# 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)
#### 3.2.5 Optimisation Results  
Each optimisation considers the combinations of six different types of PV generators (0 to 5 MW in steps of 1 MW), one type of wind turbine with 11 possibilities in parallel (0 to 10), five different types of pump-turbine reversible machines, and 10 values for storage duration, with a total number of possible combinations of 6 \(\times 1\)\(\times\) 11 \(\times\) 5 \(\times\) 10 = 3300. The control strategy is composed of four variables, each of which can assume 10 possible values, with a total of 10\({}^{4}\) = 10,000 combinations. Therefore, the total number of possible combinations is 33,000,000. An Intel i5-6500 3.2 GHz CPU with 32 GB RAM requires an average of ~7 s to simulate and evaluate each combination of components and control (over 25 years in 15 min time steps, i.e., 876,000 time steps for the simulation of each combination). We decided to use 15 min time steps to obtain high accuracy and acceptable computation time. Lower duration time steps imply an unacceptable computation time in this case. The 33,000,000 combinations required approximately 2700 days for evaluating all combinations, which is indeed inadmissible. However, using the GA, the optimisation time is reduced to admissible values. In a previous study, the optimal parameters of a typical GA used to optimise standalone hybrid renewable systems were obtained [54]. The parameters for the main GA were: maximum number of generations: 10, population: 20, crossover rate: 70%, and mutation rate: 1%. For the secondary one, the same settings were employed, except the population, which was 25. The number of cases evaluated by the main GA for the component combinations was ~160 (compared with 3300), whereas that for the control strategy (secondary GA), was ~200 (compared with 10,000), thereby obtaining a computation time of ~60 h.  
For comparison, we optimised the system without a PHS (only PV and/or wind turbines). In this case, there were only 6\(\cdot\)11 = 66 different combinations of systems (and no control strategy), obtaining the optimal combination in ~7 min, without the need for GA.  
Table 4 presents optimal systems for each project type. Annual energy values are average values (as energy is different for each year because of changes in load and resources and degradation of renewable generators). The first results column shows the optimal system without considering the PHS (wind-PV system). The other two columns show the optimal system with PHS, project type A (second column), and project type B (third column). The optimal system without a PHS has better results (lower NPC and LCOE), indicating that a PHS is not worthwhile when considering the costs. In addition, the optimal system obtained for types A and B has the same component configuration and almost the same control state points (only a difference in the minimum hydro turbine load \(P_{\%}\)), with a small difference in energy results (slight differences in pump and hydro turbine performance and in sold and bought energy because the pump turbine and reservoir are the lowest). The performance differences between Types A and B were considerably higher in systems with larger PHS sizes. \begin{table}
\begin{tabular}{c c} \hline
**Variable** & **Value** \\ \hline Lifetime & 25 years \\ \(D_{p}\) & 0.6 m \(<\)\(D_{p}\) \(<\) 1.5 m. Calculated for each case to obtain a water speed of 2.5 m/s for nominal turbine flow. \\ \(L_{p}\) & 250 m \\ \(K_{fittings}\) & 0.8 \\ \(\varepsilon\) & 0.05 mm \\ \(H_{diff}\) & 70 m \\ \(H_{LR\_max}=H_{\text{L}IR\_max}\) & 5 m \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._In both cases A and B, the optimal purchase price limit is 0.15 EUR/kWh, while the minimum hydro turbine load is 60 and 80% of the rated power (high value to reduce losses due to turbine efficiency at low power). Figure 16 shows the evolution of the main GA in the optimisation of project types A and B, where the optimal combination is found in generations #7 and #8, respectively.