# 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
(2011) demonstrated a detailed relationship between the costs from different publications and data. Their most recent data (from 2020) considered a cost of 1660 EUR/kW plus 70 EUR/kWh (head of \(\sim\)300 m, equivalent to around 56 EUR/m\({}^{3}\)). [PERSON] et al. (2019) reported a cost of 3580 EUR/kW plus 26 EUR/kWh (head of around 300 m, equivalent to around 21 EUR/m\({}^{3}\)) for \(\sim\)100 MW systems and 10 h duration. Considering the high range of costs of the different publications, we consider a relatively optimistic low cost of 1000 EUR/kW (for all the PHS components except the reservoirs) plus 25 EUR/m\({}^{3}\) (or 130 EUR/kWh) for the reservoirs as the base case of the optimisations. A useful lifespan of 50 years is considered for the PHS, and therefore, at the end of the system's lifetime (25 years), half of the PHS CAPEX is recovered as income (converted to net value considering inflation and nominal discount rates). Few studies have reported values for OPEX costs. [PERSON] et al. (2011) reported a fixed OPEX of 2% of CAPEX per year and a variable OPEX of 0.5 EUR/MWh. [PERSON] et al. (2019) show a fixed OPEX in the range 2-9 EUR/kW-yr and a variable OPEX in the range 0.19-0.84 EUR/MWh, thereby obtaining average values of 4.6 EUR/kW-yr and 0.22 EUR/MWh. A major OPEX cost of 84 EUR/kWh is expected every 20 years. If we distribute this cost over 20 years, we can add 4.2 EUR/kW-yr, obtaining a total average OPEX of 8.8 EUR/kW-yr (approximately 1% of the CAPEX per year) and 0.22 EUR/MWh. For OPEX, we used a fixed value of 1.5% CAPEX per year plus a variable OPEX of 0.35 EUR/MWh (both values approximate between those reported by [PERSON] et al. (2019) and [PERSON] et al. (2011)). \begin{table}
\begin{tabular}{c c} \hline
**Variable** & **Value** \\ \hline Location & Zaragoza (Spain) (41.66\({}^{\circ}\) N, 0.88\({}^{\circ}\) W) \\ System lifetime & 25 years \\ Electrical load (First year) & 1.2 MW peak power, 6.14 GWh annual load ([PERSON] et al. [28], Section 3.1). \\ Annual increase in electrical load & 0.5\% \\ Unmet load allowed & 0\%. \\ Maximum grid power \(P_{max\_grid}(t)\) & 2 MW \(\forall t\geq 0\) \\ Nominal discount rate \(I\) & 8\% \\ General inflation \(Inf\) & 2\% \\ Sell and purchase electricity Price & RTP (First year market price Spain 2023) \\ Access charge & 0.02 EUR/kWh fixed. \\ \(F_{PV}\) & 0.3 \\ \(F_{wind}\) & 0 \\ Mean of electricity price inflation \(Inf_{P\_E\_mean}\) & 1\% \\ Standard deviation of electricity price inflation \(\sigma_{P\_E}\) & 0.5\% \\
**PV:** & 0.855 EUR/Wac [50] \\ CAPEX & 0.5\% of CAPEX per year [51] \\ OPEX & 0 to 5 MWac, steps of 1 MWac \\ Nominal power (AC) \(P_{PV\_N\_AC}\) & 35\({}^{\circ}\) and 0\({}^{\circ}\). \\ Slope and azimuth & 25 years \\ Lifetime & 0.5\% [45] \\ \(f_{ml\_PV}\) & 43 \({}^{\circ}\)C \\ \(f_{PV\_loss}\) & 95\% \\ \(\alpha\) & \(-\)0.41\%/\({}^{\circ}\)C \\ PV inverter DC/AC ratio & 1.25 \\ Inverter efficiency \(\eta_{lim\_PV}\) & Figure 15 [52] \\ _Wind turbines:_ & 1.3 EUR/W [53] \\ CAPEX & 2\% of CAPEX per year [53] \\ OPEX & 500 kW \\ Nominal power \(P_{WT\_N}\) & 0\(-\)10 \\ Number in parallel \(N_{WT}\) & 25 years \\ Lifetime & 53 m \\ Hub height \(z_{inb}\) & 0.1 m \\ Roughness \(z_{0}\) & 0.2 [38] \\ \(f_{WT\_loss}\) & 98\% \\ Power curve & Figure 2 \\
**PHS:** & Figure 3 \\ Pump/turbine reversible machine CAPEX (inc. civil works) & 70 m \\ Pump/turbine OPEX & 1.5\% of CAPEX per year + 0.35 EUR/kWh \\ Reservoirs CAPEX & 25 EUR/m\({}^{3}\) (130 EUR/kWh considering 70 m head) \\ Lifetime & 50 years \\ Pump/turbine start-up costs & 0.1 EUR/MW [31] \\ Nominal power \(P_{P\_N}=P_{HT\_N}\) & 0.5-2.5 MW, steps of 0.5 MW \\ Nominal flow \(Q_{P\_N}=Q_{HT\_N}\) & 0.75–3.75 m\({}^{3}\)/s, steps of 0.75 m\({}^{3}\)/s \\ Efficiency curve & Figure 3 \\ Pump minimum input power & 20\% of nominal power \\ Head \(H_{diff}\) & 70 m \\ Upper reservoir duration: \(Duration\)(h) & 2–20 h, steps of 2 h \\ \(f_{LR/UR}\) & 100\% \\ \(V_{lR\_min}=V_{LR\_min}\) & 0\% \\ \hline \end{tabular}
\end{table} 
Table 3: Main characteristics of the system.