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• Design a hydrogen energy storage system-carbon capture and utilization system-based micro energy grid. • Proposed a carbon emission-green certificate equivalent interaction mechanism for multi-energy conversion and storage system. • Construct a two-stage optimal dispatching framework including day-ahead robust dispatching model and real-time rolling model. • Proposed an entropy-Shapley-based benefit allocation method considering multi-dimension impact factors. • Carried out the effectiveness and applicability analysis for the proposed dispatching scheme and benefit allocation strategy. To fully utilize the abundant renewable energy resources in county-level areas of China, this paper designs a novel structure of micro-energy grid integrating hydrogen energy storage (HES) system and carbon capture and utilization (CCU) system (HES-CCU-based MEG). And a carbon emission-green certificate equivalent interaction mechanism is established. Then, a two-stage optimal dispatching framework is proposed for mitigating the impact of uncertainty variables, including a day-ahead robust dispatching model and a real-time rolling optimization model. Thirdly, an entropy-Shapley-based benefit allocation method is constructed to allocate the benefits in dimensions of energy conservation, carbon emission reduction, and renewable power consumption among various devices. Finally, a micro-energy grid in Henan province, China, is selected as an example for case study. The results show that: (1) HES could transfer surplus renewable power and low-priced power to periods with high power prices, while CCU could achieves the cycle and utilization of CO 2 , leading to a decrease in power purchase costs and carbon emissions by 7.85% and 0.47%, respectively. (2) The two-stage optimal dispatching model gives full play to the flexibility adjustment ability of each device, mitigates the deviations caused by uncertainty variables, and formulates the optimal dispatching strategy. (3) The entropy-Shapley-based benefit allocation method could evaluate the contributions of each device in different dimensions, effectively, ensuring the rationality of benefit allocation results. Overall, the proposed model and method could utilize renewable energy resources in county-level areas, which is better to promote the clean and low-carbon transformation of the overall energy structure. [ABSTRACT FROM AUTHOR]