## 5 Conclusions  
In this paper, the impact of different PV models in a hybrid power system was investigated. The models considered were the two-diode (TD), single-diode (SD), and the ideal single-diode (ISD) models of the solar PV renewable energy system (RES). This study was also performed in terms of the reliability and emissions performance indicators. The RES considered included a PV array combined with a pumped hydro storage (PHS), which was investigated for the Al-Wehda dam, Irbid, Jordan. This impoundment was treated as the upper reservoir (UR) of the PHS of the proposed RES. Precise mathematical modelling was done on the output PV power. This was done by taking into account the recombination losses in the TD PV model. This led to a more realistic sizing and more accurate system evaluation. Furthermore, the hourly measured values of the load demand, solar irradiance, ambient temperature, and volumetric water flow rate were obtained from related institutions in Jordan. The results were obtained using the PSO and WOA optimization algorithms. The results showed that the TD realistic model is more reliable than the other models. The PSO optimal value of IR was 98.558%. The corresponding number of panels were 44,840 with a 65.052 M\(\cdot\)m\({}^{3}\) volume of the lower reservoir. It was shown that the number of PV panels decreased by 16.67% and 7.93%, respectively, for the ISD and SD compared with the TD realistic model. These high percentage differences could lead to improper sizing and underestimation of the RES. Moreover, the WOA optimal value of IR was 98.56%. The percentage changes in N\({}_{\text{PV}}\) for WOA compared with PSO were 1.78%, 4.64%, and \(-\)0.5%, for the ISD, SD, and TD models, respectively. Further, the ecological impacts of the proposed models were assessed. It showed that the TD model is more ecological, using the two optimization algorithms, compared with the other models, resulting in an emissions reduction of 21.519 and 21.529 Gg/year using PSO and WOA, respectively. These emissions reductions increased by 2.07% and 6.34%, respectively, for the SD and ISD solar PV models referring to the PSO solution. Furthermore, the GHG emissions were found to be 6.6879 and 6.64125 Gg/year in the case of the TD realistic model for PSO and WOA, respectively. These emissions increased for the SD and ISD models, respectively. Finally, uncertainty analysis on the recombination losses, series and leakage losses, and temperature were performed in order to assess the robustness of the system using the PSO algorithm. This uncertainty analysis showed that the percentage difference of the number of PV panels for the realistic TD model decreased by 12% and 20.36% from the SD and ISD models, respectively, when the \(\alpha_{2}\) values were 1.5 and 1.8. Further, the PV energy of the ISD and SD models decreased by 10.47% and 4.48%, respectively, from the TD realistic model, when the \(\alpha_{2}\) was 1.5 and 1.8. This means that the SD model is more accurate than the ISD model and closer to the realistic TD model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**SD**} & \multicolumn{2}{c}{**ISD**} \\ \hline  & \(\alpha_{2}\) **= 1.5** & \(\alpha_{2}\) **= 1.8** & \(\alpha_{2}\) **= 1.5** & \(\alpha_{2}\) **= 1.8** \\ \hline IR & 0.02 & 0.04 & 0.04 & 0.06 \\ N\({}_{\text{PV}}\) & \(-\)10.35 & \(-\)12 & \(-\)18.86 & \(-\)20.36 \\ V\({}_{\text{LR}}\) & \(-\)0.19 & \(-\)0.19 & \(-\)0.51 & \(-\)0.51 \\ EENS & 5.53 & 5.64 & 14.25 & 14.36 \\ LOLP & 5.42 & 5.52 & 13.51 & 13.61 \\ LPSP & \(-\)1.14 & \(-\)2.45 & 1.77 & \(-\)2.85 \\ E\({}_{\text{PV}_{\text{S}}}\) & \(-\)4.21 & \(-\)4.48 & \(-\)10.21 & \(-\)10.47 \\ GHG\({}_{\text{emission}}\) & 3.5 & 3.61 & 9.07 & 9.19 \\ ER & \(-\)3.11 & \(-\)3.44 & \(-\)7.34 & \(-\)7.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Uncertainty of \(\alpha\) (in %) due to recombination.