An online detection method for lithium plating in batteries

Abstract

This invention discloses an online detection method for lithium plating in batteries, relating to the field of rechargeable lithium battery technology. The method includes: S1, during multiple charging processes of the battery under test, the first 20 charging processes are recorded as normal charging processes, and a preset voltage plateau growth rate A is determined; S2, after the normal charging process, a charging process is selected every 50-100 charging processes, voltage data for all selected charging processes are extracted, the voltage plateau for each selected charging process is calculated, and the voltage plateau growth rate e for each selected charging process is determined; S3, the ratio e / A of the voltage plateau growth rate for each selected charging process to the preset voltage plateau growth rate is calculated. If e / A for multiple consecutive selected charging processes exceeds the set ratio, lithium plating is determined to have occurred in the battery. This invention directly uses voltage data during the battery charging process, eliminating the need for additional hardware costs. Data collection and judgment can be completed after charging is finished, improving efficiency.

Description

Technical Field

[0001] This invention relates to the field of rechargeable lithium battery technology, specifically to an online detection method for lithium plating in batteries. Background Technology

[0002] Batteries face the risk of lithium plating during overcharging or low-temperature charging. Lithium plating not only leads to capacity degradation and reduces the overall battery pack's lifespan, but the reaction of lithium dendrites with the electrolyte can also melt through the separator, causing localized short circuits within the battery, resulting in a rapid rise in battery temperature, and posing a risk of thermal runaway to the battery and even the entire battery pack. Although battery management systems can issue alarms by monitoring rapid changes in battery temperature, this situation already seriously threatens the safety of passengers and the vehicle. Therefore, monitoring changes in battery lithium plating at an early stage will effectively reduce the risk of thermal runaway caused by lithium plating, which is of great significance for ensuring the safety of passengers and the vehicle.

[0003] The conventional method for determining whether a battery has lithium plating is to disassemble the cell. However, this method is costly and damages the battery structure, making it unsuitable for large-scale application. Furthermore, some laboratory-level non-destructive testing methods require data that cannot be readily obtained in battery swapping scenarios, necessitating additional testing equipment, which is also expensive.

[0004] Chinese invention patent CN112776667A discloses a method for detecting lithium plating. This method collects battery voltage data in a vehicle or battery swapping station setting after charging and then calculates the voltage deviation at each time point based on the collected voltage data. When the calculated voltage deviation at a certain time point is greater than the voltage deviation at the previous time point, it triggers the calculation of the battery voltage change trend and determines whether the battery has undergone lithium plating based on the calculated voltage change trend. This patent requires additional data collection of the battery cells after charging and then resting, which requires extra waiting time and affects battery swapping efficiency.

[0005] Therefore, there is a need to develop a method that directly uses actual data from the battery charging process for lithium plating detection, which can complete the detection of lithium plating as soon as charging is finished, making it fast and efficient. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the aforementioned background technology and provide a method for lithium plating detection that directly uses actual data from the battery charging process. Lithium plating detection can be completed immediately after charging, making it fast and efficient.

[0007] The technical solution of this invention is: an online detection method for lithium plating in batteries, comprising:

[0008] S1. During the multiple charging processes of the battery under test, the first 20 to 50 charging processes are recorded as normal charging processes. The voltage data of the normal charging process within the preset SOC range is extracted, the voltage plateau of the normal charging process is calculated, and the preset voltage plateau growth rate A is determined.

[0009] S2. After the normal charging process, select a charging process every 50 to 100 charging processes, extract the voltage data of all selected charging processes within the preset SOC range, calculate the voltage plateau of each selected charging process, and determine the voltage plateau growth rate e of each selected charging process.

[0010] S3. Calculate the ratio e / A of the voltage plateau growth rate of each selected charging process to the preset voltage plateau growth rate. If the e / A of multiple consecutive selected charging processes exceeds the set ratio, it is determined that lithium plating has occurred in the battery.

[0011] In the above scheme, at preset charging intervals, voltage data from the charging process is used to determine the battery voltage plateau for the current charging cycle. Then, based on the number of charging cycles and the corresponding impedance of the battery under test, the voltage plateau growth rate for each charging cycle is determined. The voltage plateau growth rate is then compared with the preset voltage plateau growth rate A to confirm the lithium plating status of the battery in situ online. Furthermore, as the battery ages, if the lithium-ion battery does not exhibit lithium plating during use, the voltage plateau growth and the number of charging cycles show an approximately linear relationship. However, when lithium plating occurs during use, the voltage plateau will show abnormal growth. Therefore, by analyzing the changes in the voltage plateau growth rate of the lithium-ion battery at each charging cycle, it is possible to accurately determine whether lithium plating has occurred in the battery.

[0012] Preferably, in step S1, determining the preset voltage plateau growth rate A includes:

[0013] The voltage plateau of the first normal charging process is taken as the preset benchmark a, and the average value of the voltage plateaus of all normal charging processes is taken as b. Then the preset voltage plateau growth rate is calculated as A = (ba) / a*100%.

[0014] In the above scheme, considering that even if the battery model is the same, the preset voltage plateau growth rate A of the battery may be different, the voltage plateau growth rate corresponding to 20 to 50 charges of the battery under test (when lithium plating has not occurred) is taken as the preset voltage plateau growth rate A, thereby improving the accuracy of the preset voltage plateau growth rate A.

[0015] Preferably, in step S2, determining the voltage plateau growth rate e for each selected charging process includes:

[0016] The voltage plateau growth rate for each selected charging process is calculated as e = (voltage plateau of each selected charging process - a) / a * 100%.

[0017] Preferably, in step S3, if the e / A ratio is greater than or equal to a set value for at least three consecutive selected charging processes, then it is determined that lithium plating has occurred in the battery.

[0018] In the above scheme, it is considered that the voltage plateau may abnormally increase at a certain number of charging cycles due to some accidental factor, and this abnormal increase is not caused by lithium plating in the battery. Through multiple judgments, when the voltage plateau growth rate of the battery in several consecutive charging cycles is greater than the preset growth rate of the battery, it is determined that the battery has undergone lithium plating, thus avoiding misjudgment and improving the accuracy of lithium plating judgment.

[0019] Preferably, in step S3, the set ratio range is 5 to 10.

[0020] Preferably, in steps S1 and S2, the calculation of the voltage platform includes:

[0021] Multiple points are sampled within the preset SOC range to obtain the voltage corresponding to each SOC sampling point. The average value of the voltages corresponding to all SOC sampling points is taken to obtain the voltage plateau, ensuring that the charging current deviation of all SOC sampling points in the same charging process does not exceed the preset deviation range.

[0022] Furthermore, the voltages corresponding to the SOC sampling points are obtained through the following correction process:

[0023] Using the ambient temperature of the first normal charging process as the reference temperature T1, the ambient temperature of each charging process as T2, and the starting voltage collected within the preset SOC range as the reference voltage V0, the SOC sampling points of each charging process are corrected for the collected voltage V1 using the following formula to obtain the voltage V2 of V1 at the reference temperature T1.

[0024]

[0025] Where T1 is the set reference temperature, in °C;

[0026] V0 is the selected reference voltage, in units of V;

[0027] K is the temperature coefficient, with a value ranging from 2*10. 3 -5*10 3 ;

[0028] T2 is the ambient temperature during the charging process, in °C.

[0029] V1 is the actual voltage collected at the sampling point, in units of V;

[0030] V2 is the voltage after correction at the sampling point, in units of V.

[0031] In the above scheme, considering that the battery temperature will vary during the charging process due to differences in the battery's working environment and other factors in different usage cycles, the voltage V1 of the detected battery at temperature T2 is corrected by the above method so that the voltage obtained is the voltage platform V2 at the reference temperature T1, thereby improving the accuracy of the battery voltage platform and thus improving the accuracy of subsequent lithium plating confirmation.

[0032] Furthermore, the current preset deviation range for the same charging process is ≤5%.

[0033] Furthermore, the sampling frequency is set to 1–10 Hz within the preset SOC range.

[0034] Furthermore, if the preset SOC range is m to n, then m ≥ 10% SOC, n ≤ 90% SOC, and nm ≥ 50% SOC. Steps S1 and S2 use the same preset SOC range.

[0035] Furthermore, the preset SOC range is 10-90% SOC, 20-90% SOC, or 30-90% SOC. That is, m = 10% SOC, n = 90% SOC, m = 20% SOC, n = 90% SOC, or m = 30% SOC, n = 90% SOC.

[0036] When lithium plating occurs in the battery, a safety warning signal can be issued through the BMS to remind the user that the battery needs to be sent for inspection.

[0037] The beneficial effects of this invention are:

[0038] 1. This invention directly uses voltage data during battery charging, without increasing hardware costs and with zero software costs. Data collection and judgment can be completed once charging is finished, thus improving efficiency.

[0039] 2. This invention selects the voltage plateau data of the battery under test during its first 20 to 50 charging cycles (during which lithium plating has not yet occurred and the charging process is normal) to determine the preset voltage plateau growth rate A. By using data feedback from actual charging behavior, the preset voltage plateau growth rate A can be closely approximated to the battery's own performance, thereby improving its accuracy and applicability.

[0040] 3. This invention enables online, real-time detection by comparing the real-time voltage plateau growth rate e of the battery under test with a preset voltage plateau growth rate A, thus confirming whether lithium plating has occurred in the battery. This method is not only efficient and convenient, but also provides strong technical support for the real-time monitoring and evaluation of battery health.

[0041] 4. This invention takes into account that the voltage plateau may grow abnormally at a certain number of charging cycles due to some accidental factor. By making multiple judgments, the battery is determined to have lithium plating only when the voltage plateau growth rate of the battery in several consecutive charging cycles is greater than the preset growth rate of the battery. This avoids misjudgment and improves the accuracy of lithium plating judgment. Attached Figure Description

[0042] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should also be noted that, to avoid obscuring the invention with unnecessary details, the drawings only show structures and / or processing steps closely related to the solutions of this invention, while omitting other details that are not closely related to this invention. Furthermore, it should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0044] like Figure 1 As shown, the online lithium plating detection method for batteries of the present invention is generally carried out according to the following steps:

[0045] S1. During the multiple charging processes completed by the battery under test, the first 20 to 50 charging processes are recorded as normal charging processes. The voltage data of the normal charging process within the preset SOC range is extracted, the voltage plateau of the normal charging process is calculated, and the preset voltage plateau growth rate A is determined. The specific calculation process of A is as follows:

[0046] The voltage plateau of the first normal charging process is taken as the preset benchmark a, and the average value of the voltage plateaus of all normal charging processes is taken as b. Then the preset voltage plateau growth rate is calculated as A = (ba) / a*100%.

[0047] S2. After the normal charging process, select one charging process every 50 to 100 charging processes (select at equal intervals), extract the voltage data of all selected charging processes within the preset SOC range, calculate the voltage plateau of each selected charging process, and determine the voltage plateau growth rate e of each selected charging process.

[0048] Using 'a' as the baseline, the voltage plateau growth rate of each selected charging process is calculated as e = (voltage plateau of each selected charging process - a) / a * 100%.

[0049] S3. Calculate the ratio e / A of the voltage plateau growth rate of each selected charging process to the preset voltage plateau growth rate. If the e / A of at least 3 consecutive selected charging processes exceeds the set ratio, it is determined that lithium plating has occurred in the battery. The set ratio is a number between 5 and 10.

[0050] The methods for calculating the voltage plateau during normal charging and selecting the voltage plateau during charging are the same: Multiple points are sampled within the same preset SOC range (the preset SOC range can be 10-90% SOC, 20-90% SOC, or 30-90% SOC) (sampling frequency 1-10Hz) to obtain the voltage corresponding to each SOC sampling point. The average voltage of all SOC sampling points is then taken to obtain the voltage plateau. It is ensured that the charging current deviation of all SOC sampling points does not exceed the preset deviation range (i.e., the preset deviation range is ≤5%). If the deviation of a SOC sampling point exceeds the preset deviation range, that SOC sampling point is discarded and another sampling point is selected. This process continues until all SOC sampling points meet the deviation requirement. The deviation is calculated using conventional methods: Charging current deviation at each sampling point = |Current at each sampling point - Average current at all sampling points| / Average current at all sampling points * 100%.

[0051] Because the temperature varies during the charging process, the temperature at each SOC sampling point may differ. Therefore, the sampled voltage is corrected to obtain the voltage at the reference temperature. The correction method is as follows:

[0052] Using the voltage at the initial sampling point within the preset SOC range as the reference voltage V0 and the charging temperature at the initial sampling point as the reference temperature T1, the voltage V1 at the charging temperature T2 is corrected according to the following formula to obtain the voltage plateau V2 of V1 at the reference temperature T1.

[0053]

[0054] Where T1 is the set reference temperature, in °C;

[0055] V0 is the set reference voltage, in units of V;

[0056] K is the temperature coefficient, with a value ranging from 2*10. 3 -5*10 3 ;

[0057] T2 is the actual charging temperature at the sampling point, in °C;

[0058] V1 is the actual voltage collected at the sampling point, in units of V;

[0059] V2 is the voltage after correction at the sampling point, in units of V.

[0060] In this embodiment, the battery model and material type are not specifically limited. For example, the cathode material can be lithium cobalt oxide, lithium nickel cobalt manganese oxide, or lithium iron phosphate. The following describes the online lithium plating detection method for batteries in detail with specific data. All voltage data mentioned below are in volts (V).

[0061] Example 1

[0062] The online lithium plating detection method for batteries provided in this embodiment is performed according to the following steps:

[0063] S1. In the multiple charging processes of the battery under test (charged at a rate of 0.5C, battery type is NCM), the first 20 charging processes are recorded as normal charging processes. The voltage data in the range of 10-90% SOC during the normal charging process are extracted, the voltage plateau of the normal charging process is calculated, and the preset voltage plateau growth rate A is determined. The specific calculation process of A is as follows:

[0064] The voltage plateau of the first normal charging process is taken as the preset reference a, and the average value of the voltage plateau of all normal charging processes is taken as b. Then, the preset voltage plateau growth rate is calculated according to A = (ba) / a*100%. In this embodiment, a = 3.2V, b = 3.203V, and A = 0.1%.

[0065] S2. After the normal charging process, select one charging process every 50 charging processes, extract the voltage data of all selected charging processes in the range of 10-90% SOC, calculate the voltage plateau of each selected charging process, and determine the voltage plateau growth rate e of each selected charging process.

[0066] Using 'a' as the baseline, the voltage plateau growth rate of each selected charging process is calculated as e = (voltage plateau of each selected charging process - a) / a * 100%.

[0067] S3. Calculate the ratio e / A of the voltage plateau growth rate e of each selected charging process to the preset voltage plateau growth rate A. The calculation results are shown in Table 1. If e / A of at least 3 consecutive selected charging processes exceeds the set ratio, the set ratio is 5. That is, if e / A of at least 3 consecutive selected charging processes is ≥5, then it is determined that lithium plating has occurred in the battery.

[0068] Table 1 shows the growth rate e and e / A data.

[0069]

[0070] As can be seen from Table 1, the ratio e / A is less than 5. Therefore, the battery in this embodiment is considered normal and no lithium plating has occurred.

[0071] The methods for calculating the voltage plateau during normal charging in step S1 and selecting the voltage plateau during charging in step S2 are the same: multiple sampling is performed within the same preset range of 10-90% SOC, with a sampling frequency of 10Hz to obtain the voltage corresponding to each SOC sampling point. The average value of the voltages corresponding to all SOC sampling points is taken to obtain the voltage plateau. It is ensured that the charging current deviation of all SOC sampling points in the same charging process is ≤5%. If the deviation of a SOC sampling point exceeds the preset deviation range, the SOC sampling point is discarded and another sampling point is selected until all SOC sampling points meet the deviation requirements.

[0072] Example 2

[0073] The online lithium plating detection method for batteries provided in this embodiment is performed according to the following steps:

[0074] S1. During the multiple charging processes of the battery under test (charged at 1C rate, battery type is NCM), the first 20 charging processes are recorded as normal charging processes. Voltage data in the 20-90% SOC range of the normal charging process are extracted, and the voltage plateau of the normal charging process is calculated (the calculation method is the same as in Example 1). The preset voltage plateau growth rate A is determined. The specific calculation process of A is as follows:

[0075] The voltage plateau of the first normal charging process is taken as the preset reference a, and the average value of the voltage plateau of the last 10 normal charging processes is taken as b. Then, the preset voltage plateau growth rate is calculated according to A = (ba) / a*100%. In this embodiment, a = 3.21V, b = 3.2132V, and A = 0.1%.

[0076] S2. After the normal charging process, select one charging process every 50 charging processes, extract the voltage data of all selected charging processes in the range of 20-90% SOC, calculate the voltage plateau of each selected charging process (the calculation method is the same as in Example 1), and determine the voltage plateau growth rate e of each selected charging process.

[0077] Using 'a' as the baseline, the voltage plateau growth rate of each selected charging process is calculated as e = (voltage plateau of each selected charging process - a) / a * 100%.

[0078] S3. Calculate the ratio e / A of the voltage plateau growth rate of each selected charging process to the preset voltage plateau growth rate. The calculation results are shown in Table 2. If e / A ≥ 5 for at least 3 consecutive selected charging processes, it is determined that lithium plating has occurred in the battery.

[0079] Table 2 Growth rate e and e / A data

[0080]

[0081] As can be seen from Table 2, starting from the 8th selected charging process, all e / A ≥ 5. Therefore, in this embodiment, it is determined that lithium plating has occurred in the battery.

[0082] The methods for calculating the voltage plateau during normal charging in step S1 and selecting the voltage plateau during charging in step S2 are the same: multiple sampling is performed within the same preset range of 20-90% SOC, with a sampling frequency of 10Hz to obtain the voltage corresponding to each SOC sampling point. The average value of the voltages corresponding to all SOC sampling points is taken to obtain the voltage plateau. It is ensured that the charging current deviation of all SOC sampling points in the same charging process is ≤5%. If the deviation of a SOC sampling point exceeds the preset deviation range, the SOC sampling point is discarded and another sampling point is selected until all SOC sampling points meet the deviation requirements.

[0083] Example 3

[0084] The online lithium plating detection method for batteries provided in this embodiment is performed according to the following steps:

[0085] S1. In the multiple charging processes completed by the battery under test (using 2C charging rate, battery type is NCM), the first 20 charging processes are recorded as normal charging processes. The voltage data in the 30-90% SOC range of the normal charging process is extracted, and the voltage plateau of the normal charging process is calculated (the calculation method is the same as in Example 1). The preset voltage plateau growth rate A is determined. The specific calculation process of A is as follows:

[0086] The voltage plateau of the first normal charging process is taken as the preset reference a, and the average value of the voltage plateau of the last 10 normal charging processes is taken as b. Then, the preset voltage plateau growth rate is calculated according to A = (ba) / a*100%. In this embodiment, a = 3.23V, b = 3.23323V, and A = 0.1%.

[0087] S2. After the normal charging process, select one charging process every 50 charging processes, extract the voltage data of all selected charging processes in the range of 30-90% SOC, calculate the voltage plateau of each selected charging process (the calculation method is the same as in Example 1), and determine the voltage plateau growth rate e of each selected charging process.

[0088] Using 'a' as the baseline, the voltage plateau growth rate of each selected charging process is calculated as e = (voltage plateau of each selected charging process - a) / a * 100%.

[0089] S3. Calculate the ratio e / A of the voltage plateau growth rate of each selected charging process to the preset voltage plateau growth rate. The calculation results are shown in Table 3. If e / A is ≥5 for at least 3 consecutive selected charging processes, it is determined that lithium plating has occurred in the battery.

[0090] Table 3 Growth rate e and e / A data

[0091]

[0092] As can be seen from Table 3, starting from the 5th selected charging process, all e / A ≥ 5. Therefore, in this embodiment, it is determined that lithium plating has occurred in the battery.

[0093] The methods for calculating the voltage plateau during normal charging in step S1 and selecting the voltage plateau during charging in step S2 are the same: multiple sampling is performed within the same preset range of 30-90% SOC, with a sampling frequency of 10Hz to obtain the voltage corresponding to each SOC sampling point. The average value of the voltages corresponding to all SOC sampling points is taken to obtain the voltage plateau. It is ensured that the charging current deviation of all SOC sampling points in the same charging process is ≤5%. If the deviation of a SOC sampling point exceeds the preset deviation range, the SOC sampling point is discarded and another sampling point is selected until all SOC sampling points meet the deviation requirements.

[0094] Because the ambient temperature varies during the charging process, the temperature at each SOC sampling point may differ. Therefore, the first normal charging process is used as the baseline, and the voltages corresponding to the SOC sampling points during the charging process are obtained after the following correction process:

[0095] Using the ambient temperature of the first normal charging process as the reference temperature T1 (T1 = 25℃ in this embodiment), the ambient temperature of each charging process as T2, and the starting voltage collected within the preset SOC range as the reference voltage V0 (V0 = 30% SOC starting voltage in this embodiment), K = 2 * 10 3 The SOC sampling points for each charging process are corrected for the collected voltage V1 (70% SOC sampling point) using the following formula to obtain the voltage V2 of V1 at the reference temperature T1. The calculation data is shown in Table 4.

[0096]

[0097] Table 4

[0098]

[0099] As shown in Table 4, the voltage obtained by correcting V1 = 3.23V is 3.2349V at the reference temperature T1 = 25℃.

Claims

1. An online detection method for lithium plating in batteries, characterized in that, include: S1. During the multiple charging processes of the battery under test, the first 20 to 50 charging processes are recorded as normal charging processes. The voltage data of the normal charging process within the preset SOC range is extracted, the voltage plateau of the normal charging process is calculated, and the preset voltage plateau growth rate A is determined. The determination of the preset voltage plateau growth rate A includes: taking the voltage plateau of the first normal charging process as the preset benchmark a, taking the average value of the voltage plateaus of all normal charging processes as b, and then calculating the preset voltage plateau growth rate according to A=(ba) / a*100%. S2. After the normal charging process, select a charging process every 50 to 100 charging processes, extract the voltage data of all selected charging processes within the preset SOC range, calculate the voltage plateau of each selected charging process, and determine the voltage plateau growth rate e of each selected charging process. The determination of the voltage plateau growth rate e of each selected charging process includes: calculating the voltage plateau growth rate of each selected charging process according to e = (voltage plateau of each selected charging process - a) / a * 100%. In steps S1 and S2 above, the calculation of the voltage plateau includes: Multiple points are sampled within the preset SOC range to obtain the voltage corresponding to each SOC sampling point. The average value of the voltages corresponding to all SOC sampling points is taken to obtain the voltage plateau, ensuring that the charging current deviation of all SOC sampling points in the same charging process does not exceed the preset deviation range. S3. Calculate the ratio e / A of the voltage plateau growth rate of each selected charging process to the preset voltage plateau growth rate. If e / A of multiple consecutive selected charging processes is greater than or equal to the preset ratio, it is determined that lithium plating has occurred in the battery.

2. The online detection method for lithium plating in batteries as described in claim 1, characterized in that, In step S3, if the e / A ratio exceeds the set value for at least three consecutive selected charging processes, it is determined that lithium plating has occurred in the battery.

3. The online detection method for lithium plating in batteries as described in claim 1, characterized in that, In step S3, the ratio range is set to 5~10.

4. The online lithium plating detection method for batteries as described in claim 1, characterized in that, The voltages corresponding to the SOC sampling points were all obtained after the following correction process: Using the ambient temperature of the first normal charging process as the reference temperature T1, the ambient temperature of each charging process as T2, and the starting voltage collected within the preset SOC range as the reference voltage V0, the SOC sampling points of each charging process are corrected for the collected voltage V1 using the following formula to obtain the voltage V2 of V1 at the reference temperature T1. Where T1 is the set reference temperature, in °C; V0 is the selected reference voltage, in units of V; K is the temperature coefficient, with a value ranging from 2*10. 3 -5*10 3 ; T2 is the ambient temperature during the charging process, in °C; V1 is the actual voltage collected at the sampling point, in units of V; V2 is the voltage after correction at the sampling point, in units of V.

5. The online detection method for lithium plating in batteries as described in claim 1, characterized in that, The current preset deviation range for the same charging process is ≤5%.

6. The online detection method for lithium plating in batteries as described in claim 1, characterized in that, The sampling frequency is 1~10 Hz within the preset SOC range.

7. The online detection method for lithium plating in batteries as described in claim 1, characterized in that, The preset SOC range is m~n, where m≥10%SOC, n≤90%SOC, and nm≥50%SOC.

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