## 5 Case Analysis
### Investigations of a Wind Farm in Gansu Province
#### 5.1.2 Experimental Results  
CNN has more advantages than a BP neural network and support vector machine (SVM) in the field of wind power prediction, which was proven in [18]. Therefore, in order to verify the advantages of the VPBC (VMD + PSR + bi-level CNN) + PSO proposed in this paper, the performance of point prediction and interval prediction were compared and verified, respectively. Comparing the point-based forecasting results with the persistence method, CNN, and VPCB (VMD + PSR + CNN-BPNN), the interval prediction results were compared with CNN + PSO, VPCB + PSO. The above prediction algorithms were implemented in MATLAB (2014a, The MathWorks, Natick, MA, USA). 1. Point-Based Forecasting Performance  
The normalized mean absolute error (NMAE), normalized root mean square error (NRMSE) and mean absolute percentage error (MAPE) were used to evaluate the accuracy of the forecasting results. The definitions of the NMAE and NRMSE are provided in [3], and the definition of the MAPE is provided in [18]. The one-step forecasting results of the modes obtained by the five sub-models of the first-layer CNN are shown in Figure 5.  
It is observed in Figure 5 that the forecasting results of the first-layer CNN using VPBC + PSO were in good agreement with the actual modes, especially for the high-frequency modes, which is attributed to the strong periodicity of the high-frequency modes. The partial forecasting results of the VPBC method are shown in Figure 6. The NMAE, NRSME, and MAPE values of the different methods are listed in Table 1.  
Figure 6 indicates that the prediction results of the VPBC method were in good agreement with the actual wind power data, demonstrating a good performance for short-term wind power forecasting. The peak values at 180-280 points in Figure 6 show that the forecasted wind power was lower than the actual wind power. The input data for the models were the historical wind power data, and the forecasted values at a given time depended on the actual values of the previous time, so the models had certain predictive inertia. However, the VPBC method provided more accurate predictions than the other models. Figure 5: Forecasting results of the first-layer CNN based on the VPBC + PSO. VPBC: VMD + PSR + bi-level CNN. As shown in Table 1, the VPBC method had the smallest NMAE, NRMSE, and MAPE, and therefore had the highest forecasting accuracy. The VPBC method had a significantly better forecasting performance than the VPCB and persistence methods, and the historical real value of the mode in the second-layer CNN was used to modify the forecasted value. 2 Interval forecasting performance  
The PICP and PINAW indices for the different methods and different confidence levels are listed in Table 2. Figures 7-9 show the interval forecasting results of the VPBC + PSO method and CNN + PSO method for different confidence levels, and Figures 10-12 show the interval forecasting results of the VPBC + PSO method and VPCB + PSO method for different confidence levels. The results in Table 2 show that the PICP indices of the VPBC + PSO method at the 80%-90% PINC met the confidence level requirements; the method exhibited the highest reliability in terms of wind power interval forecasting, while the PINAW index was lowest for this method at the 80%-90% confidence level. This indicates that this forecasting accuracy was the highest. The VPBC + PSO method had better predictive ability than the other two methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **NMAE** & **NRSME** & **MAPE** \\ \hline VPBC & 3.69\% & 0.3339 & 6.46\% \\ CNN & 6.52\% & 0.3811 & 11.41\% \\ VPCB & 4.64\% & 0.3663 & 8.11\% \\ Persistence & 5.01\% & 0.3375 & 8.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Forecasting error indices of the different methods. NMAE: normalized mean absolute error; NRSME: normalized root mean square error; MAPE: mean absolute percentage error; VPCB: VMD + PSR + CNN-BPNN.