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It is of great significance to study the low-temperature charging aging of lithium batteries and their charging control strategies in order to promote the promotion of new energy vehicles in cold regions. This work establishes a multi stress low-temperature charging aging model based on a large amount of low-temperature charging experimental data. Taking temperature as an important influencing factor, while considering the effects of charging cut-off voltage, charging rate, and charging cycle times on battery aging. Introducing the decay acceleration factor, multiple charging stresses were combined and applied to the overall model, and the estimation accuracy of the model was simulated and tested. On this basis, genetic algorithm is introduced to optimize the charging control strategy. Based on the charging voltage, the charging process before reaching the charging cut-off voltage is divided into multiple charging stages. The charging current in each stage is used as the gene sequence of the genetic algorithm, and the charging aging rate and charging time are used as optimization objectives for iterative optimization. The simulation results show that the established low-temperature charging aging model has high parameter estimation accuracy, and the charging control strategy can effectively reduce battery aging and save charging time. The charging strategy was experimentally tested using the designed charging controller, and the test results were consistent with the simulation results. The experiment on low-temperature charging of batteries has explored the law of the impact of low-temperature charging on battery life degradation. The experimental data, aging model, and charging strategy optimization method have direct reference value.

Keywords: lithium battery; Aging modeling; Genetic algorithm; Low temperature charging; Charging strategy

In recent years, new energy vehicles have developed rapidly, and lithium batteries have become the primary energy storage equipment for new energy vehicles due to their high specific energy, high specific power, low self discharge rate, no memory effect, and long charge discharge life. Replacing fossil fuels with green and environmentally friendly lithium batteries has become an important development direction. However, there are many problems with the charging of new energy vehicles at present. Most car mounted AC chargers and DC high-power charging piles use traditional charging strategies, which are not suitable for some countries or regions with colder climates, such as Beijing, Changchun and other places in China, where sub zero temperature weather often occurs. Although some new energy vehicles preheat the battery pack before charging in low-temperature environments, there are still issues such as uneven heating of the battery cells, battery inconsistency, energy waste, and long charging times. At present, there is relatively little research on the low-temperature charging aging and charging strategies of power lithium batteries in China. The long charging time and rapid degradation rate of charging life of lithium batteries at low temperatures are important factors restricting the development of electric vehicles in low-temperature areas.

Extensive research has been conducted both domestically and internationally on the lifespan degradation model of power lithium batteries at room temperature, modeling based on the electrochemical, thermal, and aging characteristics of the battery. From the perspective of analysis methods, it can be divided into electrochemical models, relevant empirical models, and data-driven models. Gao et al. conducted cycle life experiments on lithium batteries under different charging stresses to study the aging mechanism of lithium batteries under different charging stresses, and established a lithium battery charging capacity degradation model based on relevant empirical models. Johannes et al. established a mathematical model describing the effects of temperature and voltage on calendar aging of lithium batteries through data analysis. Simon et al. studied the aging process of nickel cobalt manganese oxide lithium batteries at different temperatures and charging rates, and established a P2D electrochemical model to describe lithium-ion charging aging. Research on charging strategies is currently divided into traditional charging strategies, traditional improved charging strategies, and charging strategies based on model optimization algorithms. The traditional charging strategy is mainly represented by CC-CV (constant current constant voltage), while the traditional improved charging strategy optimizes the charging time and effective charge amount based on the traditional charging strategy. Li Lizhen et al. used dynamic programming algorithm and Markov decision algorithm to find the optimal charging curve. Compared with the traditional CC-CV charging strategy, the effective charging capacity increased by 15%, and the equivalent cycle charging capacity of the battery decreased by 30%. Hsieh et al. established a fuzzy control active charging state controller, which improved charging performance by 23% compared to the traditional CC-CV charging process.

This article focuses on the influence of different charging stresses on the capacity degradation of lithium batteries in low-temperature environments. Charging data with different charging temperatures, cut-off voltages, and charging rates were obtained through extensive cyclic charging tests. After processing and analyzing the data, a mathematical model for multi stress charging aging of lithium batteries was established. The charging strategy of the entire charging process is divided into two stages. In the first stage, the terminal voltage of the battery during charging is used as the reference, and a genetic algorithm is used to optimize the charging current curve before reaching the charging cut-off voltage. The second stage is based on the first stage and converted to constant voltage charging. Finally, the charging strategy was validated through simulation and experimental testing.

Low temperature charging experiment of lithium battery

In order to make the experimental operation convenient and representative, and to map the aging law of actual automotive power lithium batteries, a ternary lithium battery with a size model of 18650, positive electrode material of nickel cobalt aluminum (NCA), and negative electrode material of traditional graphite was selected for charge discharge aging experiments. The battery parameters are shown in Table 1.

Table 1 Battery Parameters

Conduct charging experiments considering three influencing factors: charging temperature, charging cut-off voltage, and charging current rate. For the low temperature range of 0-20 ℃, select 5 temperature test points: 0 ℃, -5 ℃, -10 ℃, -15 ℃, and -20 ℃. Select 4.0V, 4.05V, 4.1V, 4.2V, and 4.25V as charging cut-off voltage test points, and 0.2C, 0.5C, and 1C as charging rate test points. Conduct multiple cyclic charge discharge aging experiments under three different charging stresses: charging temperature, cut-off voltage, and charging current. All experiments are low-temperature charging room temperature discharging experiments, charging in CC-CV mode at preset temperature, rate, and cut-off voltage until the charging current drops to 0.02C, and the charging ends. And the discharge adopts the standard discharge system, which is to discharge at 0.5C to 2.5V at 25 ℃. Due to the significant temperature difference between charging and discharging, the battery should be placed in a constant temperature box for 3 hours before charging and discharging to ensure that the temperature inside and outside the battery reaches the preset level.

Under the same testing conditions, the same battery is used for charging cycle aging testing, and the same batch of lithium batteries is used for comparative experiments under different working conditions. Before the experimental testing, consistency screening is conducted on the batch of experimental battery samples based on capacity, internal resistance, and open circuit voltage to ensure the reliability of the test data.

2. Low temperature charging data analysis and modeling

2.1 Experimental data analysis

2.1.1 The impact of different charging temperatures on battery capacity degradation

By analyzing the experimental data, the variation curve of battery capacity degradation with the number of charging cycles at different charging temperatures can be obtained, as shown in Figure 1.

Figure 1 Charging capacity degradation curve at different temperatures

From Figure 1, it can be seen that as the temperature decreases, the charging decay rate accelerates. At a charging temperature of -20 ℃, after only 10 charging cycles, the battery capacity deteriorates by nearly 20%.

2.1.2 The impact of different cut-off voltages on battery capacity degradation

The test data of battery cyclic charge discharge capacity degradation under different charging cut-off voltages are shown in Figure 2. It can be seen that when the charging cut-off voltage is 4V, the capacity degradation is first fast and then slow. The capacity degradation curve within the voltage range of 4.05V to 4.25V is relatively flat before 4 charging cycles, with a slope close to zero and a capacity degradation of<1%. After 4 charging cycles, the degradation suddenly intensifies and shows a linear upward trend.

Figure 2 Charging capacity degradation curve under different cut-off voltages

2.1.3 The impact of different charging rates on battery capacity degradation

The experimental data of battery capacity degradation with the number of charging cycles under different charging current rates is shown in Figure 3. From the graph, it can be seen that as the number of charging cycles increases, the degradation of battery capacity also increases linearly. As the charging rate increases, the slope of the rising curve gradually increases, indicating that the degradation rate of charging capacity increases with the increase of charging rate at different charging rates. The fastest addition speed is between 0.2 and 0.5C.

Figure 3: Charging Capacity Decline Curve at Different Current Ratios

2.2 Establishment of Capacity Decline Model

Through the experimental data of multi stress charging and discharging under different charging temperatures, cut-off voltages, and charging rates, it can be concluded that the influence of charging temperature>charging rate>charging cut-off voltage on the rate of capacity degradation of the lithium battery. Therefore, we established a capacity degradation model based on capacity degradation test data at different temperatures, with charging rate and charging cut-off voltage as auxiliary influencing factors. The mathematical expressions for the capacity degradation rate model under different charging stresses, named as the charging cut-off voltage acceleration factor AU and charging rate acceleration factor AI, are shown in equations (1) and (2). Where K is the capacity decay rate; θ is the equivalent number of charging cycles for the battery; T is the charging temperature ℃. K θ, T represents the degradation rate of charging capacity when the charging temperature is T and the equivalent number of charging cycles is θ.

Fit the capacity decay curves at different temperatures as shown in Figure 4. The fitting function is a power function as shown in equations (3) and (4).

Figure 4: Curve fitting of charging capacity degradation at different temperatures

From the fitting curve, it can be seen that each temperature test point has a high degree of fitting. Next, parameters a and b will be fitted, as shown in Figure 5. There is no obvious linear relationship between parameters a, b and temperature parameters. After squaring them, it can be seen from the fitted image that a (1/3) and b (1/3) have a high degree of fit to temperature.

Figure 5: Fitting curves of parameters a and b

So the expressions for parameters a, b and charging temperature can be obtained as equations (5) and (6).

Use the same method to fit the capacity degradation curve under different charging cut-off voltages. Due to the fact that the degradation curve of charging capacity is similar to the splicing of two straight lines under different charging cut-off voltages, it is considered to be segmented with 4 charging cycles as the dividing point. In the first paragraph, the slope of the fitted line is almost zero, indicating that the charging cut-off voltage has no effect on capacity degradation in the first paragraph. The fitting of the capacity decay curve in the second paragraph is shown in Figure 6.

Figure 6: Curve fitting of charging capacity degradation under different cut-off voltages

Because the fitting result is a straight line, the parameter intercept represents the intercept of the line and the y-axis. Although it does not change linearly, it does not affect the estimation of the slope of the capacity decay curve. The slope of the fitted line directly affects the rate of capacity degradation under different charging cut-off voltages, so only considering the slope parameter can represent the impact of charging cut-off voltage on the rate of capacity degradation. Fit the slope parameters of each fitting curve again as shown in Figure 7.

Figure 7: Slope parameter fitting curve of the "voltage decay" fitting line

The fitting function expression is shown in equation (9).

(9)

The formula for calculating the capacity degradation rate KU when the charging cut-off voltage is U is shown in equation (10).

(10) In the formula, m is 197.9676; N is 98.4659 and z is 12.2760. Since the function f (θ, T) is established under the operating conditions of 0.5C-4.2V, the charging cut-off voltage of 4.2V is taken as the reference operating condition, and the ratio of the capacity degradation rate KU at the actual charging cut-off voltage to the capacity degradation rate KUref at the reference voltage is taken as the charging cut-off voltage acceleration factor AU. The expression for AU is

(11) After obtaining the mathematical expression of the acceleration factor of the charging cut-off voltage, the influence of charging rate on the low-temperature charging aging of lithium batteries is analyzed. Using -15 ℃ and 4.2V as reference conditions, the capacity degradation curve of lithium batteries under different charging rates was fitted. It was found that the data had the highest fitting degree to the exponential function during curve fitting. However, there was no linear relationship between the fitting parameters of different charging rates, which cannot be used to describe the influence of charging rates on the aging rate. Therefore, a straight line was used for fitting, as shown in Figure 8. There is a linear trend in the slope of the fitted line under different charging rates. Meanwhile, the slope parameter can reflect the rate of capacity degradation during low-temperature charging. Fit the slope parameters of the regression line for different charging rates as shown in Figure 9.

Figure 8 Linear fitting of capacity degradation under different charging rates

Figure 9: Slope parameter fitting of the line fitting the "magnification decay" curve

By fitting the curve of the experimental data, the following relationship is obtained

In the formula, h is 1.9598; C is 0.8175. Since f (θ, T) is established under the working conditions of 0.5C-4.2V, the charging rate of 0.5C is taken as the reference working condition, and the ratio of the battery capacity degradation rate KI at the actual charging current rate to the capacity degradation rate KIref at the reference working condition charging rate is taken as the charging current rate acceleration factor AI. The calculation formula is shown in equation (14).

(14) By curve fitting, the acceleration factor AU of the charging cut-off voltage and the acceleration factor AI of the charging rate are obtained. Then, a mathematical model for the low-temperature multi stress charging capacity degradation rate based on the number of charging cycles, charging temperature, charging cut-off voltage, and charging rate is constructed, as shown in equation (15).

3 Genetic Algorithm Optimization of Charging Control Strategy

Genetic algorithms (GA) are computational models that simulate natural selection and genetic biological evolution processes. They are search optimization algorithms with adaptive regulation capabilities and have good applicability to some complex nonlinear problems. In recent years, its application in path planning problems has received widespread attention due to its outstanding advantages. This article uses genetic algorithm to search for the optimal charging curve with charging aging rate and charging time as optimization objectives.

3.1 Gene coding selection

The selection of gene coding is an important part of genetic algorithms. Based on the terminal voltage of the battery during the charging process, the charging voltage range is set to 2.75-4.2V according to the selected battery type, and the voltage changes during the charging process are divided into 20 intervals. The charging current of the i-th charging interval is Ii, and the charging currents of the 20 charging stages are normalized and encoded as genes in the genetic algorithm, as shown in equation (16). The current value range for each interval is 0.01 to 1, with the unit being the charging current rate C.

(16) When the charging voltage reaches the cut-off voltage of 4.2V, the traditional constant voltage charging method is switched to continue charging until it is less than 0.02C.

3.2 Selection of fitness function

The optimization of genetic algorithm requires selecting an appropriate fitness function based on the control object. This article proposes a charging strategy based on genetic algorithm, with charging aging and charging time as optimization objectives. The traditional multi-objective optimization method is used to weight and sum the degradation of charging capacity and charging time, as shown in equation (17).

(17) In the formula, se is the calculated value of the fitness function of the genetic algorithm, and the charging current with the minimum se value is the optimal charging current for that stage. Qloss is the capacity decay rate; Qchg is the charging time consumed, and the charging strategy aims to minimize capacity degradation and shorten the charging time as much as possible; G is the weight coefficient used to adjust the weights of two optimization objectives. Section 4.2 of this article calibrates parameter g through simulation testing to select the optimal weight coefficients that meet the requirements.

The calculation formulas for Qloss and Qchg are shown in equations (18), (19), and (20), where ∆ N θ is the equivalent number of charging cycles in the k-th stage SOC is the percentage of the rated capacity related to the charging capacity of each stage, where ∆ tk is the charging time used in the kth stage, and the current is consistent within a single charging stage 'k'.

The software flowchart of the genetic algorithm is shown in Figure 10. The processes of roulette wheel algorithm, crossover mutation, and generation of new species are collectively referred to as genetic operators, which are the core steps of genetic algorithms, representing the elimination of inferior individuals, gene crossover compilation of advantageous individuals, and the process of population replacement.

Figure 10 Genetic Algorithm Software Flow Chart

4 Model validation and charging strategy validation

4.1 Model Validation

The capacity degradation rate model was simulated and validated in Matlab. The comparison between the estimated and actual values of the capacity degradation rate under different operating conditions is shown in Table 3. It can be seen that the estimation error of the established capacity degradation model is within 10%. And 80% of the reference operating conditions have an estimation error of less than 8%, indicating that the estimation accuracy of the capacity degradation model is generally high. Calculated based on a capacity degradation of 0.04 for a single effective charging cycle under -20 operating conditions, due to the charging strategy dividing the first charging process into 20 stages, the estimation error is calculated based on a maximum value of 8.39%. Therefore, the maximum estimation error for each stage is 1.707%, and the maximum capacity degradation estimation error covering all operating conditions is 34.14%. In the actual process, the maximum estimation error of 8.39% will not be reached simultaneously in all stages. Taking the median value of 5.11% for estimation, the total estimation error of the entire charging process is within 20.79%.

Table 3 Analysis of Capacity Decline Error

4.2 Calibration of Weight Coefficient g

Select the 4.2V-10cyc operating condition for calibrating the weight coefficient g. After optimizing the charging strategy, the variation curve of charging aging with the weight coefficient g of the fitness function at different temperatures is shown in Figure 11. The optimization curve of charging time with respect to the weight coefficient g is shown in Figure 12.

Figure 11 Comparison of Capacity Decline at Different Temperatures and Weight Coefficients

Figure 12 Comparison of charging time under different temperatures and weight coefficients

From the curve changes in Figure 11, it can be seen that the optimization effect on capacity degradation is better when g is around 0.15, which can maximize the reduction of charging aging and approach the optimal effect at all temperature ranges. With the increase of weight coefficients, the charging strategy's ability to suppress capacity degradation weakens, and capacity degradation gradually increases.

From Figure 12, it can be seen that as the weight coefficient g increases, the optimization of charging time by the charging strategy increases, so the charging time in each temperature range gradually decreases. The fluctuation of the -10 ℃ curve is relatively large, which may be related to the modeling of capacity degradation or measurement errors caused by experimental testing equipment. But it is evident that there is an overall downward trend.

Combining Figure 11 and Figure 12, taking into account capacity degradation and charging time, the optimal weight coefficient for the weighted sum of the fitness function is selected as 0.5-0.7.

4.3 Charging Control Strategy Simulation Test

By calibrating the weight coefficient g, selecting 0.5 as the optimal value and substituting it into the model, four sets of operating conditions covering -5 to -20 ℃ were selected for simulation testing of the control strategy. The charging current curves obtained from the tests are shown in Figures 13, 14, 15, and 16, which represent the charging curves at the cut-off voltage under each test condition. After reaching the charging cut-off voltage, it switches to constant voltage charging, and the current rate gradually decreases. In the constant voltage stage, due to the lower current rate, the impact on the aging of lithium battery charging is relatively low, so it is not included in the optimization range of genetic algorithm. From Figures 13, 14, 15, and 16, it can be seen that the average charging rate of the four test conditions before constant voltage charging decreases with decreasing temperature, which is consistent with the variation of capacity degradation rate with charging rate at low temperatures. According to experimental data, the degradation of battery life is basically the same in the four test conditions, but the amount of charged electricity before reaching the charging cut-off voltage decreases with decreasing temperature in the four test conditions.

Figure 13-5 ℃ -4.2V-30cyc test condition charging curve

Figure 14-10 ℃ -4.1V-20cyc test condition charging curve

Figure 15-15 ℃ -4.2V-8yc test condition charging curve

Figure 16-20 ℃ -4.2V-6cyc test condition charging curve

From the simulation data, it can be obtained that for the four test conditions, genetic algorithm was used to optimize the charging strategy before reaching the charging cut-off voltage. The comparison of capacity degradation data with traditional CC-CV charging conditions is shown in Table 4. From the table, it can be seen that after optimizing the charging strategy through genetic algorithm, the aging rate of the battery in a single effective charging cycle at low temperature is reduced by more than 28% compared to the traditional CC-CV charging method, with a maximum of 64%. It can be seen that optimizing the charging strategy can significantly reduce the battery capacity degradation caused by low temperature charging.

Table 4 Capacity degradation optimization effect of charging strategy

The data comparison regarding charging time is shown in Table 5. It can be seen from the table that the charging time has been optimized compared to traditional CC-CV under four charging conditions. Among them, the charging time at -10 ℃ is reduced by 22% compared to the traditional CC-CV charging method, while at -5 ℃ and -15 ℃ it is 3%. The charging time at -20 ℃ is reduced by 8%.

Table 5 Optimization effect of charging strategy on shortening charging time

-The charging time is reduced the most under the condition of 10 ℃, but the charging cut-off voltage is 4.1V. It can be seen that the lower the charging cut-off voltage, the better the optimization effect on the charging time. The amount of charged electricity decreases with the decrease of the charging cut-off voltage, which conforms to the general law of the change of charged electricity with charging time. From the data in the table, it can be seen that after optimizing the charging strategy, the charging time has been optimized under various temperature conditions.

4.4 Physical testing of charging control strategy

The traditional lithium battery charging and discharging testing equipment only has working modes such as CC, CV, CP, CC-CV, etc., which cannot achieve the charging optimization strategy proposed in this paper. Therefore, a charging device corresponding to the optimized strategy was designed, as shown in Figure 17. The charging control system uses incremental PID method to control the PWM duty cycle of the switching circuit to achieve real-time control of the charging rate. The core of the charging circuit is the BUCK circuit, which uses the IR2110S half bridge driving chip to drive the switching transistor. Real time detection of terminal voltage during the charging process, driving the control progress of the charging strategy based on the voltage detection value until the cut-off voltage is reached.

Figure 17 Charging Strategy Verification Device

The verification of the charging strategy was conducted under the condition of -15 ℃ -8cyc-4.2V. The experimental charging curve of the charging controller is shown in Figure 18.

Figure 18-15 ℃ working condition charger output current curve

From this graph, it can be seen more clearly that before reaching the charging cut-off voltage, the charging controller can output current according to the set current curve without significant ripple, and the actual charging current curve is relatively smooth- Under the working condition of 15 ℃ -8cyc-4.2V, after optimizing with genetic algorithm, the actual charging curve can be integrated in ampere hours to obtain an optimized charging capacity of 2255mA · h, which is greater than the traditional CC-CV charging strategy. The second test was conducted under this operating condition with a charge of 2208mA · h, and the capacity degradation rate under the current operating condition was calculated to be 1.62%. The capacity degradation rate and charging time of a single charging process are compared with traditional CC-CV charging methods, as shown in Table 6. The capacity degradation rate of optimized charging strategy is reduced by 47.57% compared to traditional CC-CV charging, and the charging time is reduced by 16.71%.

Table 6 Comparison of Capacity Decline and Charging Time with Traditional CC-CV Strategy

Comparing the results of the simulation test, it can be found that there is a difference between the suppression effect of the charging strategy on charging aging in the experimental test and the simulation results, and the reduction in capacity degradation rate is 16.62% smaller than the simulation results. Both simulation and physical testing results have demonstrated that the proposed charging strategy has a significant effect on optimizing the low-temperature charging performance of lithium batteries.

5. Conclusion

This article conducts a large number of low-temperature charging and discharging experiments, and establishes a multi stress charging capacity degradation model for lithium batteries at low temperatures based on the charging and discharging experimental data. Based on genetic algorithm with capacity degradation and charging time as optimization objectives, the charging strategy was optimized for the multi stress charging capacity degradation model, and the following conclusions were drawn.

(1) The aging rate of lithium batteries during charging at low temperatures increases sharply with the decrease of charging temperature, and the capacity degradation rate increases linearly after more than 5 charging cycles at temperatures below -15 ℃. Secondly, the increase in charging rate and the increase in charging cut-off voltage will accelerate the aging rate of the battery.

(2) There are many factors that affect the degradation of lithium batteries during low-temperature charging. A mathematical model established by curve fitting test data under full coverage conditions can estimate the capacity degradation rate under multi stress charging conditions with high accuracy.

(3) Genetic algorithm, as an algorithm for solving optimal solution problems, is also suitable for optimizing the charging strategy of lithium batteries. Simulation results show that using genetic algorithm to solve the multi stress charging curve at low temperatures can significantly reduce battery capacity degradation and overall charging time.

Reference: Wang Taihua, Zhang Shujie, Chen Jinggan. Modeling of Low Temperature Charging Aging of Lithium Batteries and Optimization of Charging Strategies [J]. Energy Storage Science and Technology, 2020,09 (04): 1137-1146. (WANG Taihua, ZHANG Shujie, CHEN Jingan. Low Temperature Charging Modeling and Optimization of Charging Strategies for Lithium Batteries [J] EnergyStorageScienceandTechnology,2020,09(04):1137-1146.)

First author: Wang Taihua (1976-), male, associate professor, research direction is industrial process control;

Corresponding author: Zhang Shujie, research direction is industrial process control of automotive electronic control technology.

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