Control device for secondary battery and control method of the secondary battery
The control device and method address the challenges of accurately estimating secondary battery states by using reference curves and correction processes, ensuring quick and non-destructive diagnostics with improved accuracy.
Patent Information
- Application Number
- JP2024041150
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-03-15
- Publication Date
- 2025-09-29
AI Technical Summary
Existing methods for estimating the state of secondary batteries, such as lithium-ion batteries, face challenges in accurately determining the open-circuit voltage due to distortions from electrochemical overvoltage and require long-term measurements that disrupt user convenience, while using specific function forms can lead to significant estimation errors.
A control device and method that applies current to a secondary battery, pauses it, and uses a calculation unit to read reference curves from a memory, select one based on actual measurements, and estimate open circuit voltage based on these curves, minimizing errors through a correction process.
Enables quick and accurate estimation of the secondary battery's state without destructive testing, improving user convenience by reducing the need for prolonged battery system stops and enhancing diagnostic accuracy.
Smart Images

Figure 2025141281000001_ABST
Abstract
Description
[Technical Field]
[0001] The present invention relates to a control device for a secondary battery and a control method for a secondary battery. [Background technology]
[0002] As background art in this technical field, the specification of Patent Document 1 listed below, paragraph 0080, states that "As explained above, the present invention makes it possible to know the status of the charge / discharge curve of the entire positive electrode and the charge / discharge curve of the entire negative electrode inside a secondary battery non-destructively. This makes it possible to identify the cause of battery deterioration non-destructively and to determine the lifespan with high accuracy. Furthermore, according to the present invention, by applying the results of reproduction calculations, it is also possible to determine the appropriate usage range of a deteriorated battery with high accuracy and to obtain the amount of decrease in charge / discharge reaction species non-destructively." Furthermore, the abstract of Patent Document 2 listed below states that "the open-circuit voltage measuring means 23a-1 measures the open-circuit voltage of the battery for a fixed time after a predetermined time has elapsed after charging or discharging of the battery is completed. The approximation formula determining means 23a-2 determines a predetermined power approximation formula with a negative exponent based on the difference between a plurality of open-circuit voltages and an assumed open-circuit voltage. The calculation control means 23a-3 causes the approximation formula determining means to repeatedly determine the power approximation formula by updating the assumed open-circuit voltage until the exponent of the power approximation formula becomes -0.5 or approximately -0.5, and estimates the assumed open-circuit voltage when either of the conditions is met as the open-circuit voltage." [Prior art documents] [Patent documents]
[0003] [Patent Document 1] Patent No. 4884404 [Patent Document 2] Japanese Patent Application Laid-Open No. 2002-234408 Summary of the Invention [Problem to be solved by the invention]
[0004] However, in the above-mentioned technology, there is a demand for more appropriate estimation of the state of the secondary battery. The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a secondary battery control device and a secondary battery control method that can appropriately estimate the state of a secondary battery. [Means for solving the problem]
[0005] In order to solve the above problems, the control device for a secondary battery of the present invention comprises: The battery includes an execution unit that applies current to and pauses a first secondary battery, and a calculation unit, wherein the calculation unit has the following functions: a function of reading one or more reference curves from a memory unit, the reference curves being plots of voltage values against the elapsed time during a pause period after application of current, measured in advance for the first secondary battery or another second secondary battery over a predetermined reference elapsed time or more; a function of selecting one of the reference curves based on the relationship with actual measured values measured on the first secondary battery during a pause over a data acquisition period shorter than the reference elapsed time; and a function of estimating the open circuit voltage of the first secondary battery based on the voltage value of the selected reference curve at or after the reference elapsed time. [Effects of the Invention]
[0006] According to the present invention, the state of a secondary battery can be appropriately estimated. [Brief explanation of the drawings]
[0007] [Figure 1] 1 is an example of a cross-sectional view conceptually illustrating the structure of a cell of a lithium ion battery. [Figure 2] FIG. 2 is an example of a cross-sectional view conceptually illustrating the configuration of an electrode plate assembly. [Figure 3] FIG. 1 is a conceptual block diagram of a battery system. [Figure 4] FIG. 10 is a conceptual block diagram of another battery system. [Figure 5] FIG. 10 is a conceptual block diagram of another battery system. [Figure 6]FIG. 10 is a conceptual block diagram of another battery system. [Figure 7] FIG. 2 is a block diagram conceptually illustrating an example of the configuration of a control device. [Figure 8] FIG. 10 is a diagram showing an example of actual measured values of a voltage relaxation plot during a rest period of a battery and a corrected reference curve. [Figure 9] FIG. 10 is an explanatory diagram of a case where the L2 norm is applied as an error. [Figure 10] 10 is a flowchart of a diagnostic operation processing routine. [Figure 11] FIG. 10 is a diagram illustrating an example of a result of a reproduction calculation process. [Figure 12] FIG. 10 is a diagram showing errors in the OCV estimation values for the first example and the like. [Figure 13] FIG. 10 is a diagram showing errors in the OCV estimation values for the second example and the like. DETAILED DESCRIPTION OF THE INVENTION
[0008] [Outline of the embodiment] Lithium-ion batteries are a type of non-aqueous electrolyte secondary battery with a high energy density, and are therefore used as batteries for portable devices and, more recently, electric vehicles. However, lithium-ion batteries are known to deteriorate with use, resulting in increased internal resistance and decreased charge / discharge capacity. In lithium-ion batteries, lithium metal oxide is used as the active material for the positive electrode, and carbon materials such as graphite, silicon materials, and lithium metal oxide are used as the active material for the negative electrode. The positive and negative electrodes of lithium-ion batteries are formed by adding binders and conductive agents to tiny particles of the active material to form a slurry, which is then applied to metal foil.
[0009] In a lithium-ion battery, lithium ions are released from the active material of the positive electrode during charging and are absorbed into the active material of the negative electrode during discharging. As a result of this movement of lithium ions between the electrodes, a current flows between the electrodes of an external circuit. The capacity of such a lithium-ion battery decreases due to factors such as: (1) Electrical isolation of the positive electrode active material, (2) Electrical isolation of the negative electrode active material, (3) Fixation of lithium ions moving between electrodes
[0010] In the technology applying the above-mentioned Patent Document 1, it is believed possible to obtain a charge / discharge curve of a secondary battery by a process of charging or discharging a given capacity and then holding the battery in an open circuit state to obtain the open circuit voltage (hereinafter referred to as OCV (Open Circuit Voltage)) corresponding to the charge or discharge capacity. It is also believed possible to obtain a charge / discharge curve by charging or discharging the secondary battery with a minute current value. The reason for adopting such a method is that the charge / discharge curve of a secondary battery is distorted by electrochemical overvoltage when a current is applied, making it difficult to ensure diagnostic accuracy. Therefore, obtaining a charge / discharge curve of a secondary battery requires long-term measurement, which may impair user convenience because the secondary battery system must be stopped during this period.
[0011] Furthermore, in the technology applying Patent Document 2, it is believed that the open-circuit voltage of a secondary battery can be estimated using the open-circuit voltage of the secondary battery measured within a certain time after a predetermined time has elapsed since the end of charging or discharging the secondary battery, and a predetermined power approximation equation with a negative exponent. This is expected to shorten the time the secondary battery is maintained in an open-circuit state after charging or discharging. However, the curve shape of the voltage relaxation plot in the open-circuit state of a secondary battery varies depending on factors such as the type of material constituting the secondary battery, the shape of the secondary battery, the charge or discharge current of the secondary battery, the charge rate of the secondary battery, the degree of deterioration of the secondary battery, and the temperature of the secondary battery. Therefore, estimating the OCV using only a specific function form may result in large errors. Therefore, in the embodiment described below, a method for quickly and non-destructively diagnosing the condition of a secondary battery is provided.
[0012] [First embodiment] Various embodiments will be described below with reference to the drawings. FIG. 1 is an example of a cross-sectional view conceptually showing the structure of a lithium-ion battery cell. In this figure, a cell 10 (first secondary battery) includes an electrode plate group 1, a positive electrode terminal 2, a negative electrode terminal 3, a separator 5, and an exterior material 6. The exterior material 6 is a laminate film or the like. The shape of the cell 10 is not limited to that shown in this figure, and may be rectangular as shown in this figure, or may be cylindrical (not shown).
[0013] FIG. 2 is an example of a cross-sectional view conceptually showing the configuration of the electrode plate group 1. As shown in FIG. 2, the electrode plate group 1 has a configuration in which positive electrodes 7 and negative electrodes 8 are alternately arranged so as to face each other with a separator 5 sandwiched therebetween. The structure of the electrode plate group 1 is not limited to that shown in this figure, and may be a stacked type as shown in this figure, or a wound type (not shown) produced by stacking positive electrodes 7 and negative electrodes 8 so as to face each other with a separator 5 sandwiched therebetween and then winding them.
[0014] The material of the separator 5 is not particularly limited, but for example, polypropylene is used. As the separator 5, a microporous film or nonwoven fabric made of polyolefin such as polyethylene can be used in addition to polypropylene. The positive electrode 7 and the negative electrode 8 are each made by applying a mixture of an appropriate electrode active material, a conductive agent, a binder, etc. to a current collector foil made of an appropriate metal. Metal tabs (not shown) are connected to the current collector foils of the positive electrode 7 and the negative electrode 8. The exterior packaging 6 is sealed so that only the tab portions are exposed to the outside of the exterior packaging 6. As a result, these tabs become the positive electrode terminal 2 and the negative electrode terminal 3 shown in FIG. 1.
[0015] The current collector foil of the positive electrode 7 may be made of aluminum foil having a thickness of 1 to 100 μm, perforated aluminum foil having a thickness of 1 to 100 μm and a pore size of 0.1 to 10 mm, expanded metal, or foam metal plate. In addition to aluminum, stainless steel, titanium, or the like may also be used. In this embodiment, any current collector can be used without being limited by its material, shape, manufacturing method, or the like.
[0016] The electrode active material of the positive electrode 7 preferably contains a reactive species therein. The reactive species of a lithium-ion battery is lithium ions. In this case, the electrode active material contains a lithium-containing compound capable of reversibly inserting and extracting lithium ions. The type of electrode active material of the positive electrode 7 is not particularly limited, but examples thereof include lithium cobalt oxide, manganese-substituted lithium cobalt oxide, lithium manganate, lithium nickel oxide, and lithium transition metal phosphates such as olivine-type lithium iron phosphate; Li w Ni x Co y Mn z O2 (wherein w, x, y, and z are 0 or positive values). The electrode active material of the positive electrode 7 may contain one or more of the above materials.
[0017] The current collector foil of the negative electrode 8 may be copper foil having a thickness of 1 to 100 μm, perforated copper foil having a thickness of 1 to 100 μm and a pore size of 0.1 to 10 mm, expanded metal, or foam metal plate, and may be made of stainless steel, titanium, or other materials in addition to copper. In this embodiment, any current collector can be used without being limited by the material, shape, or manufacturing method.
[0018] The electrode active material of the negative electrode 8 includes a substance capable of reversibly inserting and detaching lithium ions. The type of electrode active material of the negative electrode 8 is not particularly limited, but examples thereof include natural graphite, a composite carbonaceous material in which a coating is formed on natural graphite by a dry CVD method or a wet spray method, artificial graphite produced by firing a resin material such as epoxy or phenol or a pitch-based material obtained from petroleum or coal, silicon (Si), silicon oxide, graphite mixed with silicon or silicon oxide, a non-graphitizable carbon material, and lithium titanate Li4Ti5O 12 , niobium titanium oxide TiNb2O7, etc. The negative electrode active material may contain one or more of the above materials.
[0019] An electrolyte is impregnated in the electrode plate group 1. There are no particular limitations on the electrolyte, but in the case of a lithium ion battery, aprotic organic solvents such as ethylene carbonate (EC), propylene carbonate (PC), butylene carbonate (BC), dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), diethyl carbonate (DEC), methyl propyl carbonate (MPC), and ethyl propyl carbonate (EPC) can be used.
[0020] In addition, examples of electrolytes include those in which lithium salts such as lithium hexafluorophosphate, lithium tetrafluoroborate, lithium perchlorate, lithium iodide, lithium chloride, lithium bromide, LiB[OCOCF3]4, LiB[OCOCF2CF3]4, LiPF4(CF3)2, LiN(SO2CF3)2, and LiN(SO2CF2CF3)2, or mixed lithium salts of two or more of these are dissolved in a solvent of a mixed organic compound of two or more of these.
[0021] Alternatively, a solid electrolyte may be used instead of the electrolytic solution. The solid electrolyte is not particularly limited, but examples thereof include ion-conductive polymers such as polyethylene oxide, polyacrylonitrile, polyvinylidene fluoride, polymethyl methacrylate, polyhexafluoropropylene, and polyethylene oxide. When such a solid electrolyte is used, the separator 5 can be omitted.
[0022] FIG. 3 is a conceptual block diagram of a battery system 31. As shown in FIG. The battery system 31 includes a battery module 100 (first secondary battery), an ammeter 101, and a control device 500 (secondary battery control device, computer). The battery module 100 includes three cells 10 connected in series and three voltmeters 102 that measure the cell voltages of these cells 10. The ammeter 101 measures the current flowing through a battery pack 510 (first secondary battery). The measurement results from the ammeter 101 and voltmeter 102 are supplied to the control device 500, which controls the charging and discharging of the battery module 100. The ammeter 101 may be installed outside the control device 500 as shown in this figure, or may be included in the control device 500 (not shown).
[0023] Any power may be used to charge the battery module 100. Examples include power from a power grid, power generated by a diesel generator or the like, power generated by renewable energy sources such as solar power generation and wind power generation, regenerated power, and power supplied from a power storage system other than the battery module 100. In addition, any load may be used to discharge the battery module 100. Examples include a load built into the control device 500, a load included in a device equipped with the battery module 100, and an external load added later.
[0024] FIG. 4 is a conceptual block diagram of another battery system 32. The battery system 32 includes a battery module 100, an ammeter 101, a switch 103, a load 104, and a control device 500. The load 104 is connected to the battery module 100 via the switch 103. When charging or discharging the battery module 100, the control device 500 outputs a signal to the switch 103 to operate the switch 103. Note that although FIGS. 3 and 4 illustrate a case in which three cells 10 are included, the number of cells 10 constituting the battery module 100 is not particularly limited and may be one. The configuration of the battery module 100 is not limited to the above and may be any configuration as long as it can measure the current flowing through each cell 10 and the voltage of each cell 10. As with the battery system 31 (see FIG. 3), the control device 500 controls the charging and discharging of the battery module 100. The power used to charge the battery module 100 may be any power, and the load used to discharge the battery module 100 may also be any load.
[0025] FIG. 5 is a conceptual block diagram of another battery system 33. As shown in FIG. The battery system 33 includes a battery pack 510 and a control device 500. The battery pack 510 includes three battery modules 100 connected in parallel and three ammeters 101 that detect the current of each battery module 100. Although the illustrated example illustrates a case where the number of battery modules 100 is three, the number of battery modules 100 that make up the battery pack 510 is not particularly limited, and the battery pack 510 may be composed of only one battery module 100.
[0026] Each battery module 100 has a configuration such as that shown in Fig. 3 or 4, and outputs information such as each cell voltage to the control device 500, and each ammeter 101 outputs the input / output current to each battery module 100 to the control device 500. As with the battery systems 31 and 32 (see Figs. 3 and 4), the control device 500 controls the charging and discharging of the battery pack 510. The power used to charge the battery pack 510 is arbitrary, and the load used to discharge the battery pack 510 is also arbitrary.
[0027] FIG. 6 is a conceptual block diagram of another battery system 34. The battery system 34 includes a battery pack 510, a control device 500, and an ammeter 101. The battery pack 510 includes three battery modules 100 connected in parallel, and three switches 110 that turn on / off the current flowing through each battery module 100. When charging or discharging the battery pack 510, the control device 500 outputs a signal to the switch 110 to operate the switch 110.
[0028] This allows selective charging and discharging of specific battery modules 100, thereby reducing the number of ammeters 101 required. Although the example shown in FIG. 6 uses one ammeter 101, there may be multiple ammeters 101. The ammeter 101 may be installed outside the battery pack 510 or the control device 500 as shown in FIG. 6, or may be installed inside the control device 500 or the battery pack 510, although not shown. The configuration of the battery pack 510 is not limited to the one described above, and any configuration may be used as long as it can measure the current flowing through each battery module 100 and the voltage of each battery module 100.
[0029] FIG. 7 is a block diagram conceptually showing an example of the configuration of control device 500. As shown in FIG. 7, control device 500 includes battery state acquisition unit 400 (calculation unit), battery state determination unit 401 (calculation unit), storage unit 403, battery state calculation unit 404 (calculation unit), timer unit 405, normal operation control unit 410 (execution unit), and diagnostic operation control unit 412 (execution unit). Battery state acquisition unit 400 receives measurement signals from ammeter 101 and voltmeter 102, and outputs measurement values such as detected current values and voltage values to battery state determination unit 401.
[0030] Battery state determination unit 401 outputs the amount of electricity calculated based on the current value input from battery state acquisition unit 400 and the time based on timer unit 405 to storage unit 403 along with the time, and stores the calculated amount of electricity. At the same time, battery state determination unit 401 outputs the voltage value input from battery state acquisition unit 400 to storage unit 403 along with the time, and stores the voltage value.
[0031] The battery state determination unit 401 compares the determination value input from the battery state calculation unit 404 with the reference value input from the memory unit 403. Here, the determination value is a parameter value indicating various states of the battery module 100, and the reference value is a reference value of these parameter values. The battery state determination unit 401 then determines the state of one or more of the cell 10, the battery module 100, and the battery pack 510, and outputs the result to the memory unit 403, the battery state calculation unit 404, the normal operation control unit 410, and the diagnostic operation control unit 412.
[0032] For example, based on the battery state of charge (SOC) input from the battery state calculation unit 404, the battery state determination unit 401 outputs a signal to the normal operation control unit 410 and the diagnostic operation control unit 412 to instruct input / output control of the battery.
[0033] In the following description, the term "battery" collectively refers to the cells 10, the battery modules 100, and the battery packs 510. The storage unit 403 stores the following data as initial values. - Battery voltage (OCV) and battery SOC correspondence table, - Initial battery capacity, Battery information such as upper and lower limit voltages, maximum charge and discharge current values, etc. Positive and negative electrode information such as the reference mass of the positive electrode 7 and the negative electrode 8, and charge / discharge curves per reference area; Reference curves for one or more types of batteries. Here, the "reference curve" is a plot of the relationship between the elapsed time t and the battery voltage during rest after energization, that is, the voltage relaxation.
[0034] The batteries (first secondary battery, second secondary battery) used to obtain this reference curve are not particularly limited, but are preferably batteries having electrodes using the same active material as the battery to be controlled by control device 500, and more preferably batteries of the same type as the battery to be controlled by control device 500. This is because if the active material and battery type are the same, there is a high possibility that the shape of the voltage relaxation plot of the battery actually measured by control device 500 will match the shape of the reference curve. Furthermore, memory unit 403 stores inputs from battery state determination unit 401 and battery state calculation unit 404, and outputs the stored values to battery state determination unit 401 and battery state calculation unit 404 as necessary.
[0035] The battery state calculation unit 404 appropriately corrects the acquired measurement values and initial values to calculate physical quantities for determining the battery state, and outputs the calculated physical quantities to the battery state determination unit 401 and the storage unit 403. For example, it calculates the battery OCV based on a relaxation plot of the battery voltage actually measured during rest and a reference curve stored in the storage unit 403, and outputs the calculated OCV together with the corresponding amount of electricity flowing to the storage unit 403. The number of reference curves stored in the storage unit 403 is assumed to be n. The i-th (where 1≦i≦n) reference curve is a voltage value that is a function of the elapsed time t after the battery entered the rest state, and is expressed as "v i It can be expressed in the form of "(t)".
[0036] Furthermore, battery state calculation unit 404 calculates the battery SOC from the calculated battery OCV and a correspondence table between battery voltage (OCV) and battery SOC stored in memory unit 403, and outputs the calculated battery SOC to battery state determination unit 401. Furthermore, battery state calculation unit 404 diagnoses the battery state based on the relationship between the amount of electricity flowing and the OCV, and outputs the result to battery state determination unit 401 and memory unit 403. The method of diagnosing the battery state will be described in detail later.
[0037] The timer unit 405 inputs time information to the battery state determination unit 401 . The battery state determination unit 401 determines whether or not a diagnosis of the battery state is required. If it is determined that a diagnosis of the battery state is not required, the normal operation control unit 410 outputs a control signal for normal operation. On the other hand, if the battery state determination unit 401 determines that a diagnosis of the battery state is required, the diagnostic operation control unit 412 outputs a control signal for diagnostic operation.
[0038] The criteria for determining that a battery status diagnosis is necessary are arbitrary. For example, the criteria may include when a battery status diagnosis has not been performed for a certain period of time, when it is known in advance that the device will be stopped for a certain period of time due to maintenance or the like, or when a diagnostic process is requested by the user. From the perspective of user convenience, the user of the battery-equipped device may ultimately decide whether or not to perform a diagnostic operation. In this case, for example, the control device 500 may be provided with a display that provides information to the user and accepts input from the user. Alternatively, the control device 500 may be provided with a communication function with a device such as a smartphone that the user can use, and input to the control device 500 may be accepted from the user's device.
[0039] The configuration of the control device 500 is not limited to that shown in FIG. 7, and may be any configuration capable of determining the battery state and controlling the charging and discharging of the battery. Furthermore, the functional units shown in the control device 500 do not all need to be integrated; some functions may be processed by a separate server located at a distance using a communication function. In particular, the memory unit 403 may communicate with multiple control devices 500 via wired or wireless communication. That is, the memory unit 403 may be shared by multiple control devices 500. During both normal operation and diagnostic operation, the maximum charging and discharging current, voltage range, temperature, and the like are controlled to fall within appropriate ranges. The calculation of the battery OCV by the battery state calculation unit 404 is implemented using the procedure described below with reference to FIG. 8.
[0040] FIG. 8 is a diagram showing an example of the actually measured voltage relaxation plot during a rest period of the battery and the corrected reference curve. The actual measured value of the battery voltage during the rest period is calculated as a function of the elapsed time t after the start of the rest period, and the actual measured value V mes(t)”. However, in the example shown, the actual measured value V mes (t) is assumed to be acquired at three points of time t from the start of the rest period until the predetermined data acquisition period td has elapsed. Corrected reference curve Va i (t) is the reference curve v i (t) is corrected. The subscript i is the number of the reference curve. This corrected reference curve Va i The calculation method for (t) will be described later. i (t) and corrected reference curve Va i (t) is determined so that the elapsed time t ranges from "0" to a predetermined reference elapsed time tend. This reference elapsed time tend is longer than the data acquisition period td, and is at least 10 minutes or more, and preferably 30 minutes or more.
[0041] In FIG. 8, the corrected reference curve Va i (t) is a continuous value, which is the reference curve v i (t) is also a continuous value. However, the reference curve v i (t) and corrected reference curve Va i (t) may be a discrete value. In this case, it is possible to treat it as a pseudo-continuous value by interpolating between the discrete values. This will be the same in the following drawings. The difference value ΔV in the drawing is the actual measured value V mes (t) and the corrected standard curve Va i The sum of these difference values ΔV for all measurement points (three points in the example of Figure 8) is the total error e i (difference value). That is, the total error e i is expressed by the following equation (1).
[0042]
number
[0043] The corrected reference curve Va described above i (t) is the reference curve v iBased on (t), the curve is expressed by the following equation (2). In the following equation (2), the constant a i (first real number) and constant b i (Second real number) is the total error e in Eq. (1) i is determined so that it is minimized. Therefore, the constant a i ,b i is uniquely determined.
[0044]
number
[0045] The battery state calculation unit 404 calculates all the reference curves v stored in the storage unit 403. i (t) (where 1≦i≦n), the total error e i Then, the battery state calculation unit 404 calculates the total error e i In other words, the battery state calculation unit 404 selects one or more reference curve numbers v i (t) and the measured value V mes (t) and based on the relationship, one reference curve v i (t) Select the selected reference curve v i Corrected reference curve Va corresponding to (t) i At (t), the value at or after the reference elapsed time tend is obtained as an estimate of the battery OCV.
[0046] Here, the difference value ΔV during the rest period is relatively large immediately after the start of the rest period and tends to decrease over time. Therefore, based on equation (1), the total error e i Calculating the constant a using equation (2), i ,b i When determining the value of V, the actual measurement value V in a short period of time t mes This may result in a deterioration in the accuracy of the battery OCV estimation. i In the calculation of the total error e, a weighting function w(t) for the elapsed time t may be introduced. iis expressed by the following equation (3): The weighting function w(t) can be any function of the elapsed time t, excluding constant functions, but it is advisable to apply an activation function such as a normalized linear function or its derivative.
[0047]
number
[0048] FIG. 9 is an explanatory diagram of a case where the L2 norm is applied as the error. In Figure 9, the corrected reference curve Va i (t), measured value V mes (t) is the same as that shown in FIG. 8. In addition, the distance ΔL in the figure is the actual measured value V in a two-dimensional space with the horizontal axis being the elapsed time t and the vertical axis being the voltage value. mes From each measurement point (points based on elapsed time t and actual measurements) of (t), the corrected reference curve Va i (t) is the shortest distance. In this way, when the L2 norm is used, the total error e i is the sum of the distances ΔL.
[0049] When applying the L1 norm as the error, as shown in Figure 8, calculations can be performed by simple addition and subtraction, and if the time interval for voltage measurement during rest is aligned with the reference curve, time interpolation of the reference curve is not required. This reduces the calculation load, which is a major advantage, especially when there are a large number of reference curves.
[0050] On the other hand, when the L2 norm is used as the error, the weighting function w(t), which may be necessary when the L1 norm is used, is not required. Therefore, there is no need to consider the weighting function w(t), which has the advantage of stabilizing the battery OCV estimation results. There is no limit to whether the L1 norm or the L2 norm is used as the error, and it is possible to switch between them at any time, or to use both at the same time.
[0051] The greater the number of reference curves (n), the greater the load of calculation of the battery OCV by the battery state calculation unit 404. Therefore, in order to reduce the calculation load, it is desirable that the reference curves are not similar to each other. That is, it is desirable that the battery state calculation unit 404 judges the similarity between the reference curves, discards one of the similar reference curves, and stores only the other in the storage unit 403. The index for judging the similarity is arbitrary, but for example, d ij can be used.
[0052]
number
[0053] where v i (t) is the value of the i-th reference curve at time t, and v j (t) is the value of the jth standard curve at time t (i ≠ j). i (t)-v j (t)|" is "|v" for the elapsed time t at a predetermined interval (for example, 1 second interval). i (t)-v j (t)|". For comparison using equation (4), it is preferable to make each reference curve a curve that is translated in the vertical direction so that the value at elapsed time t is "0". d ij is a real number greater than or equal to "0", which is difficult to use as a judgment index. For example, the modified D ij may also be used.
[0054]
number
[0055] D ij is 0 <D ij ≦1, and the closer it is to 1, the higher the similarity. For example, D ij If is greater than a certain value, it is determined to be similar and either the i-th or j-th reference curve can be discarded. The threshold value for determining similarity is D ijThe value of is arbitrary, but is preferably set to about 0.6 to 0.9 in consideration of the trade-off between the estimation accuracy of the battery OCV and the calculation load.
[0056] The battery state calculation unit 404 in FIG. 7 may have a function for expanding the reference curve during operation of the battery (cell 10, battery module 100, or battery pack 510) to be measured. For example, a battery may be idle for a period of time corresponding to the reference curve, such as when the battery-equipped device is stopped. The battery state calculation unit 404 can store the voltage relaxation plot obtained at that time as a reference curve in the memory unit 403. The acquired reference curve may be translated in the vertical axis direction so that the value of the acquired reference curve at elapsed time t = 0 becomes 0, and then the similarity determination described above with respect to the existing reference curve stored in the memory unit 403 may be performed. If the similarity is high, the acquired reference curve may be discarded. Expanding the reference curve during battery operation in this way maintains the accuracy of the battery OCV estimation even when the shape of the voltage relaxation plot changes due to battery degradation or other reasons.
[0057] A set of reference curves may be created individually for each battery-equipped device, or may be shared via the cloud. When shared via the cloud, new reference curves can be registered at any time, improving the accuracy of battery OCV estimation. Note that the battery state calculation unit 404 can calculate the battery OCV during both normal operation and diagnostic operation.
[0058] 10 is a flowchart of a diagnostic operation processing routine, which is executed by the diagnostic operation control unit 412 when a diagnostic operation is performed. 10, when the process proceeds to step S2, the diagnostic operation control unit 412 controls the battery in the charge (or discharge) mode. As a result, the SOC of the battery changes in the charge (or discharge) direction. Next, when the process proceeds to step S4, the diagnostic operation control unit 412 controls the battery in the sleep mode. That is, the diagnostic operation control unit 412 puts the battery in an open circuit state for a predetermined time and records a relaxation plot of the battery voltage during that time, i.e., the transition of the battery voltage.
[0059] Next, when the process proceeds to step S6, the diagnostic operation control unit 412 determines whether the diagnostic operation has been terminated. That is, it determines whether the diagnostic operation termination determination condition has been met. If the determination here is "No," the processes from step S2 onwards are repeated. On the other hand, if the determination here is "Yes," the process of this routine ends. The diagnostic operation termination determination condition is not particularly limited, but examples include when the number of repetitions reaches a specified value, when the battery voltage reaches a target voltage, when the charge / discharge capacity reaches a target value, etc. The relaxation plot of the battery voltage measured in the sleep mode in step S4 is used to calculate the actual measured value V for calculating the battery OCV in the battery state calculation unit 404. mes (t) (see Figures 8 and 9).
[0060] Then, by repeating the loop of steps S2 to S6, charging (or discharging) is repeated and the charged (or discharged) capacity values are accumulated, and the battery state calculation unit 404 acquires an accumulated capacity value, which is the accumulated charged or discharged capacity value, and stores it in the memory unit 403. Then, the battery state calculation unit 404 acquires an estimated value of the battery OCV, i.e., open circuit voltage, corresponding to the accumulated capacity value, and stores it in the memory unit 403.
[0061] The battery state calculation unit 404 then interpolates the combination of the accumulated capacity value and the corresponding estimated open circuit voltage value to obtain the charge / discharge curve of the battery. If the sweep direction of the battery SOC is the charge direction, the obtained curve is called a charge curve, and if the sweep direction of the battery SOC is the discharge direction, the obtained curve is called a discharge curve. The "charge / discharge curve" refers to either the charge curve or the discharge curve.
[0062] To diagnose the battery state, the battery state calculation unit 404 performs a regression calculation process (reproduction calculation process) using the charge / discharge curves of the positive and negative electrodes measured in advance so as to reproduce the charge / discharge curve obtained by the above-mentioned measurement. The details of this reproduction calculation process are described in the above-mentioned Patent Document 1, but an outline thereof will be described below. (1) The battery state calculation unit 404 calculates the amount of positive electrode active material mp and the amount of negative electrode active material m n and the index C of the positional relationship of the positive electrode discharge curve p and the index C of the positional relationship of the negative electrode discharge curve n and are stored in the storage unit 403.
[0063] (2) Next, the battery state calculation unit 404 calculates m for each charge / discharge capacity for the charge / discharge curves per reference mass or reference area of the positive electrode and negative electrode recorded in the storage unit 403. p , m n After multiplying by C p , C n In this way, the battery state calculation unit 404 obtains calculated values of the charge / discharge curves of the positive electrode and the negative electrode. (3) For the calculated values of the charge / discharge curves of the positive electrode and the negative electrode obtained in this manner, the battery state calculation unit 404 obtains the calculated values of the charge / discharge curves of the battery by calculating the difference between the positive electrode potential and the negative electrode potential corresponding to the same charge / discharge capacity. (4) The battery state calculation unit 404 calculates the correction parameters (m p , m n , C p , C n ) to adjust the
[0064] FIG. 11 is a diagram illustrating an example of the result of the reproduction calculation process. The horizontal axis of Figure 11 represents the discharge capacity [Ah], with a value of "0" representing a fully charged state and a negative value representing an overcharged state. The vertical axis of Figure 11 represents the potential and voltage. The potential is based on the lithium metal electrode. Hereinafter, the unit for the potential based on the lithium metal electrode will be expressed as "V vs. Li / Li + In the figure, Vp represents the calculated positive electrode potential, Vn represents the calculated negative electrode potential, and V represents the battery voltage.
[0065] The points represented by small circles are the measured values of the battery voltage V, and the solid line is the calculated value. The calculated positive electrode potential Vp and negative electrode potential Vn are plotted so that the calculated battery voltage V overlaps the measured value. As a result, as shown in the figure, the calculated value of the battery voltage V almost matches the measured value. The battery state calculation unit 404 uses the correction parameter (m p , m n , C p , C n The battery condition is diagnosed based on the value of
[0066] That is, m p and m n are parameters that represent the capacity that the positive electrode and negative electrode can charge and discharge independently, respectively, and reflect the deterioration rate of the positive electrode and negative electrode. p and C n are parameters that represent the amount of side reactions at the positive and negative electrodes, respectively. The battery state calculation unit 404 plots these parameters over time and fits them with an appropriate function to predict future changes in each parameter. This allows the battery state calculation unit 404 to construct a future charge / discharge curve for the battery, thereby predicting the battery life.
[0067] Next, a method for determining whether or not this embodiment is applied to a control device for a secondary battery will be described. Whether or not this embodiment is applied can be confirmed by the following steps #1 to #3. Step #1: Charge or discharge the battery until it reaches an SOC (say SOC0) corresponding to an arbitrary OCV (say OCV0). Continuing to charge (or discharge) this battery at a constant current I1, for example, stops the current sensor. As a result, although the battery is actually in a powered state, the control device 500 erroneously recognizes that it has entered a sleep state. This continues for a period of time t1, approximately several minutes, and then the erroneous recognition is resolved. As a result, the system obtains an estimated OCV (say OCV1), and if the device converts the OCV into an SOC and displays it, a certain SOC (say SOC1) is displayed.
[0068] Step #2: First, as in step #1, charge or discharge the battery until the OCV reaches OCV0 and the SOC reaches SOC0. As in step #1, continue charging (or discharging) this battery at a constant current I1 while, for example, stopping the current sensor. As in step #1, this causes the control device 500 to mistakenly recognize that the battery has entered a sleep state, even though it is actually in a powered state. However, in step #2, continue this charging (or discharging) state for a time t2, which is longer than time t1. This time t2 should be set to a time of several tens of minutes or more, corresponding to the reference elapsed time tend in Figures 8 and 9, for example. When the mistaken recognition is resolved after time t2 has passed, in this embodiment, the voltage change during power supply at time t2 is stored as a new reference curve.
[0069] Step #3: First, as in step #1, charge or discharge the battery until the OCV reaches OCV0 and the SOC reaches SOC0. As in step #1, continue charging (or discharging) this battery at a constant current I1 while, for example, stopping the current sensor. As in step #1, this causes the control device 500 to mistakenly recognize that the battery has entered a sleep state, even though it is actually in a powered state. This charging (or discharging) state continues for the same time t1 as in step #1. As a result, an OCV estimated by the system (let's say OCV3) is obtained, and if the device converts the OCV into an SOC and displays it, a certain SOC (let's say SOC3) is displayed.
[0070] Assuming that the reference curves applied in steps #1 and #3 are the same, OCV1 and OCV3 will be approximately the same values, and SOC1 and SOC3 will also be approximately the same values. However, when this embodiment is applied, a reference curve is added in step #2. This reference curve is applied as the optimal reference curve in step #3, so OCV1 and OCV3 will be significantly different values, or SOC1 and SOC3 will be significantly different values.
[0071] In this way, by comparing OCV1 and OCV3 and SOC1 and SOC3, it is possible to determine whether or not this embodiment is being applied. Instead of the above-described procedure #2, a procedure of "using the battery for a certain period of time" may be applied. In this procedure, a new reference curve is added in accordance with battery degradation. Even in this case, if OCV1 and OCV3 are significantly different, or if SOC1 and SOC3 are significantly different, it is highly likely that this embodiment is being implemented.
[0072] [First Example] The effects of the first embodiment will be shown below by way of examples. FIG. 12 is a diagram showing errors in the OCV estimates for the first example and the like. The vertical axis of FIG. 12 represents the absolute error value of the OCV estimation value, and the horizontal axis represents the discharge capacity. In the first example, the first comparative example, and the second comparative example, a cylindrical cell (not shown) was fully charged, and then measurements were taken by repeating a constant current discharge period and a 30-minute rest period. The voltage measured at the end of the rest period, i.e., after 30 minutes, was regarded as the true OCV value.
[0073] The estimation error ΔVC1 in FIG. 12 is the OCV estimation error in the first comparative example. In the first comparative example, the voltage measured at the time when a predetermined data acquisition period td (see FIG. 8) has elapsed after the start of the rest period is used as the OCV estimate. The data acquisition period td in the first comparative example is "3 minutes." In the first comparative example, the error increased mainly in the discharge amount corresponding to the stage change of the graphite structure of the negative electrode.
[0074] The estimation error ΔVC2 in FIG. 12 is the OCV estimation error in the second comparative example. In the second comparative example, a voltage plot during a three-minute data acquisition period td is fitted with a predetermined function to estimate the voltage value at the end of the rest period, and the result is used as the estimated OCV value. Here, the function used is a function consisting of a power function and a logarithmic function. Depending on the fitting coefficient, this function can take only one of the power function or the logarithmic function. The error in the fitting is the L1 norm expressed by equation (1).
[0075] However, when the time variation of the voltage measurement value during the data acquisition period td is small, the error tends to increase when function fitting is applied. Therefore, in this case, as in the first comparative example, an algorithm was adopted in which the voltage measurement value at the end of the data acquisition period td is used as the OCV estimate. In the second comparative example, the OCV estimation error is reduced at discharge amounts where the error was large in the first comparative example. However, the OCV estimation error at some discharge amounts actually increased more than in the first comparative example.
[0076] The estimation error ΔV1 in Figure 12 is the OCV estimation error in the first example. In the first example, a voltage plot during a 3-minute data acquisition period td was fitted with a reference curve to estimate the voltage value at the end of the rest period, and the result was used as the OCV estimate. According to the first example, the OCV estimation error was reduced compared to the first comparative example at all discharge amounts, with the absolute error value being within 10 mV. In the first example, 100 reference curves previously acquired for another battery were used, and the fitting error was the L1 norm expressed by Equation (1). The results of the first example confirmed that this embodiment can estimate the OCV with the same accuracy over a wide SOC range, even when the rest period is shortened from 30 minutes to 3 minutes. This allows for rapid acquisition of a discharge curve for battery diagnosis.
[0077] [Second Example] FIG. 13 is a diagram showing the error of the OCV estimated value for the second example and the like. The vertical and horizontal axes in FIG. 13 have the same meanings as those in FIG. 12. The estimation errors ΔV2, ΔVC3, and ΔVC4 in FIG. 13 are the OCV estimation errors in the second embodiment, the third comparative example, and the fourth comparative example, respectively. In the second embodiment, the third comparative example, and the fourth comparative example, the data acquisition period td described above was changed from "3 minutes" to "2 minutes." However, the measurement conditions and estimation conditions other than the data acquisition period td are the same as those in the first embodiment, the first comparative example, and the second comparative example, respectively.
[0078] In the third comparative example, as in the first comparative example described above, the error increased mainly at the discharge amount corresponding to the stage change of the graphite structure of the negative electrode. In the fourth comparative example, the OCV estimation error was reduced at the discharge amount where the error was large in the third comparative example, but the OCV estimation error actually increased at some discharge amounts. On the other hand, in the second example, the OCV estimation error was reduced compared to the third comparative example at almost all discharge amounts, and the error was within 10 mV. The results of the second example confirmed that the OCV can be estimated with the same accuracy over a wide SOC range even when the rest period is shortened from 30 minutes to 2 minutes. This makes it possible to quickly obtain a discharge curve used for battery diagnosis.
[0079] [Effects of the embodiment] As described above, according to the above-described embodiment, the calculation unit (400, 401, 404) calculates one or more reference curves v, which are plots of voltage values against elapsed time t in a rest period after energization, measured in advance for a predetermined reference elapsed time t or more for the first secondary battery (10, 100, 510) or another second secondary battery. i (t) from the storage unit 403, and the actual measured value V measured for the first secondary battery (10, 100, 510) during rest over a data acquisition period td shorter than the reference elapsed time tend. mes (t) and based on the relationship, one reference curve v i (t) and the function to select the selected reference curve v iand a function of estimating the open circuit voltage of the first secondary battery (10, 100, 510) based on the voltage value at or after the reference elapsed time (t) tend. This allows the state of the first secondary battery (10, 100, 510) to be estimated quickly and appropriately.
[0080] In addition, the calculation unit (400, 401, 404) calculates each reference curve v i (t) to the first real number (a i ), and multiply the result by a second real number (b i ) to obtain the reference curve v i Corrected reference curve Va corresponding to (t) i (t) and the function to calculate each corrected standard curve Va i (t) and the measured value V mes (t) and the difference value (e i ) is minimized by each standard curve v i (t) corresponds to the first and second real numbers (a i ,b i ) and the function of estimating the open circuit voltage is based on one or more corrected reference curves Va i (t) is the actual measured value V mes (t) and the difference value (e i ) is the minimum corrected standard curve Va i It is more preferable that the voltage value at or after the reference elapsed time (t) is used to estimate the open circuit voltage of the first secondary battery (10, 100, 510). i By calculating (t), the actual measured value V mes (t) and reference curve v i A comparison with (t) can be made more appropriately.
[0081] In addition, the calculation unit (400, 401, 404) calculates the actual measured values V at multiple elapsed times t. mes (t) and the corrected standard curve Va i The sum of the absolute values of the differences with the voltage value at (t) is the difference value (e i ) is more preferable. This makes it possible to obtain the corrected reference curve Va i (t) and the measured value Vmes (t) can be more appropriately compared.
[0082] In addition, the calculation unit (400, 401, 404) calculates the actual measured values V at multiple elapsed times t. mes (t) and the corrected standard curve Va i The sum of the results of multiplying the absolute value of the difference with the voltage value at (t) by a predetermined weighting function (w(t)) is the difference value (e i ) is more preferable. In this way, by applying the weighting function (w(t)), the difference value (e i ) can be obtained.
[0083] In addition, the calculation unit (400, 401, 404) calculates the voltage value and the elapsed time t on a two-dimensional plane with the voltage value and the elapsed time t as axes. mes (t) Multiple measurement points and the corrected reference curve Va for each measurement point i The sum of the distance ΔL from the nearest point at (t) is the difference value (e i ) is even more preferable. This eliminates the need to consider the weighting function w(t), and makes it possible to stabilize the estimation result of the battery state.
[0084] In addition, when a rest period longer than the reference elapsed time "t end " occurs in the first secondary battery (10, 100, 510), the calculation unit (400, 401, 404) calculates a new reference curve v based on the voltage of the first secondary battery (10, 100, 510) during the rest period. i It is more preferable to generate (t) so that a new reference curve can be added while the first secondary battery (10, 100, 510) is in operation.
[0085] Furthermore, it is more preferable that the storage unit 403 communicates with a plurality of secondary battery control devices (500) by wire or wirelessly. i (t) can be shared.
[0086] Furthermore, it is more preferable that the execution unit (410, 412) repeatedly executes a current-carrying operation, which is charging or discharging, and a resting operation for the first secondary battery (10, 100, 510), and the calculation unit (400, 401, 404) further includes a function for acquiring, at each resting operation, a cumulative capacity value that is a capacity value of accumulated charging or discharging in the first secondary battery (10, 100, 510) and an open-circuit voltage estimate value that is an estimate of the open-circuit voltage of the first secondary battery (10, 100, 510), a function for storing the cumulative capacity value and the open-circuit voltage estimate value in the storage unit 403, and a function for acquiring a charge curve or a discharge curve of the first secondary battery (10, 100, 510) based on the cumulative capacity value and the open-circuit voltage estimate value. This makes it possible to acquire a charge curve or a discharge curve of the first secondary battery (10, 100, 510).
[0087] [Variations] The present invention is not limited to the above-described embodiment, and various modifications are possible. The above-described embodiment is an example for explaining the present invention in an easy-to-understand manner, and is not necessarily limited to an embodiment having all of the described configurations. Furthermore, other configurations may be added to the configurations of the above-described embodiment, and some of the configurations may be replaced with other configurations. Furthermore, the control lines and information lines shown in the figures are those considered necessary for explanation, and do not necessarily represent all control lines and information lines necessary in the product. In reality, it can be assumed that almost all configurations are interconnected. Possible modifications of the above-described embodiment include, for example, the following.
[0088] (1) Since the hardware of the control device 500 in the above embodiment can be realized by a general computer, the processes corresponding to the above-mentioned block diagrams and flowcharts, and programs for executing the various processes described above may be stored on a storage medium (a computer-readable storage medium on which a program is recorded) or distributed via a transmission path.
[0089] (2) In the above embodiment, the processes corresponding to the block diagrams and flowcharts, as well as the various other processes described above, are described as software processes using programs. However, some or all of these processes may be replaced with hardware processes using an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array), etc.
[0090] (3) The various processes executed in the above embodiment may be executed by a server computer via a network (not shown), and the various data stored in the above embodiment may also be stored in the server computer. [Explanation of symbols]
[0091] 10 cells (first secondary battery) 100 Battery module (first secondary battery) 400 Battery status acquisition unit (calculation unit) 401 Battery state determination unit (calculation unit) 403 Storage section 404 Battery state calculation unit (calculation unit) 410 Normal operation control unit (execution unit) 412 Diagnostic operation control unit (execution unit) 500 Control device (control device for secondary battery, computer) 510 Battery pack (first secondary battery) t elapsed time td Data acquisition period ΔL distance a i Constant (first real number) b i constant (second real number) e i Total error (difference value) tend Reference elapsed time
Claims
1. an execution unit that executes power supply and power halt for the first secondary battery; and a calculation unit; The calculation unit a function of reading from a storage unit one or more reference curves, which are plots of voltage values against elapsed time during a rest period after energization, measured in advance for a predetermined reference elapsed time or more for the first secondary battery or another second secondary battery; a function of selecting one of the reference curves based on a relationship between the reference curve and actual values measured on the first secondary battery during a rest period over a data acquisition period shorter than the reference elapsed time; and a function of estimating an open circuit voltage of the first secondary battery based on the voltage value at or after the reference elapsed time of the selected reference curve. A control device for a secondary battery.
2. The calculation unit a function of calculating a corrected reference curve corresponding to each of the reference curves by multiplying each of the reference curves by a first real number and adding a second real number to the multiplication result; a function of determining the first and second real numbers corresponding to each of the reference curves so that a difference value between each of the corrected reference curves and the actual measurement value is minimized; The function of estimating the open circuit voltage is to estimate the open circuit voltage of the first secondary battery as the voltage value at or after the reference elapsed time of the corrected reference curve, of which the difference value from the actual measurement value is the smallest, among the one or more corrected reference curves.
2. The secondary battery control device according to claim 1, wherein:
3. The calculation unit The difference value is the sum of absolute values of the differences between the actual measured values at a plurality of elapsed times and the voltage values on the corrected reference curve.
3. The secondary battery control device according to claim 2, wherein:
4. The calculation unit The difference value is the sum of the results obtained by multiplying the absolute values of the differences between the actual measured values at a plurality of elapsed times and the voltage values on the corrected reference curve by a predetermined weighting function.
3. The secondary battery control device according to claim 2, wherein:
5. The calculation unit In a two-dimensional plane having axes of the voltage value and the elapsed time, the sum of distances between a plurality of measurement points based on the elapsed time and the actual measurement values and the nearest points on the corrected reference curve for each of the measurement points is set as the difference value.
3. The secondary battery control device according to claim 2, wherein:
6. The calculation unit When the pause period of the first secondary battery is equal to or longer than the reference elapsed time, a new reference curve is generated based on the voltage of the first secondary battery during the pause period.
3. The secondary battery control device according to claim 2, wherein:
7. The storage unit Communicate with multiple secondary battery control devices via wired or wireless communication 7. The secondary battery control device according to claim 6, wherein:
8. the execution unit repeatedly executes a current-carrying operation, which is charging or discharging, and a pause operation with respect to the first secondary battery; The calculation unit a function of acquiring, each time the pause operation is performed, an accumulated capacity value that is a capacity value of accumulated charge or discharge in the first secondary battery, and an open circuit voltage estimated value that is an estimated value of an open circuit voltage of the first secondary battery; a function of storing the cumulative capacitance value and the estimated open circuit voltage value in the storage unit; and a function of acquiring a charge curve or a discharge curve of the first secondary battery based on the accumulated capacity value and the estimated open circuit voltage value.
8. The secondary battery control device according to claim 1, wherein the secondary battery control device comprises: a power supply;
9. a step of energizing and pausing the first secondary battery; reading out from a storage unit one or more reference curves, which are plots of voltage values against elapsed time during a rest period after energization, measured in advance for a predetermined reference elapsed time or more for the first secondary battery or another second secondary battery; selecting one of the reference curves based on a relationship between the reference curve and actual values measured on the first secondary battery during a rest period over a data acquisition period shorter than the reference elapsed time; and estimating an open circuit voltage of the first secondary battery based on the voltage value at or after the reference elapsed time of the selected reference curve. A method for controlling a secondary battery.
Citation Information
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