## 3 System Layout
### Battery Bank  
The battery bank is required to store excess energy from sunny days to provide the load with the power needed when there is a shortage of PV-generated power (during cloudy days and nights). Lead-acid VARTA OPzS batteries with a rated voltage of 2 volts were selected to store the excess energy. The batteries are of type 10 OPz S1000. Figure 10: Daily average solar irradiation (W/m\({}^{2}\)) [19,20]. The capacity of the battery in kWh (\(E_{Battery}\)) was calculated as per Equation (3), and it has been found that a 46.184 kWh storage capacity is needed, while the depth of discharge (\(DOD\)) is considered to be 80% (State of Charge (SOC) = 20%); the battery's efficiency is 80%, the inverter's efficiency is 95%, and the safety factor is 1.3 [21,22]. \[E_{Battery}=\frac{\textit{Maximum 24 hours period shortage in kWh/day}}{DOD*\eta_{b}*\eta_{inv}}*SF \tag{3}\]  
The required number of batteries (\(Batt_{num}\)) has been calculated using Equation (4), and it has been found that 24 batteries are required to fully cover the load for one day of autonomy (\(DOA\)) for the selected plant in the Jordan Valley. \[Batt_{num}=\frac{E_{Battery}[kWh]*1000}{\textit{Battery capacity in Ah*Battery's voltage}} \tag{4}\]  
The 24 batteries were connected in series to give a total voltage of 48 Volts. Battery reduction is a major benefit when using a variable pressure design, as mentioned earlier. Thus, four scenarios are discussed to examine the effect on the needed energy storage. For this purpose, several factors were taken in calculating \(Batt_{num}\), which were raw water flow rate, inlet pressure, permeate water flow rate, and permeate water conductivity. In these calculations, there are reference values, which are mainly dependent on a constant inlet pressure for 24 h per day to satisfy the requirements of the system. The other scenarios were built assuming a variable pressure over the day, depending on the amount of insolation. Thus, the higher the insolation, the higher the inlet pressure, and vice versa. The number of batteries was calculated for the reference scenario, as well as for the other scenarios, depending on the assumption for a 24 h period of operation in kWh/m\({}^{3}\). However, in the case of variable pressure, the number of batteries was calculated for each pressure level and period of the day separately, and then summed up together. As shown in Table 3, the overall energy storage capacity for the testing apparatus was around 2 kWh using the constant pressure desalination plant, where the operating pressure is fixed to be 48 bar. This value is reduced while controlling the operating pressure in all other scenarios. The minimum energy storage capacity was achieved when applying scenario four, where three periods of time were applied: 14 h at low irradiation, 8 h at medium irradiation, and only 2 h at maximum irradiation. Pressure values where selected to be 40, 44, and 58 bars respectively. It is also noted that the permeate flow rate is reduced with an average of 18% for the four scenarios and this is to be considered one of the disadvantages of this design. It is also noted that in Scenario 4, the conductivity of the permeate water has increased by a factor of ~2%, referring to the reference state. As a result, adapting Scenario 4 on the desalination plant, as shown in Table 3, will reduce the required number of batteries from 1 to 0.8 per unit (pu), considering 2.0188 kWh as the reference battery energy (1 pu), where no pressure variation is performed, and will also reduce the permeate flow rate by a factor of 20% and increase the total conductivity of the permeate water by ~2%.