Method for measuring optimal charging temperature interval of sodium ion battery cell
By testing the capacity and performance indicators of sodium-ion cells at different temperatures, a mathematical model was established to determine the optimal charging temperature range, solving the problem of undetermined charging temperature for sodium-ion batteries and improving battery performance and lifespan.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG CHANGYI NADIAN ENERGY STORAGE CO LTD
- Filing Date
- 2026-02-03
- Publication Date
- 2026-05-01
AI Technical Summary
Current technology has failed to determine the optimal charging temperature range for sodium-ion batteries, affecting their battery performance and lifespan.
By conducting constant-capacity and charge-discharge cycle tests on sodium-ion cells at different temperatures, recording the capacity retention rate, cell DC internal resistance, and charge-discharge efficiency, a mathematical model was established and fitted to determine the optimal charging temperature.
Quickly and accurately determine the optimal charging temperature range for sodium-ion batteries to reduce performance loss and improve battery charging and discharging efficiency and lifespan.
Smart Images
Figure CN121955780A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of battery performance analysis by testing electrochemical variables, and specifically relates to a method for determining the optimal charging temperature range of sodium-ion batteries. Background Technology
[0002] Sodium-ion batteries are a type of battery that uses Na+ to generate sodium-ion batteries. + The charging and discharging process involves continuous insertion and extraction between the positive and negative electrodes of a sodium-ion battery. Sodium-ion batteries are rechargeable batteries. The positive electrode material, primarily composed of layered transition metal oxides, polyanionic compounds, or Prussian blue-like compounds, is a crucial factor affecting cell voltage and cycle stability. During charging, sodium ions are extracted from the positive electrode material, flow through the electrolyte, and insert into the negative electrode. The negative electrode material of sodium-ion batteries is mainly hard carbon or titanium-based. During discharging, sodium ions flow back from the negative electrode to the positive electrode, while electrons form a current through the external circuit.
[0003] Sodium-ion batteries have a wider charging temperature range compared to lithium-ion batteries. At low temperatures, due to the smaller Stokes radius of sodium ions, the migration resistance of sodium ions in the electrolyte is reduced, resulting in better conductivity. Therefore, sodium-ion batteries often have better capacity retention than lithium-ion batteries at low temperatures. At high temperatures, the cathode materials commonly used in sodium-ion batteries also have higher thermal decomposition temperatures, and the chemical properties of sodium make it less prone to side reactions at high temperatures. In other words, sodium-ion batteries have better high-temperature stability than lithium-ion batteries.
[0004] Sodium-ion batteries offer significant advantages over lithium-ion batteries in terms of low-temperature performance and high-temperature safety. However, due to the diversity of their material systems and reaction kinetics, current technology has not provided a definitive optimal charging temperature range, nor has it offered a method for determining this range. With the maturation of sodium-ion battery technology and the advancement of research, it has been discovered that battery capacity, efficiency, and internal resistance at different temperatures have a crucial impact on battery performance. Determining the optimal charging temperature range is beneficial for reducing battery performance degradation and waste, and extending battery life. Summary of the Invention
[0005] This invention discloses a method for determining the optimal charging temperature range of sodium-ion batteries. This method can obtain the optimal charging temperature of sodium-ion batteries under different temperatures, thereby determining the optimal charging temperature range and improving the performance of sodium-ion batteries.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for determining the optimal charging temperature range of a sodium-ion battery cell includes the following steps: Step 1: Perform capacity determination on sodium-ion battery cells with the same consistency at different temperatures to obtain the actual capacity of the sodium-ion battery cells at different temperatures; Step 2: Select the corresponding temperature where the actual capacity is within the preset rated capacity deviation range, and conduct charge-discharge cycle tests on the sodium-ion cells at the selected temperatures. After the cells have cycled to a stable state, record the capacity retention rate, DC internal resistance, and charge-discharge efficiency of the sodium-ion cells at each temperature. Step 3: Based on the capacity retention rate, cell DC internal resistance and charge / discharge efficiency, a mathematical model is made for the optimal charging performance index F(T). It is assumed that F(T) has a quadratic function relationship with temperature T. The quadratic model is fitted, and the coefficients of the quadratic function are calculated. The calculated coefficients are substituted into the original quadratic function, and the derivative of the quadratic function is calculated. The derivative is set to 0, and the optimal charging temperature T can be solved. Step 4: Use R 2 The values were used to validate the quadratic regression model; Step 5: After successful verification, the obtained optimal charging temperature T is expanded to obtain the optimal charging temperature range for sodium-ion cells.
[0007] Furthermore, in step one, there are multiple sodium-ion cells at each temperature, and the number is the same. The actual capacity at each temperature is taken as the average value.
[0008] Furthermore, in step one, the different temperatures are specifically selected as follows: -20℃, -10℃, 0℃, 10℃, 15℃, 20℃, 25℃, 30℃, 35℃, 40℃, 50℃, and 60℃.
[0009] Furthermore, in step two, the corresponding temperatures within ±3% of the rated capacity are selected.
[0010] Furthermore, in step two, when the sodium-ion battery cell has been cycled to the same number of cycles and the rate of change between the current cycle and the previous cycle is less than 0.05%, it enters a stable state.
[0011] Furthermore, in step two, the sodium-ion battery cell undergoes a 1C discharge current cycle test at different temperatures.
[0012] Furthermore, in step two, the data on capacity retention rate, cell DC internal resistance, and charge / discharge efficiency are obtained as follows: Capacity retention rate calculation formula: Capacity retention rate = (Termination capacity / Initial capacity) × 100% The formula for calculating charge / discharge efficiency is: Charge / discharge efficiency = [(Discharge current × Time to discharge to cutoff voltage) / (Charging current × Charging time)] × 100% The method for measuring the DC internal resistance of a battery cell is as follows: 1): Use 50% SOC and 20% SOC of sodium-ion cells at various temperatures as calibration points; 2): Select a time when the battery cell has reached a stable state during cycling to measure the DC internal resistance; 3) When measuring the DC internal resistance of sodium-ion cells, the current should be 2C and the time point should be 2S. 4): The formula for calculating DC internal resistance is as follows: DcIR is the DC internal resistance, V1 is the voltage value of 2C discharge for 2S, and V0 is the static voltage value at 50% SOC or 20% SOC.
[0013] Furthermore, in step three, F(T) = ω1 × capacity retention rate + ω2 × charge / discharge efficiency − ω3 × [(DC internal resistance / reference internal resistance) - 1], where ω1 is the weighting coefficient of the cell capacity retention rate, ω2 is the weighting coefficient of the cell charge / discharge efficiency, ω3 is the weighting coefficient of the cell DC internal resistance, and the reference internal resistance is the standard value set for the internal resistance of the sodium-ion cell. The quadratic relationship between F(T) and temperature T is expressed as: y = aT² + bT + c. Using the least squares method for fitting, the linear regression equation is calculated, and the values of a, b, and c are obtained. Substituting these calculated values into y = aT² + bT + c, the derivative is taken and set to zero to obtain the solution. .
[0014] Furthermore, in step four, the formula for R² is as follows:
[0015] In the above formula, SS E The sum of squared residuals, i.e., the sum of squared differences between the actual values and the model predictions; SS T It is the total sum of squares of deviations, that is, the sum of squares of the differences between the actual values and the actual mean.
[0016] Furthermore, in step five, T±3℃ is taken as the optimal charging temperature range for the sodium-ion battery cell.
[0017] This invention provides a method for rapidly determining the optimal charging temperature range of sodium-ion batteries. This method can conveniently, quickly, and accurately obtain the optimal charging temperature range of sodium-ion batteries, which helps to reduce performance loss and waste of sodium-ion batteries and improve the charging and discharging efficiency and service life of the batteries. Attached Figure Description
[0018] Figure 1 This is a flowchart of the method for determining the optimal charging temperature range of the sodium-ion battery cell according to the present invention. Detailed Implementation
[0019] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
[0020] Example 1: This example discloses a method for determining the optimal charging temperature range of a sodium-ion battery cell, combined with... Figure 1 As shown, the method includes the following steps: Step 1: Take multiple sodium-ion cells of the same batch with identical characteristics, and place them in battery test cabinets at different temperatures to determine their actual capacity.
[0021] Specifically, in this embodiment, a sodium-ion battery of model 33140 was selected for testing. This battery has a rated capacity of 10Ah, and the temperature gradient design is as follows: -20℃, -10℃, 0℃, 10℃, 15℃, 20℃, 25℃, 30℃, 35℃, 40℃, 50℃, 60℃. Three cells were taken at each temperature, totaling 36 cells across 12 temperatures. These cells were placed in a 5V 30Ah battery test chamber for capacity determination. Cells with abnormal capacity were removed, and the average actual capacity data of the cells at each temperature was obtained. The average actual capacity data obtained in this test is shown in Table 1 below. temperature -20℃ -10℃ 0℃ 10℃ 15℃ 20℃ Capacity (mAh) 9348 9529 9685 10039 10060 10119 temperature 25℃ 30℃ 35℃ 40℃ 50℃ 60℃ Capacity (mAh) 10135 10153 10198 10216 9670 9514 Step 2: Eliminate the temperature presets where the actual capacity differs significantly from the preset rated capacity. Perform 1C charge-discharge cycle tests on the selected sodium-ion cells at the selected temperatures. After the cells reach a stable state, record the capacity retention rate, DC internal resistance, and charge-discharge efficiency of the sodium-ion cells at each temperature.
[0022] Specifically, based on the data in Table 1, during this screening, temperatures corresponding to average actual capacity within ±3% of rated capacity were retained, while temperatures not meeting the above requirements were eliminated. Therefore, the temperature range selected for this test was 10℃~40℃ (subsequent tests were conducted at 10℃, 15℃, 20℃, 25℃, 30℃, 35℃, and 40℃ respectively). During the cell cycle test, when the sodium-ion cell reached the same number of cycles (350 cycles selected in this case) and the rate of change between the current cycle and the previous cycle was less than 0.05%, it entered a stable state. Then, the cell's capacity retention rate, DC internal resistance, and charge / discharge efficiency were recorded at each temperature.
[0023] Among them, the capacity retention rate of a battery cell is the ratio of the remaining capacity to the initial capacity under certain conditions. In sodium-ion batteries, controlling capacity decay and maintaining electrode stability are the ways to enhance the capacity retention rate, accounting for 30% to 40% of the cell performance. The formula for calculating the capacity retention rate is as follows: Capacity retention rate = (Termination capacity / Initial capacity) × 100% The charge / discharge efficiency of a battery cell is the ratio of output energy to input energy during the charge / discharge process. It directly reflects the proportion of energy loss during conversion and is a crucial indicator of cell performance, accounting for 40% to 50% of the overall cell performance. The formula for calculating charge / discharge efficiency is as follows: Charge / discharge efficiency = [(discharge current × time to discharge to cutoff voltage) / (charging current × charging time)] × 100% The DC internal resistance of a battery cell refers to the resistance of the battery's internal components to current flow. It is an important indicator affecting the cell's charging and discharging efficiency and temperature, accounting for 10% to 20% of the cell's performance. The DC internal resistance of the cells at various temperatures was measured using the following method: 1): Use 50% SOC and 20% SOC of sodium-ion cells at various temperatures as calibration points; 2): Select a time when the cell has cycled 350 times to measure the DC internal resistance; 3) When measuring the DC internal resistance of sodium-ion cells, the current should be 2C and the time point should be 2S. 4): The formula for calculating DC internal resistance is as follows: DcIR=(V0-V1) / (2C), where DcIR is the DC internal resistance, V1 is the voltage value of 2C discharge for 2S, and V0 is the static voltage value at 50%SOC or 20%SOC.
[0024] After completing this step of the test, the data shown in Table 2 below was obtained: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ Capacity retention 96.37% 96.79% 97.27% 97.35% 97.32% 92.46% 90.73% Charge and discharge efficiency 98.53% 98.79% 99.43% 99.75% 99.65% 98.42% 97.96% Internal resistance ratio 101.52% 100.76% 99.85% 99.70% 99.39% 98.94% 98.48% In Table 2 above, the data for capacity retention rate, charge / discharge efficiency, and internal resistance ratio are all average values. The internal resistance ratio is the average ratio of the actual DC internal resistance of the cell to the reference internal resistance. The reference internal resistance of the cell tested in this study is 2.20 mΩ, which is the standard value set for the internal resistance of the production batch of this cell.
[0025] Step 3: Let F(T) be the optimal charging performance index, and let F(T) = ω1 × capacity retention rate + ω2 × charge / discharge efficiency − ω3 × [(DC internal resistance / reference internal resistance) - 1], where ω1 is the weighting coefficient of cell capacity retention rate, ω2 is the weighting coefficient of cell charge / discharge efficiency, and ω3 is the weighting coefficient of cell DC internal resistance. In this test, ω1 = 0.3, ω2 = 0.5, and ω3 = 0.2 are taken. Substituting the data in Table 2 into the F(T) expression, the data in Table 3 below can be obtained: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ F(T) 0.7787 0.7828 0.7893 0.7914 0.7914 0.7816 0.7650 Step 4: Establish a quadratic regression equation, fit its parameters, fit the quadratic model using the least squares method, calculate its linear regression equation, calculate the coefficients a, b, and c, and differentiate the quadratic function. Set the derivative to 0 to obtain the optimal charging temperature T, T = -b / (2a).
[0026] Establish a quadratic model: y = aT² + bT + c, and use the least squares method to derive the following system of normal equations:
[0027] In the above formula, n represents the number of variables with different temperatures T as the independent variable; y represents the optimal charging performance index obtained at different temperatures based on experimental data in step three above. Solving the above system of equations, we can obtain the constants a = -0.0000901, b = 0.00421, and c = 0.74298. Substituting these constants a, b, and c into the quadratic function relationship, we can obtain: y = -0.0000901T 2 Taking the derivative of the quadratic function +0.00421T+0.74298 and setting the derivative y=0, we obtain the optimal charging temperature T=23.36℃, T≈23℃. Therefore, the value T obtained from the derivative is the optimal charging temperature of the battery cell.
[0028] Step 5: Use R 2 The values were used to validate the quadratic regression model.
[0029]
[0030] The formula for R² is:
[0031] SS E It is the sum of squared residuals, which is the sum of squares of the differences between the actual values and the model predictions.
[0032] SS T It is the total sum of squares of deviations, that is, the sum of squares of the differences between the actual values and the actual mean.
[0033] In this test, , Based on the above formula, the data shown in Table 4 below can be obtained:
[0034] Based on the data in Table 4 and the above expression, we can obtain:
[0035] The closer the R² value is to 1, the better the model fit. Generally, R² is... 2 A value of ≥0.7 indicates that the model has a high degree of fit. The R² value in this test already meets the above requirements, indicating that the model of this invention has a high degree of fit.
[0036] Step Six: Through the above verification, it is known that the model of the present invention meets the requirements. In order to more conveniently achieve the control of the optimal charging temperature in practice, the temperature range can be appropriately expanded according to the obtained optimal charging temperature T. In this embodiment, T±3℃ is taken as the optimal charging temperature range of sodium-ion battery, that is, the optimal temperature range is 20℃~26℃.
[0037] Step 7: The optimal temperature range of 20℃~26℃ obtained above was verified through the example. The battery cell tested in this test was cycled for another 500 cycles, and its capacity retention rate was recorded. After 500 cycles, the capacity retention rate data of the battery cell is shown in Table 5 below: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ Capacity retention 92.14% 93.15% 94.44% 95.17% 94.13% 87.37% 85.60% The data in Table 5 above shows that the capacity retention rate of the battery cell is optimal when the charging temperature is between 20 and 26°C. Therefore, through this verification, 20 to 26°C is the optimal charging temperature range for the experimental battery cell, which also shows that the measurement method given in this invention is feasible.
[0038] Example 2: To further verify the test results of Example 1, 36 new sodium-ion cells of the same model and batch used in Example 1 were selected and tested again according to the steps given in Example 1, serving as Example 2 of the present invention. The entire testing process in Example 2 is the same as in Example 1. To simplify Example 2, this example only shows the experimental data and calculation results that differ from those in Example 1; other content is omitted, and Example 1 can be referred to for execution.
[0039] The average actual capacity data obtained in this embodiment is shown in Table 6 below: temperature -20℃ -10℃ 0℃ 10℃ 15℃ 20℃ Capacity (mAh) 9350 9502 9689 10062 10081 10123 temperature 25℃ 30℃ 35℃ 40℃ 50℃ 60℃ Capacity (mAh) 10134 10147 10168 10245 9628 9441 In this embodiment, the temperature screening still retains the corresponding temperature range where the average actual capacity is within ±3% of the rated capacity, that is, the temperature range screened in this test is 10℃~40℃.
[0040] The test results obtained in this embodiment, corresponding to the data in Table 2 of Embodiment 1, are shown in Table 7 below: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ Capacity retention 96.36% 96.98% 97.23% 97.37% 97.31% 92.83% 90.47% Charge and discharge efficiency 98.61% 98.75% 99.31% 99.55% 99.67% 98.85% 97.93% Internal resistance ratio 101.21% 100.61% 100.15% 99.85% 99.55% 98.94% 98.03% The test results obtained in this embodiment, corresponding to the data in Table 3 of Embodiment 1, are shown in Table 8 below: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ F(T) 0.7791 0.7835 0.7879 0.7901 0.7912 0.7749 0.7650 After solving the system of equations in this embodiment, the calculated constants are as follows: a = -0.000083, b = 0.00374, c = 0.74848. Therefore, the quadratic function expression in this embodiment is: y=-0.000083T 2 +0.00374T+0.74848 By taking the derivative of the above quadratic function and setting the derivative y=0, we can obtain the optimal charging temperature T=22.50℃, T≈23℃.
[0041] In this embodiment, R is used. 2 When validating the quadratic regression model, the following relationship holds:
[0042] Based on the above formula, the data shown in Table 9 below can be obtained:
[0043] Based on the data in Table 9 and the above expression, we can obtain:
[0044] Based on the above calculations, the optimal charging temperature range for the sodium-ion battery cell in this embodiment is 20℃~26℃.
[0045] The optimal temperature range of 20℃~26℃ obtained above was verified, and the battery cell tested in this study was then used as a reference. The cells were cycled for 500 cycles, and their capacity retention was recorded. The capacity retention data of the cells after 500 cycles are shown in Table 10 below: temperature 10℃ 15℃ 20℃ 25℃ 30℃ 35℃ 40℃ Capacity retention 92.51% 93.97% 94.25% 95.01% 94.05% 87.99% 83.93% The data in Table 10 above shows that the capacity retention rate of the battery cell is optimal when the charging temperature is between 20 and 26°C. Therefore, through this verification, 20 to 26°C is the optimal charging temperature range for the battery cell in this embodiment. The two tests in Embodiment 1 and Embodiment 2 above both demonstrate that the measurement method given in this invention is feasible.
[0046] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for determining the optimal charging temperature range of a sodium-ion battery cell, characterized in that: Includes the following steps: Step 1: Perform capacity determination on sodium-ion battery cells with the same consistency at different temperatures to obtain the actual capacity of the sodium-ion battery cells at different temperatures; Step 2: Select the corresponding temperature where the actual capacity is within the preset rated capacity deviation range, and conduct charge-discharge cycle tests on the sodium-ion cells at the selected temperatures. After the cells have cycled to a stable state, record the capacity retention rate, DC internal resistance, and charge-discharge efficiency of the sodium-ion cells at each temperature. Step 3: Based on the capacity retention rate, cell DC internal resistance and charge / discharge efficiency, a mathematical model is made for the optimal charging performance index F(T). It is assumed that F(T) has a quadratic function relationship with temperature T. The quadratic model is fitted, and the coefficients of the quadratic function are calculated. The calculated coefficients are substituted into the original quadratic function, and the derivative of the quadratic function is calculated. The derivative is set to 0, and the optimal charging temperature T can be solved. Step 4: Use R 2 The values were used to validate the quadratic regression model; Step 5: After successful verification, the obtained optimal charging temperature T is expanded to obtain the optimal charging temperature range for sodium-ion cells.
2. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step one, there are multiple sodium-ion cells at each temperature, and the number is the same. The actual capacity at each temperature is taken as the average value.
3. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step one, the specific temperatures selected are as follows: -20℃, -10℃, 0℃, 10℃, 15℃, 20℃, 25℃, 30℃, 35℃, 40℃, 50℃, and 60℃.
4. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step two, the corresponding temperatures that are within ±3% of the rated capacity are selected.
5. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step two, when the sodium-ion battery cell has been cycled to the same number of cycles and the rate of change between the current cycle and the previous cycle is less than 0.05%, it enters a stable state.
6. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step two, the sodium-ion battery cell undergoes a 1C discharge current cycle test at different temperatures.
7. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step two, the data on capacity retention rate, cell DC internal resistance, and charge / discharge efficiency are obtained as follows: Capacity retention rate calculation formula: Capacity retention rate = (Termination capacity / Initial capacity) × 100% The formula for calculating charge / discharge efficiency is: Charge / discharge efficiency = [(Discharge current × Time to discharge to cutoff voltage) / (Charging current × Charging time)] × 100% The method for measuring the DC internal resistance of a battery cell is as follows: 1): Use 50% SOC and 20% SOC of sodium-ion cells at various temperatures as calibration points; 2): Select a time when the battery cell has reached a stable state during cycling to measure the DC internal resistance; 3) When measuring the DC internal resistance of sodium-ion cells, the current should be 2C and the time point should be 2S. 4): The formula for calculating DC internal resistance is as follows: DcIR is the DC internal resistance, V1 is the voltage value of 2C discharge for 2S, and V0 is the static voltage value at 50% SOC or 20% SOC.
8. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step three, F(T) = ω1 × capacity retention rate + ω2 × charge / discharge efficiency − ω3 × [(DC internal resistance / reference internal resistance) - 1], where ω1 is the weighting coefficient of the cell capacity retention rate, ω2 is the weighting coefficient of the cell charge / discharge efficiency, ω3 is the weighting coefficient of the cell DC internal resistance, and the reference internal resistance is the standard value set for the internal resistance of the sodium-ion cell. The quadratic relationship between F(T) and temperature T is expressed as: y = aT² + bT + c. Using the least squares method for fitting, the linear regression equation is calculated, and the values of a, b, and c are obtained. Substituting these calculated values into y = aT² + bT + c, the derivative is taken and set to zero to obtain the solution. .
9. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step four, the formula for R² is as follows: In the above formula, SS E The sum of squared residuals, i.e., the sum of squared differences between the actual values and the model predictions; SS T It is the total sum of squares of deviations, that is, the sum of squares of the differences between the actual values and the actual mean.
10. The method for determining the optimal charging temperature range of a sodium-ion battery cell according to claim 1, characterized in that: In step five, T±3℃ is taken as the optimal charging temperature range for sodium-ion batteries.