The drive toward achieving carbon peaking and carbon neutrality has significantly accelerated the deployment of renewable energy technologies. Electrical energy storage provides an effective solution to enhance wind penetration. Furthermore, an energy management strategy is essential for optimizing the energy storage system. In this paper, we propose a hybrid energy storage system that combines a compressed carbon dioxide energy storage system with a power-to-gas device, and we introduce a new energy management strategy. Firstly, a comparison is made between the proposed strategy and two alternative strategies through system volume optimization. Subsequently, three additional cases are analyzed to validate the consistency of the results. A sensitivity analysis is then conducted. The comparison results indicate that the levelized cost of electricity (LCOE) for the new energy management strategy is reduced by 25.63% and 24.49% compared to the other two strategies. Furthermore, the new energy management strategy outperformed the other three cases, reinforcing the consistency of the comparison results. The sensitivity analysis suggests that a lower cost of polymer electrolyte membrane electrolyzer (PEME) leads to higher PEME design power and a lower LCOE. Additionally, an increase in prediction time results in reduced wind curtailment energy, lower total cost, and a decreased LCOE. Conversely, a lower energy threshold results in higher instances of insufficient energy, increased total cost, and a higher LCOE.