## 3 Case Study
### Performance Comparison Analysis of Different Solar Irradiance Forecasting Models
#### 3.5.1 Comparison Analysis of Sunny Days  
As previously shown in Table 5, the DWT-CNN-LSTM forecasting model of sunny days performs best at WD level 1 among different WD levels. So in this part, the DWT-CNN-LSTM model at WD level 1 is compared with six solar irradiance forecasting models, namely CNN-LSTM (i.e., our proposed model without WD), artificial neural network (ANN), and manually extracted features (ANN, persistence forecasting, CNN and LSTM). As for the manually extracted features-ANN model, the relevant statistical features and their corresponding expressions are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Weather Types**} & \multirow{2}{*}{**Error Index**} & \multicolumn{5}{c}{**Wavelet Decomposition (WD) Level**} \\ \cline{3-6}  & & **Level 1** & **Level 2** & **Level 3** & **Level 4** & **without WD** \\ \hline \multirow{3}{*}{Sunny} & MAE & 17.131 & 17.379 & 18.249 & 18.498 & 16.573 \\  & RMSE & 34.299 & 34.429 & 35.844 & 36.477 & 33.101 \\  & R & 0.992 & 0.991 & 0.989 & 0.987 & 0.993 \\ \hline \multirow{3}{*}{Cloudy} & MAE & 62.144 & 66.499 & 67.425 & 68.552 & 66.661 \\  & RMSE & 91.099 & 95.377 & 96.374 & 98.551 & 96.641 \\  & R & 0.965 & 0.963 & 0.958 & 0.957 & 0.959 \\ \hline \multirow{3}{*}{Rainy} & MAE & 131.384 & 130.194 & 136.847 & 138.257 & 132.83 \\  & RMSE & 181.392 & 180.079 & 184.963 & 187.241 & 182.97 \\  & R & 0.865 & 0.866 & 0.847 & 0.832 & 0.857 \\ \hline \multirow{3}{*}{Heavy rainy} & MAE & 68.212 & 62.160 & 64.161 & 65.840 & 63.448 \\  & RMSE & 96.490 & 94.977 & 97.203 & 103.880 & 96.373 \\ \cline{1-1}  & R & 0.657 & 0.663 & 0.651 & 0.619 & 0.647 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The performance comparison of DWT-CNN-LSTM model at different WD levels using the dataset of Desert Rock Station. The performance comparisons of different sunny days' forecasting models using the dataset of Elizabeth City State University and Desert Rock Station are respectively shown in Tables 8 and 9. In Table 8, the prediction accuracy of DWT-CNN-LSTM (WD level 1) is worse than the single CNN-LSTM without WD. The corresponding conclusion can be drawn that the application of DWT based solar irradiance sequence decomposition does not improve the forecasting performance. The reason behind this phenomenon has already been explained in Section 3.5. As for our proposed model without WD (i.e., CNN-LSTM), it is superior to manually extracted features-ANN. This further verifies the ability of CNN to automatically and effectively extract representative and significant information from the raw input data. Additionally, ANN, persistence forecasting, and ARIMA models perform worse than CNN-LSTM, which also validates the advisability of applying the combined DL models in solar irradiance forecasting. By comparing among CNN-LSTM, CNN and LSTM, the comparing results also verify the reasonableness of the tandem connection of CNN and LSTM, because the performance evaluation (based on MAE, RMSE and R) results of CNN-LSTM are all better than those of CNN and LSTM. The above similar results can also be found in Table 9. \begin{table}
\begin{tabular}{c c} \hline \hline
**Statistical Features** & **Expression** \\ \hline Variance 1 & \(Z_{var}=(1/n)\sum_{i=1}^{n}(z_{i}-\mu)^{2}\) \\ Maximum & \(Z_{\text{max}}=\text{max}(z)\) \\ Skewness & \(Z_{skew}=E\Big{[}((z-\mu)/\sigma)^{3}\Big{]}\) \\ Kurtosis & \(Z_{skew}=E\Big{[}((z-\mu)/\sigma)^{4}\Big{]}\) \\ Average & \(Z_{aver}=(1/n)\sum_{i=1}^{n}z_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The list of manually extracted features.