# 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  
Increasing the similarity between the training sample and the test sample can indirectly improve the prediction accuracy of the model. The weather conditions in the same months every year were similar, so the data set was divided into four quarters. In the experiment, one-month data for each quarter was selected as the test data set, and the three-month data in the same quarter of the previous year was used as the training data set. For example, the data from 1 to 31 May 2014 were used as test data, and the data from April, May, and June 2013 as training data. Since the prior assumption of the GP model conforms to the normal distribution, the normal distribution theory can be used to calculate the probability prediction result of the photovoltaic power. The mean and variance of the variable to be predicted can be obtained by the GP model. The mean is used to indicate the prediction. The mean is used to represent the predicted value of the variable. Combined with the mean and the variance, we can obtain the probability prediction results, so as to obtain the upper and lower limits of the confidence interval at different confidence levels. The confidence interval can be expressed as follows:\[(\mu-\frac{\sigma}{n}z_{\alpha/2},\mu+\frac{\sigma}{n}z_{\alpha/2}) \tag{22}\]  
where \(\mu\) is the mean value,\(\sigma\) is the standard deviation, and \(z_{\alpha/2}\) can be obtained by looking up the table. If the confidence level is 0.95, \(z_{\alpha/2}=1.96\). In this paper, the IMGWO is compared with the GWO and PSO. The results are shown in Figure 3. The fitness value and iteration number of the IMGWO are 0.1065 and 25 times, respectively. The fitness value and iteration number of the GWO are 0.1086 and 38 times, respectively. The fitness value and iteration number of the PSO are 0.1146 and 18 times, respectively. Therefore, the IMGWO has a faster convergence speed and better fitness than the GWO. Although the convergence speed of the PSO is better than the IMGWO, the fitness value is larger than that of the IMGWO, indicating that the PSO falls into the local optimum. From the above analysis, it can be proven that the IMGWO has a stronger global search ability and better search speed. Figure 4 shows the IMSPGP model prediction results of seven days selected from May. The first four days are sunny, the last three days are cloudy, and the shaded parts represent 95% confidence intervals, 80% confidence intervals, and 50% confidence intervals, respectively. The photovoltaic output shows with certain regularity that the point prediction result is more accurate, the prediction interval is slightly wider at the peak, and the overall prediction accuracy is higher. As can be seen from Table 2, IMSPGP had the smallest RMSE and CRPS, with optimal prediction performance, whether representing a sunny or rainy day. It should be explained that although the PISAW of the IMSPGP model is larger than that of the GP model and the SPGP model for sunny days, the PICP value is larger than that of the other two models. In this case, it is necessary to consider the size of the comprehensive evaluation criterion CRPS. Because the IMPSGP model has the smallest CRPS, it is shown that the model does improve the prediction effect. Figure 4: Point forecast and interval forecast over seven days using IMSPGP. Figure 3: Comparison of fitness values. To obtain the probability prediction results of IMLSSVM, this paper first calculates the prediction error of the IMLSSVM model for the whole year of 2012. The model is tested in different seasons. As can be seen from Table 3, the IMLSSVM has better predictive performance than the LSSVM. In terms of point prediction performance among the models, IMSPGP generally has the highest accuracy. As a whole, the IMLSSVM model is better than the QRNN model. In order to increase the diversity of the model, the data of the error distribution are obtained by using the IMLSSVM instead of the IMSPGP.