# Thermoeconomic Analysis of Concentrated Solar Power Plants Based on Supercritical Power Cycles
## 2 Materials and Methods
### The Comparative Analysis as Function of the Receiver Configuration  
The comparative analysis is based on different receiver configurations, keeping the receiver thermal power constant. The CO\({}_{2}\) temperature at the receiver inlet and outlet as well as the CO\({}_{2}\) pressure at the receiver inlet are also constant, as well as the geometric characteristics of the compact structure inside the panel, as shown in Table 5.  
By keeping the previous characteristics constant, a comparative analysis can be conducted to evaluate the performance of the solar receiver under different number and size of the absorber panel by means of the following parameters: the energy and exergy efficiencies referred to the receiver, the solar subsystem, and the solar thermal power plant (Equations (6)-(10)). This type of analysis, including both energy and exergy efficiencies, is very useful for analysing STPPs, particularly when the working fluid in the solar receiver is a gas, and pressure drop is therefore an important factor to consider [30,31].  
\[\eta_{en,\;receiver}=\frac{\dot{Q}_{comp,CO2,\;receiver}}{\dot{Q}_{solar,receiver}} \tag{6}\]  
\[\eta_{ex,receiver}=\frac{\Delta Ex_{CO2,receiver}}{\Delta Ex_{solar,receiver}} \tag{7}\]  
\[\eta_{en,\;solar,subsystem}=\eta_{opt}\cdot\eta_{th},\;receiver \tag{8}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Global Receiver Parameters**} \\ \hline Thermal power (\(MW_{th}\)) & 103.42 \\ \hline CO\({}_{2}\) temperature at the receiver inlet (\({}^{\circ}\)C) & 494.8 \\ \hline CO\({}_{2}\) temperature at the receiver outlet (\({}^{\circ}\)C) & 700 \\ \hline CO\({}_{2}\) pressure at the receiver inlet (bar) & 55 \\ \hline \multicolumn{2}{c}{Compact structure parameters} \\ \hline Pass 1 & \\ \hline Channel dimensions (mm \(\times\) mm) & \(10\times 10\) \\ \hline Number of channel rows & 6 \\ \hline Plate thickness (mm) & 1 \\ \hline Frontal/back plate thickness (mm) & 1.5 \\ \hline Thickness between channels (mm) & 3 \\ \hline Average fluid velocity (m/s) & 15 \\ \hline Pass 2 & \\ \hline Channel Dimensions (mm \(\times\) mm) & 5 \(\times\) 5 \\ \hline Number of channel rows & 6 \\ \hline Plate thickness (mm) & 1 \\ \hline Frontal/back plate thickness (mm) & 1.5 \\ \hline Thickness between channels (mm) & 3 \\ \hline Average fluid velocity (m/s) & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Geometric and thermo-fluid dynamic parameters of the solar receiver that remain constant in the comparative analysis.  
\[\eta_{ex,\ solar\_subsystem}=\eta_{opt}\cdot\eta_{ex}\text{,\ receiver} \tag{9}\]  
\[\eta_{en,\ STPP}=\eta_{opt}\cdot\eta_{en,\ solar\_subsystem}\cdot\eta\text{ \ cycle} \tag{10}\]  
In previous equations, \(\hat{Q}_{conv,CO2,receiver}\) is the total heat gain by convection in the receiver; \(\hat{Q}_{solar,receiver}\) is the concentrated solar radiation incident on the receiver; \(\Delta Ex_{CO2,receiver}\) is the total exergy gain in the receiver; \(\Delta Ex_{solar,receiver}\) is the exergy associated to the solar radiation incident on the receiver, given by Parrot equation [32]; \(\eta_{opt}\) is the optical efficiency of the heliostat field; and \(\eta_{cycle}\) is the thermal efficiency of the sCO\({}_{2}\) cycle, equal to 48.41% in all the cases, as seen in Table 1.  
The comparative analysis will be conducted from a thermal and optical perspective in Section 3.1, while an economic analysis will be performed in Section 3.2.