## 3 Modelling and Simulation
### Basic Model
#### 3.1.1 Further Development of the Model  
As a first step, the storage fluid was changed from water to molten salt. For this purpose, a predefined fluid introduced with APROS 6 is used, which is referred to as SOLAR_SALT1. This can be found in the database and describes the binary nitrate salt Solar Salt used in the industry, which is also used in the comparison process of Andasol 2. In APROS, a fluid is defined by the correlation of five material properties as a function of temperature. The required material properties are density, dynamic viscosity, specific heat capacity, thermal conductivity, and adiabatic compressibility. The next objective was to equalise the pressure in the individual storage tanks to a constant pressure level of 1 bar. This pressure equalisation is required because APROS assumes that empty space in the tank is filled by a non-condensable gas and is not filled with selected fluid. If the pressure is now set to 1 bar in the initial state and the level is set to, e.g., 4 m, there is an increase in pressure when fluid is pumped into the tanks as the volume of the unfilled area decreases. As a first solution, the two tanks are connected to each other, whereby the connection point of both tanks is set at a height of 13.9 m. This results in a large fluctuation around the ambient pressure during a working cycle. The reason for this is that the pressure is the same in both storage tanks, but in the discharge state there is significantly more gas in the hot tank than in the cold one, which results in an increase in the total pressure due to thermal expansion. The second and final approach is to use pressure equaliser tanks. These are also implemented with the Heat_TANK component and connected to the storage tanks at a height of 13.9 m. The level of pressure equaliser is set to 5 m. In addition, the two components are removed from the dynamic simulation using the Exclude From Simulation function. This means that they do not change their state during the simulation; thus, the equaliser tanks always remain at a pressure of 1 bar and a fill level of 5 m. As expected, the pressure now remains at 1 bar during a working cycle. This completes the modelling of the process work area, as shown in Figure 5.  
Next, the charge and discharge processes were implemented in the APROS model. The thermal energy available in the model is determined by the radiant power of the sun and the temperature is controlled via the mass flow. In order to enable a later validation of the system, exactly 1025 \(MW_{th}h\) are fed into the system, which exactly corresponds to the amount of energy required to fully charge the storage unit. It can be seen from [25] that in the tests carried out on Andasol 2, a charging time of approximately 10 h is expected. Accordingly, the charging period is set to 10 h in the modelling. In order to keep the regulation as close as possible to reality, sunrise and sunset are also taken into account. In order to supply \(1025\;MW_{th}h\) to the system in 10 h, the system must be charged with a constant charge power of \(102.5\;MW_{th}\). The integral of the charging power over time corresponds to the thermal energy supplied to the system. During the night, in order to obtain the same thermal energy for the same period of daytime operation, the charge power must be increased. From Figure 6, in the left figure, it can be seen that the difference between a constant power and the consideration of the sunrise and sunset is exactly the thermal energy that would be supplied to the system in 40 min by a constant charging power of \(102.5\;MW_{th}h\). The power must be selected accordingly so that the \(1025\;MW_{th}h\) would be reached in 9 h and 20 min, which leads to the following calculation:  
\[\frac{1025\;MW_{th}h}{9.33\;\text{h}}=109.82\;MW_{th} \tag{1}\]  
The required charging power is thus \(109.82\;MW_{th}\). This is implemented using the GRADIENT component. This is a dynamic component that limits the rate at which the value of an input signal can change.