# A Novel Hybrid CSP-PV Power Plant Based on Brayton Supercritical CO\({}_{2}\) Thermal Machines
## 2 Methodology
### Heat Engine  
A Brayton supercritical CO\({}_{2}\) power cycle has been selected for the heat engine [21], recommended by the National Renewable Energy Laboratory of the US for future concentrated solar power plants [26]. This power cycle is chosen mainly for its compactness and efficient operation at moderate temperatures. The high efficiencies achieved by S-CO2 power cycles [21] are due to the proximity of the compressor inlet to the critical point of CO\({}_{2}\) (31.1 \({}^{\circ}\)C and 73.8 bar), which reduces the work required for compression. However, that proximity can cause density variations, which can be managed by setting the compressor inlet pressure at 85 bar to strike a balance between stable operation and reduced compression energy consumption [22]. Another challenge that may arise in the compressor is the occurrence of phase-change phenomena resulting from local flow accelerations. Operating in the two-phase region can negatively impact compressor performance, causing erosion and degradation of certain components. To carefully design the main compressor while considering these challenges is crucial to prevent such issues and ensure the reliable functioning of the power cycle. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point** & **Pressure [bar]** & **Temperature [\({}^{\circ}\)C]** & **Enthalpy [kJ/kg]** \\ \hline
1 & 85.00 & 415.0 & 377.3 \\
2 & 300.0 & 604.1 & 590.8 \\
3 & 294.0 & 388.5 & 318.3 \\
4 & 90.31 & 261.4 & 199.6 \\
5 & 88.5 & 370.0 & 324.5 \\
6 & 86.73 & 599.1 & 596.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties at state points (Figure 3) of the heat pump. Figure 4: Pressure-enthalpy diagram of the heat pump. Furthermore, working close to the critical point also poses a problem in a simple recuperated Brayton cycle. The specific heat of CO2 in the low-pressure stream of the recuperator is lower than that in the high-pressure stream, resulting in an imbalanced temperature profile that prevents achieving maximum performance in the heat recovery process. This problem is commonly addressed by dividing the recuperator into two units, leading to the implementation of a re-compression cycle [21]. Based on Figure 3, which illustrates the heat engine employed in this study, the CO2 exiting the turbine (HET) absorbs thermal energy from the molten salts in the molten salt/CO2 heat exchanger (MSHE) (8-9) and transfers it to the cold stream (16-7) in the high-temperature recuperator (HTR), reaching the turbine's inlet condition. After leaving the HTR, the hot stream once again transfers thermal energy (10-11) in the low-temperature recuperator (LTR) to the cold stream (13-14). Notably, the mass flow rate of the cold stream in the LTR (high-pressure stream) is lower than that of the hot stream (low-pressure stream). This factor is crucial in recompression cycles to achieve balance in the LTR since the high-pressure stream has a higher specific heat than the low-pressure stream. The division of mass flow rate occurs at the inlet (11) of the precooler (PC). Then, the main flow undergoes cooling (11-12) and compression (12-13) in the main compressor (MC), while the remaining flow (14-15) is directly sent to the auxiliary compressor (AC). As this stream is compressed without previous cooling, it reaches an appropriate temperature to be mixed with the cold stream leaving the LTR (14-15-16), forming the cold stream that enters the HTR. The turbine's isentropic efficiency is assumed to be 92%, and an efficiency of 88% is considered for both compressors [25]. A temperature approach of 5 K is employed in the HTR and 5.5 K in the LTR. The approach temperature in the MSHE has been set to 10 K. The outlet pressure of the main compressor is set to 300 bar, with an inlet temperature of 35 \({}^{\circ}\)C and an inlet pressure of 85 bar. Pressure drops of 2% are considered for each stream of the heat exchangers [21]. Table 2 outlines the characteristics of the state points within the heat engine. To provide a visual representation of these points, Figure 5 illustrates the p-h diagram.