## 3 Methodology
### Energy Analysis  
A mass balance and energy balance are conducted for each component. The equations obtained are summarized in Table 3.  
The parameter \(SR\) indicated the split ratio. This parameter is defined as the mass flow rate circulating through the recompression compressor and the mass flow rate circulating through the turbine by Equation (5). \[SR=\frac{\dot{m}_{CO2,RC}}{\dot{m}_{CO2,T}} \tag{5}\]  
The solar to thermal efficiency of the solar block \(\eta_{SB}\) (heliostat field, central receiver and tower) is defined as the ratio between the power absorbed by the molten salts \(\dot{Q}_{HTF}\) in the receiver and the total power incident in the heliostat field \(\dot{Q}_{s}\). The thermal power absorbed by the molten salts is determined by calculating the power absorbed by the solar receiver \(\dot{Q}_{rec}\) and accounting for losses due to radiation \(\dot{Q}_{rad}\) and convection \(\dot{Q}_{con}\). \[\eta_{SB}=\frac{\dot{Q}_{HTF}}{\dot{Q}_{s}}=\frac{\dot{Q}_{rec}-\dot{Q}_{rad}- \dot{Q}_{con}}{\dot{Q}_{s}}=\alpha\eta_{hel}-\frac{Fe_{rec}\sigma\Big{(}T_{R}^ {4}-T_{sky}^{4}\Big{)}+h_{con}(T_{R}-T_{0})}{C\cdot DNI} \tag{6}\]  
where \(\alpha\) is the receiver absorptivity, \(\eta_{hel}\) is the heliostat field efficiency, \(C\) is the concentration ratio, \(\epsilon_{rec}\) is the receiver emissivity, \(\sigma\) is the Stefan-Boltzmann constant, \(F\) is the view factor, \(T_{R}\) is the receiver surface temperature, \(T_{sky}\) is the sky temperature, \(h_{con}\) is the receiver heat transfer coefficient and \(DNI\) is the direct normal irradiance [W/m\({}^{2}\)]. The surface \begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value** \\ \hline Cooling water inlet temperature & 25 \({}^{\circ}\)C \\ Cooling water outlet temperature & 35 \({}^{\circ}\)C \\ Inlet compressor temperature & 35 \({}^{\circ}\)C \\ Rated power & 10 MW \\ Effectiveness recuperator & 86\% \\ Turbine isentropic efficiency & 90\% \\ Compressor isentropic efficiency & 85\% \\ Maximum pressure & 250 bar \\ Pressure ratio & 27-3.3 \\ \hline \end{tabular}
\end{table} 
Table 2: Input parameters assumed for the energy analysis. \begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Energy Balance** \\ \hline Solar system & \(\dot{Q}_{HTF}=\eta_{SB}Q_{s}=\dot{m}_{HTF}(h_{13}-h_{14})\) \\ IHE & \(\dot{Q}_{HTF}=\dot{m}_{CO2}(h_{2}-h_{1})=\dot{m}_{HTF}(h_{13}-h_{14})\) \\ T & \(\dot{W}_{T}=\dot{m}_{CO2}(h_{2}-h_{3})\) \\ HTR & \(\dot{Q}_{HTF}=\dot{m}_{CO2}(h_{1}-h_{10})=\dot{m}_{CO2}(h_{3}-h_{4})\) \\ LTR & \(\dot{Q}_{LTR}=\dot{m}_{CO2}(h+SK)(h_{2}-h_{T})=\dot{m}_{CO2}(h_{4}-h_{5})\) \\ RC & \(\dot{W}_{RC}=\dot{m}_{CO2}SR(h_{5}-h_{9})\) \\ MC & \(\dot{W}_{AC}=\dot{m}_{CO2}(1-SR)(h_{6}-h_{7})\) \\ PC & \(\dot{Q}_{PC}=\dot{m}_{CO2}(1-SR)(h_{5}-h_{6})=\dot{m}_{w}(h_{12}-h_{11})\) \\ M & \(\dot{m}_{CO2}h_{10}=\dot{m}_{CO2}(1-SR)h_{8}+\dot{m}_{CO2}SRh_{9}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Energy balance equations for each component. temperature of the receiver is calculated from the transfer coefficient from the receiver surface to HTF [19]. The sky temperature \(T_{\rm sky}\) is calculated using the equation provided by [24]. Equation (6) is derived from the model proposed by reference [19]. Table 4 provides the value of the different parameters required to calculated the solar to thermal efficiency of the solar block using the Equation (6). The input parameters assumed for the calculation of the solar to thermal efficiency of the solar block are summarized in Table 4. These values are obtained from the reference [19]. The thermal efficiency of the cycle power is defined as the ratio between the net power produced and the thermal power absorbed by the cycle (Equation (7)). \[\eta_{PB}=\frac{\dot{W}_{N}}{Q_{HTF}} \tag{7}\]  
The overall thermal efficiency of the systems is defined as the ratio of the net power and the incident power of the heliostat field.