored solution methodology that leverages a lifted decision rule to achieve adaptive and non-anticipative scheduling, and derive an equivalent mixed-integer linear programming reformulation as opposed to the relaxed reformulation in the existing literature. Case studies demonstrate that the proposed scheduling approach is more cost-effective than the state-of-the-art methods.