# Improved Probability Prediction Method Research for Photovoltaic Power Output
## 4 Experiment
### Experiment and Analysis
#### 4.3.1 Analysis of Experiment Results for the Single Models
Figure 5 shows a scatter plot of the predicted and actual power generation of the IMLSSVM model for the whole year of 2012. As shown in the figure, the data are not evenly distributed. Therefore, when segmenting the predicted power, the number of data in each interval will be different according to the principle of equalization. In order to make the number of samples in each interval roughly the same, the final division of the intervals is shown in Table 4 after several tests. At the first interval, the length is very short, so the range is set to this value. The approximate number of samples in each interval is beneficial to the fitting effect of the parameter estimation, while ensuring the reliability and stability of the error statistics. In order to find the estimation method that can best describe the model error distribution, this paper uses the normal distribution, T-location-scale distribution, logistic distribution, and KDE method to estimate the probability density of the error values in five intervals. As shown in Figure 6, sub-graphs (a), (b), (c), (d), and (e) represent intervals 1, 2, 3, 4, and 5, respectively. The histogram represents the distribution of errors. It can be seen from the figure that there are different error distributions among different power intervals, so it is feasible to use different probability density functions among different power intervals. In addition, it shows that the probability density curve obtained by the KDE method fits better with error distribution map. Therefore, this paper will use the KDE method to estimate the probability density of different intervals. \begin{table}
\begin{tabular}{c c c c c} \hline Interval & [0,0.05] & [0.05,0.2] & [0.2,0.4] & [0.4,0.65] & [0.65,1] \\ Number of Samples & 1268 & 905 & 925 & 951 & 911 \\ \hline \end{tabular}
\end{table} 
Table 4: Statistics of samples in each interval. Figure 6: Comparison of error probability density functions in different intervals. After obtaining the probability density function of each interval, the power interval which the point prediction value of the IMLSSVM belongs to is determined. Then, the probability density function of the interval is used as the probability density function of the prediction point, thereby obtaining the probability distribution. In Figure 7, the forecasting result of seven days in May using IMLSSVM is shown. Compared with Figure 4, the interval width of the IMLSSVM model is similar to the IMSPGP model at the same confidence level. In the high-power interval, the value of width becomes larger, but in the low-power interval, the value of width is slightly smaller than the IMSPGP model, which is related to the peak-tail characteristic of the probability density function in interval I. The cumulative distribution function graph of each model at multiple time points is made to further analyze the probability distribution of the model, as shown in Figure 8. The characteristic of the IMSPGP curve is relatively flat and the performance is general. The QRNN model has steep curve characteristics in different prediction models, indicating that it has the characteristics of sharp peaks and thin tails, and the sharpness features are obvious. As shown in sub-graph (b) and (d), when the power is small, IMLSSVM has increased sharpness compared with other predictive models, and the cumulative distribution function is better. But when the power value becomes large, the predicted cumulative distribution function is not so prominent in many predictive models. It can be known from the above analysis, the three prediction models have different prediction effects.