Battery diagnostic method, diagnostic device, diagnostic system, and diagnostic program

Abstract

To provide a battery diagnostic method capable of estimating impedance components of a battery and parameters related to the impedance components in detail and appropriately.SOLUTION: A battery diagnostic method according to an embodiment includes measuring the frequency characteristics of the impedance of a battery at each of three or more SOC values different from one another within an SOC range of charging or discharging of the battery under predetermined conditions. The diagnostic method includes calculating a diffusion coefficient of the positive electrode active material of the battery on the basis of the measurement results of the frequency characteristics of the impedance at the lowest SOC value among the three or more SOC values, and calculates a diffusion coefficient of the negative electrode active material of the battery on the basis of the measurement results of the frequency characteristics of the impedance at the highest SOC value among the three or more SOC values.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] An embodiment of the present invention relates to a battery diagnostic method, a diagnostic device, a diagnostic system, and a diagnostic program. [Background technology]

[0002] In recent years, the state of a battery, including its degradation state, has been diagnosed for secondary batteries and other batteries by estimating the capacity and potential of each of the positive and negative electrodes, or by estimating the impedance component of the battery. In diagnosing the state of a battery, for example, the battery is charged or discharged under predetermined conditions, and the time changes in the current and voltage of the battery are measured as a charge curve or a discharge curve. The charge curve or the discharge curve measured during charging or discharging under the predetermined conditions is then analyzed to calculate the capacity and potential of each of the positive and negative electrodes. In diagnosing the state of a battery, for example, a current waveform with a periodically changing current value is input to the battery at each of multiple frequencies, thereby measuring the frequency characteristics of the battery's impedance. Then, one or more of the battery's impedance components are estimated by analyzing the frequency characteristics of the measured battery impedance.

[0003] As described above, in diagnosing the state of a battery, from the viewpoint of improving the accuracy of the diagnosis, it is necessary to estimate the impedance components of the battery and parameters related to the impedance components in a detailed and appropriate manner. For example, by analyzing the frequency characteristics of the impedance of the battery as described above, it is possible to estimate the Warburg impedance (diffusion resistance) of the battery as one of the impedance components. In diagnosing the state of a battery, it is necessary to estimate the impedance components in a more detailed and appropriate manner, for example, by estimating both the components resulting from the diffusion process in the positive electrode and the components resulting from the diffusion process in the negative electrode for the Warburg impedance and parameters related to the Warburg impedance. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2023 / 100241 [Patent Document 2] International Publication No. 2023 / 095263 [Patent Document 3] Japanese Patent Application Laid-Open No. 2024-9689 [Patent Document 4] Japanese Patent Application Publication No. 2018-77259 [Patent Document 5] Japanese Patent Application Publication No. 2020-92598 [Non-patent literature]

[0005] [Non-Patent Document 1] Yukun Xi et al., “Comparative study of the electrochemical performance of LiNi0.5Co0.2Mn0.3O2 and LiNi0.8Co0.1Mn0.1O2 cathode materials for lithium ion batteries” Solid State Ionics 327 (2018), p27-p31 [Non-patent document 2] C. Ho et al., “Application of AC Techniques to the Study of Lithium Diffusion in Tungsten Trioxide Thin Films” Journal of The Electrochemical Society Vol. 127, No. 2, p343-p350, February 1980 Summary of the Invention [Problem to be solved by the invention]

[0006] The problem to be solved by the present invention is to provide a battery diagnostic method, diagnostic device, diagnostic system, and diagnostic program that enable detailed and appropriate estimation of the impedance components of a battery and parameters related to the impedance components. [Means for solving the problem]

[0007] In an embodiment, a battery diagnostic method measures the impedance-frequency characteristics of a battery at three or more different SOC values ​​within a SOC range during charging or discharging of the battery under predetermined conditions. The diagnostic method calculates the diffusion coefficient of the battery's positive electrode active material based on the measurement results of the impedance-frequency characteristics at the lowest SOC value among the three or more SOC values, and calculates the diffusion coefficient of the battery's negative electrode active material based on the measurement results of the impedance-frequency characteristics at the highest SOC value among the three or more SOC values. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a schematic diagram showing an example of a battery diagnostic system according to an embodiment. [Figure 2] FIG. 2 is a schematic diagram illustrating internal state parameters that indicate the internal state of a battery. [Figure 3] FIG. 3 is a schematic diagram illustrating an example of a process for calculating the capacity and potential of each of the positive and negative electrodes of a battery based on the time changes in the current and voltage of the battery during charging under predetermined conditions in an embodiment. [Figure 4] FIG. 4 is a flowchart showing an example of processing performed by a processing circuit or the like by executing a capacity calculation program in the embodiment. [Figure 5] FIG. 5 is a circuit diagram schematically illustrating an example of an equivalent circuit of a battery used in fitting calculations for calculating the impedance component of the battery in the embodiment. [Figure 6] FIG. 6 is a schematic diagram illustrating the impedance components of a battery. [Figure 7]FIG. 7 is a flowchart showing an example of processing performed by a processing circuit or the like by executing an impedance component calculation program in the embodiment. [Figure 8] FIG. 8 is a schematic diagram showing an example of processing using an electrochemical model, which is performed by a processing circuit or the like in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, embodiments will be described with reference to the drawings.

[0010] Fig. 1 is a schematic diagram showing an example of a battery diagnostic system according to an embodiment. As shown in Fig. 1, the diagnostic system 1 includes a battery-equipped device 2 and a diagnostic device 3. The battery-equipped device 2 is equipped with a battery 5, a control circuit 6, a storage medium 7, and a communication module 8. The battery-equipped device 2 also is equipped with a drive circuit 11, a current detection circuit 12, and a voltage detection circuit 13. Examples of the battery-equipped device 2 include large-scale power storage devices for power systems, smartphones, vehicles, stationary power supply devices, robots, drones, etc., and examples of vehicles that can be the battery-equipped device 2 include railcars, electric buses, electric cars, plug-in hybrid cars, and electric motorcycles, etc.

[0011] The battery 5 is a battery that is the target of the diagnosis described below, and is, for example, a secondary battery such as a lithium-ion secondary battery. The battery 5 may be formed from a single cell (single battery), or may be a battery module or cell block formed by electrically connecting a plurality of single cells. When the battery 5 is formed from a plurality of single cells, the plurality of single cells may be electrically connected in series or in parallel. The battery 5 may also have both a series connection structure in which a plurality of single cells are connected in series and a parallel connection structure in which a plurality of single cells are connected in parallel. The battery 5 may also be any of a battery string in which a plurality of battery modules are electrically connected, a battery array, and a storage battery. In one example, in a battery module in which a plurality of single cells are electrically connected, the diagnosis described below may be performed on each of the plurality of single cells as a diagnosis target.

[0012] In the battery-equipped device 2, a BMU (battery management unit) is configured by a control circuit 6 and a storage medium 7. The control circuit 6 manages the battery 5 by controlling the charging and discharging of the battery 5, etc. The control circuit 6 is configured by a processor or an integrated circuit, etc., and the processor that configures the control circuit 6 includes any of a CPU (Central Processing Unit), ASIC (Application Specific Integrated Circuit), microcomputer, FPGA (Field Programmable Gate Array), and DSP (Digital Signal Processor). The control circuit 6 may be configured by one processor or multiple processors. The storage medium 7 is either a main storage device such as a memory or an auxiliary storage device. Examples of the storage medium 7 include a magnetic disk, an optical disk (CD-ROM, CD-R, DVD, etc.), a magneto-optical disk (MO, etc.), and a semiconductor memory. The battery-equipped device 2 may be provided with only one memory or multiple memories that serve as the storage medium 7.

[0013] The communication module 8 is composed of a communication interface of the battery-equipped device 2, etc. The control circuit 6 communicates with processing devices external to the battery-equipped device 2, including the diagnostic device 3, via the communication module 8. The control circuit 6 performs processing by executing programs stored in a storage medium, etc. The programs executed by the control circuit 6 may be stored in a computer (server) connected via a network such as the Internet, or in a server in a cloud environment, etc. In this case, the control circuit 6 downloads the programs via the network. The control circuit 6 also performs processing based on commands received from the outside via the communication module 8.

[0014] The control circuit 6 controls the charging and discharging of the battery 5 by controlling the driving of the drive circuit 11, for example. The control circuit 6 switches between a state in which the battery 5 is charged and a state in which the battery 5 is discharged, for example, by switching the driving state of the drive circuit 11. Furthermore, when the battery 5 is being charged, the control circuit 6 controls the driving of a power supply (not shown) that supplies power to the battery 5 and the driving of the drive circuit 11, thereby adjusting the magnitude of the current input to the battery 5, etc. The power supply that supplies power to the battery 5 may be mounted on the battery-equipped device 2, or may be provided externally to the battery-equipped device 2.

[0015] The current detection circuit 12 and the voltage detection circuit 13 constitute a measurement unit 10 that detects and measures parameters related to the battery 5. The measurement unit 10 periodically measures parameters related to the battery 5 while the battery 5 is being charged or discharged, etc. In the measurement unit 10, the current detection circuit 12 periodically detects and measures the current flowing through the battery 5, and the voltage detection circuit 13 periodically detects and measures the voltage applied to the battery 5, as parameters related to the battery 5. In one example, the measurement unit 10 includes a temperature sensor (not shown) in addition to the current detection circuit 12 and the voltage detection circuit 13. In this case, the temperature sensor periodically detects and measures the temperature of the battery 5 as a parameter related to the battery 5.

[0016] The diagnostic device 3 diagnoses the state of the battery 5 to be diagnosed, including the state of degradation of the battery 5. In one example shown in FIG. 1 etc., the diagnostic device 3 is a processing device (computer) such as a server provided outside the battery-equipped device 2, and is capable of communicating with the battery-equipped device 2 via a network. The diagnostic device 3 includes a processing circuit 21, a storage medium 22, a communication module 23, and a user interface 25. The processing circuit 21 is composed of a processor or an integrated circuit, etc., and the processor, etc. constituting the processing circuit 21 includes any of a CPU, an ASIC, a microcomputer, an FPGA, a DSP, etc. The processing circuit 21 may be composed of one processor, etc., or multiple processors, etc. The storage medium 22 is either a main storage device such as a memory, or an auxiliary storage device. The diagnostic device 3 may be provided with only one memory, etc., serving as the storage medium 22, or with multiple memories, etc.

[0017] The processing circuit 21 performs processing by executing programs and the like stored in the storage medium 22. In the example of FIG. 1 , a data management program 27 and a diagnostic program 28 are stored in the storage medium 22 as programs executed by the processing circuit 21. The processing circuit 21 writes data to the storage medium 22 and reads data from the storage medium 22 by executing the data management program 27. The processing circuit 21 also performs processing for diagnosing the battery 5, which will be described later, by executing the diagnostic program 28. The diagnostic program 28 includes a capacity calculation program 31, an impedance component calculation program 32, and a parameter update program 33. In the example of FIG. 1 , an electrochemical model 35 simulating the battery 5 is stored in the storage medium 22 of the diagnostic device 3.

[0018] In one example, the diagnostic device 3 is configured from a plurality of processing devices (computers), such as a plurality of servers, and the processors of the plurality of processing devices cooperate to perform the processing described below in diagnosing the battery 5. In another example, the diagnostic device 3 is configured from a cloud server in a cloud environment. The infrastructure of the cloud environment is configured from a virtual processor, such as a virtual CPU, and a cloud memory. Therefore, when the diagnostic device 3 is configured from a cloud server, the virtual processor performs the processing described below in diagnosing the battery 5, instead of the processing circuit 21. And the cloud memory has the function of storing programs, data, etc., similar to the storage medium 22.

[0019] In one example, the program executed by the processing circuit 21 and the storage medium 22 storing data used in the processing of the processing circuit 21 are provided in a computer separate from the battery-equipped device 2 and the diagnostic device 3. In this case, the diagnostic device 3 is connected via a network to the computer in which the storage medium 22 and the like are provided. In another example, the diagnostic device 3 is mounted on the battery-equipped device 2. In this case, in the diagnostic device 3, a processor or the like mounted on the battery-equipped device 2 performs the below-described processing for diagnosing the battery 5 in place of the processing circuit 21.

[0020] The communication module 23 is composed of a communication interface and the like of a processing device that constitutes the diagnostic device 3. The processing circuit 21 communicates with devices and the like external to the diagnostic device 3, including the battery-equipped device 2, via the communication module 23. Operations and the like related to the diagnosis of the battery 5 are input to the user interface 25 by users and the like of the diagnostic device 3 and the diagnostic system 1. For this reason, the user interface 25 is provided with any of buttons, a mouse, a touch panel, a keyboard, and the like as an operation unit through which operations are input by users and the like. The user interface 25 also has a notification unit that notifies information related to the diagnosis of the battery 5. The notification unit notifies the information by either a screen display or sound emission, etc. Note that the user interface 25 may be provided separately from the processing device that constitutes the diagnostic device 3.

[0021] In the embodiment, the diagnostic device 3 and the like perform the following processing in diagnosing the state of the battery 5, including the degradation state of the battery 5. The state of the battery 5 is diagnosed by the processing circuit 21 and the like executing the diagnostic program 28. When diagnosing the state of the battery 5, the processing circuit 21 of the diagnostic device 3 transmits a command to measure measurement data to be used for diagnosis to the battery-equipped device 2 via the communication module 23. Then, the control circuit 6 of the battery-equipped device 2 measures the measurement data in response to receiving the command from the diagnostic device 3 via the communication module 8. Then, after measuring the measurement data, the control circuit 6 of the battery-equipped device 2 transmits the measurement data to the diagnostic device 3 via the communication module 8. Then, the processing circuit 21 of the diagnostic device 3 receives the measurement data from the battery-equipped device 2 via the communication module 23 and acquires the measurement data.

[0022] To measure the measurement data, the control circuit 6 charges or discharges the battery 5 under predetermined conditions by controlling the drive circuit 11 and the power supply, etc. Then, while the battery 5 is being charged or discharged under the predetermined conditions, the measurement unit 10 measures the above-mentioned parameters related to the battery 5 at each of a plurality of measurement points. At this time, the current detection circuit 12 measures the current of the battery 5 at each of the plurality of measurement points, and the voltage detection circuit 13 measures the voltage of the battery 5 at each of the plurality of measurement points. Furthermore, in one example, the measurement unit 10 measures the temperature of the battery 5 in addition to the current and voltage of the battery 5 at each of the plurality of measurement points.

[0023] Since the measurement of the parameters related to the battery 5 is performed as described above during charging or discharging of the battery 5 under predetermined conditions, the measurement data acquired by the processing circuit 21 indicates the time changes (time history) of the parameters related to the battery 5 during charging or discharging under the predetermined conditions. Therefore, the measurement data indicates the time changes (time history) of the current and voltage of the battery 5 during charging or discharging under the predetermined conditions. In other words, the measurement data indicates the charge curve or discharge curve of the battery 5 during charging or discharging under the predetermined conditions. Furthermore, in one example, the measurement data indicates the time changes (time history) of the temperature of the battery 5 during charging or discharging under the predetermined conditions in addition to the current and voltage of the battery 5.

[0024] Here, the predetermined conditions for charging or discharging include the C rate during charging or discharging and the SOC range of the battery 5 during charging or discharging. In one example, in addition to the C rate and SOC range, the temperature range of the battery 5 during charging or discharging is specified as the predetermined conditions. While the battery 5 is being charged or discharged under the predetermined conditions, the battery 5 is charged or discharged at the C rate specified as the predetermined condition, and the battery 5 is charged or discharged in a state where the SOC value of the battery 5 falls within the SOC range specified as the predetermined condition. The C rate specified as the predetermined condition is set to a relatively low value, for example, 0.1 C or less.

[0025] The SOC range that satisfies the predetermined condition is set to be equal to or greater than the lower limit SOC value ηl and equal to or less than the upper limit SOC value ηu. Furthermore, when charging or discharging under the predetermined condition, a start SOC value, which is the SOC value of the battery 5 at the start of charging or discharging, and a finish SOC value, which is the SOC value of the battery 5 at the end of charging or discharging, are specified as the predetermined condition. When charging the battery 5 under the predetermined condition, the start SOC value is set to the lower limit SOC value ηl, and the finish SOC value is set to the upper limit SOC value ηu. When discharging the battery 5 under the predetermined condition, the start SOC value is set to the upper limit SOC value ηu, and the finish SOC value is set to the lower limit SOC value ηl.

[0026] In this embodiment, at least one of the control circuit 6 of the battery-equipped device 2 and the processing circuit 21 of the diagnostic device 3 calculates the charge amount (charge amount) and SOC value of the battery 5 based on the measurement results of the measurement unit 10 of parameters related to the battery 5, including the current and voltage of the battery 5. At this time, the charge amount and SOC value of the battery 5 are calculated for each of multiple measurement points at which the current and voltage of the battery 5 are measured. Therefore, at least one of the control circuit 6 and the processing circuit 21 calculates the time changes (time history) of the charge amount and SOC of the battery 5.

[0027] In one example, the real-time charge amount of the battery 5 is calculated based on the charge amount of the battery 5 at a predetermined time point and the change in the current of the battery 5 over time from the predetermined time point. For example, the real-time charge amount of the battery 5 is calculated by adding the time-integrated value of the current of the battery 5 from the predetermined time point to the charge amount of the battery 5 at the predetermined time point. In another example, data indicating the relationship between the charge amount and the voltage of the battery 5 is stored in the storage medium 22 or the like. Then, the real-time charge amount of the battery 5 is calculated based on the real-time voltage of the battery 5 and the data indicating the relationship between the charge amount and the voltage of the battery 5.

[0028] Furthermore, for the battery 5, a lower limit voltage Vl and an upper limit voltage Vu are specified for voltage. For the battery 5, a state in which the voltage during charging or discharging under specific conditions reaches the lower limit voltage Vl is specified as a state in which the SOC value is 0%, and a state in which the voltage during charging or discharging under specific conditions reaches the upper limit voltage Vu is specified as a state in which the SOC value is 100%. For the battery 5, the charge capacity (charge charge amount) during charging under specific conditions until the SOC value changes from 0% to 100% or the discharge capacity (discharge charge amount) during discharging under specific conditions until the SOC value changes from 100% to 0% is specified as the battery capacity. The SOC value of the battery 5 is the ratio of the remaining charge (remaining capacity) until the SOC value reaches 0 to the battery capacity of the battery 5. Note that the specific conditions used to specify the lower limit voltage Vl, the upper limit voltage Vu, and the battery capacity may be set to the same conditions as the above-mentioned predetermined conditions, or may be set to conditions different from the above-mentioned predetermined conditions, such as the C rate and temperature range.

[0029] In this embodiment, the control circuit 6 and the processing circuit 21 charge or discharge the battery 5 under the predetermined conditions as described above, and measure the frequency characteristics of the impedance of the battery 5 at each of three or more different SOC values ​​within the SOC range defined as the predetermined conditions. As a result, the frequency characteristics of the impedance of the battery 5 are measured at each of three or more SOC values ​​within the SOC range equal to or greater than the lower limit SOC value ηl and equal to or less than the upper limit SOC value ηu.

[0030] When measuring the frequency characteristics of the impedance of the battery 5 at each of three or more SOC values, the control circuit 6 of the battery-equipped device 2 controls the drive circuit 11 and power supply in response to commands from the diagnostic device 3, thereby causing a current to flow through the battery 5 with a current waveform whose current value changes periodically. As a result, a current waveform whose current value changes periodically is input to the battery 5. At this time, the control circuit 6 inputs a current waveform whose current value changes periodically at each of a plurality of frequencies to the battery 5. The current waveform input to the battery 5 when measuring the frequency characteristics of the impedance may be a sine wave (sine wave), or may be a current waveform other than a sine wave, such as a triangular wave or a sawtooth wave.

[0031] In one example, in measuring the frequency characteristics of the impedance of the battery 5, an AC current having a current waveform whose flow direction changes periodically is input to the battery 5. In another example, while the battery 5 is being charged or discharged under the predetermined conditions described above, an AC current waveform is superimposed on the charging current or discharging current of the battery 5. In this case, the superimposed current, in which the AC current waveform is superimposed on the charging current or discharging current, has a current value that changes periodically around the locus of the time change of the charging current or discharging current. For example, the superimposed current has a current value that changes periodically around a C rate that is set as a predetermined condition.

[0032] The measurement unit 10 uses the current detection circuit 12 and voltage detection circuit 13 to measure the current and voltage of the battery 5 at each of a plurality of measurement points in a state in which a current waveform whose current value changes periodically as described above is being input to the battery 5. The control circuit 6 then transmits the measurement results of the current and voltage of the battery 5 in a state in which a current waveform whose current value changes periodically to the battery 5 as part of the measurement data to the diagnostic device 3 via the communication module 8. Therefore, the measurement data acquired by the processing circuit 21 of the diagnostic device 3 indicates the time changes (time history) of the current and voltage of the battery 5 in a state in which a current waveform whose current value changes periodically is being input to the battery 5.

[0033] When measuring the frequency characteristics of the impedance of the battery 5 for each of three or more SOC values, the processing circuit 21 calculates the frequency characteristics of the impedance of the battery 5 based on the time changes in the current and voltage of the battery 5 when a current waveform whose current value changes periodically is input to the battery 5. In one example, a current waveform is input to the battery 5 at each of a plurality of frequencies, and the processing circuit 21 etc. calculates, for each of the plurality of frequencies, the peak-to-peak value (fluctuation range) of the periodic change in the current of the battery 5 and the peak-to-peak value (fluctuation range) of the periodic change in the voltage of the battery 5. Then, the processing circuit 21 etc. calculates the impedance of the battery 5 from the ratio of the peak-to-peak value of the voltage to the peak-to-peak value of the current for each of the plurality of frequencies. As a result, the impedance of the battery 5 at each of the plurality of frequencies is calculated as the frequency characteristics of the impedance of the battery 5.

[0034] In another example, while a current waveform of a reference frequency is being input to the battery 5, the time changes of the current and voltage of the battery 5 are measured. Then, the processing circuitry 21, etc. performs a Fourier transform on the time changes of the current and voltage of the battery 5 while the current waveform is being input to the battery 5, and calculates the frequency spectrum of the current and voltage of the battery 5 as the frequency characteristics of the current and voltage of the battery 5. The calculated frequency spectrum of the current and voltage of the battery 5 includes components of the reference frequency as well as integer multiples of the reference frequency. Then, based on the frequency characteristics of the current and voltage of the battery 5, the processing circuitry 21, etc. calculates an autocorrelation function of the time change of the current of the battery 5 and a cross-correlation function between the time change of the current and the time change of the voltage of the battery 5. Then, the processing circuitry 21, etc. calculates the frequency characteristics of the impedance of the battery 5 using the autocorrelation function and the cross-correlation function. At this time, the frequency characteristics of the impedance are calculated, for example, by dividing the cross-correlation function by the autocorrelation function.

[0035] When measuring the frequency characteristics of the impedance of the battery 5 for each of three or more SOC values, for example, a complex impedance plot (Cole-Cole plot) of the impedance is obtained as a measurement result of the frequency characteristics of the impedance. The complex impedance plot shows the impedance of the battery 5 for each of a plurality (numerous) frequencies. The complex impedance plot also shows the real component and the imaginary component of the impedance of the battery 5 for each of the plurality of frequencies.

[0036] A method for measuring the frequency characteristics of the impedance of a battery by inputting a current waveform whose current value changes periodically to the battery is shown in Patent Document 1 (WO 2023 / 100241), Patent Document 2 (WO 2023 / 095263), Patent Document 3 (JP 2024-9689 A), etc. In addition, a complex impedance plot is shown in Patent Document 2 and Non-Patent Document 1 (Yukun Xi et al., "Comparative study of the electrochemical performance of LiNi 0.5 Co 0.2 Mn 0.3 O2 and LiNi 0.8 Co 0.1 Mn 0.1 O2cathode materials for lithium ion batteries” Solid State Ionics 327 (2018), p27-p31) and Non-Patent Document 2 (C. Ho et al., “Application of AC Techniques to the Study of Lithium Diffusion in Tungsten Trioxide Thin Films” Journal of The Electrochemical Society Vol. 127, No. 2, p343-p350, February 1980) and others.

[0037] Here, the highest maximum SOC value ηmax and the lowest minimum SOC value ηmin are defined among the three or more SOC values ​​for which the frequency characteristics of the impedance of the battery 5 are measured. In this embodiment, the frequency characteristics of the impedance of the battery 5 are measured for each of the three or more SOC values, so the frequency characteristics of the impedance are measured for each of the highest SOC value ηmax and the lowest SOC value ηmin, and the frequency characteristics of the impedance are measured for one or more SOC values ​​between the highest SOC value ηmax and the lowest SOC value ηmin.

[0038] Furthermore, the three or more SOC values ​​including the maximum SOC value ηmax and the minimum SOC value ηmin, i.e., the three or more SOC values ​​measured using the impedance-frequency characteristics, fall within the SOC range for charging or discharging under the specified conditions. Therefore, the minimum SOC value ηmin is equal to or greater than the lower limit SOC value ηl of the SOC range for charging or discharging under the specified conditions, and all SOC values ​​other than the minimum SOC value ηmin among the three or more SOC values ​​are higher than the lower limit SOC value ηl. Furthermore, the maximum SOC value ηmax is equal to or less than the upper limit SOC value ηu of the SOC range for charging or discharging under the specified conditions, and all SOC values ​​other than the maximum SOC value ηmax among the three or more SOC values ​​are lower than the upper limit SOC value ηu.

[0039] In a preferred example of the embodiment, a minimum SOC value ηmin between 0% and 5% is set as the minimum SOC value ηmin, and the frequency characteristics of the impedance of the battery 5 at the minimum SOC value ηmin are measured. Then, a maximum SOC value ηmax between 95% and 100% is set as the maximum SOC value ηmax, and the frequency characteristics of the impedance at the maximum SOC value ηmax are measured. Therefore, in this example, the lower limit SOC value ηl of the SOC range for charging or discharging under predetermined conditions is set to an SOC value between 0% and 5% and equal to or less than the minimum SOC value ηmin. Then, the upper limit SOC value ηu of the SOC range for charging or discharging under predetermined conditions is set to an SOC value between 95% and 100% and equal to or greater than the maximum SOC value ηmax.

[0040] In the preferred example described above, the impedance frequency characteristics of the battery 5 are measured at one or more SOC values ​​in the range of more than 5% and less than 95%, in addition to the minimum SOC value ηmin and the maximum SOC value ηmax. Therefore, the three or more SOC values ​​at which the impedance frequency is measured include the minimum SOC value ηmin and the maximum SOC value ηmax described above, as well as one or more SOC values ​​in the range of more than 5% and less than 95%.

[0041] Furthermore, in this embodiment, similar to the above-described preferred example, it is more preferable to measure the impedance frequency characteristics of the battery 5 at each of the minimum SOC value ηmin and the maximum SOC value ηmax, and also at one or more SOC values ​​in the range of 40% to 60%. In this case, the three or more SOC values ​​at which the impedance frequency is measured include the above-described minimum SOC value ηmin and maximum SOC value ηmax, as well as one or more SOC values ​​in the range of 40% to 60%.

[0042] In one embodiment, in diagnosing the state of the battery 5, the battery 5 is charged under predetermined conditions, and the SOC value of the battery 5 reaches the minimum SOC value ηmin either before or immediately after the start of charging under the predetermined conditions. Then, the impedance-frequency characteristics are measured for the battery 5 at the minimum SOC value ηmin before or immediately after the start of charging under the predetermined conditions. When measuring the impedance-frequency characteristics at the minimum SOC value ηmin before the start of charging, the minimum SOC value ηmin will be the same height as the lower-limit SOC value ηl of the SOC range for charging under the predetermined conditions. Furthermore, when measuring the impedance-frequency characteristics at the minimum SOC value ηmin immediately after the start of charging, the minimum SOC value ηmin will be the same height as the lower-limit SOC value ηl or slightly higher than the lower-limit SOC value ηl.

[0043] In this example, the SOC value of the battery 5 reaches the maximum SOC value ηmax either after or immediately before the end of charging under the specified conditions. Then, the impedance-frequency characteristics are measured for the battery 5 at the maximum SOC value ηmax after or immediately before the end of charging under the specified conditions. When measuring the impedance-frequency characteristics at the maximum SOC value ηmax after the end of charging, the maximum SOC value ηmax will be the same as the upper limit SOC value ηu of the SOC range of charging under the specified conditions. When measuring the impedance-frequency characteristics at the maximum SOC value ηmax immediately before the end of charging, the maximum SOC value ηmax will be the same as or slightly lower than the upper limit SOC value ηu.

[0044] In this example, the impedance frequency characteristics of the battery 5 are measured at one or more SOC values ​​while the SOC value of the battery 5 increases from the minimum SOC value ηmin to the maximum SOC value ηmax during charging under predetermined conditions. By measuring the impedance frequency characteristics as described above, in this example, the impedance frequency characteristics of the battery 5 are measured for each of three or more SOC values ​​including the minimum SOC value ηmin and the maximum SOC value ηmax within the SOC range of charging under predetermined conditions, i.e., within the SOC range that is equal to or greater than the lower limit SOC value ηl, which is the starting SOC value, and equal to or less than the upper limit SOC value ηu, which is the ending SOC value.

[0045] In another example of the embodiment, in diagnosing the state of the battery 5, the battery 5 is discharged under predetermined conditions, and the SOC value of the battery 5 reaches the maximum SOC value ηmax either before or immediately after the start of discharge under the predetermined conditions. Then, the impedance-frequency characteristics are measured for the battery 5 at the maximum SOC value ηmax before or immediately after the start of discharge under the predetermined conditions. When the impedance-frequency characteristics at the maximum SOC value ηmax are measured before the start of discharge, the maximum SOC value ηmax has the same height as the upper limit SOC value ηu of the SOC range of discharge under the predetermined conditions. Furthermore, when the impedance-frequency characteristics at the maximum SOC value ηmax are measured immediately after the start of discharge, the maximum SOC value ηmax has the same height as the upper limit SOC value ηu or is slightly lower than the upper limit SOC value ηu.

[0046] In this example, the SOC value of the battery 5 becomes the minimum SOC value ηmin either after or immediately before the end of discharge under the specified conditions. Then, the impedance frequency characteristics are measured for the battery 5 with the minimum SOC value ηmin after or immediately before the end of discharge under the specified conditions. When measuring the impedance frequency characteristics at the minimum SOC value ηmin after the end of discharge, the minimum SOC value ηmin is the same as the lower limit SOC value ηl of the SOC range of discharge under the specified conditions. When measuring the impedance frequency characteristics at the minimum SOC value ηmin immediately before the end of discharge, the minimum SOC value ηmin is the same as or slightly higher than the lower limit SOC value ηl.

[0047] In this example, the impedance frequency characteristics of the battery 5 are measured at one or more SOC values ​​while the SOC value of the battery 5 decreases from the maximum SOC value ηmax to the minimum SOC value ηmin due to discharge under predetermined conditions. By measuring the impedance frequency characteristics as described above, in this example, the impedance frequency characteristics of the battery 5 are measured for each of three or more SOC values ​​including the minimum SOC value ηmin and the maximum SOC value ηmax within the SOC range of discharge under predetermined conditions, i.e., within the SOC range that is equal to or less than the upper limit SOC value ηu, which is the start SOC value, and equal to or greater than the lower limit SOC value ηl, which is the end SOC value.

[0048] In the embodiments and the like, in diagnosing the state of the battery 5, the processing circuit 21 acquires, as part of the measurement data, the time changes of the current and voltage of the battery 5 during charging or discharging under predetermined conditions, as described above. Also, the processing circuit 21 measures the frequency characteristics of the impedance of the battery 5 at each of three or more different SOC values ​​within the SOC range of charging or discharging the battery 5 under the predetermined conditions, as described above, and the three or more SOC values ​​for which the frequency characteristics of the impedance are measured include the maximum SOC value ηmax and the minimum SOC value ηmin.

[0049] The processing circuitry 21 etc. estimates the internal state of the battery 5 based on the time changes in the current and voltage of the battery 5 during charging or discharging under predetermined conditions. At this time, the processing circuitry 21 etc. calculates the capacity, potential and parameters related thereto for each of the positive and negative electrodes of the battery 5 based on the time changes in the current and voltage. The calculation of the capacity, potential and the like for each of the positive and negative electrodes of the battery 5 and the estimation of the internal state of the battery 5 are performed by the processing circuitry 21 etc. executing a capacity calculation program 31.

[0050] In estimating the internal state of the battery 5, internal state parameters of the battery 5 are calculated. The internal state parameters include a positive electrode capacity Mp, which is the capacity of the positive electrode, a parameter related to the positive electrode capacity Mp, a parameter related to the potential of the positive electrode, and a parameter related to the charge amount (charge amount) of the positive electrode. The internal state parameters also include a negative electrode capacity Mn, which is the capacity of the negative electrode, a parameter related to the negative electrode capacity Mn, a parameter related to the potential of the negative electrode, and a parameter related to the charge amount (charge amount) of the negative electrode.

[0051] In calculating the capacity and potential of each of the positive and negative electrodes of the battery 5 and estimating the internal state of the battery 5, the processing circuit 21 etc. analyzes the time changes in the current and voltage of the battery 5 during charging or discharging under predetermined conditions. That is, an analysis of the charge curve of the battery 5 during charging under predetermined conditions or an analysis of the discharge curve of the battery 5 during discharging under predetermined conditions is performed. Note that in calculating the capacity and potential of each of the positive and negative electrodes of the battery 5 and estimating the internal state of the battery 5, in addition to the time changes in the current and voltage of the battery 5 during charging or discharging under predetermined conditions, the time changes in the temperature of the battery 5 may also be analyzed.

[0052] FIG. 2 is a schematic diagram illustrating internal state parameters that indicate the internal state of a battery. In FIG. 2, the horizontal axis represents the charge Q, and the vertical axis represents the potential E. As shown in FIG. 2, in battery 5, a lower limit potential Epl and an upper limit potential Epu are defined for the positive electrode potential, which is the potential of the positive electrode. The positive electrode potential increases as the charge (charge amount) of the positive electrode increases. Furthermore, the charge amount when the positive electrode potential is at the lower limit potential Epl is the initial charge (initial charge amount) Qpl of the positive electrode, and the charge amount when the positive electrode potential is at the upper limit potential Epu is the upper limit charge (upper limit charge amount) Qpu of the positive electrode. The charge amount of the positive electrode from the initial charge Qpl to the upper limit charge Qpu is the positive electrode capacity Mp of battery 5, which corresponds to the amount of charge and discharge that the positive electrode of battery 5 can perform.

[0053] In addition, in the battery 5, a lower limit potential Enl and an upper limit potential Enu are defined for the negative electrode potential, which is the potential of the negative electrode, and the negative electrode potential decreases as the charge amount (charge amount) of the negative electrode increases. In addition, in the negative electrode, the charge amount when the negative electrode potential is at the upper limit potential Enu is the initial charge amount (initial charge amount) Qnl of the negative electrode, and the charge amount when the negative electrode potential is at the lower limit potential Enl is the upper limit charge amount (upper limit charge amount) Qnu of the negative electrode. The charge amount of the negative electrode from the initial charge amount Qnl to the upper limit charge amount Qnu is the negative electrode capacity Mn of the battery 5, which corresponds to the amount that the negative electrode of the battery 5 can charge and discharge.

[0054] The internal state parameters of the battery 5 include the positive electrode capacity Mp and the negative electrode capacity Mn as described above, as well as the initial positive electrode charge Qp1 and the initial negative electrode charge Qn1. The internal state parameters of the battery 5 also include the positive electrode mass, which is a parameter corresponding to the positive electrode capacity Mp, and the negative electrode mass, which is a parameter corresponding to the negative electrode capacity Mn. The positive electrode mass can be calculated based on the positive electrode capacity Mp and the type of material forming the positive electrode. Similarly, the negative electrode mass can be calculated based on the negative electrode capacity Mn and the type of material forming the negative electrode. The internal state parameters of the battery 5 also include the positive electrode capacity retention rate and the negative electrode capacity retention rate. Here, the positive electrode capacity retention rate is the ratio of the estimated positive electrode capacity to the positive electrode capacity at the start of use, and the negative electrode capacity retention rate is the ratio of the estimated negative electrode capacity to the negative electrode capacity at the start of use.

[0055] The internal state parameters of the battery 5 also include an operation window shift (SOW), which is the difference between the initial charge Qp1 of the positive electrode and the initial charge Qn1 of the negative electrode. The operation window shift is a parameter related to the charge and potential of the positive electrode, as well as the charge and potential of the negative electrode. The internal state parameters of the battery 5 also include a parameter related to the resistance component of the battery 5. Note that FIG. 2 also shows the battery capacity Mb of the battery 5. As described above, the battery capacity Mb corresponds to the amount of charge required for the voltage of the battery 5 (the difference between the positive electrode potential and the negative electrode potential) to change from the lower limit voltage Vl to the upper limit voltage Vu.

[0056] In this embodiment, relationship data indicating the relationship between the internal state of the battery 5 and at least one of the voltage and current of the battery 5 is stored in the storage medium 22 or the like. The relationship data indicates a formula or function or the like for calculating at least one of the voltage and current of the battery 5 using any of the internal state parameters described above, for example, a formula or the like for calculating the voltage of the battery 5 using at least the positive electrode capacity Mp, the negative electrode capacity Mn, the initial positive electrode charge Qp1, and the initial negative electrode charge Qn1. Note that the relationship data may indicate the relationship between the internal state of the battery 5 and at least one of the current and voltage for each of a plurality of temperatures that are different from each other.

[0057] When analyzing a charge curve of the battery 5 during charging under predetermined conditions or a discharge curve of the battery 5 during discharging under predetermined conditions, the processing circuit 21 and the like perform a fitting calculation (regression calculation) using at least the time changes in the voltage and current of the battery 5 indicated by the measurement data and the relationship between the internal state of the battery 5 and at least one of the current and voltage of the battery 5 indicated by the relationship data. At this time, the fitting calculation is performed using one or more internal state parameters as variables in a calculation formula or the like that calculates at least the voltage and current of the battery 5 from the internal state of the battery 5, and the internal state parameters that serve as variables are calculated. Furthermore, in the fitting calculation, for example, for each amount of charge measured for the voltage of the battery 5, the values ​​of the internal state parameters that serve as variables are determined so that the difference between the voltage calculation result using the calculation formula or the like indicated by the relationship data and the voltage measurement result in the measurement data is as small as possible.

[0058] The processing circuit 21 and the like perform fitting calculations as described above to calculate one or more internal state parameters that serve as variables in the fitting calculations. This allows, for example, the positive electrode capacity Mp and the negative electrode capacity Mn to be calculated, as well as the initial positive electrode charge Qp1, which is a parameter related to the potential and charge amount of the positive electrode, and the initial negative electrode charge Qn1, which is a parameter related to the potential and charge amount of the negative electrode. Methods for calculating the internal state parameters of a battery by analyzing a charge curve of a battery during charging under specified conditions are disclosed in Patent Document 4 (JP 2018-77259 A) and Patent Document 5 (JP 2020-92598 A), among others. Patent Documents 4 and 5 also calculate the internal state parameters of a battery by performing fitting calculations using at least the measurement results of the time changes in the battery current and voltage during charging under specified conditions and the relationship between the internal state of the battery and the battery voltage and current.

[0059] Furthermore, in analyzing the charge curve or discharge curve, the processing circuit 21 and the like use the calculation results of internal state parameters including the positive electrode capacity Mp and the negative electrode capacity Mn to calculate the potentials of the positive electrode and the negative electrode, and the relationship of the potentials of the positive electrode and the negative electrode to the charge amount of the battery 5. In one example, the calculation results of the internal state parameters are used to calculate the relationship of the potentials of the positive electrode and the negative electrode to the charge amount of the battery 5 when charging or discharging is performed under the above-mentioned predetermined conditions. In another example, the calculation results of the internal state parameters are used to calculate the relationship of the open circuit potentials of the positive electrode and the negative electrode to the charge amount of the battery 5.

[0060] In the embodiments and the like, the relationship data indicates, for example, a calculation formula for calculating the potential of each of the positive electrode and the negative electrode using the internal state parameters. In one example, the relationship data indicates, for example, a calculation formula for calculating the positive electrode potential using the positive electrode capacity Mp, the initial charge amount Qp1 of the positive electrode, and the charge amount Q of the battery 5, and a calculation formula for calculating the negative electrode potential using the negative electrode capacity Mn, the initial charge amount Qn1 of the negative electrode, and the charge amount Q of the battery 5. The processing circuitry 21 and the like then calculate the positive electrode potential and the relationship of the positive electrode potential with respect to the charge amount Q of the battery 5 based on the calculation results of the positive electrode capacity Mp and the initial charge amount Qp1 of the positive electrode obtained by the fitting calculation and the calculation formula indicated in the relationship data. The processing circuitry 21 and the like also calculate the negative electrode potential and the relationship of the negative electrode potential with respect to the charge amount Q of the battery 5 based on the calculation results of the negative electrode capacity Mn and the initial charge amount Qn1 of the negative electrode obtained by the fitting calculation and the calculation formula indicated in the relationship data.

[0061] Formulas for calculating the potentials of the positive electrode and the negative electrode using the internal state parameters are shown in Patent Documents 4 and 5. Patent Documents 4 and 5 also show methods for calculating the internal state parameters by fitting calculation as described above, and then using the calculated internal state parameters to calculate the potentials of the positive electrode and the negative electrode, and the relationship between the charge amount of the battery and the potentials of the positive electrode and the negative electrode.

[0062] FIG. 3 is a schematic diagram illustrating an example of a process for calculating the capacity and potential of each of the positive and negative electrodes of a battery based on the time changes in the current and voltage of the battery during charging under predetermined conditions in an embodiment. In the example of FIG. 3, the time change in the charge Q of the battery 5 during charging under predetermined conditions is calculated based on the time changes in the current and voltage of the battery 5 during charging under predetermined conditions. Then, the relationship shown in graph β1 of FIG. 3 is calculated as the relationship between the charge Q of the battery 5 and the voltage V of the battery 5 during charging under predetermined conditions. In graph β1 of FIG. 3, the horizontal axis represents the charge Q, and the vertical axis represents the voltage V. In addition, in graph β1, the relationship between the charge Q and the voltage V of the battery 5 is shown as a charging curve V(Q).

[0063] In the example of Figure 3, the capacity, potential, etc. are calculated for each of the positive electrode and negative electrode of the battery 5 by, for example, analyzing the charging curve V(Q). At this time, as described above, a fitting calculation is performed using at least the charging curve V(Q) and the relationship between the internal state and at least one of the current and voltage of the battery 5 shown in the relationship data, and internal state parameters including the positive electrode capacity Mp and the negative electrode capacity Mn, etc. are calculated. Then, the relationship between the charge amount Q and the potential of each of the positive electrode and negative electrode is calculated using the calculation results of the internal state parameters obtained by the fitting calculation and equations for calculating the potentials of each of the positive electrode and negative electrode from the internal state parameters.

[0064] In the example of Fig. 3, the relationship shown in graph β2 is calculated as the relationship between the charge amount Q of battery 5 and the potentials of the positive and negative electrodes during charging under specified conditions. In graph β2 of Fig. 3, the horizontal axis represents the charge amount Q, and the vertical axis represents the potential E. Also in graph β2, the relationship between the charge amount Q and the positive electrode potential Ep is shown by the positive electrode potential curve Ep(Q), and the relationship between the charge amount Q and the negative electrode potential En is shown by the negative electrode potential curve En(Q).

[0065] Fig. 4 is a flowchart showing an example of processing performed by a processing circuit, etc., by executing a capacity calculation program in an embodiment. The example processing of Fig. 4 is performed each time the battery 5 is charged or discharged under predetermined conditions and the time changes in the current and voltage of the battery 5 during charging or discharging under the predetermined conditions are measured by the measurement unit 10, etc. When the example processing of Fig. 4 is started, the processing circuit 21, etc., acquires the time changes in the current and voltage of the battery 5 during charging or discharging under the predetermined conditions as part of the measurement data (S101).

[0066] The processing circuitry 21 etc. then performs fitting calculations using at least the time changes in the current and voltage of the battery 5 and the relationship of the internal state to at least one of the current and voltage of the battery 5, and calculates internal state parameters including the positive electrode capacity Mp and the negative electrode capacity Mn etc. through the fitting calculations (S102).The processing circuitry 21 etc. then calculates the potentials of the positive electrode and the negative electrode and the relationship between the charge amount Q and the potentials of the positive electrode and the negative electrode using the calculation results of the internal state parameters and equations for calculating the potentials of the positive electrode and the negative electrode from the internal state parameters (S103).

[0067] In the embodiments and the like, in diagnosing the state of the battery 5, the processing circuitry 21 and the like estimate and calculate the impedance components and parameters related to the impedance components of the battery 5 by, for example, analyzing the frequency characteristics of the impedance of the battery 5 at each of the three or more SOC values ​​described above. The calculation of the impedance components and parameters related to the impedance components of the battery 5 is performed by the processing circuitry 21 and the like executing the impedance component calculation program 32.

[0068] Here, the impedance components of the battery 5 include the contact resistance, the charge transfer impedance of each of the positive and negative electrodes, and the Warburg impedance. The contact resistance is also called ohmic resistance and includes a resistance component in the lithium transfer process in the electrolyte, etc. The charge transfer impedance corresponds to the impedance component generated in the charge transfer process, which is one of the processes constituting the reaction, in each of the positive and negative electrodes. In the charge transfer impedance of each of the positive and negative electrodes, the resistance component is also called charge transfer resistance. The Warburg impedance corresponds to the impedance component generated in the ion diffusion process and is also called diffusion resistance. The Warburg impedance includes an impedance component resulting from the diffusion process in the positive electrode (positive electrode active material) and an impedance component resulting from the diffusion process in the negative electrode (negative electrode active material).

[0069] The storage medium 22 stores an equivalent circuit model including information related to the equivalent circuit of the battery 5. In the equivalent circuit of the equivalent circuit model, a plurality of circuit parameters (circuit constants) corresponding to the impedance components of the battery 5 are set. The circuit parameters are parameters that indicate the electrical characteristics of the circuit elements provided in the equivalent circuit. For example, the equivalent circuit includes resistors, capacitors, and impedance elements as circuit elements, and resistance, capacitance (capacitance), impedance, etc. are set for the resistors, capacitors, and impedance elements, respectively, as circuit parameters. Furthermore, when a constant phase element (CPE) is used instead of a capacitor as a circuit element of the equivalent circuit, capacitance and Debye's empirical parameters are set as the circuit parameters of the CPE. In one example, at least the contact resistance, the charge transfer resistance of each of the positive and negative electrodes, and the Warburg impedance are set as circuit parameters in the equivalent circuit.

[0070] Furthermore, the equivalent circuit model stored in the storage medium 22 indicates the relationship between the circuit parameters of the equivalent circuit and the impedance of the battery 5. The relationship between the circuit parameters and the impedance of the battery 5 may, for example, be represented by a formula for calculating the real and imaginary components of the impedance from the circuit parameters (circuit constants). In this case, the formula calculates the real and imaginary components of the impedance of the battery 5 using the circuit parameters, frequency, etc. In diagnosing the state of the battery 5, the processing circuit 21 calculates the impedance components of the battery 5 using the equivalent circuit model as follows, for example, for each of the three or more SOC values ​​described above for which the frequency characteristics of the impedance are measured.

[0071] When calculating the impedance component for any one of three or more SOC values, the processing circuit 21 etc. performs a fitting calculation using at least the measurement results of the impedance frequency characteristics at that SOC value and the relationship between the circuit parameters indicated in the equivalent circuit model and the impedance of the battery 5. At this time, the fitting calculation is performed using the circuit parameters of the equivalent circuit corresponding to the impedance component of the battery 5 as variables, and the circuit parameters that become the variables are calculated. Furthermore, in the fitting calculation, the values ​​of the circuit parameters that become the variables are determined so that, at each of the multiple frequencies at which the impedance is measured, the difference between the impedance calculation result using the calculation formula etc. indicated in the equivalent circuit model and the impedance measurement result is as small as possible.

[0072] By performing the fitting calculation as described above, the impedance components of the battery 5, which are set as circuit parameters in the equivalent circuit, are calculated. For example, when the contact resistance, the charge transfer resistance of each of the positive and negative electrodes, and the Warburg impedance are set as circuit parameters, the contact resistance, the charge transfer resistance of each of the positive and negative electrodes, and the Warburg impedance are calculated by the fitting calculation. Battery equivalent circuits and the like are shown in Patent Document 1, Patent Document 2, Patent Document 3, Non-Patent Document 1, Non-Patent Document 2, etc. Furthermore, methods for calculating the circuit parameters (circuit constants) of the equivalent circuit by performing fitting calculations using measurement results of the frequency characteristics of the battery impedance and an equivalent circuit model of the battery are shown in Patent Document 1, Patent Document 2, Patent Document 3, etc.

[0073] 5 is a circuit diagram schematically illustrating an example of a battery equivalent circuit used in fitting calculations to calculate the impedance components of a battery in an embodiment. In the example equivalent circuit of FIG. 5, contact resistance Rs, positive electrode charge transfer resistance Rctp, negative electrode charge transfer resistance Rctn, and Warburg impedance Zw are set as circuit parameters. In addition to charge transfer resistance Rctp, capacitance Cp and Debye's empirical parameter αp are set as circuit parameters in the equivalent circuit as impedance components corresponding to the positive electrode charge transfer impedance. In addition to charge transfer resistance Rctn, capacitance Cn and Debye's empirical parameter αn are set as circuit parameters as impedance components corresponding to the negative electrode charge transfer impedance.

[0074] In the example equivalent circuit of Fig. 5, CPEs CPEp and CPEn are used as circuit elements. The capacitance Cp and Debye's empirical parameter αp are circuit parameters of CPEp, and the capacitance Cn and Debye's empirical parameter αn are circuit parameters of CPEn. In embodiments, the circuit parameters of the example equivalent circuit of Fig. 5 are calculated by fitting calculation as described above, and the contact resistance Rs, the positive electrode charge transfer resistance Rctp, the negative electrode charge transfer resistance Rctn, and the Warburg impedance Zw are calculated as impedance components of the battery 5 for each of three or more SOC values.

[0075] Fig. 6 is a schematic diagram illustrating the impedance components of a battery. Fig. 6 shows a complex impedance plot (Cole-Cole plot), where the horizontal axis indicates the real component Zre of the impedance and the vertical axis indicates the imaginary component -Zim of the impedance. Fig. 6 also shows a locus Zb as an example of the frequency characteristics of the impedance of the battery 5. The locus Zb indicates impedance at lower frequencies as it moves toward the arrow X1 side.

[0076] The locus Zb also shows an arc portion Ab and a linear portion Lb. The arc portion Ab has a convex shape toward the negative side of the imaginary component. The locus Zb also shows the linear portion Lb on the positive side of the real component, that is, on the low frequency side, relative to the arc portion Ab. The linear portion Lb also shows an increase in the absolute value of the negative imaginary component as the absolute value of the positive real component increases. The arc portion Ab is dominated by the charge transfer impedance of the positive and negative poles, and the impedance component of the arc portion Ab is mainly composed of the charge transfer impedance of the positive and negative poles. The linear portion Lb is dominated by the Warburg impedance, and the impedance component of the linear portion Lb is mainly composed of the Warburg impedance.

[0077] Furthermore, the locus Zb passes through the axis of the real component Zre at intercept Yb. Intercept Yb is located on the negative side of the real component with respect to the center of the arc portion Ab. When the impedance frequency characteristic is locus Zb, the value of the real component at intercept Yb corresponds to the resistance value of contact resistance Rs, which is one of the impedance components. In one example of the embodiments, instead of calculating the contact resistance Rs using the fitting calculation described above, the intercept Yb where the locus of the impedance frequency characteristic passes through the axis of the real component is identified based on the measurement results of the impedance frequency characteristic. Then, the value of the real component at intercept Yb is calculated as the contact resistance Rs.

[0078] FIG. 6 also shows a locus Zctp as an example of the frequency characteristics of the charge transfer impedance of the positive electrode, and a locus Zctn as an example of the frequency characteristics of the charge transfer impedance of the negative electrode. The locus Zctp shows an arc portion Actp that is convex on the negative side of the imaginary component, and the locus Zctn shows an arc portion Actp that is convex on the negative side of the imaginary component. The diameter of the arc portion Actp of the locus Zctp corresponds to the resistance value of the charge transfer resistance Rctp of the positive electrode, and the diameter of the arc portion Actn of the locus Zctn corresponds to the resistance value of the charge transfer resistance Rctn of the negative electrode. Note that the loci of the frequency characteristics of the charge transfer impedance of each of the positive electrode and the negative electrode are shown in Patent Documents 1 and 2, etc.

[0079] In one example of the embodiment, at least the positive electrode charge transfer impedance Zctp and the negative electrode charge transfer impedance Zctn are set as circuit parameters in the equivalent circuit, and the equivalent circuit model shows a calculation formula for calculating the impedance of the battery 5 using the charge transfer impedances Zctp and Zctn and frequency. Then, a fitting calculation is performed using at least the measurement results of the frequency characteristics of the impedance of the battery 5 and the calculation formula for calculating the impedance from the charge transfer impedances Zctp and Zctn and frequency, thereby calculating the frequency characteristics of the positive electrode and negative electrode charge transfer impedances Zctp and Zctn. In this case, the fitting calculation is performed using the impedance component at the arc portion Ab in the measurement results of the frequency characteristics of the impedance of the battery 5. Then, in the frequency characteristics of the positive electrode charge transfer impedance Zctp, the diameter of the arc portion Actp is calculated as the charge transfer resistance Rctp, and in the frequency characteristics of the negative electrode charge transfer impedance Zctn, the diameter of the arc portion Actn is calculated as the charge transfer resistance Rctn.

[0080] In the embodiments and the like, in diagnosing the state of the battery 5, the processing circuit 21 and the like calculate the contact resistance Rs of the battery 5, the exchange current density of each of the positive electrode and the negative electrode, and the diffusion coefficient (intra-solid diffusion coefficient) of each of the positive electrode active material and the negative electrode active material as the impedance component of the battery 5 and parameters related to the impedance component. The exchange current density is a parameter related to the charge transfer resistance and the charge transfer impedance, and the diffusion coefficient is a parameter related to the Warburg impedance.

[0081] The contact resistance Rs of the battery 5 is calculated based on the measurement results of the impedance-frequency characteristics at one or more of the three or more SOC values ​​described above. The processing circuit 21 and other components calculate the contact resistance Rs as described above using the measurement results of the impedance-frequency characteristics for each of the three or more SOC values. When the contact resistance Rs is calculated for only one SOC value, the calculated resistance value of the contact resistance Rs is derived as the final calculated value of the contact resistance Rs. When the contact resistance Rs is calculated for multiple SOC values, the average or median of the calculated resistance values ​​of the contact resistance Rs is derived as the final calculated value of the contact resistance Rs.

[0082] The exchange current densities of the positive and negative electrodes are calculated based on the measurement results of the impedance-frequency characteristics at one or more SOC values ​​other than the maximum SOC value ηmax and the minimum SOC value ηmin among the three or more SOC values ​​described above. To calculate the exchange current density I0p of the positive electrode, the processing circuit 21 and other circuits calculate the charge transfer resistance Rctp of the positive electrode as described above using the measurement results of the impedance-frequency characteristics for each of the one or more SOC values ​​other than the maximum SOC value ηmax and the minimum SOC value ηmin. When the charge transfer resistance Rctp is calculated for only one SOC value, the calculated resistance value of the charge transfer resistance Rctp is derived as the final calculated value of the charge transfer resistance Rctp. When the charge transfer resistance Rctp is calculated for multiple SOC values, the average or median of the calculated resistance values ​​of the charge transfer resistance Rctp is derived as the final calculated value of the charge transfer resistance Rctp. The processing circuit 21 and other circuits calculate the exchange current density I0p of the positive electrode using the final calculated value of the charge transfer resistance Rctp.

[0083] Furthermore, in calculating the negative electrode exchange current density I0n, the processing circuit 21 and the like calculate the negative electrode charge transfer resistance Rctn as described above using the measurement results of the impedance frequency characteristics for each of at least one SOC value other than the maximum SOC value ηmax and the minimum SOC value ηmin. When the charge transfer resistance Rctn is calculated for only one SOC value, the calculated resistance value of the charge transfer resistance Rctn is derived as the final calculated value of the charge transfer resistance Rctn. When the charge transfer resistance Rctn is calculated for multiple SOC values, the average or median of the calculated resistance values ​​of the charge transfer resistance Rctn is derived as the final calculated value of the charge transfer resistance Rctn. The processing circuit 21 and the like use the final calculated value of the charge transfer resistance Rctn to calculate the negative electrode exchange current density I0n.

[0084] Here, Non-Patent Document 2 discloses a method for calculating exchange current density using charge transfer resistance. In one example of the embodiments, the processing circuit 21 and the like calculate the exchange current density I0p of the positive electrode using the charge transfer resistance Rctp of the positive electrode, similarly to Non-Patent Document 2, and calculate the exchange current density I0n of the negative electrode using the charge transfer resistance Rctn of the negative electrode, similarly to Non-Patent Document 2. In this case, parameters, calculation formulas, functions, and the like used for calculating the exchange current densities I0p and I0n are stored in the storage medium 22.

[0085] In some embodiments, the charge transfer resistances Rctp and Rctn and the exchange current densities I0p and I0n are preferably calculated as described above using the measurement results of the impedance-frequency characteristics at one or more SOC values ​​in the range of greater than 5% and less than 95%. In a more preferred example, the charge transfer resistances Rctp and Rctn and the exchange current densities I0p and I0n are calculated as described above using the measurement results of the impedance-frequency characteristics at one or more SOC values ​​in the range of greater than 40% and greater than 60%.

[0086] The diffusion coefficient Dsp of the positive electrode active material is calculated based on the measurement results of the impedance frequency characteristics at the minimum SOC value ηmin. In calculating the diffusion coefficient Dsp of the positive electrode active material, the processing circuit 21 and the like calculate the Warburg impedance Zw as described above using the measurement results of the impedance frequency characteristics for the minimum SOC value ηmin. In the embodiment and the like, the calculation result of the Warburg impedance Zw at the minimum SOC value ηmin is derived as the Warburg impedance Zwp of the positive electrode. In other words, the calculation result of the Warburg impedance Zw at the minimum SOC value ηmin is derived as the impedance component of the Warburg impedance Zw that is attributable to the diffusion process in the positive electrode. Then, the processing circuit 21 and the like calculate the diffusion coefficient Dsp of the positive electrode active material using the calculation result of the Warburg impedance Zwp of the positive electrode.

[0087] The diffusion coefficient Dsn of the negative electrode active material is calculated based on the measurement results of the impedance frequency characteristics at the maximum SOC value ηmax. In calculating the diffusion coefficient Dsn of the negative electrode active material, the processing circuit 21 and the like calculate the Warburg impedance Zw as described above using the measurement results of the impedance frequency characteristics for the maximum SOC value ηmax. In the embodiment and the like, the calculation result of the Warburg impedance Zw at the maximum SOC value ηmax is derived as the negative electrode Warburg impedance Zwn. In other words, the calculation result of the Warburg impedance Zw at the maximum SOC value ηmax is derived as the impedance component of the Warburg impedance Zw that is attributable to the diffusion process at the negative electrode. Then, the processing circuit 21 and the like calculate the diffusion coefficient Dsn of the negative electrode active material using the calculation result of the negative electrode Warburg impedance Zwn.

[0088] Here, Non-Patent Document 1 and Non-Patent Document 2 disclose a method for calculating the diffusion coefficient of an active material using Warburg impedance. In one example of the embodiments, the processing circuit 21 or the like calculates the diffusion coefficient Dsp of the positive electrode active material using the Warburg impedance Zwp of the positive electrode, similar to Non-Patent Document 1 or Non-Patent Document 2, and calculates the diffusion coefficient Dsn of the negative electrode using the Warburg impedance Zwn of the negative electrode, similar to Non-Patent Document 1 or Non-Patent Document 2. In this case, the parameters, calculation formulas, functions, and the like used to calculate the diffusion coefficients Dsp and Dsn are stored in the storage medium 22.

[0089] 7 is a flowchart showing an example of processing performed by a processing circuit, etc., by executing an impedance component calculation program in an embodiment. The example processing of FIG. 7 is performed each time the frequency characteristics of the impedance of the battery 5 are measured at three or more different SOC values ​​within the SOC range in which the battery 5 is charged or discharged under predetermined conditions. When the example processing of FIG. 7 is started, the processing circuit 21, etc., acquires measurement results of the frequency characteristics of the impedance at three or more SOC values ​​including the maximum SOC value ηmax and the minimum SOC value ηmin (S111).

[0090] The processing circuitry 21 etc. then performs fitting calculations for each of the three or more SOC values ​​using at least the measurement results of the impedance frequency characteristics and the relationship between the circuit parameters of the equivalent circuit and the impedance of the battery 5, and calculates the impedance components of the battery 5 through the fitting calculations (S112). The processing circuitry 21 etc. then calculates the contact resistance Rs of the battery 5 as described above based on the calculation results of the impedance components at one or more of the three or more SOC values ​​(S113). The processing circuitry 21 etc. also calculates the charge transfer resistance Rctp of the positive electrode and the charge transfer resistance Rctn of the negative electrode as described above based on the calculation results of the impedance components at one or more of the three or more SOC values ​​other than the minimum SOC value ηmin and the maximum SOC value ηmax (S114). The processing circuitry 21 etc. then calculates the exchange current density I0p of the positive electrode using the charge transfer resistance Rctp (S115), and calculates the exchange current density I0n of the negative electrode using the charge transfer resistance Rctn (S116).

[0091] Furthermore, the processing circuit 21 etc. calculates the Warburg impedance Zwp of the positive electrode as described above based on the calculation result of the impedance component at the minimum SOC value ηmin (S117). Then, the processing circuit 21 etc. calculates the diffusion coefficient Dsp of the positive electrode active material using the Warburg impedance Zwp (S118). Furthermore, the processing circuit 21 etc. calculates the Warburg impedance Zwn of the negative electrode as described above based on the calculation result of the impedance component at the maximum SOC value ηmax (S119). Then, the processing circuit 21 etc. calculates the diffusion coefficient Dsn of the negative electrode active material using the Warburg impedance Zwn (S120).

[0092] In the embodiments, the processing circuit 21 performs processing using an electrochemical model 35 stored in the storage medium 22. FIG. 8 is a schematic diagram showing an example of processing using the electrochemical model performed by the processing circuit in the embodiments. As shown in FIG. 8, in the embodiments, when using the electrochemical model 35, the processing circuit 21 inputs the usage conditions of the battery 5 to the electrochemical model 35 (arrow γ1). Information about the usage conditions of the battery 5 is input by a user of the diagnostic device 3 and the diagnostic system 1, for example, via the user interface 25. Examples of the usage conditions of the battery 5 include the C rate for charging or discharging the battery 5, the temperature range during use of the battery 5, the start SOC value at the start of charging or discharging the battery 5, and the duration of continuing charging or discharging the battery 5. In one example, instead of the duration of continuing charging or discharging, the end SOC value at the end of charging or discharging the battery 5 may be input as the usage condition.

[0093] The electrochemical model 35 outputs the battery characteristics of the battery 5 in response to the input of usage conditions (arrow γ2). For example, the battery characteristics output are the time changes in the current and voltage of the battery 5 when used according to the input usage conditions. In this case, a charge curve or a discharge curve of the battery 5 when used according to the input usage conditions is output. Alternatively, an IV characteristic showing the relationship between the current and voltage of the battery 5 when used according to the input usage conditions may be output as the battery characteristics. In one example, the electrochemical model 35 is input with the instruction to charge the battery 5 from an SOC value of 50% at a C rate of 2C for 30 seconds in an environment of −20° C. Then, the electrochemical model 35 outputs the charge curve and IV characteristic when used according to the input usage conditions.

[0094] In addition, electrochemical parameters are set in the electrochemical model 35. In the electrochemical model 35, the aforementioned diffusion coefficients Dsp and Dsn are set as parameters, and exchange current densities I0p and I0n, contact resistance Rs, and the like may also be set. In addition, in the electrochemical model 35, the positive electrode capacity Mp, the negative electrode capacity Mn, and the potentials of the positive electrode and the negative electrode at a reference charge amount may also be set as electrochemical parameters. In addition, in the electrochemical model 35, relational expressions and the like indicating the relationships between multiple parameters related to the battery 5 are set. In one example, in the electrochemical model 35, relational expressions for calculating the respective potentials of the positive electrode and the negative electrode from the charge amount are set. The electrochemical model 35 calculates the battery characteristics when used in accordance with the use conditions using the input use conditions and the set electrochemical parameters and relational expressions, and outputs the calculated battery characteristics.

[0095] Furthermore, in the embodiment, when the state of the battery 5 is diagnosed, the diffusion coefficients Dsp, Dsn, exchange current densities I0p, I0n, contact resistance Rs, etc. are calculated as described above. Then, after calculating the diffusion coefficients Dsp, Dsn, etc., the processing circuitry 21, etc. updates the diffusion coefficients Dsp, Dsn, etc. set as electrochemical parameters in the electrochemical model 35 to correspond to the calculation results calculated in the diagnosis (arrow γ3). As a result, the diffusion coefficients Dsp, Dsn, etc. set as electrochemical parameters in the electrochemical model 35 are updated to correspond to the calculation results calculated based on the measurement results of the impedance frequency characteristics in the diagnosis. The processing circuitry 21, etc. executes the parameter update program 33 to update the electrochemical parameters, etc. of the electrochemical model 35.

[0096] In addition, if the exchange current densities I0p, I0n, contact resistance Rs, positive electrode capacity Mp, negative electrode capacity Mn, etc. are set as electrochemical parameters in the electrochemical model 35, these electrochemical parameters are also updated in accordance with the calculation results of the diagnosis. In addition, if relational expressions for calculating the potentials of the positive electrode and negative electrode from the amount of charge are set in the electrochemical model 35, these relational expressions are also updated in accordance with the relationship between the amount of charge calculated in the diagnosis and the potentials of the positive electrode and negative electrode.

[0097] In the electrochemical model 35, the electrochemical parameters and relational expressions, etc. are updated in accordance with the calculation results of the diagnosis, so that the electrochemical parameters, etc., become values, etc. that correspond to the state of the battery 5 at the time the diagnosis was performed. By updating the electrochemical parameters and relational expressions, etc., the electrochemical parameters of the electrochemical model 35 are changed, for example, from values, etc. that correspond to the state at the start of use of the battery 5 to values, etc. that correspond to the state of the battery 5 in real time. Furthermore, in the electrochemical model 35, the electrochemical parameters and relational expressions, etc. are updated in accordance with the calculation results of the diagnosis, so that even if the same usage conditions are input, the battery characteristics output after the electrochemical parameters, etc. are updated will differ from the battery characteristics output before the electrochemical parameters, etc. are updated.

[0098] As described above, in this embodiment, the impedance-frequency characteristics of battery 5 are measured at three or more different SOC values ​​within the SOC range of battery charge or discharge under predetermined conditions. Then, based on the measurement results of the impedance-frequency characteristics at the lowest SOC value ηmin among the three or more SOC values, the diffusion coefficient Dsp of the positive electrode active material is calculated, and based on the measurement results of the impedance-frequency characteristics at the highest SOC value ηmax among the three or more SOC values, the diffusion coefficient Dsn of the negative electrode active material is calculated.

[0099] Here, in a low SOC range, such as 5% or less, ion diffusion hardly occurs in the negative electrode (negative electrode active material). Therefore, in the low SOC range, the majority of the Warburg impedance is accounted for by the impedance component due to the diffusion process in the positive electrode, and the impedance component due to the diffusion process in the negative electrode is hardly generated. Therefore, by setting the lower limit SOC value ηl of the SOC range for charge or discharge under specified conditions to a low SOC range and setting the minimum SOC value ηmin to the same level as the lower limit SOC value ηl or slightly higher than the lower limit SOC value ηl, the Warburg impedance Zw calculated at the minimum SOC value ηmin can be used as the Warburg impedance Zwp of the positive electrode. The Warburg impedance Zw calculated at the minimum SOC value ηmin can then be used as the Warburg impedance Zwp of the positive electrode to appropriately calculate the diffusion coefficient Dsp of the positive electrode active material.

[0100] Furthermore, in a high SOC range, such as 95% or higher, ion diffusion in the positive electrode (positive electrode active material) hardly occurs. Therefore, in the high SOC range, the majority of the Warburg impedance is accounted for by the impedance component resulting from the diffusion process in the negative electrode, and the impedance component resulting from the diffusion process in the positive electrode is almost nonexistent. Therefore, by setting the upper limit SOC value ηu of the SOC range for charge or discharge under specified conditions to a high SOC range and setting the maximum SOC value ηmax to the same value as the upper limit SOC value ηu or slightly lower than the upper limit SOC value ηu, the Warburg impedance Zw calculated at the maximum SOC value ηmax can be used as the Warburg impedance Zwn of the negative electrode. The Warburg impedance Zw calculated at the maximum SOC value ηmax can then be used as the Warburg impedance Zwn of the negative electrode to appropriately calculate the diffusion coefficient Dsn of the negative electrode active material.

[0101] Since the diffusion coefficients Dsp and Dsn are calculated as described above, in this embodiment, it is possible to appropriately estimate both the components attributable to the diffusion process in the positive electrode and the components attributable to the diffusion process in the negative electrode for the Warburg impedance and parameters related to the Warburg impedance. Therefore, it is possible to appropriately estimate the impedance components and parameters related to the impedance components of the battery 5 in detail.

[0102] In a preferred example of the embodiment, the minimum SOC value ηmin is set to any SOC value between 0% and 5%, and the frequency characteristics of the impedance at the minimum SOC value ηmin are measured. This allows for an appropriate measurement result of the frequency characteristics of the impedance at the minimum SOC value ηmin, in which the impedance component resulting from the diffusion process in the positive electrode accounts for the majority of the Warburg impedance. Therefore, the Warburg impedance Zwp of the positive electrode and the diffusion coefficient Dsp of the positive electrode active material can be more appropriately calculated using the frequency characteristics of the impedance at the minimum SOC value ηmin.

[0103] In a preferred example of the embodiment, the maximum SOC value ηmax is defined as any SOC value between 95% and 100%, and the frequency characteristics of the impedance at the maximum SOC value ηmax are measured. This allows for an appropriate measurement result of the frequency characteristics of the impedance at the maximum SOC value ηmax, in which the impedance component resulting from the diffusion process in the negative electrode accounts for the majority of the Warburg impedance. Therefore, the frequency characteristics of the impedance at the maximum SOC value ηmax can be used to more appropriately calculate the Warburg impedance Zwn of the negative electrode and the diffusion coefficient Dsn of the negative electrode active material.

[0104] In the embodiments, the contact resistance Rs and the charge transfer resistances of the positive and negative electrodes are calculated as the impedance components of the battery 5, and the exchange current densities of the positive and negative electrodes are calculated as parameters related to the impedance components, thereby allowing the impedance components of the battery 5 and parameters related to the impedance components to be estimated in more detail.

[0105] In the present embodiment, the charge transfer resistance and exchange current density of each of the positive and negative electrodes of the battery 5 are calculated based on the measurement results of the impedance-frequency characteristics at one or more SOC values ​​other than the minimum SOC value ηmin and the maximum SOC value ηmax among the three or more SOC values. Here, the reaction in the charge transfer process is stable in each of the positive and negative electrodes, except for a low SOC region, such as 5% or less, and a high SOC region, such as 95% or more. In this embodiment, since the impedance-frequency characteristics are measured at three or more SOC values, even if the minimum SOC value ηmin is set to a low SOC region and the maximum SOC value ηmax is set to a high SOC region, one or more SOC values ​​other than the minimum SOC value ηmin and the maximum SOC value ηmax can be set to an SOC region where the reaction in the charge transfer process at the positive and negative electrodes is stable. Then, the charge transfer resistance and exchange current density of each of the positive and negative electrodes can be appropriately calculated based on the impedance-frequency characteristics at the SOC values ​​set to the SOC region where the reaction in the charge transfer process is stable.

[0106] In a more preferred example of the embodiment, in addition to the minimum SOC value ηmin and the maximum SOC value ηmax, the impedance-frequency characteristics are measured at one or more SOC values ​​in the range of 40% or more and 60% or more. Then, the charge transfer resistances Rctp and Rctn and the exchange current densities I0p and I0n are calculated using the measurement results of the impedance-frequency characteristics at one or more SOC values ​​in the range of 40% or more and 60% or more. In the SOC range of 40% or more and 60% or more, the reactions in the charge transfer process at the positive electrode and the negative electrode are more reliably stabilized. Therefore, by calculating the charge transfer resistances Rctp and Rctn and the exchange current densities I0p and I0n using the measurement results at one or more SOC values ​​in the range of 40% or more and 60% or more, the charge transfer resistances and the exchange current densities at the positive electrode and the negative electrode can be more appropriately calculated.

[0107] Furthermore, in the embodiments, the capacity and potential of each of the positive and negative electrodes are calculated based on the time-dependent changes in the current and voltage of the battery 5 during charging or discharging under predetermined conditions. Therefore, the capacity and potential of each of the positive and negative electrodes are appropriately calculated in addition to the impedance component of the battery 5 and parameters related to the impedance component. Therefore, the real-time state of the battery can be estimated more precisely and appropriately.

[0108] In one embodiment, the impedance frequency characteristics are measured for a battery 5 with the lowest SOC value ηmin before or immediately after the start of charging under predetermined conditions. In another embodiment, the impedance frequency characteristics are measured for a battery 5 with the lowest SOC value ηmin after or immediately before the end of discharging under predetermined conditions. Therefore, the measurement of the impedance frequency characteristics at the lowest SOC value ηmin is appropriately performed along with the measurement of data used to calculate the capacities of the positive and negative electrodes, etc.

[0109] In one embodiment, the impedance frequency characteristics are measured for the battery 5 with the maximum SOC value ηmax after or immediately before the end of charging under predetermined conditions. In another embodiment, the impedance frequency characteristics are measured for the battery 5 with the maximum SOC value ηmax before or immediately after the start of discharging under predetermined conditions. Therefore, the measurement of the impedance frequency characteristics at the maximum SOC value ηmax is appropriately performed along with the measurement of data used to calculate the capacities of the positive and negative electrodes, etc.

[0110] In one embodiment, the impedance frequency characteristics are measured at one or more SOC values ​​while the SOC value of battery 5 increases from the minimum SOC value ηmin to the maximum SOC value ηmax due to charging under predetermined conditions. In another embodiment, the impedance frequency characteristics are measured at one or more SOC values ​​while the SOC value of battery 5 decreases from the maximum SOC value ηmax to the minimum SOC value ηmin due to discharging under predetermined conditions. Therefore, in addition to measuring data used to calculate the capacities of the positive and negative electrodes, the impedance frequency characteristics are appropriately measured at one or more SOC values ​​other than the minimum SOC value ηmin and the maximum SOC value ηmax.

[0111] Furthermore, in the embodiments and the like, the diffusion coefficients and the like of the positive electrode active material and the negative electrode active material set as electrochemical parameters in the electrochemical model 35 are updated in accordance with the calculation results calculated based on the measurement results of the impedance frequency characteristics in the diagnosis. As a result, the electrochemical parameters and the like of the electrochemical model 35 are updated to values ​​and the like corresponding to the real-time state of the battery 5. Because the electrochemical parameters of the electrochemical model 35 are updated as described above, battery characteristics corresponding to the real-time state of the battery 5 are appropriately output from the electrochemical model 35 in response to the input of the usage conditions.

[0112] Because the battery characteristics corresponding to the real-time state of the battery 5 are appropriately output from the electrochemical model 35, it becomes possible to evaluate with high accuracy the real-time state of the battery 5, such as the real-time degradation state of the battery 5, based on the output results from the electrochemical model 35. For example, it becomes possible to evaluate with high accuracy the starting performance of the battery 5 in a low-temperature environment, the performance of the battery 5 when fast-charging at a high C-rate, the maximum input to the battery 5, the maximum output from the battery 5, and the safety performance of the battery 5, based on the output results from the electrochemical model 35.

[0113] Because the battery characteristics corresponding to the state of the battery 5 in real time are appropriately output from the electrochemical model 35, it becomes possible to appropriately select the use of the battery 5 when recycling, based on the output results from the electrochemical model 35. For example, for a battery 5 installed in a vehicle used in low-temperature logistics, it becomes possible to appropriately determine, based on the output results from the electrochemical model 35, whether it can be upcycled into a railway vehicle, whether it can be reused as a stationary power source, and whether it has deteriorated to the point where it should be discarded.

[0114] In at least one of the above-described embodiments or examples, the impedance-frequency characteristics of a battery are measured at three or more different SOC values ​​within a SOC range during charging or discharging of the battery under predetermined conditions. The diffusion coefficient of the battery's positive electrode active material is calculated based on the measurement results of the impedance-frequency characteristics at the lowest SOC value among the three or more SOC values, and the diffusion coefficient of the battery's negative electrode active material is calculated based on the measurement results of the impedance-frequency characteristics at the highest SOC value among the three or more SOC values. This makes it possible to provide a battery diagnostic method, diagnostic device, diagnostic system, and diagnostic program that enable detailed and appropriate estimation of the battery's impedance components and parameters related to the impedance components.

[0115] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0116] 1...diagnostic system, 2...battery-equipped device, 3...diagnostic device, 5...battery, 6...control circuit, 10...measuring unit, 21...processing circuit, 22...storage medium, 28...diagnostic program, 31...capacity calculation program, 32...impedance component calculation program, Rs...contact resistance, Rctp, Rctn...charge transfer resistance, I0p, I0n...exchange current density, Zw, Zwp, Zwn...Warburg impedance, Dsp, Dsn...diffusion coefficient.

Claims

1. measuring the frequency characteristics of the impedance of the battery at each of three or more different SOC values ​​within an SOC range for charging or discharging the battery under predetermined conditions; calculating a diffusion coefficient of a positive electrode active material of the battery based on a measurement result of the frequency characteristics of the impedance at a lowest SOC value among the three or more SOC values, and calculating a diffusion coefficient of a negative electrode active material of the battery based on a measurement result of the frequency characteristics of the impedance at a highest SOC value among the three or more SOC values; A battery diagnostic method comprising:

2. 2. The diagnostic method of claim 1, further comprising calculating an exchange current density of each of the positive electrode and the negative electrode of the battery based on a measurement result of the frequency characteristics of the impedance at any one or more SOC values ​​other than the minimum SOC value and the maximum SOC value among the three or more SOC values.

3. The diagnostic method of claim 1 , further comprising calculating a contact resistance of the battery based on a measurement result of the frequency characteristic of the impedance at any one or more of the three or more SOC values.

4. 2. The diagnostic method of claim 1, further comprising calculating a capacity and a potential for each of the positive electrode and the negative electrode of the battery based on the time changes of the current and the voltage of the battery during the charging or discharging under the predetermined conditions.

5. Measuring the frequency characteristics of the impedance at each of the three or more SOC values ​​includes: measuring the frequency characteristics of the impedance at the minimum SOC value, the minimum SOC value being any SOC value in the range of 0% or more and 5% or less; measuring the frequency characteristics of the impedance at the maximum SOC value, the maximum SOC value being any SOC value in the range of 95% or more and 100% or less; measuring the frequency characteristics of the impedance at one or more SOC values ​​in a range of more than 5% and less than 95%; The diagnostic method according to any one of claims 1 to 4, comprising:

6. Measuring the frequency characteristics of the impedance at each of the three or more SOC values ​​includes: measuring the frequency characteristics of the impedance for the battery with the lowest SOC value before or immediately after the start of charging under the predetermined conditions; measuring the frequency characteristics of the impedance for the battery with the highest SOC value after or immediately before the end of charging under the predetermined conditions; measuring the frequency characteristics of the impedance at one or more SOC values ​​while the SOC value of the battery increases from the minimum SOC value to the maximum SOC value by the charging under the predetermined conditions; The diagnostic method according to any one of claims 1 to 4, comprising:

7. Measuring the frequency characteristics of the impedance at each of the three or more SOC values ​​includes: measuring the frequency characteristics of the impedance for the battery with the highest SOC value before or immediately after the start of discharging under the predetermined conditions; measuring the frequency characteristics of the impedance for the battery with the lowest SOC value after or immediately before the end of the discharge under the predetermined conditions; measuring the frequency characteristics of the impedance at one or more SOC values ​​while the SOC value of the battery decreases from the highest SOC value to the lowest SOC value due to the discharge under the predetermined condition; The diagnostic method according to any one of claims 1 to 4, comprising:

8. 5. The diagnostic method according to claim 1, further comprising: outputting battery characteristics of the battery in response to input of usage conditions; and updating, for an electrochemical model of the battery in which electrochemical parameters including the diffusion coefficients of the positive electrode active material and the negative electrode active material are set, the diffusion coefficients of the positive electrode active material and the negative electrode active material that have been set in response to a calculation result calculated based on the measurement result of the frequency characteristic of the impedance.

9. measuring the frequency characteristics of the impedance of the battery at each of three or more different SOC values ​​within an SOC range for charging or discharging the battery under predetermined conditions; calculating a diffusion coefficient of a positive electrode active material of the battery based on a measurement result of the frequency characteristics of the impedance at a lowest SOC value among the three or more SOC values, and calculating a diffusion coefficient of a negative electrode active material of the battery based on a measurement result of the frequency characteristics of the impedance at a highest SOC value among the three or more SOC values; A diagnostic device comprising a processor.

10. The diagnostic device of claim 9; the battery in which the diffusion coefficients of the positive electrode active material and the negative electrode active material are calculated by the diagnostic device; A diagnostic system for the battery comprising:

11. On the computer, measuring the frequency characteristics of the impedance of the battery at each of three or more different SOC values ​​within an SOC range for charging or discharging the battery under predetermined conditions; calculating a diffusion coefficient of a positive electrode active material of the battery based on a measurement result of the frequency characteristic of the impedance at a lowest SOC value among the three or more SOC values, and calculating a diffusion coefficient of a negative electrode active material of the battery based on a measurement result of the frequency characteristic of the impedance at a highest SOC value among the three or more SOC values; Battery diagnostic program.

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