# Improved Probability Prediction Method Research for Photovoltaic Power Output
## 4 Experiment
### Experiment and Analysis
#### 4.3.2 Analysis of Experiment Results for the Combined Model  
In order to obtain a better weight coefficient, this paper uses the arithmetic average method (M1), continuous ranking probability score reciprocal method (M2), IGWO combination method (M3), and entropy method (M4) for comparison and analysis. The CRPS value is taken as the fitness value when  
Figure 8: Cumulative distribution function graph.  
Figure 7: Point forecast and interval forecast over seven days using IMLSSVM.  
the IGWO combination method is used. The number of wolves is set to 30, and the maximum number of iterations is 50. The three weight coefficients of the three single models are variables, and the range are all [0, 1].  
Table 5 shows the CRPS of each model in different intervals. It is shown that in the same interval, each mode has a different CRPS. It is feasible to use the combination with variable intervals and weights.  
Table 6 shows the weight coefficients of each model obtained by the combination method, where w1, w2, and w3 are the weight coefficient values of IMSPGP, QRNN, and IMLSSVM, respectively. According to the weighting coefficients of each model, the CRPS of various combined models can be obtained, as shown in Table 7. It can be seen from Table 7 that among the four combined methods, the IGWO combination method has the smallest CRPS under different weather types (that is, the probability prediction accuracy is the best among the four methods). Therefore, the three models are combined using the IGWO combination method.  
Figure 9 is the comparison of point prediction errors over seven days for various prediction models. The RMSE values of the combined model, IMLSSVM model, IMSPGP model, and QRNN model are 0.0380, 0.0468, 0.0439, and 0.0573, respectively. The combined model has the best predictive performance. In Figure 10, subgraph (a), (b), (c), and (d) are cumulative distribution functions for interval I, II, III, and IV, respectively. The CRPS values in the four intervals are shown in Table 8. Referring to Figure 10 and Table 8, the combined model can obtain the lowest CRPS for the predicted points at interval II and IV. In the other two intervals, it is not optimal. That indicates that the combined  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Interval**} & \multirow{2}{*}{**Weight**} & \multicolumn{5}{c}{**Sunny**} & \multicolumn{5}{c}{**Rainy**} \\ \cline{3-10}  & & **M1** & **M2** & **M3** & **M4** & **M1** & **M2** & **M3** & **M4** \\ \hline \multirow{4}{*}{I} & w1 & 0.3  
In order to further verify the stability and accuracy of the combined model, the data in May, August, November, and February is taken for further verification analysis. The results of each indicator are shown in Table 9. Whether it is sunny or rainy, the CRPS values of the combined model are the smallest. However, on sunny days, there is a case where the IMSPGP model has higher prediction accuracy than the combined model in terms of point prediction. The main reason is that the CRPS is adopted as a fitness value in the IMGWO combination method. Taking the results of May as an example, the combined model has the smallest CRPS value for either sunny days or rainy days. It should be noted that, on sunny days, the PINAW of the IMLSSVM model is smaller than that of the combined model, and the PICP of the IMLSSVM model is larger than the PICP of the combined model. The PINAW and the PICP describe the 95% confidence interval index, which can reflect the probability prediction performance to a certain extent. The CRPS can describe the probability prediction performance comprehensively. According to the comprehensive analysis, the combined model prediction performance improves upon the single model, and has good stability and practicability since the CRPS of the combined model is smaller. A more-accurate probability prediction of the PV power means that uncertainty is reduced, thereby lowering the operating costs of the energy system.