Under the global “dual carbon” goals, reducing carbon emissions has become a critical mission worldwide. Electric vehicles, as nearly pollution-free transportation tools, are experiencing rapid development, with their numbers and battery capacities continuously increasing. In China, the electric vehicle market is expanding at an unprecedented rate, driven by government policies and technological advancements. The accurate identification of electric vehicle operating states is essential for power grid scheduling, enabling functions such as peak shaving, valley filling, and efficient energy utilization. This paper proposes a parameter identification technique for electric vehicle charging models based on intelligent algorithms, focusing on charging efficiency in both constant and dynamic states. By combining the least squares method and ensemble learning, we achieve high computational efficiency and improved accuracy, supporting the integration of China EV into smart grids.
The charging process of electric vehicles involves complex dynamics influenced by factors like battery capacity, charging power, and grid conditions. Traditional methods for state of charge (SOC) estimation, such as ampere-hour integration, open-circuit voltage, and Kalman filtering, often fall short in practical applications. With advancements in artificial intelligence, AI-based approaches have shown promise in enhancing SOC estimation accuracy. However, many existing methods rely on complex equivalent circuit models or extensive datasets, making them unsuitable for real-time grid-side applications. This study addresses these limitations by developing a macroscopic charging model and employing intelligent algorithms for online parameter identification, ensuring simplicity and precision in SOC tracking for China EV fleets.
The electric vehicle charging model is constructed based on typical charging characteristics, considering slow charging modes common in residential areas or low-voltage parks. The charging demand (S) for a single electric vehicle is related to the current battery SOC and maximum capacity $C_{\text{max}}$ as follows:
$$ S = (1 – \text{SOC}) \cdot C_{\text{max}} $$
At time $t$, the SOC is updated based on the charging power $P$ and charging efficiency $\delta_{\text{ch}}$:
$$ \text{SOC}_t = \text{SOC}_{t-1} + \frac{P_t \Delta t \delta_{\text{ch}}}{C_{\text{max}}} $$
To ensure battery safety, the charging power must adhere to limits:
$$ P_{\text{dis.max}} \leq P \leq P_{\text{char.max}} $$
where $P_{\text{dis.max}}$ and $P_{\text{char.max}}$ are the maximum discharge and charge powers, respectively. Discretizing the charging period into $N$ intervals of duration $\Delta t$ simplifies the computation, assuming constant power within each interval. This model forms the foundation for parameter identification, focusing on $\delta_{\text{ch}}$ as a key variable influenced by operational states.
For parameter identification, we first consider the charging efficiency as a constant value, where a linear relationship exists between charging power and the temporal difference of SOC. The least squares method is employed for online identification due to its simplicity and efficiency in solving linear models. The overall framework involves detecting change points between constant power and trickle charging phases using dual temporal difference values. The change point is identified when:
$$ (\text{SOC}(t) – \text{SOC}(t-1)) – (\text{SOC}(t-1) – \text{SOC}(t-2)) \leq 0 $$
Once change points are detected, segmented fitting is applied using the least squares method. The ordinary least squares (OLS) solution for parameter vector $X$ in the linear model $y = AX + \epsilon$ is derived as:
$$ X = (A^T A)^{-1} A^T y $$
This approach ensures unbiased and efficient estimates under normal error distributions. To validate the method, simulation data is generated based on charging order statistics from a university in China, reflecting typical SOC patterns for electric vehicles. The dataset includes SOC values at the start and end of charging, with means of 0.360 and 0.889, respectively, and standard deviations of 0.197 and 0.147. Battery capacities are set to common values: 100 kW·h, 80 kW·h, 60 kW·h, 30 kW·h, and 25 kW·h, with a charging power of 7 kW. The SOC-time and SOC-power curves are simulated, as shown in the embedded figure, illustrating the charging behavior across different capacities.
The performance is evaluated using mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE):
$$ \text{MAE} = \frac{1}{n} \sum_{i=1}^{n} | \hat{y}_i – y_i | $$
$$ \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i – y_i)^2 $$
$$ \text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i – y_i)^2} $$
Table 1 presents the error metrics for the least squares-based identification under different battery capacities, comparing scenarios without change point detection, constant power charging, and trickle charging. The results demonstrate lower errors in constant power phases due to stable operating conditions and sufficient data, while trickle charging segments show higher variability.
| Battery Capacity | Scenario | MAE | MSE | RMSE |
|---|---|---|---|---|
| 100 kW·h | No Change Point | 7.14e-7 | 6.01e-13 | 7.75e-7 |
| Constant Power | 1.36e-7 | 1.86e-14 | 1.36e-7 | |
| Trickle Charging | 4.42e-7 | 2.96e-11 | 5.44e-7 | |
| 80 kW·h | No Change Point | 9.73e-7 | 9.93e-13 | 9.96e-7 |
| Constant Power | 1.10e-7 | 4.45e-14 | 2.11e-7 | |
| Trickle Charging | 1.01e-5 | 1.21e-10 | 1.10e-5 | |
| 60 kW·h | No Change Point | 2.32e-6 | 6.56e-12 | 2.56e-6 |
| Constant Power | 7.22e-7 | 5.21e-13 | 7.22e-7 | |
| Trickle Charging | 1.21e-5 | 2.24e-10 | 1.50e-5 | |
| 30 kW·h | No Change Point | 6.57e-6 | 5.11e-11 | 7.15e-6 |
| Constant Power | 3.87e-6 | 1.50e-11 | 3.88e-6 | |
| Trickle Charging | 5.39e-5 | 4.45e-9 | 6.67e-5 | |
| 25 kW·h | No Change Point | 5.89e-6 | 3.49e-11 | 5.91e-6 |
| Constant Power | 5.86e-6 | 3.44e-11 | 5.87e-6 | |
| Trickle Charging | 1.97e-4 | 3.97e-8 | 1.99e-4 |
In real-world scenarios, charging efficiency for electric vehicles fluctuates due to factors like output power, charging mode, battery capacity, and grid conditions. Linear models may not capture these complexities, and least squares can be sensitive to outliers. Thus, we propose an ensemble learning-based approach for online parameter identification. This method uses a sliding window mean difference algorithm for real-time change point detection. When a significant change in charging mode is detected, an Adaboost-based algorithm estimates the dynamic charging efficiency. The sliding window width is set to 40 samples, with a threshold of 0.0001 for mean differences.
Adaboost, a Boosting ensemble method, builds an additive model by sequentially integrating weak learners. The model is expressed as:
$$ f(x) = \sum_{m=1}^{M} \beta_m G(x; \gamma_m) $$
The forward stage-wise algorithm minimizes the loss function $L(y, f(x))$ at each step:
$$ (\beta_m, \gamma_m) = \arg \min_{\beta, \gamma} \sum_{i=1}^{N} L(y_i, f_{m-1}(x_i) + \beta G(x_i; \gamma)) $$
For regression tasks with squared loss $L(y, f(x)) = (y – f(x))^2$, the negative gradient simplifies to the residual $y – f(x)$, guiding the base model to fit errors from previous iterations. Decision trees are chosen as base models for their ability to handle nonlinear relationships and dynamic complexity, making them suitable for edge deployment in China EV charging infrastructure.
Simulation data is generated similarly to the least squares approach, with charging efficiency sampled from a normal distribution (mean 0.9, variance 0.08), clipped to [0.75, 0.99]. The dataset is split into training and testing sets, with 1000 samples reserved for testing. Change points are detected using the sliding window method, and SOC and power data before and after changes are used as inputs for the Adaboost model. Experiments are conducted for each battery capacity, and results are summarized in Table 2.
| Battery Capacity | MAE | MSE | RMSE |
|---|---|---|---|
| 100 kW·h | 8.67e-7 | 4.01e-12 | 8.67e-7 |
| 80 kW·h | 8.70e-7 | 6.34e-11 | 1.02e-6 |
| 60 kW·h | 3.99e-6 | 4.09e-11 | 3.99e-6 |
| 30 kW·h | 6.42e-6 | 6.78e-10 | 6.46e-6 |
| 25 kW·h | 8.90e-6 | 5.01e-9 | 1.25e-5 |
The results indicate that the ensemble learning approach outperforms the least squares method, particularly for larger battery capacities where longer charging durations provide more stable data. Errors increase with smaller capacities due to shorter charging cycles and higher variability, but overall, the method achieves accurate charging efficiency identification. This supports the effective integration of electric vehicles into power grids, facilitating energy management and sustainability goals.
In conclusion, this study develops an electric vehicle charging model and employs intelligent algorithms for parameter identification. The least squares method provides efficient solutions for constant efficiency scenarios, while ensemble learning handles dynamic conditions with higher accuracy. The identified parameters enable precise SOC estimation, enhancing grid scheduling capabilities. This technology not only optimizes power system operations but also promotes the synergistic development of electric vehicles and smart grids, contributing to carbon reduction efforts in China and beyond. Future work will explore real-time implementation in large-scale China EV networks and incorporate additional factors like temperature and battery degradation.