## 5 Results and Analysis
### System Optimization and Comparison  
In this study, \(\eta_{\text{stor}}\) and \(c_{\text{P,tot}}\) are selected as the optimization objectives, and the liquid CO\({}_{2}\) pressure, as well as compressor and turbine isentropic efficiencies, and CO\({}_{2}\) evaporation pressure are selected as the key parameters. To obtain the system maximum \(\eta_{\text{stor}}\) and the minimum \(c_{\text{P,tot}}\) at certain weights, the NSGA-II genetic algorithm method [37] is used to optimize system key variables. The parametric boundaries are listed in Table 10, which adds terminal temperature differences in the heat exchangers to minimize the pinch point to 5 with other varied key parameters. Since the performance of the algorithm relies on the iteration times and the population size, and the mutation factor and crossover factor determine the diversity of the new generation, we have used different parameter values to compare the performances, and the final parametric settings of NSGA-II are shown in Table 11. Table 12 exhibits the algorithm optimization result. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Unit** & **Range** \\ \hline Storage pressure & MPa & 6.5–7.1 \\ Evaporation pressure of CO\({}_{2}\) & MPa & 5.0–6.0 \\ Compressor isentropic efficiency & \% & 75.0–85.0 \\ Turbine isentropic efficiency & \% & 80.0–90.0 \\ Hot terminal temperature difference in TES2 & K & 20.0–25.0 \\ Cold terminal temperature difference in TES2 & K & 25.0–30.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Variation of key parameters [54; 58]. Figure 15: Influence of \(P_{\text{evap}}\) on the system exergy performance and related component exergy loss. The calculation results of the system performance corresponding to the optimal parameters are listed in Table 13, and \(\eta_{\text{stor}}\) reaches 75.30%, while \(c_{\text{P,tot}}\) reaches USD 41.17\(\cdot\)GJ\({}^{-1}\). Figure 16 shows the Pareto frontier distribution, which is composed of non-dominated solutions. According to Figure 16, \(c_{\text{P,tot}}\) rises with the increase in \(\eta_{\text{stor}}\), meaning that a compromise exists between \(c_{\text{P,tot}}\) and \(\eta_{\text{stor}}\). The ideal point has the maximum energy storage efficiency and the minimum system unit product cost, while the non-ideal point has the minimum energy storage efficiency and the maximum system unit product cost. The optimal solution occurs at point A, from which the distance to the ideal point is minimal [44]. Table 14 gives the optimal operating parameters of eight kinds of energy storage technologies in the literature, and they can be mainly divided into five kinds, including CAES, AA-CAES, LCES, TC-CCES, and SC-CCES. Table 14 also lists some new ESSs grounded on the TC-CCES and SC-CCES technologies, including a trough solar heat storage \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Unit** & **Value** \\ \hline Storage pressure & MPa & 6.6 \\ Compressor isentropic efficiency & \% & 80.9 \\ Turbine isentropic efficiency & \% & 90.0 \\ Evaporation pressure of CO\({}_{2}\) & MPa & 5.1 \\ Hot terminal temperature difference in TES2 & K & 20.5 \\ Cold terminal temperature difference in TES2 & K & 25.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Corresponding parameters for system to achieve system optimal performance. Figure 16: Pareto frontier solution of the system energy storage efficiency with total unit product cost. trans-critical compressed CO\({}_{2}\) energy storage (STC-CCES), a trough solar heat storage supercritical compressed CO\({}_{2}\) energy storage (SSC-CCES), a trans-critical compressed CO\({}_{2}\) energy storage system combined heat pump (TCES-HP). Table 15 gives the optimization values of \(\eta_{\text{stor}}\), corresponding to the above eight energy storage technologies. It could be seen that \(\eta_{\text{stor}}\) of the proposed system is higher than that of other seven ESS technologies and close to the STC-CCES system, indicating that the proposed system has great development potential and research value.