## 3 Experiment and Results
### Experimental Results and Analysis  
This section presents the results from the three experiments on the forecasting performance of the proposed novel model. 5.1 Experiment I: The Forecasting Performance of the Combined Models Optimized by Different Optimization Algorithms  
Based on the historical wind speed and wind power time series, four experiments were designed to analyze and contrast the developed combined model with the sub-model forecasting models. Experiment I contrasted combined models with different numbers of sub-models in terms of their forecasting performances and analyzed the ability of the proposed model with five sub-models to forecast wind speed and wind power. The wind speed and wind power forecasting performance were evaluated by eight metrics. For Site 1, the proposed combined model had the best forecasting performance for both wind speed forecasting and wind power forecasting. Specifically, the mean absolute percentage error (MAPE) value was 6.51% for wind speed forecasting and 13.21% for wind power forecasting, smaller than those of the other combined models and sub-models. The relevant characteristics of the models used for Site 1 are shown in Figure 2.  
For Site 2, the best mean absolute error (MAE), root-mean-square error (RMSE), mean absolute percentage error (MAPE), and standard deviation of absolute percentage error (STDAPE) were all obtained with the developed combined method for wind speed forecasting, with values of 0.2608, 0.3783, 6.90%, and 6.41%, respectively. For wind power forecasting, the best forecasting metrics were obtained with the proposed combined model shown in Table 4. This confirms the good performance of the proposed combined model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Data Sets**} & \multirow{2}{*}{**Frequency**} & \multicolumn{2}{c}{**Site 1**} & \multicolumn{2}{c}{**Site 2**} \\ \cline{3-5}  & & **Eigenvalue** & \(\sum_{i=1}^{r}\lambda_{i}/\sum_{i=1}^{d}\lambda_{i}\) & **Eigenvalue** & \(\sum_{i=1}^{r}\lambda_{i}/\sum_{i=1}^{d}\lambda_{i}\) \\ \hline \multirow{2}{*}{Wind Speed} & Low & 1–13 & 97.763 & 1–13 & 95.5416 \\  & High & 14–24 & 2.2357 & 14–24 & 4.4584 \\ \multirow{2}{*}{Wind Power} & Low & 1–13 & 96.2804 & 1–13 & 95.5364 \\  & High & 14–24 & 3.7196 & 14–24 & 4.4636 \\ \hline \multirow{2}{*}{**Data Sets**} & \multirow{2}{*}{**Frequency**} & \multicolumn{2}{c}{**Site 3**} & \multicolumn{2}{c}{**Site 4**} \\ \cline{3-5}  & & **Eigenvalue** & \(\sum_{i=1}^{r}\lambda_{i}/\sum_{i=1}^{d}\lambda_{i}\) & **Eigenvalue** & \(\sum_{i=1}^{r}\lambda_{i}/\sum_{i=1}^{d}\lambda_{i}\) \\ \hline \multirow{2}{*}{Wind Speed} & Low & 1–13 & 98.0989 & 1–13 & 99.1851 \\  & High & 14–24 & 1.9011 & 14–24 & 0.8149 \\ \multirow{2}{*}{Wind Power} & Low & 1–13 & 94.3994 & 1–13 & 92.8841 \\  & High & 14–24 & 5.6006 & 14–24 & 7.1159 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results for four sites after SSA. For Site 3, the wind speed forecasting accuracy of the combined model with five sub-models was significantly better than that of the combined models with less than five sub-models. This means that increasing the number of sub-models can improve the forecasting accuracy of the combined model. The forecasting results of the combined model for Site 4 were similar to those obtained for previous sites; the proposed combined model provided better forecasting results in the first season. Taking wind power forecasting as an example, the lowest MAPE value, obtained with the advanced model, was 13.66%. The combined model with two sub-models had the worst forecasting result, having a MAPE value of 18.48% (the forecasting results of the sub-models are shown in Table 11). Table 4 also shows that the goodness of fit values for different combined models were over 0.9, indicating that combined models have a reduced forecasting error. Figure 2: Wind speed and wind power forecasting result in first season. **Remark 1**.