# A Novel Hybrid CSP-PV Power Plant Based on Brayton Supercritical CO\({}_{2}\) Thermal Machines
## 3 Results  
Equations (12) and (13) provide the expression for the efficiency (\(\eta_{HE}\)) of the heat engine and the \(COP\) of the heat pump, respectively. The subscripts in these equations correspond to the same acronyms used for the cycle components. The ratio between the mass flow rate of the main compressor and the turbine of the heat engine is determined to be 0.6772, derived from the LTR balance (same terminal temperature difference at both extremes). It is important to note that the product of the heat engine efficiency and the coefficient of performance (Equation (14)) represents the ratio of energy production to the energy input from the PV field. This value is slightly greater than 1. This result allows considering the proposed plant as a PV field with storage with certain gain [39]. In the design of the proposed plant, a pressure drop of 2% has been considered in each heat exchanger stream, in order to limit its size. If a lower pressure drop had been chosen, the ratio defined by Equation (14) would have been greater [39]. Thus, the recovery of the PV power supplied to the heat pump is possible with the chosen technology. \[\eta_{HE}=\frac{W_{GEN}}{Q_{MSHE}}=\frac{(h_{7}-h_{8})-\left(\frac{\dot{m}_{MC}}{ m_{HET}}\right)\cdot(h_{13}-h_{12})-\left(\frac{\dot{m}_{AC}}{m_{HET}}\right) \cdot(h_{15}-h_{11})}{h_{9}-h_{8}}=44.4\% \tag{12}\]  
\[COP=\frac{Q_{MSHP}}{W_{MOT}}=\frac{h_{6}-h_{1}}{(h_{2}-h_{1})-(h_{3}-h_{4})}=2.32 \tag{13}\]  
\[\eta_{HE}\cdot COP=\frac{W_{GEN}}{W_{MOT}}=1.03 \tag{14}\]  
The energy balance of the plant is presented in Tables 5 and 6. The sizing of the solar field, with a capacity of 128 MWth, is based on the dimensions of existing CSP plants in Spain that utilize parabolic trough collectors without storage [19]. As a reference, these plants produce 50 MWe. To ensure the ability to evacuate a portion of the power during production while storing the remainder for later use, the MSHE heat exchanger has been designed to be half the size of the MSHP. Thus, half of the thermal energy discharged by the heat pump is stored in the molten salt tanks. However, for the sake of flexibility, the storage capacity of the tanks has been doubled, being able to store all the heat discharged by the heat pump. This configuration enables the plant to prevent the risk of curtailments. Figures 6 and 7 compare the performance of conventional hybrid CSP-PV plant with a novel hybrid design under two scenarios: design energy storage (a) and maximum storage (b). To ensure a valid comparison, the sizes of the PV and PTC fields are identical in both cases, determined based on the configuration of the novel design. To simplify the analysis, a solar radiation period of 6 equivalent hours has been assumed. In Figure 6a, the conventional hybrid CSP-PV plant produces 97 MW of power from the PV field and stores 128 MW of thermal energy from the PTC field during the 6 h of radiation. Subsequently, in the next 6 h, 50 MW of power is produced through the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Component**} & **Heat Duty or Power** & **Mass Flow Rate** \\  & **[MW]** & **[kg/s]** \\ \hline Main Compressor (MC) & 12 & 349 \\ Auxiliary Compressor (AC) & 14 & 167 \\ Turbine (HET) & 76 & 516 \\ Generator (GEN) & 50 & — \\ CO\({}_{2}\)/CO\({}_{2}\) (HTR) & 226 & 516/516 \\ CO\({}_{2}\)/CO\({}_{2}\) (LTR) & 779 & 516/349 \\ Molten salts/CO\({}_{2}\) (MSHE) & 113 & 399/516 \\ CO\({}_{2}\)/Water (PC) & 63 & 349/2995 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Energy balance at the design point of the heat engine (Figure 2). In the heat exchangers, the hot stream is designed in the first place.