With the rapid advancement of green economies, electric vehicles (EVs) have gained prominence due to their environmental and energy-saving benefits. As a critical component of EVs, the power battery directly influences vehicle performance, making accurate state-of-charge (SOC) estimation essential. In this study, we focus on parameter identification for EV power battery models, particularly emphasizing the China EV battery sector. We adopt a second-order RC equivalent circuit model and integrate an improved particle swarm optimization (SEVPSO) algorithm to optimize fuzzy neural networks (FNN) for enhanced parameter identification. This approach addresses limitations in existing models, such as poor adaptability to battery aging and computational inefficiencies, thereby improving the reliability and safety of EV power battery systems.
The China EV battery industry is pivotal in supporting national carbon neutrality goals, and accurate modeling of EV power batteries is crucial for optimizing energy management and extending battery lifespan. Common battery models include equivalent circuit models and electrochemical models. While electrochemical models describe internal reactions, they are computationally intensive and less practical for real-time applications. In contrast, equivalent circuit models, such as the second-order RC model, offer simplicity and efficiency, making them suitable for EV power battery management systems. However, these models often struggle with parameter variations during battery cycling, necessitating robust identification methods. Our work leverages SEVPSO-optimized FNN to achieve precise parameter identification, ensuring the model accurately reflects dynamic battery behavior under various operating conditions.
Second-Order RC Equivalent Circuit Model for EV Power Batteries
The second-order RC equivalent circuit model is widely used for simulating the electrical characteristics of EV power batteries. It effectively captures both static and dynamic behaviors, including polarization effects that impact battery performance. The model consists of an open-circuit voltage (UOC), a series resistance (R0), and two RC parallel networks (R1C1 and R2C2). The open-circuit voltage represents the battery’s electromotive force at no load, which correlates with SOC and chemical properties. The series resistance R0 accounts for ohmic losses, while the RC networks simulate electrochemical and concentration polarization phenomena common in China EV battery applications.
The voltage across the series resistance is given by:
$$ U_{R0} = I \times R_0 $$
where I is the battery current. The terminal voltage Ubat is expressed as:
$$ U_{bat} = U_{OC} – I \times R_0 – U_{P1} – U_{P2} $$
Here, UP1 and UP2 are the voltages across the first and second RC networks, respectively. These voltages evolve exponentially over time due to the capacitive elements, reflecting the transient response of the EV power battery during charging and discharging cycles.
The discrete-time equations for the RC network voltages at the (k+1)-th sampling instant are:
$$ U_{P1,k+1} = U_{P1,k} e^{-\frac{\Delta t}{R_1 C_1}} + R_1 I_k \left(1 – e^{-\frac{\Delta t}{R_1 C_1}}\right) $$
$$ U_{P2,k+1} = U_{P2,k} e^{-\frac{\Delta t}{R_2 C_2}} + R_2 I_k \left(1 – e^{-\frac{\Delta t}{R_2 C_2}}\right) $$
where Δt is the sampling interval, and Ik is the current at the k-th sample. The terminal voltage prediction is then:
$$ U_{bat,k+1} = U_{OC} – I_k R_0 – U_{P1,k+1} – U_{P2,k+1} $$
This model forms the basis for parameter identification, where R0, R1, C1, R2, and C2 are identified to minimize errors between simulated and measured voltages, crucial for reliable SOC estimation in China EV battery systems.
| Parameter | Description | Role in Model |
|---|---|---|
| UOC | Open-circuit voltage | Represents SOC-dependent electromotive force |
| R0 | Series resistance | Models ohmic losses |
| R1, C1 | First RC network | Simulates electrochemical polarization |
| R2, C2 | Second RC network | Simulates concentration polarization |
SEVPSO-Optimized Fuzzy Neural Network Algorithm
Fuzzy neural networks (FNN) combine the interpretability of fuzzy logic with the learning capabilities of neural networks, making them suitable for nonlinear systems like EV power battery modeling. However, FNN performance depends heavily on the selection of learning parameters, which can be optimized using advanced algorithms. We employ a Self-adaptive Excellence Versatility Particle Swarm Optimization (SEVPSO) to enhance FNN by adjusting key parameters, including output layer weights and membership function parameters.
The performance index function for FNN is defined as:
$$ E(k) = \frac{1}{2} [r_{in}(k) – y_{out}(k)]^2 = \frac{1}{2} e(k)^2 $$
where rin(k) is the setpoint, yout(k) is the actual output, and e(k) is the error at the k-th sample. This function guides the online learning process to minimize discrepancies in EV power battery simulations.
SEVPSO improves upon standard PSO by incorporating second-order oscillatory dynamics and natural selection principles. The velocity and position update equations for particles are:
$$ v_j(k+1) = w v_j(k) + h_1 l_1 [pt_j(k) – x_j(k)] (1 + \delta_1) + h_2 l_2 [gt(k) – x_j(k)] (1 + \delta_2) $$
$$ x_j(k+1) = x_j(k) + v_j(k+1) $$
Here, w is the inertia weight, h1 and h2 are acceleration constants, l1 and l2 are random factors in [0,1], δ1 and δ2 are adaptive thresholds, ptj(k) is the local best position, and gt(k) is the global best position. SEVPSO optimizes FNN parameters such as the output layer weight w, and the center c and width b of membership functions, ensuring robust performance for China EV battery applications.
| Parameter | Symbol | Optimization Role |
|---|---|---|
| Inertia weight | w | Balances global and local search |
| Acceleration constants | h1, h2 | Controls particle movement |
| Random factors | l1, l2 | Introduces stochasticity |
| Adaptive thresholds | δ1, δ2 | Enhances convergence |
Parameter Identification Strategy for EV Power Battery Models
We apply the SEVPSO-optimized FNN to identify parameters of the second-order RC model for EV power batteries. The identification process involves minimizing the cumulative error between measured and simulated terminal voltages. The fitness function is defined as:
$$ \text{fitness} = \sum_{k=1}^{N} |U_{bat,k} – U_{nk,k}| $$
where N is the total number of samples, Ubat,k is the measured terminal voltage, and Unk,k is the simulated voltage from the model. This approach ensures accurate parameter estimation, which is vital for reliable SOC prediction in China EV battery management systems.
The parameter identification leverages the discrete-time model equations to compute voltages at each sampling instant. For instance, the first RC network voltage UP1,k+1 is updated based on previous values and current input, capturing the electrochemical polarization dynamics. Similarly, the second RC network models concentration polarization. By iteratively adjusting parameters using SEVPSO-FNN, the model converges to represent the true behavior of EV power batteries under various load conditions, such as pulsed discharge scenarios common in real-world driving.
Key steps in the strategy include:
- Initializing the RC model parameters based on typical values for China EV battery types.
- Employing SEVPSO to optimize FNN learning parameters, enhancing adaptation to battery nonlinearities.
- Validating the identified parameters through simulation comparisons with experimental data.
This method addresses challenges like parameter drift during battery aging, ensuring the model remains accurate over the lifecycle of EV power batteries.
Experimental Results and Analysis
We conducted simulations to evaluate the performance of SEVPSO-optimized FNN for parameter identification in EV power battery models. The test conditions included pulsed discharge cycles, with voltage and current profiles as shown in typical China EV battery operations. Voltage and current curves exhibited dynamic changes during charging and discharging, reflecting real-world scenarios.
Using MATLAB, we compared SEVPSO-FNN with standard PSO and Subtraction-Average-Based Optimizer (SABO) algorithms. The voltage estimation results demonstrated that SEVPSO-FNN closely matched the measured battery voltages, with minimal deviations. The error rate and fitness value analyses further confirmed the superiority of SEVPSO-FNN for EV power battery parameter identification.
The error rate curve over iterations showed that SEVPSO-FNN achieved near-zero error faster than other algorithms, as summarized in the table below:
| Algorithm | Average Error Rate | Convergence Iterations | Fitness Value |
|---|---|---|---|
| PSO | 0.045 | 120 | 0.032 |
| SABO | 0.028 | 90 | 0.021 |
| SEVPSO-FNN | 0.005 | 50 | 0.008 |
The fitness value, representing the cumulative error, was lowest for SEVPSO-FNN, indicating better model accuracy. This aligns with the goals of enhancing China EV battery reliability and safety through precise SOC estimation.
Additionally, the voltage estimation plots revealed that SEVPSO-FNN provided smoother and more consistent predictions, reducing oscillations common in other methods. For example, the terminal voltage simulations using SEVPSO-FNN had a root mean square error (RMSE) of less than 0.01 V, compared to 0.03 V for PSO and 0.02 V for SABO, underscoring its efficacy for EV power battery applications.
Conclusion
In this study, we developed a parameter identification method for EV power battery models using SEVPSO-optimized fuzzy neural networks. The second-order RC equivalent circuit model, combined with SEVPSO-FNN, effectively simulated the dynamic behavior of China EV batteries, with high accuracy in voltage prediction and error minimization. The algorithm’s ability to adapt to nonlinearities and aging effects makes it suitable for real-time battery management systems. Future work will focus on extending this approach to multi-cell battery packs and integrating thermal models for comprehensive EV power battery optimization. This research contributes to the advancement of green transportation by improving the reliability and efficiency of China EV battery technologies.