# Short-Term Power Load Prediction of VMD-LSTM Based on ISSA Optimization
## 5 Experiment and Analysis
### Example 1 Experiment  
To comprehensively validate the proposed method's effectiveness in seasonal electric load forecasting, time-series data from a Tetuan City region were employed. For seasonal validation, mid-season months (January for winter, April for spring, July for summer, and October for autumn) were selected, aligning with typical peak or off-peak load patterns. The load data were collected at 10 min intervals to enable the fine-grained modeling of load dynamics, with the dataset partitioned into training (70%), validation (10%), and test (20%) sets using chronological partitioning. This configuration yields 3024 training samples, 432 validation samples, and 864 test samples per month, preserving temporal dependency for a realistic model evaluation. (1) No VMD used  
The January load forecasting results in Figure 8 demonstrate that the GRU and BiLSTM outperform the feedforward model and achieve a superior peak load prediction due to their temporal dependency modeling capability. Notably, the load curve exhibits the strongest volatility and most complex temporal features at peaks and valleys, where traditional forecasting methods often show a weak learning performance. The method proposed in this paper effectively addresses this limitation: integrating the Improved Sparrow Search Algorithm (ISSA) significantly enhances performance and the ISSA-LSTM reduces the \(E_{RMSE}\), \(E_{MAE}\), and \(E_{MAPE}\) by 78.34%, 76.66%, and 72.24% compared to LSTM, as quantified in Table 4. The ISSA-LSTM prediction curve closely aligns with actual loads, particularly during diurnal peaks and nighttime valleys, attributed to the ISSA's optimized hyperparameters. This optimization resolves the single LSTM's weakness in capturing non-stationary features. Compared with the SSA-LSTM model, the \(E_{MAPE}\) of the ISSA-LSTM decreased by 28.77%, which indicates that the ISSA is better for LSTM hyperparameter optimization compared with the original SSA, which is because the ISSA is more uniform for population initialization, which effectively avoids falling into the local optimal solution and improves the ability of the global search of the population. Figure 8: Comparison of forecast results for January. (2) VMD used  
To avoid over-decomposition (causing modal aliasing or introducing spurious noise) and under-decomposition (resulting in insufficient data separation), the VMD mode number \(K\) is constrained within the range of 4-9. The relationship between the permutation entropy (PE) values of decomposed components and \(K\) is quantified in Table 5, where the optimal \(K\) is identified as the smallest integer minimizing PE while ensuring component stationarity. As observed from Table 5, the mean permutation entropy (PE) of each decomposed load component reaches its minimum when the decomposition level reaches \(K=5\). Permutation entropy, a measure of time-series complexity, quantifies the regularity of a sequence such that lower PE values indicate higher regularity, while higher PE values reflect greater complexity. Furthermore, excessive decomposition levels may introduce computational redundancy without improving interpretability. Considering the trade-off between sequence regularity and computational efficiency, the optimal decomposition number is determined to be \(K=5\). The corresponding decomposition results of the load sequence are illustrated in Figure 9.  
Table 6 demonstrates that the VMD-ISSA-LSTM and the VMD-ISSA-GRU outperform non-optimized counterparts by leveraging the ISSA for hyperparameter optimization. Specifically, the VMD-ISSA-LSTM achieves \(E_{MAPE}\) reductions of 94.6%, 47.78%, 82.97%, and 78.73%, while the VMD-ISSA-GRU reduces the \(E_{MAPE}\) by 93.22%, 34.44%, 78.62%, and 73.3%. These improvements are statistically significant, confirming the superiority of the ISSA-driven hyperparameter tuning.