## 4 Discussions and Comparison  
To test the prediction effect of the model proposed in this paper, we compared the results of the following prediction models: (1) the single prediction models (ARMA, DBN) used in this paper; (2) the common neural network prediction model, RNN and Gradient Boost Decision Tree (GBDT) in literature [46; 47], used on a representative basis; (3) the combined prediction model, Discrete Wavelet Transformation (DWT) in literature [48] and traditional EMD and EEMD are used on a representative basis. The prediction results for each model are shown in Figure 11.  
Figure 11: _Cont._  
Figure 10: VMD-ARMA-DBN combination forecast results. Figure 11: _Cont_. From the simulation results shown in Figures 10 and 11, the VMD-ARMA-DBN combined models have a better tracking and fitting ability for the PV output curve. Compared to the single models, the combined model prediction accuracy (after using the modal decomposition technique) shows different degrees of improvement. Figure 12 is a bar graph demonstrating the absolute error of prediction in each model. From the perspective of the absolute error distribution of the prediction results, the stability of the prediction accuracy for the single models is poor, and the error distribution interval is large. Among them, the absolute error distribution interval of each model is [0, 24.7821], [0.0051, 22.2464], [0.0082, 22.3289], [0.0363, 22.6686], [0.0005, 8.8306], [0.0018, 8.7955], [0.0008, 10.5322], and [0.0017, 6.6526], respectively, and the prediction error median is 0.1692, 0.2791, 0.2708, 0.4523, 0.5926, 0.3078, 0.0351, and 0.1414, respectively. The absolute error distribution of the VMD-ARMA-DBN model is more concentrated and the median of the error is the smallest, which is the most ideal of the eight groups of prediction models. In summary, the VMD-based multi-frequency combined forecasting model presented in this paper is superior to other models. To compare the prediction effects of each  
Figure 11: Prediction results for multiple models. (**a**) ARMA model prediction results; (**b**) DBN model prediction results; (**c**) RNN model prediction results; (**d**) GBDT model prediction results; (**e**) EMD-ARMA-DBN model prediction results; (**f**) EEMD-ARMA-DBN model prediction results; (**g**) DWT-RNN-LSTM model prediction results. RNN: Recurrent Neural Network; GBDT: Gradient Boost Decision Tree; EEMD: Ensemble Empirical Mode Decomposition; DWT: Discrete Wavelet Transformation; LSTM: Long Short-Term Memory. Figure 12: Simulation results of each model: absolute error box plot. model more intuitively, we used quantitative evaluation indicators. Table 6 shows the evaluation results for each model. First, it can be concluded from Figure 12 and Table 6 that, compared with the single prediction models containing ARMA, DBN, RNN, and GBDT, the introduction of the modal decomposition method has a great influence on the accuracy of the prediction results. The modal decomposition method is used to effectively decompose the original PV output, and the prediction method is selected according to the characteristics of different modal vectors, which can make the prediction result more accurate and stable, and the result can be anticipated. The PV system power output has high volatility, variability, and randomness; through modal decomposition it can effectively eliminate the unrelated noise components to make each component easier to predict. In the single prediction models, the error of the ARMA prediction model is the largest, which is not suitable for effectively tracking the undecomposed solar PV output; DBN, RNN and GBDT belong to machine learning, and the prediction error is essentially the same. However, the parameters of the RNN prediction model are more difficult to choose and more easily fall into the local optimum, and GBDT is easy to over-fit for complex models. However, combined prediction methods can effectively avoid these problems.