# Deep Neural Network and Long Short-Term Memory for Electric Power Load Forecasting
## 4 Case Studies and Discussion
### Comparison and Analysis of Long-Term Electric Power Load Forecasting  
Table 5 shows the proposed DNN and LSTM comparisons for long-term power load forecasting. For the prediction error, the MAE (MW), RMSE (MW), CVRMSE (%), MAPE (%), R\({}^{2}\), and calculation time (ms) were adopted for the long-term electric power load forecasting. For long-term electric power forecasting, the MAE, RMSE, CVRMSE (%), and MAPE of company B (\(\Delta_{B}\)) with a constant power consumption pattern indicated better performance than the proposed LSTM, with values of 0.03 MW, 0.04 MW, 0.15%, and 0.27%, respectively. The calculation time for company B was better than that of the proposed LSTM by an average of 29.8 ms. The R\({}^{2}\) for company B implied that the DNN and LSTM approached approximately 0.99. The MAE, RMSE, CVRMSE (%), and MAPE of company T (\(\Delta_{T}\)) with irregular power consumption patterns showed a better performance than the proposed LSTM, with the proposed DNN being 0.05 MW, 0.21 MW, 0.16%, and 0.07%, respectively. The calculation time of company T was better than that for the proposed LSTM. The proposed DNN was 29.81 ms on average. The R\({}^{2}\) of company T for DNN and LSTM was approached approximately 0.99. The comparison results of MAE, RMSE, CVRMSE (%), MAPE, R\({}^{2}\), and calculation time for the proposed DNN and LSTM illustrated that the DNN and LSTM of company B (better power consumption pattern) outperformed that of company T (an irregular power consumption pattern). The comparison of the MAE, RMSE, CVRMSE (%), MAPE, R\({}^{2}\), and the calculation time of the proposed DNN (\(\Delta_{DNN}\)) indicated that company B outperformed company T by 0.05 MW, 0.04 MW, 0.08%, 0.15%, 0, and 0.84 ms, respectively. Moreover, the comparison of the MAE, RMSE, CVRMSE (%), MAPE, R\({}^{2}\), and calculation time of the proposed LSTM (\(\Delta_{LSTM}\)) showed that company B outperformed company T by 0.07 MW, 0.21 MW, 0.06%, 0.35%, 0, and 0.85 ms, respectively. In addition, MAE, RMSE, CVRMSE (%), MAPE, R\({}^{2}\), and calculation time of \(\Delta_{DNN}\) were higher than those of \(\Delta_{LSTM}\) by 0.08 MW, 0.25 MW, 0.31%, 0.34%, 0 and 59.61 ms, respectively.  
Figure 13a,b show the errors between the actual and predicted values of the proposed DNN and LSTM, respectively, for company B in 2019. The error range in Figure 13a is from \(-\)0.4 to 0.5, while that in Figure 13b is from \(-\)1 to 0.8. As described in Table 4, the proposed DNN method outperformed the proposed LSTM.  
Figure 14a,b show the errors between the actual and predicted values of the proposed DNN and LSTM, respectively, for company T in 2019. The error range in Figure 14a is from \(-\)0.8 to 1, while that in Figure 14b is from \(-\)5 to 3.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multicolumn{3}{c}{**Company B**} & \multicolumn{3}{c}{**Company T**} & \multicolumn{3}{c}{**\(\Delta\)**} \\ \cline{2-9}  & **DNN** & **LSTM** & \(\Delta_{B}\) & **DNN** & **LSTM** & \(\Delta_{T}\) & \(\Delta_{DNN}\) & \(\Delta_{LSTM}\) \\  & **(A)** & **(B)** & **(A-B)** & **(C)** & **(D)** & **(C–D)** & **(A–C)** & **(B–D)** \\ \hline MAE (MW) & 0.02 & 0.05 & \(-\)0.03 & 0.07 & 0.12 & \(-\)0.05 & \(-\)0.05 & \(-\)0.07 \\ RMSE (MW) & 0.04 & 0.08 & \(-\)0.04 & 0.08 & 0.29 & \(-\)0.21 & \(-\)0.04 & \(-\)0.21 \\ CVRMSE (\%) & 0.15 & 0.30 & \(-\)0.15 & 0.06 & 0.23 & \(-\)0.17 & \(-\)0.09 & 0.07 \\ MAPE (\%) & 0.21 & 0.48 & \(-\)0.27 & 0.06 & 0.13 & \(-\)0.07 & 0.15 & 0.35 \\ R\({}^{2}\) & 0.99 & 0.99 & 0 & 0.99 & 0.99 & 0 & 0 & 0 \\ Time (ms) & 11.98 & 41.78 & \(-\)29.8 & 12.82 & 42.63 & \(-\)29.81 & \(-\)0.84 & \(-\)0.85 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of the DNN and LSTM performances for long-term electric power load forecasting.  
Figure 14: Error between the actual and predicted values using the proposed DNN and LSTM (company T).  
Figure 13: Error between the actual and predicted values using the proposed DNN and LSTM (company B).