# Simulation and Optimisation of Utility-Scale PV-Wind Systems with Pumped Hydro Storage
## 3 Computational Results and Discussion
### Model Validation  
The optimal LSS system found by [PERSON] et al. [28] (the lowest LCOE system) was simulated, and the results were compared. This system for electrifying an urban community (1.2 MW peak power and 6.14 GWh annual energy consumption) in Southern Libya consisted of a 1000 kWp solar PV array and 5000 kW wind turbine farm coupled with a PHS of 166,532 m\({}^{3}\) volume capacity (upper reservoir), fixed static head of 70 m, and reversible pump-turbine of 1 MW with a fixed value of 88% total efficiency. Purchasing electricity from the grid was not allowed; however, surplus energy (when the upper reservoir is full and no more energy can be stored by PHS) could be sold (at a fixed price). [PERSON] et al. also considered the AC grid to be sufficiently large to absorb all excess energy (no grid limit); the water through the penstock was laminar flow (which is not usual); and the water reservoir evaporation and seepage were neglected. The load distribution during the year was estimated using the data shown in Ref. [28]. As [PERSON] et al. did not show the values of \(D_{P}\), \(L_{P}\), \(K_{fittings}\), and \(\varepsilon\), we estimated \(D_{P}=1\) m and \(L_{P}=250\) m, \(K_{fittings}=0.8\), and \(\varepsilon=0.05\) mm, thereby calculating the penstock losses without any previous assumption of turbulence. In addition, we assumed that the lower reservoir had the same capacity as the upper reservoir. Table 2, first and second rows, shows the main results obtained by [PERSON] et al. [28] and our results, respectively. The results obtained by [PERSON] et al. [28] and our results are almost the same. Unmet load obtained by [PERSON] et al. was reported to be 0% (all demand covered), while in our case, we found 0.4% (unmet load is possible because the system was not allowed to purchase energy from the grid). This small difference in the unmet load can be attributed to the distribution of the load during the year, which in our case was estimated from the average monthly values shown in ref. [28]. However, it is impossible to exactly reproduce the load profile of all years because of penstock losses (because of the assumptions of length, diameter and pipe data), considering that [PERSON] et al. assumed laminar flow (which is not true for reasonable diameters). [PERSON] et al. did not consider PV and wind turbine power decay over the years in a real system. In addition, it is common for the load demand to increase over time. Further, the variable efficiencies of the turbine and pump modes (variable-speed Francis pump-turbine, efficiency in Figure 3 obtained from Refs. [43; 44]) and variations in reservoir height must be considered to obtain accurate results. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline
**Total Renewable Generation (GWh/Year)** & **Energy Injected to the Grid (\%)** & **Direct Supply to the Load from Renewable Sources (\%)** & **Demand Covered by Hydro Turbine (\%)** & **Demand Covered** **Unmet Load (\%)** \\ \hline [PERSON] et al.’s optimal system (lowest LCOE) [28]. & 14.6 & 57.1 & 85 & 15 & 0 \\ \hline This work, assuming the same inputs as [PERSON] et al. [28], simulating their optimal system (with several assumptions). & 14.72 & 57.6 & 84.6 & 15.4 & 0.4 \\ \hline This work, same inputs as [PERSON] et al. [28] plus a variable head, pump–turbine variable efficiencies, and simulating 25 years. & 14.33 av. & 53.08 av. & 83.92 av. & 16.6 av. & 1.41 av. \\ \hline \end{tabular}
\end{table} 
Table 2: Results of the optimal system obtained by [PERSON] et al. [28] and comparison with this work. We simulated the same system considering variable head (assuming \(H_{LR\_max}=H_{UR\_max}=5\) m, same maximum height for both reservoirs) for 25 years considering a PV power decay of \(f_{red\_PV}=0.5\%\) annually [45], wind turbine power decay of \(f_{red\_WT}=0.2\%\) annually [38], and increase in load consumption of 0.5% annually (Figure 4).