## 5 Experimental Results and Discussion  
The three PVPF methods were implemented using MATLAB on a computer equipped with an Intel Core\({}^{TM}\) i7-6 core processor and 16 GB RAM. The results are shown in Figure 5, which presents time-series plots for the testing datasets of the three models, focusing on the period from 3 January 2016, from 00:00 to 8 January 2016, at 00:00, covering 120 hourly observations, ranging from observation no. 1047 to 1167. The values of, nRMSE, RankCorr, and R\({}^{2}\) for the AHW, LSTM, and HM methods are summarized in Table 3 for different training/test data ratios. Notably, both the LSTM and HM models outperformed the AHW model in terms of predicting the PV power output data regardless of the ratio of training to testing data. One of the main reasons why LSTM outperforms the AHW approach is that it can capture long-term dependencies in the data more effectively. The HM method, obtained by combining AHW and LSTM in forecasting PV power generation, can outperform approach compared to each approach alone. This is because the AHW and LSTM are forecasting methods that can complement each other. The AHW is useful for modeling time-series data with a strong seasonal component. It can capture underlying patterns and trends in the data and provide accurate forecasts. However, it may not be effective for capturing short-term fluctuations in data. By contrast, LSTM is effective for learning and modeling complex relationships between variables and making accurate predictions based on the patterns they have learned. However, LSTM may not be as effective as AHW in capturing seasonal patterns in data. According to recent research, it is possible to compare our methods with those presented in previous studies. Specifically, [39] analyzed six techniques for predicting PV \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Parameters** & **Intervals** \\ \hline \(H\) & Number of hidden layers & [1,2,3,4] \\ \(N\) & Number of hidden neurons & [50, \(\cdots\),200] \\ \(Bi\) & Use BiLSTM layers & [false, true] \\ \(LR\) & Initial Learning Rate & [\(10^{-2}\), 1] \\ \(L2\) & L2 Regularization & [\(10^{-10}\), \(10^{-2}\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyperparameter, corresponding label for the LSTM method, and definition sets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**PVPF Method** & **Optimized Parameters** & **Configuration Time [s]** \\ \hline AHW & \(\alpha=0.92\), \(\beta=1\), & \\  & \(\gamma=1.19\cdot 10^{-06}\), \(s=24\) & 47.331 \\ \hline LSTM & \(H=4\), \(N=61\), \(Bi=true\), & \\  & \(LR=0.010\), \(L2=5.23\cdot 10^{-08}\) & 1242.229 \\ \hline HM & \(H=2\), \(N=63\), \(Bi=true\), & \\  & \(LR=0.010\), \(L2=1.25\cdot 10^{-10}\) & 1455.378 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal hyperparameters values of three PVPF methods (AHW, LSTM, and HM). The GA was implemented in case of AHW and BO algorithm in the case of LSTM and HM. production using the same case study employed in our study. The authors in [39] concluded that CNN is one of the most suitable models for predicting PV production, as it achieved an R\({}^{2}\) value of 0.98 in the same case study. From Table 3, it can be observed that our proposed HM technique achieves an R\({}^{2}\) value greater than 0.99 on the training dataset, and approximately equal to 0.98 or greater than 0.98 on the testing dataset. Consequently, it can be inferred that the proposed HM technique produces results that are either equivalent or superior to those of other approaches, including the outperforming approach reported in the literature [39]. Notably, our results pertain to the most challenging scenario, which involves generating forecasts during both the daytime and nighttime, as addressed in [39]. By combining the AHW and LSTM methods, we could capture both seasonal patterns and short-term fluctuations in the data. The AHW model can provide a baseline forecast for the data, whereas LSTM can refine the forecast by capturing the complex relationships between the variables.