Weather Based-Electricity Load Forecasting Using Empirical Wavelet Decomposition and Bi-LSTM With Attention, Case Study in Bali

Accurate forecasting of electrical load plays a vital role for power system operators in ensuring supply reliability, improving operational efficiency, and reducing generation costs. With the increasing demand fluctuations and the growing integration of renewable energy sources, the development of advanced intelligent forecasting methods has become increasingly important. In this study, a deep learning-based framework for short-term load forecasting is proposed, integrating a Bidirectional Long Short-Term Memory (Bi-LSTM) network enhanced with an attention mechanism, along with frequency-domain signal decomposition using the Empirical Wavelet Decomposition (EWD). The review of related works is structured around two main perspectives: forecasting approaches for electricity load and the application of signal decomposition techniques in power system prediction.

2.1 Electricity forecasting

The accuracy of electricity load forecasting is a cornerstone of modern power system management. Reliable forecasting allows utility providers to synchronize electricity generation with real-time consumer demand, thereby ensuring a stable supply of energy while simultaneously minimizing operational costs. This alignment is becoming increasingly difficult to achieve as power grids are exposed to higher levels of demand volatility and the growing penetration of renewable energy sources, both of which introduce significant uncertainty into load profiles. Consequently, there has been a strong shift from traditional statistical techniques such as autoregressive models (e.g. ARIMA, SARIMA) [3-5] and regression-based approaches toward more advanced, data-driven methodologies like Long Short-Term Memory (LSTM) networks [6] and convolutional architectures [7] that are capable of capturing the complex, nonlinear, and dynamic patterns inherent in electricity consumption data.

In recent years, hybrid forecasting architectures that combine signal processing and deep learning techniques have demonstrated remarkable improvements in prediction accuracy. For instance, Nabavi et al. [10] presented a model that integrates the Discrete Wavelet Transform (DWT) with Long Short-Term Memory (LSTM) networks. Their results showed that the DWT-LSTM framework outperforms standard LSTM, NARX, and Support Vector Machine (SVM) models in both short-term and long-term scenarios, achieving mean absolute percentage errors (MAPE) as low as 0.29–0.59% for hour-ahead predictions across datasets from Iran and Germany [10]. Similarly, Park and Hwang [11]proposed a two-stage multi-step forecasting framework that combines LightGBM with an Attention-BiLSTM sequence-to-sequence structure. Their model demonstrated improvements of more than 3% in MAPE compared with conventional deep learning baselines, highlighting the benefits of integrating attention mechanisms and boosting techniques in load prediction tasks [11].

Further supporting this trend, Wang et al. [12] introduced a CNN-BiLSTM-Attention model that incorporates secondary data cleaning and variational mode decomposition (VMD) as a preprocessing step. Their study revealed that careful data preprocessing, when combined with hybrid architectures, can significantly reduce forecasting errors compared with simpler recurrent models [10]. Collectively, these works underline an emerging research direction: the combination of advanced signal decomposition methods with attention-augmented deep recurrent networks provides a robust framework for dealing with the noisy, multiscale, and highly nonlinear characteristics of electricity demand data.

Hybrid models possess the advantage of alleviating the intrinsic limits of independent forecasting methods.  Individual models such as ARIMA have difficulties with nonlinear patterns [3, 4], and traditional deep learning networks may be susceptible to noise in unprocessed data; however, a hybrid architecture effectively distributes workloads.  The signal decomposition component (DWT) functions as a preprocessor to eliminate noise and streamline the time series by disaggregating it into more stable, frequency-based subsequence [10, 12]. This procedure enables the ensuing deep learning model (LSTM, Bi-LSTM) to concentrate on acquiring intricate temporal relationships from these enhanced inputs instead of the unrefined, noisy data, resulting in more resilient and precise predictions [8, 9].

Motivated by these advances, the present work proposes a forecasting framework that first preprocesses load time series using signal decomposition wavelet based to extract multi-resolution frequency components and suppress noise. The transformed signals are then fed into a Bidirectional Long Short-Term Memory (Bi-LSTM) network equipped with an attention mechanism. The Bi-LSTM architecture is particularly suited for this task as it processes data in both forward and backward directions, capturing contextual information from past and future states simultaneously [13, 14], while the attention mechanism dynamically prioritizes the most influential time steps in the sequence. By unifying signal decomposition with deep sequential modelling, the proposed approach aims to achieve highly accurate and robust electricity load forecasting, thereby contributing to more reliable and cost-efficient power system operations.

2.2 Bidirectional Long-Short Term Memory

The Bidirectional Long Short-Term Memory (BiLSTM) model represents a significant improvement over the conventional LSTM architecture, LSTM the LSTM architecture is shown in Figure 1. This framework leverages the capability of two independent LSTMs operating simultaneously, one in the forward direction and the other in the backward direction. Over time, BiLSTM has established itself as a powerful machine learning technique, widely adopted across various research domains. One notable example is presented by Yu et al. [14] a Bi-directional Long Short-Term Memory (Bi-LSTM) framework was proposed to model movement uncertainty in crowdsourced human trajectories under complex urban environments. The model integrates GNSS data with pedestrian motion features such as gait length and heading deviation and demonstrates superior performance compared to baseline models including LSTM, MLP, and 1D-CNN. Experimental results show that the Bi-LSTM model achieves an average prediction error of just 1.82 meters and a coverage ratio of 98.1%, significantly outperforming traditional uncertainty modeling approaches like UB, AUB, and BAEE. This highlights Bi-LSTM’s robustness and adaptability in predicting spatial deviations caused by GNSS signal occlusion and urban complexity.in classification accuracy, recall, and F1-score.

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Figure 1. LSTM architecture

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Figure 2. Bi-LSTM architecture

Structurally, Bi-LSTM employs two parallel stacks of LSTM layers that process the input sequence in opposite temporal directions, as illustrated in the Figure 2. The forward LSTM layer processes the sequence chronologically from earlier time steps h(t-1) to later ones (t+1), propagating information from the past. The backward LSTM layer processes the sequence in reverse, from future time steps (t+1) back to previous ones (t-1), capturing contextual information from the future. For any given time step t, the hidden state generated by the forward layer (representing past context) and the hidden state generated by the backward layer (representing future context) are combined typically by concatenation to form a comprehensive output vector. This integration of information from both temporal directions enables BiLSTM to capture richer contextual dependencies compared to traditional unidirectional LSTM models [13, 14].

2.3 Attention mechanism

The attention mechanism has become a central concept in deep learning, inspired by human cognitive processes that selectively focus on the most informative aspects of incoming data. By allowing neural networks to dynamically emphasize relevant features while suppressing less useful information, attention improves computational efficiency and enhances predictive accuracy across diverse tasks, including image captioning, speech recognition, and text classification. Over time, it has developed into various forms such as soft, hard, self-attention, and multi-head attention, and has been successfully integrated into architectures like RNNs and CNNs. Beyond improving performance, attention also contributes to interpretability, as the visualization of attention weights provides insights into the model’s decision-making process [15].

In parallel, the evolution of attention has further shaped modern deep learning, particularly with the emergence of the Transformer architecture. Unlike earlier models that relied on recurrence or convolution, Transformers rely solely on attention mechanisms, marking a significant paradigm shift in how sequence modelling is approached. Originating from biologically inspired ideas of selective focus, attention has matured into a flexible and powerful computational tool, enabling breakthroughs across domains such as neural machine translation and multimodal learning. As the field continues to advance, attention remains a foundational component for building adaptive, context-aware, and highly effective neural network systems [16].

Eq. (1) defines the context vector c_t, which is derived as a weighted sum of the hidden representations h_j. Here, $\alpha_{t j}$ corresponds to the attention coefficients that determine the relative importance of each hidden state with respect to the current time step. By assigning higher weights to more informative features and lower weights to less significant ones, the attention mechanism enables the model to selectively focus on the most relevant parts of the input sequence while constructing c_t.

$c_t=\sum_{j=1}^t \alpha_{t j} h_j$                     (1)

The architecture of the attention mechanism, as shown in Figure 3, shows how context vectors are generated by integrating information from multiple hidden states. At each decoding step t, the model computes alignment scores between the current hidden state h_t and all encoder hidden states h_i. These scores are then normalized using the softmax function to produce attention weights $\alpha_{t i}$, which indicate the relative contribution of each hidden state. The weighted sum of hidden states forms the context vector c_t, which is combined with the decoder hidden state h_t to generate the output y_t. This process allows the decoder to adaptively focus on different parts of the input sequence depending on the current prediction step. In practice, this mechanism improves model ability to capture long-range dependencies, reduces information loss commonly found in fixed-length context representations, and enhances both accuracy and interpretability [16].

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Figure 3. Attention mechanism

In the BiLSTM with Attention model, the process starts with a Bidirectional LSTM layer. This layer extracts information from both directions of the time sequence. Next, a Dropout layer reduces the risk of overfitting. A second Bidirectional LSTM deepens the representation of temporal features, and another Dropout layer follows it. Then, an Attention layer highlights important features in the data sequence. The results are processed by a third Bidirectional LSTM, which is also followed by Dropout to maintain learning stability. Finally, the output layer produces the final prediction value. The sequence of this architectural model is shown in the Figure 4.

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Figure 4. Visualization of proposed BiLSTM with attention

2.4 Empirical Wavelet Decomposition

EWD is a frequency domain-based signal analysis method developed to adaptively decompose complex signals into several empirical modes based on their energy spectrum characteristics [16, 17]. Unlike the Discrete Wavelet Transform (DWT), which uses fixed basis functions such as Haar or Daubechies, EWD constructs wavelet filter banks empirically through signal spectrum segmentation. This approach makes EWD more flexible for analyzing nonlinear and nonstationary signals such as electricity loads affected by weather variations, consumption behavior, and seasonal patterns [2, 18].

The methodology involves three main steps. First, the signal’s spectrum is segmented into distinct regions, each corresponding to a unique mode of the signal. Next, an empirical wavelet filter bank is constructed to match the frequency content of each segment, ensuring perfect reconstruction of the signal. Finally, the signal is filtered through these wavelets, yielding a detailed time-frequency decomposition. Mathematically, f(t) represents the signal, EWD decomposes it into like writen in Eq. (2).

$f(t)=\sum_k W_k(t)+R(t)$                     (2)

where, $W_k(t)$ are the wavelet coefficients, and $R(t)$ is the residual signal not captured by wavelet. The empirical wavelet are defined by Eq. (3), with $\psi k(t)$ representing the adaptive wavelet basis functions.

$W_k(t)=(f(t), \psi k(t))$                     (3)

The empirical wavelet is based on the segmentation of the Fourier spectrum of a signal $f(t)$ into N distinct frequency bands. This segmentation is defined by a set of boundaries $\left\{\omega_i\right\} N_i=0$, where $\omega_0=0$ and $\omega_N=\pi$. For each segment, an empirical scaling function $\phi_n(\omega)$ and an empirical wavelet function $\psi n(\omega)$ are constructed. The empirical scaling function is defined as shown in Eq. (4).

$\phi_n(\omega)=\left\{\begin{array}{c}1, \omega \in\left[0, \omega_1\right] \\ \cos \left(\frac{\pi}{2} \frac{\omega-\omega_1}{\omega_2-\omega_1}\right), \omega \in\left(\omega_1, \omega_2\right] \\ 0, \text {otherwise}\end{array}\right.$                       (4)

Similarly, the empirical wavelet functions is defined for n = 2, N as show in Eq. (5).

$\psi_n(\omega)=\left\{\begin{array}{c}\sin \left(\frac{\pi}{2} \frac{\omega-\omega_{n-1}}{\omega_n-\omega_{n-1}}\right), \omega \in\left(\omega_{n-1}, \omega_n\right) \\ \cos \left(\frac{\pi}{2} \frac{\omega-\omega_n}{\omega_{n+1}-\omega_n}\right), \omega \in\left(\omega_n, \omega_{n+1}\right) \\ 0, \text {otherwise}\end{array}\right.$                  (5)

$f(t)=\sum_{n=1}^N\left(f_n\right)$                      (6)

$f_n(t)=F^{-1}\left[\hat{f}(\omega) \cdot \psi_n(\omega)\right]$                   (7)

Given functions 5 , the decomposes a signal $f(t)$ into $N$ components as follows in Eq. (6) where each component $f_n(t)$ is obtained by applying the inverse Fourier transform to the product of the signals Fourier transform and the respective filter is show in Eq. (7), where $f(t)$ is the original signal in the time domain, while $\widehat{f}(\omega)$ is the Fourier transform of that signal in the frequency domain. The function $\psi_n(\omega)$ acts as the n -th empirical wavelet or frequency filter that extracts signal components at a specific frequency band. The operation $F^{-1}$ meaning (inverse Fourier transform) then converts the result in the frequency domain back to the time domain, producing $f_n(t)$, the $n$-th empirical mode. Thus, each $f_n(t)$ represents a portion of the signal with specific frequency characteristics, and empirical modes can reconstruct the original signal [9, 19].

The aim in this research is to develop a weather-based power load forecasting system for Bali by integrating Empirical Wavelet Decomposition Bi-directional long short-term memory with attention mechanism. This section presents the results obtained from the proposed model under a variety of experimental scenarios designed to evaluate its forecasting performance. Each scenario has been carefully structured to highlight different aspects of the model’s capability, including the influence of weather parameters, the role of temporal features, the impact of wavelet-based signal decomposition, and the effect of training data length on predictive accuracy. By systematically analysing these scenarios, we aim to provide a comprehensive understanding of the model’s strengths and limitations when applied to electricity load forecasting in the Bali region.

The presentation of results is organized to facilitate a clear comparison across scenarios. First, we discuss the outcomes related to the selection of weather variables, identifying which parameters contribute most significantly to prediction accuracy. Next, we evaluate the role of temporal features such as hour of the day, day of the week, and seasonal indicators, which are expected to capture the cyclic behaviour of electricity consumption. We then examine the benefits of incorporating wavelet decomposition into the modelling pipeline, demonstrating how signal decomposition enhances the representation of weather data and improves forecasting precision. Finally, we assess how different lengths of training data influence the model’s generalization ability, offering insights into the trade-off between computational efficiency and predictive performance.

Through this structured approach, the reported results not only validate the effectiveness of the Bi-LSTM with Attention framework combined with wavelet decomposition but also provide a solid basis for discussing practical implications and potential areas for further improvement.

This research has 4 sensitivity test scenarios for each feature; the Table 2 contains the test scenarios in this research.

Table 2. Sensitivity test scenarios

4.1 Weather

Based on the results summarized in Tables 3 and 4, it is evident that the selection of input features has a substantial impact on the forecasting performance of the Bi-LSTM with Attention model. Table 3 presents the correlation coefficients between weather parameters and electricity load, while Table 4 compares the forecasting performance of different weather-based input configurations. When using temperature (t2m) alone as the input, the model achieved relatively poor performance, with a Correlation Coefficient (CC) of 0.44, Root Mean Square Error (RMSE) of 113.3 MW, and a Mean Absolute Percentage Error (MAPE) of 11.47%. This outcome indicates that temperature by itself is insufficient to fully capture the variability of electricity load.

Table 3. Result of correlation coefficient between weather and electricity load

Table 4. Result of Bi-LSTM-Attention with various weather

In contrast, the combination of temperature (t2m) and solar radiation (ssrd) provided the best results, with a CC of 0.93, a significantly reduced RMSE of 45.58 MW, and the lowest MAPE of 4.18%. This demonstrates that the inclusion of solar radiation as an additional feature greatly enhances the model’s predictive accuracy, making this input configuration the most effective among all tested scenarios.

Other combinations, such as t2m with ssrd and surface pressure (spr), maintained a high CC value of 0.93 but led to increased RMSE (55.5 MW) and MAPE (5.27%). Similarly, adding wind speed (wnd) alongside t2m, ssrd, and spr further degraded performance, with CC dropping to 0.89, RMSE rising to 74.34 MW, and MAPE increasing to 6.46%. These results suggest that including additional variables that are less strongly correlated with electricity load can negatively affect the model’s generalization ability. Figure 15 visualizes the actual and predicted electricity load using temperature and solar radiation as input features.

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Figure 15. Actual and prediction with weather data (temperature and solar radiation)

Figures 16-19 illustrates the correlation between electricity load and wind speed. Therefore, the most effective configuration identified in this study is the Bi-LSTM with Attention model using temperature (t2m) and solar radiation (ssrd) as inputs, as this combination delivers the highest accuracy, lowest prediction error, and overall best balance across all performance metrics. the combination of temperature (t2m) and solar radiation (ssrd) yielded the best performance, with a CC of 0.93, RMSE of 45.58 MW, and the lowest MAPE of 4.18%.

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Figure 16. Electricity load and wind speed

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Figure 17. Electricity load and temperature

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Figure 18. Electricity load and solar radiation

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Figure 19. Electricity load and pressure

4.2 Time feature

The results, presented in Table 5, highlight clear differences in model performance across these feature sets. When weather data were combined with the hour feature, the model achieved particularly strong results, with a Correlation Coefficient (CC) of 0.93, RMSE of 46.45 MW, and the lowest Mean Absolute Percentage Error (MAPE) of 3.71%. This indicates that electricity load in the study region is highly sensitive to intra-day variations, and that the hour feature enables the model to capture these fluctuations effectively. When the day feature was added alongside weather and hour, however, performance slightly decreased, with CC dropping to 0.92, RMSE rising to 55.83 MW, and MAPE increasing to 5.02%. This suggests that day of the month alone provides limited information for capturing short-term demand variations.

Table 5. Result of Bi-LSTM-Attention with various time feature

The inclusion of the day of the week (dow) feature together with weather and hour improved stability compared to the day-only configuration, yielding CC of 0.93, RMSE of 46.14 MW, and MAPE of 4.20%. This outcome reflects the influence of weekly consumption cycles, which can enhance prediction accuracy to a certain extent. Finally, extending the input feature set by adding month information produced the highest CC value of 0.94, but with slightly increased RMSE (46.26 MW) and MAPE (4.27%) relative to the hour-only setup. Although this suggests that monthly patterns contribute to capturing broader seasonal trends, the results confirm that their predictive value is secondary compared to the dominant effect of hourly variations.

Taken together, these findings demonstrate that the hour feature is the most influential temporal variable when combined with weather data, as it delivers the most accurate and reliable forecasts with the lowest MAPE. While additional temporal indicators such as day, dow, and month can marginally improve correlation, they introduce higher errors that reduce practical forecasting accuracy. Therefore, the combination of weather and hour was selected as the most optimal input configuration, as it strikes the best balance between strong correlation (CC = 0.93) and forecasting accuracy (MAPE = 3.71%).

4.3 Wavelet decomposition results

To further refine the model performance, signal decomposition using wavelet-based was applied to the selected weather features, specifically temperature (t2m) and solar radiation (ssrd), which had previously been identified as the most effective variables when combined with the hour feature. The purpose of this decomposition was to reduce high-frequency fluctuations and noise in the input data, thereby enabling the model to better capture the underlying trends of electricity consumption. In this process, only the approximation component (A) of the decomposed signal was retained, while the high-frequency detail component (H) was discarded, as it was considered less informative for load forecasting.

Table 6. Result of Bi-LSTM-Attention

The results of this experiment, as summarized in Table 6, show that the integration of wavelet decomposition with weather data produced notable improvements in model performance. Specifically, the Bi-LSTM with Attention model using the normal input achieved a Correlation Coefficient (CC) of 0.93, RMSE of 46.45 MW, and MAPE of 3.71%. When the weather features were pre-processed with wavelet decomposition, the CC value remained unchanged at 0.93, but the RMSE improved to 42.58 MW, demonstrating a reduction in prediction error. However, the MAPE slightly increased to 3.92%, indicating a minor trade-off in percentage-based accuracy. Figure 20 presents the prediction results obtained using wavelet decomposed features, while Figure 21 shows the prediction results without applying wavelet decomposition. The comparison between these two figures demonstrates that incorporating wavelet decomposition leads to smoother forecasting results, effectively reducing short-term fluctuations and noise in the predicted electricity load.

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Figure 20. Prediction results with wavelet

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Figure 21. Prediction result without wavelet

Overall, these findings confirm that wavelet decomposition contributes positively to stabilizing and smoothing the input signals, particularly by reducing noise-related variations that could mislead the learning process. Although the improvement is more apparent in RMSE rather than MAPE, this step further enhances the robustness of the forecasting framework, ensuring more consistent predictions under fluctuating weather conditions.

4.4 Training data length

Following the integration of wavelet decomposition into the weather inputs, further experiments were conducted to evaluate the impact of training data length on forecasting performance. The Bi-LSTM with Attention model was trained using three different training windows 3 months, 6 months, and 12 months.

Table 7. Result of Bi-LSTM-Attention with various length

The results, presented in Table 7, show that the training length significantly influences the accuracy and robustness of the forecasting model. With a 3-month training dataset, the model achieved a Correlation Coefficient (CC) of 0.93, RMSE of 42.58 MW, and MAPE of 3.92%. Extending the training length to 12 months, however, did not yield better results, as performance declined slightly with CC of 0.94, RMSE of 50.4 MW, and MAPE of 4.38%. Interestingly, the optimal configuration was obtained when the model was trained on 6 months of data, producing the best forecasting outcomes with CC of 0.95, RMSE of 37.48 MW, and MAPE of 3.26%. Figures 22-24 illustrate the visual differences in prediction performance across various training data lengths. Figure 22 shows the results for a 12-month training period, Figure 23 presents the outcomes for 6 months of training, and Figure 24 displays the predictions based on 3 months of training data. These visual comparisons highlight that the 6-month training window show stable and forecasts.

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Figure 22. Prediction results with length 12 months

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Figure 23. Prediction results with length 6 months

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Figure 24. Prediction results with length 3 months

These findings suggest that providing the model with too little historical data limits its ability to learn complex load–weather interactions, while excessively long training windows may introduce outdated or less relevant patterns that reduce generalization performance. The 6-month window offered the best balance between capturing sufficient variability in the input features and avoiding overfitting to long-term seasonal fluctuations.

Overall, this analysis highlights the importance of selecting an appropriate training length in electricity load forecasting. By combining wavelet decomposition with a 6-month training dataset, the Bi-LSTM with Attention model achieved its best predictive accuracy, reinforcing the effectiveness of the proposed framework for STLF.

4.5 Model comparison

The final stage of the evaluation involved comparing the proposed Bi-LSTM with Attention model incorporating wavelet decomposition against several benchmark models, including Bi-LSTM, XGBoost, AdaBoost, and MLP, all tested with normal input configurations. The performance results are presented in Table 8, which compares the proposed Bi-LSTM with Attention model incorporating wavelet decomposition against several benchmark models. Figure 25 provides a visual comparison of all models, clearly illustrating the performance differences across the Bi-LSTM, Bi-LSTM with Attention, XGBoost, AdaBoost, and MLP models.

Table 8. Result of Bi-LSTM-Attention with various model

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Figure 25. Model comparison

Specifically, the Bi-LSTM with Attention using wavelet decomposition achieved the highest performance across all metrics, with a Correlation Coefficient (CC) of 0.95, RMSE of 37.48 MW, and MAPE of 3.26%. These results represent a significant improvement compared to the same architecture without wavelet decomposition, where CC was 0.94, RMSE increased to 56.76 MW, and MAPE rose to 5.38%. Similarly, while tree-based models such as XGBoost and AdaBoost demonstrated competitive results, with RMSE values of 42.59 MW and 43.2 MW respectively, and MAPE values of 3.55% and 3.96%, they still fell short of the proposed method in terms of both accuracy and robustness. The MLP model performed the weakest overall, with a CC of 0.92, RMSE of 61.86 MW, and MAPE of 5.37%.

To ensure that the forecasting accuracy is statistically proven, a t-test was performed on BiLSTM without attention and BiLSTM with attention based on the RMSE value. The results show a t-statistic of 276.48 and a p-value of 1.03 × 10⁻⁹, which is far below the threshold of 0.05, indicating that BiLSTM-Attention exhibits a statistically significant improvement. Furthermore, the 95% confidence interval for the RMSE difference between 87.41 MW and 89.19 MW indicates a consistent and substantial decrease in forecasting error.

These findings confirm that the integration of wavelet decomposition with Bi-LSTM and Attention not only enhances the model’s capability in handling high-frequency noise in weather data but also establishes it as the most effective approach among the tested models. By leveraging the combined strengths of temporal feature extraction, attention mechanisms, and signal decomposition, the proposed framework delivers the most accurate and reliable electricity load forecasting results in the study.

This research was funded by Kementerian Pendidikan, Kebudayaan, Riset dan Teknologi, Republik Indonesia, research grant numbers 125/C3/DT.05.00/PL/2025 and 060/LIT07/PPM-LIT/2025.