WO2024111364A1 - インピーダンス検出装置及びインピーダンス検出方法 - Google Patents

インピーダンス検出装置及びインピーダンス検出方法 Download PDF

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Publication number
WO2024111364A1
WO2024111364A1 PCT/JP2023/039264 JP2023039264W WO2024111364A1 WO 2024111364 A1 WO2024111364 A1 WO 2024111364A1 JP 2023039264 W JP2023039264 W JP 2023039264W WO 2024111364 A1 WO2024111364 A1 WO 2024111364A1
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Prior art keywords
impedance
measurement data
secondary battery
current
voltage
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PCT/JP2023/039264
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English (en)
French (fr)
Japanese (ja)
Inventor
良介 森
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Nuvoton Technology Corp Japan
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Nuvoton Technology Corp Japan
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Priority to EP23894376.5A priority Critical patent/EP4624958A4/en
Priority to CN202380079753.3A priority patent/CN120202418A/zh
Priority to JP2024560037A priority patent/JPWO2024111364A1/ja
Publication of WO2024111364A1 publication Critical patent/WO2024111364A1/ja
Priority to US19/207,919 priority patent/US20250271505A1/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/389—Measuring internal impedance, internal conductance or related variables
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M10/00—Secondary cells; Manufacture thereof
    • H01M10/42—Methods or arrangements for servicing or maintenance of secondary cells or secondary half-cells
    • H01M10/48—Accumulators combined with arrangements for measuring, testing or indicating the condition of cells, e.g. the level or density of the electrolyte
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10—Energy storage using batteries

Definitions

  • This disclosure relates to an impedance detection device and an impedance detection method.
  • LiBs lithium-ion batteries
  • SOH State of Health
  • SOP State of Power
  • SOC State of Charge
  • Patent Document 1 discloses a system that creates a Nyquist plot from impedance for each frequency and estimates element parameters from the created Nyquist plot.
  • Patent Document 1 has the problem that the element parameters cannot be estimated accurately due to the influence of inductive components inside the secondary battery.
  • the present disclosure provides an impedance detection device and an impedance detection method that can estimate the element parameters of an equivalent circuit model of a secondary battery more accurately than ever before.
  • An impedance detection device is an impedance detection device that detects the internal impedance of a secondary battery, and includes an acquisition unit that acquires at least one of current measurement data and voltage measurement data at I (I is a natural number equal to or greater than 2) times in the transient response of the secondary battery when a predetermined current or a predetermined voltage is supplied to the secondary battery, and a calculation unit that calculates the internal impedance of the secondary battery based on at least one of the current measurement data and the voltage measurement data.
  • I is a natural number equal to or greater than 2
  • the calculation unit includes a first calculation unit that calculates the I pieces of impedance data using at least one of the voltage measurement data and the current measurement data, and a second calculation unit that calculates element parameters of the equivalent circuit model of the secondary battery based on an M (M is a natural number equal to or greater than 2)-order equation that is obtained from an equivalent circuit model of the secondary battery and indicates the internal impedance of the secondary battery as a linear sum of multiple terms, and the I pieces of impedance data.
  • M is a natural number equal to or greater than 2
  • the M-order equation is an equation based on a theoretical value of the transient response of the internal impedance according to the predetermined current or the predetermined voltage.
  • An impedance detection method for detecting the internal impedance of a secondary battery, and includes an acquisition step of acquiring at least one of current measurement data and voltage measurement data at I (I is a natural number of 2 or more) times in a pulse response of the secondary battery when a predetermined current or a predetermined voltage is supplied to the secondary battery, and a calculation step of calculating the internal impedance of the secondary battery based on at least one of the current measurement data and the voltage measurement data.
  • the I pieces of impedance data are calculated using at least one of the voltage measurement data and the current measurement data, and element parameters of the equivalent circuit model of the secondary battery are calculated based on an M (M is a natural number of 2 or more) order equation that is obtained from an equivalent circuit model of the secondary battery and indicates the internal impedance of the secondary battery as a linear sum of multiple terms, and the I pieces of impedance data.
  • M is a natural number of 2 or more
  • the M order equation is an equation based on a theoretical value of the transient response of the internal impedance according to the predetermined current or the predetermined voltage.
  • the impedance detection device can estimate the element parameters of an equivalent circuit model of a secondary battery more accurately than ever before.
  • FIG. 1 is a diagram showing a schematic configuration of an impedance detection system according to a first embodiment.
  • FIG. 2 is a diagram showing an equivalent circuit model of a battery cell including an internal impedance according to the first embodiment.
  • FIG. 3 is a diagram showing a circuit in which the electrode surface component in the internal impedance according to the first embodiment is replaced with a series connection of a plurality of RC parallel circuits.
  • FIG. 4 is a block diagram showing a functional configuration of the impedance detection device according to the first embodiment.
  • FIG. 5 is a flowchart showing the operation of the impedance detection device according to the first embodiment.
  • FIG. 6 is a diagram showing a schematic diagram of the input current to the battery cell and the output voltage from the battery cell according to the second embodiment.
  • FIG. 7 is a flowchart showing the operation of the impedance detection device according to the second embodiment.
  • FIG. 8 is a diagram showing the battery characteristics of the battery cell used in the verification.
  • FIG. 9A is a diagram showing various measurement data of the first battery cell.
  • FIG. 9B is a diagram showing various measurement data of the second battery cell.
  • FIG. 10A is a diagram showing the estimation result of an internal parameter (series resistance R 0 ) in the impedance detection device according to the present disclosure.
  • FIG. 10B is a diagram showing the estimation result of the internal parameter (serial connection value C tot ) in the impedance detection device according to the present disclosure.
  • FIG. 11A is a diagram showing a first example of measurement data of an input current and an output voltage of a first battery cell measured by a method according to a conventional example.
  • FIG. 11B is a diagram showing a second example of measurement data of the input current and output voltage of the first battery cell measured by the method according to the conventional example.
  • FIG. 11C is a diagram showing a third example of measurement data of the input current and output voltage of the first battery cell measured by a method according to the conventional example.
  • FIG. 12A is a diagram showing a Nyquist plot of the first battery cell obtained by the method according to the conventional example.
  • FIG. 12B is a diagram showing a Nyquist plot of the second battery cell obtained by the method according to the conventional example.
  • An impedance detection device is an impedance detection device that detects the internal impedance of a secondary battery, and includes an acquisition unit that acquires at least one of current measurement data and voltage measurement data at I (I is a natural number equal to or greater than 2) times in the transient response of the secondary battery when a predetermined current or a predetermined voltage is supplied to the secondary battery, and a calculation unit that calculates the internal impedance of the secondary battery based on at least one of the current measurement data and the voltage measurement data.
  • I is a natural number equal to or greater than 2
  • the calculation unit includes a first calculation unit that calculates the I pieces of impedance data using at least one of the voltage measurement data and the current measurement data, and a second calculation unit that calculates element parameters of the equivalent circuit model of the secondary battery based on an M (M is a natural number equal to or greater than 2)-order equation that is obtained from an equivalent circuit model of the secondary battery and indicates the internal impedance of the secondary battery as a linear sum of multiple terms, and the I pieces of impedance data.
  • M is a natural number equal to or greater than 2
  • the M-order equation is an equation based on a theoretical value of the transient response of the internal impedance according to the predetermined current or the predetermined voltage.
  • the impedance detection device can calculate the element parameters without using a Nyquist plot, and therefore can calculate the element parameters with almost no effect from the inductive reactance of the secondary battery. Therefore, the impedance detection device according to one aspect of the present disclosure can estimate the element parameters of the equivalent circuit model of the secondary battery with greater accuracy than conventional methods.
  • the specified current or the specified voltage may be a pulse current or a pulse voltage.
  • the second calculation unit may calculate the element parameters by assuming that the I pieces of impedance data are equal to the M-th order equation.
  • the element parameters can be calculated by substituting I pieces of impedance data into an M-th order equation. Because the impedance data does not substantially contain an inductive component, the impedance detection device can estimate the element parameters of the equivalent circuit model of the secondary battery with greater accuracy than conventional methods.
  • the M-th order equation may include the multiple terms obtained by expanding the theoretical value of the transient response of the internal impedance of the secondary battery obtained from the equivalent circuit model of the secondary battery with respect to time, the multiple terms may include (M+1) coefficients, and the second calculation unit may calculate each of the (M+1) coefficients by assuming that the I pieces of impedance data and the M-th order equation are equal, and calculate the element parameters based on the calculated (M+1) coefficients.
  • the impedance detection device calculates the (M+1) coefficients of an Mth order equation, making it possible to calculate element parameters without using a Nyquist plot.
  • the I coefficients may be greater than the (M+1) coefficients, and the (M+1) coefficients may be calculated using the least squares method.
  • the equivalent circuit model of the secondary battery may have a configuration in which one or more parallel circuits of a capacitor and a resistor are connected in series to a series resistor, and the second calculation unit may calculate at least the series resistance as the element parameter of the secondary battery.
  • the equivalent circuit model of the secondary battery may have a configuration in which one or more parallel circuits of a capacitor and a resistor are connected in series to a series resistor, and the second calculation unit may calculate the total value of the capacitors in at least one or more of the parallel circuits as an element parameter of the secondary battery.
  • the acquisition unit may acquire each of the current measurement data and the voltage measurement data
  • the first calculation unit may calculate the I pieces of impedance data by dividing the I pieces of current measurement data at the same corresponding time from the I pieces of voltage measurement data.
  • the impedance detection device can estimate the element parameters using more accurate impedance data, and therefore can estimate the element parameters with greater precision.
  • An impedance detection method for detecting the internal impedance of a secondary battery, and includes an acquisition step of acquiring at least one of current measurement data and voltage measurement data at I (I is a natural number equal to or greater than 2) times in a pulse response of the secondary battery when a predetermined current or a predetermined voltage is supplied to the secondary battery, and a calculation step of calculating the internal impedance of the secondary battery based on at least one of the current measurement data and the voltage measurement data.
  • the I pieces of impedance data are calculated using at least one of the voltage measurement data and the current measurement data, and element parameters of the equivalent circuit model of the secondary battery are calculated based on an M (M is a natural number equal to or greater than 2) order equation that is obtained from an equivalent circuit model of the secondary battery and indicates the internal impedance of the secondary battery as a linear sum of multiple terms, and the I pieces of impedance data.
  • M is a natural number equal to or greater than 2
  • the M order equation is an equation based on a theoretical value of the transient response of the internal impedance according to the predetermined current or the predetermined voltage.
  • each figure is a schematic diagram and is not necessarily an exact illustration. Therefore, for example, the scales and the like do not necessarily match in each figure.
  • substantially the same configuration is given the same reference numerals, and duplicate explanations are omitted or simplified.
  • ordinal numbers such as “first” and “second” do not refer to the number or order of components, unless otherwise specified, but are used for the purpose of avoiding confusion between and distinguishing between components of the same type.
  • FIG. 1 (Embodiment 1)
  • FIG. 1 An impedance detection system including an impedance detection device according to the present embodiment will be described with reference to FIGS. 1 to 5.
  • FIG. 1 An impedance detection system including an impedance detection device according to the present embodiment will be described with reference to FIGS. 1 to 5.
  • Fig. 1 is a diagram showing a schematic configuration of an impedance detection system 1 according to the present embodiment.
  • the impedance detection system 1 according to the present embodiment can be mounted on various application devices such as electric vehicles (EVs) and industrial machines.
  • EVs electric vehicles
  • the impedance detection system 1 includes a battery charger 10, a battery pack 20, a voltage measurement device 30, a shunt resistor 40, a current measurement device 50, and an impedance detection device 60.
  • the battery charger 10, the battery pack 20, and the shunt resistor 40 are connected in series. In other words, the battery charger 10, the battery pack 20, and the shunt resistor 40 form a series circuit.
  • the battery charger 10, the voltage measurement device 30, the shunt resistor 40, and the current measurement device 50 form a measurement circuit that supplies a pulse current or pulse voltage to the secondary battery and holds current measurement data and voltage measurement data at I (I is a natural number equal to or greater than 2) times during the pulse response of the secondary battery.
  • the battery charger 10 is a power source for supplying a pulse current or a pulse voltage to the battery pack 20.
  • the battery charger 10 supplies a pulse current for charging or discharging the battery pack 20.
  • voltage data for each of the multiple battery cells 21 of the battery pack 20 is acquired as measurement data.
  • the rise time and fall time of the pulse current are assumed to be 0 seconds.
  • the pulse current is also referred to as the input current.
  • the rise time and fall time are also referred to as the pulse rise time and pulse fall time.
  • the battery pack 20 is configured by connecting multiple battery cells 21 in series or in parallel. In this embodiment, the battery pack 20 is configured by connecting multiple battery cells 21 in series. Each of the multiple battery cells 21 is a secondary battery, for example a lithium ion battery, but may be other secondary batteries such as nickel-metal hydride batteries.
  • the battery pack 20 functions as a power source and supplies power to a load. When the impedance detection system 1 is mounted on an EV, the load is, for example, the EV's motor, but is not particularly limited thereto.
  • Each of the multiple battery cells 21 is connected at both ends to the voltage measuring device 30 via multiple voltage detection lines.
  • Fig. 2 is a diagram showing an equivalent circuit model of the battery cell 21 including the internal impedance according to this embodiment.
  • the battery cell 21 is configured to include a positive electrode, a negative electrode, and an electrolyte.
  • the equivalent circuit model of the battery cell 21 is formed by the open circuit voltage V OCV , an inductive component, and an internal impedance.
  • the inductive component may be included in the internal impedance.
  • the internal impedance is formed by an electrolyte component caused by the electrolyte, an electrode surface component caused by the electrode surface, and an active material component caused by the active material.
  • the open circuit voltage V OCV is the voltage of the battery cell 21 when no current is flowing through the battery cell 21, and is, for example, a voltage that serves as a DC (Direct Current) type voltage source.
  • the inductive component is formed by the inductive reactance L and resistance R L caused by the internal impedance of the battery cell 21.
  • the time constant due to the inductive reactance L and resistance R L is, for example, 1 ⁇ sec or less. Also, the width of the above-mentioned pulse current (the time width during which one pulse current is supplied) is sufficiently longer than the time constant due to the inductive reactance L and resistance R L.
  • the electrolyte component is the impedance caused by the electrolyte itself of the battery cell 21, and is the main component of the series resistance R 0.
  • the series resistance R 0 increases.
  • the electrode surface component is an impedance caused by the surfaces of the positive and negative electrodes, and is expressed by a parallel circuit of Cdl , which is expressed as a so-called CPE (Constant Phase Element), and a resistance Rct .
  • CPE Constant Phase Element
  • Rct Resistance
  • the CPE is a virtual element for expressing the behavior of the electrolyte of the battery cell 21, and its impedance ZCPE is expressed by the following formula 1.
  • Q in formula 1 is a constant equivalent to the capacitance of a normal capacitor
  • ⁇ is a constant that takes a decimal value between 0 and 1.
  • the time constant of the impedance caused by the electrode surface is several msec.
  • the active material (diffusion) component is an impedance caused by the inside of the positive electrode and the negative electrode, and is the so-called Warburg impedance ZW .
  • the time constant of the impedance caused by the active material is several seconds or more, which is much larger than the transient response time span of interest in the impedance detection system 1. Therefore, since the influence of the active material on the estimation of the internal impedance of the present disclosure is very small, the description of the active material is omitted in the following description.
  • the internal impedance is considered to be composed of an electrolyte component and an electrode surface component.
  • the electrode surface component is often expressed as a serial connection of multiple RC parallel circuits for mathematical analysis.
  • FIG. 3 is a diagram showing a circuit in which the electrode surface component in the internal impedance according to this embodiment has been replaced with a serial connection of multiple RC parallel circuits.
  • FIG. 3(a) shows the circuit before being replaced with a serial connection of multiple RC parallel circuits
  • FIG. 3(b) shows the circuit after being replaced with a serial connection of multiple RC parallel circuits.
  • one parallel circuit of Cdl and resistor Rct represented by CPE indicating the electrode surface component is represented by a serial connection of four RC parallel circuits.
  • the four RC parallel circuits include a parallel circuit of a capacitor C1 and resistor R1 , a parallel circuit of a capacitor C2 and resistor R2 , a parallel circuit of a capacitor C3 and resistor R3 , and a parallel circuit of a capacitor C4 and resistor R4 .
  • the total capacitor of the capacitors C1 to C4 is also referred to as a serial connection value Ctot .
  • the serial connection value Ctot means the total value of the capacitors in a parallel circuit of at least one capacitor and resistor.
  • the number of RC parallel circuits connected in series is just an example, and is appropriately determined depending on the type of the battery cell 21, etc.
  • the number of RC parallel circuits connected in series may be one or more.
  • the equivalent circuit model of the battery cell 21 has a configuration in which one or more parallel circuits of a capacitor and a resistor are connected in series to a series resistor R0 , and may have a configuration in which, for example, two or more parallel circuits of a capacitor and a resistor are connected in series to a series resistor R0 .
  • the number of battery cells 21 in the battery pack 20 and the voltage of each of the battery cells 21 are not particularly limited.
  • Each of the battery cells 21 may be, for example, a battery cell of the same specification.
  • the voltage measuring device 30 measures the voltage of the battery pack 20.
  • the voltage measuring device 30 is configured to be able to measure the voltage of each of the multiple battery cells 21 individually.
  • the voltage measuring device 30 may be configured to include an IC (Integrated Circuit) for measuring the voltage of the battery cells 21.
  • the voltage measurement device 30 measures the voltage of multiple battery cells 21 sequentially (in a chronological order), for example.
  • the shunt resistor 40 is a current detection resistor for detecting the current flowing through the above-mentioned series circuit.
  • the shunt resistor 40 is connected in series with the battery pack 20.
  • the shunt resistor 40 is connected between the negative side of the battery pack 20 (e.g., the negative electrode of the battery cell 21) and the battery charger 10. There are no particular limitations on the resistance value of the shunt resistor 40.
  • the current measuring device 50 detects the current flowing through the battery pack 20.
  • the current measuring device 50 is a resistance detection type current sensor that uses a shunt resistor 40, but may also be a magnetic field detection type current sensor.
  • the current measuring device 50 may be configured to include an IC for current measurement.
  • the impedance detection device 60 detects the internal impedance of the secondary battery. In this embodiment, the impedance detection device 60 detects the internal impedance of at least one of the multiple battery cells 21 and the entire battery pack 20 based on the voltage measurement data from the voltage measurement device 30 and the current measurement data from the current measurement device 50.
  • the impedance detection device 60 estimates the element parameters of the equivalent circuit model of the battery cell 21 using estimation based on pulse response, rather than using the method of estimating element parameters from a Nyquist plot described in the above-mentioned Patent Document 1.
  • the estimation accuracy of the element parameters may decrease due to the influence of inductive components, but the impedance detection device 60 uses estimation based on pulse response, so is less susceptible to the influence of inductive components and can accurately estimate the element parameters.
  • the estimation based on pulse response is an estimation method in which a pulsed current (or voltage) is input to the battery cell 21 and the input current (or input voltage) and a deviation voltage from the open circuit voltage VOCV of the battery cell 21 are measured.
  • the estimation based on pulse response can also be said to be an estimation method in which element parameters of an equivalent circuit model of the battery cell 21 are estimated from the transient response shape of the IR drop of the internal impedance of the battery cell 21.
  • the impedance detection device 60 will be described as being mounted, for example, in an EV, like the other components of the impedance detection system 1, but this is not limiting and the impedance detection device 60 may be provided separately from the other components.
  • the impedance detection device 60 may be configured as a server device or the like that is communicably connected to the EV.
  • FIG. 4 is a block diagram showing the functional configuration of the impedance detection device 60 according to this embodiment.
  • the impedance detection device 60 can be realized by an MPU (Micro Processor Unit) and a memory, etc. Furthermore, the processing by each of the functional blocks of the impedance detection device 60 is usually realized by a program execution unit such as a processor reading and executing software (programs) recorded on a recording medium such as a ROM.
  • a program execution unit such as a processor reading and executing software (programs) recorded on a recording medium such as a ROM.
  • the impedance detection device 60 includes an acquisition unit 61, a first calculation unit 62, an expansion unit 63, an equation formulation unit 64, a coefficient estimation unit 65, and a parameter estimation unit 66.
  • the coefficient estimation unit 65 and the parameter estimation unit 66 form a second calculation unit 60a, and the first calculation unit 62 and the second calculation unit 60a form a calculation unit 60b.
  • the calculation unit 60b calculates the internal impedance of the battery cell 21 based on the current measurement data and the voltage measurement data.
  • the acquisition unit 61 is an interface (e.g., a hardware interface) that acquires current measurement data and voltage measurement data at I (I is a natural number equal to or greater than 2) times during the pulse response of the battery pack 20 when a pulse current or pulse voltage is supplied to the battery pack 20.
  • the acquisition unit 61 acquires measurement data of the current flowing through the battery pack 20 and voltage measurement data for each of the multiple battery cells 21.
  • the acquisition unit 61 may acquire the current measurement data and voltage measurement data by wired communication (e.g., communication via wiring formed on a board) or may acquire the current measurement data and voltage measurement data by wireless communication.
  • the first calculation unit 62 detects the rising or falling time of the input current or input voltage, and calculates I pieces of impedance data by dividing the current measurement data from the voltage measurement data after the rising or falling time.
  • the voltage measurement data and current measurement data are time-series data including measurement data for at least I times, and the first calculation unit 62 divides the voltage measurement data and current measurement data for the same times.
  • I indicates the number of time points (the number of measurement points) at which measurements are taken to estimate the equivalent circuit parameters. Note that the number of voltage measurement data and current measurement data acquired by the acquisition unit 61 is greater than I, as it also includes data for detecting the rising or falling time of the input current or input voltage.
  • the I impedance data may be calculated by dividing each of the I voltage measurement data by an average current calculated from the I current measurement data, or by dividing the expected peak value of the pulse current by the expected peak value if the expected peak value is known.
  • the I impedance data may be calculated by dividing the average voltage calculated from the I voltage measurement data or the expected peak value of the pulse voltage by each of the I current measurement data if the expected peak value is known.
  • the impedance data does not substantially include, for example, an inductive component.
  • the voltage measurement data and the current measurement data may be data at a time that is not or is less affected by, for example, an inductive component.
  • the detection of the rise or fall time of the input current or input voltage may be performed by detecting the time when the first pulse peak value is obtained from the time series measurement data of the input current or input voltage, or by using another detection method.
  • the peak value may include an error, and for example, the time when the value is within ⁇ 5% of the average value calculated from I current measurement data or the expected peak value may be detected as the rise or fall time of the input current or input voltage.
  • the expansion unit 63 approximates an M-th order equation (for example, see Equation 4 described later) obtained from the equivalent circuit model of the battery cell 21 and expressing the internal impedance of the battery cell 21 as a linear sum of multiple terms (for example, each term of a polynomial shown in Equation 4 described later).
  • the expansion unit 63 approximates an M-th order equation (for example, see Equation 4 described later) expressed by multiple terms obtained by expanding the theoretical value Z(t) of the transient response of the internal impedance of the equivalent circuit model of the battery cell 21 with respect to time t (measurement time).
  • the expansion unit 63 obtains an M-th order equation, for example, by expanding the theoretical value Z(t) of the transient response into powers of time t.
  • the equation formulation unit 64 formulates I simultaneous equations for calculating each coefficient of the M-th order equation based on the I pieces of impedance data calculated by the first calculation unit 62 and the M-th order equation that has been power-expanded by the expansion unit 63.
  • the coefficient estimation unit 65 estimates the measurement coefficients, which are the coefficients of the Mth-order equation, by solving the I simultaneous equations formulated by the equation formulation unit 64.
  • the parameter estimation unit 66 estimates the element parameters based on the estimated measured coefficients of the M-th order equation and the theoretical coefficients of the M-th order equation (for example, see Equations 5 and 6 described below).
  • Fig. 5 is a flow chart showing the operation (impedance detection method) of the impedance detection device 60 according to this embodiment.
  • steps S10 and S20 and steps S30 and S40 shown in FIG. 5 are executed is not particularly limited, and they may be executed in parallel, or steps S30 and S40 may be executed before step S10. Also, while the flowchart shown in FIG. 5 is executed periodically, for example, steps S30 and S40 do not need to be executed every time, and may be executed at least once (for example, only the first time) at any timing.
  • the acquisition unit 61 acquires the measurement results of the pulse response of the battery pack 20 (S10).
  • the acquisition unit 61 acquires current measurement data including I times and voltage measurement data for each of the multiple battery cells 21.
  • the acquisition unit 61 outputs the acquired current measurement data and voltage measurement data to the first calculation unit 62.
  • the pulse response of the battery pack 20 is achieved by supplying a pulse current from the battery charger 10 to the battery pack 20.
  • Each of the I times is the time during which one pulse current is supplied.
  • multiple pulse responses may be obtained, and the average of multiple measured values at the same time may be taken for I times relative to the start time of each pulse current.
  • the first calculation unit 62 calculates I measurement values Z meas (ti) (impedance data) by dividing the current measurement data from the voltage measurement data (S20). The first calculation unit 62 outputs the measurement values Z meas (ti) calculated for each of the I time points to the equation formulation unit 64.
  • the expansion unit 63 also acquires a theoretical value Z(t) of the transient response of the equivalent circuit model of the battery cell 21 (S30).
  • the theoretical value Z(t) of the transient response is a theoretical value of the pulse response of the internal impedance of the battery cell 21.
  • the expansion unit 63 may acquire the theoretical value Z(t) of the transient response stored in a memory unit (not shown), or may acquire the theoretical value Z(t) of the transient response via the acquisition unit 61.
  • the theoretical value Z(t) of the transient response after the rise or fall of the input current is expressed by the following Equation 2. However, in Equation 2, the time of the rise or fall of the input current is set to 0 [sec].
  • ⁇ Cn is expressed by the following formula 3.
  • ⁇ Cn indicates the reciprocal of the time constant.
  • the input current or input voltage is, for example, a current or voltage whose shape allows the theoretical value Z(t) of the transient response of the internal impedance of the battery cell 21 to be expressed by equivalent circuit parameters.
  • the input current e.g., pulse current
  • the input voltage e.g., pulse voltage
  • the expansion unit 63 performs power expansion of the theoretical value Z(t) at time t and replaces the coefficient (measurement coefficient) with A m (S40).
  • the expansion unit 63 performs Maclaurin expansion of Equation 2, for example, to approximate it to an M-th order equation, as shown in Equation 4.
  • the Maclaurin expansion is an example of power expansion.
  • Equations 5 and 6 are obtained by substituting the coefficients with A m . Equations 5 and 6 show the relationship between the coefficients A m and the element parameters. A 0 and A m are examples of M+1 theoretical coefficients.
  • the M-th order equation is expressed as a polynomial that approximates the theoretical value Z(t) of the transient response of the internal impedance of the battery cell 21 obtained from the equivalent circuit model of the battery cell 21 by a power of time t (measurement time).
  • the M-th order equation can also be said to be an equation that expands over time as an approximation of the theoretical impedance obtained from the equivalent circuit model of the battery cell 21.
  • the M-th order equation does not have a reactance component, for example.
  • the M-th order equation can also be said to be an equation based on the theoretical value Z(t) of the transient response of the internal impedance of the battery cell 21 according to a specified current or a specified voltage.
  • the order M is appropriately selected according to the purpose or required estimation accuracy. By increasing the order M, the estimation accuracy of the element parameters can be improved. Furthermore, by decreasing the order M, the amount of calculation required to estimate the element parameters can be reduced.
  • Equation 2 The method of expanding Equation 2 into an M-th order equation is not limited to the Maclaurin expansion, and a power series expansion of another function may be used.
  • An example of a power series expansion of another function is the Taylor expansion.
  • the equation formulation unit 64 formulates simultaneous equations by comparing the measured values Z meas (t i ) with the power expansion of t of the theoretical values Z(t) (S50).
  • the equation formulation unit 64 formulates simultaneous equations based on the I measured values Z meas (t i ) calculated by the first calculation unit 62 and the M-th order equation expanded by the expansion unit 63.
  • the equation formulation unit 64 formulates multiple simultaneous equations shown in Equation 7 below, assuming that the measured values Z meas (t i ) at the same time and the M-th order equation are equal.
  • Equation 7 I simultaneous equations are created, as shown in Equation 7.
  • the coefficient estimation unit 65 estimates the coefficient A m by solving the I simultaneous equations formulated by the equation formulation unit 64 (S60).
  • the coefficient estimation unit 65 calculates (M+1) coefficients A m when the measured values Z meas (t i ) of the I impedance data are substituted into an M-th order equation.
  • the coefficient A m calculated in this way by the simultaneous equations using the actual measurement data is an example of a measurement coefficient.
  • the coefficient estimation unit 65 may estimate the coefficient A m by transforming Equation 7 into a matrix format and substituting the letters in Equations 8, 9, and 10 below.
  • the coefficient set ⁇ can be estimated using an estimation method such as the least squares method.
  • the coefficient set ⁇ using the least squares method it is estimated using the following equation 11.
  • p 1 , p 2 , . . . indicate the weights of the measurement points at times t 1 , t 2 , .
  • the coefficient estimating section 65 may estimate the coefficient A m by the least squares method.
  • the parameter estimation unit 66 calculates the element parameters by assuming that the (M+1) theoretical coefficients are equal to the (M+1) measured coefficients.
  • the estimated value of coefficient A0 can be used as is in any case for the estimated value of series resistance R0 , so parameter estimation unit 66 sets coefficient A0 to series resistance R0 .
  • the impedance detection device 60 to estimate the series resistance R0 and the serial connection value Ctot in the element parameters of the equivalent circuit model of the battery cell 21 shown in Fig. 3(b). Note that the impedance detection device 60 only needs to estimate at least one of the series resistance R0 and the serial connection value Ctot .
  • the impedance detection device 60 may calculate at least the series resistance R0 as the element parameter of the battery cell 21, and may calculate a total value of the capacitors in at least one parallel circuit of a capacitor and a resistor (serial connection value Ctot ) as the element parameter of the battery cell 21.
  • the second calculation unit 60a calculates the element parameters of the equivalent circuit model of the battery cell 21 based on (M+1) theoretical coefficients and I impedance data.
  • Fig. 6 is a diagram showing the shapes of the input current to the battery cell 21 and the output voltage from the battery cell 21 according to this embodiment.
  • Fig. 6(a) is a diagram showing the input current to the battery cell 21
  • Fig. 6(b) is a diagram showing the output voltage when the input current shown in Fig. 6(a) is input to the battery cell 21.
  • the pulse rise time of the input current is not 0.
  • the input current rises from 0 [A] (0%) to Ip [A] (100%) between time t a and time t b .
  • Time t a is the time when the application of the pulse current by the battery charger 10 is started.
  • Time t b is the time when the current reaches Ip.
  • Ip is, for example, the peak value of the pulse current by the battery charger 10.
  • the change in current is represented by, for example, a slope D.
  • the relationship of the following formula 16 is also established.
  • the input current pulse fall time is not zero.
  • the rise time and fall time of the input current differ from those in embodiment 1.
  • Fig. 7 is a flowchart showing the operation (impedance detection method) of the impedance detection device 60 according to the present embodiment.
  • the impedance detection method according to this embodiment further includes step S110 between steps S10 and S20 shown in FIG. 5.
  • the first calculation unit 62 calculates the times t a and t b (S110). For example, the first calculation unit 62 calculates the times t a and t b from the time series data of the current measurement data from the current measurement device 50. When the waveform of the input current is unknown, the first calculation unit 62 calculates the slope D and the values of the times t a and t b in advance from the measured current value. Examples of the calculation method include a method using the relationship between two measurement points between the times t a and t b , and a least squares method using three or more measurement points, but are not limited to these.
  • the times t a and t b are relative times with a certain time as the reference (0 [sec]), and for example, the start time of acquiring the current measurement data and the voltage measurement data may be used as the reference, or either of the times t a and t b calculated in step S110 may be used as the reference.
  • the first calculation unit 62 calculates I measurement values Z meas (ti) (impedance data) by dividing the current measurement data from the voltage measurement data (S20), as in the first embodiment.
  • the first calculation unit 62 then outputs the calculated measurement values Z meas (ti) of the impedance data to the equation formulation unit 64.
  • the first calculation unit 62 also outputs the calculated times t a and t b to the parameter estimation unit 66.
  • the developing unit 63 also acquires (S30) a theoretical value Z(t) of the transient response of the equivalent circuit model of the battery cell 21.
  • the theoretical value Z(t) of the transient response is a theoretical value of the pulse response of the internal impedance of the battery cell 21.
  • the theoretical value Z(t) of the transient response after time tb is expressed by the following equation 17.
  • the expansion unit 63 expands the theoretical value Z(t) of the transient response in powers of t and replaces the coefficients with A m (S40).
  • the expansion unit 63 obtains Equation 18 and Equation 19 by, for example, expanding Equation 17 in Maclaurin expansion and replacing the coefficients with A m .
  • the coefficients A 0 and A m are an example of the M+1 theoretical coefficients.
  • the coefficient estimation unit 65 estimates the coefficient A m by solving the I simultaneous equations formulated by the equation formulation unit 64 (S60).
  • the coefficient estimation unit 65 calculates (M+1) coefficients A m when the I measured values Z meas (t i ) are substituted into an M-th order equation.
  • the calculated A m is an example of a measurement coefficient.
  • the parameter estimation unit 66 calculates Bm from Equation 14 and Equation 19, and uses that value to calculate the series resistance R0 from Equation 18.
  • step S110 may be omitted if the rise time and fall time are known numbers, even if they are finite values.
  • the results of verification of the estimation accuracy of the internal impedance in the impedance detection device 60 according to each of the above-mentioned embodiments will be described with reference to Fig. 8 to Fig. 12B.
  • the first battery cell 21 is a battery cell 21 that is close to new
  • the second battery cell 21 is a battery cell 21 that has deteriorated to a certain extent.
  • the element parameters of the battery cell 21 are assumed to be element parameters (see Fig. 8 below) extracted from an actual lithium ion battery (18650 type).
  • FIG. 8 is a diagram showing the battery characteristics of the battery cell 21 used in the verification.
  • the first battery cell and the second battery cell have the battery characteristics shown in FIG. 8.
  • the battery characteristics of the first battery cell and the second battery cell shown in FIG. 8 are values estimated by the AC impedance method.
  • the element parameters also include high-frequency inductive components (L, R L in FIG. 8) contained in the battery cell 21 (for example, a lithium ion battery).
  • the battery cell 21 for example, a lithium ion battery.
  • the theoretical battery internal impedance value is regarded as virtual measurement data (virtual measurement data), and the internal parameter estimation flow of the present disclosure is executed.
  • the virtual measurement data shown in the following FIG. 9A etc. also takes into account the high-frequency inductive component contained in the battery cell 21.
  • the virtual measurement data is data on a circuit in which the circuit on the electrode surface in the dashed frame in FIG. 2 is replaced with the circuit shown in FIG. 3(b).
  • Fig. 9A shows various measurement data of the first battery cell.
  • Fig. 9B shows various measurement data of the second battery cell.
  • FIG. 9A and (a) of FIG. 9B show time series data (current measurement data) of the input current, with the horizontal axis representing time and the vertical axis representing the current value.
  • the data shown in (a) of FIG. 9A and (a) of FIG. 9B corresponds to data acquired from the current measuring device 50.
  • FIG. 9A and (b) of FIG. 9B show time series data (voltage measurement data) of the output voltage, with the horizontal axis representing time and the vertical axis representing the voltage value.
  • the data shown in (b) of FIG. 9A and (b) of FIG. 9B corresponds to data acquired from the voltage measurement device 30.
  • FIG. 9A and (c) of FIG. 9B show time series data (impedance data) of impedance (internal impedance), with the horizontal axis representing time and the vertical axis representing impedance.
  • the data shown in (c) of FIG. 9A and (c) of FIG. 9B are calculated by the first calculation unit 62.
  • the impedance shown in (c) of FIG. 9A is calculated from (a) and (b) of FIG. 9A.
  • the impedance shown in (c) of FIG. 9B is calculated from (a) and (b) of FIG. 9B.
  • data after time 0 [sec] is used to estimate the internal parameters.
  • a large amount of data close to time 0 [sec] e.g., the first half of the pulse current width
  • the estimation accuracy can be improved.
  • Using a large amount here means that data from the first half of the pulse current width is used more than data from the second half of the pulse current width.
  • a large amount of data far from time 0 [sec] e.g., the second half of the pulse current width
  • it is possible to reduce the influence of noise Using a large amount here means that data from the second half of the pulse current width is used more than data from the first half of the pulse current width.
  • Time 0 [sec] is the time when the pulse current supplied to the battery cell 21 reaches a peak value (here, 1.8 [A]), and corresponds to time tb shown in FIG. 6(a), for example.
  • Fig. 10A is a diagram showing the estimation results of the internal impedance (series resistance R 0 ) in the impedance detection device 60 according to the present disclosure.
  • Fig. 10B is a diagram showing the estimation results of the internal impedance (serial connection value C tot ) in the impedance detection device 60 according to the present disclosure.
  • the power expansion is of three types: quadratic function, quartic function, and sextic function.
  • the time t i is 120 [ ⁇ sec], 180 [ ⁇ sec], 240 [ ⁇ sec], ..., 1020 [ ⁇ sec], and the sampling interval is 60 [ ⁇ sec]. In other words, the number of measurement points I is 16.
  • the estimation method for the coefficient A m in step S60 employs the weighted least squares method, and the weights are the powers of the reciprocal of time in the cases of a quadratic function, a quartic function, and a sextic function.
  • the weights are the powers of the reciprocal of time in the cases of a quadratic function, a quartic function, and a sextic function.
  • the measurement results of the series resistance R 0 include the items of rising/falling slope [ ⁇ sec], true value, quadratic function, quartic function, and sextic function.
  • the rising/falling slope [ ⁇ sec] is the value of the time (t b ⁇ t a ), that is, the rising/falling time, and there are three types: 10 ⁇ sec, 200 ⁇ sec, and 500 ⁇ sec.
  • the true value indicates the series resistance R0 measured by an AC impedance method.
  • the quadratic function, the quartic function, and the sextic function represent the estimation results of the series resistance R 0 , which is an example of the internal impedance, when estimated using a function in which the degree M of an M-th order equation is 2, 4, and 6.
  • the measurement result of the serial connection value C tot includes items such as rising/falling slope [ ⁇ sec], true value, quadratic function, quartic function, and sextic function.
  • the rising/falling slope [ ⁇ sec] is the value of the time (t b ⁇ t a ) and has three values: 10 ⁇ sec, 200 ⁇ sec, and 500 ⁇ sec.
  • the true value indicates the serial connection value C tot measured by an AC impedance method.
  • the quadratic function, the quartic function, and the sextic function indicate the estimation results of the serial connection value C tot , which is an example of the internal impedance, when estimated using a function in which the degree M of an M-th order equation is 2, 4, and 6.
  • the conventional method is a method for estimating element parameters from a Nyquist plot, as shown in Patent Document 1.
  • FIGS. 11A to 11C are diagrams showing examples of measurement data of the input current and output voltage of the first battery cell measured by the method according to the conventional example.
  • the rise/fall times are different in Fig. 11A, where the rise/fall time is 10 [ ⁇ sec], Fig. 11B, where the rise/fall time is 200 [ ⁇ sec], and Fig. 11C, where the rise/fall time is 500 [ ⁇ sec].
  • the sampling interval is 60 [ ⁇ sec]
  • the number of Fourier transform (FFT) points is 256
  • the measurement data of the output voltage is the theoretical value of the output voltage for the input current of a circuit in which the inductive component shown in Fig. 2 is connected in series to the circuit shown in Fig. 3(b), and is used as the virtual measurement data.
  • Figure 12A is a diagram showing the Nyquist plot of the first battery cell obtained by the method of the conventional example.
  • (a) of Figure 12A is plotted based on Figure 11A
  • (b) of Figure 12A is plotted based on Figure 11B
  • (c) of Figure 12A is plotted based on Figure 11C.
  • Figure 12B is a diagram showing the Nyquist plot of the second battery cell obtained by the method of the conventional example.
  • Figures 12A(a) and 12B(a) show Nyquist plots when the rise/fall time is 10 [ ⁇ sec]
  • Figures 12A(b) and 12B(b) show Nyquist plots when the rise/fall time is 200 [ ⁇ sec]
  • Figures 12A(c) and 12B(c) show Nyquist plots when the rise/fall time is 500 [ ⁇ sec].
  • the horizontal axis indicates the real part of the AC impedance
  • the vertical axis indicates the imaginary part of the AC impedance.
  • the Nyquist plot varies depending on the rise/fall time. For example, when the rise/fall time is extremely small (10 ⁇ sec in this case), uncertainty arises in the rise/fall positions as described above, which is thought to be one of the causes of the Nyquist plot not being drawn accurately. Also, when the rise/fall time is extremely large (500 ⁇ sec in this case), the frequency components on the high-frequency side of the input current pulse become extremely small as described above, which is thought to be one of the causes of the poor depiction accuracy of the Nyquist plot at points on the high-frequency side.
  • the sampling interval e.g., 60 [ ⁇ sec]
  • the time constant e.g., 1 [ ⁇ sec] or less
  • the sampling interval is set to be equal to or less than the time constant, it is possible to obtain information on the transient response due to the inductive reactance L and resistance R L.
  • the sampling interval of ICs currently in practical use is approximately 60 [ ⁇ sec], and it is difficult to realize an IC that operates at a sampling interval that is equal to or less than the time constant due to the inductive reactance L and resistance R L.
  • the impedance detection device 60 can estimate (e.g., calculate) the element parameters without using a Nyquist plot, and therefore can estimate (e.g., calculate) the element parameters almost without being affected by the inductive reactance of the battery cell 21. Therefore, the impedance detection device 60 according to one aspect of the present disclosure can estimate the element parameters of the equivalent circuit model of the battery cell 21 with greater accuracy than conventional methods.
  • the impedance detection device has been described as a device that detects the individual impedance of multiple battery cells in a battery pack, but the device may also detect the impedance of the entire battery pack by measuring the voltage of the entire battery pack using the voltage measurement device 30.
  • the impedance detection device includes an expansion unit, but this is not limiting.
  • the impedance detection device may include a storage unit that stores the expanded M-order equation instead of the expansion unit.
  • the element parameters may be estimated using an impulse response or a ramp response.
  • the theoretical value Z(t) of the transient response of the internal impedance used in (Equation 2) also uses a theoretical value according to the response used.
  • the impulse current or ramp current is an example of a predetermined current
  • the impulse voltage or ramp voltage is an example of a predetermined voltage.
  • a switch pulse generating device e.g., a pulse generator, etc.
  • a voltage waveform acquiring device e.g., an oscilloscope, etc.
  • a computing device e.g., a PC (Personal Computer), etc.
  • each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for each component.
  • Each component may be realized by a program execution unit such as a CPU or processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.
  • the division of functional blocks in the block diagram is one example, and multiple functional blocks may be realized as one functional block, one functional block may be divided into multiple blocks, or some functions may be transferred to other functional blocks. Furthermore, the functions of multiple functional blocks having similar functions may be processed in parallel or in a time-shared manner by a single piece of hardware or software.
  • the impedance detection device may be realized as a single device, or may be realized by multiple devices.
  • the components of the impedance detection device may be distributed in any way among the multiple devices.
  • the device that executes steps S10 and S20 shown in FIG. 5 may be a different device from the device that executes steps S30 and S40 shown in FIG. 5.
  • the communication method between the multiple devices is not particularly limited, and may be wireless communication or wired communication. Furthermore, wireless communication and wired communication may be combined between the devices.
  • each component described in the above embodiment may be realized as software, or may be realized as an LSI, which is typically an integrated circuit. These may be individually integrated into one chip, or may be integrated into one chip to include some or all of them.
  • LSI is used, but depending on the degree of integration, it may be called IC, system LSI, super LSI, or ultra LSI.
  • the method of integration is not limited to LSI, and may be realized with a dedicated circuit (a general-purpose circuit that executes a dedicated program) or a general-purpose processor. After LSI manufacture, a programmable FPGA (Field Programmable Gate Array) or a reconfigurable processor that can reconfigure the connection or settings of circuit cells inside the LSI may be used.
  • a programmable FPGA Field Programmable Gate Array
  • reconfigurable processor that can reconfigure the connection or settings of circuit cells inside the LSI may be used.
  • an integrated circuit technology that replaces LSI appears due to advances in semiconductor technology or a different
  • Another aspect of the present disclosure may be a computer program that causes a computer to execute each of the characteristic steps included in the impedance detection method shown in either FIG. 5 or FIG. 7.
  • the program may be a program to be executed by a computer.
  • one aspect of the present disclosure may be a non-transitory computer-readable recording medium on which such a program is recorded.
  • such a program may be recorded on a recording medium and distributed or circulated.
  • the distributed program may be installed in a device having another processor, and the program may be executed by that processor, thereby making it possible to cause that device to perform each of the above processes.
  • This disclosure is useful for systems that manage batteries, etc.

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PCT/JP2023/039264 2022-11-24 2023-10-31 インピーダンス検出装置及びインピーダンス検出方法 Ceased WO2024111364A1 (ja)

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