# A Novel Hybrid CSP-PV Power Plant Based on Brayton Supercritical CO\({}_{2}\) Thermal Machines
## 2 Methodology
### Economic Model  
The estimated investment cost (fixed capital investment, FCI, based on [34]) has been determined. The total cost can be split into direct and indirect costs, with indirect costs considered to be 25% of the direct costs. Indirect costs encompass engineering, supervision, construction, and contingencies. Direct costs include on-site costs (piping instrumentation and controls, equipment) and off-site expenses (civil works, land and service facilities). For this study, the off-site costs have been incorporated into the solar field and the storage systems, which are directly accounted for in the direct costs. The remaining portion of the facility's cost is determined based on the purchased equipment cost (PEC) by multiplying it by a factor of 2.18, taken from a study from Sandia National Laboratory [35] for a recompression Brayton supercritical CO\({}_{2}\) cycle of 10 MWe [35]. This study has been also used to estimate the cost of the heat engine and heat pump cycles. The PCHEs' costs are obtained by scaling them according to the number of modules. An escalation factor of 0.4 [34] is applied, with a base PEC of USD 5 M for the HTR and REC, and a number of modules of 4.46. For the remaining PCHEs, the base PEC is assumed as USD 3 M and a number of modules of 3.1. These cost figures are based on data from 2013 [35]. The cost difference in the PCHEs is due to the different operating conditions in the HTR and REC and the rest of the PCHEs: the HTR and REC operate at high temperatures, necessitating a high-strength alloy such as Inconel 617. In contrast, the other heat exchangers can be manufactured using a standard SS 316 material [36]. The sizing of the H\({}^{2}\)X heat exchangers has yet to be investigated. Instead, the specific cost (USD/kW) obtained for PCHEs within a similar temperature range has been considered to estimate the investment required. Equations (6)-(9) represent the escalation process required to estimate the investment in turbomachinery, in the generator of the heat engine and the motor in the heat pump, respectively, taken from [37]. In these equations, \(W\) stands for the electricity power (produced by the heat engine and consumed by the heat pump) in MW, \(p\) for the highest pressurein bar, and \(T\) for the highest temperature in Celsius degrees. Finally, the \(PEC\) of the set is given in USD million. \[f_{W}=\left(\frac{W}{10}\right)^{0.68} \tag{6}\]  
\[f_{p}=\left(\frac{p}{200}\right)^{-0.6} \tag{7}\]  
\[f_{T}=\frac{3.35+\left(\frac{T}{1000}\right)^{7.8}}{3.35+\left(\frac{650}{1000} \right)^{7.8}} \tag{8}\]  
\[PEC=f_{W}\cdot f_{p}\cdot f_{T}\cdot 6 \tag{9}\]  
The thermal energy storage cost has been estimated from the NREL Gen3 roadmap for CSP [26], considering a two-tank solar salt system from Abengoa as a reference. The costs provided include both on-site and off-site expenses, representing direct costs. The volume of the cold tank serves as the baseline (15,700 m\({}^{3}\)), and an escalation factor of 0.8 is used. The base cost breakdown is: hot tank, USD 10.016 M; cold tank, USD 4.361 M; tank insulation, USD 3.724 M; foundations, USD 3.050 M; structural steel, USD 0.666 M; electrical installations, USD 0.481 M; site works, USD 0.339 M; and instrumentation, USD 0.212 M. The cost of the salt inventory varies linearly and is calculated at a specific cost of USD 1100/tonne. For the solar field investment cost estimation, a specific cost of USD 152 per solar aperture area has been considered, with reference to 2020 [38]. A time scaling technique is applied using the Chemical Engineering Plant Cost Index (CEPCI) to account for data from different dates. The CEPCI value for 2013 (applicable to molten salt loops, PCHEs, and turbomachines) is 567.3, while the value for 2020 (the year the results are referenced) is 596.2. A preliminary calculation of the LCOE is performed, considering just the known investment, previously determined.