# Simulation and Optimisation of Utility-Scale PV-Wind Systems with Pumped Hydro Storage
## 3 Computational Results and Discussion
### Optimisation of an LSS System (System with Load Consumption)
#### 3.2.4 Components  
Six sizes of AC-coupled PV generators were considered, from 0 to 5 MWac in steps of 1 MW, with an azimuth of 0\({}^{\circ}\) (south faced) and a slope of 35\({}^{\circ}\) to maximise the annual generation. Each PV generator included its own inverter with a DC/AC ratio of 1.25. The inverter efficiency curves are presented in Figure 15.  
Pitch-controlled variable speed wind turbines of 500 kW (output curve in Figure 2), from 0 to 10 in parallel, were considered in the optimisation. We considered a PV of 0 MW and 0 wind turbines in parallel, i.e., the possibility of not including PV or wind turbines in the system. Variable-speed pump-turbine reversible machines from 0 to 2.5 MW in steps of 0.5 MW were considered. The upper and lower reservoirs had the same capacity, and their capacity was obtained with a duration ranging from 2 to 20 h in steps of 2 h.  
Figure 14: Daily average hourly electricity sell price for the different years, all referred to the beginning of the system (year 0) (EUR/kWh). Figure 15: PV Inverter efficiency. Table 3 lists the main characteristics of the components used in the optimisation. The component characteristics were obtained from [PERSON] et al. (2018), except for the assumptions and values obtained from the different references (specified). The wind turbine hub height was set to 53 m (the recommendation of the most important manufacturer for their 500 kW wind turbines) instead of the value of 80 m used by [PERSON] et al. (2018). PV and wind turbine costs were obtained from different studies (specified). For the PHS costs, the total investment cost (CAPEX) of a PHS plant depends on many factors, and there is high variability. Some studies simply provide the total cost per kW of rated power; however, it is important to separate the total PHS cost into two concepts:  
1. The cost of all the PHS components, using a price per kW of rated power of the machines (including machines and civil works: powerhouse with pump turbines, tunnel, penstock, transmission, etc., except the reservoirs). 2. The cost of the reservoirs, using a price per kWh of energy storage or per m\({}^{3}\) of upper reservoir volume. Some references provide a price per kWh for the reservoirs, while others provide a price per m\({}^{3}\). Considering that the stored energy (J) is calculated as the upper reservoir volume (m\({}^{3}\)) \(\times\) water density (kg/m\({}^{3}\)) \(\times\) g (m/s\({}^{2}\)) \(\times\) height (m), we obtained energy (kWh) = 0.002725 \(\times\) volume (m\({}^{3}\)) \(\times\) height (m) using 1000 kg/m\({}^{3}\) for water density, and this value of energy was used to convert EUR/kWh and EUR/m\({}^{3}\) of the upper reservoir volume. In the following references, costs are shown in dollars, and to convert them into euros, we assume USD 1 = EUR 0.9. [PERSON] et al. (2011) showed values of the total PHS cost from a low estimate for the USA of 2250 EUR/kW (for 9 h power plant duration) to a high estimate of 3150 EUR/kW (for 18 h power plant duration). IRENA (2018) considers CAPEX from 555 to 2220 EUR/kW. [PERSON] and [PERSON] (2018) used a value of 1000 EUR/kW for an 80 MW turbine, a 70 MW pump, and a water reservoir duration of 7 h. [PERSON] et al. (2019) used 950 EUR/kW for the pump station, 1322 EUR/kW for the hydro station (different machines), and 79.4 EUR/m\({}^{3}\) for the upper reservoir (with a 110 m head, equivalent to 265 EUR/kWh). [PERSON] et al. (2019) showed a wide range of PHS CAPEX: 376-969 EUR/kW plus 8-126 EUR/kWh for the reservoirs, thereby obtaining average values of 528 EUR/kW + 68 EUR/kWh; however, grid interconnections and infrastructure requirements were not included. [PERSON] et al. (2019) showed costs ranging from 1026 to 1205 EUR/kW plus from 13 to 183 EUR/kWh for the reservoirs. [PERSON] et al. considered a CAPEX of 547 EUR/kW plus 2.7 EUR/m\({}^{3}\) for reservoirs (with a 70 m head, equivalent to 14 EUR/kWh); these costs are too low and seem unrealistic. [PERSON] et al.