# Short-Term Power Load Prediction of VMD-LSTM Based on ISSA Optimization
## 5 Experiment and Analysis
### Example 1 Experiment
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & **RMSE** & **MAE** & **MAPE** & \(\mathbf{R^{2}}\) \\ \hline VMD+MLP & 2001.793 & 1526.295 & 0.087 & 0.7991 \\ VMD+GRU & 194.987 & 150.36 & 0.009 & 0.9981 \\ VMD+LSTM & 901.112 & 552.269 & 0.0276 & 0.9593 \\ VMD+BiLSTM & 501.163 & 386.788 & 0.0221 & 0.9875 \\ VMD-SSA-LSTM & 236.234 & 168.452 & 0.0087 & 0.9972 \\ VMD+ISSA-LSTM & 104.982 & 78.848 & 0.0047 & 0.9994 \\ VMD+ISSA-GRU & 141.247 & 100.078 & 0.0059 & 0.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Prediction results using the VMD. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **MAPE** & \(\mathbf{R^{2}}\) \\ \hline MLP & 2507.245 & 1750.557 & 0.0964 & 0.6881 \\ GRU & 595.862 & 481.433 & 0.0275 & 0.9824 \\ LSTM & 1618.641 & 1081.296 & 0.0562 & 0.87 \\ BiLSTM & 614.801 & 457.115 & 0.0288 & 0.9811 \\ SSA-LSTM & 568.124 & 413.67 & 0.0219 & 0.984 \\ ISSA-LSTM & 350.546 & 252.363 & 0.0156 & 0.9939 \\ ISSA-GRU & 378.244 & 284.721 & 0.0159 & 0.9929 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: No VMD used. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**K** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline mean & 0.9571 & 0.9546 & 0.9964 & 1.0314 & 1.06 & 1.0954 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The value of the entropy of each component. The visual inspection of the VMD results demonstrates a reduction in load complexity, as unprocessed load data directly used for prediction lead to significantly larger forecasting errors and increased prediction difficulty. By integrating Variational Mode Decomposition (VMD) with predictive models, the hybrid forecasting framework achieves an improved performance. Quantitative results are presented in Figure 10 and Table 6.  
Figure 10: Comparison of prediction results using VMD in January. Figure 9: The VMD results. As can be seen from Table 6, the ISSA-LSTM and ISSA-GRU exhibit the most pronounced improvements, with the \(E_{MAPE}\) reduced by 69.87% and 62.89%, respectively, compared to their non-decomposed baselines. These results statistically confirm that VMD significantly enhances the prediction accuracy across all tested models. Mechanistically, this improvement arises because VMD addresses the inherent volatility and non-stationarity of load sequences by decomposing them into intrinsic mode functions (IMFs) with distinct temporal scales. This decomposition mitigates the complexity of the prediction task by transforming non-stationary data into stationary sub-sequences, aligning with the time-frequency analysis principles of the mode decomposition family. Table 6 reveals that the proposed method outperforms the VMD-ISSA-GRU with the \(E_{RMSE}\) reduced by 25.67%, the \(E_{MAE}\) by 21.21%, and the \(E_{MAPE}\) by 20.34%. This improvement is attributed to the architectural difference between LSTM and the GRU: the GRU merges the forget gate and input gate into a single update gate, potentially discarding critical long-term dependencies in complex decomposed load sequences. Although the VMD and ISSA optimization enhance the GRU's performance, the GRU's simplified gating mechanism limits its feature representation capacity for non-stationary intrinsic mode functions (IMFs), leading to a suboptimal hyperparameter tuning compared to the LSTM-based architecture. Table 6 quantitatively validates that the proposed ISSA-based method outperforms VMD-SSA-LSTM, with the \(E_{RMSE}\) reduced by 55.56%, the \(E_{MAE}\) by 53.19%, and the \(E_{MAPE}\) by 45.98%. These improvements significantly surpass the SSA-based baseline, confirming the effectiveness of the ISSA in addressing the SSA's inherent limitations (e.g., premature convergence and suboptimal parameter exploration). To further validate the generalizability of the proposed method, out-of-sample prediction experiments were conducted using the April, July, and October load profiles (Figures 11-13).