# Wind Power Short-Term Prediction Based on LSTM and Discrete Wavelet Transform
## 5 Results and Analysis  
The experimental results confirm that the db7 wavelet function was suitable for decomposing and reconstructing the wind power raw data shown in Figure 5 to obtain an approximate signal and one detail signal, as shown in Figure 6.  
Figure 7 shows one-step forecasting results of wind farm 1, three-step forecasting results of wind farm 2, and five-step forecasting results of wind farm 3. It can be seen that the prediction accuracy of the proposed method is the best compared with the benchmarks. Figure 5: Power values generated by the wind turbine registered every 15 mins. Figure 6: Results of DWT for wind farm 1. Figure 8 shows the mean absolute percentage error (MAPE) of one-step forecasting for farm 1, the MAPE of three-step forecasting for farm 2, and the MAPE of five-step forecasting for farm 3. The MAPE of the proposed method was the lowest. Figure 7: Forecasting results of the six methods. Figure 8: Mean absolute percentage error (MAPE) of wind power forecasting. In order to further verify the validity and performance of the proposed prediction method, three evaluation indexes including the mean absolute error (MAE), the mean absolute percent error (MAPE), and the root mean square error (RMSE), were selected to evaluate the performance of every method according to Equations (18)-(20). The experimental results including MAE, MAPE, and RMSE of the original data test set are shown in Tables 1-3. \[MAE=\frac{1}{N}\sum_{i=1}^{N}|y\_real_{i}-y\_pred_{i}| \tag{18}\]  
\[MAPE=\frac{1}{N}\sum_{i=1}^{N}\Bigl{|}\frac{y\_real_{i}-y\_pred_{i}}{y\_real_{i }}\Bigr{|}*100 \tag{19}\]  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{N}(y\_real_{i}-y\_pred_{i})^{2}}{N}} \tag{20}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Step** & **Algorithms** & **MAE/MW** & **MAPE/\%** & **RMSE/MW** \\ \hline \multirow{8}{*}{1} & DWT\_LSTM & 10.12 & 3.01 & 14.22 \\  & DWT\_RNN & 13.95 & 3.41 & 21.23 \\  & DWT\_BP & 16.42 & 4.85 & 22.80 \\  & LSTM & 28.31 & 4.80 & 39.27 \\  & RNN & 29.10 & 5.17 & 40.51 \\  & BP & 32.26 & 5.53 & 41.66 \\ \hline \multirow{8}{*}{2} & DWT\_LSTM & 18.98 & 4.01 & 27.11 \\  & DWT\_RNN & 26.27 & 4.29 & 40.08 \\  & DWT\_BP & 28.53 & 4.55 & 44.96 \\  & LSTM & 24.83 & 3.39 & 35.43 \\  & RNN & 29.93 & 7.45 & 50.48 \\  & BP & 34.57 & 5.79 & 52.83 \\ \hline \multirow{8}{*}{3} & DWT\_LSTM & 29.48 & 5.15 & 41.33 \\  & DWT\_RNN & 30.66 & 6.33 & 43.51 \\  & DWT\_BP & 36.51 & 6.98 & 51.08 \\ \cline{1-1}  & LSTM & 40.73 & 7.41 & 59.02 \\ \cline{1-1}  & RNN & 41.23 & 7.81 & 61.26 \\ \cline{1-1}  & BP & 46.59 & 8.92 & 65.15 \\ \hline \multirow{8}{*}{4} & DWT\_LSTM & 37.70 & 6.66 & 53.32 \\  & DWT\_RNN & 40.23 & 7.02 & 58.11 \\ \cline{1-1}  & DWT\_BP & 43.19 & 8.77 & 62.96 \\ \cline{1-1}  & LSTM & 47.18 & 8.13 & 68.51 \\ \cline{1-1}  & RNN & 46.65 & 8.52 & 68.54 \\ \cline{1-1}  & BP & 50.75 & 8.61 & 71.04 \\ \hline \multirow{8}{*}{5} & DWT\_LSTM & 45.23 & 8.10 & 63.22 \\  & DWT\_RNN & 46.36 & 11.54 & 63.67 \\ \cline{1-1}  & DWT\_BP & 55.87 & 12.34 & 75.11 \\ \cline{1-1}  & LSTM & 54.32 & 9.91 & 77.12 \\ \cline{1-1}  & RNN & 55.01 & 10.27 & 78.96 \\ \cline{1-1}  & BP & 56.42 & 10.79 & 77.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation indexes of farm 1. RNN: recurrent neural network; BP: back-propagation; MAE: mean absolute error; RMSE: root mean square error.