Multi-Time-Scale Distributionally Robust Dispatch of Hydrogen-Based Integrated Energy System Based on Wasserstein Distance

To address the coordinated economic, low-carbon, and robust operation problem caused by source–load forecast uncertainty in hydrogen-based integrated energy systems, this paper proposes a multi-time-scale distributionally robust scheduling framework based on the Wasserstein distance. First, a hydrogen-based polygeneration model is established by coordinating an electrolyzer, a hydrogen storage tank, a methanation reactor, and a hydrogen fuel cell. A dual-heat-source organic Rankine cycle is further introduced to recover waste heat from the microturbine and hydrogen fuel cell, thereby strengthening the coupling among electricity, heat, gas, and hydrogen. Second, a source–load coordination mechanism is developed by integrating pre-contracted stepped demand response with output-based carbon allocation and stepped carbon trading. On this basis, a two-stage day-ahead Wasserstein distributionally robust optimization model is formulated to account for joint wind-power and multi-energy-load forecast errors, while 15 min intraday and 5 min real-time rolling optimization are used to correct scheduling deviations. Finally, mechanism-ablation, physical-feasibility, uncertainty-handling, and parameter-sensitivity studies are conducted. The results show that M-5 reduces the total operating cost and net carbon emissions by 13.66% and 23.87%, respectively, relative to M-1, while reducing the wind-curtailment rate from 16.43% to zero. Among the tested uncertainty-handling methods, W-DRO achieves the lowest held-out total cost with a 3% shortfall rate, and the lowest-cost range is obtained for Wasserstein radii of 0.02–0.05. These results demonstrate that the proposed framework provides a favorable case-specific trade-off among economic performance, carbon reduction, renewable-energy accommodation, and operational robustness.