In recent years, the global push for sustainable transportation has led to an unprecedented surge in the adoption of battery EV cars. Accurate forecasting of the charging load demand for these vehicles has therefore become a critical challenge for power grid operators and charging infrastructure planners. Traditional forecasting methods often struggle to capture the complex, nonlinear, and highly volatile patterns inherent in battery EV car charging data, which are influenced by a multitude of factors including user behavior, time of day, weather, and seasonal variations. This paper presents a novel hybrid deep learning framework designed to address these challenges, integrating sophisticated data preprocessing, signal decomposition, and feature extraction techniques to achieve high-precision short-term forecasts.
The core of our methodology lies in a multi-stage pipeline. First, raw charging load data is cleansed using a Gaussian Mixture Model (GMM) combined with a K-Nearest Neighbors (KNN) algorithm to handle missing values and outliers effectively. Second, the preprocessed signal is decomposed into its intrinsic modes using Variational Mode Decomposition (VMD). The complexity of each mode is then evaluated using Sample Entropy (SE), allowing for the reconstruction of a simplified yet informative signal by grouping modes with similar entropy values. Finally, this refined signal is fed into a hybrid Convolutional Neural Network-Bidirectional Long Short-Term Memory (CNN-BiLSTM) model. The CNN layer extracts salient local patterns and features from the sequential data, while the subsequent BiLSTM layer captures the complex long-term temporal dependencies and context from both past and future states within the sequence. This combination proves highly effective for modeling the dynamics of battery EV car charging loads.
Methodology
The proposed forecasting framework is systematic and involves several key stages, as summarized in the table below. Each stage addresses a specific challenge in time series forecasting for battery EV car infrastructure.
| Stage | Component | Primary Function |
|---|---|---|
| 1. Data Preparation | GMM-KNN | Detection and imputation of missing values and outliers. |
| 2. Signal Analysis | VMD-SE | Decomposition of load sequence and reconstruction based on complexity. |
| 3. Feature Learning & Forecasting | CNN-BiLSTM | Extraction of local features and modeling of temporal dependencies for prediction. |
| 4. Evaluation | MAE, RMSE, R² | Quantitative assessment of model performance. |
1. Data Preprocessing with GMM-KNN
The quality of input data is paramount. Battery EV car charging datasets often contain anomalies and gaps due to meter malfunctions or communication errors. We employ a two-step preprocessing technique. First, a Gaussian Mixture Model (GMM) is fitted to the data. A GMM assumes the data is generated from a mixture of several Gaussian distributions and is effective for modeling complex, multi-modal data like charging loads from diverse battery EV car users. The probability density function for a data point \(x\) is given by:
$$
p(x) = \sum_{k=1}^{K_g} \pi_k \mathcal{N}(x | \mu_k, \Sigma_k)
$$
where \(K_g\) is the number of Gaussian components, \(\pi_k\) is the mixing coefficient for the \(k\)-th component, and \(\mathcal{N}(x | \mu_k, \Sigma_k)\) is the Gaussian distribution with mean \(\mu_k\) and covariance \(\Sigma_k\). Data points with a probability density below a set threshold (e.g., the 0.1 percentile) are flagged as outliers. Consecutive zero values, indicating potential data loss, are also identified. These zero values are replaced by synthetic samples \(\tilde{x}\) drawn from the fitted GMM: \(\tilde{x} \sim \mathcal{N}(\mu_k, \Sigma_k)\).
Second, the identified outlier values (non-zero anomalies) are imputed using a K-Nearest Neighbors (KNN) regressor. For each outlier \(x_{outlier}\), its \(K_k\) nearest neighbor normal data points \(\{x_1, x_2, …, x_{K_k}\}\) are found based on Euclidean distance in the time-feature space. The outlier is then replaced by their mean:
$$
x_{replaced} = \frac{1}{K_k} \sum_{j=1}^{K_k} x_j
$$
This GMM-KNN hybrid approach ensures robust handling of both missing data and various types of outliers in battery EV car load profiles.
2. Signal Decomposition and Reconstruction with VMD-SE
Charging load for battery EV cars is a non-stationary signal with multiple overlapping frequency components. Directly modeling such a signal is difficult. Variational Mode Decomposition (VMD) is a powerful adaptive technique that decomposes a signal \(x(t)\) into \(K_v\) discrete band-limited Intrinsic Mode Functions (IMFs) \(u_k(t)\), each with a specific center frequency \(\omega_k\). It solves the following constrained optimization problem:
$$
\min_{\{u_k\},\{\omega_k\}} \left\{ \sum_{k=1}^{K_v} \|\partial_t[(\delta(t) + \frac{j}{\pi t}) * u_k(t)] e^{-j\omega_k t}\|_2^2 \right\} \\
\text{s.t.} \sum_{k=1}^{K_v} u_k(t) = x(t)
$$
The solution is obtained via the Alternating Direction Method of Multipliers (ADMM), iteratively updating each IMF and its center frequency.
However, not all IMFs contribute equally to the predictive signal; some may represent noise or irrelevant high-frequency fluctuations. To filter these out, we compute the Sample Entropy (SE) for each IMF. SE measures the complexity and regularity of a time series. A higher SE indicates greater randomness. For a time series of length \(N\), SE is defined as:
$$
\text{SampEn}(m, r, N) = -\ln \frac{A^m(r)}{B^m(r)}
$$
where \(B^m(r)\) is the probability that two sequences of length \(m\) are similar within tolerance \(r\), and \(A^m(r)\) is the probability for sequences of length \(m+1\). We then group IMFs with similar SE values (difference < 0.1) and sum them to form a reconstructed, simplified signal. This VMD-SE step effectively denoises the battery EV car load data and extracts its multi-scale characteristics.
3. The Hybrid CNN-BiLSTM Forecasting Model
The reconstructed load signal is fed into a hybrid deep learning model combining CNN and BiLSTM layers. This architecture is specifically chosen to capture both spatial (local) and temporal dependencies in the battery EV car charging sequence.
Convolutional Neural Network (CNN): The 1D convolutional layer scans the input sequence with filters to extract local patterns and features, such as sharp rises during evening charging peaks. The operation for a single filter is:
$$
y_i = \sum_{j=1}^{F} \omega_j \cdot x_{i+j-1} + b
$$
where \(y_i\) is the output feature, \(\omega_j\) are the filter weights, \(F\) is the filter size, \(x_{i+j-1}\) is the input subsequence, and \(b\) is the bias. Batch normalization and ReLU activation follow to stabilize and accelerate training.
Bidirectional LSTM (BiLSTM): The features extracted by the CNN are then processed by a BiLSTM layer. A standard LSTM unit addresses the vanishing gradient problem via gating mechanisms (forget gate \(f_t\), input gate \(i_t\), output gate \(o_t\)) and a cell state \(C_t\):
$$
\begin{aligned}
f_t &= \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \\
i_t &= \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \\
\tilde{C}_t &= \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) \\
C_t &= f_t * C_{t-1} + i_t * \tilde{C}_t \\
o_t &= \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \\
h_t &= o_t * \tanh(C_t)
\end{aligned}
$$
where \(\sigma\) is the sigmoid function. A BiLSTM consists of two independent LSTMs processing the sequence forward and backward, concatenating their outputs. This allows the model to learn from both past and future context in the sequence, crucial for understanding the patterns of battery EV car charging which are influenced by daily routines (past) and upcoming periods of low/high demand (implicit future context within the training window).
The final layers consist of a fully connected network that maps the BiLSTM’s high-level temporal features to the predicted load value for the next time step(s).
Experimental Analysis and Results
We validated our proposed VMD-SE-CNN-BiLSTM model using a real-world dataset from a battery EV car charging station in a major southern Chinese city, containing 15-minute interval data for the entire year of 2022.
Preprocessing and Decomposition Results
The GMM-KNN preprocessing successfully identified and corrected anomalous data points, resulting in a cleaner and more consistent time series suitable for analysis. Subsequent VMD processing decomposed the signal into \(K_v=6\) IMFs. The Sample Entropy for each IMF was calculated, as shown in the table below:
| Intrinsic Mode Function (IMF) | Sample Entropy Value |
|---|---|
| IMF1 | 0.6468 |
| IMF2 | 0.5947 |
| IMF3 | 0.5545 |
| IMF4 | 0.3793 |
| IMF5 | 0.1880 |
| IMF6 | 1.4113 |
Based on the SE values, IMFs were grouped (e.g., IMF1-IMF3; IMF4-IMF5) and summed to create a reconstructed signal that retained the primary load characteristics while reducing complexity and noise. This reconstructed signal was used as the input for all subsequent forecasting models.
Forecasting Performance and Comparative Analysis
We compared our model against three benchmark models: a standard LSTM, a BiLSTM, and a CNN-BiLSTM (without VMD-SE preprocessing). Forecasting was conducted and evaluated separately for each season (Spring, Summer, Autumn, Winter) to assess robustness under different demand patterns for battery EV car charging. The performance was measured using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the Coefficient of Determination (R²).
$$
\begin{aligned}
\text{MAE} &= \frac{1}{N} \sum_{i=1}^{N} |y_i – \hat{y}_i| \\
\text{RMSE} &= \sqrt{\frac{1}{N} \sum_{i=1}^{N} (y_i – \hat{y}_i)^2} \\
R^2 &= 1 – \frac{\sum_{i=1}^{N} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{N} (y_i – \bar{y})^2}
\end{aligned}
$$
The comprehensive results are presented in the table below. The data clearly demonstrates the incremental improvement offered by each component of our methodology and the superior performance of the full VMD-SE-CNN-BiLSTM model.
| Season | Model | MAE (kW) | RMSE (kW) | R² |
|---|---|---|---|---|
| Spring | LSTM | 195.457 | 256.741 | 0.968 |
| BiLSTM | 190.518 | 246.132 | 0.970 | |
| CNN-BiLSTM | 183.338 | 228.523 | 0.974 | |
| VMD-SE-CNN-BiLSTM | 153.196 | 189.365 | 0.982 | |
| Summer | LSTM | 228.516 | 302.580 | 0.932 |
| BiLSTM | 222.842 | 292.869 | 0.937 | |
| CNN-BiLSTM | 193.512 | 242.563 | 0.957 | |
| VMD-SE-CNN-BiLSTM | 188.717 | 227.677 | 0.962 | |
| Autumn | LSTM | 164.618 | 221.841 | 0.939 |
| BiLSTM | 154.126 | 214.210 | 0.943 | |
| CNN-BiLSTM | 150.765 | 212.647 | 0.944 | |
| VMD-SE-CNN-BiLSTM | 108.717 | 131.678 | 0.979 | |
| Winter | LSTM | 176.986 | 247.501 | 0.829 |
| BiLSTM | 173.819 | 239.821 | 0.839 | |
| CNN-BiLSTM | 161.477 | 218.856 | 0.866 | |
| VMD-SE-CNN-BiLSTM | 76.064 | 96.239 | 0.974 |
Analysis: The results show a consistent trend of improving accuracy with model sophistication. The standalone LSTM and BiLSTM models perform reasonably well but show limitations in handling complex fluctuations. The CNN-BiLSTM model shows a significant drop in MAE and RMSE, particularly in Summer and Winter, highlighting the benefit of CNN’s local feature extraction for battery EV car load patterns.
Our proposed VMD-SE-CNN-BiLSTM model consistently achieves the best performance across all seasons and metrics. The most dramatic improvements are seen in Autumn and Winter, where it reduces the MAE by approximately 34% and 57% respectively compared to the CNN-BiLSTM model. The R² values, exceeding 0.97 in three out of four seasons, confirm an excellent fit to the actual battery EV car charging load data. This superior performance underscores the critical value of the VMD-SE preprocessing stage in denoising and simplifying the load signal, allowing the subsequent deep learning model to learn the most relevant temporal dynamics more effectively.
Conclusion
This paper has successfully developed and demonstrated a robust short-term forecasting framework for battery EV car charging load. The integration of GMM-KNN for data cleansing, VMD-SE for multi-scale signal analysis and reconstruction, and a hybrid CNN-BiLSTM model for feature learning and temporal modeling creates a powerful pipeline. The experimental results on a full year of real-world data confirm that this approach significantly outperforms conventional deep learning models like LSTM, BiLSTM, and even a combined CNN-BiLSTM that lacks the sophisticated preprocessing stage. The model exhibits high accuracy and strong robustness across different seasonal patterns, which is essential for the reliable operation and planning of charging infrastructure for the growing fleet of battery EV cars. Future work will focus on incorporating a broader range of external factors, such as detailed user behavior patterns, real-time electricity pricing, and local event data, into the model framework to further enhance its predictive power and practical utility in smart grid applications.