Electric vehicles (EVs) have emerged as a pivotal component of clean energy transportation, offering advantages such as reduced environmental pollution, decreased dependence on petroleum resources, and mitigation of climate change. As the world increasingly prioritizes sustainable energy, the proliferation of EVs has surged. Accurate prediction of EV charging loads is critical for the stable operation and planning of power systems. Such predictions enable scientific planning of charging infrastructure, optimization of charging strategies, enhancement of power supply efficiency, and reduction of load fluctuations, ultimately facilitating greater integration of renewable energy sources. In this paper, I present a novel approach to address the challenges of short-term charging load prediction for regional EVs, leveraging a combination of Grey Limited Dynamic Spectrum Clustering (GLDSC) and a ConvAutoformer model.
INTRODUCTION
The rapid growth of EVs has introduced significant volatility to power grid loads. Traditional load prediction methods often struggle to capture the complex spatiotemporal patterns and behavioral uncertainties inherent in EV charging. My research aims to develop a robust prediction framework that improves accuracy by integrating advanced clustering and deep learning techniques.
Motivation and Background
EV charging behavior is influenced by diverse factors, including user habits, travel patterns, and environmental conditions. These factors lead to highly nonlinear and dynamic load profiles. Existing studies have employed various clustering algorithms, such as K-means and spectral clustering, to segment load data, but these often rely on Euclidean distance, which fails to adequately capture temporal similarities in charging curves. Additionally, deep learning models like LSTM and Transformer have shown promise in load prediction, but they face challenges in handling long-range dependencies and maintaining prediction stability over time.
Literature Review
In the realm of clustering, studies have shown that grouping EV charging loads into similar patterns can enhance prediction accuracy. For example, spectral clustering has been used to address nonlinear data distributions, but its reliance on Euclidean distance limits performance. In load prediction, Transformer-based models like Autoformer have demonstrated superiority in time-series forecasting, but they often suffer from prediction oscillations at extreme values, limiting precision.
My work builds upon these foundations by introducing GLDSC, which integrates Grey Relational Degree (GRD) with Limited Dynamic Time Warping (LDTW) to improve clustering accuracy, and ConvAutoformer, which enhances feature extraction through dual convolutional layers, addressing the limitations of traditional methods.
METHODOLOGY
Fundamental Algorithm Principles
Spectral Clustering (SC)
Spectral clustering is a graph theory-based method that transforms clustering into a combinatorial optimization problem. For EV charging load data, SC helps identify distinct charging patterns by mapping data points to a graph where vertices represent samples and edge weights denote similarity. The key steps of SC are as follows:
- Similarity Matrix Construction:\(A_{ij} = \begin{cases} \exp\left(\frac{-\|s_i – s_j\|}{2\sigma^2}\right), & i \neq j \\ 0, & i = j \end{cases}\) where \(\sigma^2\) controls the decay of Euclidean distance.
- Laplacian Matrix Construction: Construct the degree matrix D where \(D_{ii} = \sum_j A_{ij}\), then:\(L = D^{-1/2}AD^{-1/2}\)
- Eigenvalue Decomposition: Compute the top k eigenvectors of L to form a matrix X, which is normalized to Y using:\(Y_{ij} = \frac{X_{ij}}{\sqrt{\sum X_{ij}^2}}\)
- K-means Clustering: Apply K-means to Y to obtain final clusters.
However, traditional SC’s reliance on Euclidean distance motivates my improvement using GLDSC, which replaces Euclidean distance with a GRD-LDTW hybrid metric.
Autoformer Model
Autoformer is a Transformer-based architecture designed for long-term time-series forecasting. It decomposes sequences into trend and periodic components, making it suitable for EV load data, which exhibits strong periodicity. The model structure includes:
- Sequence Decomposition: Splits the input sequence \(\chi \in \mathbb{R}^{L \times d}\) into trend \(\chi_1\) and periodic \(\chi_*\) components:\(\chi_1 = \text{AvgPool}(\text{Padding}(\chi))\) \(\chi_* = \chi – \chi_1\)
- Encoder-Decoder Framework: The encoder processes historical periodic components, while the decoder integrates trend and periodic information for prediction. The auto-correlation mechanism uses Fast Fourier Transform (FFT) to capture temporal dependencies efficiently.
However, Autoformer can suffer from prediction oscillations, prompting my modification through ConvAutoformer to enhance feature extraction.
GLDSC-ConvAutoformer Hybrid Model
Data Preprocessing
- Z-score Normalization: To eliminate magnitude effects, I normalize EV load data using:\(P_i’ = \frac{P_i – \mu_i}{\sigma_i}\) where \(\mu_i\) and \(\sigma_i\) are the mean and standard deviation of the i-th load sequence.
- Grey Limited Dynamic Spectrum Clustering (GLDSC): My proposed GLDSC algorithm improves traditional SC by:
- Using LDTW to compute distance matrices, addressing pathological alignments in DTW while reducing computation time.
- Incorporating GRD based on LDTW distance:\(\gamma(X_0, X_i) = \frac{\min_m \min_n |x_0(t_0) – x_i(t_i)| + \xi \max_m \max_n |x_0(t_0) – x_i(t_i)|}{\text{LDTW}(X_0, X_i)/\lambda + \xi \max_m \max_n |x_0(t_0) – x_i(t_i)|}\) where \(\xi = 0.5\) is the 分辨 coefficient, and \(\lambda\) is the path length of LDTW.
- The GRD matrix replaces the similarity matrix in SC, constructing the Laplacian matrix for improved clustering.
ConvAutoformer Architecture
My ConvAutoformer model enhances Autoformer by adding dual 1D convolutional layers for feature extraction:
- Convolutional Layers: Two layers with kernel sizes \(3 \times 1\) and \(2 \times 1\), and kernel counts 7 and 5, respectively, to extract multi-scale temporal features from clustered load data.
- Integration with Autoformer: The convolutional output feeds into the Autoformer encoder, which processes periodic components, while the decoder accumulates trend components for prediction.
GLDSC-ConvAutoformer Workflow
The hybrid model workflow is as follows:
- Preprocess EV load data via Z-score normalization.
- Apply GLDSC to cluster loads into groups with similar periodicity, using GRD-LDTW for similarity measurement.
- For each cluster, use ConvAutoformer with dual convolutions to extract features and predict loads.
- Reconstruct final predictions by summing cluster-wise forecasts.
EXPERIMENTAL DESIGN
Dataset Description
I evaluated the model using charging transaction data from electric buses in a city, collected from December 1–31, 2019. The dataset includes:
- 103 unique charging cards, each with 1,488 sampling points (30-minute intervals).
- Meteorological data (temperature, rainfall) as auxiliary features.
The dataset was split as:
- 70% for training (\(N_{train} = 1037\))
- 10% for validation (\(N_{val} = 150\))
- 20% for testing (\(N_{test} = 297\))
Model Parameters
Key parameters for the GLDSC-ConvAutoformer model include:
- GLDSC: Window width = 3, slope = 1 for LDTW; cluster number determined by silhouette coefficient.
- ConvAutoformer:
- Convolutional layer 1: Kernel size \(3 \times 1\), kernels = 7
- Convolutional layer 2: Kernel size \(2 \times 1\), kernels = 5
- Autoformer: pred_len = 1, label_len = 2, seq_len = 4, e_layers = 4, d_layers = 1, n_heads = 8, d_model = 48, batch_size = 3
Evaluation Metrics
I used two standard metrics to assess prediction accuracy:
- Mean Absolute Error (MAE):\(E_{MAE} = \frac{1}{n} \sum_{i=1}^{n} |y_i – y_{ik}|\)
- Mean Square Error (MSE):\(E_{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i – y_{ik})^2\) where \(y_i\) is the predicted value, \(y_{ik}\) is the actual value, and n is the number of samples.
RESULTS AND DISCUSSION
GLDSC Clustering Results
Using the elbow method, I determined the optimal cluster number \(k = 5\), as shown by the silhouette coefficient trend. Table 1 summarizes the cluster sizes:
| Cluster | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Count | 360 | 183 | 1179 | 1069 | 407 |
Clusters 0, 2, 3, and 4 exhibit distinct periodic and trend patterns, while cluster 1 (residual) shows a stable trend with minimal periodicity. The GLDSC algorithm effectively segments loads into groups with similar charging behaviors, reducing volatility and randomness.
Prediction Performance Comparison
I compared the GLDSC-ConvAutoformer model with several baselines:
- Traditional neural networks: TCN, LSTM
- Transformer-based models: Transformer, Informer, Reformer, Autoformer
- Self-comparative models: ConvAutoformer, GLDSC-Autoformer
Table 2 shows the MAE and MSE results on the test set:
| Model | MAE | MSE |
|---|---|---|
| LSTM | 0.895 | 0.392 |
| TCN | 0.812 | 0.370 |
| Transformer | 0.586 | 0.255 |
| Informer | 0.517 | 0.207 |
| Reformer | 0.402 | 0.165 |
| Autoformer | 0.385 | 0.142 |
| ConvAutoformer | 0.277 | 0.098 |
| GLDSC-Autoformer | 0.259 | 0.095 |
| GLDSC-ConvAutoformer | 0.129 | 0.026 |
The results demonstrate that my proposed model outperforms all baselines, with MAE and MSE reductions of up to 85.6% and 93.4% compared to LSTM. The combination of GLDSC and ConvAutoformer synergistically improves feature extraction and clustering, leading to more accurate predictions.
Error Analysis
Figure 1 (not shown) illustrates prediction errors for different models. Traditional networks (TCN, LSTM) exhibit high volatility, while Transformer-based models struggle with local fitting. My model shows the smallest error margins, particularly for cluster 1 (residual), which has an MSE of 0.420 but contributes minimally to overall error due to its small load proportion.
CONCLUSION
In this study, I have proposed a GLDSC-ConvAutoformer model for short-term EV charging load prediction, addressing the challenges of volatility and low accuracy in traditional methods. Key contributions include:
- GLDSC Algorithm: By integrating LDTW with GRD with spectral clustering, I improved clustering accuracy, enabling better capture of periodic charging patterns. This reduces the impact of randomness on prediction.
- ConvAutoformer Model: The addition of dual convolutional layers to Autoformer enhances feature extraction from clustered data, mitigating prediction oscillations and improving fit to real-world loads.
- Experimental Validation: The model achieved significantly higher accuracy than state-of-the-art methods, with MSE 66.494% lower than Autoformer alone. This demonstrates its effectiveness for grid scheduling and renewable energy integration.
Future work will focus on expanding the model to handle real-time data streams and incorporating more contextual factors, such as dynamic pricing and user mobility patterns, to further enhance practical applicability.