## 5 Conclusions  
In this paper, a preliminary analysis and systematic comparison of three S-CO\({}_{2}\) power generation cycles using solar energy by the parabolic trough solar collector are studied. Firstly, the effects of the turbine inlet temperature and pressure, compressor inlet temperature and pressure on specific work, overall efficiency, and cost of core equipment of S-CO\({}_{2}\) Brayton cycles are discussed. After that, multi-objective optimizations are studied, taking the specific work and the cost of core equipment as the objectives. The optimized Pareto sets obtained through multi-objective optimizations are used to compare different cycle layouts. The main conclusion follows:  
1. It results in an optimal specific work ranging between 30 and 70 kW/kg, and optimal cost of core equipment ranging between $155,000 and $210,000 USD for the simple recuperated cycle. The values of the optimization objectives extend between 27 and 65 kW/kg for specific work and between $255,000 and $365,000 USD for cost of core equipment in the intercooling cycle. Moreover, the values of the optimization objectives extend between 25 and 50 kW/kg for specific work and from $270,000 and $370,000 USD for cost of core equipment in the recompression cycle. 2. The simple recuperation cycle layout shows more excellent performance than the intercooling cycle layout and the recompression cycle layout in terms of cost, while the advantage in specific work of the intercooling cycle layout and the recompression cycle layout is not obvious. 3. The sensitivity analysis of a typical optimization result of a simple regeneration cycle shows that the change of parameters have little influence on the cost of core equipment and much influence on specific work. 4. Through this study, it can be found that the turbine inlet temperature is low using a parabolic trough solar collector, and the complex SCO\({}_{2}\) Brayton cycles are not dominant. 5. The preliminary analysis and systematic comparison in this study can be useful in selecting cycle layout using solar energy by a parabolic trough solar collector when there are requirements for \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables** & **Value** &
\begin{tabular}{c} **Cost of Core** \\ **Equipment/k5** \\ \end{tabular} & **Specific Work/kW\(\cdot\)kg\({}^{-1}\)** \\ \hline \multirow{2}{*}{Turbine inlet temperature} & 363.62 \({}^{\circ}\)C & 182.33(-0.90\%) & 48.36(-4.60\%) \\  & 401.90 \({}^{\circ}\)C & 185.57(+0.86\%) & 53.00(4.56\%) \\ \hline \multirow{2}{*}{Turbine inlet pressure} & 16.29 MPa & 179.40(-2.49\%) & 47.42(-6.45\%) \\  & 18.00 MPa & 188.16(+2.27\%) & 53.64(+5.82\%) \\ \hline \multirow{2}{*}{Compressor inlet pressure} & 8.38 MPa & 188.54(+2.48\%) & 54.19(+6.90\%) \\  & 9.26 MPa & 179.38(-2.50\%) & 47.29(-6.71\%) \\ \hline \multirow{2}{*}{Isentropic efficiency of turbine} & 80.75\% & 182.77(-0.65\%) & 47.45(-6.39\%) \\  & 89.25\% & 185.17(+0.64\%) & 53.93(+6.39\%) \\ \hline \multirow{2}{*}{Isentropic efficiency of compressor} & 76\% & 185.30(+0.72\%) & 49.95(-1.46\%) \\  & 84\% & 182.71(-0.69\%) & 51.37(+1.34\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sensitivity analysis results. the specific work and the cost of core equipment. Moreover, it can also provide reference for the comparison and selection of other cycle types. In future studies, a comprehensive analysis of investments profitability based on more accurate cost accounting methods will obtain more practical system comparison results. For components, improving the manufacturing level of turbine machinery and reducing its cost will make the S-CO\({}_{2}\) power generation cycles more competitive. Conceptualization, L.S. and Y.X. ; investigation, L.S. and Y.W. ; methodology, L.S. and D.W.; resources, Y.X. ; software, L.S., and Y.X. ; supervision, L.S. and D.W.; validation L.S. and Y.W. ; writing--original draft preparation, L.S. and Y.W. ; writing--review and editing, L.S. and Y.X.