Distributionally Robust Optimal Scheduling With Heterogeneous Uncertainty Information: A Framework for Hydrogen Systems

Distributionally robust optimization (DRO) has emerged as a favored methodology for addressing the uncertainties stemming from renewable energy sources. However, existing DRO frameworks primarily focus on single types of uncertainty characteristics, such as moments. Exploring novel ambiguity sets that encompass heterogeneous uncertainty information to mitigate decision conservatism is thus an essential and strategic move. This paper introduces a day-ahead optimal scheduling model tailored for electricity-hydrogen systems under renewable uncertainty, with embedded technologies of hydrogen production, storage, and utilization. Three novel ambiguity sets enriched with the moment, Wasserstein distance, and unimodality information are adeptly devised. Building upon these elaborated ambiguity sets, we develop efficient and scalable reformulations of the expected objective function and uncertain constraints, leading to either a tractable mixed-integer second-order cone programming problem or a linear programming problem. We validate the effectiveness and operating flexibility of the proposed electricity-hydrogen model using both a 6-bus test system and the IEEE 118-bus test system. Furthermore, we demonstrate the superior cost performance and computational efficiency of our developed DRO approaches.