# Research on Short-Term Wind Power Forecasting by Data Mining on Historical Wind Resource
## 5 Numerical Case of Interval Prediction
### LUBE-Elman Interval Prediction  
The network structure of the Elman neural network (ENN) is divided into four parts--an input layer, a hidden layer, an undertaking layer and an output layer--as illustrated in Figure 4. The input layer can be used to transmit the raw data; the imported weighted data are mapped linearly or nonlinearly through the transfer function of the hidden layer; and finally, the processed data are performed by the linear weighted method in the output layer. The framework of the LUBE-Elman interval prediction is shown in Figure 4. For the multi-input and dual-output Elman model, the weights and thresholds in the model can be given arbitrarily and selected optimally.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**MAE (\%)**} \\ \cline{2-5}  & **Part one** & **Part two** & **Part three** & **Part four** \\ \hline Primitive model & 20.05 & 13.51 & 3.85 & 5.09 \\ \hline The new model & 8.57 & 5.06 & 2.56 & 3.87 \\ \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**RMSE (\%)**} \\ \cline{2-5}  & **Part one** & **Part two** & **Part three** & **Part four** \\ \hline Primitive model & 23.99 & 14.83 & 4.48 & 6.93 \\ \hline The new model & 16.09 & 7.29 & 3.58 & 5.09 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental results of two models.  
According to the previous method, we obtained similar continuous time intervals from the training samples. The training set is expressed as \(T=\left\{(x_{i},p_{1})\,{}_{i=1}^{N}\right\}\), where \(x_{i}\) represents the input parameters of the model, including the historical wind speed, wind direction, temperature and pressure, and \(p_{1}\) is the historical wind power. The testing set is expressed as \(P=\left\{(x_{i},p_{2})\,{}_{i=1}^{N}\right\}\), and then determined given the confidence interval and confidence probability of \(100(1-\alpha)\%\), where \(\alpha\) represents confidence, and it is 0.9 in this paper. The prediction interval is \(I_{P}^{\alpha}(x_{i})\).  
\[I_{P}^{\alpha}(x_{i})=\left[L_{t}^{\alpha}(x_{i}),U_{t}^{\alpha}(x_{i})\right] \tag{11}\]  
where \(L_{t}^{\alpha}(x_{i})\) means the lower limit of the prediction interval, and \(U_{t}^{\alpha}(x_{i})\) means the upper limit of the prediction interval.  
The training set and testing set are normalized, and the normalized interval is \((0,1)\). The normalized expression is as follows:  
\[\begin{array}{c}P_{i}=\left(P-P_{\text{imin}}\right)/\left(P_{\text{max}}-P _{\text{imin}}\right)\\ T_{i}=\left(T-T_{\text{imin}}\right)/\left(T_{\text{imax}}-T_{\text{imin}}\right) \end{array} \tag{12}\]  
There are four input eigenvectors and one output vector in the model. Where \(w^{1}\), \(w^{2}\) and \(w^{3}\) are the weight of the first stage, the weight of the second stage and the weight from the hidden layer to the output layer, respectively. \(x(i)\), \(i\) = 1,2,3,4, represents the input eigenvector, including wind speed, direction, pressure and temperature. \(x_{i}(k)\) is the K-th value of the eigenvector.\(f(*)\) is the transfer function of the middle layer neural network. The expression is as follows:  
\[\begin{array}{c}x(i)=f(w^{1}x_{i}(k)+w^{2}(u(k-1)))\\ x_{i}(k)=x(k-1)\\ y(i)=g(w^{3}x(i))\end{array} \tag{13}\]  
The final output value is the weighted summation of each eigenvector, as follows:  
\[y=\sum_{i=1}^{4}g(w^{3}x(i)) \tag{14}\]  
In the training process, the weights and thresholds of the given hidden layer will not be changed, but the parameters of the output layer will be changed. The prediction interval will be obtained from optimal weights based on the calculation by the least square method.  
Figure 4: The network of Elman interval prediction.