Cooperative robust optimization of hydrogen integrated energy systems for economic dispatch under uncertainty with bidirectional power conversion and progressive stepwise carbon emission trading mechanisms

This study presents a novel cooperative optimization paradigm for hydrogen-integrated multi-energy systems that addresses prevailing gaps in decarbonized energy dispatch under uncertainty. Leveraging a cooperative approach, the proposed framework enables the coordinated scheduling and mutual interaction among electricity, hydrogen, heat, and gas subsystems to optimize system-wide performance. By integrating a bidirectional hydrogen conversion model with a progressive step-based carbon trading mechanism, the cooperative structure enhances flexibility, resilience, and economic feasibility. Unlike traditional robust or stochastic models, a two-stage robust optimization (TSRO) approach is employed to capture both worst-case volatility and adaptive decision-making in real-time cooperative operations. The model introduces an innovative energy architecture that includes power-to-hydrogen, hydrogen-to-power, and hydrogen energy storage modules, thereby overcoming the limitations of conventional unidirectional hydrogen strategies. Empirical simulations benchmark the performance of four operational scenarios and demonstrate that the cooperative TSRO-based model with hydrogen integration and carbon trading reduces total cost by 12.8 % and carbon emissions by 13.6 % compared to conventional deterministic approaches. Furthermore, comparative analysis with stochastic and classic robust models highlights the superior trade-off achieved by the cooperative TSRO in balancing reliability, sustainability, and operational cost. This work contributes a methodologically distinct and practically scalable solution to real-world energy planning under uncertainty, with implications for future carbon-neutral urban systems. The framework's adaptability to broader uncertainties, including wind fluctuations, is also proposed as a direction for future expansion.