## 3 Case Study
### The Comparison  
For more intuitive comparative analysis, this paper uses the MAE, MSE, and RMSE mentioned above to compare the prediction results of this paper with that of the Auto-Regressive Moving Average Model (ARMA) and DBN single prediction model and the EMD, EEMD, and VMD decomposition combined prediction models. For the single prediction model, the original photovoltaic output data are directly used for modeling and prediction; for the decomposition combined prediction model, the original photovoltaic output data are first decomposed using EMD, EEMD and VMD, and then each frequency component is predicted using DBN, and finally the prediction results of each frequency component are integrated to obtain a final prediction photovoltaic output value. For the comparison results of the models, the comparison results of Yunnan photovoltaic power station data are shown in Table 5, and the comparison results of Gansu photovoltaic power station data are shown in Table 6.  
decomposition-combined prediction model improved by 50.2% compared with the ARMA, and by 41.3% compared with the DBN; for the MAE of EEMD decomposition-combined prediction model improved by 62.9% compared with the ARMA, and by 56.3% compared with the DBN; and for the MAE of VMD decomposition-combined prediction model improved by 78.3% compared with the ARMA, and by 74.4% compared with the DBN. In the decomposition-combined prediction model, the VMD decomposition-combined model has higher prediction accuracy than the EEMD and EMD decomposition-combined model. For example, for the RMSE, the prediction accuracy of VMD combined decomposition model respectively improved by 45.8% and 55% compared with the EEMD decomposition-combined model and the EMD decomposition-combined model. It can be seen that after using VMD to decompose the photovoltaic output, the prediction accuracy is greatly improved. After considering the influence of the characteristic factors, the prediction accuracy is further improved. It can be seen from Table 4 that for MAE, RMSE and TIC, the prediction model of this paper improved respectively by 60.0%, 35.4% and 42.4% compared with the VMD decomposition-combined model. It can be seen that for the Yunnan photovoltaic power station data, the prediction accuracy of model in this paper is higher.  
It can also be seen from Table 6 that the accuracy of the decomposition-combined prediction model is better than that of the single prediction model, while the prediction model of this paper has higher prediction accuracy than other decomposition-combined prediction models; for example, the MAE of this paper improved by 58.0% compared with the VMD decomposition-combined prediction model, and by 74.1% compared with the EEMD decomposition-combined prediction model, by 79.9% compared with the EMD decomposition-combined model, by 90.1% compared with the DBN model, and by 91.6% compared with the ARMA model.  
Based on the comparison of the prediction results of the above two photovoltaic power station, it can be seen that after using the VMD to decompose the photovoltaic output data into modal components with different wave characteristics and using mRMR to analyze the influence of each influencing factor on each frequency component, the prediction accuracy of this paper exceeds that of the traditional decomposition-combined prediction model and the single prediction model. In addition, this paper uses the rolling prediction method in the prediction process, that is, the actual value is continuously absorbed into the model during the prediction process. For example, at moment \(t\), after finishing predicting the value at moment \(t\), the true value of the moment \(t\) and the corresponding influence component are added to the model to predict the value at the next moment. Therefore, this paper can make real-time continuous prediction of photovoltaic output.