# A Novel Hybrid CSP-PV Power Plant Based on Brayton Supercritical CO\({}_{2}\) Thermal Machines
## 2 Methodology  
### Concept  
In countries with a high share of intermittent renewable energies (wind and PV), curtailments often occur during hours of solar radiation. Therefore, it is interesting to analyse the scenario where all PV production is stored, considering both conventional and novel hybrid configurations. Equation (1) represents the energy balance in the storage system. It can be applied to both configurations, where \(Q\) stands for thermal energy, \(W\) represents power, and subscripts \(PV\), \(SF\), and \(TES\) denote photovoltaic, solar field, and thermal energy stored, respectively. For the conventional configuration, Equation (2) describes the exergy balance in the storage system, while Equation (3) corresponds to the novel system including the heat pump in the control volume. In these equations, \(T\) stands for the average entropic temperature [20] of thermal sources or reservoirs, and \(I\) represents exergy destroyed or irreversibility. The subscript 0 refers to the ambient state (dead state), _conv_ means conventional, and _nov_ means novel. Comparing Equations (3) and (2) reveals that the novel plant supplies more exergy to the heat engine. This is due to the fact that in the conventional case, the stored energy matches the PTC solar field temperature (380 \({}^{\circ}\)C/290 \({}^{\circ}\)C), whereas in the novel case, it corresponds to a central tower receiver temperature level (589 \({}^{\circ}\)C/405 \({}^{\circ}\)C) [19], thanks to the heat pump effect. In other words, the stored energy temperature in the conventional case is the same as the solar field temperature. By combining Equations (2) and (3), Equation (4) is obtained, where \(COP\) represents the coefficient of performance of the heat pump, and \(COP_{max}\) denotes its maximum value, assuming that all processes are totally reversible (Equation (5)). Equation (4) reveals the lower exergy destruction in the heat pump compared to the Joule effect, which is always irreversible. \[W_{PV}+Q_{SF}=Q_{TES} \tag{1}\]  
\[W_{PV}+Q_{SF}\cdot\left(1-\frac{T_{0}}{T_{SF}}\right)=Q_{TES}\cdot\left(1- \frac{T_{0}}{T_{SF}}\right)+I_{conv} \tag{2}\]  
\[W_{PV}+Q_{SF}\cdot\left(1-\frac{T_{0}}{T_{SF}}\right)=Q_{TES}\cdot\left(1- \frac{T_{0}}{T_{TES-nov}}\right)+I_{nov} \tag{3}\]  
\[I_{conv}-I_{nov}=\left(\frac{T_{0}}{T_{SF}}\right)\cdot\left(\frac{Q_{TES}}{ COP_{max}}\right)=\left(\frac{T_{0}}{T_{SF}}\right)\cdot\left(\frac{COP}{ COP_{max}}\right)\cdot W_{PV} \tag{4}\]  
\[COP_{max}=\frac{T_{TES-nov}}{T_{TES-nov}-T_{SF}} \tag{5}\]  
Figure 3 depicts the proposed layout, providing a detailed overview of the heat pump and heat engine components. The heat pump employs a reverse recuperated Brayton cycle,  
while the heat engine utilizes a recompression Brayton power cycle, both with supercritical CO\({}_{2}\). In both cases, the heat exchangers that employ molten salts (MSHP in the heat pump and MSHE in the heat engine) have been relocated to the low-pressure side of the cycle. This modification is required because both Brayton cycles operate with a maximum pressure of 300 bar. To handle such a high pressure, printed circuit heat exchangers (PCHE) are typically employed in S-CO2 applications [21]. Based on diffusion bonding, PCHEs can withstand high pressures due to their manufacturing process. However, the channels in these heat exchangers are too narrow, leading to clogging issues when using molten salts. The allocation of molten salt heat exchangers in the proposed layouts enables using a heat exchanger with wide channels for the salt, avoiding clogging issues [22]. One possible option for that kind of heat exchanger might be a hybrid printed circuit heat exchanger, where the layers of one of the streams are replaced with a plate-and-fin structure, becoming a combination of a PCHE and a plate-fin heat exchanger (PFHE).