## 3 Case Study
### Performance Comparison Analysis of Different Solar Irradiance Forecasting Models
#### 3.5.3 Comparison Analysis under Rainy Days  
In terms of the rain day, it is discussed in Section 3.5 that the corresponding DWT-CNN-LSTM model performs best at level 2 whether using the dataset of Elizabeth City State University or Desert Rock Station. Therefore, as shown in Tables 12 and 13, the DWT-CNN-LSTM (WD level 2) is compared with other forecasting models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Forecasting Models** & **MAE** & **RMSE** & **R** \\ \hline DWT-CNN-LSTM (WD level 1) & 62.761 & 91.098 & 0.965 \\ CNN-LSTM & 63.661 & 96.641 & 0.959 \\ CNN & 64.339 & 95.373 & 0.961 \\ LSTM & 66.752 & 97.523 & 0.954 \\ Manually extracted features-ANN & 128.06 & 165.98 & 0.817 \\ ANN & 69.522 & 100.811 & 0.950 \\ Persistence forecasting & 74.413 & 114.369 & 0.939 \\ ARIMA & 89.543 & 150.192 & 0.865 \\ \hline \hline \end{tabular}
\end{table}
Table 11: The performance comparison of different cloudy days’ forecasting models using the dataset of Desert Rock Station.  
Figure 8: Actual and forecasted solar irradiance on cloudy day pattern using dataset of Elizabeth City State University.  
When CNN-LSTM and DWT-CNN-LSTM (WD level 2) are compared, the results and the reasons for them are similar to those discussed in Section 3.5.3. Specifically, the MAE is lowered from 93.694 in CNN-LSTM to 89.503 in DWT-CNN-LSTM. The RMSE is lowered from 142.194 in CNN-LSTM to 139.133 in DWT-CNN-LSTM. At the same time, the R has also been improved from 0.743 in CNN-LSTM to 0.757 in DWT-CNN-LSTM. The lower MAE and RMAE denote smaller differences between forecasted and true solar irradiance data, and the higher R also represents that the forecasted solar irradiance curve is closer to the true one. Therefore, the application of the DWT based sequence decomposition also helps the improvement of forecasting performance. Additionally, the combined CNN-LSTM shows better forecasting performance than the rest models (i.e., single DL models and traditional forecasting models). This indicates that the reasonable combination of DL models can better take advantage of the CNN and LSTM.  
In sum, the improved DL models (i.e., DWT-CNN-LSTM) not only leverages the advantages of DWT to obtain subsequences with good behavior (e.g., more stable variances and fewer outliers) in terms of regularity, but also absorbs the superiority of CNN-LSTM to automatically extract abstract features and find long dependencies. Similar results can also be found in Table 13. Figure 9 shows the actual and forecasted solar irradiance curve on rainy day pattern using dataset of Elizabeth City State University.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Forecasting Models** & **MAE** & **RMSE** & **R** \\ \hline DWT-CNN-LSTM (WD level 2) & 130.194 & 180.079 & 0.866 \\ CNN-LSTM & 132.831 & 181.973 & 0.857 \\ CNN & 132.755 & 183.076 & 0.857 \\ LSTM & 133.007 & 184.332 & 0.855 \\ Manually extracted features-ANN & 184.352 & 225.887 & 0.769 \\ ANN & 138.045 & 186.553 & 0.829 \\ Persistence forecasting & 155.661 & 205.340 & 0.788 \\ ARIMA & 177.053 & 210.119 & 0.772 \\ \hline \hline \end{tabular}
\end{table}
Table 13: The performance comparison of different rainy days’ forecasting models using the dataset of Desert Rock Station.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Forecasting Models** & **MAE** & **RMSE** & **R** \\ \hline DWT-CNN-LSTM (WD level 2) & 89.503 & 139.133 & 0.757 \\ CNN-LSTM & 93.694 & 142.194 & 0.743 \\ CNN & 94.773 & 143.072 & 0.737 \\ LSTM & 95.089 & 142.877 & 0.741 \\ Manually extracted features-ANN & 132.321 & 189.842 & 0.639 \\ ANN & 97.894 & 147.818 & 0.736 \\ Persistence forecasting & 114.338 & 173.497 & 0.680 \\ ARIMA & 132.066 & 181.681 & 0.656 \\ \hline \hline \end{tabular}
\end{table}
Table 12: The performance comparison of different rainy days’ forecasting models using the dataset of Elizabeth City State University.