With the rapid growth of the electric car industry, particularly in China EV markets, the integration of electric vehicles into power grids has become a critical focus for sustainable energy systems. The charging behavior of electric cars exhibits strong randomness and high volatility, leading to challenges in accurately predicting short-term charging loads at charging stations. As electric cars serve as mobile energy storage units and participate in vehicle-to-grid services, forecasting their charging loads is essential to mitigate adverse impacts on grid stability. This study addresses these challenges by proposing a hybrid model that combines Crested Porcupine Optimizer, Variational Mode Decomposition, and Bidirectional Long Short-Term Memory networks for short-term charging load forecasting. The approach incorporates multiple influencing factors, such as historical temperature, date types, and holidays, to form an input feature matrix, optimizes decomposition parameters adaptively, and leverages deep learning for precise predictions. Experimental results demonstrate significant improvements in forecasting accuracy, highlighting the model’s potential for enhancing grid management in the context of China EV expansion and global electric car adoption.
The proliferation of electric cars worldwide, driven by environmental concerns and technological advancements, has positioned China EV markets as leaders in this transition. However, the unpredictable nature of electric car charging behaviors introduces fluctuations that complicate load forecasting. Traditional methods often fail to capture the non-stationary characteristics of charging data, necessitating advanced techniques that account for multiple factors and decompose complex signals. This research introduces a novel framework that integrates optimization algorithms, signal processing, and neural networks to address these issues. By focusing on short-term forecasting, the model supports real-time decision-making for charging station operators and grid administrators, ensuring efficient energy distribution and reduced operational costs.
The core of the proposed method lies in its multi-stage architecture. First, historical charging load data from electric car charging stations are combined with external factors like temperature and temporal indicators to create a comprehensive input dataset. This dataset undergoes preprocessing to handle missing values and outliers, ensuring data quality. Subsequently, the Variational Mode Decomposition technique is applied to decompose the load sequence into intrinsic mode functions, which represent simpler, more stable components. The decomposition parameters are optimized using the Crested Porcupine Optimizer, a meta-heuristic algorithm that enhances decomposition efficiency by minimizing envelope entropy. Finally, the Bidirectional Long Short-Term Memory network processes these components to generate forecasts, leveraging its ability to capture temporal dependencies in both forward and backward directions. This combination effectively reduces the non-stationarity of electric car charging loads and improves prediction reliability.
To validate the model, experiments were conducted using real-world data from electric car charging stations, simulating scenarios relevant to China EV infrastructure. The results were compared against standalone and other hybrid models, with performance metrics such as Root Mean Squared Error and Mean Absolute Error indicating superior accuracy. The following sections detail the methodology, experimental setup, and results, emphasizing the role of optimization and decomposition in handling the complexities of electric car charging behavior. Tables and equations are provided to illustrate key concepts and quantitative analyses, ensuring a thorough understanding of the model’s mechanics and benefits.
Methodology
The proposed CPO-VMD-BiLSTM model for short-term charging load forecasting in electric car charging stations involves several key steps. The input features include historical charging load data, temperature records, date types, and holiday information, which are normalized to eliminate scale differences. Let the input feature matrix be represented as $X = [x_1, x_2, \dots, x_n]$, where each $x_i$ corresponds to a time-step instance. Normalization is performed using:
$$x^*_i = \frac{x_i – x_{\text{min}}}{x_{\text{max}} – x_{\text{min}}}$$
where $x^*_i$ is the normalized value, and $x_{\text{min}}$ and $x_{\text{max}}$ are the minimum and maximum values in the dataset, respectively. This step ensures that all features contribute equally to the model, enhancing convergence during training.
The Variational Mode Decomposition is then applied to the historical charging load sequence $f(t)$ to decompose it into $K$ intrinsic mode functions $u_k(t)$, where $k = 1, 2, \dots, K$. The VMD process involves constructing a variational problem to minimize the sum of the bandwidths of each mode, subject to the constraint that the sum of the modes equals the original signal. The objective function is formulated as:
$$\min_{\{u_k\}, \{\omega_k\}} \left\{ \sum_{k=1}^K \left\| \partial_t \left[ \left( \delta(t) + \frac{j}{\pi t} \right) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 \right\}$$
subject to $\sum_{k=1}^K u_k(t) = f(t)$, where $\{u_k\}$ and $\{\omega_k\}$ are the sets of mode functions and their center frequencies, $\partial_t$ denotes the partial derivative, $\delta(t)$ is the Dirac delta function, $j$ is the imaginary unit, and $*$ represents convolution. To solve this constrained problem, the augmented Lagrangian function is introduced:
$$\mathcal{L}(\{u_k\}, \{\omega_k\}, \lambda) = \alpha \sum_{k=1}^K \left\| \partial_t \left[ \left( \delta(t) + \frac{j}{\pi t} \right) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 + \left\| f(t) – \sum_{k=1}^K u_k(t) \right\|_2^2 + \langle \lambda(t), f(t) – \sum_{k=1}^K u_k(t) \rangle$$
where $\alpha$ is the penalty factor, and $\lambda(t)$ is the Lagrange multiplier. The alternating direction method of multipliers is used to iteratively update the modes and center frequencies until convergence.
The Crested Porcupine Optimizer is employed to optimize the VMD parameters $K$ and $\alpha$, which are crucial for effective decomposition. The CPO algorithm mimics the defense mechanisms of crested porcupines, including visual, sound, scent, and attack strategies, to explore and exploit the search space. The population initialization is given by:
$$\vec{X}_i = \vec{L} + \vec{r} \times (\vec{U} – \vec{L}), \quad i = 1, 2, \dots, N’$$
where $\vec{X}_i$ is the $i$-th candidate solution, $\vec{L}$ and $\vec{U}$ are the lower and upper bounds of the search space, $N’$ is the population size, and $\vec{r}$ is a random vector between 0 and 1. The population size is dynamically reduced using a cyclic reduction technique:
$$N = N_{\text{min}} + (N’ – N_{\text{min}}) \times \left(1 – \left(\frac{t \% T_{\text{max}}}{T}\right)^{T_{\text{max}} / T}\right)$$
where $N$ is the updated population size, $N_{\text{min}}$ is the minimum size, $t$ is the current evaluation, $T$ is the cycle variable, and $T_{\text{max}}$ is the maximum number of evaluations. The exploration phase utilizes visual and sound strategies:
$$\vec{x}^{t+1}_i = \vec{x}^t_i + \tau_1 \times |2 \times \tau_2 \times \vec{x}^t_{\text{CP}} – \vec{y}^t_i|$$
$$\vec{x}^{t+1}_i = (1 – \vec{U}_1) \times \vec{x}^t_i + \vec{U}_1 \times (\vec{y}^t_i + \tau_3 \times (\vec{x}^t_{r_1} – \vec{x}^t_{r_2}))$$
$$\vec{y}^t_i = \frac{\vec{x}^t_i + \vec{x}^t_r}{2}$$
where $\vec{x}^t_{\text{CP}}$ is the best solution at evaluation $t$, $\tau_1$, $\tau_2$, $\tau_3$ are random numbers, $\vec{U}_1$ is a binary vector, and $r$, $r_1$, $r_2$ are random indices. The development phase employs scent and attack strategies:
$$\vec{x}^{t+1}_i = (1 – \vec{U}_1) \times \vec{x}^t_i + \vec{U}_1 \times (\vec{x}^t_{r_1} + S^t_i \times (\vec{x}^t_{r_2} – \vec{x}^t_{r_3}) – \tau_3 \times \vec{\delta} \times \gamma^t \times S^t_i)$$
$$\vec{x}^{t+1}_i = \vec{x}^t_{\text{CP}} + (\alpha (1 – \tau_4) + \tau_4) \times (\delta \times \vec{x}^t_{\text{CP}} – \vec{x}^t_i) – \tau_5 \times \delta \times \gamma^t \times \vec{F}^t_i$$
where $S^t_i$ is the scent diffusion factor, $\gamma^t$ is the defense factor, $\delta$ controls the search direction, $\alpha$ is the convergence factor, and $\vec{F}^t_i$ is the average force. The fitness function for optimization is the envelope entropy $E_p$, defined as:
$$E_p = -\sum_{i=1}^N p(i) \lg p(i)$$
$$p(i) = \frac{a(i)}{\sum_{i=1}^N a(i)}$$
where $a(i)$ is the envelope signal obtained from the Hilbert transform. Minimizing $E_p$ ensures optimal decomposition by reducing mode mixing and improving component separation.
After decomposition, the Bidirectional Long Short-Term Memory network processes each intrinsic mode function along with the input features. The BiLSTM consists of forward and backward LSTM layers, allowing it to capture dependencies in both temporal directions. The LSTM unit computations are as follows:
$$f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f)$$
$$i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i)$$
$$o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o)$$
$$\tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C)$$
$$C_t = f_t * C_{t-1} + i_t * \tilde{C}_t$$
$$h_t = o_t * \tanh(C_t)$$
where $f_t$, $i_t$, and $o_t$ are the forget, input, and output gates, respectively; $C_t$ is the cell state; $h_t$ is the hidden state; $\sigma$ is the sigmoid activation function; and $W$ and $b$ are weight matrices and bias vectors. The BiLSTM combines forward hidden states $\vec{h}_t$ and backward hidden states $\overleftarrow{h}_t$ to form the final output $h_t = [\vec{h}_t, \overleftarrow{h}_t]$. This architecture enhances the model’s ability to learn complex temporal patterns in electric car charging data.
The forecasting performance is evaluated using Root Mean Squared Error, Mean Absolute Error, and the coefficient of determination $R^2$:
$$E_{\text{RMSE}} = \sqrt{\frac{1}{n} \sum_{k=1}^n (\hat{y}_k – y_k)^2}$$
$$E_{\text{MAE}} = \frac{1}{n} \sum_{k=1}^n |\hat{y}_k – y_k|$$
$$R^2 = 1 – \frac{\sum_{k=1}^n (\hat{y}_k – y_k)^2}{\sum_{k=1}^n (y_k – \bar{y})^2}$$
where $\hat{y}_k$ is the predicted value, $y_k$ is the actual value, $\bar{y}$ is the mean of actual values, and $n$ is the number of samples. Lower RMSE and MAE values indicate better accuracy, while $R^2$ closer to 1 signifies a better fit.
Experimental Setup and Data Analysis
To assess the model, data from electric car charging stations were utilized, reflecting scenarios akin to those in China EV deployments. The dataset included historical charging loads, temperature readings, and calendar information over a one-year period, with hourly sampling. Data preprocessing involved handling missing values using median absolute deviation and filling gaps with adjacent time-step averages. The dataset was split into training and testing sets in a 7:3 ratio, and all features were normalized to the [0, 1] range.
The CPO algorithm was configured with a population size of 10 and 20 iterations, searching for optimal VMD parameters within $K \in [4, 10]$ and $\alpha \in [400, 3000]$. Comparative analyses with Particle Swarm Optimization and Grey Wolf Optimizer were conducted to highlight CPO’s effectiveness. The BiLSTM network was implemented with 10 hidden neurons and a learning rate of 0.005, trained using backpropagation through time. The following table summarizes the parameter settings for the optimization algorithms:
| Parameter | Value |
|---|---|
| Dimensions | 2 |
| Population Size | 10 |
| Iterations | 20 |
| $\alpha$ Range | 400-3000 |
| $K$ Range | 4-10 |
The decomposition results using CPO-optimized VMD yielded five intrinsic mode functions, each representing different frequency components of the original charging load signal. The table below shows the optimal parameters found by each optimization algorithm:
| Optimization Algorithm | $\alpha$ | $K$ |
|---|---|---|
| PSO | 969.0540 | 7.6823 |
| GWO | 543.4636 | 5.4749 |
| CPO | 418.8863 | 5.1219 |
These parameters were used to decompose the charging load data, and the resulting IMFs were fed into the BiLSTM model for forecasting. The performance of the proposed CPO-VMD-BiLSTM model was compared against standalone BiLSTM, VMD-BiLSTM, and other optimized variants. The evaluation metrics demonstrated the superiority of the proposed approach, as detailed in the results section.
Results and Discussion
The forecasting results indicate that the CPO-VMD-BiLSTM model significantly outperforms other models in predicting short-term charging loads for electric car stations. The decomposition of historical loads into IMFs reduced non-stationarity, enabling the BiLSTM network to capture intricate patterns more effectively. The following table compares the performance metrics across different models:
| Forecasting Model | RMSE | MAE | $R^2$ |
|---|---|---|---|
| BiLSTM | 5.4488 | 3.6581 | 0.82832 |
| VMD-BiLSTM | 4.1663 | 3.0763 | 0.89955 |
| PSO-VMD-BiLSTM | 3.2217 | 2.3442 | 0.93993 |
| GWO-VMD-BiLSTM | 2.7298 | 1.8933 | 0.95636 |
| CPO-VMD-BiLSTM | 2.1366 | 1.0548 | 0.97521 |
The CPO-VMD-BiLSTM model achieved the lowest RMSE and MAE values, with reductions of 41.23% and 59.04% on average compared to other models, respectively. This highlights the efficacy of integrating optimization and decomposition techniques for electric car charging load forecasting. The $R^2$ value of 0.97521 indicates a strong correlation between predicted and actual loads, reinforcing the model’s reliability.
Analysis of the individual IMF forecasts revealed that components with lower frequencies, such as IMF1, had higher accuracy due to their stable nature, while higher-frequency components posed more challenges. The equation for IMF1’s prediction performance is given by:
$$E_{\text{RMSE, IMF1}} = 0.18009, \quad E_{\text{MAE, IMF1}} = 0.15184, \quad R^2_{\text{IMF1}} = 0.99979$$
This demonstrates that decomposition effectively isolates predictable elements, contributing to overall forecast improvement. The robustness of the model makes it suitable for applications in dynamic environments, such as China EV charging networks, where demand fluctuations are common.
Conclusion
This study presents a comprehensive approach to short-term charging load forecasting for electric car charging stations, emphasizing the importance of multi-factor integration and optimized signal decomposition. The CPO-VMD-BiLSTM model successfully addresses the randomness and volatility inherent in electric car charging behavior, achieving notable accuracy gains. The use of Crested Porcupine Optimizer for parameter tuning enhances the decomposition process, while the Bidirectional Long Short-Term Memory network leverages temporal dependencies for precise predictions. The findings underscore the potential of this hybrid model in supporting grid stability and energy management, particularly in the context of China EV market growth. Future work could explore real-time implementation and adaptation to varying geographic conditions, further advancing the sustainability of electric car ecosystems.