## 5 Numeric Results and Discussion  
The following section presents the results obtained with the four models developed for the prediction of PV generation. The results are presented in different ways; first, the averages of the error metrics for the month of July are shown. Then, the results are analyzed in a graphical form. Afterward, the difference in the behavior of the models depending on whether the day is sunny or cloudy is shown. Finally, the percentage errors of the models are calculated. Table 6 shows the average of the metrics for the entire month of July. If results are analyzed in terms of the R\({}^{2}\) metric, the SVR model clearly stands out from the others, with a value of 0.93. Even so, it is worth mentioning that the R\({}^{2}\) results obtained with the other \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hyper-Parameters** & **Lower Bounds** & **Upper Bounds** & **\#Samples** \\ \hline \(C\) & \(10^{-1}\) & \(10^{6}\) & 50 \\ \(\epsilon\) & \(10^{-3}\) & \(1\) & 50 \\ \(\gamma\) & \(10^{-6}\) & 10 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specifications of the hyper-parameter search space. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**N\({}^{\circ}\) of Neurons** & **Input Delay** & **Feedback Delay** & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{8}{*}{1} & 0 & 1 & 186.253 & 306.610 & 0.850 \\  & 0 & 2 & 178.890 & 300.114 & 0.850 \\  & 0 & 3 & 170.447 & 285.746 & 0.863 \\  & 0 & 4 & 175.752 & 296.368 & 0.848 \\  & 1 & 1 & 178.735 & 297.446 & 0.856 \\  & 1 & 2 & 182.403 & 303.188 & 0.849 \\  & 1 & 3 & 178.704 & 300.948 & 0.843 \\  & 1 & 4 & 175.490 & 295.415 & 0.850 \\  & 0 & 1 & 203.762 & 338.190 & 0.854 \\  & 0 & 2 & 233.423 & 375.512 & 0.812 \\  & 0 & 3 & 209.042 & 351.111 & 0.779 \\  & 0 & 4 & 178.290 & 305.830 & 0.842 \\  & 1 & 1 & 160.204 & 274.975 & 0.877 \\  & 1 & 2 & 148.465 & 255.714 & 0.881 \\  & 1 & 3 & 151.524 & 261.359 & 0.877 \\  & 1 & 4 & 190.125 & 327.298 & 0.810 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error results were obtained with the NARX model combining the different numbers of neurons and delays. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hyper-Parameters** & **Lower Bounds** & **Upper Bounds** & **\#Samples** \\ \hline \(C\) & \(10^{-1}\) & \(10^{6}\) & 50 \\ \(\epsilon\) & \(10^{-3}\) & \(1\) & 50 \\ \(\gamma\) & \(10^{-6}\) & \(10\) & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the hyper-parameter tuning based on Bayesian optimization. three models are actually good. Another outstanding performance is the MAE and RMSE values obtained by the analytical model, which are twice as high as those obtained with the rest of the models. Figures 11-14 below show the predictions of PV generation during a week in July. In general, all four models are able to detect the PV generation pattern, differentiating between night and midday hours. As mentioned, all four models perform well, and this is also reflected in the figures. However, it is worth mentioning that in some aspects, models behave differently. The FFNN, NARX, and SVR models are able to reach the maximum generation peaks. Nevertheless, the FFNN model presents some complications on 22 and 23 July, which are more cloudy days. In this aspect, the SVR and NARX models show a greater ability to cope with sudden peaks. The NARX model particularly stands out on cloudy days. This model shows good behavior in dealing with constant changes. Nevertheless, it should be mentioned that at the beginning of the generation day, the NARX technique forecasts a little production when in reality, it is lower. Seeing how well the NARX model performs against cloudy days, we can conclude that its lower \(\mathbb{R}^{2}\) value compared to the others may be due to the fact that most of the days in the month of July are sunny days. Finally, the analytical model has difficulties in reaching the maximum generation peaks on each day, especially on the 23 rd and 25 th of July. In addition, the simulation generates a small lag in energy production.