Charging control device, mobile terminal device, charging control method and program
The charge control device addresses battery storage deterioration by calculating and adjusting the full charge voltage based on integrated deterioration, effectively maintaining battery capacity and safety.
Patent Information
- Application Number
- JP2023542199
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2021-08-19
- Filing Date
- 2022-03-07
- Publication Date
- 2025-10-28
- Estimated Expiration
- 2042-03-07
AI Technical Summary
Existing charging control methods fail to effectively suppress battery storage deterioration despite reducing battery expansion, leading to decreased charge capacity and safety issues.
A charge control device with a processor that calculates the integrated amount of battery storage deterioration and adjusts the full charge voltage accordingly to minimize storage deterioration and maintain battery capacity.
The solution effectively suppresses battery storage deterioration while maintaining charge capacity by gradually reducing the full charge voltage based on the accumulated deterioration, thereby minimizing capacity loss and enhancing safety.
Smart Images

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Abstract
Description
[Technical Field]
[0001] The present disclosure relates to a charge control device, a mobile terminal device, a charge control method, and a program. [Background technology]
[0002] Batteries installed in mobile terminal devices may expand due to repeated charging, and the greater the amount of battery expansion, the lower the charge capacity and the lower the safety. It is also known that the amount of expansion caused by repeated charging and discharging of a battery tends to increase in proportion to the full charge voltage. Therefore, in order to keep the amount of battery expansion at a constant level, mobile terminal devices implement charging control that gradually reduces the full charge voltage of the battery as the cumulative amount of damage to the battery caused by battery expansion (hereinafter sometimes referred to as "expansion damage") increases. [Prior art documents] [Patent documents]
[0003] [Patent Document 1] Japanese Patent Publication No. 2020-068607 Summary of the Invention [Problem to be solved by the invention]
[0004] However, since the main purpose of charging control based on the accumulated amount of expansion damage is to suppress battery expansion, even if charging control based on the accumulated amount of expansion damage is performed, it is difficult to suppress storage deterioration of the battery.
[0005] Therefore, the present disclosure proposes a technique that can suppress storage deterioration of a battery. [Means for solving the problem]
[0006] The charge control device of the present disclosure includes a charging circuit and a processor. The charging circuit charges the battery until the battery voltage reaches a full charge voltage. The processor calculates an integrated amount of storage deterioration of the battery and reduces the full charge voltage as the integrated amount increases. [Brief explanation of the drawings]
[0007] [Figure 1] 1 is a diagram illustrating a configuration example of a mobile terminal device according to a first embodiment of the present disclosure. [Figure 2] 3A to 3C are diagrams illustrating an example of the operation of the charge control device according to the first embodiment of the present disclosure. [Figure 3] FIG. 4 is a diagram illustrating an example of a method for calculating a full charge residence time cumulative value according to the first embodiment of the present disclosure. [Figure 4] FIG. 4 is a diagram illustrating an example of a method for calculating a full charge residence time cumulative value according to the first embodiment of the present disclosure. [Figure 5] FIG. 4 is a diagram illustrating an example of a method for calculating a full charge residence time cumulative value according to the first embodiment of the present disclosure. [Figure 6] 10 is a graph showing the relationship between the accumulated full charge residence time value and the accumulated amount of storage deterioration according to the second embodiment of the present disclosure. [Figure 7] FIG. 10 is a diagram illustrating an example of the operation of the charge control device according to the second embodiment of the present disclosure. [Figure 8] FIG. 10 is a diagram illustrating a configuration example of a mobile terminal device according to a fourth embodiment of the present disclosure. [Figure 9] 10 is a graph showing the relationship between a full charge voltage value and a storage deterioration rate according to a fourth embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION
[0008] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the following embodiments, the same components or processes will be denoted by the same reference numerals, and redundant description may be omitted.
[0009] The technology of the present disclosure will be described in the following order. [Embodiment 1] <Configuration of mobile terminal device> <Charging control device operation> <Calculating the cumulative full charge residence time> <Calculation example 1> <Calculation example 2> <Calculation example 3> <Calculation example 4> [Embodiment 2] [Embodiment 3] [Embodiment 4] [Embodiment 5] [Effects of the disclosed technology]
[0010] [Embodiment 1] <Configuration of mobile terminal device> Fig. 1 is a diagram illustrating a configuration example of a mobile terminal device according to a first embodiment of the present disclosure. In Fig. 1, the mobile terminal device 1a includes a charge control device 10a, a battery 20, a charging terminal 30, and a memory 40. The charge control device 10a includes a charging circuit 11, a processor 12, and an ADC (Analog-to-Digital Converter) 13.
[0011] Examples of the mobile terminal device 1a include smart devices such as smartphones and tablet terminals, and notebook personal computers. Examples of the processor 12 include a central processing unit (CPU), a digital signal processor (DSP), and a field programmable gate array (FPGA). Examples of the memory 40 include a random access memory (RAM), a read only memory (ROM), and a flash memory. An example of the battery 20 is a lithium ion battery.
[0012] When the battery 20 is to be charged, a commercial power source is connected to the mobile terminal device 1a via the charging terminal 30, and the commercial power source charges the battery 20. The commercial power source is connected to the charging terminal 30 via an AC adapter (not shown), and the AC adapter converts, for example, 100V AC commercial power into 5V DC power.
[0013] The voltage of the battery 20 is input to the ADC 13. The ADC 13 detects the voltage value of the battery 20 (hereinafter, may be referred to as the “battery voltage value”), converts the detected analog voltage value into a digital voltage value, and outputs the converted digital battery voltage value to the processor 12.
[0014] Processor 12 controls charging circuit 11 to control charging of battery 20. When a commercial power source is connected to charging terminal 30 via an AC adapter, processor 12 causes charging circuit 11 to start charging battery 20. When charging circuit 11 charges battery 20, processor 12 also causes charging circuit 11 to continue charging battery 20 until the battery voltage value reaches a full charge voltage value.
[0015] The processor 12 also calculates the accumulated amount of storage deterioration of the battery 20 (hereinafter sometimes referred to as the "accumulated amount of storage deterioration"), and controls the full charge voltage value based on the calculated accumulated amount of storage deterioration.
[0016] The charging circuit 11 uses DC power supplied from the AC adapter to charge the battery 20 under the control of the processor 12 until the battery voltage value reaches a fully charged voltage value.
[0017] <Charging control device operation> FIG. 2 is a diagram illustrating an example of the operation of the charge control device according to the first embodiment of the present disclosure.
[0018] The processor 12 calculates the cumulative value (hereinafter sometimes referred to as the "accumulated full-charge residence time") of the elapsed time that the battery 20 has remained in a fully charged state (hereinafter sometimes referred to as the "full-charge residence time") as the accumulated amount of storage deterioration. Then, as shown in FIG. 2, the processor 12 decreases the full-charge voltage value Vf [V] as the accumulated full-charge residence time value Tf [h] increases. For example, when the accumulated full-charge residence time value Tf reaches a threshold value THA1, the processor 12 decreases the full-charge voltage value Vf from a maximum value Vf1 to Vf2. When the accumulated full-charge residence time value Tf reaches a threshold value THA2, the processor 12 decreases the full-charge voltage value Vf from Vf2 to Vf3. For example, when the accumulated full-charge residence time value Tf reaches a threshold value THA3, the processor 12 decreases the full-charge voltage value Vf from Vf3 to Vf4. When the accumulated full-charge residence time value Tf reaches a threshold value THA4, the processor 12 decreases the full-charge voltage value Vf from Vf4 to Vf5. As shown in FIG. 2, in the first embodiment, the time during which the full charge voltage value Vf is set to Vf1, the time during which the full charge voltage value Vf is set to Vf2, the time during which the full charge voltage value Vf is set to Vf3, and the time during which the full charge voltage value Vf is set to Vf4 are all equal to time TA.
[0019] <Calculating the cumulative full charge residence time> 3, 4, and 5 are diagrams illustrating an example of a method for calculating the accumulated full charge residence time value according to the first embodiment of the present disclosure. Hereinafter, the method for calculating the accumulated full charge residence time value will be described with reference to four calculation examples, Calculation Examples 1 to 4.
[0020] <Calculation example 1> 3, processor 12 measures full charge residence time t1, starting from the point when constant current (CC) charging by charging circuit 11 is completed (i.e., the point when the battery voltage value reaches full charge voltage value Vf) and ending from the point when mobile terminal device 1a starts to be driven by battery 20 (i.e., the point when the AC adapter is removed from charging terminal 30 and discharging from battery 20 starts). Processor 12 then calculates the accumulated value of full charge residence time t1 as full charge residence time accumulated value Tf.
[0021] <Calculation example 2> 3, the processor 12 measures the full charge residence time t2, starting from the point when CV (Constant Voltage) charging by the charging circuit 11 is completed and ending from the point when the mobile terminal device 1a starts to be driven by the battery 20 (i.e., the point when the AC adapter is removed from the charging terminal 30 and discharging from the battery 20 starts).The processor 12 then calculates the accumulated value of the full charge residence time t2 as the accumulated full charge residence time value Tf.
[0022] <Calculation example 3> 4, the processor 12 uses a threshold value THV that is smaller than the full charge voltage value Vf to measure the time during which the battery voltage value is equal to or greater than the threshold value THV as the full charge residence time t3. Then, the processor 12 calculates the accumulated value of the full charge residence time t3 as the full charge residence time accumulated value Tf.
[0023] <Calculation example 4> 5, the processor 12 measures the time during which the charging rate of the battery 20 is 100% as the full charge residence time t4. Then, the processor 12 calculates the accumulated value of the full charge residence time t4 as the full charge residence time accumulated value Tf.
[0024] The first embodiment has been described above.
[0025] [Embodiment 2] The second embodiment differs from the first embodiment in that the time at which the full charge voltage value Vf is set to Vf1, the time at which the full charge voltage value Vf is set to Vf2, the time at which the full charge voltage value Vf is set to Vf3, and the time at which the full charge voltage value Vf is set to Vf4 are different from one another.
[0026] FIG. 6 is a graph showing the relationship between the accumulated full charge residence time and the accumulated amount of storage degradation according to the second embodiment of the present disclosure. As shown in FIG. 6, the accumulated amount of storage degradation is directly proportional to the accumulated full charge residence time Tf. Furthermore, the larger the full charge voltage value Vf (Vf1>Vf2>Vf3>Vf4>Vf5), the larger the slope r of the directly proportional graph (r1>r2>r3>r4>r5). The slope r of the graph in FIG. 6 corresponds to the rate of increase of the accumulated amount of storage degradation (hereinafter sometimes referred to as the "storage degradation rate"). In other words, as the full charge voltage value Vf decreases, the rate of storage degradation decreases.
[0027] Therefore, in the second embodiment, a threshold value according to the storage deterioration rate is used as the threshold value of the full charge residence time cumulative value Tf, as shown in Fig. 7. Fig. 7 is a diagram illustrating an example of the operation of the charge control device according to the second embodiment of the present disclosure.
[0028] In FIG. 7, the threshold values THB2, THB3, and THB4 for the full charge residence time cumulative value Tf are set based on the threshold value THB1 and in accordance with the storage deterioration rate, for example, according to equations (1), (2), and (3). THB2 = THB1 × (r1 / r2) … (1) THB3 = THB1 × (r1 / r3) … (2) THB4 = THB1 × (r1 / r4) … (3)
[0029] Processor 12 reduces full charge voltage value Vf from maximum value Vf1 to Vf2 when full charge residence time cumulative value Tf reaches threshold value THB1, reduces full charge voltage value Vf from maximum value Vf2 to Vf3 when full charge residence time cumulative value Tf reaches threshold value THB2, reduces full charge voltage value Vf from Vf3 to Vf4 when full charge residence time cumulative value Tf reaches threshold value THB3, and reduces full charge voltage value Vf from Vf4 to Vf5 when full charge residence time cumulative value Tf reaches threshold value THB4.
[0030] As a result of setting the thresholds THB2, THB3, and THB4 as described above, the time TB4 during which the full charge voltage value Vf is set to Vf4 is longer than the time TB3 during which the full charge voltage value Vf is set to Vf3. Also, the time TB3 during which the full charge voltage value Vf is set to Vf3 is longer than the time TB2 during which the full charge voltage value Vf is set to Vf2. Also, the time TB2 during which the full charge voltage value Vf is set to Vf2 is longer than the time TB1 during which the full charge voltage value Vf is set to Vf1.
[0031] The second embodiment has been described above.
[0032] [Embodiment 3] The third embodiment differs from the first embodiment in that the full charge residence time cumulative value Tf is calculated based on the storage deterioration rate.
[0033] The processor 12 calculates the accumulated full charge residence time Tf according to, for example, equation (4). In equation (4), "ta1" indicates the full charge residence time when the full charge voltage value Vf is Vf1, "ta2" indicates the full charge residence time when the full charge voltage value Vf is Vf2, "ta3" indicates the full charge residence time when the full charge voltage value Vf is Vf3, "ta4" indicates the full charge residence time when the full charge voltage value Vf is Vf4, and "ta5" indicates the full charge residence time when the full charge voltage value Vf is Vf5. Tf=ta1+ta2·(r2 / r1)+ta3·(r3 / r1) +ta4·(r4 / r1)+ta5·(r5 / r1) …(4)
[0034] As in the first embodiment, the processor 12 reduces the full charge voltage value Vf from the maximum value Vf1 to Vf2 when the accumulated full charge residence time value Tf reaches the threshold value THA1, and reduces the full charge voltage value Vf from Vf2 to Vf3 when the accumulated full charge residence time value Tf reaches the threshold value THA2. Furthermore, the processor 12 reduces the full charge voltage value Vf from Vf3 to Vf4 when the accumulated full charge residence time value Tf reaches the threshold value THA3, and reduces the full charge voltage value Vf from Vf4 to Vf5 when the accumulated full charge residence time value Tf reaches the threshold value THA4.
[0035] By calculating the full charge residence time cumulative value Tf according to equation (4) and using the same threshold values THA1, THA2, THA3, and THA4 as in embodiment 1, as in embodiment 2, the time during which the full charge voltage value Vf is set to Vf4 is longer than the time during which the full charge voltage value Vf is set to Vf3, the time during which the full charge voltage value Vf is set to Vf3 is longer than the time during which the full charge voltage value Vf is set to Vf2, and the time during which the full charge voltage value Vf is set to Vf2 is longer than the time during which the full charge voltage value Vf is set to Vf1.
[0036] The third embodiment has been described above.
[0037] [Embodiment 4] The fourth embodiment differs from the first embodiment in that the mobile terminal device further includes a temperature sensor.
[0038] Fig. 8 is a diagram showing a configuration example of a mobile terminal device according to a fourth embodiment of the present disclosure. In Fig. 8, the mobile terminal device 1b includes a charge control device 10b, a battery 20, a charging terminal 30, and a memory 40. The charge control device 10b includes a charging circuit 11, a processor 12, an ADC 13, and a temperature sensor 14. The battery 20 may include the temperature sensor 14.
[0039] The temperature sensor 14 detects the temperature of the battery 20 (hereinafter, sometimes referred to as the “battery temperature”) and outputs the detected battery temperature to the processor 12.
[0040] The processor 12 calculates the accumulated amount of storage deterioration based on the battery temperature.
[0041] FIG. 9 is a graph showing the relationship between the full charge voltage value and the storage degradation rate according to Embodiment 4 of the present disclosure. In FIG. 9, "TP1", "TP2", and "TP3" indicate the battery temperature (TP1 < TP2 < TP3). As shown in FIG. 9, when the battery temperature is constant, the higher the full charge voltage value Vf, the higher the storage degradation rate. Also, when the full charge voltage value Vf is constant, the higher the battery temperature, the higher the storage degradation rate.
[0042] Therefore, the processor 12 calculates the storage degradation amount SD according to Equation (5). Further, the processor 12 calculates the cumulative value of the storage degradation amount SD as the storage degradation integrated amount. The function f shown in Equation (5) has the full charge voltage value Vf, the battery temperature TP, and the stay time Tm at a constant Vf and a constant TP as variables, and is derived based on the relationship between the full charge voltage value, the battery temperature, and the storage degradation rate, for example, using multiple regression analysis. SD = f(Vf, TP, Tm) …(5)
[0043] Then, when the storage degradation integrated amount reaches the threshold THC1, the processor 12 decreases the full charge voltage value Vf from the maximum value Vf1 to Vf2, and when the storage degradation integrated amount reaches the threshold THC2, the processor 12 decreases the full charge voltage value Vf from Vf2 to Vf3. Also, when the storage degradation integrated amount reaches the threshold THC3, the processor 12 decreases the full charge voltage value Vf from Vf3 to Vf4, and when the storage degradation integrated amount reaches the threshold THC4, the processor 12 decreases the full charge voltage value Vf from Vf4 to Vf5. Note that "THC1 < THC2 < THC3 < THC4".
[0044] The above describes Embodiment 4.
[0045] [Embodiment 5] Each of the processes described above by the processor 12 may be realized by having the processor 12 execute a program corresponding to each process. For example, a program corresponding to each of the processes described above may be stored in the memory 40, and the program may be read from the memory 40 and executed by the processor 12. Alternatively, the program may be stored in a program server connected to the mobile terminal devices 1a and 1b via any network, downloaded from the program server to the mobile terminal devices 1a and 1b, and executed therein. Alternatively, the program may be stored in a recording medium readable by the mobile terminal devices 1a and 1b, read from the recording medium, and executed therein. Examples of recording media readable by the mobile terminal devices 1a and 1b include portable storage media such as memory cards, USB memories, SD cards, flexible disks, magneto-optical disks, CD-ROMs, DVDs, and Blu-ray (registered trademark) discs. The program may be written in any language and in any description method, and may be in any format, such as source code or binary code. Furthermore, a program is not necessarily limited to being constructed as a single entity, but may be constructed in a distributed manner as multiple modules or multiple libraries, or may achieve its functions by working together with other programs, such as an OS.
[0046] The fifth embodiment has been described above.
[0047] [Effects of the disclosed technology] As described above, the charge control device (charge control devices 10a and 10b of the embodiment) of the present disclosure includes a charging circuit (charging circuit 11 of the embodiment) and a processor (processor 12 of the embodiment). The charging circuit charges the battery (battery 20 of the embodiment) until the voltage value of the battery reaches a full charge voltage value. The processor calculates the accumulated amount of storage deterioration of the battery and reduces the full charge voltage value as the accumulated amount of storage deterioration increases.
[0048] In this way, it is possible to suppress the storage deterioration of the battery. In addition, while decreasing the full charge voltage value of the battery reduces the battery capacity and shortens the usable time after the battery is fully charged, by gradually decreasing the full charge voltage value from the maximum full charge voltage value in accordance with an increase in the accumulated amount of storage deterioration, it is possible to suppress the storage deterioration of the battery while suppressing the decrease in battery capacity.
[0049] The processor also calculates the accumulated full charge residence time, which is the cumulative value of the elapsed time that the battery has remained in a fully charged state, as the accumulated amount of storage deterioration, and reduces the full charge voltage value when the accumulated full charge residence time reaches a threshold value.
[0050] In this way, the accumulated amount of storage deterioration can be calculated accurately, and the full charge voltage value can be reliably reduced in accordance with an increase in the accumulated amount of storage deterioration.
[0051] The processor may use a threshold value according to the rate of increase of the accumulated amount of storage deterioration as the threshold value for the accumulated full charge residence time, or may calculate the accumulated full charge residence time based on the rate of increase of the accumulated amount of storage deterioration.
[0052] This makes it possible to maintain a constant rate of decrease in battery capacity, thereby minimizing the decrease in battery capacity and suppressing storage deterioration of the battery.
[0053] The processor also calculates the accumulated amount of storage deterioration based on the temperature of the battery.
[0054] In this way, the storage deterioration integrated amount can be calculated taking into account the storage deterioration rate that changes depending on the temperature of the battery, and therefore the storage deterioration integrated amount can be calculated with high accuracy.
[0055] The effects described in this specification are merely examples and are not limiting, and other effects may also be present.
[0056] The disclosed technology can also be configured as follows. (1) a charging circuit for charging the battery until the voltage value of the battery reaches a fully charged voltage value; a processor that calculates an integrated amount of storage deterioration of the battery and reduces the full charge voltage value in accordance with an increase in the integrated amount; A charging control device comprising: (2) the processor calculates an accumulated value of the elapsed time that the battery has remained in a fully charged state as the integrated amount, and reduces the full charge voltage value when the accumulated value reaches a threshold value. The charging control device according to (1) above. (3) The processor measures the elapsed time from the point when CC charging by the charging circuit is completed to the point when discharging from the battery is started. The charging control device according to (2) above. (4) The processor measures the elapsed time from a point when CV charging by the charging circuit is completed to a point when discharging from the battery is started. The charging control device according to (2) above. (5) the processor uses the threshold value according to an increasing rate of the integrated amount. The charging control device according to (2) above. (6) the processor calculates the cumulative value based on an increasing rate of the integrated amount; The charging control device according to (2) above. (7) the processor calculates the integrated amount based on the temperature of the battery; The charging control device according to (1) above. (8) A mobile terminal device comprising the charge control device according to (1) above. (9) A charge control method for a battery that is charged until its voltage value reaches a full charge voltage value, comprising: Calculating an integrated amount of storage deterioration of the battery; decreasing the full charge voltage value in accordance with an increase in the integrated amount; Charging control method. (10) A program for causing a processor to execute charge control for a battery that is charged until a voltage value reaches a full charge voltage value, Calculating an integrated amount of storage deterioration of the battery; decreasing the full charge voltage value in accordance with an increase in the integrated amount; A program for causing the processor to execute a process. [Explanation of symbols]
[0057] 1a, 1b Portable terminal device 10a, 10b Charging control device 11 Charging circuit 12 processors 13 ADC 14 Temperature Sensor 20 Battery 30 Charging terminal 40 memory
Claims
1. a charging circuit for charging the battery until the voltage value of the battery reaches a fully charged voltage value; a processor that calculates an integrated amount of storage deterioration of the battery and reduces the full charge voltage value in accordance with an increase in the integrated amount; Equipped with The processor: an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; using the threshold value according to the rate of increase of the integrated amount; Charging control device.
2. a charging circuit for charging the battery until the voltage value of the battery reaches a fully charged voltage value; a processor that calculates an integrated amount of storage deterioration of the battery and reduces the full charge voltage value in accordance with an increase in the integrated amount; Equipped with The processor: an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; calculating the cumulative value based on the rate of increase of the integrated amount; Charging control device.
3. A portable terminal device comprising the charge control device according to claim 1 or 2.
4. A charge control method for a battery that is charged until its voltage value reaches a full charge voltage value, comprising: Calculating an integrated amount of storage deterioration of the battery; Decreasing the full charge voltage value in accordance with an increase in the integrated amount; an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; using the threshold value according to the rate of increase of the integrated amount; Charging control method.
5. A charge control method for a battery that is charged until its voltage value reaches a full charge voltage value, comprising: Calculating an integrated amount of storage deterioration of the battery; Decreasing the full charge voltage value in accordance with an increase in the integrated amount; an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; calculating the cumulative value based on the rate of increase of the integrated amount; Charging control method.
6. A program for causing a processor to execute charge control for a battery that is charged until a voltage value reaches a full charge voltage value, Calculating an integrated amount of storage deterioration of the battery; Decreasing the full charge voltage value in accordance with an increase in the integrated amount; an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; using the threshold value according to the rate of increase of the integrated amount; A program for causing the processor to execute a process.
7. A program for causing a processor to execute charge control for a battery that is charged until a voltage value reaches a full charge voltage value, Calculating an integrated amount of storage deterioration of the battery; Decreasing the full charge voltage value in accordance with an increase in the integrated amount; an accumulated value of the elapsed time that the battery has remained in a fully charged state is calculated as the integrated amount, and when the accumulated value reaches a threshold value, the fully charged voltage value is reduced; calculating the cumulative value based on the rate of increase of the integrated amount; A program for causing the processor to execute a process.
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