Adaptive-step-size distributed optimization of integrated energy system cluster with differentiated heat sources

To address the issues of poor operational efficiency, low renewable energy accommodation, and limited stakeholder cooperation in non-interconnected integrated energy system (IES), this paper proposes an integrated energy system cluster (IESC) architecture incorporating a hybrid storage system that combines long-duration hydrogen storage with short-duration battery storage. To fully exploit the synergistic potential among IESs, they are categorized according to heat-source temperature grades (high-grade vs. low-grade). A bi-level optimization framework is established, consisting of centralized operator dispatch at the upper level and decentralized system coordination at the lower level. The upper level optimizes storage capacity configuration by minimizing total investment cost while maximizing installed capacity, whereas the lower level minimizes each IES's total operational cost via distributed unit commitment. The bi-level model is decoupled and solved using a commercial solver for the upper level and an adaptive-step-size regularized alternating direction multiplier method (AR-ADMM) for the lower level. Simulation results demonstrate that the proposed strategy achieves superior economic performance and significantly improves renewable energy utilization.