# Power Load Demand Forecasting Model and Method Based on Multi-Energy Coupling
## 4 Case Analysis
### Comparative Analysis and Conclusions  
In order to verify the effect of the model, this paper calculated the multi-energy coupling forecasting results, total load demand forecasting results and load calculation results of mRMR-AFWA-LSSVM, AFWA-LSSVM, LSSVM, and AFWA-SVM four models respectively. The final forecasting results of the model are shown in Table 8, and in order to show the model fitting effect more intuitively, we presented the results as shown in Figure 9. Among them, mRMR-AFWA-LAAVM and AFWA-LSSVM model had the best fitting effect, LSSVM model was the second, and AFWA-SVM was the last. Figure 8: Model forecasting results. Figure 9: Forecasting results of four models. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Actual**} & \multicolumn{3}{c}{**mMRMR-AFWA-LAAVM**} & \multicolumn{3}{c}{**AFWA-LSSVM**} & \multicolumn{3}{c}{**LSSVM**} & \multicolumn{3}{c}{**AFWA-SVM**} \\ \hline
**Integrated** & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Integrated**} & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Integrated**} & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Integrated**} & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Integrated**} & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Load**} \\
**Energy** & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**LOAD**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**Load**} & \multicolumn{1}{c}{**Load**} \\ \hline
43.53 & 1144.58 & 1101.05 & 44.01 & 1157.58 & 1113.57 & 43.57 & 1160.97 & 1117.41 & 43.10 &  
We compared and evaluated the performance of forecasting models from six aspects: model calculation time (t), mean square error (MSE), root mean square error (RMSE), average absolute error (MAE), average absolute percentage error (MAPE), determination coefficient (\(R^{2}\)), and the first five indicators are the smaller the better, but \(R^{2}\) is the larger the better. The calculation formula is as follows. \[MSE=\frac{1}{N}{\sum\limits_{n=1}^{N}}{\left({\hat{X}_{(n)}-X_{(n)}}\right)^{2}}, \tag{25}\]  
\[RMSE=\sqrt{\frac{1}{N}{\sum\limits_{n=1}^{N}}{\left({\hat{X}_{(n)}-X_{(n)}} \right)^{2}}}, \tag{26}\]  
\[MAE=\frac{1}{N}{\sum\limits_{n=1}^{N}}{\left|{X_{(n)}-\hat{X}_{(n)}}\right|}, \tag{27}\]  
\[MAPE=\frac{1}{N}{\sum\limits_{n=1}^{N}}{\left|{\frac{{X_{(n)}-\hat{X}_{(n)}} }{{X_{(n)}}}}\right|}\times 100\%, \tag{28}\]  
\[R^{2}=\frac{SSR}{SST}=\frac{\sum\limits_{n=1}^{N}{\left({\hat{X}_{(n)}-\overline {X}_{(n)}}\right)^{2}}}{\sum\limits_{n=1}^{N}{\left({X_{(n)}-\overline{X}_{(n )}}\right)^{2}}}, \tag{29}\]  
where, \(N\) is the number of forecasting data groups, \(n\) is the forecasting number group, \(\hat{X}_{(n)}\) is the forecasting result, \(X_{(n)}\) is the actual value, \(\overline{X}_{(n)}\) is the actual average value, \(SSR\) is the sum of squares of the regression, and \(SST\) is the total sum of squares. The calculation results are as shown in Table 9.  
By analyzing the calculation results, it can be found that, for the five indexes of MSE, RMSE, MAE, MAPE, and \(R^{2}\), the forecasting accuracy effect was AFWA-LSSVM \(>\) mRMR-AFWA-LSSVM \(>>\) LSSVM-AFWA-SVM. In the multi-energy coupling forecasting, their MAPE differs 0.07%, 5.39%, and -0.90%; and in the total demand forecasting, their MAPE differs 0.05%, 2.19%, and 0.58%. However, in the total computing time, LSSVM \(<\) AFWA-SVM \(<<\) mRMR-AFWA-LSSVM \(<\) AFWA-LSSVM. The time they spent was 8.94 s, 17.5 s, 140.99 s, and 151.33 s respectively. After mRMR selection, AFWA-LSSVM's forecasting accuracy decreased slightly and the forecasting time consumption also decreased.