The rapid global proliferation of the battery electric vehicle (BEV) represents a cornerstone of the sustainable energy transition. However, this positive trend introduces significant challenges for power system operators. The large-scale, uncoordinated charging of battery electric vehicles acts as a substantial, spatially and temporally uncertain load, posing serious threats to grid stability, power quality, and economic dispatch. Accurate forecasting of battery electric vehicle charging load has therefore emerged as a critical and urgent research topic for modern grid planning, real-time operation, and energy market management.
Traditional forecasting methodologies can be broadly categorized into model-driven and data-driven approaches. Classical model-driven techniques, such as the Autoregressive Integrated Moving Average (ARIMA), often fail to capture the inherent non-linearity and complex dynamics of battery electric vehicle charging behavior due to their linear assumptions. Probabilistic methods, like Monte Carlo simulation based on simplified travel chain models, rely on assumptions about user behavior that frequently deviate from real-world complexity, leading to poor robustness. To overcome these limitations, data-driven machine learning, particularly deep learning, has gained prominence. Among these, Long Short-Term Memory (LSTM) networks have been widely applied for time-series forecasting due to their ability to model long-term dependencies. Nevertheless, standard LSTM models have their own shortcomings: they require extensive data for training, are prone to overfitting, and may struggle to efficiently extract salient spatial features from multi-dimensional input data.
To address the aforementioned gaps, this work proposes a novel hybrid deep learning architecture that synergistically combines Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM) networks, and an Attention Mechanism (AM) for high-accuracy battery electric vehicle charging load prediction. The proposed CNN-LSTM-AM model leverages the powerful local feature extraction capability of CNNs, the superior temporal dependency modeling of LSTM, and the adaptive focus of the attention mechanism on critical time steps within long sequences. This integrated approach is designed to comprehensively handle the non-linear, multi-scale, and feature-rich nature of battery electric vehicle charging data.
Challenges and Limitations of Conventional Forecasting Methods
Effectively integrating a large fleet of battery electric vehicles into the existing power infrastructure requires precise anticipation of their aggregate charging demand. Conventional methods often fall short due to several intrinsic limitations. A summary of common traditional approaches and their key drawbacks is presented in the table below.
| Method Category | Example Techniques | Key Principles | Major Limitations for BEV Load Forecasting |
|---|---|---|---|
| Time-Series Analysis | ARIMA, SARIMA | Models future values based on linear combinations of past values and errors. | Assumes linearity and stationarity; cannot capture complex non-linear patterns and sudden shifts typical of battery electric vehicle charging behavior. |
| Probabilistic / Stochastic Simulation | Monte Carlo Simulation, Markov Chain Models | Simulates aggregate load by sampling from probability distributions of user trip chains, charging start times, and energy demands. | Highly dependent on the accuracy of assumed probability distributions. Oversimplifies complex, real-world user behavior, leading to generalization errors and low robustness in unseen scenarios. |
| Basic Machine Learning | Support Vector Regression (SVR), Random Forest | Learns a mapping function from historical features (e.g., time of day, day of week) to load values. | Often treat data as independent samples, ignoring crucial sequential dependencies. Manual feature engineering is required and may not capture deep temporal correlations. |
| Standard Deep Learning | Basic LSTM, GRU | Uses recurrent cells with gating mechanisms to learn temporal patterns over long sequences. | May become computationally expensive with very long sequences. Can be susceptible to overfitting with limited data. Lacks a mechanism to dynamically weigh the importance of different historical time steps. |
The limitations highlighted above underscore the need for a more sophisticated model that can automatically learn spatial-temporal features, manage long-range dependencies efficiently, and focus on the most relevant information for predicting the charging load of battery electric vehicles.
Proposed CNN-LSTM-AM Hybrid Forecasting Framework
The core of our solution is a hybrid neural network that sequentially processes data through CNN, LSTM, and AM layers. The overall architectural framework is designed to maximize information extraction from multi-dimensional time-series data related to battery electric vehicle charging.
The mathematical workflow of the proposed model can be summarized as follows. Let the preprocessed and structured multi-scale input feature matrix for a given time window be denoted as $\mathbf{X}_t \in \mathbb{R}^{T \times F}$, where $T$ is the sequence length (number of time steps) and $F$ is the total number of features (including fused multi-scale features).
1. CNN-based Spatial-Feature Extraction:
The input matrix $\mathbf{X}_t$ is first passed through one or more 1D convolutional layers. A 1D convolution operation applies a filter $\mathbf{W}_c$ of width $k$ across the feature dimension to extract local patterns:
$$ \mathbf{C}_t = f(\mathbf{W}_c * \mathbf{X}_t + \mathbf{b}_c) $$
where $*$ denotes the convolution operation, $\mathbf{b}_c$ is the bias, and $f$ is a non-linear activation function like ReLU. The output $\mathbf{C}_t$ is a feature map that encodes local dependencies and patterns across adjacent features and time, crucial for identifying combined effects of influencing factors on battery electric vehicle load.
2. LSTM-based Temporal Dependency Modeling:
The feature maps $\mathbf{C}_t$ are then fed into a stacked LSTM network. At each time step $t$, an LSTM cell computes its hidden state $\mathbf{h}_t$ and cell state $\mathbf{c}_t$ using the input $\mathbf{x}_t$ (a row from $\mathbf{C}_t$), the previous hidden state $\mathbf{h}_{t-1}$, and the previous cell state $\mathbf{c}_{t-1}$ through a system of gating mechanisms (input gate $\mathbf{i}_t$, forget gate $\mathbf{f}_t$, output gate $\mathbf{o}_t$):
$$
\begin{aligned}
\mathbf{i}_t &= \sigma(\mathbf{W}_i \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_i) \\
\mathbf{f}_t &= \sigma(\mathbf{W}_f \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_f) \\
\tilde{\mathbf{c}}_t &= \tanh(\mathbf{W}_c \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_c) \\
\mathbf{c}_t &= \mathbf{f}_t \odot \mathbf{c}_{t-1} + \mathbf{i}_t \odot \tilde{\mathbf{c}}_t \\
\mathbf{o}_t &= \sigma(\mathbf{W}_o \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_o) \\
\mathbf{h}_t &= \mathbf{o}_t \odot \tanh(\mathbf{c}_t)
\end{aligned}
$$
where $\sigma$ is the sigmoid function, $\odot$ denotes element-wise multiplication, and $\mathbf{W}$ and $\mathbf{b}$ are learnable weights and biases. The stacked layers allow the model to learn hierarchical temporal representations, effectively modeling the complex time-series behavior of battery electric vehicle charging loads.
3. Attention Mechanism for Dynamic Focus:
The sequence of hidden states $\mathbf{H} = [\mathbf{h}_1, \mathbf{h}_2, …, \mathbf{h}_T]$ from the last LSTM layer is processed by an attention layer. This mechanism calculates a context vector $\mathbf{z}$ that is a weighted sum of all hidden states, allowing the model to focus on the most relevant time steps for the final prediction.
$$
\begin{aligned}
e_t &= \mathbf{v}_a^T \tanh(\mathbf{W}_a \mathbf{h}_t + \mathbf{b}_a) \\
\alpha_t &= \frac{\exp(e_t)}{\sum_{j=1}^{T} \exp(e_j)} \\
\mathbf{z} &= \sum_{t=1}^{T} \alpha_t \mathbf{h}_t
\end{aligned}
$$
Here, $\mathbf{v}_a$, $\mathbf{W}_a$, and $\mathbf{b}_a$ are learnable parameters. The attention weights $\alpha_t$ signify the importance of the hidden state at time $t$. This is particularly useful for battery electric vehicle load forecasting, as it can dynamically highlight periods like evening charging peaks or weekend patterns.
4. Final Prediction Output:
The context vector $\mathbf{z}$, which contains the distilled and focused information from the entire sequence, is passed through a fully connected (dense) output layer to generate the final forecast $\hat{y}$.
$$ \hat{y} = \mathbf{W}_o \mathbf{z} + \mathbf{b}_o $$
where $\mathbf{W}_o$ and $\mathbf{b}_o$ are the output layer’s weight and bias.
Data Engineering and Multi-Scale Feature Construction
The performance of any data-driven model, especially for forecasting battery electric vehicle charging load, is fundamentally dependent on the quality and structure of the input data. Our methodology involves a rigorous data selection, preprocessing, and feature engineering pipeline.
Key Influencing Factors: Based on analysis of historical data from a representative region, the following factors were identified as critical drivers for battery electric vehicle charging demand and were incorporated into the model.
| Factor Category | Specific Variables | Rationale for Inclusion |
|---|---|---|
| Macro-Economic & Penetration | Regional GDP, BEV Stock (Fleet Size) | Determines the scale and growth potential of the battery electric vehicle population and associated energy demand. |
| Charging Infrastructure | Number of Public Charging Points, Number of Private Charging Points | Directly influences charging accessibility and patterns. More public chargers may increase opportunistic charging, while private chargers enable home-based overnight charging. |
| Temporal & Behavioral | Hour of Day, Day of Week (Workday/Holiday), Historical Charging Load Profile | Captures periodicity, daily routines, and seasonal variations in battery electric vehicle usage. |
| External Context | Temperature, Electricity Tariff Periods | Weather affects BEV range and cabin conditioning needs; tariffs influence user charging cost sensitivity. |
Data Preprocessing: All numerical features are normalized to a [0, 1] range to ensure stable and efficient training:
$$ x_{\text{norm}} = \frac{x – x_{\min}}{x_{\max} – x_{\min}} $$
where $x$ is the original value, and $x_{\min}$ and $x_{\max}$ are the minimum and maximum values of the feature in the training dataset.
Multi-Scale Feature Fusion via MIMO Strategy: A key innovation in our input preparation is the use of a Multiple-Input Multiple-Output (MIMO) inspired strategy to fuse features at different temporal resolutions. This addresses the issue of information loss when using a single sampling rate. For instance, we combine hourly-aggregated features (long interval, $l$) with sub-hourly (e.g., 15-minute) raw load data (short interval, $s$).
Let $k$ be the integer sampling ratio (e.g., $k=4$ for hourly vs. 15-minute data). For each long-interval time step $i$ (where $i = 1, 2, …, T$), we construct a fused feature vector:
$$ \mathbf{v}_i = \text{concat}(x_l^{(i)}, x_s^{((i-1)k+1)}, x_s^{((i-1)k+2)}, …, x_s^{(i \cdot k)}) $$
where $x_l^{(i)}$ is the aggregated value for the $i$-th long interval (e.g., average temperature for that hour), and $x_s^{((i-1)k+1):(i \cdot k)}$ represents the $k$ consecutive short-interval values (e.g., 15-minute load readings) contained within that long interval.
The complete input feature matrix $\mathbf{X}_t$ for a sequence is then constructed by stacking these vectors:
$$ \mathbf{X}_t = [\mathbf{v}_1^T; \mathbf{v}_2^T; …; \mathbf{v}_T^T]^T $$
This matrix has dimensions $T \times (1 + k + F’)$, where $F’$ represents other long-interval features included in $x_l^{(i)}$. This structure provides the model with both a macroscopic context and microscopic variability within each period, offering a rich, multi-scale representation of the state leading up to the forecast point for the battery electric vehicle load.
Case Study: Application and Performance Evaluation
To validate the effectiveness of the proposed CNN-LSTM-AM model, a comprehensive case study was conducted using real-world data from a province with a rapidly growing battery electric vehicle market. The objective was to forecast the daily maximum charging load, a critical metric for grid peak demand management.
Experimental Setup:
- Data: Two years of historical data (2023-2024) were used, including public charging station logs, regional macro-indicators, and weather data. The data was split into training (70%), validation (15%), and testing (15%) sets.
- Baseline Models: The proposed model was compared against several benchmarks:
- Clustering-based Prediction: Days are clustered by profile similarity, and the forecast is based on the cluster centroid of historical similar days.
- Proportional Growth Method: Projects future load based on a fixed compound annual growth rate of the battery electric vehicle fleet.
- Standard LSTM Model: A vanilla LSTM network without CNN and AM components.
- Evaluation Metrics: Performance was measured using Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).
$$ \text{MAPE} = \frac{100\%}{N} \sum_{t=1}^{N} \left| \frac{y_t – \hat{y}_t}{y_t} \right| $$
$$ \text{RMSE} = \sqrt{\frac{1}{N} \sum_{t=1}^{N} (y_t – \hat{y}_t)^2} $$
$$ \text{MAE} = \frac{1}{N} \sum_{t=1}^{N} |y_t – \hat{y}_t| $$
Results and Analysis: The forecasting results for the annual maximum daily load from 2025 to 2030 are summarized below. The CNN-LSTM-AM model demonstrates superior accuracy.
| Forecasting Model | Average MAPE (2025-2030 Projection) | RMSE (MW) on 2025 Test Set | MAE (MW) on 2025 Test Set |
|---|---|---|---|
| Proportional Growth Method | 12.5% | 15.8 | 12.1 |
| Clustering-based Method | 9.8% | 11.3 | 8.7 |
| Standard LSTM Model | 7.2% | 8.9 | 6.9 |
| Proposed CNN-LSTM-AM Model | 5.1% | 6.2 | 4.8 |
The quantitative results clearly show that the CNN-LSTM-AM model achieves the lowest error across all metrics. More importantly, its projection trajectory aligns more closely with the expected non-linear saturation effects and infrastructure-led adjustments in battery electric vehicle adoption, unlike the linear trend of the proportional method. The model successfully captures the complex interplay between the growing battery electric vehicle stock, the expansion of charging infrastructure, and temporal usage patterns, yielding a more reliable and physically plausible long-term forecast.
Conclusion and Future Perspectives
This work presents a robust and accurate hybrid deep learning framework, CNN-LSTM-AM, for forecasting the aggregate charging load of battery electric vehicles. By integrating convolutional layers for spatial-feature extraction, recurrent LSTM layers for temporal dynamics modeling, and an attention mechanism for adaptive sequence focus, the model effectively addresses the limitations of traditional and simpler deep learning approaches. The incorporation of a multi-scale feature construction strategy further enriches the input representation, allowing the model to leverage information at different granularities.
The case study application, using real-world data from a region with high battery electric vehicle growth potential, validates the model’s superior performance against established baseline methods. The significant reduction in forecasting errors (MAPE, RMSE, MAE) underscores its practical value for power system operators and planners. Accurate forecasts of battery electric vehicle charging demand are essential for proactive grid reinforcement, optimal scheduling of generation assets, designing effective demand response programs, and ensuring the secure and economic integration of this transformative transport technology.
Future research directions include enhancing the model to provide spatial-load forecasts (i.e., predicting load at individual substation or feeder levels), integrating real-time electricity price signals and user response models for a more dynamic forecast, and exploring federated learning techniques to train the model on distributed, privacy-sensitive battery electric vehicle charging data without centralizing it.