## 4 Results and Discussion
#### Forecasting Results Based on Data Set 1: Parking Lot Canopy Array Datasets  
The principal feature of the PV power output is its intermittency. This unpredicted fluctuation in solar PV power could lead to many challenges including power generation control and storage management. Essentially, it is crucial to appropriately forecast PV power output to guarantee reliable operation and economic integration in the power grid. In the first case study, the above-trained models will be evaluated using the testing solar PV power output starting from 30 June to 6 July 2017 collected from Parking lot canopy array. Forecasting outputs using the eight deep learning models using test measurements are displayed in Figure 7. These results illustrate the goodness of deep learning models for PV power forecasting. Also, to show clearly the accordance of the measured and the forecast outputs from the investigated deep learning models, the scatter plots are presented in Figure 8. Figure 8 shows that the forecasted data from RBM and SAE models are moderately correlated with the actual PV power output. The forecasting with ConvLSTM is relatively weakly correlated with the measured power data. On the other hand, the forecasted power with RNN-based models and the VAE model are strongly correlated with the measured PV power. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Methods** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{RBM} & learning rate & 0.0005 \\  & Gibbs sampling (k) & 5 \\  & Training epochs & 500 \\  & Layers & 01 \\ \hline SEAS & Learning rate & 0.0005 \\  & Training epochs & 500 \\  & Layers & 04 \\ \hline VAE & Learning rate & 0.0005 \\  & Training epochs & 500 \\  & Layers & 05 \\ \hline RNN & Learning rate & 0.0005 \\  & Training epochs & 500 \\ \hline GRU & Learning rate & 0.0005 \\  & Training epochs & 200 \\ \hline LSTM & Learning rate & 0.0005 \\  & Training epochs & 200 \\ \hline BiLSTM & Learning rate & 0.0005 \\  & Training epochs & 200 \\ \hline ConvLSTM & Learning rate & 0.0005 \\  & Training epochs & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tuned parameters in the considered methods. Now, to quantitatively evaluate the forecasting accuracy of the eight considered models based on the testing data, five statistical indexes are computed and listed in Table 3. Also, we compared the eight the forecasting results of the ten deep learning models with two baseline machine learning models:  
Figure 8: Scatter graphs of PV power forecasting and measurements using the eight models: (**a**) LSTM, (**b**) GRU, (**c**) RNN, (**d**) BiLSTM, (**e**) ConvLSTM, (**f**) RBM, (**g**) SAE, and (**h**) VAE. Figure 7: Forecasting results from the eight models using the testing datasets: (**a**) Long Short-Term Memory Networks (LSTM), (**b**) gated recurrent unit (GRU), (**c**) recurrent neural network (RNN), (**d**) Bidirectional LSTM (BiLSTM), (**e**) Convolutional LSTM (ConvLSTM), (**f**) Restricted Boltzmann Machine (RBM), (**g**) stacked autoencoder (SAE) and (**h**) VAE. LR and SVR (Table 3). For this application, ConvLSTM performs poorly in terms of the forecasting accuracy compared to the other models and cannot track well the variability of PV power and does not describe the most variance in the data (i.e., EV = 0.832). Moderate forecasting performance are obtained using RBM and SAE by explaining respectively 0.929 and 0.932 of the total variance in the testing PV power data. The results of this investigation exhibit also that the VAE model provides accurate forecast in comparison to the other models by achieving PV power forecast with lower RMSE, MAE, and higher NRMSE (%) as well as the highest R2, EV values closer to 1 that means that most of the variance in the data is captured by the VAE model. Specifically, the VAE model achieved the highest R2 of 0.992 and the lower RMSE (6.891) and MAE (5.595). We highlight that this is the first time that the VAE model is used for solar PV power output forecasting.