Comprehensive performance analysis of a trans-critical CO₂ energy storage system with coupled flexible cold energy storage regulation based on entransy analysis

In recent years, trans-critical compressed CO₂ energy storage technology has garnered significant attention due to its potential for large-scale, high-density electrical energy storage without geographical or environmental constraints. As a critical component in trans-critical compressed CO₂ energy storage systems, the cold energy storage unit significantly impacts energy storage efficiency and density. Compared with extensive research on thermal storage units, current studies of cold energy storage remain limited to lumped parameter modeling, lacking comprehensive dynamic thermodynamic evolution mechanisms and systematic optimization strategies. This paper therefore presents a novel trans-critical compressed CO₂ energy storage system incorporating indirect heat exchange with coupled stepped phase change cold energy storage, based on stepped phase change structure optimization. The developed one-dimensional unsteady-state cold energy storage model demonstrates less than 6% deviation from experimental data. Using this validated model, 4E performance analysis (energy, exergy, entransy, and economic) is conducted for the stepped phase change cold energy storage unit. And an entransy-based evaluation methodology is proposed, incorporating quantitative metrics including transient thermal resistance and root-mean-square temperature. This study conducts thermodynamic performance analysis of the cold energy storage unit and the entire operational process of the energy storage system, revealing the optimization potential of the cold energy storage unit within the system. The results demonstrate that the stepped phase change cold energy storage unit achieves transient thermal resistances of only 20% and 13% of single-stage phase change cold energy storage units during charging/discharging processes. The optimized cascade configuration reduces cold energy storage unit costs by 55% while maintaining equivalent energy storage capacity. When the phase change stages increase from N=2 to N=10, cold energy storage capacity grows by 28%, accompanied by system efficiency enhancement from 43.35% to 63.61%. Multi-objective optimization demonstrated that the proposed trans-critical compressed CO₂ energy storage system achieves an optimal efficiency of 66.94%, with an investment cost per output power (ICPP) of 0.2258 $/kWh.