With the rapid adoption of battery electric vehicles worldwide, the charging load from these vehicles poses significant challenges to power grid stability and operational efficiency. Accurate spatio-temporal prediction of battery electric vehicle charging load is crucial for optimizing charging infrastructure planning and grid management. Traditional methods often fail to fully capture the complex dependencies in both time and space, as well as the influence of multiple external factors such as electricity pricing, weather conditions, and charging station occupancy. In this article, I propose a novel fusion model called Spatio-Temporal Graph Convolutional and Squeeze-and-Excitation Network (STGC-SENet) to address these limitations. This model integrates periodic temporal patterns, spatial correlations, and multi-factor features to enhance prediction accuracy for battery electric vehicle charging load.
The proliferation of battery electric vehicles has led to dynamic and spatially distributed charging loads that vary with time, user behavior, and environmental conditions. Predicting these loads requires modeling both temporal dependencies (e.g., daily and weekly cycles) and spatial interactions among charging stations across urban areas. Existing approaches, such as Long Short-Term Memory (LSTM) networks or convolutional neural networks (CNNs), often treat time and space separately, neglecting their inherent coupling. Moreover, while factors like real-time electricity prices or weather can impact battery electric vehicle charging behavior, most models lack mechanisms to dynamically weigh these factors based on their relevance. To overcome these issues, STGC-SENet combines graph convolutional networks for spatial topology learning, temporal convolutions for multi-scale periodic patterns, and a channel attention layer for adaptive feature fusion. This integration allows the model to leverage rich, multi-source data for robust predictions.
In the following sections, I detail the methodology of STGC-SENet, including the formal definitions, architectural components, and mathematical formulations. I then present experimental results based on real-world urban charging data, comparing STGC-SENet with baseline models and analyzing the sensitivity to periodic factors and input features. The article concludes with a discussion of implications and future research directions for battery electric vehicle charging load prediction.
Methodology
The STGC-SENet model is designed to predict the spatio-temporal charging load of battery electric vehicles by integrating multiple factors. The overall framework consists of four key modules: a Periodic Temporal Segment Extraction (PTSE) block, a Spatio-Temporal Graph Convolutional (STGC) block, a Squeeze-and-Excitation (SE) layer, and a Final Fusion layer. I define the problem and each component below.
Problem Definition
Consider an urban area represented as a graph $G = (V, E, A)$, where $V$ is the set of $N$ spatial nodes (e.g., traffic zones or charging stations), $E$ is the set of edges denoting connectivity, and $A \in \mathbb{R}^{N \times N}$ is a weighted adjacency matrix capturing spatial relationships. The weight between nodes $i$ and $j$ is inversely proportional to the distance between their charging clusters, emphasizing closer correlations. At each time step $t$, each node has $F$ features (e.g., charging load, occupancy rate), denoted as $x_{t, i, f} \in \mathbb{R}$ for node $i$ and feature $f$. The historical input over $T_a$ time steps is a tensor $X_t = (x_1, x_2, \dots, x_{T_a}) \in \mathbb{R}^{T_a \times N \times F}$. The goal is to predict the future charging load for all nodes over $T_p$ time steps, output as $Y_t = (y_t, y_{t+1}, \dots, y_{t+T_p}) \in \mathbb{R}^{T_p \times N}$, where $y_{t,i}$ is the charging load for battery electric vehicles at node $i$ and time $t$.
Periodic Temporal Segment Extraction Block
To capture multi-scale temporal patterns in battery electric vehicle charging load, the PTSE block extracts three types of periodic segments from the input data: recent, daily, and weekly. Let $q$ be the sampling frequency per day (e.g., $q=24$ for hourly data). For a current time $t_0$, the segments are defined as follows:
Recent segment (length $T_r$):
$$X_r = (x_{t_0 – T_p \times r}, x_{t_0 – T_p \times r + 1}, \dots, x_{t_0}) \in \mathbb{R}^{T_r \times N \times F},$$
where $r$ is the number of recent slices, each of length $T_p$.
Daily segment (length $T_d$):
$$X_d = (x_{t_0 – q \times d – T_p}, x_{t_0 – q \times d – T_p + 1}, \dots, x_{t_0 – q \times d}, \dots, x_{t_0 – q}) \in \mathbb{R}^{T_d \times N \times F},$$
where $d$ is the number of daily slices.
Weekly segment (length $T_w$):
$$X_w = (x_{t_0 – 7 \times q \times w – T_p}, x_{t_0 – 7 \times q \times w – T_p + 1}, \dots, x_{t_0 – 7 \times q \times w}, \dots, x_{t_0 – 7 \times q}) \in \mathbb{R}^{T_w \times N \times F},$$
where $w$ is the number of weekly slices.
These segments are processed in parallel to account for different periodicities in battery electric vehicle charging behavior.
Spatio-Temporal Graph Convolutional Block
The STGC block models spatial and temporal dependencies simultaneously. For spatial modeling, I use graph convolutional networks (GCNs) based on Chebyshev polynomials to capture topological correlations among nodes. Given the graph Laplacian $L = I_N – D^{-1/2} A D^{-1/2}$, where $D$ is the degree matrix, the spectral graph convolution for an input signal $x$ is:
$$g_\theta *_\mathcal{G} x = \sum_{k=0}^{K-1} \theta_k T_k(\tilde{L}) x,$$
where $\theta_k$ are Chebyshev coefficients, $T_k$ are Chebyshev polynomials, $\tilde{L} = 2L/\lambda_{\text{max}} – I_N$, and $K$ is the polynomial order. This allows aggregation of information from $K$-hop neighbors. The spatial convolution is followed by a ReLU activation $\phi$.
For temporal modeling, a 2D convolution with kernel size $1 \times 3$ is applied along the time dimension. Let $\Phi$ denote the temporal convolution kernel. For the $r$-th layer, the output is:
$$X^{(r)} = \phi \left( \Phi * \left[ \text{ReLU}(g_\theta *_\mathcal{G} \hat{X}^{(r-1)}) \right] \right) \in \mathbb{R}^{F \times N \times T_a},$$
where $*$ denotes standard convolution. To mitigate network degradation, a residual connection is added by passing the input through a $1 \times 1$ convolution and summing with the STGC output, yielding $P_C$.
Squeeze-and-Excitation Layer
The SE layer adaptively recalibrates feature channels to emphasize important factors for battery electric vehicle charging load prediction. It consists of two operations: Squeeze and Excitation. Given the input $P_C \in \mathbb{R}^{C \times N \times T_a}$ with $C$ channels, the Squeeze operation applies global average pooling to produce channel-wise statistics:
$$z_c = F_{\text{sq}}(P_C) = \frac{1}{N \times T_a} \sum_{i=1}^{N} \sum_{j=1}^{T_a} P_C(i, j, c).$$
The Excitation operation uses two fully connected layers to capture channel dependencies:
$$s_c = F_{\text{ex}}(z, W) = \sigma(W_2 \cdot \text{ReLU}(W_1 \cdot z)),$$
where $W_1 \in \mathbb{R}^{C/r’ \times C}$ and $W_2 \in \mathbb{R}^{C \times C/r’}$ are learned weights, $r’$ is a reduction ratio, and $\sigma$ is the sigmoid function. The output is a recalibrated tensor $\tilde{Y}_C = P_C \odot s_c$, where $\odot$ denotes channel-wise multiplication.
Final Fusion Layer
The outputs from the three periodic segments (recent, daily, weekly) are fused using learned weights to combine multi-scale temporal information:
$$\hat{Y} = V_r \odot \hat{Y}_r + V_d \odot \hat{Y}_d + V_w \odot \hat{Y}_w,$$
where $V_r, V_d, V_w$ are parameters that weight the contributions of each segment, and $\hat{Y}_r, \hat{Y}_d, \hat{Y}_w$ are the processed outputs for each segment. This fusion enables the model to adaptively balance periodic patterns for battery electric vehicle charging load prediction.
Experimental Setup and Results
To evaluate STGC-SENet, I conducted experiments using real-world data from an urban battery electric vehicle charging network. The dataset includes charging load, charging pile occupancy, real-time electricity prices, charging pile counts (fast/slow), and meteorological data (precipitation, temperature) over one month. The area is divided into 247 traffic zones, and data is sampled every 5 minutes. I normalized the data using Zero-Mean standardization and split it into training (60%), validation (20%), and test (20%) sets. The prediction horizon is set to $T_p = 12$ steps (1 hour ahead). Model parameters include Chebyshev polynomial order $K=2$, convolution kernel size of 64, and SE reduction ratio $r’=4$. I use Mean Squared Error (MSE) as the loss function, Adam optimizer with learning rate 0.001, and batch size 32.
Performance Comparison with Baseline Models
I compared STGC-SENet against three baseline models: LSTM, Multi-View Spatio-Temporal Graph Convolutional Network (MSTGCN), and Attention-Based Spatio-Temporal Graph Convolutional Network (ASTGCN). Evaluation metrics include Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). The results are summarized in Table 1.
| Model | MAE | RMSE | MAPE | Training Time per Epoch (s) |
|---|---|---|---|---|
| LSTM | 9.99 | 37.39 | 0.21 | 6.23 |
| MSTGCN | 7.19 | 26.28 | 0.40 | 18.2 |
| ASTGCN | 7.73 | 26.21 | 0.45 | 25.66 |
| STGC-SENet | 6.63 | 25.90 | 0.21 | 19.28 |
STGC-SENet achieves the lowest MAE (6.63), RMSE (25.90), and MAPE (0.21), outperforming all baselines. Specifically, compared to LSTM, MAE decreases by 3.36 (33.63% improvement); compared to MSTGCN, MAE decreases by 0.56 (7.78% improvement); and compared to ASTGCN, MAE decreases by 1.10 (14.23% improvement). The SE layer effectively enhances key features without significant computational overhead, as training time per epoch is comparable to MSTGCN. These results demonstrate the efficacy of integrating multi-factor fusion and attention mechanisms for battery electric vehicle charging load prediction.
Sensitivity Analysis of Periodic Factors
To assess the impact of periodic temporal segments, I varied the combinations of recent ($r$), daily ($d$), and weekly ($w$) slices, using only charging load as input. The baseline is $r1d0w0$ (one recent slice). Table 2 shows the MAE for different configurations.
| Configuration | Description | MAE |
|---|---|---|
| r1d0w0 | Baseline (recent only) | 6.63 |
| r4d0w0 | Four recent slices | 7.05 |
| r1d1w0 | One recent, one daily slice | 5.45 |
| r1d2w0 | One recent, two daily slices | 5.12 |
| r1d3w0 | One recent, three daily slices | 4.97 |
| r1d0w1 | One recent, one weekly slice | 6.50 |
| r1d0w2 | One recent, two weekly slices | 6.78 |
| r1d0w3 | One recent, three weekly slices | 7.10 |
Adding daily slices consistently improves prediction accuracy, with MAE dropping to 4.97 for $r1d3w0$. This indicates strong daily periodicity in battery electric vehicle charging load, likely due to regular user routines. In contrast, increasing recent slices degrades performance, suggesting overfitting to short-term noise. Weekly slices provide modest improvement with one slice but worsen with more, possibly due to data limitations (only one month of data). Thus, daily cycles are most critical for battery electric vehicle charging load prediction.
Sensitivity Analysis of Input Factors
I evaluated the effect of integrating multiple factors: charging load ($F_v$), charging pile occupancy ($F_o$), real-time electricity price ($F_p$), weighted charging pile count ($F_n$), and precipitation ($F_w$). The weighted count $F_n$ is computed as $F_n = 0.8 \times K_c + 0.2 \times M_c$, where $K_c$ and $M_c$ are fast and slow charging pile counts, respectively, emphasizing the role of fast charging for battery electric vehicles. Using the periodic configuration $r1d1w1$, Table 3 presents results for different factor combinations.
| Factors | MAE | RMSE | MAPE |
|---|---|---|---|
| $F_v$ only | 5.17 | 16.50 | 0.27 |
| $F_v + F_o$ | 5.10 | 16.36 | 0.25 |
| $F_v + F_p$ | 5.16 | 16.29 | 0.27 |
| $F_v + F_n$ | 5.32 | 16.54 | 0.34 |
| $F_v + F_w$ | 5.26 | 16.41 | 0.30 |
| $F_v + F_o + F_p$ | 5.08 | 16.16 | 0.24 |
| $F_v + F_o + F_n$ | 5.14 | 16.36 | 0.24 |
| $F_v + F_o + F_w$ | 5.17 | 16.33 | 0.29 |
| MSTGCN ($F_v + F_o + F_p$) | 6.12 | 16.43 | 0.51 |
The best performance is achieved with $F_v + F_o + F_p$, yielding MAE of 5.08, RMSE of 16.16, and MAPE of 0.24. This represents a 1.74% reduction in MAE compared to using only charging load. Charging pile occupancy ($F_o$) and real-time electricity price ($F_p$) are highly correlated with battery electric vehicle charging load, as occupancy reflects immediate demand and pricing influences user behavior. In contrast, precipitation ($F_w$) and weighted charging pile count ($F_n$) do not improve predictions significantly; $F_n$ may be too static, and $F_w$ may have sparse data. STGC-SENet outperforms MSTGCN even with the same factors, highlighting the benefit of the SE layer for dynamic feature recalibration in multi-factor fusion for battery electric vehicle charging load prediction.
Multi-Time-Scale Prediction Analysis
To examine prediction accuracy across different time scales, I selected two representative traffic zones—one with strong periodicity and one with weak periodicity in battery electric vehicle charging load. Figure 1 illustrates the predicted versus actual loads for 5-minute and 1-hour horizons. The strong-periodicity zone shows smoother error curves and closer alignment, especially at the 5-minute scale. As the prediction horizon lengthens to 1 hour, errors increase slightly due to accumulated uncertainties. This underscores the model’s capability to handle short-term fluctuations while maintaining robustness over longer periods for battery electric vehicle charging load.
Discussion
The STGC-SENet model effectively addresses the spatio-temporal prediction of battery electric vehicle charging load by integrating periodic patterns, graph-based spatial dependencies, and multi-factor attention. The key innovations include the PTSE block for capturing daily and weekly cycles, the STGC block for simultaneous spatio-temporal modeling, and the SE layer for adaptive feature fusion. Experimental results confirm that daily periodicity is crucial, and factors like charging pile occupancy and real-time electricity prices significantly enhance prediction accuracy. These insights can inform grid operators and urban planners in optimizing charging infrastructure for battery electric vehicles.
However, limitations exist. The dataset spans only one month, which may restrict the model’s ability to learn long-term weekly patterns. Future work should incorporate larger datasets with diverse seasonal variations. Additionally, while the SE layer improves feature weighting, more sophisticated attention mechanisms (e.g., transformer-based approaches) could be explored to capture complex interactions among factors. Integrating traffic flow data or user behavior patterns could further refine predictions for battery electric vehicle charging load. Moreover, the model assumes a static graph structure; dynamic graphs that evolve over time might better represent changing urban mobility patterns.
Conclusion
In this article, I proposed STGC-SENet, a fusion model for spatio-temporal prediction of battery electric vehicle charging load driven by multi-factor integration. The model leverages periodic temporal segments, graph convolutional networks, and channel attention to dynamically capture temporal dependencies, spatial correlations, and feature importance. Experiments on real-world data demonstrate superior performance over baseline models, with MAE reductions of up to 33.63%. Sensitivity analyses reveal that daily cycles and factors like charging pile occupancy and real-time electricity prices are most impactful, whereas static or sparse factors offer limited gains. These findings contribute to advancing predictive analytics for battery electric vehicle charging infrastructure, supporting sustainable urban energy management. Future research will focus on extending data coverage, refining fusion strategies, and incorporating additional contextual factors to enhance the robustness of battery electric vehicle charging load predictions.
The widespread adoption of battery electric vehicles necessitates accurate load forecasting to ensure grid stability. By integrating multiple data sources and adaptive mechanisms, STGC-SENet provides a scalable solution for urban areas. As battery electric vehicle penetration grows, such models will become increasingly vital for smart grid operations and policy-making, ultimately facilitating the transition to sustainable transportation systems.