A two-stage Bi-level dispatch optimization framework for island-based electricity–heat–hydrogen–freshwater systems with full-spectrum solar spectral splitting

Full-spectrum solar spectral splitting enhances renewable energy utilization, offering a novel approach to ensuring reliable island energy supply. However, significant solar irradiance uncertainty, coupled with differing dynamic characteristics across the island system's electricity, heat, hydrogen and freshwater subsystems, poses challenges for stable operation. To address these challenges, this study proposes a two-stage, bi-level optimization strategy. In the first stage, we formulate a distributionally robust optimization (DRO) model by constructing a Wasserstein distance-based uncertainty set to identify the worst-case scenario. This yields a minimum-cost operational schedule designed to mitigate fluctuations induced by renewable variability. In the second stage, we develop a bi-level rolling optimization framework. The upper level performs long-term rolling optimization for heat energy supply and water storage, while the lower level executes short-term power dispatch by treating seawater desalination as a flexible load. Shared state variables facilitate interaction between levels to accommodate dynamic time-scale mismatches among heterogeneous energy carriers. Simulation results for a representative summer day demonstrate that, compared to conventional single-level optimization, the proposed two-stage, bi-level method reduces the system's generation–load imbalance by 60.11% and decreases operational costs by 4.4% relative to traditional multi-time-scale dispatch methods.