JP7616487B2 - Battery impedance estimation device and battery impedance estimation method - Google Patents

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based on Japanese Application No. 2022-93011, filed on June 8, 2022, the contents of which are incorporated herein by reference.

The present disclosure relates to an apparatus and method for estimating the impedance of a secondary battery.

Various techniques have been proposed for estimating the impedance of secondary batteries such as lithium-ion batteries. For example, in Patent Document 1, when a step-like current is applied to a battery, the parameters are estimated by sweeping the impedance parameters and performing curve fitting on the measured voltage response waveform data for a time response formula established from an assumed battery model. In Patent Document 2, an AC excitation current is generated, the current flowing through the battery and the battery terminal voltage are measured, and the impedance is estimated by calculation.

Patent No. 7041848 International Publication No. 2020/003841

The technology of Patent Document 1 allows easy measurement, but requires high-speed sampling of measurement data, resulting in a huge amount of data to be handled. Furthermore, curve fitting also requires repeated trial and error, which requires huge computing power. Furthermore, the technology of Patent Document 2 allows impedance to be obtained for any frequency, but requires measurements for many frequencies to estimate parameters, which takes a long time. Furthermore, a circuit that generates an excitation current must be added to obtain impedance, which increases costs.

The present disclosure has been made in consideration of the above circumstances, and its purpose is to provide a battery impedance estimation device and method that can estimate battery impedance without requiring enormous computing power or dedicated circuitry.

According to the battery impedance estimation device of claim 1, the current excitation unit passes an excitation current through the battery, and the voltage measurement unit A/D converts and measures the terminal voltage of the battery. When the control unit instructs the current excitation unit to pass current through the battery and causes the voltage measurement unit to start measuring the terminal voltage, the impedance estimation unit calculates a time constant from voltage waveform data for a certain section after a predetermined time has elapsed since the battery was passed through, and estimates the impedance of the battery from that time constant.

In the terminal voltage waveform that changes in response to the passage of current through a battery, there is a time domain in which the resistive, inductive, and capacitive components of the battery's impedance are dominant. Therefore, by analyzing the terminal voltage waveform and performing calculations on the time domain in which the capacitive component is dominant, the time constant can be found. Once the time constant is found, the capacitive component of the impedance can be found. This makes it possible to estimate the battery impedance without requiring huge computing power or dedicated circuits.

Specifically , in the impedance estimation unit, the integral value calculation unit obtains a first integral value by integrating the voltage value in a first integral period after a predetermined time has elapsed since the battery was energized, and obtains a second integral value by integrating the voltage value in a second integral period that follows the first integral period and has the same length as the first integral period. The time constant calculation unit measures a voltage value Ve after a predetermined time has elapsed since the second integral period, and, assuming that the lengths of the first and second integral periods are period Tint, obtains a time constant τ from the ratio of the first integral value minus the product of the voltage value Ve and the period Tint, which is equal to the length of each integral period, to the second integral value minus the product of the voltage value Ve and the period Tint, where Tint is the length of each of the first and second integral periods.

Furthermore , the impedance estimation unit measures the terminal voltage V0 and current I0 of the battery before the initial measurement unit applies current to the battery. The extreme value measurement unit determines the maximum or minimum value Vm of the terminal voltage of the battery within a certain period from the time when current is applied to the battery, and measures the current Im of the battery that flowed at the time when the maximum or minimum value Vm was indicated.

When measuring the voltage value Ve, the impedance calculation unit measures the battery current Ie at that time and calculates the resistive component R0 of the battery impedance using the following equation:
R0=(Vm-V0)/(Im-I0)
The capacitive resistance component R1 of the battery impedance is calculated using the following formula:
R1=(Ve-V0)/(Ie-I0)-R0
The capacitance value C1 of the capacitive part of the battery impedance is calculated by the following formula: C1 = τ / R1
and calculate.

The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a functional block diagram showing a configuration of a battery impedance estimation device in a first embodiment; FIG. 2 is a diagram showing an impedance model of a battery; FIG. 3 is a diagram showing a Cole-Cole plot of a battery; FIG. 4 is a diagram showing a response voltage waveform when a step-like excitation current is applied to a battery; FIG. 5 is a flowchart showing the contents of an impedance estimation process. FIG. 6 is a timing chart corresponding to the process shown in FIG. FIG. 7 is a functional block diagram showing a configuration of a battery impedance estimation device in a second embodiment; FIG. 8 is a timing chart corresponding to the impedance estimation process. FIG. 9 is a functional block diagram showing a configuration of a battery impedance estimation device in a third embodiment; FIG. 10 is a timing chart corresponding to the impedance estimation process. FIG. 11 is a functional block diagram showing a configuration of a battery impedance estimation device in a fourth embodiment; FIG. 12 is a functional block diagram showing a configuration of a battery impedance estimation device in a fifth embodiment; FIG. 13 is a flowchart showing the contents of an impedance estimation process. FIG. 14 is a timing chart corresponding to the process shown in FIG. FIG. 15 is a timing chart showing an excitation current waveform in the sixth embodiment.

First Embodiment
As shown in FIG. 1, the battery impedance estimation device of this embodiment is connected to an assembled battery 2 formed by connecting a plurality of unit batteries 1, which are, for example, lithium ion secondary batteries, in series. An analog filter 3 is connected to both ends of each unit battery 1. One voltage measurement unit 4 is provided for each number of unit batteries 1 connected in series, for example, about 8 to 40. In the voltage measurement unit 4, a ΔΣ A/D converter 5 and a digital filter 6 are connected in series to each analog filter 3. The voltage measurement unit 4 also includes a voltage measurement control unit 7 and a communication unit 8. The output terminals of each digital filter 6 are connected to the input terminals of the voltage measurement control unit 7. The voltage measurement control unit 7, which corresponds to the impedance estimation unit, analyzes the voltage response waveform data to estimate the impedance of the battery 1.

A current detection resistor 9 is connected to the lowest potential side of the battery pack 2. An analog filter 3 is also connected to both ends of the current detection resistor 9. A current measurement unit 11 is connected to the analog filter 3. The current measurement unit 11 includes a ΔΣ type A/D converter 12, a digital filter 13, a current measurement control unit 14, and a communication unit 15, which are connected in series. A current excitation unit 16 is connected in parallel to the series circuit of the battery pack 2 and the current detection resistor 9. The current excitation unit 16 applies a charging current to the battery pack 2 or causes a discharging current to flow from the battery pack 2. The current passed through the battery pack 2 to perform impedance estimation is referred to as an "excitation current."

The voltage measurement unit 4, current measurement unit 11 and current excitation unit 16 are controlled by an overall control unit 17. The overall control unit 17 includes a communication unit 18, a calculation unit 19 and a control unit 20. The communication unit 18 is daisy-chain connected to the communication units 8 of the voltage measurement units 4(1) and 4(2) and the communication unit 15 of the current measurement unit 11. The control unit 20 outputs a current excitation command directly to the current excitation unit 16. The above constitutes the battery impedance estimation device 21.

Figure 2 shows an equivalent circuit model of the internal impedance of a typical secondary voltage, with inductive, resistive, capacitive and diffusive components connected in series. Figure 3 is a Cole-Cole plot, which shows the trajectory of battery impedance versus frequency plotted on a complex plane. As shown in Figure 4, when the current flowing through the battery is changed in roughly stepped fashion, the battery terminal voltage that can be observed from outside appears as the sum of the internal voltage waveforms corresponding to each impedance component.

In other words, the terminal voltage waveform that changes in response to the passage of current through the battery has a time domain in which the resistive, inductive, and capacitive components of the battery's impedance are dominant. Therefore, the time constant τ can be found by analyzing the terminal voltage waveform and performing calculations on the time domain in which the capacitive component is dominant.

Next, the operation of this embodiment will be described. As in the case shown in Figure 4, the response voltage waveform is analyzed when the current flowing through the battery 1 is changed in an approximately stepped manner. As shown in Figures 5 and 6, when the control unit 20 of the overall control unit 17 transmits a waveform analysis instruction to the voltage measurement unit 4 and the current measurement unit 11 (S1), the voltage measurement unit 4 and the current measurement unit 11 measure the voltage V0 and current I0 of the battery 1 at that time (S2). Step S2 corresponds to the initial measurement unit.

The control unit 20 also instructs the current excitation unit 16 to apply an excitation current to the battery pack 2 (S3). The application of the excitation current here means changing the current flowing through the battery pack 2 in a roughly step-like manner from I0 to I1, as shown in Fig. 6. The apparent current waveform becomes the waveform when the battery 1 starts discharging or stops charging.

The voltage measurement unit 4 measures the terminal voltage V(t) of the battery 1 in the section from time t0 to t3 when the excitation current is applied (S4). Here, the section from time t0 to t1 is the time region where inductive impedance is dominant. Time t2 is the point where the response section corresponding to inductivity ends and resistive impedance becomes dominant and changes. And the section from time t2 to t6 is the time region where capacitive impedance is dominant. Incidentally, since the response corresponding to diffusive impedance is extremely slow, it can be considered to reach approximately 0 V in a short period of time.

For measurements, it is desirable to make the amplitude of the response voltage somewhat large. Therefore, it is desirable to set the step excitation current value (I0-I1) to a somewhat large value, for example, 0.1 A to 100 A or more. Since the impedance of the battery is, for example, about 1 mΩ, a step excitation current value of 100 A results in a response voltage amplitude of about 100 mV.

In the next step S5, the maximum value of the voltage V(t) is found from the measurement result in step S4, and is designated as V2, and the current value measured at the time when the voltage V2 is measured is designated as I2. Then, the resistive component R0 of the impedance is calculated by the formula (1). Step S5 corresponds to the extreme value measurement section. Note that the voltage V2 corresponds to the voltage Vm, and the current I2 corresponds to the current Im.
R0=(V2-V0)/(I2-I0)...(1)

In the following steps S6 and S7, the voltage V(t) is integrated over the first integration period from time t3 to t4 and the second integration period from time t4 to t5 to obtain the first integration value INT1 and the second integration value INT2. The first integration period and the second integration period are set to the same length Tint. Steps S6 and S7 correspond to the integral value calculation section. The actual first integration value INT1 and second integration value INT2 are calculated by subtracting (V6 x Tint) from the integration result.

In step S8, the voltage V6 at time t6 when the change in the voltage value is estimated to have converged is measured. The current value I6 at time t6 is also measured. Then, the parallel resistance component R1 of the capacitive component of the impedance is calculated by equation (2) (S9). Note that the voltage V6 corresponds to the voltage Ve, and the current I6 corresponds to the current Ie.
R1=(V6-V0)/(I6-I0)-R0...(2)

In the next step S10, the time constant τ of the capacitive component is calculated as follows. Step S10 corresponds to a time constant calculation unit. In order to simplify the calculation, the voltage V6 at the time when the capacitive response ends is set to 0 V, and the change voltage value in the capacitive response is set to Vc.
The time constant τ is R1 × C1. The change in the terminal voltage of battery 1 due to the capacitive component, V(t), is given by

The integral value is

The integral values INT1 and INT2 are

When we divide the integral value INT2 by INT1, we get

Taking the logarithm of both sides of equation (7), we get

Therefore, the time constant τ is (9).

In the next step S11, the capacitive component C1 is calculated by dividing the time constant τ by the parallel resistance component R1 calculated in step S9. Here, from the viewpoint of calculation accuracy, that is, in order to obtain a highly accurate ratio of the integral values INT1 and INT2, it is better to make the start time t3 of the first integration period earlier. Therefore, it is desirable to make the times t2 and t3 coincident.

As described above, according to this embodiment, in the battery impedance estimation device 21, the current excitation unit 16 passes an excitation current through the battery 1, and the voltage measurement unit 4 A/D converts and measures the terminal voltage V(t) of the battery 1. When the control unit 20 of the overall control unit 17 instructs the current excitation unit 16 to pass current through the battery 1 and causes the voltage measurement unit 7 to start measuring the terminal voltage V(t), the voltage measurement control unit 7 calculates a time constant τ from voltage waveform data for a certain section after a predetermined time has elapsed, which is usually about 1 ms to 100 ms when the response due to the series resistance component and the inductive component ends, from the time point when current is passed through the battery 1, and estimates the capacitance component C1 of the impedance of the battery 1 from that time constant τ. This makes it possible to estimate the impedance of the battery 1 without requiring a huge computing capacity or a dedicated circuit.

More specifically, the voltage measurement control unit 7 obtains a first integral value INT1 by integrating the voltage value in a first integral period after a predetermined time has elapsed since the time when the battery 1 was energized, and obtains a second integral value INT2 by integrating the voltage value in a second integral period following the first integral period. Then, the voltage value V6 is measured after a predetermined time has elapsed since the second integral period, and the time constant τ is obtained from the ratio of the product of the voltage value V6 and the integral period Tint subtracted from the first integral value INT1 to the product obtained by subtracting the above product from the second integral value INT2.

Furthermore, the voltage measurement control unit 7 measures the terminal voltage V0 and current I0 of the battery 1 before energizing the battery 1, and within a certain period of time, usually 1 ms to 100 ms from the time of energization when the response due to the series resistance component and the inductive component ends, determines the maximum value V2 of the terminal voltage V(t) of the battery 1, and measures the battery current I2 that flowed at the time when the maximum value V2 was shown. Then, the current I6 that was passed through the battery 1 when the voltage value V6 was measured is measured, and the resistive resistance component R0 of the battery impedance is calculated using equation (1), the capacitive resistance component R1 is calculated using equation (2), and the capacitance value C1 of the capacitive part is calculated using equation (9). In this way, the resistance components R0 and R1 of the battery impedance, and the capacitance value C1 of the capacitive part can be specifically calculated.

Second Embodiment
Hereinafter, the same parts as those in the first embodiment are denoted by the same reference numerals and their explanations are omitted, and only the different parts are explained. A battery impedance estimation device 21A of the second embodiment shown in Fig. 7 includes a current measurement unit 11A and a general control unit 17A instead of the current measurement unit 11 and the general control unit 17. The difference from the battery impedance estimation device 21 of the first embodiment is that, as shown in Fig. 8, a control unit 20A of the general control unit 17A issues only an excitation instruction to the current excitation unit 16, and a waveform analysis instruction to the voltage measurement unit 4 is issued by a current measurement control unit 14A of the current measurement unit 11A.

That is, the current measurement control unit 14A detects that the current excitation unit 16 has applied a step-like excitation current by analyzing the current waveform data. Then, when application of the excitation current is detected, a waveform analysis instruction is given to the voltage measurement unit 4 via the communication unit 15.

Third Embodiment
A battery impedance estimation device 21B of the third embodiment shown in Fig. 9 is obtained by replacing the current excitation unit 16 in the battery impedance estimation device 21A of the second embodiment with a current excitation unit 16B, and by replacing the overall control unit 17A with an overall control unit 17B. The difference from the battery impedance estimation device 21A of the second embodiment is that, as also shown in Fig. 10, a control unit 20B of the overall control unit 17B does not issue an excitation instruction to the current excitation unit 16B. The current excitation unit 16B spontaneously applies an excitation current to the battery pack 2. The subsequent process is the same as in the second embodiment.

Fourth Embodiment
A battery impedance estimation device 22 of the fourth embodiment shown in Fig. 11 is obtained by replacing the voltage measurement units 4(1) and 4(2) in the battery impedance estimation device 21B of the third embodiment with voltage measurement units 23(1) and 23(2). The voltage measurement unit 23 includes a multiplexer 24, and an analog filter 3 corresponding to each battery 1 is connected to the multiplexer 24. The A/D converter 5 and the digital filter 6 are integrated into one set, and the voltage measurement control unit 7A is connected to one digital filter 6. According to the fourth embodiment configured as described above, the number of A/D converters 5 and digital filters 6 can be reduced, and the battery impedance estimation device 22 can be configured to be compact.

Fifth Embodiment
A battery impedance estimation device 25 of the fifth embodiment shown in Fig. 12 is configured by replacing the voltage measurement unit 4 and the current measurement unit 11A in the battery impedance estimation device 21B of the third embodiment with voltage and current measurement units 26 connected to n batteries 1, respectively. The voltage and current measurement unit 26 includes a voltage detection unit 27, a voltage measurement control unit 7A, a current detection unit 28, a voltage measurement control unit 14A, and a communication unit 8. The voltage detection unit 27 is an integration of the analog filter 3, the A/D converter 5, and the digital filter 6. The current detection unit 28 is an integration of the A/D converter 12 and the digital filter 13.

Sixth Embodiment
In the sixth embodiment, as shown in Fig. 13, steps S1 to S5 in the flow chart of the first embodiment are replaced with steps S12 to S14. Since step S1 is not included, the configuration of the battery impedance estimation device corresponds to those of the third and subsequent embodiments. In step S12, the current measurement control unit 14A detects the application of the excitation current, and issues a waveform analysis instruction to the voltage measurement unit 4 via the communication unit 15. Then, the voltage measurement unit 4 measures the voltage value V0 (S13).

In the next step S14, instead of finding the maximum voltage value as in step S5, the voltage at time t2, a certain time after time t0, is measured as V2 as shown in FIG. 14, and the resistive resistance component R0 of the battery impedance is found from equation (1). That is, the excitation current may ring due to the inductance component of the current path, but if the structure and shape of the battery 1 and wiring are determined, the ringing will converge within a known time. Therefore, as in the sixth embodiment, even if the voltage V2 is measured at time t2, a certain time after time t0, it can be measured with sufficient accuracy.

Seventh Embodiment
15 shows a seventh embodiment in which the excitation current applied to the battery 1 is increased in a substantially stepped manner from a current value I0 to a current value I1. The apparent current waveform is equal to the waveform at the start of charging the battery 1 or at the end of discharging. Basically, all of the embodiments can be applied, but in the case of the first embodiment, in step S5, the minimum value of the voltage is measured as voltage V2 instead of the maximum value.

Other Embodiments
The function of the impedance estimation unit does not necessarily have to be provided in the voltage measurement unit.
The present invention may be applied to secondary batteries other than lithium ion batteries.
Although the present disclosure has been described based on the embodiment, it is understood that the present disclosure is not limited to the embodiment or structure. The present disclosure also includes various modifications and modifications within the equivalent range. In addition, various combinations and forms, and other combinations and forms including only one element, more than one element, or less than one element, are also within the scope and concept of the present disclosure.

Claims (8)

A current excitation unit (16) that applies an excitation current to the battery (1);
a voltage measuring unit (4, 23, 27) for measuring the terminal voltage of the battery by A/D conversion;
A control unit (20) that controls the current excitation unit and the voltage measurement unit;
an impedance estimation unit (7, 7A) that, when the control unit issues an instruction to the current excitation unit to energize the battery and causes the voltage measurement unit to start measuring the terminal voltage, calculates a time constant from voltage waveform data for a certain section after a predetermined time has elapsed from the time when the current is applied to the battery, and estimates the impedance of the battery from that time constant ;
The impedance estimation unit
A first integral value is calculated by integrating the voltage value during a first integral period after a predetermined time has elapsed since the battery was energized,
an integral value calculation unit that integrates a voltage value within a second integral period that follows the first integral period and has the same length as the first integral period to obtain a second integral value;
measuring a voltage value Ve after a predetermined time has elapsed since the second integration period;
If the length of the first and second integration periods is a period Tint,
the first integral value minus the product of the voltage value Ve and the period Tint;
a time constant calculation unit that calculates a time constant τ from a ratio of the second integral value minus the product of the voltage value Ve and the period Tint;
an initial measurement unit that measures a terminal voltage V0 and a current I0 of the battery before energizing the battery;
Measure the current of the battery together with the terminal voltage of the battery;
an extreme value measurement unit that determines a maximum or minimum value Vm of a terminal voltage of the battery within a certain period from the time when a current is applied to the battery, and measures a current Im of the battery at the time when the maximum or minimum value Vm is indicated;
When measuring the voltage value Ve, a current Ie of the battery is measured at that time;
The resistive component R0 of the impedance of the battery is calculated using the following formula:
R0=(Vm-V0)/(Im-I0)
The capacitive resistance component R1 of the impedance of the battery is calculated using the following formula:
R1=(Ve-V0)/(Ie-I0)-R0
The capacitance value C1 of the capacitive part of the impedance of the battery is expressed by the following formula:
C1=τ/R1
and an impedance calculation unit that calculates the impedance of a battery by the above method. A current excitation unit (16) that applies an excitation current to the battery;
a voltage measuring unit (4, 23, 27) for measuring the terminal voltage of the battery by A/D conversion;
a current measuring unit (11A) that performs A/D conversion on the current passed through the battery and analyzes the measured current waveform data;
A control unit (20A) for controlling the current excitation unit;
The control unit instructs the current excitation unit to energize the battery;
When the current measurement unit detects that current flow to the battery has started based on the analysis result of the current waveform data and receives an instruction to analyze the voltage waveform data,
an impedance estimation unit (7, 7A) that calculates a time constant from voltage waveform data for a certain section after a predetermined time has elapsed since a current is applied to the battery, and estimates the impedance of the battery from that time constant ;
The impedance estimation unit
A first integral value is calculated by integrating the voltage value during a first integral period after a predetermined time has elapsed since the battery was energized,
an integral value calculation unit that integrates a voltage value within a second integral period that follows the first integral period and has the same length as the first integral period to obtain a second integral value;
measuring a voltage value Ve after a predetermined time has elapsed since the second integration period;
If the length of the first and second integration periods is a period Tint,
the first integral value minus the product of the voltage value Ve and the period Tint;
a time constant calculation unit that calculates a time constant τ from a ratio of the second integral value minus the product of the voltage value Ve and the period Tint;
an initial measurement unit that measures a terminal voltage V0 and a current I0 of the battery before energizing the battery;
Measure the current of the battery together with the terminal voltage of the battery;
an extreme value measurement unit that determines a maximum or minimum value Vm of a terminal voltage of the battery within a certain period from the time when a current is applied to the battery, and measures a current Im of the battery at the time when the maximum or minimum value Vm is indicated;
When measuring the voltage value Ve, a current Ie of the battery is measured at that time;
The resistive component R0 of the impedance of the battery is calculated using the following formula:
R0=(Vm-V0)/(Im-I0)
The capacitive resistance component R1 of the impedance of the battery is calculated using the following formula:
R1=(Ve-V0)/(Ie-I0)-R0
The capacitance value C1 of the capacitive part of the impedance of the battery is expressed by the following formula:
C1=τ/R1
and an impedance calculation unit that calculates the impedance of a battery by the above method. A current excitation unit (16B) that applies an excitation current to the battery;
a voltage measuring unit (4, 23, 27) for measuring the terminal voltage of the battery by A/D conversion;
a current measuring unit (11A) that performs A/D conversion on an excitation current passed through the battery and analyzes the measured current waveform data;
When the current measurement unit detects that current flow to the battery has started based on the analysis result of the current waveform data and inputs an instruction to analyze the waveform data,
an impedance estimation unit (7, 7A) that calculates a time constant from voltage waveform data for a certain section after a predetermined time has elapsed since a current is applied to the battery, and estimates the impedance of the battery from that time constant ;
The impedance estimation unit
A first integral value is calculated by integrating the voltage value during a first integral period after a predetermined time has elapsed since the battery was energized,
an integral value calculation unit that integrates a voltage value within a second integral period that follows the first integral period and has the same length as the first integral period to obtain a second integral value;
measuring a voltage value Ve after a predetermined time has elapsed since the second integration period;
If the length of the first and second integration periods is a period Tint,
the first integral value minus the product of the voltage value Ve and the period Tint;
a time constant calculation unit that calculates a time constant τ from a ratio of the second integral value minus the product of the voltage value Ve and the period Tint;
an initial measurement unit that measures a terminal voltage V0 and a current I0 of the battery before energizing the battery;
Measure the current of the battery together with the terminal voltage of the battery;
an extreme value measurement unit that determines a maximum or minimum value Vm of a terminal voltage of the battery within a certain period from the time when a current is applied to the battery, and measures a current Im of the battery at the time when the maximum or minimum value Vm is indicated;
When measuring the voltage value Ve, a current Ie of the battery is measured at that time;
The resistive component R0 of the impedance of the battery is calculated using the following formula:
R0=(Vm-V0)/(Im-I0)
The capacitive resistance component R1 of the impedance of the battery is calculated using the following formula:
R1=(Ve-V0)/(Ie-I0)-R0
The capacitance value C1 of the capacitive part of the impedance of the battery is expressed by the following formula:
C1=τ/R1
and an impedance calculation unit that calculates the impedance of a battery by the above method. The battery impedance estimation device according to claim 1 , wherein the certain period is from 1 millisecond to 100 milliseconds. The battery impedance estimation device according to claim 1 , wherein the predetermined time is between 1 millisecond and 100 milliseconds. A current is applied to the battery while measuring the terminal voltage of the battery;
obtaining a first integral value by integrating a voltage value during a first integral period after a predetermined time has elapsed since a current was applied to the battery;
integrating the voltage value during a second integration period that follows the first integration period and has the same length as the first integration period to obtain a second integration value;
measuring a voltage value Ve after a predetermined time has elapsed since the second integration period;
If the length of the first and second integration periods is a period Tint,
the first integral value minus the product of the voltage value Ve and the period Tint;
A time constant τ is calculated from a ratio of the second integral value minus the product of the voltage value Ve and the period Tint ;
Before energizing the battery, a terminal voltage V0 and a current I0 of the battery are measured;
Measure the current of the battery together with the terminal voltage of the battery;
A maximum or minimum terminal voltage Vm of the battery is obtained within a certain period of time from when the battery is energized, and a current Im of the battery is measured at the time when the maximum or minimum terminal voltage Vm is obtained;
When measuring the voltage value Ve, a current Ie of the battery is measured at that time;
The resistive component R0 of the impedance of the battery is calculated using the following formula:
R0=(Vm-V0)/(Im-I0)
The capacitive resistance component R1 of the impedance of the battery is calculated using the following formula:
R1=(Ve-V0)/(Ie-I0)-R0
The capacitance value C1 of the capacitive part of the impedance of the battery is calculated using the following formula:
C1=τ/R1
Battery impedance estimation method. The method for estimating battery impedance according to claim 6 , wherein the predetermined time period is between 1 millisecond and 100 milliseconds. 8. The method of claim 7 , wherein the certain period is between 1 millisecond and 100 milliseconds.

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