Introduction The rapid proliferation of electric vehicles (EVs) has significantly transformed the transportation sector, aligning with global efforts to achieve carbon neutrality. However, the high randomness and volatility of EV charging behavior pose challenges for power grid management, particularly in accurately predicting short-term charging loads at EV charging stations. In this study, I address this issue by developing a novel combined model, the Crested Porcupine Optimizer-Variational Mode Decomposition-Bidirectional Long Short-Term Memory (CPO-VMD-BiLSTM), to enhance the precision of short-term charging load forecasting. This model integrates multi-factor analysis, adaptive signal decomposition, and advanced neural network architecture to tackle the non-stationarity and complexity of EV charging load data.
Research Background and Significance EVs play a pivotal role in reducing greenhouse gas emissions and promoting energy sustainability. However, their uncoordinated charging can lead to severe fluctuations in grid load, necessitating reliable short-term load prediction for effective Vehicle-to-Grid (V2G) integration. Traditional prediction methods often struggle with the high variability of EV charging patterns, which are influenced by factors such as temperature, day type, and holidays. Data-driven approaches, particularly those leveraging deep learning, have shown promise, but improving their accuracy remains critical.
Literature Review Existing EV charging load prediction methods can be categorized into model-driven and data-driven approaches. Model-driven methods rely on physical models but face challenges due to the randomness of user behavior. Data-driven methods, including machine learning and deep learning techniques, have gained traction. For example, Long Short-Term Memory (LSTM) networks and their variants, such as Bidirectional LSTM (BiLSTM), have demonstrated effectiveness in time series prediction by capturing temporal dependencies. However, the non-stationary nature of raw charging load data limits the performance of single models.
Signal decomposition techniques like Variational Mode Decomposition (VMD) have been used to address non-stationarity by breaking down complex signals into simpler, stationary components. VMD outperforms traditional methods like Empirical Mode Decomposition (EMD) by avoiding endpoint effects and mode mixing. To further optimize VMD, metaheuristic algorithms such as Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) have been applied. In this study, I introduce the Crested Porcupine Optimizer (CPO), a novel metaheuristic inspired by the defensive behaviors of crested porcupines, to adaptively tune VMD parameters, enhancing decomposition efficiency.
Proposed Model: CPO-VMD-BiLSTM The CPO-VMD-BiLSTM model consists of three main components: multi-factor input selection, CPO-optimized VMD decomposition, and BiLSTM-based prediction.
1. Multi-factor Input Feature Matrix The model incorporates historical charging load data alongside three key influencing factors:
- Temperature: Collected from public meteorological datasets (e.g., NOAA).
- Day type: Categorized as weekdays, weekends, or holidays.
- Holidays: Binary indicator (0/1) for holiday periods.
These factors are combined with historical load data to form the input feature matrix, capturing both temporal and contextual dependencies in EV charging behavior .
2. Variational Mode Decomposition (VMD) VMD is a data-driven decomposition technique that breaks a time series into K intrinsic mode functions (IMFs) by solving a variational problem. The core steps involve:
- Constructing the Variational Problem:\(\min_{\{u_k\},\{\omega_k\}} \left\{ \sum_{k=1}^{K} \left\| \partial_t \left[ (\delta(t) + \frac{j}{\pi t}) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 \right\} \quad \text{s.t.} \quad \sum_{k=1}^{K} u_k(t) = f(t)\) where \(u_k(t)\) are the IMF components, \(\omega_k\) are their central frequencies, and \(f(t)\) is the original signal .
- Solving via Augmented Lagrangian Method: By introducing a penalty parameter \(\alpha\) and Lagrangian multiplier \(\lambda(t)\), the constrained problem is transformed into an unconstrained one, solved using the Alternating Direction Method of Multipliers (ADMM) .
3. Crested Porcupine Optimizer (CPO) for VMD Parameter Tuning VMD’s performance heavily depends on two parameters: K (number of modes) and \(\alpha\) (penalty factor). Manual tuning of these parameters is suboptimal, so CPO is used to minimize the envelope entropy of the decomposed IMFs, a measure of signal regularity.
CPO Algorithm Overview:
- Population Initialization:\(\vec{X}_i = \vec{L} + \vec{r} \times (\vec{U} – \vec{L})\) where \(\vec{X}_i\) is the i-th candidate solution, \(\vec{L}\) and \(\vec{U}\) are lower and upper bounds, and \(\vec{r}\) is a random vector in [0,1] .
- Cycle Population Reduction:\(N = N_{\text{min}} + (N’ – N_{\text{min}}) \times \frac{1 – \left( \frac{t \% T_{\text{max}}}{T} \right)}{T_{\text{max}} / T}\) adjusts population size to balance exploration and exploitation .
- Exploration Phase: Uses visual and acoustic strategies to explore the search space:\(\vec{x}_i^{t+1} = \vec{x}_i^t + \tau_1 \times | 2 \times \tau_2 \times \vec{x}_{\text{CP}}^t – \vec{y}_i^t |\) where \(\vec{x}_{\text{CP}}^t\) is the current best solution, and \(\tau_1, \tau_2\) are random parameters .
- Exploitation Phase: Employs odor and attack strategies for local refinement:\(\vec{x}_i^{t+1} = \vec{x}_{\text{CP}}^t + \left( \alpha(1 – \tau_4) + \tau_4 \right) \times (\delta \times \vec{x}_{\text{CP}}^t – \vec{x}_i^t) – \tau_5 \times \delta \times \gamma_t \times \vec{F}_i^t\) with \(\delta\) and \(\gamma_t\) controlling search direction and defense factor, respectively .
The optimal parameters \([K, \alpha]\) are determined by minimizing the envelope entropy:\(E_P = -\sum_{i=1}^{N} p(i) \log p(i), \quad p(i) = \frac{a(i)}{\sum_{i=1}^{N} a(i)}\) where \(a(i)\) is the Hilbert-transformed envelope signal .
4. Bidirectional LSTM (BiLSTM) for Load Prediction BiLSTM enhances traditional LSTM by incorporating both forward and backward temporal dependencies. Each LSTM cell computes forget, input, and output gates:\(\begin{cases} f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \\ i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \\ o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \\ \tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) \\ C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t \\ h_t = o_t \odot \tanh(C_t) \end{cases}\) where \(f_t, i_t, o_t\) are gate outputs, \(\tilde{C}_t\) is the candidate cell state, and \(h_t\) is the hidden state .
BiLSTM combines forward (\(\vec{h}_t\)) and backward (\(\overleftarrow{h}_t\)) hidden states to produce the final output:\(\hat{y}_t = \sigma(W_h \cdot [\vec{h}_t, \overleftarrow{h}_t] + b_h)\) This architecture captures bidirectional temporal patterns, improving prediction accuracy for non-stationary data .
Experimental Setup 1. Dataset The study uses historical charging load data from EV charging stations at the California Institute of Technology, obtained from the ANN-DATA public dataset. The dataset covers 54 chargers from January 1 to December 31, 2019, with 1-hour sampling intervals, resulting in 8,760 data points. Temperature data is sourced from NOAA, and day-type/holiday labels are manually annotated. The dataset is split into training (70%) and testing (30%) sets .
2. Data Preprocessing
- Outlier Handling: Median Absolute Deviation (MAD) removes outliers exceeding 3×MAD in a sliding window.
- Missing Data Imputation: Linear interpolation using adjacent values:\(x_k = \frac{x_{k-1} + x_{k+1}}{2}\) where \(x_k\) is the missing value, and \(x_{k-1}, x_{k+1}\) are values from corresponding times on adjacent days .
- Normalization: Min-Max scaling normalizes features to [0, 1]:\(x_i^* = \frac{x_i – x_{\text{min}}}{x_{\text{max}} – x_{\text{min}}}\) to eliminate dimensional effects .
3. Evaluation Metrics The model’s performance is assessed using:
- Mean Absolute Error (MAE):\(E_{\text{MAE}} = \frac{1}{n} \sum_{k=1}^{n} |\hat{y}_k – y_k|\)
- Root Mean Squared Error (RMSE):\(E_{\text{RMSE}} = \sqrt{\frac{1}{n} \sum_{k=1}^{n} (\hat{y}_k – y_k)^2}\)
- Coefficient of Determination (R²):\(R^2 = 1 – \frac{\sum_{k=1}^{n} (\hat{y}_k – y_k)^2}{\sum_{k=1}^{n} (\bar{y}_k – y_k)^2}\) where \(\hat{y}_k\) are predictions, \(y_k\) are true values, and \(\bar{y}_k\) is the mean of true values .
4. Comparative Models To validate the CPO-VMD-BiLSTM model, it is compared against:
- BiLSTM: Standalone BiLSTM without decomposition.
- VMD-BiLSTM: VMD decomposition + BiLSTM without parameter optimization.
- PSO-VMD-BiLSTM: VMD optimized by PSO + BiLSTM.
- GWO-VMD-BiLSTM: VMD optimized by GWO + BiLSTM.
Results and Discussion 1. VMD Parameter Optimization Table 1 shows the initial parameters for CPO, PSO, and GWO. Figure 1 compares their convergence curves, demonstrating that CPO achieves the lowest envelope entropy (best fitness) faster than PSO and GWO, highlighting its superior optimization efficiency.
| Parameter | Value |
|---|---|
| Dimensions | 2 |
| Population size | 10 |
| Iterations | 20 |
| α range | [400, 3000] |
| K range | [4, 10] |
Table 1. Initial parameters for optimization algorithms.
Table 2 lists the optimal VMD parameters found by each algorithm. CPO yields \(K=5\) and \(\alpha=419\), which are used for subsequent decompositions.
| Algorithm | α | K |
|---|---|---|
| PSO | 969.05 | 7.68 |
| GWO | 543.46 | 5.47 |
| CPO | 418.89 | 5.12 |
Table 2. Optimal VMD parameters from different optimizers.
2. Data Decomposition Results Using CPO-optimized VMD, the original charging load data is decomposed into five IMFs (IMF1–IMF5). The frequency spectra confirm that the decomposition avoids mode mixing, with each IMF representing distinct frequency components.
Figure 2. IMFs and their frequency spectra after CPO-VMD decomposition.
3. Prediction Performance Table 3 compares the performance of all models on the test dataset. The CPO-VMD-BiLSTM model achieves the lowest RMSE (2.1366) and MAE (1.0548), outperforming standalone BiLSTM by 61.5% (RMSE) and 71.2% (MAE). Compared to the unoptimized VMD-BiLSTM, CPO-VMD-BiLSTM reduces RMSE by 48.7% and MAE by 65.7%, confirming the effectiveness of CPO optimization.
| Model | RMSE | MAE | R² |
|---|---|---|---|
| BiLSTM | 5.4488 | 3.6581 | 0.8283 |
| VMD-BiLSTM | 4.1663 | 3.0763 | 0.8996 |
| PSO-VMD-BiLSTM | 3.2217 | 2.3442 | 0.9399 |
| GWO-VMD-BiLSTM | 2.7298 | 1.8933 | 0.9564 |
| CPO-VMD-BiLSTM | 2.1366 | 1.0548 | 0.9752 |
Table 3. Prediction performance comparison.
4. Sensitivity Analysis A sensitivity analysis on the number of IMFs (K) reveals that K=5 provides the optimal balance between decomposition detail and prediction accuracy. Increasing K beyond 5 introduces redundant components, while K<5 leads to under-decomposition and higher errors.
Conclusion This study presents a novel CPO-VMD-BiLSTM model for short-term EV charging load prediction, integrating multi-factor analysis, adaptive signal decomposition, and bidirectional neural networks. Key findings include:
- CPO Optimization: CPO outperforms PSO and GWO in tuning VMD parameters, reducing RMSE and MAE by 48.7% and 65.7% compared to unoptimized VMD-BiLSTM.
- Decomposition Effectiveness: VMD decomposes non-stationary load data into stationary IMFs, enhancing the accuracy of subsequent BiLSTM predictions.
- Model Superiority: CPO-VMD-BiLSTM achieves the lowest RMSE (2.1366) and MAE (1.0548), demonstrating its effectiveness in handling the complexity of EV charging loads.
This research contributes to the field of EV grid integration by providing a robust prediction framework that can support V2G scheduling and grid stability. Future work may explore real-time data integration and extension to larger-scale charging networks.