## 4 Cost Functions
### Molten Salt Storage  
The molten salt storage was modeled as a conventional two-tank solution with one hot tank and one cold tank, as illustrated in Figure 7 (left). The hot tank and cold tank temperatures were set equal to \(T_{max}\) and \(T_{min}\), respectively. The thermal storage is charged with steam via a heat exchanger and discharged similarly by reversing the flow. The cost function for molten salt storage thus includes the costs for heat storage material, storage tanks and insulation, heat exchangers, pumps and electric motors. Of these, the costs for pumps, electric motors and the heat exchanger depend only on heat load, whereas the costs for the remaining components depend only on thermal storage capacity. Figure 7 (right) illustrates the approach for calculating the required salt volume and flow rate, and consequently the required sizes for heat exchangers, pumps and electric motors are calculated for each capacity and load in the specified range. As the heat storage material, a novel ternary salt mixture called Yara MOST, which is a blend of Ca(NO\({}_{3}\))\({}_{2}\), KNO\({}_{3}\) and NaNO\({}_{3}\), was considered [26]. The benefits of Yara MOST as opposed to other salts applied in concentrated solar plant (CSP) applications are among others its low melting point (131 \({}^{\circ}\)C) reducing the risk of freezing, wider operational temperature range, almost no corrosion and lower cost. The use of Yara MOST as a heat transfer fluid and TES medium has been tested at industrial scale at a parabolic trough CSP plant in Portugal [27]. A constant price at the lower limit obtained from the supplier, equal to 0.7 \(\mathrm{\upmu}\)\  
insulation costs were obtained from the cost database, with maximum tank temperature and surface area for each tank as input. Molten salt steam generators generally consist of several heat exchanger steps [28; 29]. For the present study, only the evaporation stage was considered in order to be consistent with the other storage technologies. The evaporator was assumed to be a U-type stainless steel heat exchanger with water flowing in the tubes and salt in the shell side. For calculating the heat transfer coefficient for water in the evaporator, the Gungor and Winterton correlation was applied [30]. For the heat transfer coefficient for the salt flowing across the tube bundle, the approach given by [PERSON] [31] was followed, assuming a staggered tube arrangement and a triangular pitch with \(P_{t}=1.25d_{o}\), with an outer tube diameter \(d_{o}\) of 0.023 mm. The overall heat transfer coefficient and thus the required heat transfer area was calculated for a range of loads and numbers of tubes, \(N_{tubes}\). The tube bundle diameter was calculated from basis of the number of tubes using correlations given in [32], and the shell diameter was estimated to be 1.1 times the bundle diameter. From the range of obtained heat transfer areas, only those that satisfied the following condition were considered [32]:  
\[D_{shell}<L_{tube}<10D_{shell} \tag{41}\]  
where \(D_{shell}\) is the shell diameter and \(L_{tube}\) is the length of a tube. For each load, the minimum heat transfer area satisfying this condition was selected. Finally, using the selected heat transfer areas, a linear function for the area as a function of load was obtained to be applied in the optimization model in order to minimize the computation time. The  
Figure 7: Sketch of the molten salt TES system in charging and discharging modes (**left**) and calculation of storage parameters and selection of pumps and motors for molten salt storage (**right**). same procedure was applied for obtaining the required number of tubes for each load, which was needed in calculating the pressure drop as explained in the following section. The cost function for the salt pump was obtained using the cost database with salt flow rate and pressure drop as the input parameters.