Battery diagnosing device and battery diagnosing method

Abstract

The purpose of the present invention is to provide a technique capable of accurately and quickly diagnosing a battery state without accumulating measurement data in advance. A battery diagnosing device according to the present invention: identifies a first frequency at which a component attributable to the diffusion resistance of an equivalent circuit of a battery starts to appear in a Nyquist diagram of the battery; identifies a second frequency at which, in phase-frequency characteristics of each of voltage and current, a phase of the voltage and a phase of the current coincide with one another; and diagnoses a state of the battery using real parts of a first impedance of the battery at the first frequency and a second impedance of the battery at the second frequency (see Fig. 8)

Description

Battery diagnostic device and battery diagnostic method

[0001] The present invention relates to a technique for diagnosing the state of a battery.

[0002] For the safe use of secondary batteries, it is important to have a technology that can accurately diagnose the battery condition, such as (a) whether an aged battery meets the requirements for the desired application, such as capacity and output, and (b) when the battery life will end.

[0003] Battery diagnosis is performed using measurement data such as battery voltage, battery current, and battery temperature. This measurement data may contain outliers. Outliers indicate battery failure or a sign of such a failure. Therefore, it is necessary to detect the occurrence of outliers at an early stage and take appropriate measures.

[0004] The following Patent Document 1 describes a technology (see abstract): "The voltage of a battery cell is measured, and the current flowing through the battery cell is measured. The OCV (Open Circuit Voltage) of the battery cell is estimated based on the measured voltage, the measured current, and an equivalent circuit model based on the electrochemistry of the battery cell. At least one of the positive electrode and the negative electrode of the battery cell is a mixed electrode containing multiple materials. The equivalent circuit model is a model that includes a diffusion resistance component for each of the multiple materials used in the positive electrode and the negative electrode."

[0005] WO2020 / 129477

[0006] Outliers are typically detected by comparing measured values ​​with a decision threshold. However, it is difficult to predict the nature of outliers caused by random faults. Therefore, it is equally difficult to set an appropriate decision threshold for detecting outliers.

[0007] Conventional diagnostic methods such as those described in Patent Document 1 are believed to be able to diagnose batteries by estimating the OCV. However, in order to properly remove outliers when estimating the OCV, it is believed that data on both outliers and normal values ​​must be accumulated. This is because it is generally difficult to predict outliers in advance. Therefore, conventional diagnostic methods are premised on the accumulation of such data, and therefore may be limited in the situations in which they can be applied.

[0008] The present invention has been made in consideration of the above-mentioned problems, and aims to provide a technology that can accurately and quickly diagnose the battery state without accumulating measurement data in advance.

[0009] A battery diagnostic device according to the present invention identifies a first frequency at which a component due to diffusion resistance in an equivalent circuit of the battery begins to appear in a Nyquist diagram of the battery, identifies a second frequency at which the phase of the voltage and the phase of the current match in the phase-frequency characteristics of the voltage and the current, and diagnoses the state of the battery using the real parts of a first impedance of the battery at the first frequency and a second impedance of the battery at the second frequency.

[0010] The battery diagnostic device according to the present invention can accurately and quickly diagnose the battery state without storing measurement data in advance. Other issues, configurations, effects, etc. will become clear from the description of the following embodiments.

[0011] 1 is an equivalent circuit diagram of a secondary battery cell 1. FIG. 2 is an equivalent circuit diagram for impedance diagnosis. FIG. 3 is an example of a Nyquist diagram of a secondary battery. FIG. 4 is an example of plotting measured values ​​of a Nyquist diagram. FIG. 4 shows an example of measuring battery characteristics using a rising wave or a falling wave. FIG. 5 shows current waveforms and voltage waveforms during a charging operation of a secondary battery and a subsequent rest period. FIG. 6 shows current waveforms and voltage waveforms during a discharging operation of a secondary battery and a subsequent rest period. FIG. 7 is a diagram plotting the phase frequency characteristics of battery voltage and battery current. FIG. 8 is a diagram showing impedances corresponding to ω1 and ωb, respectively. FIG. 9 is a diagram showing impedances corresponding to ω1 and ωb, respectively. FIG. 10 is a diagram showing a decrease in battery capacity over the number of days of use of a secondary battery. FIG. 11 is a diagram explaining a method of diagnosing the deterioration acceleration of a secondary battery. FIG. 12 is an example of Nyquist plots of a normal battery cell and an abnormal battery cell. FIG. 13 is a diagram explaining a method of diagnosing whether a battery cell is abnormal. FIG. 14 is a flowchart explaining a method of diagnosing a secondary battery. FIG. 15 is a flowchart explaining another method of diagnosing a secondary battery. FIG. 16 is a block diagram of a battery diagnosis device 100 according to a second embodiment. 10 is an example of a user interface provided by the calculation unit 120.

[0012] 1 is an equivalent circuit diagram of a secondary battery cell 1. The equivalent circuit is a circuit in which a solution resistor, a negative electrode RC circuit, a positive electrode RC circuit, and a diffusion resistor are connected in series in this order.

[0013] Figure 2 is an equivalent circuit diagram for impedance diagnosis. A secondary battery cell 1 has an impedance Zc. An AC voltage Vin is applied to the secondary battery cell 1, and an amplified voltage Vo corresponding to a reference resistance r0 is obtained. Zc is expressed by the following formula: Zc = -r0 · (Vin / Vo). Impedance characteristics such as those shown in Figures 3A and 3B, which will be described later, are measured by applying such an AC signal to the battery.

[0014] FIG. 3A is an example of a Nyquist diagram for a secondary battery. Here, the theoretical shape is shown, not the actual waveform. The left arc in FIG. 3A corresponds to the negative electrode, the right arc corresponds to the positive electrode, and the straight line corresponds to the diffusion resistance. When the frequency of the current input to the battery is changed, the waveform in each region of FIG. 3A can be detected in accordance with the change. The vertices of the arcs in FIG. 3A correspond to the time constant T ａｎｏｄｅ and the positive electrode time constant T ｃａｔｈｏｄｅ Corresponds to.

[0015] Among the frequencies of the AC signals input to the battery when measuring impedance, the time constant T ｃａｔｈｏｄｅ The corresponding one is ω0 = 1 / T ｃａｔｈｏｄｅ Furthermore, the frequency at which the component corresponding to the diffusion resistance begins to appear on the horizontal axis of the Nyquist diagram is set to ω1.

[0016] 3B shows an example of a plot of measured values ​​on a Nyquist diagram. The point corresponding to frequency ω1 appears as an inflection point. The point corresponding to frequency ω0 corresponds to a region where the gradient of the plot is approximately linear.

[0017] 4 shows an example of measuring battery characteristics using a rising wave or a falling wave. The rising wave here refers to a current signal that has a certain length of time between the start and end of interruption of the discharge current, as shown in FIG. 6 (described later). The falling wave here refers to a current signal that has a certain length of time between the start and end of interruption of the charge current, as shown in FIG. 5 (described later).

[0018] When obtaining the phase frequency characteristics and ωb shown in FIG. 7, which will be described later, such a rising wave or falling wave is applied to the battery, and a Fourier transform is performed using the response signal obtained at that time.

[0019] Figure 5 shows the current and voltage waveforms during the charging operation and the subsequent rest period of a secondary battery. When the charging operation is stopped (the charging current is cut off), the absolute value of the battery current decreases, and the battery voltage also decreases. When the current cutoff is completed (i.e., when the charging current becomes zero), the system enters a rest period, and the battery voltage gradually decreases over time.

[0020] The time length from the start to the completion of the interruption of the charging current is defined as τa = 1 / (2 × ωa). When obtaining ωb shown in FIG. 7 (described later), a current waveform satisfying 1 / (2 × ω0) < τa < 1 / (2 × ω1) is applied to the battery. If the charging current is interrupted instantaneously (i.e., within a time period shorter than τa), a component corresponding to the battery's negative electrode will appear on the Nyquist diagram. As will be explained in FIG. 7 (described later), in this invention, the battery is diagnosed using a component corresponding to the battery's positive electrode, so it is not desirable to obtain characteristics corresponding to the battery's negative electrode. Therefore, when obtaining the phase-frequency characteristics shown in FIG. 7 (described later), the battery current interrupted during τa (shown in FIG. 5) is used. Since interruption during τa is sufficient, it is not necessary to apply AC current to the battery.

[0021] Figure 6 shows the current and voltage waveforms during the discharge operation and the subsequent rest period of a secondary battery. When the discharge operation is stopped (the discharge current is cut off), the absolute value of the battery current decreases and the battery voltage also increases. The time length τa from the start to the completion of the discharge current cut-off is the same as in Figure 5.

[0022] 7 is a diagram plotting the phase-frequency characteristics of the battery voltage and the battery current. The frequency at which the phase of the battery voltage and the phase of the battery current coincide on the phase-frequency characteristics is designated ωb. ωb is smaller than ωnyq (>ω0), which corresponds to the Nyquist frequency, and larger than ω1.

[0023] When the output current phase and output voltage phase of an RC equivalent circuit are the same, the current component flowing through the capacitor portion of the circuit can be ignored. That is, the R component of the RC equivalent circuit can be calculated from the output voltage / output current of the RC equivalent circuit. In other words, at this frequency, the R component of the positive RC equivalent circuit (i.e., the positive electrode resistance) can be calculated from the output voltage / output current of the RC equivalent circuit. Therefore, in this embodiment, the positive electrode resistance is measured using ωb, and the battery condition is diagnosed based on this. The real part rb of the impedance corresponding to ωb can be calculated, for example, by dividing the amplitude of the battery voltage at ωb by the amplitude of the battery current at ωb on the phase-frequency characteristic.

[0024] FIG. 8 is a diagram showing the impedances corresponding to ω1 and ωb, respectively. Circles indicate Nyquist plots, and pluses indicate impedance plots when the currents described in FIGS. 5 and 6 are applied. In the plots of FIG. 8, the real part of the impedance corresponding to ω1 (first frequency) is designated as r1, and the real part of the impedance corresponding to ωb (second frequency) is designated as rb. If |r1-rb| is equal to or less than a threshold, the battery can be diagnosed as being normal. Alternatively, if |rb / r1| is equal to or less than a threshold, the battery can be diagnosed as being normal. These diagnostic criteria are substantially equivalent, so either may be used.

[0025] In a normal battery, it is known that ω0 and ω1 are within a range close to each other to some extent. Therefore, ωb, which is between ω0 and ω1, is also close to ω1 to some extent. In other words, r1 and rb are also considered to be similarly close. Therefore, in the present invention, the battery is diagnosed based on whether the difference between r1 and rb is sufficiently small. The diagnostic criteria in Figure 8 are based on this idea.

[0026] FIG. 9 is a diagram showing the impedances corresponding to ω1 and ωb, respectively. The following diagnostic method can also be used as an alternative to that shown in FIG. 8. The frequency at which the Nyquist plot intersects the real axis (the point corresponding to the solution resistance) is defined as ω3, and the real part of the impedance at this point is defined as r3. If |(r1-r3)-(rb-r3)| is equal to or less than a threshold, the battery can be diagnosed as normal. Alternatively, if |(rb / r3) / (r1 / r3)| is equal to or less than a threshold, the battery can be diagnosed as normal. These diagnostic criteria are essentially equivalent, so either can be used.

[0027] Furthermore, if the battery is normal, the battery's State of Health (SOH) can be calculated. Since SOH (or maximum charge capacity) and (rb-r3) are inversely proportional, SOH can be calculated from (rb-r3) by referencing data describing the correspondence between the two.

[0028] Fig. 10 shows the decrease in battery capacity over the number of days of use of a secondary battery. Generally, the chargeable capacity of a secondary battery gradually decreases with the number of days of use, and the rate of decrease (i.e., the acceleration of deterioration) gradually increases as the number of days of use increases. Therefore, when diagnosing the battery condition, the acceleration of deterioration at that time may also be diagnosed. A specific method for doing this is described below.

[0029] FIG. 11 is a diagram illustrating a method for diagnosing the degradation acceleration of a secondary battery. r1 and rb on a Nyquist plot are obtained in the same manner as in FIGS. 8 and 9. In a battery with advanced degradation, the difference between r1 and rb is large. Therefore, if (r1 - rb) > threshold, it can be diagnosed that the degradation acceleration is high. Alternatively, if (r1 / rb) > threshold, it can be diagnosed that the degradation acceleration is high. These diagnostic criteria are essentially equivalent, so either can be used.

[0030] 12 is a diagram illustrating Nyquist plots of a normal battery cell and an abnormal battery cell. The Nyquist plot of an abnormal battery cell may have characteristics different from those of a normal battery cell, which can be used to determine whether the battery is abnormal, as described below.

[0031] 13 is a diagram illustrating a method for diagnosing whether a battery cell is abnormal. Unlike normal battery cells, abnormal battery cells have r1<rb. Therefore, if r1 is smaller than rb, the battery cell can be considered abnormal.

[0032] FIG. 14 is a flowchart illustrating a method for diagnosing a secondary battery. This flowchart describes the above-described diagnostic procedure in a flow chart format. Each step can be performed by the calculation unit 120, which will be described later. Each step in FIG. 14 will be described below.

[0033] (FIG. 14: Step S1401: Part 1) The calculation unit 120 acquires the following parameters. These parameters may be acquired by actual measurement or may be acquired as known values ​​based on the battery performance specifications: (a) a frequency ω0 corresponding to the positive electrode RC time constant of the battery's equivalent circuit; (b) a frequency ω1 at which a component corresponding to the diffusion resistance begins to appear on the Nyquist diagram; and (c) a frequency ωa (ω1<ωa<ω0) corresponding to a time length τa from the start to the completion of interruption of the discharge current / charge current.

[0034] (FIG. 14: Step S1401: Part 2) The calculation unit 120 acquires the battery voltage waveform when a battery current of τa=1 / (2×ωa) is applied.

[0035] (FIG. 14: Step S1402) The calculation unit 120 performs a Fourier transform (FFT) on the battery voltage and battery current before and after the discharge or charge current is cut off. The sampling frequency is 1 / (2ωa).

[0036] (FIG. 14: Steps S1403 to S1404) The calculation unit 120 identifies a frequency ωb at which the phases of the battery voltage and the battery current match in the phase-frequency characteristics of each other (S1403). The calculation unit 120 calculates the real part rb of the battery impedance at ωb (S1404).

[0037] (FIG. 14: Step S1405) An AC current with a frequency ω1 is input to the battery. The calculation unit 120 calculates the real part r1 of the battery impedance at ω1.

[0038] (FIG. 14: Steps S1406 to S1408) The calculation unit 120 determines whether |r1-rb| is equal to or less than a threshold value (S1406). If it is equal to or less than the threshold value (S1406: Yes), the battery is diagnosed as normal. An AC current with a frequency ω3 is input to the battery. The calculation unit 120 calculates rb-r3 (S1407) and estimates the SOH of the battery by referring to data describing the correspondence between rb-r3 and the SOH (or maximum charge capacity) (S1408).

[0039] (FIG. 14: Step S1409) If |r1-rb| exceeds the threshold, the battery is assumed to be abnormal (as in the state shown in FIGS. 12 and 13) or in a state of advanced degradation (as in the state shown in FIGS. 10 and 11). The calculation unit 120 compares r1-rb with the threshold. If (r1-rb) > the threshold, it is diagnosed that the rate of degradation is high. If rb is greater than r1, it is diagnosed that the battery is abnormal (i.e., in the state shown in FIG. 13).

[0040] (FIG. 14: Steps S1406, S1409: Supplementary Information) As explained in FIG. 8, in S1406, |rb / r1| may be used instead of |r1-rb|. As explained in FIG. 11, in S1409, (r1 / rb) may be used instead of (r1-rb). The threshold value may be changed depending on which one is used. In S1409, the deterioration acceleration (first deterioration acceleration) when (r1-rb) > threshold value and the deterioration acceleration (second deterioration acceleration) when (r1 / rb) > threshold value may be the same or different values.

[0041] Fig. 15 is a flowchart illustrating another method for diagnosing a secondary battery. This flowchart uses the method described in Fig. 9 instead of the method described in Fig. 8. Each step can be performed by the calculation unit 120, which will be described later. S1501 and S1502 are performed instead of S1405 and S1406, respectively. The other steps are the same as those in Fig. 14.

[0042] (FIG. 15: Step S1501) AC currents at frequencies ω1 and ω3 are input to the battery. The calculation unit 120 calculates the real parts r1 and r3 of the battery impedance at ω1 and ω3, respectively.

[0043] (FIG. 15: Step S1502) The calculation unit 120 determines whether |(r1-r3)-(rb-r3)| is equal to or less than a threshold value. If it is equal to or less than the threshold value (S1502: Yes), the battery is diagnosed as normal. Since the impedance real part r3 at frequency ω3 has already been acquired in S1501, there is no need to acquire it again in S1407.

[0044] <Embodiment 2> Fig. 16 is a block diagram of a battery diagnostic device 100 according to Embodiment 2 of the present invention. The battery diagnostic device 100 is a device that diagnoses the battery state using the method described in Embodiment 1. The battery diagnostic device 100 includes a detection unit 110, a calculation unit 120, and a storage unit 130. The detection unit 110 acquires measurement results of the battery voltage and battery current. The calculation unit 120 implements the diagnostic method described in Embodiment 1. The storage unit 130 stores data used by the calculation unit 120 (e.g., parameters acquired in S1401 that are stored in advance, and data describing the relationship between rb-r3 and charge capacity).

[0045] Fig. 17 is an example of a user interface provided by the calculation unit 120. The calculation unit 120 can generate a user interface such as that shown in Fig. 17 and present it on a display device such as a display. The user interface can present, for example, the following information: (a) ω0, ω1, ωa, ωb; (b) Nyquist plot; (c) r1, rb, r3; and (d) diagnosis results.

[0046] <Regarding Modifications of the Present Invention> The present invention is not limited to the above-described embodiments and includes various modifications. For example, the above-described embodiments have been described in detail to clearly explain the present invention, and the present invention is not necessarily limited to those including all of the described configurations. Furthermore, it is possible to replace part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment. Furthermore, it is possible to add, delete, or replace part of the configuration of each embodiment with other configurations.

[0047] In the above embodiments, ω1 is typically 5 times or less than ω0 (ω1≦5ω0). Therefore, when obtaining the phase-frequency characteristics of the battery voltage and battery current to specify ωb, it is necessary to apply to the battery a current waveform in which τa described in FIGS. 5 and 6 is defined according to ω1 and ω0 that satisfy these conditions.

[0048] In the above embodiments, the calculation unit 120 can be configured by hardware such as a circuit device that implements its functions, or can be configured by a calculation device such as a CPU (Central Processing Unit) that executes software that implements its functions.

[0049] In the above embodiment, the reason for using the characteristics corresponding to the positive pole on the Nyquist diagram will be explained below. If the characteristics on the negative pole side are used, there is a possibility that the values ​​of r1, rb, etc. in the present invention will approximately match the solution resistance value (r3). This will hinder diagnosis because it will be difficult to determine the values ​​of the acquired real parts of the impedances. Therefore, in the present invention, the characteristics on the positive pole side are used.

[0050] 100: Battery diagnostic device 110: Detection unit 120: Calculation unit 130: Storage unit

Claims

1. A battery diagnostic device for diagnosing the state of a battery, comprising: a detection unit which acquires detection values ​​of the voltage and current output by the battery; and a calculation unit which diagnoses the state of the battery, wherein the calculation unit identifies a first frequency at which a component due to a diffusion resistance of an equivalent circuit of the battery begins to appear in a Nyquist diagram of the battery; the calculation unit identifies a second frequency at which the phase of the voltage and the phase of the current match each other in the phase-frequency characteristics of the voltage and the current when a rising current or a falling current is applied to the battery; the calculation unit acquires a first impedance of the battery at the first frequency and a second impedance of the battery at the second frequency, respectively; and the calculation unit diagnoses the state of the battery using a real part of the first impedance and a real part of the second impedance, the calculation unit identifies the second frequency based on a waveform when a time length from when the rising current starts to rise to when it finishes rising or a time length from when the falling current starts to fall to when it finishes falling is a value between a value determined based on a time constant of a positive RC circuit of the equivalent circuit and a value determined based on the first frequency.

2. The battery diagnostic device of claim 1, characterized in that the calculation unit diagnoses the battery as normal if the absolute difference between the real part of the first impedance and the real part of the second impedance is equal to or less than a threshold value, or the calculation unit diagnoses the battery as normal if the ratio of the real part of the second impedance to the real part of the first impedance is equal to or less than a threshold value.

3. The battery diagnostic device of claim 1, characterized in that: the calculation unit identifies a third frequency at which a component due to the solution resistance of the equivalent circuit begins to appear in the Nyquist diagram; the calculation unit obtains a real part of a third impedance of the battery at the third frequency; the calculation unit obtains a correspondence relationship between a difference obtained by subtracting the real part of the third impedance from the real part of the second impedance and a deterioration state of the battery; and the calculation unit estimates the deterioration state of the battery using the correspondence relationship.

4. The battery diagnostic device of claim 1, characterized in that the calculation unit estimates that the battery is deteriorating at a first degradation acceleration if the real part of the first impedance is greater than the real part of the second impedance by a predetermined value or more, the calculation unit estimates that the battery is deteriorating at a rate less than the first degradation acceleration if the real part of the first impedance is not greater than the real part of the second impedance by the predetermined value or more, the calculation unit estimates that the battery is deteriorating at a second degradation acceleration if the ratio of the first impedance to the real part of the second impedance is greater than a predetermined value, and the calculation unit estimates that the battery is deteriorating at a rate less than the second degradation acceleration if the ratio of the first impedance to the real part of the second impedance is less than the predetermined value.

5. The battery diagnostic device according to claim 1, wherein said calculation unit diagnoses that said battery is abnormal if the real part of said second impedance is greater than the real part of said first impedance.

6. The battery diagnostic device according to claim 1, wherein the calculation unit identifies a third frequency at which a component due to the solution resistance of the equivalent circuit begins to appear in the Nyquist diagram; the calculation unit acquires a real part of a third impedance of the battery at the third frequency; the calculation unit diagnoses the battery as normal if an absolute difference between a first difference obtained by subtracting the real part of the third impedance from the real part of the first impedance and a second difference obtained by subtracting the real part of the third impedance from the real part of the second impedance is equal to or less than a threshold value; the calculation unit obtains a first ratio of the real part of the first impedance to the real part of the third impedance and a second ratio of the real part of the second impedance to the real part of the third impedance; and the calculation unit diagnoses the battery as normal if a ratio of the second ratio to the first ratio is equal to or less than a threshold value.

7. The battery diagnostic device according to claim 6, characterized in that the calculation unit obtains a correspondence relationship between a difference obtained by subtracting the real part of the third impedance from the real part of the second impedance and a deterioration state of the battery, and the calculation unit estimates the deterioration state of the battery using the correspondence relationship.

8. The battery diagnostic device of claim 6, wherein the calculation unit estimates that the battery is deteriorating at a first degradation acceleration if the real part of the first impedance is greater than the real part of the second impedance by a predetermined value or more, the calculation unit estimates that the battery is deteriorating at a rate less than the first degradation acceleration if the real part of the first impedance is not greater than the real part of the second impedance by the predetermined value or more, the calculation unit estimates that the battery is deteriorating at a rate less than the first degradation acceleration if the ratio of the first impedance to the real part of the second impedance is greater than a predetermined value, and the calculation unit estimates that the battery is deteriorating at a rate less than the second degradation acceleration if the ratio of the first impedance to the real part of the second impedance is less than the predetermined value.

9. The battery diagnostic device according to claim 6, wherein said calculation unit diagnoses that said battery is abnormal if the real part of said second impedance is greater than the real part of said first impedance.

10. The battery diagnostic device according to claim 1, characterized in that the calculation unit performs a Fourier transform on the current and the voltage using a value greater than the reciprocal of the time constant of the positive RC circuit of the equivalent circuit as a Nyquist frequency, and the calculation unit obtains the real part of the second impedance based on the result of the Fourier transform.

11. The battery diagnostic device of claim 1, characterized in that the calculation unit identifies the second frequency within a frequency region lower than the Nyquist frequency in the phase frequency characteristics of the voltage and the current, and obtains the real part of the second impedance by dividing the amplitude of the voltage at the second frequency by the amplitude of the current at the second frequency.

12. The battery diagnostic device according to claim 1, wherein the first frequency is equal to or less than five times the reciprocal of the time constant of the positive RC circuit of the equivalent circuit.

13. A battery diagnostic method for diagnosing a battery state, comprising the steps of: acquiring detection values ​​of the voltage and current output by the battery; and diagnosing the state of the battery, wherein in the diagnosing step, a first frequency is identified at which a component due to a diffusion resistance of an equivalent circuit of the battery begins to appear in a Nyquist diagram of the battery; in the diagnosing step, a second frequency is identified at which the phase of the voltage and the phase of the current match in the phase-frequency characteristics of the voltage and the current when a rising current or a falling current is applied to the battery; in the diagnosing step, a first impedance of the battery at the first frequency and a second impedance of the battery at the second frequency are acquired; and in the diagnosing step, the state of the battery is diagnosed using the real part of the first impedance and the real part of the second impedance, the diagnosing step identifies the second frequency based on a waveform when a time length from when the rising current starts to rise until it finishes rising or a time length from when the falling current starts to fall until it finishes falling is a value between a value determined based on a time constant of a positive RC circuit of the equivalent circuit and a value determined based on the first frequency.

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