Abstract
This article proposes a new method that provides a highly accurate charge state dependent multi-stage constant current (MCC) charging algorithm for electric vehicle batteries. This algorithm significantly reduces charging time by avoiding lithium plating, while not accelerating the aging process. Firstly, with the help of three electrode measurement technology, the relationship between current rate, state of charge, and lithium plating was experimentally analyzed, and a charging algorithm based on SOC (State of Charge) dependence was proposed. Secondly, a SOC estimation algorithm based on extended Kalman filter was developed in MATLAB/Simulink environment to achieve high-precision SOC estimation and precise control of the charging process. The experimental results show that the root mean square error (RMSE) of the SOC estimation is 1.08%, and the charging time is reduced by 30% in the range of 0% to 80% SOC.
1. Introduction
The influencing factors of charging time and the limitations of existing charging protocols: The global public charging quantity and fast charging share have increased in the past decade, but charging time not only depends on charger capacity, but also on battery characteristics, environmental conditions, and charging protocols. The standard charging protocol for LIB is constant current constant voltage (CC-CV), which includes two stages: constant current (CC) and constant voltage (CV). The long CV stage limits the reduction of total charging time, and high charging current may lead to lithium plating, affecting battery life and safety. Therefore, the impact of charging protocol on battery life cannot be ignored.
Research background and advantages of multi-stage constant current charging protocol: In order to optimize the balance between charging time, efficiency, and battery life, multiple charging protocols have been proposed, among which multi-stage constant current charging (MCC) protocol has been widely studied. The MCC protocol can reduce charging time and extend battery cycle life, and its stage transition can be based on SOC interval or voltage upper limit. The main challenge is to determine the optimal number of CC stages, current rate, and conversion conditions for MCC charging, which can be solved using Taguchi methods, optimization algorithms, or by detecting Li plating to determine the optimal charging current mode.
The innovation and article structure of this study
Innovation point: This study integrates the SOC threshold obtained from three electrode battery experiments with a high-precision SOC estimator for MCC charging algorithm, developing a scalable charging current guide for standard commercial batteries, eliminating the need for a physical third electrode in applications and the need for extensive battery testing during the charging protocol development stage, aiming to reduce charging time and prevent accelerated battery aging caused by fast charging.
Structure of this article: Firstly, the optimal charging mode is designed using the three electrode method, and an experimental three electrode battery is reconstructed from a commercial 21700 NMC battery; Secondly, develop an extended Kalman filter (EKF) based SOC estimator suitable for battery management systems (BMS); Then conduct battery testing to verify the performance of the method, perform aging testing, and compare the MCC protocol with standard CC-CV charging; Finally, provide a conclusion.
2. Materials and Methods
Electrochemical characteristic analysis: Conduct three electrode measurement analysis on the electrode of the 21700 NMC commercial cylindrical battery. Firstly, discharge the battery to the lower limit voltage after 5 standard cycles according to the manufacturer's specifications. Open the battery in an argon glove box, remove and process the electrodes, and prepare a three electrode battery. Due to the characteristics of LIB electrode materials, additional reference electrodes are required to observe the processes of the working electrode and the counter electrode separately. The electrochemical characteristics of the experimental three electrode battery are similar to those of commercial batteries. By determining the electrode coating area and specific capacity, conducting tests at different charging and discharging rates, observing the anode and cathode potentials, determining the critical SOC of lithium plating at different C-rates, and normalizing the MCC protocol to make it applicable to commercial batteries, the experiment was conducted at 25 ° C and will need to be validated under different environmental conditions in the future.
| Lower Cut-Off Voltage Umin |
Upper Cut-Off Voltage Umax |
Charge Mode | Discharge Mode | Temperature |
| 2.65 V | 4.2 V | CC-CV, C/2 rate | CC, 1C rate | 25℃ |
Battery modeling and parameter identification: Using a Thevenin equivalent circuit model (ECM) with a single RC branch to simulate the electrical characteristics of LIB, the model parameters (including open circuit voltage, ohmic resistance, polarization resistance, and capacitance) are accurately determined in increments of 10% SOC at different temperatures and charge discharge directions through hybrid pulse power characteristic (HPPC) testing. The parameter values are compiled into a 3D lookup table to lay the foundation for SOC estimation.
State of Charge Estimation: The SOC variation of LIB can be expressed as a function of time, and Coulomb counting is the basic estimation method based on this, but there are errors. Therefore, an Extended Kalman Filter (EKF) is used for SOC estimation. EKF effectively solves the challenges in SOC estimation by linearizing nonlinear systems and combining current, voltage, and temperature measurement signals. Its algorithm includes two main steps: prediction and update. Based on Thevenin ECM and SOC definitions, process and measurement equations are given in the discrete-time domain. EKF assumes that process noise and measurement noise are independent zero mean Gaussian noise processes, and linearizes the measurement function through Jacobi matrix.
Aging analysis: Conduct cyclic testing on three batteries using standard charging procedures and two batteries using MCC charging algorithm, with capacity testing and direct current internal resistance (RiDC) testing every 50 cycles. The capacity test adopts the standard CCCV charging program to charge and discharge at 1C current to the lower limit voltage. The RiDC test applies 1C current pulses at different SOC levels and measures the internal resistance. The aging degree of the battery is described by calculating the state of health (SOH) of the battery, which is defined as the ratio of the actual capacity to the initial reference capacity. The aging test is conducted until the end of the battery life (80% SOH).
3. Results
Electrochemical characteristic analysis results
Changes in electrode potential at different C-rates: Figure 4 shows the analysis results of the electrochemical characteristics of a three electrode battery at 25 ° C, used to determine the maximum charging rate dependent on SOC. Figure 4a shows the potential of the anode and cathode relative to the reference electrode and the overall battery potential during C/10 rate charging. During charging, the anode potential decreases while the cathode potential increases. At C/10 rate, the anode potential is not lower than 0V and there is no lithium plating. Figure 4b shows the variation of anode potential with SOC at different C-rates. The higher the C-rate, the greater the negative shift of anode potential. When C ≥ C/2, it may be lower than 0V, and as the C-rate increases, the maximum SOC at anode potential>0V gradually decreases. MCC charging protocol design: Based on the above results, a multi-stage constant current (MCC) charging curve was designed. Figure 5 shows the SOC dependent charging stages, and Table 3 summarizes the details of each stage. Compared with the standard CCCV charging protocol, the MCC protocol has a time advantage in the low SOC range, charging to 80% SOC is about 30% faster than standard charging, and MCC charging is also about 10% faster when fully charged.
| SOC Range (%) | 0-15 | 15-40 | 40-80 | 80-95 | 95-100 |
| SOC Share (%) | 15 | 25 | 40 | 15 | 5 |
| C-Rate | 2 C | 1 C | C/2 | C/5 | CV |
| Charging Time (min.) | 4.5 | 15 | 48 | 45 | - |
Parameter identification and battery modeling results
Model parameter determination: Analyze the HPPC test results in Matlab and use the "fminsearch()" function to determine the open circuit voltage, resistance, and capacitance parameters of the battery model at different temperatures and SOC levels. Analyze the impact of temperature on battery capacity, incorporate the capacity test results into a temperature related 2D lookup table, and find that SOC has limited influence on model parameters. To simplify, consider it as a constant in the formula.
Model validation: The battery model and SOC estimator are validated by fully discharging the test battery, followed by dynamic current testing at different charging rates and SOC levels. Simulate the same test sequence in MATLAB/Simulink environment and compare it with experimental data using root mean square error (RMSE) evaluation. The RMSE of voltage simulation is 7.09 mV. Although there is a significant error when the battery is fully discharged, the model performance is robust and can accurately capture the battery voltage dynamics under different load conditions.
Results of SOC estimator based on EKF: Verify the SOC estimator based on EKF at 25 ° C and compare the SOC value estimated by EKF algorithm with the reference SOC value obtained by Coulomb counting method. The test current has a resolution of 1 mA and an accuracy of 0.1%. At the initial stage, there was a deviation between the estimated SOC by EKF and the reference SOC. As the testing progressed quickly, the RMSE was 1.08%. The algorithm was able to accurately track SOC, especially during the charging phase, and could precisely control the charging current.
Aging performance results of MCC charging algorithm
Aging test results: Figure 10 shows the aging test results. Three standard charging and two MCC charging batteries were tested, and the deviation between each group of batteries can be ignored. During the early stage of aging testing (up to 90% SOH), the aging rate of MCC charging is slightly slower. When considering the mean value, MCC charged batteries reach 80% SOH at the end of their lifespan about 50 cycles earlier than standard charged batteries, but the overall effect on aging rate is not significant. The battery charged by MCC showed a slight decrease in SOH after 850 cycles due to testing interruption.
Internal resistance change result: The figure shows the changes in the total internal resistance (R ₀+R ₁) of the battery under two charging protocols at 25 ° C and 50% SOC. The difference in initial resistance and SOH value is due to different battery storage times. The internal resistance of batteries with both charging methods decreased slightly in the early stages of aging, and then increased with aging. The MCC charging algorithm did not cause additional lithium plating, which is consistent with the capacity test results, indicating that the MCC algorithm maintains the integrity of the battery aging characteristics.
4. Discussion and Summary
Research contribution to battery MCC charging technology: By integrating high-precision SOC estimators and applying them to commercial cylindrical batteries (NMC battery chemistry), contribution is made to battery MCC charging technology. The successful integration has facilitated the transfer of precise SOC thresholds obtained from three electrode battery experiments to the commercial battery level, enhancing practical applications and bridging the gap between experimental insights and industrial implementation.
Aging optimized MCC charging algorithm: An aging optimized, SOC dependent MCC charging algorithm is introduced, which reduces charging time without accelerating battery degradation by reducing lithium plating risk. The importance of combining electrochemical analysis, modeling, and estimation techniques to address key challenges in battery charging was emphasized, and SOC was used as a transfer parameter to ensure that laboratory results can be extended to industrial applications.
The advantages of charging mode and protocol: The optimal charging mode can be determined through experimental three electrode batteries, and the anode potential can be monitored to detect lithium plating. The proposed MCC charging protocol combined with the SOC threshold obtained from experiments is more stable compared to traditional voltage based MCC protocols, and is less affected by factors such as temperature changes and electrochemical hysteresis.
The role and experimental results of SOC estimator: A SOC estimator based on Extended Kalman Filter (EKF) was developed, with an RMSE of 1.08%, suitable for Battery Management Systems (BMS). The experimental results show that compared with the traditional constant current constant voltage (CC-CV) charging method, this method can reduce the time to reach 80% SOC by 30% without accelerating the aging process.