A shapley value profit allocation method for integrated energy system with hydrogen-electric hybrid vehicle aggregator via matrix semi-tensor product

The integration of hydrogen-electric hybrid vehicle (HEHV) with integrated energy systems (IES) offers a promising solution to alleviate range anxiety and support grid peak-shaving. However, the cooperative operation of multiple IESs and HEHV aggregator faces challenges in benefit allocation and renewable energy uncertainty management. This study proposes a collaborative optimization model based on cooperative game theory and matrix semi-tensor product (MSTP). First, the improved Vine Tree-based R-Vine Copula method is adopted to expand the uncertain scenario set, and an IES-HEHV cooperative game model based on the distributionally robust optimization (DRO) model is established. Second, on the basis of considering cooperation feasibility, the MSTP-improved Shapley value method is used to achieve efficient and fair benefit allocation among participants, thereby ensuring the sustainability of the alliance. Finally, simulations demonstrate that the DRO model achieves a better balance between economy and robustness, providing a feasible path and theoretical support for the operation of multi-agent integrated systems. Furthermore, compared with traditional methods, the proposed model in this paper reduces the total operating cost by 7.01% and improves the benefit allocation efficiency by 14%–34%.