As an integral part of the global transition towards sustainable energy, electric vehicles (EVs) have gained significant traction worldwide, with China’s EV market emerging as a pivotal force in shaping the future of transportation. The rapid proliferation of electric vehicles, particularly in China, has introduced complex challenges for power grid management due to the inherent randomness and volatility of charging behaviors. Accurately predicting short-term charging loads at EV charging stations is crucial for optimizing grid operations, enabling vehicle-to-grid (V2G) services, and supporting the integration of renewable energy sources. In this study, I propose a hybrid forecasting model that combines Crested Porcupine Optimizer (CPO), Variational Mode Decomposition (VMD), and Bidirectional Long Short-Term Memory (BiLSTM) networks to address the non-stationary nature of EV charging loads. By incorporating multiple influencing factors—such as historical temperature, day type, and holiday indicators—alongside decomposed load data, the model aims to enhance prediction accuracy and reliability for China’s evolving EV infrastructure.
The stochastic nature of electric vehicle charging patterns stems from diverse user behaviors, environmental conditions, and temporal factors, leading to high fluctuations in load profiles. Traditional forecasting methods often struggle to capture these dynamics, resulting in suboptimal grid scheduling and potential stability issues. To overcome these limitations, I leverage advanced signal processing and deep learning techniques. The core of my approach involves decomposing the raw charging load data into intrinsic mode functions (IMFs) using VMD, which is optimized by the CPO algorithm to adaptively determine key parameters. These IMFs, along with contextual features, are then fed into a BiLSTM network to exploit temporal dependencies in both forward and backward directions. This combination effectively mitigates the non-stationarity of EV loads while capturing intricate patterns for improved short-term forecasts.
In the context of China’s electric vehicle expansion, the need for precise load forecasting is amplified by the country’s ambitious carbon neutrality goals and the growing adoption of EVs in urban areas. The proposed CPO-VMD-BiLSTM model not only addresses technical challenges but also aligns with practical applications in smart grid management. For instance, by accurately predicting charging demands, grid operators can implement effective V2G strategies, where electric vehicles serve as mobile energy storage units, thereby enhancing grid resilience and promoting energy efficiency. This study demonstrates the model’s efficacy through comprehensive experiments, comparing it with standalone and other hybrid models using metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). The results underscore the potential of this approach to support the sustainable growth of China’s EV ecosystem.
The mathematical foundation of the Variational Mode Decomposition (VMD) method is central to the proposed model. VMD decomposes a signal $f(t)$ into $K$ mode functions $u_k(t)$, where $k = 1, 2, \ldots, K$, by solving a constrained variational problem. The objective is to minimize the sum of the bandwidths of each mode, expressed 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 the constraint $\sum_{k=1}^K u_k(t) = f(t)$. Here, $\partial_t$ denotes the partial derivative, $\delta(t)$ is the Dirac delta function, $*$ represents convolution, $j$ is the imaginary unit, and $\omega_k$ is the center frequency of the $k$-th mode. To solve this, the augmented Lagrangian function is introduced:
$$ \mathcal{L}(\{u_k\}, \{\omega_k\}, \lambda) = \alpha \sum_{k=1}^K \left\| \partial_t \left[ \left( \delta(t) + \frac{j}{\pi t} \right) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 + \left\| f(t) – \sum_{k=1}^K u_k(t) \right\|_2^2 + \left\langle \lambda(t), f(t) – \sum_{k=1}^K u_k(t) \right\rangle $$
where $\alpha$ is the penalty factor and $\lambda(t)$ is the Lagrange multiplier. The alternating direction method of multipliers (ADMM) is employed to iteratively update the modes and center frequencies, ensuring efficient decomposition of the electric vehicle charging load data into stable IMFs.
The Crested Porcupine Optimizer (CPO) is a meta-heuristic algorithm inspired by the defense mechanisms of crested porcupines, including visual, sound, scent, and physical attacks. It is used to optimize the VMD parameters—specifically, the number of modes $K$ and the penalty factor $\alpha$—to avoid manual setting and enhance decomposition performance. The CPO algorithm initializes a population of candidate solutions and employs a cyclic population reduction technique to balance exploration and exploitation. The position update equations for the exploration phase, based on visual and sound strategies, are given by:
$$ \vec{x_i}^{t+1} = \vec{x_i}^t + \tau_1 \times \left| 2 \times \tau_2 \times \vec{x_{CP}}^t – \vec{y_i}^t \right| $$
and
$$ \vec{x_i}^{t+1} = (1 – \vec{U_1}) \times \vec{x_i}^t + \vec{U_1} \times \left( \vec{y_i}^t + \tau_3 \times (\vec{x_{r_1}}^t – \vec{x_{r_2}}^t) \right) $$
where $\vec{y_i}^t = \frac{\vec{x_i}^t + \vec{x_r}^t}{2}$, $\tau_1$, $\tau_2$, $\tau_3$ are random numbers, $\vec{U_1}$ is a binary vector, and $\vec{x_{CP}}^t$ is the best solution at iteration $t$. For the development phase, scent and attack strategies are used:
$$ \vec{x_i}^{t+1} = (1 – \vec{U_1}) \times \vec{x_i}^t + \vec{U_1} \times \left( \vec{x_{r_1}}^t + S_i^t \times (\vec{x_{r_2}}^t – \vec{x_{r_3}}^t) – \tau_3 \times \delta \times \gamma^t \times S_i^t \right) $$
and
$$ \vec{x_i}^{t+1} = \vec{x_{CP}}^t + \left( \alpha (1 – \tau_4) + \tau_4 \right) \times \left( \delta \times \vec{x_{CP}}^t – \vec{x_i}^t \right) – \tau_5 \times \delta \times \gamma^t \times \vec{F_i}^t $$
Here, $S_i^t$ is the scent diffusion factor, $\gamma^t$ is the defense factor, $\delta$ controls the search direction, and $\vec{F_i}^t$ represents the average force. The fitness function for optimization is the envelope entropy $E_p$, defined as:
$$ E_p = -\sum_{i=1}^N p(i) \lg p(i) $$
with $p(i) = \frac{a(i)}{\sum_{i=1}^N a(i)}$, where $a(i)$ is the envelope signal obtained from the Hilbert transform. Minimizing $E_p$ ensures optimal decomposition of the electric vehicle charging load data.
The Bidirectional Long Short-Term Memory (BiLSTM) network is employed for time-series forecasting due to its ability to capture long-term dependencies in both forward and backward directions. Each LSTM unit incorporates input, forget, and output gates to regulate information flow. The update equations for a standard LSTM are:
$$ \begin{aligned}
f_t &= \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \\
i_t &= \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \\
o_t &= \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \\
\tilde{C}_t &= \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) \\
C_t &= f_t * C_{t-1} + i_t * \tilde{C}_t \\
h_t &= o_t * \tanh(C_t)
\end{aligned} $$
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 function; and $W$ and $b$ denote weights and biases. In the BiLSTM architecture, two LSTM layers—one processing the sequence forward and the other backward—are combined, allowing the model to learn from past and future contexts simultaneously. This is particularly beneficial for electric vehicle charging load prediction, where patterns may depend on both historical and upcoming events.
To validate the proposed CPO-VMD-BiLSTM model, I conducted experiments using a dataset representative of China’s EV charging infrastructure. The dataset includes historical charging load data, temperature records, and categorical variables for day type and holidays, preprocessed to handle missing values and outliers. The input features are normalized to eliminate scale differences, and the data is split into training and testing sets. The decomposition of load data into IMFs using CPO-optimized VMD parameters is illustrated in the table below, which summarizes the optimal values obtained for different optimization algorithms.
| Optimization Algorithm | Penalty Factor $\alpha$ | Number of Modes $K$ |
|---|---|---|
| Particle Swarm Optimization (PSO) | 969.05 | 8 |
| Grey Wolf Optimizer (GWO) | 543.46 | 5 |
| Crested Porcupine Optimizer (CPO) | 418.89 | 5 |
The performance of the proposed model is compared against standalone BiLSTM, unoptimized VMD-BiLSTM, and other optimized variants. The evaluation metrics—RMSE, MAE, and R²—are calculated as follows:
$$ \text{RMSE} = \sqrt{\frac{1}{n} \sum_{k=1}^n (\hat{y}_k – y_k)^2} $$
$$ \text{MAE} = \frac{1}{n} \sum_{k=1}^n |\hat{y}_k – y_k| $$
$$ R^2 = 1 – \frac{\sum_{k=1}^n (\hat{y}_k – y_k)^2}{\sum_{k=1}^n (y_k – \bar{y})^2} $$
where $\hat{y}_k$ is the predicted load, $y_k$ is the actual load, $\bar{y}$ is the mean of actual loads, and $n$ is the number of test samples. The results, presented in the table below, demonstrate the superiority of the CPO-VMD-BiLSTM model in forecasting electric vehicle charging loads.
| Forecasting Model | RMSE | MAE | R² |
|---|---|---|---|
| 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 achieves the lowest RMSE and MAE, indicating higher accuracy and robustness. Specifically, compared to the unoptimized VMD-BiLSTM, it reduces RMSE by 48.72% and MAE by 65.71%, highlighting the importance of parameter optimization. Moreover, when compared to other optimized models, it shows an average reduction of 27.71% in RMSE and 49.65% in MAE, underscoring the efficacy of the CPO algorithm in enhancing decomposition quality. These improvements are critical for managing the grid impacts of China’s electric vehicle adoption, as precise load forecasts enable better resource allocation and V2G integration.
In conclusion, the integration of CPO-optimized VMD with BiLSTM provides a powerful framework for short-term electric vehicle charging load forecasting. By addressing the non-stationarity and randomness of EV loads through adaptive decomposition and deep learning, the model offers significant advancements in prediction accuracy. This approach not only supports the operational efficiency of charging stations but also contributes to the stability of power grids amidst the growing penetration of electric vehicles in China. Future work could explore real-time applications and the incorporation of additional factors, such as user behavior analytics and renewable energy generation patterns, to further refine forecasts for the evolving China EV landscape.