## 3 Methodology  
The energy and exergy analyses are carried out using Equation Engineering Solver (EES) [15]. The thermophysical properties of CO\({}_{2}\), molten salts and water are calculated with the libraries included in EES. The following assumptions are adopted to develop both analysis:  
* The system operates in steady conditions.
* The variations in kinetic and potential energies are neglected.
* Pressure drops and heat losses are not considered in the design of heat exchangers and pipes.
* A model based on effectiveness has been used for the recuperators. The effectiveness of each recuperator (Equations (1) and (2)) considers the side with the lower heat capacity [2]. \[\varepsilon_{HTR}=\begin{cases}\frac{T_{3}-T_{4}}{T_{3}-T_{10}}&\text{if minimum in hot side}\\ \\ \frac{T_{1}-T_{10}}{T_{3}-T_{10}}&\text{if minimum in cold side}\end{cases}\] (1) \[\varepsilon_{LTR}=\begin{cases}\frac{T_{3}-T_{5}}{T_{4}-T_{7}}&\text{if minimum in hot side}\\ \\ \frac{T_{3}-T_{7}}{T_{4}-T_{7}}&\text{if minimum in cold side}\end{cases}\] (2)
* The power block absorbs the thermal power provided by the solar block in the intermediate heat exchanger, a counter-flow heat exchanger with a minimum temperature difference of 15 K between the molten salts and the S-CO\({}_{2}\) (Equation (3)) [18]. This value is different from the S-CO\({}_{2}\)/S-CO\({}_{2}\) heat exchanger, where the minimum temperature difference is 5 K [19]. The assumption of equal entropy generation at both terminals of this heat exchanger will be made (Equation (4)) [18]. \[T_{13}=T_{2}+15\text{ K}\] (3) \[\int\text{d}Q\bigg{(}\frac{1}{T_{13}}-\frac{1}{T_{2}}\bigg{)}=\int\text{d}Q \bigg{(}\frac{1}{T_{14}}-\frac{1}{T_{1}}\bigg{)}\] (4)
* The salt storage tank is well-insulated, and therefore, heat losses are considered negligible.  
Table 2 summarizes the input parameters assumed for this study. The rated power is assumed to be 10 MW, which corresponds to the scale of a demonstration plant [20]. The cooling water inlet and outlet temperatures for the precooler are 25 \({}^{\circ}\)C and 35 \({}^{\circ}\)C, following the recommendation of the reference [21]. It is hypothesised that the compressor inlet temperature is 35 \({}^{\circ}\)C, a supposition that is in accordance with the recommendations set out in the references [21,22]. The efficiency of the power cycle significantly increases with higher recuperator effectiveness. It is asserted that an effectiveness level that exceeds 90% may not be economically viable, as indicated by reference [22]. For this work, a conservative value of 86% is assumed. The assumed values for isentropic efficiency of the turbine (90%) and compressor (85%) are typical values that have been documented in the extant literature [23]. The maximum cycle pressure, defined as the pressure at the outlet of the main compressor, is constant at 250 bar. This value signifies the upper limit of the mechanical strength of the materials commonly employed in S-CO\({}_{2}\) at operating temperatures [1]. Throughout the study, this maximum cycle pressure remains constant. The minimum pressure, which is the pressure at the inlet of the main compressor, is determined based on the pressure ratio. The maximum temperature for each type of molten salt, which is the temperature at the outlet of the solar receiver, has been assumed to be the highest possible, as shown in Table 1. Themaximum temperature of the molten salt determines the turbine inlet temperature on the power cycle by Equation (4). It is well established that the efficiency of the power cycle improves as the maximum turbine inlet temperature increases.  
The energy, the exergy and sizing analyses are summarized in Sections 3.1, 3.2 and 3.3, respectively.