## 6 Conclusions  
This paper puts forward a novel ESS based on the compressed CO\({}_{2}\) phase-change system. The system performance is calculated and analyzed first, then the parametric study is conducted and the multi-objective optimization is finally applied. The primary conclusions are below:  
1. Under the basic operation condition, the system energy storage efficiency, the unit product cost, and the system exergy efficiency can reach 71.04%, USD 40.03/GJ, and 71.21%, respectively. The optimization sequence of system components is confirmed by the \(\dot{Z}_{k}+\dot{C}_{D,k}\): the compressor, turbine, TES3, TES2, TES4, evaporator, condenser, throttle valve, TES1, cooler. For the compressor and the turbine, they have unignorable proportions in \(\dot{Z}_{k}+\dot{C}_{D,k}\) of 58.6% and 25.7%, indicating that decreasing the investment cost of the compressor and improving the isentropic efficiency of the turbine can greatly reduce the system total operation cost. 2. Increasing \(P_{\rm liq}\) and \(\eta_{\rm C}\) is conducive to improving the system energy storage efficiency, while the system unit product cost has the opposite change. For \(\eta_{\rm T}\), the system energy storage efficiency rises with its increase, and the system unit product cost demonstrates a U curve trend. When increasing \(P_{\rm evap}\), the system energy efficiency demonstrates a tendency of rising firstly and then going down, while the system unit product cost presents the reverse tendency. Referring to the above regulation, the system energy storage efficiency and the system unit product cost have a trade-off under four varied parameters. Meanwhile, increasing \(P_{\rm liq}\), \(\eta_{\rm T}\), and \(\eta_{\rm C}\) is conducive to improving the system exergy efficiency, and \(P_{\rm evap}\) has the optimal point to improve the system exergy performance. In addition, \(\eta_{\rm C}\) and \(\eta_{\rm T}\) have the most important impact on the system exergy efficiency. 3. The system energy storage efficiency and the system unit product cost can reach 75.30% and USD 41.17/GJ with optimal key parameters, respectively. Compared with the CAES (where the energy storage efficiency is 60.65%), AA-CAES (where the energy storage efficiency is 67.22%), LCES (where the energy storage efficiency is 56.64%), TC-CCES (where the energy storage efficiency is 60.69%), SC-CCES (where the energy storage efficiency is 73.02%), SSC-CCES (where the energy storage efficiency is 67.72%), STC-CCES (where the energy storage efficiency is 77.75%), and TCES-HP (where the energy storage efficiency is 66%), the phase-change energy storage system in this paper has great superiority in terms of system energy storage efficiency. The new compressed CO\({}_{2}\) phase-change energy storage system has good application prospects due to its advantages of high system energy storage efficiency, low investment and operation cost, and flexible and stable operation conditions. At present, the compressed CO\({}_{2}\) phase-change energy storage system is at the initial stage of system design and thermodynamic and exergoeconomic study. Future research work will start from further system performance analysis, such as advanced exergy analysis, design and analysis of system components, and performance analysis under off-design conditions. After the system theoretical analysis, the practical applications of the system, such as combining it with renewable power generation, will be studied. Conceptualization and investigation, S.L., D.W., D.Z. and Y.X. ; Data curation, S.L. ; Methodology, S.L. and D.W.; Writing--original draft preparation, S.L. ; Writing--Review and Editing, S.L., D.W. and D.Z. ; Resources, Y.X. ; Validation, Y.X. All authors have read and agreed to the published version of the manuscript. The work was fully supported by University Joint Program of Shaanxi Province Key Research Project-Major Project (2022 GXLH-01-17). Not applicable.