Coordinated sizing and operation of wind-solar-hydrogen system: Coupling stack-level dispatch and state machine with IMOPSO

This study develops a coordinated sizing-operation framework integrating proton exchange membrane stack-level dispatch, a dwell-time state machine, and improved multi-objective particle swarm optimization (IMOPSO). Embedding stack-level logic into candidate evaluation links equipment protection with system-level techno-economic optimization. When capacities were optimized separately for each strategy, the proposed strategy achieved the lowest capital expenditure, levelized cost of electricity, and levelized cost of hydrogen, at 107.42 million CNY, 0.67 CNY/kWh, and 14.08 CNY/kg, respectively. It also suppressed cold starts while maintaining stack utilization, balancing operational performance and degradation-related switching protection. Across ten paired runs, IMOPSO increased mean hypervolume by 0.59% and reduced mean inverted generational distance by 22.07% relative to its conventional counterpart. The battery and hydrogen storage showed dominant variation periods of 12 and 84 h, respectively. These results confirm that the battery primarily buffers short-term and intraday power fluctuations, whereas the hydrogen pathway supports slower cross-day energy shifting.