# ForecastNet Wind Power Prediction Based on Spatio-Temporal Distribution
## 3 Results and Discussion
### Analysis of Probability Density Prediction Results  
In order to verify the prediction effect of ForecastNet on the uncertainty of the spatio-temporal distribution of wind power, the hidden layer of ForecastNet is improved. Different hidden layer connection methods such as MLP, CNN, and attention mechanism fully connected network are chosen to analyze their effects on the prediction effect. The rolling forecast is used to predict the wind power, and each time the data of the next 12 time points are predicted, the multi-step prediction is performed to predict the distribution of wind power in the next 2 days. The prediction results of different prediction steps in the multi-step prediction process were randomly selected, and the prediction intervals at different confidence levels (80%, 85%, and 90%) are shown in Figure 12.  
As can be seen from the Figure 12, the prediction intervals of each probabilistic prediction model cover most of the real values more accurately, and the trends in the upper and lower limits of the prediction intervals are also consistent with the trend in the wind power. The wind power prediction intervals obtained at different confidence levels are different, and the larger the confidence level, the wider the given prediction interval. The specific prediction evaluation indexes are shown in Table 3.  
Different variants can be obtained by changing the hidden layer structure of ForecastNet. As can be seen from Table 3, the highest coverage of prediction intervals at different confidence levels is achieved by the CNNFN model, with interval coverage of reliability metrics at 90%, 85%, and 80%, and confidence levels of 100%, 98.95%, and 95.32%, respectively. However, interval coverage that is too high may cause the average width of the intervals to rise. The average width of the intervals of the CNNFN model is also the highest among the three models, which is 72.11 kW, 67.75 kW, and 63.31 kW at 90%, 85%, and 80% confidence levels, respectively. The wider the average width of the intervals in the case of certainty of the interval coverage, the less practical significance of the interval prediction. Figure 11: Multi-step prediction error curves for different numbers of THPO. Both the ADFN model and the MLPFN model obtained relatively good prediction results, and the predicted interval coverages obtained are up to the pre-specified confidence level. At confidence levels of 90%, 85%, and 80%, the interval coverage of the MLPFN model is higher than that of the ADFN model by 4.11%, 4.28%, and 3.59%, respectively. However, the average width of the intervals of the ADFN is narrower, which is reduced by 34.19%, 35.41%, and 35.17% compared with that of the MLPFN model, respectively, achieving better prediction results. Combining the above analyses, it can be concluded that the prediction effects of the ADFN and MLPFN models are better than that of the CNNFN model. The ADFN model achieves a narrower interval prediction width based on the attention mechanism at the confidence level of interval coverage, and it is able to better fit the trend in wind power. The CNNFN model, on the other hand, obtained 100% interval coverage at a higher confidence level, making the prediction intervals less meaningful in practice. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Confidence Levels \%** & **Models** & **Interval Coverage/\%** & **Average Width of the Interval/kW** \\ \hline \multirow{4}{*}{80} & CNNFN & 95.32 & 63.31 \\  & MLPFN & 87.26 & 50.46 \\  & ADFN & 83.67 & 32.71 \\  & CNNFN & 98.95 & 67.75 \\  & MLPFN & 90.89 & 54.36 \\  & ADFN & 86.61 & 35.11 \\  & CNNFN & 100.0 & 72.11 \\
90 & MLPFN & 94.54 & 59.95 \\  & ADFN & 90.43 & 39.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of evaluation indexes for the different models. Figure 12: Comparison of wind power prediction intervals for different ForecastNet models. In addition, predictions are made for the three different classes of wind turbines obtained from the previous clustering.