# Two-Stage Short-Term Power Load Forecasting Based on SSA-VMD and Feature Selection
## 5 Experiment and Results
### Results
#### 5.4.2 Analysis of SVGM-FE Forecasting Results  
In order to further verify the effectiveness of SSA-VMD for load data decomposition, the effectiveness of constructing hybrid forecasting models based on SSA-VMD, and the effectiveness of error correction in two-stage forecasting for load component forecast values, this paper builds the model SSA-VMD-GRU-MLR (SVGM) and a two-stage forecasting model SVGM-EF. The newly constructed models were used to forecast the load values on 10 January 2015.  
The statistical analysis in Table 6 and Figure 10 leads to the following conclusions. The hybrid forecasting models SVGM and SVGM-FE, constructed after SSA-VMD decomposition, have significantly improved forecasting accuracy compared to the GRU forecasting model and the MLR forecasting model. Compared to the GRU model, the RMSE of the SVGM model decreased by 146.665 MW (36.52 percentage points), the MAE decreased by 159.268 MW (44.92 percentage points), and the MAPE decreased by 51.61 percentage points. Compared to the MLR model, the RMSE of the SVGM model decreased by 138.120 MW (35.14 percentage points), MAE decreased by 162.495 MW (45.42 percentage points), and MAPE decreased by 52.88 percentage points. The experiments demonstrate the effectiveness of constructing a hybrid forecasting model based on SSA-VMD. Compared with the SVGM model, the RMSE of the SVGM-FE model decreased by 77.099 MW (30.25 percentage points), the MAE decreased by 60.357 MW (30.91 percentage points), and the MAPE decreased by 23.56 percentage points. In terms of computing time, the SVGM-FE has the longest computing time of 204.812 s, which means it is able to meet the time requirements in practical applications.  
Tables 5 and 6 show that the forecasting accuracy of SVLM-FE is the highest, followed by SVGM-FE, then SVLM, and SVGM ranks the fourth, thus further validating the effectiveness of the two-stage short-term load forecasting method constructed based on SSA-VMD.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE/MW** & **MAE/MW** & **MAPE/\%** & **Computing Time/s** \\ \hline
**SVGM–FE** & **177.798** & **134.930** & **1.979** & **204.812** \\ SVGM & 254.897 & 195.287 & 2.589 & 179.133 \\ GRU & 401.552 & 354.555 & 5.350 & 65.686 \\ MLR & 393.017 & 357.782 & 5.494 & 1.621 \\ \hline \hline \end{tabular}
\end{table}
Table 6: SVGM–FE and other models’ evaluation criteria of Place 1.  
Figure 10: Comparison of the evaluation criteria of SVGM–FE and other models in Place 1.  
Due to the better forecasting performance of SVLM-FE than SVGM-FE, the LSTM was used in the forecasting method proposed in this paper for the high frequency component. In terms of computing time, although the computing time of SVLM-FE is 71.346 s longer than SVGM-FE, SVLM-FE has higher forecasting accuracy, and the computing time of SVLM-FE can meet the time requirements in realistic scenarios, which proves the superiority of the performance of the proposed forecasting method, SVLM-FE.  
As shown in Figure 11, the forecasting values of the SVGM model are closer to the true values than the single GRU and MLR forecasting models; after the second stage of error correction, the errors in the forecasting values obtained by SVGM-FE are further reduced, and the best performance is achieved at both peak and trough load values, including at small peaks and troughs, where the SVGM-FE model forecasts values closest to the true values. SVGM-FE achieves a better forecasting performance for the details of the trend of load values over the next 24 moments. These experimental results further demonstrate the validity of the hybrid SSA-VMD-based model and the superiority of the second stage of forecasting with correction for error. Moreover, the forecasting accuracy of SVLM-FE is higher than that of SVGM-FE, so the final model proposed in this paper is SVLM-FE.