# ForecastNet Wind Power Prediction Based on Spatio-Temporal Distribution
## 3 Results and Discussion
### Analysis of Probability Density Prediction Results
Figures 13-15 demonstrate the probability density predictions of the ADFN model over the next two days. The more common probabilistic prediction models selected for comparison at the 90% confidence level are LSTM (combination of long short-term memory network and Gaussian mixture density model) and the QRGBM model (gradient booster using quantile output). Table 4 shows the corresponding prediction results. As can be seen from Table 4, the turbines in the high wind speed and high output units and the turbines in the high wind speed and low output units achieve the given confidence level when uncertainty prediction is made for turbines in different clusters at the 90% confidence level. The highest interval coverage is obtained by QRGBM in the prediction results, with 99.50%, 88.13%, and 97.01%, respectively. However, the interval width of QRGBM is wider than the other models, reaching 452.58 kW, 358.46 kW, and 329.57 kW, respectively. The overly wide interval width will lead to less valid information available in the prediction results. The LSTM and ADFN models have similar interval coverages. For type 0 (high wind speed and high output units), the ADFN model obtains a slightly narrower average width of intervals, but it is wider for other types, and its average width of intervals increases by 5.23% and 4.34% compared to LSTM model. ADFN, based on the attention mechanism, with a small increase in interval coverage, also increases the average width of intervals by a certain amount, with better prediction results. For type 2 (low wind speed and low output units), the interval coverages of all three models do not reach the confidence level, and the prediction effects are not good. Furthermore, this paper randomly selected the probability density function of the ADFN prediction model at different wind turbines and different time prediction points from the multi-step prediction, as shown in Figure 16.  
The straight line perpendicular to the x-coordinate axis in Figure 16 is the true value at that prediction moment, and the curve is the probability density distribution of the corresponding model. From Figure 16, it can be seen that the probability density curve is complete and smooth, and there is no missing, very high, or very low values. The curve is also not too broad or too narrow, indicating that the prediction effect of the algorithm is appropriate. Most of the real values in the prediction results of the ADFN model fall near the highest probability points of the probability density curve, such as when t = 167, t = 110, t = 100, and t = 0. This indicates that the algorithm predicts with a high accuracy. When the actual wind power value is in the vicinity of the crest of the probability density curve, it indicates that the real value of wind power falls in the high probability interval given by the interval prediction, and the prediction error of these moments is small. When t = 20, the real value of wind power deviates from the center of the probability curve, and when t = 30, the deviation is even further away. This indicates that the prediction error at these moments is large, and the prediction interval may not even cover the real value of wind power. In the probability density curve results obtained from the test set, the prediction results are reliable if most of the actual values are close to the center range of the curve and only a small number of actual values deviate farther. If most of the actual values are deviated or even far away from the position of the peak of the probability density curve, the obtained probability density prediction results are unreliable. In summary, the ADFN prediction model is reliable in predicting the probability density of different wind turbines.