Simulation method, simulation apparatus, and program

Abstract

This simulation method is a method for calculating a voltage response of a secondary battery using an equivalent circuit model, the simulation method including a step for acquiring a parameter of an electrical characteristic of the equivalent circuit model, a step for acquiring current information, voltage information and temperature information, a step for identifying an SOC from the voltage information, a step for calculating an OCV using the SOC and current information, a step for calculating a first voltage drop using the current information and the parameter, a step for calculating a second voltage drop using the current information, the temperature information and the parameter, a step for calculating a third voltage drop using the current information and the parameter, and a step for calculating the voltage response from the OCV, the first voltage drop, the second voltage drop and the third voltage drop, wherein the second voltage drop is calculated on the basis of the Butler-Volmer equation, and the third voltage drop is calculated on the basis of a time domain equation applied to a circuit model including a constant phase element CPE.

Description

[Technical Field]

[0001] This invention relates to a simulation method, a simulation apparatus, and a program. [Background technology]

[0002] Methods for simulating the electrical characteristics of secondary batteries using equivalent circuit models are known from Patent Documents 1, 2, and 3. Patent Documents 1 and 2 include RC parallel circuits in their equivalent circuit models. Patent Document 3 includes a CPE (Constant Phase Element) in its equivalent circuit model. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2018-40684 [Patent Document 2] Japanese Patent Publication No. 2019-219275 [Patent Document 3] Japanese Patent Publication No. 2019-191029 [Overview of the project] [Problems that the invention aims to solve]

[0004] In the configurations described in Patent Documents 1 and 2, time constants are set in the equivalent circuit model using RC parallel circuits, but only one time constant can be set with a single RC parallel circuit. On the other hand, secondary batteries generally have many time constants due to the large number of components. For this reason, it was difficult to improve the accuracy of the simulation when setting time constants using RC parallel circuits. Furthermore, although CPE is used in Patent Document 3, the formula representing the impedance of the CPE in Patent Document 3 is described as a frequency domain formula using angular frequency ω. In such Patent Document 3, even when attempting to simulate the voltage response of a secondary battery using an equivalent circuit model given a current profile over a certain time series, it was not possible to obtain the voltage response of the secondary battery in the time domain.

[0005] The present invention has been made in view of the above, and aims to provide a simulation method, simulation apparatus, and program that can simulate the voltage response of a secondary battery in the time domain with higher accuracy. [Means for solving the problem]

[0006] One aspect of the present invention is a simulation method for calculating the voltage response of a secondary battery using an equivalent circuit model, comprising the steps of: obtaining parameters indicating the electrical characteristics of the equivalent circuit model; obtaining current information indicating the current at multiple time points obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery; identifying the state of charge (SOC) of the secondary battery from the voltage information; calculating the OCV using the SOC and the current information; and using the current information and the parameters to calculate the linear resistance included in the equivalent circuit model. The method comprises the steps of: calculating a first voltage drop due to the resistance component; calculating a second voltage drop due to the nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters; calculating a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters; and calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase-constant element CPE.

[0007] Another aspect of the present invention is a simulation device for calculating the voltage response of a secondary battery by setting an equivalent circuit model, comprising: an acquisition unit that acquires parameters indicating the electrical characteristics of the equivalent circuit model, current information indicating the current at multiple time points obtained by dividing a period in which a predetermined current profile is given into multiple sampling times, voltage information indicating the initial voltage of the secondary battery, and temperature information indicating the temperature of the secondary battery; an identification unit that identifies the SOC of the secondary battery from the voltage information; a first calculation unit that calculates the OCV using the SOC and the current information; and a first calculation unit that uses the current information and the parameters to calculate the linear resistance component included in the equivalent circuit model. The system comprises a second calculation unit for calculating the voltage drop, a third calculation unit for calculating the second voltage drop due to the nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters, a fourth calculation unit for calculating the third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters, and a fifth calculation unit for calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase-constant element CPE.

[0008] Another aspect of the present invention is a program for setting up an equivalent circuit model and calculating the voltage response of a secondary battery, comprising the steps of: obtaining parameters indicating the electrical characteristics of the equivalent circuit model; obtaining current information indicating the current at multiple time points obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery; identifying the state of charge (SOC) of the secondary battery from the voltage information; calculating the OCV using the SOC and the current information; and using the current information and the parameters to determine the linear resistance component included in the equivalent circuit model. The information processing device is made to perform the following steps: calculate a first voltage drop; calculate a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters; calculate a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and parameters; and calculate the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase constant element CPE. [Effects of the Invention]

[0009] According to the present invention, the voltage response of a secondary battery in the time domain can be simulated with higher accuracy by using a constant-phase element CPE based on a current profile reference. [Brief explanation of the drawing]

[0010] [Figure 1] Figure 1 shows the equivalent circuit model used in the present invention. [Figure 2] Figure 2 is a graph showing a comparative example of the voltage response VMEAS and the voltage response Vsim calculated according to appropriately defined RL, i0, α, p, T, RT, ch, and RT, dis. [Figure 3]Figure 3 is a graph showing a comparative example of the voltage response VMEAS and the voltage response Vsim calculated according to appropriately defined RL, i0, α, p, T, RT, ch, and RT, dis. [Figure 4] Figure 4 is a graph showing the time-series change of current based on the current profile given when the voltage response VMEAS shown in Figures 2 and 3 is obtained. [Figure 5] Figure 5 is a flowchart showing the processing flow performed in Embodiment 1. [Figure 6] Figure 6 is a block diagram showing the configuration of the simulation device. [Figure 7] Figure 7 is a block diagram showing the configuration of the voltage calculation unit and its inputs and outputs. [Figure 8] Figure 8 is a block diagram showing the configuration of the simulation device. [Figure 9] Figure 9 shows an example of data related to the simulation conditions. [Figure 10] Figure 10 shows the relationship between RL, which represents the electrical resistance of a linear resistance section, the initial temperature, and SOC. [Figure 11] Figure 11 shows the relationship between p, one of the values ​​that determine the characteristics of CPE, the initial temperature, and SOC. [Figure 12] Figure 12 is a flowchart showing the processing flow performed in Embodiment 2. [Figure 13] Figure 13 is a block diagram showing the configuration of an information processing device. [Modes for carrying out the invention]

[0011] The embodiments will be described in detail below with reference to the drawings. However, the present invention is not limited by these embodiments. Each embodiment is illustrative, and it goes without saying that partial substitution or combination of the configurations shown in different embodiments is possible. From Embodiment 2 onward, descriptions of matters common to Embodiment 1 will be omitted, and only the differences will be described. In particular, similar effects and benefits due to similar configurations will not be mentioned sequentially for each embodiment.

[0012] (Embodiment 1) Figure 1 shows an equivalent circuit model 1 used in the present invention. Equivalent circuit model 1 includes a power supply unit 11, a nonlinear resistance unit 12, a linear resistance unit 13, and a transient response unit 20.

[0013] The power supply unit 11 acts as a secondary battery. The voltage V shown in Figure 1. OC This indicates the open-circuit voltage (OCV) of the power supply unit 11.

[0014] The nonlinear resistor 12 is connected to the current flowing through the nonlinear resistor 12 and the voltage V across the ends of the nonlinear resistor 12. NL It behaves as an electrical resistance whose relationship with Z is not proportional. In Figure 1, Z BV The part labeled (i0,α) represents the nonlinear resistance component of the nonlinear resistance section 12. This nonlinear resistance component is an impedance that represents the voltage drop when a certain current flows through the nonlinear resistance section 12. Voltage V NL This represents the voltage drop caused by the voltage drop. The nonlinear resistance component can be determined based on the Butler-Volmer equation described later. i0 represents the exchange current. α represents the charge transfer coefficient.

[0015] The linear resistor 13 is connected to the current flowing through the linear resistor 13 and the voltage V across the ends of the linear resistor 13. L It behaves as an electrical resistance proportional to its relationship with [the given value].

[0016] The transient response section 20 includes a CPE 21, a first element 30, and a second element 40. The first element 30 has a first diode 31 and a charging resistor 32 connected in series. The second element 40 has a second diode 41 and a discharge resistor 42 connected in series. The CPE 21 behaves as a constant phase element (CPE). The CPE 21, the first element 30, and the second element 40 are connected in parallel.

[0017] As shown in FIG. 1, the first diode 31 is set as an element that allows current to flow from the first terminal 15 to the second terminal 16 of the equivalent circuit model 1 and does not allow reverse current to flow. Also, the second diode 41 is set as an element that allows current to flow from the second terminal 16 to the first terminal 15 of the equivalent circuit model 1 and does not allow reverse current to flow. Therefore, the equivalent circuit model 1 is set such that no current flows through the second element 40 by the second diode 41 under the condition that a charging current is applied, and no current flows through the first element 30 by the first diode 31 under the condition that a discharging current is applied. The charging resistor 32 and the discharging resistor 42 behave as electrical resistances.

[0018] Z in FIG. 1 CPE What is described as (p, T) is the impedance that represents the voltage drop by the CPE21. The voltage V T indicates the voltage that drops due to such a voltage drop. p and T are values that determine the characteristics of the CPE21. In the equivalent circuit model 1, the provision of the first element 30 and the second element 40 is useful when the characteristics of the secondary battery to be simulated by the equivalent circuit model 1 are different between discharging and charging.

[0019] The equivalent circuit model 1 is not an actual circuit, but is virtually set by arithmetic processing by the simulation devices 50 and 70 and the information processing device 90 described later. The equivalent circuit model 1 is set to perform a simulation that reproduces the voltage response of a secondary battery such as a lithium ion battery by arithmetic operation by the information processing device 90.

[0020] As a configuration example of a lithium ion battery which is a secondary battery reproduced by the equivalent circuit model 1, the main positive electrode active material is lithium iron phosphate (LFP: LiFePO4), lithium cobalt oxide (LiCoO2), lithium nickel cobalt manganese oxide (Li(Ni x Mn y Co z )O2, x + y + z = 1, x, y, and z are each 0 or more and 1 or less) or lithium nickel cobalt aluminum oxide (Li(Ni a Cob Al c Examples include lithium-ion batteries in which the θ is O2, a+b+c=1, and a, b, and c are each between 0 and 1, and the main negative electrode active material is graphite or a mixture of graphite and silicon oxide. In the following description of Embodiment 1, it is assumed that the voltage response of the lithium-ion battery is reproduced by the equivalent circuit model 1. When the term "reproduced target" is used, it refers to the lithium-ion battery in question. The secondary battery reproduced by the equivalent circuit model 1 is not limited to this, and may be a secondary battery with a different configuration.

[0021] Prior to the simulation using Equivalent Circuit Model 1, data on the target of reproduction is acquired. Specifically, the State of Charge (SOC) of the target of reproduction is adjusted within the range of 10% to 90%. The temperature of the target of reproduction is also adjusted within the range of -10°C to 50°C. The temperature of the target of reproduction is preferably the battery surface temperature. A predetermined current profile is then applied to the thus adjusted target of reproduction. This predetermined current profile, as shown in Figure 4 (described later), represents a current pattern that combines, over time, the current that charges the target of reproduction (charging current), the current that causes discharge from the target of reproduction (discharge current), and a current of no current (0 amperes) that does not cause intentional charging or intentional discharge of the target of reproduction. The voltage response V of the target of reproduction that occurs while this predetermined current profile is applied is then calculated. MEAS (See Figures 2 and 3) The voltage response V is measured. MEAS And, voltage response V MEAS The conditions under which the result was obtained are associated with the predetermined current profile and treated as data related to the reproducible target. Voltage response V MEAS The conditions under which the result is obtained include the state of clock (SOC) and temperature of the target system immediately before the predetermined current profile is applied to the target system. Furthermore, in Embodiment 1, the SOC-OCV data described later is also included in the data relating to the target system. The data relating to the target system functions as the source data.

[0022] In the following, when referred to as the true value, the voltage response V MEASThis refers to the voltage response V that occurs between the first terminal 15 and the second terminal 16 when the predetermined current profile described above is applied to the equivalent circuit model 1 via the first terminal 15 and the second terminal 16 under the same conditions as when the true value was obtained. sim Therefore, the voltage response V MEAS This is intended to reproduce the same characteristics as the target of reproduction using equivalent circuit model 1.

[0023] Voltage response V sim This can be expressed as shown in equation (1) below. That is, the voltage response V sim This is the voltage V shown in Figure 1. OC And, voltage V NL And, voltage V L And, voltage V T It is the sum of and . V sim =V OC +V T +V NL +V L ...(1)

[0024] Below, voltage V OC , voltage V NL , voltage V L , voltage V T The specific derivation methods for each of these will be explained in order. In this explanation, the time during which a predetermined current profile is applied will be referred to as the application time. At some point within the application time, the current generated in the reproduction target when the predetermined current profile is applied to the reproduction target will be denoted as i(t). Here, the value of t in i(t) corresponds to the application time. Note that t=0 indicates the time before the application time, i.e., the initial state. Therefore, in Embodiment 1, i(0) is 0 amperes because it is before the predetermined current profile is applied. Also, if the sampling time is 0.1 seconds, i(0.1) indicates the current at the point 0.1 seconds after the predetermined current profile has been applied to the reproduction target. In this case, i(0.2) indicates the current at the point 0.2 seconds after the predetermined current profile has been applied to the reproduction target. The sampling time is not limited to 0.1 seconds but can be any time.

[0025] Furthermore, in the description of Embodiment 1, various values ​​other than current may also be shown using (t) to indicate their value at a certain point in time. For example, the voltage V corresponding to the change in i(t) OC , voltage V NL , voltage V L , voltage V T Each change in V OC (t), V NL (t), V L (t), V T It can be shown as (t). Since the equivalent circuit model 1 is set up for the purpose of reproducing the object to be reproduced, V is set so that the current considered to be flowing through the equivalent circuit model 1 becomes i(t). OC (t), V NL (t), V L (t), V T (t) is derived. Therefore, the voltage response V corresponding to i(t) is given by sim V sim Let (t). From equation (1), V sim (t) = V OC (t)+V T (t)+V NL (t)+V L It can be expressed as (t).

[0026] In Embodiment 1, seven variable parameters are set in the equivalent circuit model 1 to reproduce the same electrical characteristics as the target of reproduction. These seven variable parameters are R L i0, α, p, T, R T,ch and R T,dis That is. R L This indicates the electrical resistance of the linear resistance section 13. T,ch This indicates the electrical resistance of the charging resistor 32. T,dis This represents the electrical resistance of the discharge resistance 42. Also, as mentioned above, i0 represents the exchange current. α represents the charge transfer coefficient. p and T are values ​​that determine the characteristics of CPE21.

[0027] First, the voltage V OC This will be explained. As mentioned above, the voltage V OCThis is the OCV of the power supply unit 11. Since the equivalent circuit model 1 is intended to replicate a secondary battery, the power supply unit 11 is set to behave as a secondary battery and be capable of charging and discharging.

[0028] The actual OCV (Overcurrent Voltage) of a secondary battery is considered to be the voltage under no load, when neither charging nor discharging is occurring. However, the voltage of a secondary battery immediately after charging or discharging tends to be unstable. Therefore, it is common practice to use the voltage of the secondary battery after sufficient time has elapsed, empirically necessary for the voltage to stabilize, as the OCV. This elapsed time is typically around one hour. In other words, if the secondary battery has not been charged or discharged for about one hour before the start of OCV measurement, the voltage of the secondary battery at the start of measurement can be considered the OCV.

[0029] The OCV of a secondary battery corresponds to the State of Charge (SOC) of that secondary battery. In Embodiment 1, data showing the correspondence between the SOC and OCV to be acquired is included in the data related to the reproducible object as the aforementioned SOC-OCV data. The SOC-OCV data is data showing the correspondence between the SOC value and the OCV value within the range of SOC that the reproducible object can take (for example, from 0% representing a completely discharged state to 100% representing a fully charged state). Such data showing the correspondence between the SOC and OCV of the reproducible object is created in advance by measuring the OCV of each object after a sufficient amount of time has been ensured for the voltage to stabilize, with each reproducible object having a different SOC.

[0030] Voltage V OC The initial value of V is the same as the voltage response of the reproducible target as shown in the data on the reproducible target described above. The initial state refers to the state of the reproducible target before a predetermined current profile is given. That is, V OC (0) is equivalent to the initial OCV of the target system and is identified from the data related to the target system.

[0031] V OC(t) is the OCV value corresponding to the SOC value shown in the SOC-OCV data included in the data relating to the object to be reproduced. In other words, the correspondence between the SOC and OCV of the power supply unit 11 at a certain point in time (t) is the same as the correspondence between the SOC and OCV shown in the SOC-OCV data of the object to be reproduced.

[0032] The State of Charge (SOC) of a secondary battery changes when it is in a charging or discharging state, i.e., when current is flowing. The SOC of a secondary battery depends on the amount of current that flows during charging and the amount of current that flows during discharging. As mentioned above, a predetermined current profile includes the charging current and the discharging current. How the SOC of the power supply unit 11 increases or decreases from the start of measurement according to the charging current and discharging current given by the predetermined current profile can be calculated based on the amount of charging current and the amount of discharging current, i.e., i(t). Also, V represents the OCV of the power supply unit 11 at a certain point (t) after the predetermined current profile has been applied. OC (t) can be considered to correspond to the SOC of the power supply unit 11 at a certain point in time (t). Therefore, by calculating the SOC of the power supply unit 11 at a certain point in time (t) based on i(t), and identifying the OCV corresponding to the calculated SOC from the SOC-OCV data to be reproduced by the equivalent circuit model 1, V OC (t) can be derived.

[0033] Furthermore, when obtaining the true value, the OCV is not measured each time a predetermined current profile is given, nor are such measured OCV values ​​included in the data related to the object being reproduced. On the other hand, considering that Equivalent Circuit Model 1 is a simulation that does not actually perform charging and discharging of a secondary battery, the change in OCV that occurs while a predetermined current profile is given is V OC It is derived as (t). That is, V OC(t) is the OCV corresponding to the SOC of the power supply unit 11 at a specific point in time (t), and merely corresponds to the SOC-OCV data. In other words, the fact that a predetermined current profile is given to the equivalent circuit model 1 means that the "state in which neither charging nor discharging of the secondary battery is occurring" does not elapse sufficiently, resulting in "conditions unsuitable for measuring OCV", is not met. OC This is ignored when deriving (t).

[0034] Next, voltage V NL This will be explained. As explained with reference to Figure 1, the voltage V NL This represents the voltage drop caused by the voltage drop resulting from the nonlinear resistance component of the nonlinear resistance section 12. Here, i(t) and V NL The relationship between (t) and can be expressed by the following equation (2). That is, V in equation (2) NL (t) is the voltage V at a certain point in time (t). NL This shows the value.

number

[0035] Equation (2) is the Butler-Bolmer equation. In equation (2), exp is a function that represents a power of a number with base e, where e is Napier's number. Also, F in equation (2) is the Faraday constant, a physical constant that represents the absolute value of the charge per unit amount of electrons. Also, R in equation (2) is the gas constant, a physical constant introduced as a constant in the ideal gas law. Also, θ in equation (2) is the absolute temperature of the battery reproduced by equivalent circuit model 1. θ reflects the value corresponding to the temperature of the reproduced object included in the data relating to the reproduced object. Since θ is absolute temperature (unit: Kelvin), the temperature of the reproduced object in Celsius temperature as described above is converted to absolute temperature and substituted into θ. Of course, the temperature of the reproduced object included in the data relating to the reproduced object may be converted to absolute temperature beforehand.

[0036] In equation (2), i0 represents the exchange current, as described above. The exchange current is the internal current generated by the insertion and removal of reactants in the electrolyte solution between the positive and negative electrodes and the electrolyte solution when there is no load, such as when a secondary battery like a lithium-ion battery is neither charging nor discharging. In the case of a lithium-ion battery, the reactant is lithium ions. The value of i0 indicates the magnitude of the exchange current.

[0037] As mentioned above, α in equation (2) represents the charge transfer coefficient. α generally takes a value within the range of 0 to 1. A battery with α = 0.5 indicates that the ease of charging and discharging reactions are equal. In actual lithium-ion batteries, the ease of charging and discharging reactions are not necessarily equal; the closer the value of α is to 0, the more easily charging reactions occur, and the closer the value of α is to 1, the more easily discharging reactions occur.

[0038] By the way, equation (2) is equivalent to equation (3) below. By using equation (3), V NL (t) can be derived more easily.

number

[0039] In equations (2) and (3), F and R are constants, and θ is determined based on data relating to the object to be reproduced. Therefore, once α and i0 are determined, V NL (t) is also determined. By appropriately determining i0 and α, the trend of the electrical characteristics of the target that equivalent circuit model 1 reproduces, i.e., secondary batteries such as lithium-ion batteries, can be reproduced with higher accuracy.

[0040] V NL (t) can be determined using numerical analysis. As a specific example, in Embodiment 1, V NL As a numerical analysis algorithm to find (t), the Newton-Raphson method or the secant method is used, but other algorithms may also be used. Define α and i0 and V as the solution to equation (3). NL(t) may be calculated sequentially, or a two-dimensional look-up table (LUT: Look Up Table) showing the solution according to α and i0 may be created in advance, and V NL (t) may be obtained analytically by referring to the LUT.

[0041] From equations (2) and (3), an inverse function for obtaining V NL (t) can also be derived. The inverse function can be expressed as in the following equation (4). By using equation (4), V NL (t) can be calculated without using an analytical method such as the numerical analysis described above.

Number

[0042] Next, the voltage V L will be described. As described with reference to FIG. 1, the voltage V L is the voltage across the linear resistance portion 13 corresponding to the current flowing through the linear resistance portion 13, and the current and the voltage are proportional. Since the current at a certain time point (t) is i(t), V L (t) can be expressed as in the following equation (5). R L in equation (5) represents the electrical resistance of the linear resistance portion 13 as described above. That is, by appropriately determining R L representing the electrical resistance of the linear resistance portion 13, V L (t) corresponding to i(t) can be calculated from equation (5). V L (t)=i(t)×R L ···(5)

[0043] Next, the voltage V T will be described. As described with reference to FIG. 1, the voltage V T represents the voltage dropped due to the voltage drop by the CPE21.

[0044] When a certain current profile is given to the equivalent circuit model 1, the voltage drop due to CPE21 at any time is different between charging and discharging. Charging refers to the time when a current flows in the direction from the first terminal 15 side, through the equivalent circuit model 1, and towards the second terminal 16 side. Discharging refers to the time when a current with the voltage V OC of the equivalent circuit model 1 as the power source flows towards the first terminal 15, that is, when the direction of the current is from the second terminal 16, through the equivalent circuit model 1, and towards the first terminal 15 side. Assuming that the current profile is the predetermined current profile described above, V T [nΔt] during charging can be expressed as in the following formula (6). Also, V T [nΔt] during discharging can be expressed as in the following formula (7). [Number]

[0045] In formulas (6) and (7), [nΔt] represents the product of n indicating the data number and Δt indicating the sampling time. For example, when the sampling time is 0.1 second as described above, Δt = 0.1. Therefore, by setting nΔt = t, V T [nΔt] can be regarded as V T (t). Also, with the same concept, [kΔt] represents the product of k indicating the data number less than n and Δt indicating the sampling time. For example, i[kΔt] represents the current flowing through the equivalent circuit model 1 at the time of kΔt.

[0046] As mentioned above, p and T are values ​​that determine the characteristics of CPE21. Of these, p is an index that indicates the characteristics of CPE21. p takes a value in the range of -1 to 1. When p=1, it indicates that CPE21 behaves as a capacitor. When p=0.5, it indicates that CPE21 behaves as a Warburg impedance. When p=0, it indicates that CPE21 behaves as an electrical resistance. When p=-1, it indicates that CPE21 behaves as an inductance. The value of T is a constant that indicates the degree of electrical influence due to the behavior of CPE21 indicated by the value of p. Therefore, the electrical characteristics of CPE21 are determined by the combination of p and T.

[0047] To elaborate, in the electrochemical reactions between the electrodes and the electrolyte solution during the charging and discharging of secondary batteries such as lithium-ion batteries, electron transfer and diffusion occur in parallel. Electron transfer is a reaction that results in the movement of electrons between the electrodes and reactants in the electrolyte solution. Diffusion is a reaction in which reactants in the electrolyte solution move toward the electrodes. Here, the rate of the electrode reaction is determined by the slower of the two rates (rate-limiting) between electron transfer and diffusion. The electrical characteristics of the secondary battery change depending on whether the electron transfer reaction is relatively slow or diffusion is relatively slow. For example, the Warburg impedance mentioned above represents the diffusion resistance when diffusion is slower (diffusion-limited). The p and T values ​​of CPE21 are determined so as to reproduce the electrical characteristics of such secondary batteries.

[0048] Depending on the p and T values ​​of CPE21, some of the current flowing through the transient response section 20 may also flow through the charging resistor 32 or the discharging resistor 42. Specifically, for example, when p=1, CPE behaves as a capacitor, so, similar to an RC parallel circuit, most of the current flows through CPE21 at the beginning, and almost none flows through the charging resistor 32 or the discharging resistor 42. As time passes, the current flowing through CPE approaches 0, and most of it flows through the charging resistor 32 or the discharging resistor 42. When p=0, CPE21 behaves as a resistor, so current flows in parallel with CPE21 and the resistors (32, 42) according to their respective values. When p is between 0 and 1, it behaves as both a capacitor and a resistor, so the current flowing through CPE21 and the charging resistor 32 or the discharging resistor 42 changes depending on their respective values ​​and time.

[0049] In equations (6) and (7), Γ represents the gamma function, which can be expressed as shown in equation (8) below for any positive real number x.

number

[0050] Based on equation (8), the following equation (9) holds for a natural number n. Γ(n)=(n-1)!···(9)

[0051] R in equation (6) T,ch As mentioned above, this represents the electrical resistance of the charging resistor 32. Also, R in equation (7) T,dis As mentioned above, this indicates the electrical resistance of the discharge resistance 42. T,ch , R T,dis By appropriately determining p and T, we can obtain V from equations (6) and (7). T (t) can be calculated.

[0052] Based on the calculations from equations (1) to (9) above, R L i0, α, p, T, R T,ch and R T,dis By appropriately defining V sim (t) = V OC (t)+V T (t)+V NL(t)+V L (t) can be calculated.

[0053] As described above, in Embodiment 1, the voltage response V shown is the result of the simulation using the equivalent circuit model 1. sim Then, the voltage response V MEAS It is required to reproduce the voltage response V at a certain point in time (t). MEAS V MEAS Let (t) be V MEAS (t) and V sim It is desirable that the evaluation value, which represents the result of comparing (t) with a predetermined comparison evaluation algorithm, satisfies the predetermined evaluation criteria. Examples of predetermined comparison evaluation algorithms for deriving the evaluation value include the Root Mean Squared Error (RMSE), mean squared error, mean absolute error, etc., but other comparison evaluation algorithms may also be used.

[0054] For example, let's consider the case where RMSE is used as a method for deriving evaluation values. First, let's look at a certain R L i0, α, p, T, R T,ch and R T,dis The combination is adopted, and by calculation based on equations (1) to (9), V sim (t) is calculated. V sim (t) and V MEAS If the evaluation value showing the comparison result with (t) is greater than the threshold, the criterion is not met, R L i0, α, p, T, R T,ch and R T,dis Another combination is adopted in which at least one of the options has been changed, and V again sim (t) is calculated. If the evaluation value becomes smaller (for example, below the threshold), V sim V by (t) MEAS (t) is considered to have been reproduced, and V sim When (t) is calculated, R L i0, α, p, T, R T,ch and R T,dis The combination of these results in a voltage response V sim This is determined as a parameter necessary for the calculation of V.sim (t) V MEAS (t) is pre-set to ensure sufficient accuracy in reproduction.

[0055] R L i0, α, p, T, R T,ch and R T,dis For each combination, at least one, preferably multiple, combination patterns are prepared in advance and available as data. R using this prepared data... L i0, α, p, T, R T,ch and R T,dis So, if the criteria are not met, R L i0, α, p, T, R T,ch and R T,dis If at least one of them is changed, then V again sim (t) and the evaluation value are calculated. Here, R L i0, α, p, T, R T,ch and R T,dis One mechanism for changing at least one of these factors is evolutionary algorithms, such as genetic algorithms, but it is not limited to these; other similarly functioning mechanisms can be employed.

[0056] Figures 2 and 3 show the voltage response V MEAS And, appropriately defined R L i0, α, p, T, R T,ch and R T,dis Voltage response V calculated accordingly sim This is a graph showing a comparative example of the two. Figure 4 shows the voltage response V shown in Figures 2 and 3. MEAS This graph shows the time-series change of current due to the current profile given when the result is obtained. In the graphs in Figures 2 and 3, the horizontal axis is time and the vertical axis is voltage. That is, the graphs shown in Figures 2 and 3 show the voltage due to the voltage response that occurs during the time when the predetermined current profile described above is given on the horizontal axis. Figure 3 is an enlarged view of the graph in Figure 2, showing the period from 1025 seconds to 1250 seconds.

[0057] In the graphs shown in Figures 2 and 3, the solid line “experiment” represents the voltage response V MEAS This shows the voltage response V. Also, the dashed line “simulation” represents the voltage response V. sim This shows the voltage response V as shown in Figures 2 and 3. sim The voltage response V MEAS This is essentially the same as the appropriate R. L i0, α, p, T, R T,ch and R T,dis The voltage response V calculated by calculations based on equations (1) to (9) is sim The voltage response V MEAS It can reproduce this with high precision.

[0058] The voltage response V described above sim Calculation and R L i0, α, p, T, R T,ch and R T,dis The process for determining the combination will be explained with reference to the flowchart in Figure 5.

[0059] Figure 5 is a flowchart showing the processing flow performed in Embodiment 1. First, data related to the reproducible target, including the true value, is acquired (step S1). Specifically, as described above, the voltage response V is treated as the true value. MEAS , the voltage response V MEAS The conditions under which the result was obtained, and the voltage response V MEAS When the data is obtained, the predetermined current profile given to the target of reproduction, the SOC-OCV data of the target of reproduction, etc., are associated with it and treated as data related to the target of reproduction.

[0060] Next, the voltage response V of equivalent circuit model 1 sim Candidate values ​​for the parameters necessary for the calculation are set (Step S2). Specifically, the above R L i0, α, p, T, R T,ch and R T,dis At least one combination of these values ​​is pre-selected as a candidate value.

[0061] Next, the calculation of the voltage drop across the nonlinear resistance section 12 (step S3), the calculation of the voltage drop across the linear resistance section 13 (step S4), the calculation of the voltage drop across the transient response section 20 (step S5), and the calculation of the OCV (step S6) are performed sequentially. The processes from step S3 to step S6 can be performed in any order, in parallel, or with some or all of the order shown in Figure 5 changed. The process in step S3 calculates the voltage V mentioned above. NL The following is derived through calculation. The above-mentioned voltage V is obtained through the process in step S4. L The following is derived through calculation. The above voltage V is obtained through the process in step S5. T The following is derived through calculation. The above voltage V is obtained through the process in step S6. OC This is derived through calculation.

[0062] After the processing from step S3 to the completion of step S6, the voltage response V sim The calculation is performed (step S7). That is, based on equation (1) above, the voltage V NL , voltage V L , voltage V T , voltage V OC Voltage response V due to the summation of the following sim The calculation is performed.

[0063] After the processing in step S7, an evaluation value is derived as a comparative evaluation between the calculated value and the true value (step S8). Specifically, the voltage response V obtained from the calculation in step S7 is derived. sim The calculated value is used, and an evaluation value is derived that shows the result of comparing the calculated value and the true value using the predetermined comparison and evaluation algorithm described above.

[0064] After processing in step S8, a determination is made as to whether the evaluation value meets the criteria (step S9). For example, if the predetermined comparison evaluation algorithm is RMSE as described above, if the evaluation value is less than or equal to the threshold, it is determined that the evaluation value meets the criteria (step S9; Yes), and if the evaluation value is greater than the threshold, it is determined that the criteria are not met (step S9; No).

[0065] If the evaluation value is determined not to meet the criteria in step S9 (step S9; No), the process proceeds to step S2. In the second and subsequent steps of step S2, the candidate values ​​are reset. In resetting the candidate values, the mechanism of the genetic algorithm described above is used, R L i0, α, p, T, R T,ch and R T,dis The process involves changing at least one of the following.

[0066] If the evaluation value is determined to meet the criteria in step S9 (step S9; Yes), then the candidate value adopted by the most recent step S2 is R. L i0, α, p, T, R T,ch and R T,dis However, the voltage response V sim These parameters are determined as necessary for the calculation (Step S10).

[0067] Next, an example configuration for the process described with reference to Figure 5 will be explained with reference to Figures 6 and 7.

[0068] Figure 6 is a block diagram showing the configuration of the simulation device 50. The simulation device 50 includes a data storage unit 51, a parameter input unit 52, a voltage calculation unit 60, a voltage comparison unit 54, and a parameter recalculation unit 55.

[0069] The data storage unit 51 stores data input to the simulation device 50 from an external source and data output by the voltage comparison unit 54. The data input to the simulation device 50 from an external source includes the data related to the object to be reproduced as described above and pre-prepared R L i0, α, p, T, R T,ch and R T,dis This is candidate value data that shows at least one combination. The parameter input unit 52 reads the data stored in the data storage unit 51 and outputs it to the voltage calculation unit 60.

[0070] Figure 7 is a block diagram showing the configuration of the voltage calculation unit 60 and its inputs and outputs. The voltage calculation unit 60 comprises a nonlinear resistance voltage calculation unit 61, a linear resistance voltage calculation unit 62, a transient response voltage calculation unit 63, an OCV calculation unit 64, and a voltage response calculation unit 65.

[0071] The nonlinear resistance voltage calculation unit 61 calculates the voltage V NL The linear resistance voltage calculation unit 62 calculates the voltage V L The transient response voltage calculation unit 63 calculates the voltage V T The OCV calculation unit 64 performs calculations to derive the voltage V OC Calculations are performed to derive the R. The calculations performed by the nonlinear resistance voltage calculation unit 61, the linear resistance voltage calculation unit 62, the transient response voltage calculation unit 63, and the OCV calculation unit 64 take into account the candidate value data input from the parameter input unit 52 to the voltage calculation unit 60 as needed. L i0, α, p, T, R T,ch and R T,dis The individual values ​​of each parameter, i(t) indicated by a predetermined current profile included in the data related to the object to be reproduced, and SOC-OCV data are referenced.

[0072] The voltage response calculation unit 65 calculates the voltage V derived by the calculation of the nonlinear resistance voltage calculation unit 61. NL And the voltage V derived by the calculation of the linear resistance voltage calculation unit 62 L And the voltage V derived by the calculation of the transient response voltage calculation unit 63 T And the voltage V derived by the OCV calculation unit 64 OC Adding these together gives the voltage response V sim The voltage response calculation unit 65 performs calculations to derive the derived voltage response V. sim Data showing this, and the voltage response V included in the data related to the object being reproduced. MEAS The data showing and are output to the voltage comparison unit 54. Note that the voltage response V MEAS The data indicating this is transferred to the voltage response calculation unit 65 via at least one of the following: the nonlinear resistance voltage calculation unit 61, the linear resistance voltage calculation unit 62, the transient response voltage calculation unit 63, and the OCV calculation unit 64.

[0073] The voltage comparison unit 54 calculates the voltage response V indicated by the data input from the voltage response calculation unit 65. sim and voltage response V MEAS The voltage response V is compared and evaluated, an evaluation value is derived, and a decision is made based on the evaluation value. That is, the voltage comparison unit 54 makes a decision, sim The R used in the calculation L i0, α, p, T, R T,ch and R T,dis Voltage response V sim It is determined whether the parameters necessary for calculating the voltage response V will be finalized. sim The R used in the calculation L i0, α, p, T, R T,ch and R T,dis Voltage response V sim If a determination is made to confirm the parameters necessary for the calculation, the voltage comparison unit 54 outputs data indicating this to the data storage unit 51. The data storage unit 51 then outputs the voltage response V sim The parameter R was determined to be necessary for the calculation of L i0, α, p, T, R T,ch and R T,dis This is stored in a way that makes it distinguishable from the candidate value. On the other hand, the voltage response V sim The R used in the calculation L i0, α, p, T, R T,ch and R T,dis Voltage response V sim If a decision is made not to determine which parameters are necessary for the calculation, the data and the latest R L i0, α, p, T, R T,ch and R T,dis The data indicating this is output to the parameter recalculation unit 55.

[0074] The parameter recalculation unit 55 is R L i0, α, p, T, R T,ch and R T,dis The parameters are reset by the parameter recalculation unit 55. L i0, α, p, T, R T,ch and R T,disAfter resetting, the parameter input unit 52 receives the R that the parameter recalculation unit 55 has reset. L i0, α, p, T, R T,ch and R T,dis The output is sent to the voltage calculation unit 60.

[0075] Of the processes described with reference to Figure 5, the process in step S1 and the first step S2 are performed by inputting data to the data storage unit 51. The process in step S3 is performed by the nonlinear resistance voltage calculation unit 61. The process in step S4 is performed by the linear resistance voltage calculation unit 62. The process in step S5 is performed by the transient response voltage calculation unit 63. The process in step S6 is performed by the OCV calculation unit 64. The process in step S7 is performed by the voltage response calculation unit 65. The processes in steps S8 and S9 are performed by the voltage comparison unit 54. If the evaluation value is determined not to meet the criteria in the process in step S9 (step S9; No), the process in step S2 is performed by the parameter recalculation unit 55. The process in step S10 is performed by the voltage comparison unit 54 and the data storage unit 51.

[0076] The data storage unit 51, parameter input unit 52, voltage calculation unit 60, voltage comparison unit 54, and parameter recalculation unit 55 may each be implemented by individual circuits or combinations of multiple circuits, or they may be implemented by a single circuit integrating some or all of these functions. Furthermore, as shown in Figure 13 later, the same functions as those shown in Figure 7 may be implemented by so-called software processing.

[0077] (Embodiment 2) Next, Embodiment 2 will be described. In Embodiment 2, the voltage response V sim R as a parameter required for the calculation L i0, α, p, T, R T,ch and R T,disHowever, this is assumed to be predetermined by Embodiment 1. In other words, Embodiment 2 assumes that the equivalent circuit model 1 already has an environment in place that can reproduce the target of reproduction. Embodiment 2 simulates the voltage response under arbitrary conditions using the equivalent circuit model 1.

[0078] Figure 8 is a block diagram showing the configuration of the simulation device 70. The simulation device 70 comprises an input unit 71, a SOC acquisition unit 72, a data holding unit 80, a nonlinear resistance voltage calculation unit 61, a linear resistance voltage calculation unit 62, a transient response voltage calculation unit 63, an OCV calculation unit 64, a voltage response calculation unit 65, and an output unit 75.

[0079] The input unit 71 receives input of data to be stored in the data storage unit 80. The data stored in the data storage unit 80 is the SOC-OCV data 81 and parameters 82, which will be described later. The input unit 71 also receives input of data related to the simulation conditions that are given to the equivalent circuit model 1 in Embodiment 2.

[0080] Figure 9 shows an example of data related to simulation conditions. The data related to simulation conditions includes initial conditions and changing conditions that vary in units of sampling time.

[0081] In the example in Figure 9, the data related to the simulation conditions is in a table format with four columns ("Time", "Current", "Voltage", and "Temperature"). Multiple records included in the data related to the simulation conditions each have a different value set in the "Time" field. Records with a value of "0" in the "Time" field represent the initial conditions. Records with a value other than "0" in the "Time" field represent the changing conditions. In the example in Figure 9, 0.1 seconds is used as the sampling time, similar to that exemplified in Embodiment 1.

[0082] A value of "0" in the "Time" field is equivalent to t=0 in Embodiment 1. In other words, the "Time" value in the table shown in Figure 9 represents the value of t in Embodiment 1. Therefore, the initial condition represents the state of t=0. The initial condition has values ​​set in the respective fields of "Current," "Voltage," and "Temperature."

[0083] The "Current" value in the table shown in Figure 9 represents the current supplied to the equivalent circuit model 1 from an external source. In other words, the "Current" value represents the value of i(t) in Embodiment 1. Therefore, the "Current" value in the data related to the simulation conditions functions as the current profile in Embodiment 2. It can be said that the predetermined current profile in Embodiment 1 is substantially the same data. The predetermined current profile functions as current information. For example, in the example in Figure 9, the "Current" value of the initial conditions, i.e., i(0), is 0 amperes. Also, the "Voltage" value represents the voltage response of the equivalent circuit model 1, i.e., V sim (t) is shown. The "voltage" value under the initial conditions functions as voltage information indicating the initial voltage of the secondary battery. In the example shown in Figure 9, V sim (0) is 3.6 volts. The "Temperature" value indicates the temperature of the secondary battery reproduced by equivalent circuit model 1. Therefore, in the example shown in Figure 9, the initial temperature of the secondary battery reproduced by equivalent circuit model 1 is 25°C in Celsius. The "Temperature" value functions as temperature information indicating the temperature of the secondary battery.

[0084] The change conditions correspond to a predetermined current profile in Embodiment 1. In the example in Figure 9, the current at time 0.1 seconds is 0.5 amperes, and the current at time 0.2 seconds is 0.6 amperes. Therefore, the change conditions shown by the data in Figure 9 are i(0.1)=0.5 and i(0.2)=0.6. In Figure 9, the figures for time 0.3 and beyond are omitted, but in reality, the current at time 0.3 seconds and beyond may also be included in the change conditions.

[0085] In the data related to the simulation conditions, it is desirable to set the sign of "current" to be opposite for charging and discharging, such as setting the charging current to positive and the discharging current to negative, or vice versa. Furthermore, it is desirable that "temperature" be the temperature assumed to be the battery surface temperature of the secondary battery reproduced by equivalent circuit model 1. Note that in the explanation referring to Figure 9, "temperature" is set only for the initial conditions, but if a simulation is performed that takes into account that a temperature change occurs within a given time for a predetermined current profile, "temperature" may be set for some or all of the records included in the change conditions.

[0086] The SOC acquisition unit 72 refers to the SOC-OCV data 81 stored in the data holding unit 80 and acquires the SOC corresponding to the voltage and temperature under the initial conditions. As described above, the OCV of a secondary battery corresponds to the SOC of that secondary battery. Therefore, if the OCV of the secondary battery or the equivalent circuit model 1 that reproduces the secondary battery is identified, the SOC corresponding to the OCV can be identified. The SOC acquisition unit 72 considers the value of "voltage" under the initial conditions as the OCV of the equivalent circuit model 1 at time t=0 and identifies the SOC corresponding to the OCV of the equivalent circuit model 1. The SOC-OCV data 81 is the same data as the SOC-OCV data included in the data related to the object to be reproduced in Embodiment 1.

[0087] The nonlinear resistance voltage calculation unit 61, linear resistance voltage calculation unit 62, transient response voltage calculation unit 63, OCV calculation unit 64, and voltage response calculation unit 65 of Embodiment 2 are the same as the nonlinear resistance voltage calculation unit 61, linear resistance voltage calculation unit 62, transient response voltage calculation unit 63, OCV calculation unit 64, and voltage response calculation unit 65 described with reference to Figure 7 in the description of Embodiment 1. However, the voltage response calculation unit 65 of Embodiment 2 outputs to the output unit 75. In addition, the nonlinear resistance voltage calculation unit 61, linear resistance voltage calculation unit 62, and transient response voltage calculation unit 63 of Embodiment 2 refer to parameters corresponding to the value of "temperature" included in the initial conditions and the value of SOC identified by the SOC acquisition unit 72 from the data stored in the data holding unit 80 as parameter 82. Hereinafter, when initial temperature is mentioned, it refers to the value of "temperature" included in the initial conditions. The OCV calculation unit 64 functions as the first calculation unit. The linear resistance voltage calculation unit 62 functions as a second calculation unit. The nonlinear resistance voltage calculation unit 61 functions as a third calculation unit. The transient response voltage calculation unit 63 functions as a fourth calculation unit. The voltage response calculation unit 65 functions as a fifth calculation unit.

[0088] Figure 10 shows the electrical resistance of the linear resistor section 13, R L Figure 10 shows the relationship between the initial temperature and the State of Charge (SOC). Figure 11 shows the relationship between p, one of the values ​​that determine the characteristics of the CPE21, the initial temperature, and the SOC. The vertical variable parameter "temperature" in Figures 10 and 11 corresponds to the initial temperature. Also, the vertical variable parameter "SOC" in Figures 10 and 11 corresponds to the SOC value identified by the SOC acquisition unit 72.

[0089] The data shown in Figures 10 and 11 are data included in parameter 82, which is a so-called LUT. This shows that the parameter can change depending on the initial temperature and SOC. For example, if the initial temperature is 25°C in Celsius and the SOC value identified by the SOC acquisition unit 72 is 50 percent, the linear resistance voltage calculation unit 62 calculates the value of the field in the LUT shown in Figure 10 where "temperature" is 25 and "SOC" is 50.L This value is adopted. In this case, the transient response voltage calculation unit 63 adopts the value of the field in the LUT shown in Figure 11 where "temperature" is 25 and "SOC" is 50 as the value of p.

[0090] R L i0, α, p, T, R T,ch and R T,dis Of these, refer to Figures 10 and 11 and R L While an explanation has been given regarding p, similarly, the values ​​of the parameters corresponding to the initial temperature and SOC are adopted for the other parameters as well. The determination of the parameter values ​​corresponding to the different initial temperatures and SOCs is performed in Embodiment 1 by acquiring data on the reproducible target corresponding to the different initial temperatures and SOCs. The data acquired in this way is input as parameter 82, together with the SOC-OCV data 81 described above, via the input unit 71 and stored in the data holding unit 80.

[0091] The output unit 75 outputs the voltage response V output by the voltage response calculation unit 65. sim The data showing this is output as a simulation result corresponding to the data related to the simulation conditions.

[0092] In the second embodiment, the nonlinear resistance voltage calculation unit 61 calculates the voltage V corresponding to the predetermined α and i0. NL The solution is determined in advance, and the voltage V corresponding to the combination of α and i0 is calculated. NL By storing a two-dimensional LUT showing the voltage V in the nonlinear resistance voltage calculation unit 61 or in a data holding unit 80 that can be accessed from the nonlinear resistance voltage calculation unit 61, the voltage V NL This can be determined analytically.

[0093] The input unit 71, SOC acquisition unit 72, data holding unit 80, nonlinear resistance voltage calculation unit 61, linear resistance voltage calculation unit 62, transient response voltage calculation unit 63, OCV calculation unit 64, voltage response calculation unit 65, and output unit 75 may each be implemented by individual circuits or combinations of multiple circuits, or they may be implemented by a single circuit integrating some or all of these functions. Furthermore, as shown in Figure 13 later, the same functions as those shown in Figure 7 may be implemented by so-called software processing.

[0094] The processing flow performed in Embodiment 2, as described above, will now be explained with reference to the flowchart in Figure 12.

[0095] Figure 12 is a flowchart showing the processing flow in Embodiment 2. First, parameters related to the model are input (step S21). Specifically, the SOC-OCV data 81 and parameters 82 described above are input to the simulation device 70 via the input unit 71 and stored in the data holding unit 80.

[0096] Next, data related to the simulation conditions is input (step S22). For example, data indicating the initial conditions and change conditions, as explained with reference to Figure 9, is input to the simulation device 70 via the input unit 71.

[0097] Next, in step S22, the OCV is identified based on the initial conditions included in the data related to the simulation conditions entered (step S23). Specifically, the SOC acquisition unit 72 refers to the SOC-OCV data 81 and identifies the OCV corresponding to the "voltage" value indicated by the initial conditions.

[0098] After the processing in step S23, the processing in steps S3, S4, S5, S6, and S7 is performed, similar to Embodiment 1. This results in a voltage response V corresponding to the combination of the model parameters input in step S21 and the simulation condition data input in step S22.sim This is calculated.

[0099] After processing in step S7, the output unit 75 outputs the voltage response V calculated by the voltage response calculation unit 65. sim Output (step S29).

[0100] In summary, according to Embodiment 2, the voltage response of the secondary battery (voltage response V) can be determined using the equivalent circuit model 1. sim When calculating the parameters (R) that represent the electrical characteristics of the equivalent circuit model 1, L i0, α, p, T, R T,ch and R T,dis The steps include obtaining the current information (i(t)) at multiple points in time, where the period over which a predetermined current profile is given is divided into multiple sampling time intervals (Δt), and obtaining the initial voltage (V) of the secondary battery. sim Steps include: obtaining voltage information indicating (0)) and temperature information indicating the temperature of the secondary battery (for example, the initial temperature mentioned above); identifying the SOC of the secondary battery from the voltage information; and using the identified SOC and the current information to obtain OCV (voltage V OC The steps include calculating the current information and the parameters, and using that current information and the parameters, the first voltage drop (voltage V) due to the linear resistance component (linear resistance section 13) included in the equivalent circuit model 1. L The steps include calculating the current information, temperature information, and parameters, and calculating the second voltage drop (voltage V) due to the nonlinear resistance component (nonlinear resistance section 12) included in the equivalent circuit model 1. NL The steps include calculating the current information and the parameters, and using that current information and the parameters, the third voltage drop (voltage V) due to the transient response component (transient response section 20) included in the equivalent circuit model 1. T The method comprises the steps of calculating the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on Butler-Volmer's formula (formula (3) or formula (4)), and the third voltage drop is calculated based on time-domain formulas (formulas (6) and (7)) applicable to a circuit model including CPE21.

[0101] This allows the third voltage drop to be calculated based on a time-domain equation. Therefore, by simulating the voltage response of the secondary battery in equivalent circuit model 1 when a predetermined current profile is given, the time-domain voltage response of the secondary battery can be determined. Furthermore, because the transient response section 20 is a circuit model that includes a CPE, the time constant of the secondary battery can be simulated with higher accuracy compared to setting the time constant using an RC parallel circuit. Thus, according to Embodiment 2, the time-domain voltage response of the secondary battery can be simulated with higher accuracy.

[0102] Furthermore, the transient response component (transient response section 20) is a circuit model that includes linear resistances (charging resistance 32, discharge resistance 42), and by setting the system so that current flows through these linear resistances depending on the state of the CPE 21, the asymmetry between the charging current and the discharge current that can occur in a secondary battery can be reproduced with high accuracy.

[0103] Furthermore, the transient response component (transient response section 20) includes a first element 30 formed by connecting a charging resistor 32 representing the charging resistance component and a first diode 31 in series, and a second element 40 formed by connecting a discharge resistor 42 representing the discharge resistance component and a second diode 41 in series. The circuit model is such that CPE21, the first element 30, and the second element 40 are connected in parallel. Under conditions where a charging current is applied to the equivalent circuit model 1, the second diode 41 prevents current from flowing through the second element 40, and under conditions where a discharge current is applied to the equivalent circuit model 1, the first diode 31 prevents current from flowing through the first element 30. This allows for a more accurate reproduction of the asymmetry between the charging current and the discharging current that can occur in a secondary battery.

[0104] Also, the second voltage drop (voltage V NL The second voltage drop can be analytically determined by deriving the coefficient (i0) representing the exchange current and the charge transfer coefficient (α) from the coefficients included in the Butler-Volmer equation, and by referring to a corresponding LUT.

[0105] Also, the second voltage drop (voltage V NL) is expressed by the inverse function of the Butler-Volmer equation (see equation (4)), and is calculated using an equation with current as a variable, thus allowing V to be calculated without using analytical methods. NL (t) can be calculated.

[0106] Furthermore, according to Embodiment 1, based on the raw data showing the true value of the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the predetermined current profile is applied to the secondary battery, and the temperature of the secondary battery, OCV (voltage V OC ), the first voltage drop (voltage V L ), the second voltage drop (voltage V NL ) and the third voltage drop (voltage V T Voltage response (V) calculated from ) sim ) is the parameter (R) that reproduces the true value L i0, α, p, T, R T,ch and R T,dis This identifies the relevant factors. This allows for more accurate simulations of secondary batteries using equivalent circuit model 1.

[0107] Furthermore, according to Embodiment 1, the parameter (R L i0, α, p, T, R T,ch and R T,dis By pre-determining the voltage response (V) in Embodiment 2, sim This reduces the computational load required to calculate the voltage response (V) at each time point. In other words, it allows for faster acquisition of the voltage response when an arbitrary current profile is applied to the secondary battery reproduced in equivalent circuit model 1. In addition, it allows for the acquisition of the voltage response (V) corresponding to the current (i(t)) at each time point. sim (t)) can be simulated in more real time.

[0108] Furthermore, according to Embodiment 1, the parameter (R L i0, α, p, T, R T,ch and R T,dis By identifying ) in advance, V effectively sim (t) = V MEAS (t) can be treated as such. Therefore, the V of the secondary battery that we want to simulate in equivalent circuit model 1 OCEven if (t) is unknown, V in equation (1) OC As the object to be sought, V sim , V L , V NL , V T By calculating this, we can work backwards to find V OC We can find V obtained in this way. OC Therefore, the State of Charge (SOC) of the secondary battery can also be calculated. Consequently, the SOC response of the secondary battery according to the current profile can also be simulated.

[0109] The following describes the configuration for performing simulations using so-called software processing, with reference to Figure 13.

[0110] Figure 13 is a block diagram showing the configuration of the information processing device 90. The information processing device 90 comprises a storage unit 91, an arithmetic unit 92, an input unit 93, and an output unit 94.

[0111] The storage unit 91 stores the software program read by the arithmetic unit 92 and the data referenced in relation to the execution process of the software program. Hereinafter, when simply referred to as "program," it refers to the software program executed by the arithmetic unit 92. Specifically, the storage unit 91 shown in Figure 13 stores the voltage response calculation program 100. The voltage response calculation program 100 includes a simulation module 101, simulation condition data 102, SOC-OCV data 103, parameter identification data 104, and a parameter identification module 105.

[0112] The simulation module 101 is a program for performing processing corresponding to Embodiment 2. That is, the simulation module 101 is a program for the information processing device 90 to perform the same functions as the simulation device 70 described with reference to Figure 9, virtually setting up an equivalent circuit model 1 and calculating the voltage response V based on the processing flow described with reference to Figure 12. sim Outputs.

[0113] The simulation condition data 102 is the same as the data relating to the simulation conditions in Embodiment 2, and is data indicating the initial conditions and the changing conditions.

[0114] The SOC-OCV data 103 is the same as the SOC-OCV data included in the data relating to the object to be reproduced in Embodiment 1 and the SOC-OCV data 81 of Embodiment 2, and is data that shows the correspondence between the SOC and OCV of the secondary battery that is the subject of the simulation.

[0115] The parameter identification data 104 is the same as parameter 82 in Embodiment 2, and the voltage response V sim R as a parameter required for the calculation L i0, α, p, T, R T,ch and R T,dis This data demonstrates that...

[0116] The parameter identification module 105 is a program for performing processing corresponding to Embodiment 1. That is, the simulation module 101 is a program for the information processing device 90 to perform the same functions as the simulation device 50 described with reference to Figures 6 and 7, virtually setting up an equivalent circuit model 1 and R based on the processing flow described with reference to Figure 3. L i0, α, p, T, R T,ch and R T,dis Confirm.

[0117] The arithmetic unit 92 includes an arithmetic circuit that reads a program from the storage unit 91 and performs execution processing. The arithmetic unit 92 refers to the simulation condition data 102, SOC-OCV data 103, and parameter identification data 104 in conjunction with the execution processing of the simulation module 101. Furthermore, the arithmetic unit 92 refers to data related to the target to be reproduced, which is input via the input unit 93 in conjunction with the execution processing of the parameter identification module 105. The parameter identification data 104 may reflect the output results from the execution processing of the parameter identification module 105. In other words, the information processing device 90 may be configured to enable the execution of the simulation module 101 after the execution processing of the parameter identification module 105. Of course, the information processing device 90 may also be configured to enable the execution of the simulation module 101 by pre-determining the parameter identification data 104 in the storage unit 91.

[0118] The input unit 93 receives input to the information processing device 90. Specifically, the input unit 93 includes, for example, a human interface such as a keyboard or mouse that can receive input from an operator. The input unit 93 functions as the input unit 71 of Embodiment 2. The input unit 93 also receives input of data related to the object to be reproduced.

[0119] The output unit 94 outputs according to the processing content performed by the information processing device 90. Specifically, the output unit 94 includes, for example, a display device such as an image display. Configurations that communicate with external information processing devices, such as those that function as a NIC (Network Interface Controller), or interfaces that can connect to external storage devices capable of storing various types of data, such as data related to the target of reproduction, can function as both the input unit 93 and the output unit 94.

[0120] Although the above explanation omits mentioning the number of SOC-OCV data points for the sake of clarity, if there are multiple secondary batteries being simulated, SOC-OCV data corresponding to each secondary battery will be prepared. Furthermore, even for a single secondary battery, if the correspondence between SOC and OCV changes depending on the battery temperature, SOC-OCV data corresponding to the temperature may be prepared. This will allow for more accurate simulations.

[0121] The embodiments described above are provided to facilitate understanding of the present invention and are not intended to limit its interpretation. The present invention may be modified or improved without departing from its spirit, and equivalents thereof are also included.

[0122] This disclosure may take the following configuration, as described above, or alternatively.

[0123] (1) One aspect of the present invention is a simulation method for calculating the voltage response of a secondary battery using an equivalent circuit model, comprising the steps of: obtaining parameters that show the electrical characteristics of the equivalent circuit model; obtaining current information that shows the current at multiple time points obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information that shows the initial voltage of the secondary battery; and temperature information that shows the temperature of the secondary battery; identifying the SOC of the secondary battery from the voltage information; calculating the OCV using the SOC and the current information; and using the current information and the parameters to determine the line included in the equivalent circuit model. The method comprises the steps of: calculating a first voltage drop due to a resistive component; calculating a second voltage drop due to a nonlinear resistive component included in the equivalent circuit model using the current information, the temperature information, and the parameters; calculating a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; and calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase-constant element CPE.

[0124] (2) In the simulation method described in (1) above, the transient response component is represented as a circuit model including a linear resistor, and is set to a state in which current flows through the linear resistor depending on the state of the constant-phase element CPE.

[0125] (3) In the simulation method of (1) above, the transient response component includes a first element formed by connecting a charging resistor representing the charging resistance component and a first diode in series, and a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and is set as a circuit model in which the constant phase element CPE, the first element and the second element are connected in parallel, and under conditions in which a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing to the second element, and under conditions in which a discharge current is applied to the equivalent circuit model, the first diode prevents current from flowing to the first element.

[0126] (4) In the simulation methods described in (1) to (3) above, the second voltage drop is derived by referring to a LUT corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation.

[0127] (5) In the simulation methods described in (1) to (3) above, the second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation.

[0128] (6) In the simulation methods described in (1) to (5) above, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value, based on raw data showing the true value of the voltage response of a secondary battery to which a predetermined current profile is given, the SOC before the predetermined current profile is given to the secondary battery, and the temperature of the secondary battery.

[0129] (7) Another aspect of the present invention is a simulation device for setting an equivalent circuit model and calculating the voltage response of a secondary battery, comprising: an acquisition unit that acquires parameters indicating the electrical characteristics of the equivalent circuit model, current information indicating the current at multiple time points obtained by dividing a period in which a predetermined current profile is given into multiple sampling times, voltage information indicating the initial voltage of the secondary battery, and temperature information indicating the temperature of the secondary battery; an identification unit that identifies the SOC of the secondary battery from the voltage information; a first calculation unit that calculates the OCV using the SOC and the current information; and a linear resistance component included in the equivalent circuit model using the current information and the parameters. The system comprises a second calculation unit for calculating a first voltage drop, a third calculation unit for calculating a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters, a fourth calculation unit for calculating a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and parameters, and a fifth calculation unit for calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase-constant element CPE.

[0130] (8) In the simulation apparatus described in (7) above, the transient response component is represented as a circuit model including a linear resistor, and is set to a state in which current flows through the linear resistor depending on the state of the constant-phase element CPE.

[0131] (9) In the simulation apparatus described in (7) above, the transient response component includes a first element formed by connecting a charging resistor representing the charging resistance component and a first diode in series, and a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and is set as a circuit model in which the constant phase element CPE, the first element and the second element are connected in parallel, and under conditions in which a charging current is supplied to the equivalent circuit model, the second diode prevents current from flowing through the second element, and under conditions in which a discharge current is supplied to the equivalent circuit model, the first diode prevents current from flowing through the first element.

[0132] (10) In the simulation apparatus described in (7) to (9) above, the second voltage drop is derived by referring to the LUT corresponding to the coefficient representing the exchange current and the charge transfer coefficient among the coefficients included in the Butler-Volmer equation.

[0133] (11) In the simulation apparatus described in (7) to (9) above, the second voltage drop is calculated by an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation.

[0134] (12) In the simulation apparatus described in (7) to (11) above, the parameters are obtained such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value, based on raw data showing the true value of the voltage response of a secondary battery to which a predetermined current profile has been given, the SOC before the predetermined current profile was given to the secondary battery, and the temperature of the secondary battery.

[0135] (13) Another aspect of the present invention is a program for setting an equivalent circuit model and calculating the voltage response of a secondary battery, comprising the steps of: obtaining parameters that show the electrical characteristics of the equivalent circuit model; obtaining current information that shows the current at multiple time points obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information that shows the initial voltage of the secondary battery; and temperature information that shows the temperature of the secondary battery; identifying the SOC of the secondary battery from the voltage information; calculating the OCV using the SOC and the current information; and using the current information and the parameters to determine the linear resistance component included in the equivalent circuit model. The information processing device is made to perform the following steps: calculate a first voltage drop; calculate a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters; calculate a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; and calculate the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, wherein the second voltage drop is calculated based on the Butler-Volmer equation, and the third voltage drop is calculated based on a time-domain equation applied to a circuit model including a phase constant element CPE.

[0136] (14) In the program of (13) above, the transient response component is defined as a circuit model including a linear resistor, and is set to a state in which current flows through the linear resistor depending on the state of the constant-phase element CPE.

[0137] (15) In the program of (13) above, the transient response component includes a first element formed by connecting a charging resistor representing the charging resistance component and a first diode in series, and a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and is set as a circuit model in which the constant phase element CPE, the first element and the second element are connected in parallel, and under conditions in which a charging current is supplied to the equivalent circuit model, the second diode prevents current from flowing to the second element, and under conditions in which a discharge current is supplied to the equivalent circuit model, the first diode prevents current from flowing to the first element.

[0138] (16) In the programs described in (13) to (15) above, the second voltage drop is derived by referring to the LUT corresponding to the coefficient representing the exchange current and the charge transfer coefficient among the coefficients included in the Butler-Volmer equation.

[0139] (17) In the programs described in (13) to (15) above, the second voltage drop is calculated by an equation in which the current is a variable, which is expressed by the inverse function of the Butler-Volmer equation.

[0140] (18) In the programs described in (13) to (17) above, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value, based on raw data showing the true value of the voltage response of a secondary battery to which a predetermined current profile has been given, the SOC before the predetermined current profile was given to the secondary battery, and the temperature of the secondary battery. [Explanation of Symbols]

[0141] 1. Equivalent Circuit Model 11 Power supply section 12 Nonlinear Resistance Section 13 Linear Resistor Section 20 Transient response section 30 The first element 31 First diode 32 Charging resistance 40 The second element 41 Second diode 42 Discharge Resistance 50,70 Simulation devices 81 SOC-OCV data 82 parameters 90 Information Processing Equipment 100 Voltage Response Calculation Program

Claims

1. A simulation method for calculating the voltage response of a secondary battery using an equivalent circuit model, The steps include obtaining parameters that represent the electrical characteristics of the equivalent circuit model, The steps include obtaining current information indicating the current at multiple points in time, obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery. The steps include identifying the State of Control (SOC) of the secondary battery from the voltage information, A step of calculating the OCV using the SOC and the current information, A step of calculating a first voltage drop due to the linear resistance component included in the equivalent circuit model using the current information and the parameters, A step of calculating a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters, A step of calculating a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters, A step of calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, It has, The second voltage drop is calculated based on the Butler-Bolmer equation, The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE. Simulation method.

2. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well. The simulation method according to claim 1.

3. The transient response component is, The first element consists of a charging resistance component and a first diode connected in series, The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel. Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element. Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element. The simulation method according to claim 1.

4. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation. The simulation method according to any one of claims 1 to 3.

5. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation. The simulation method according to any one of claims 1 to 3.

6. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value. The simulation method according to any one of claims 1 to 3.

7. A simulation device that sets up an equivalent circuit model and calculates the voltage response of a secondary battery, An acquisition unit that acquires parameters indicating the electrical characteristics of the equivalent circuit model, current information indicating the current at multiple points in time when a period for which a predetermined current profile is given is divided into multiple sampling times, voltage information indicating the initial voltage of the secondary battery, and temperature information indicating the temperature of the secondary battery. A unit for identifying the SOC of the secondary battery from the voltage information, A first calculation unit that calculates the OCV using the SOC and the current information, A second calculation unit calculates a first voltage drop due to a linear resistance component included in the equivalent circuit model using the current information and the parameters, A third calculation unit calculates a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters. A fourth calculation unit that calculates a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters, A fifth calculation unit that calculates the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, Equipped with, The second voltage drop is calculated based on the Butler-Bolmer equation, The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE. Simulation device.

8. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well. The simulation apparatus according to claim 7.

9. The transient response component is, The first element consists of a charging resistance component and a first diode connected in series, The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel. Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element. Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element. The simulation apparatus according to claim 7.

10. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation. The simulation apparatus according to any one of claims 7 to 9.

11. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation. The simulation apparatus according to any one of claims 7 to 9.

12. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are obtained such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value. The simulation apparatus according to any one of claims 7 to 9.

13. This is a program for setting up an equivalent circuit model and calculating the voltage response of a secondary battery. The steps include obtaining parameters that represent the electrical characteristics of the equivalent circuit model, The steps include obtaining current information indicating the current at multiple points in time, obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery. The steps include identifying the State of Control (SOC) of the secondary battery from the voltage information, A step of calculating the OCV using the SOC and the current information, A step of calculating a first voltage drop due to the linear resistance component included in the equivalent circuit model using the current information and the parameters, A step of calculating a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters, A step of calculating a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters, A step of calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop, The information processing device is made to execute this, The second voltage drop is calculated based on the Butler-Bolmer equation, The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE. program.

14. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well. The program according to claim 13.

15. The transient response component is, The first element consists of a charging resistance component and a first diode connected in series, The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel. Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element. Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element. The program according to claim 13.

16. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation. The program according to any one of claims 13 to 15.

17. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation. The program according to any one of claims 13 to 15.

18. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value. The program according to any one of claims 13 to 15.

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