In recent years, the rapid development of renewable energy systems has increased the demand for efficient and reliable energy storage solutions. Energy storage cells play a critical role in stabilizing power grids and ensuring continuous energy supply. However, the performance degradation of energy storage cells over time poses significant challenges to their operational safety and efficiency. Accurate and rapid detection of the state of health (SOH) and state of power (SOP) of energy storage cells is essential for predictive maintenance and optimizing their lifecycle. Traditional methods, such as capacity measurement and open-circuit voltage techniques, often suffer from long detection times and low accuracy, limiting their practical application in real-time monitoring systems. To address these limitations, we propose a novel rapid detection technology based on AC impedance, which integrates mathematical analysis, the Levenberg-Marquardt (L-M) algorithm for impedance parameter identification, and a combination of backpropagation (BP) neural networks and the bisection method for SOH and SOP estimation. This approach enables fast and precise assessment of energy storage cell status, providing a foundation for intelligent management systems.
The core of our technology lies in the construction of an impedance parameter identification model that leverages mathematical analysis and the L-M algorithm. Energy storage cells exhibit complex electrochemical behaviors, which can be modeled using equivalent circuit models (ECMs). We employ a fractional-order impedance model that incorporates inductive elements to enhance high-frequency characteristics. The initial parameters are derived from AC impedance spectrum data, and the model is optimized through nonlinear least squares fitting. The parameter initialization is expressed as:
$$ Q_w = \frac{1}{N} \sum_{i=1}^{N} \frac{1}{\omega_i^2} \left[ Z_{\text{Re}}(\omega_i) – Z_{\text{Re-dl}}(\omega_i) – R_{\text{ohm}} \right]^2 + \left[ Z_{\text{Im}}(\omega_i) – Z_{\text{Im-dl}}(\omega_i) \right]^2 $$
where \( Q_w \) represents the parameter value, \( N \) is the number of data points, \( \omega_i \) is the frequency of the impedance spectrum, \( Z_{\text{Re}}(\omega_i) \) and \( Z_{\text{Im}}(\omega_i) \) are the real and imaginary parts of the impedance spectrum, respectively, \( Z_{\text{Re-dl}}(\omega_i) \) and \( Z_{\text{Im-dl}}(\omega_i) \) are the real and imaginary parts under parallel conditions, and \( R_{\text{ohm}} \) is the ohmic resistance. This mathematical解析 provides a foundation for parameter identification but may lack precision due to dispersed frequency points in the impedance spectrum of energy storage cells. To improve accuracy, we integrate the L-M algorithm, which solves nonlinear least squares problems efficiently. The objective function for the L-M algorithm is defined as:
$$ F(P) = \frac{1}{2} \| f(P) \|^2 = \frac{1}{2} \sum_{j=1}^{n} \left[ f_{\text{Re}, j}^2(P) + f_{\text{Im}, j}^2(P) \right] $$
where \( F(P) \) is the objective function value, \( P \) is the parameter vector, \( f_{\text{Re}, j}(P) \) and \( f_{\text{Im}, j}(P) \) are the real and imaginary error functions, and \( n \) is the number of frequency points. The L-M iteration formula is given by:
$$ P_{k+1} = P_k – \left[ J_f^T J_f + \mu \text{diag}(I) \right]^{-1} J_f^T f(P_k) $$
where \( J_f \) is the Jacobian matrix, \( \mu \) is a damping parameter controlling the step size, and \( \text{diag}(I) \) is the identity matrix. This combined approach ensures robust identification of impedance parameters, which are crucial for assessing the internal state of energy storage cells.
Following impedance parameter identification, we design a rapid detection technology that utilizes BP neural networks for SOH estimation and the bisection method for SOP assessment. The BP neural network is employed to handle the nonlinear relationship between impedance parameters and SOH. The output of the neural network is computed as:
$$ y_i = f \left( \sum_{i=1}^{n} w_{ji} x_i + b_j \right) $$
where \( y_i \) is the output of the \( i \)-th neuron, \( f \) is the activation function, \( w_{ji} \) is the weight from the \( i \)-th input neuron to the \( j \)-th hidden neuron, \( x_i \) is the input parameter (e.g., voltage, internal resistance), and \( b_j \) is the bias term. The network is trained with data from energy storage cells at different aging stages to accurately predict SOH. For SOP estimation, we apply the bisection method to determine the maximum safe current and power output. The target current is calculated iteratively as:
$$ I_{\text{target}} = \frac{I_{\min} + I_{\max}}{2} $$
where \( I_{\min} \) and \( I_{\max} \) are the minimum and maximum current limits, initially set to 0 and the safe current limit, respectively. The power output is then evaluated using:
$$ P_{\text{current}} = V \cdot I_{\text{target}} $$
where \( V \) is the voltage of the energy storage cell. The iteration continues until \( P_{\text{current}} \) converges to the target power. This integrated approach allows for comprehensive state assessment of energy storage cells, combining SOH and SOP metrics for rapid detection.
To validate our technology, we conducted experiments using lithium-ion energy storage cells (model 18650) under controlled conditions. The test setup included a constant current-constant voltage power supply (Agilent 6614C), an electronic load (BK Precision 8500), and an AC impedance measuring instrument (BioLogic VMP3). The algorithms were implemented in Python for simulation and analysis. We compared the performance of our AC impedance-based method with traditional capacity measurement and open-circuit voltage methods. The results demonstrate significant improvements in accuracy and detection speed for energy storage cells.
The accuracy of SOH estimation using BP neural networks was evaluated against traditional methods. The following table summarizes the SOH prediction errors for four energy storage cells with different health states:
| Cell Type | Actual SOH (%) | AC Impedance SOH (%) | Error (%) | Traditional Capacity SOH (%) | Error (%) |
|---|---|---|---|---|---|
| A | 100 | 99.8 | 0.2 | 98.5 | 1.5 |
| B | 93.54 | 93.1 | 0.44 | 92.0 | 1.54 |
| C | 82.31 | 81.9 | 0.41 | 80.0 | 2.31 |
| D | 69.85 | 69.3 | 0.55 | 68.0 | 1.85 |
The average error for the AC impedance method is 0.4%, compared to 1.8% for the traditional capacity method, indicating a 1.4% improvement in accuracy. This enhancement is attributed to the ability of AC impedance to capture detailed electrochemical information through small-signal perturbations, enabling more precise parameter identification for energy storage cells.
For SOP estimation, the bisection method was compared with traditional estimation techniques. The absolute errors in SOP prediction are summarized below:
| Method | Average Absolute Error |
|---|---|
| Bisection Method | 15.38 |
| Traditional Estimation | 38.75 |
The bisection method reduces the error by approximately 60%, demonstrating its effectiveness in estimating the power state of energy storage cells. This is crucial for applications requiring real-time power management, such as electric vehicles and grid-scale energy storage systems.
Detection time is a critical factor for practical deployment. We measured the detection times for eight different states of energy storage cells using AC impedance, capacity measurement, and open-circuit voltage methods. The results are presented in the following table:
| Battery State | AC Impedance Time (min) | Capacity Method Time (min) | Open-Circuit Voltage Time (min) |
|---|---|---|---|
| State 1 | 1.5 | 5.2 | 8.9 |
| State 2 | 1.6 | 5.5 | 9.1 |
| State 3 | 1.7 | 5.7 | 9.3 |
| State 4 | 1.8 | 5.8 | 9.4 |
| State 5 | 1.65 | 5.6 | 9.0 |
| State 6 | 1.75 | 5.9 | 9.5 |
| State 7 | 1.7 | 5.4 | 8.8 |
| State 8 | 1.68 | 5.5 | 9.2 |
The average detection time for the AC impedance method is 1.68 minutes, which is 69% faster than the capacity method (5.58 minutes) and 81.5% faster than the open-circuit voltage method (9.12 minutes). This significant reduction in time is due to the rapid acquisition of impedance spectra and efficient parameter optimization, making our technology suitable for online monitoring of energy storage cells.
The integration of mathematical analysis, L-M algorithm, BP neural networks, and bisection method provides a comprehensive framework for state detection of energy storage cells. The mathematical analysis ensures accurate initial parameter estimation, while the L-M algorithm refines these parameters through iterative optimization. The BP neural network captures complex nonlinear relationships for SOH prediction, and the bisection method enables precise SOP estimation. This synergy addresses the limitations of traditional methods, which often require lengthy procedures and are prone to environmental influences.
In conclusion, our proposed AC impedance-based rapid detection technology offers a robust solution for assessing the state of energy storage cells. The method achieves high accuracy in SOH and SOP estimation, with significant reductions in detection time. Future work will focus on incorporating temperature effects and extending the technology to various types of energy storage cells, such as solid-state batteries and flow batteries, to enhance its applicability in diverse operating conditions. This technology paves the way for real-time intelligent management systems that optimize the performance and longevity of energy storage cells in renewable energy applications.