Simulation method, simulation device, 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

Simulation method, simulation device, and program

[0001] The present invention relates to a simulation method, a simulation device, and a program.

[0002] Methods for simulating the electrical characteristics of a secondary battery using an equivalent circuit model are known from Patent Documents 1, 2, and 3. In Patent Documents 1 and 2, an RC parallel circuit is included in the equivalent circuit model. In Patent Document 3, a CPE (Constant Phase Element) is included in the equivalent circuit model.

[0003] JP 2018-40684 A JP 2019-219275 A JP 2019-191029 A

[0004] In the configurations described in Patent Documents 1 and 2, a time constant is set in an equivalent circuit model using an RC parallel circuit, but only one time constant can be set per RC parallel circuit. On the other hand, secondary batteries generally have multiple time constants due to the large number of components. For this reason, it is difficult to improve the accuracy of simulations by setting time constants using an RC parallel circuit. Furthermore, although Patent Document 3 employs a CPE, the equation for the impedance of the CPE is described as a frequency domain equation using an angular frequency ω. In Patent Document 3, even when attempting to simulate the voltage response of a secondary battery when a certain time-series current profile is given using an equivalent circuit model, 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 has an object to provide a simulation method, a simulation device, and a program that can simulate the voltage response of a secondary battery in the time domain with higher accuracy.

[0006] A simulation method according to one aspect of the present invention is a simulation method for calculating a voltage response of a secondary battery using an equivalent circuit model, the simulation method including the steps of: acquiring parameters indicating electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; acquiring voltage information indicating an initial voltage of the secondary battery; and acquiring temperature information indicating a temperature of the secondary battery; specifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; and calculating a linear resistance included in the equivalent circuit model using the current information and the parameters. calculating a first voltage drop due to a resistive component included in the equivalent circuit model using the current information, the temperature information, and the parameters; calculating a second voltage drop due to a nonlinear resistive 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 constant phase element (CPE).

[0007] A simulation device according to another aspect of the present invention is a simulation device that sets an equivalent circuit model and calculates a voltage response of a secondary battery, the simulation device including: an acquisition unit that acquires parameters indicating electrical characteristics of the equivalent circuit model; current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; voltage information indicating an initial voltage of the secondary battery; and temperature information indicating a temperature of the secondary battery; an identification unit that identifies an SOC of the secondary battery from the voltage information; a first calculation unit that calculates an OCV using the SOC and the current information; and a first calculation unit that calculates an OCV using a linear resistance component included in the equivalent circuit model using the current information and the parameters. a third calculation unit that calculates 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; a fourth calculation unit that calculates a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; and 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, 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 constant phase element CPE.

[0008] A program according to another aspect of the present invention is a program for setting an equivalent circuit model and calculating a voltage response of a secondary battery, the program including the steps of: acquiring parameters indicating electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; voltage information indicating an initial voltage of the secondary battery; and temperature information indicating a temperature of the secondary battery; specifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; and calculating a voltage response of a secondary battery using a linear resistance component included in the equivalent circuit model using the current information and the parameters. The method causes an information processing device to execute the steps of: calculating a first voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters; calculating a second 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 constant phase element CPE.

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

[0010] FIG. 1 is a diagram showing an equivalent circuit model used in the present invention. ＭＥＡＳ and an appropriately defined R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The voltage response V calculated according to ｓｉｍ 3 is a graph showing a comparison between the voltage response V ＭＥＡＳ and an appropriately defined R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The voltage response V calculated according toｓｉｍ 4 is a graph showing a comparison between the voltage response V ＭＥＡＳ FIG. 5 is a graph showing a time series change in current according to a current profile given when the current is obtained. FIG. 5 is a flowchart showing the flow of processing performed in embodiment 1. FIG. 6 is a block diagram showing the configuration of a simulation device. FIG. 7 is a block diagram showing the configuration of a voltage calculation unit and input / output of the voltage calculation unit. FIG. 8 is a block diagram showing the configuration of a simulation device. FIG. 9 is a diagram showing an example of data related to simulation conditions. FIG. 10 is a graph showing R indicating the electrical resistance of a linear resistance unit. Ｌ 11 is a diagram showing the relationship between p, which is one of the values ​​that determine the characteristics of the CPE, and the initial temperature and SOC. FIG. 12 is a flowchart showing the flow of processing performed in embodiment 2. FIG. 13 is a block diagram showing the configuration of an information processing device.

[0011] The following describes embodiments in detail with reference to the drawings. However, the present invention is not limited to these embodiments. Each embodiment is an example, and it goes without saying that partial substitution or combination of the configurations shown in different embodiments is possible. From embodiment 2 onwards, a description of matters common to embodiment 1 will be omitted, and only the differences will be described. In particular, similar effects resulting from similar configurations will not be mentioned in each embodiment.

[0012] 1 is a diagram showing an equivalent circuit model 1 used in the present invention. The equivalent circuit model 1 includes a power supply section 11, a nonlinear resistance section 12, a linear resistance section 13, and a transient response section 20.

[0013] The power supply unit 11 behaves as a secondary battery. ＯＣ indicates the open circuit voltage (OCV) of the power supply unit 11.

[0014] The nonlinear resistance section 12 is connected to the current flowing through the nonlinear resistance section 12 and the voltage V ＮＬ In Figure 1, Z ＢＶ (i０ , α) represents the nonlinear resistance component of the nonlinear resistance section 12. The nonlinear resistance component is an impedance that represents a voltage drop when a certain current flows through the nonlinear resistance section 12. ＮＬ represents the voltage drop due to the voltage drop. The nonlinear resistance component can be calculated based on the Butler-Volmer equation described later. ０ denotes the exchange current, and α denotes the charge transfer coefficient.

[0015] The linear resistor 13 is connected to the current flowing through the linear resistor 13 and the voltage V between both ends of the linear resistor 13. Ｌ It behaves as an electrical resistance proportional to

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

[0017] 1 , the first diode 31 is configured as an element that passes current in the direction from the first terminal 15 to the second terminal 16 of the equivalent circuit model 1, but does not pass current in the reverse direction. The second diode 41 is configured as an element that passes current in the direction from the second terminal 16 to the first terminal 15 of the equivalent circuit model 1, but does not pass current in the reverse direction. Therefore, the equivalent circuit model 1 is configured so that the second diode 41 prevents current from flowing to the second element 40 when a charging current is applied, and so that the first diode 31 prevents current from flowing to the first element 30 when a discharging current is applied. The charging resistor 32 and the discharging resistor 42 behave as electrical resistances.

[0018] In FIG. ＣＰＥ The voltage V is the impedance representing the voltage drop across the CPE 21. Ｔindicates the voltage drop due to the voltage drop. p and T are values ​​that determine the characteristics of CPE 21. In equivalent circuit model 1, the provision of first element 30 and second element 40 is useful when the characteristics of the secondary battery that is the target of simulation by equivalent circuit model 1 differ between discharge and charge.

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

[0020] As an example of the configuration 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: LiFePO ４ ), lithium cobalt oxide (LiCoO ２ ), lithium nickel cobalt manganese oxide (Li(Ni ｘ Mn ｙ Co ｚ ) O ２ , 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 Co ｂ Al ｃ ) O ２ , a+b+c=1, where a, b, and c are each 0 or greater and 1 or less), 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 equivalent circuit model 1. Furthermore, the term "reproduced target" refers to the lithium ion battery. The secondary battery reproduced by equivalent circuit model 1 is not limited to this, and may be a secondary battery with another configuration.

[0021] Prior to a simulation using the equivalent circuit model 1, data relating to the object to be reproduced is acquired. Specifically, the state of charge (SOC) of the object to be reproduced is adjusted within a range of 10% to 90%. Furthermore, the temperature of the object to be reproduced is adjusted within a range of -10°C to 50°C. The temperature of the object to be reproduced is preferably the battery surface temperature. A predetermined current profile is applied to the object to be reproduced adjusted in this manner. The predetermined current profile, as shown in FIG. 4 (described later), for example, indicates a current pattern in which a current that charges the object to be reproduced (charging current), a current that causes discharge from the object to be reproduced (discharging current), and no current (0 amperes) that does not cause intentional charging or intentional discharging of the object to be reproduced are combined in a time series. The voltage response V of the object to be reproduced that occurs while the predetermined current profile is applied is ＭＥＡＳ (See Figures 2 and 3) is measured. ＭＥＡＳ and voltage response V ＭＥＡＳ The conditions under which the voltage response V is obtained are associated with the predetermined current profile, and are treated as data relating to the object to be reproduced. ＭＥＡＳ The conditions under which the predetermined current profile is obtained include the SOC and temperature of the object to be reproduced immediately before the predetermined current profile is applied to the object to be reproduced. Furthermore, in the first embodiment, the SOC-OCV data, which will be described later, is also included in the data related to the object to be reproduced. The data related to the object to be reproduced functions as the original data.

[0022] Hereinafter, when the true value is written, the voltage response V ＭＥＡＳ In the first embodiment, when the above-described predetermined current profile 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 is obtained, the voltage response V ｓｉｍ By this, the voltage response V ＭＥＡＳ That is, in the first embodiment, the equivalent circuit model 1 reproduces electrical characteristics that are substantially the same as the object to be reproduced.

[0023] Voltage response V ｓｉｍ can be expressed as the following equation (1). That is, the voltage response V ｓｉｍ is the voltage V shown in FIG.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] Hereinafter, voltage V ＯＣ , voltage V ＮＬ , voltage V Ｌ , voltage V Ｔ Specific methods for deriving each of the above will be described in order. In the following description, the time during which a predetermined current profile is applied will be referred to as the application time. The current generated in the target to be reproduced by applying the predetermined current profile to the target to be reproduced at a certain point during the application time will be referred to 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 the first embodiment, i(0) is 0 amperes, since it is before the predetermined current profile is applied. Furthermore, 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 begins to be applied to the target to be reproduced. Furthermore, in this case, i(0.2) indicates the current at the point 0.2 seconds after the predetermined current profile begins to be applied to the target to be reproduced. The sampling time is not limited to 0.1 seconds and can be any value.

[0025] In the description of the first embodiment, various values ​​other than current may also be indicated by using (t) at a certain point in time. For example, the voltage V ＯＣ , voltage V ＮＬ , voltage V Ｌ , voltage V Ｔ Each change in V ＯＣ (t), V ＮＬ (t), V Ｌ (t), V Ｔ Since the equivalent circuit model 1 is set with the aim of reproducing the object to be reproduced, V is set so that the current considered to flow in 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 according to i(t) is ｓｉｍ V ｓｉｍ (t), then V from equation (1) ｓｉｍ (t) = V ＯＣ (t) + V Ｔ (t) + V ＮＬ (t) + V Ｌ This can be expressed as (t).

[0026] In the first embodiment, seven variable parameters are set in order to reproduce electrical characteristics similar to those of the object to be reproduced in the equivalent circuit model 1. The seven variable parameters are R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ It is. Ｌ represents the electrical resistance of the linear resistor portion 13. Ｔ，ｃｈ indicates the electrical resistance of the charging resistor 32. Ｔ，ｄｉｓ represents the electrical resistance of the discharge resistor 42. As described above, i ０ denotes the exchange current. α denotes the charge transfer coefficient. p and T are values ​​that determine the characteristics of CPE21.

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

[0028] The OCV of an actual secondary battery is considered to be the voltage under no load, i.e., when neither charging nor discharging is performed. However, the voltage of a secondary battery tends to be unstable immediately after charging or discharging is completed. For this reason, it is common to determine the OCV as the voltage of a secondary battery after a sufficient elapsed time has elapsed after charging or discharging, which is empirically required for the voltage to stabilize. This elapsed time is, for example, approximately one hour. In other words, if the secondary battery has not been charged or discharged for approximately one hour before the start of OCV measurement, the voltage of the secondary battery at the start of measurement can be considered to be the OCV.

[0029] The OCV of a secondary battery corresponds to the SOC of the secondary battery. In the first embodiment, data indicating the correspondence between the SOC and OCV of the acquisition target is included in the data related to the reproduction target as the above-described SOC-OCV data. The SOC-OCV data is data indicating the correspondence between the SOC value and the OCV value within a range of SOCs that the reproduction target can have (for example, from 0% indicating a fully discharged state to 100% indicating a fully charged state). Such data indicating the correspondence between the SOC and OCV of the reproduction target is created in advance by measuring the OCV of each of the reproduction targets when the reproduction targets have different SOCs, after ensuring a sufficient amount of time has elapsed until the voltage stabilizes.

[0030] Voltage V ＯＣ The initial value of V is the same as the voltage response in the initial state of the voltage response of the object to be reproduced indicated by the data relating to the object to be reproduced described above. The initial state refers to the state of the object to be reproduced at the time before the predetermined current profile is applied. That is, V ＯＣ (0) is the same value as the OCV of the initial state of the object to be reproduced, and is identified from the data related to the object to be reproduced.

[0031] V ＯＣ (t) is the OCV value corresponding to the SOC value indicated by the SOC-OCV data included in the data related to the reproduction target. That is, the correspondence relationship between the SOC and OCV of the power supply unit 11 at a certain time point (t) is the same as the correspondence relationship between the SOC and OCV indicated by the SOC-OCV data of the reproduction target.

[0032] When the secondary battery is in a charging state or a discharging state, i.e., when a current is flowing, the SOC of the secondary battery changes. The SOC of the secondary battery depends on the amount of current flowing during charging and the amount of current flowing during discharging. As described above, the predetermined current profile includes a charging current and a 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 the 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, which indicates the OCV of the power supply unit 11 at a certain point (t) after the predetermined current profile begins to be given, is ＯＣi(t) can be considered to correspond to the SOC of the power supply unit 11 at the certain time point (t). Therefore, by calculating the SOC of the power supply unit 11 at the certain time point (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] Note that when acquiring the true value, the OCV is not measured every time a predetermined current profile is applied, and such measured OCV values ​​are not included in the data related to the object to be reproduced. On the other hand, in the equivalent circuit model 1, taking into consideration that it is a simulation that does not involve charging and discharging an actual secondary battery, the change in OCV that occurs while a predetermined current profile is applied is calculated based on the V ＯＣ (t), i.e., V ＯＣ (t) is the OCV corresponding to the SOC of the power supply unit 11 at a specific time point (t), and merely corresponds to the SOC-OCV data. In other words, when a predetermined current profile is given to the equivalent circuit model 1, the "conditions that are not suitable for measuring the OCV" are established due to the "state in which the secondary battery is neither charged nor discharged" not having elapsed sufficiently. ＯＣ It is ignored in the derivation of (t).

[0034] Next, the voltage V ＮＬ As described with reference to FIG. ＮＬ represents the voltage drop caused by the voltage drop due to the nonlinear resistance component of the nonlinear resistance unit 12. ＮＬ The relationship between (t) and V in Equation (2) can be expressed as follows: ＮＬ (t) is the voltage V at a certain time (t) ＮＬ Indicates the value of

[0035] Equation (2) is the Butler-Volmer equation. In equation (2), exp is a function indicating the power of a number with e as the base. Here, e is Napier's constant. Furthermore, F in equation (2) is the Faraday constant. The Faraday constant is a physical constant corresponding to the charge (absolute value) per electron mass. Furthermore, R in equation (2) is the gas constant. The gas constant is a physical constant introduced as a constant in the equation of state for an ideal gas. Furthermore, θ in equation (2) is the absolute temperature of the battery reproduced by the equivalent circuit model 1. θ reflects a value corresponding to the temperature of the object to be reproduced, which is included in the data related to the object to be reproduced. Note that θ is the absolute temperature (unit: Kelvin), so the temperature of the object to be reproduced, expressed in Celsius temperature as described above, is converted to absolute temperature and substituted for θ. Of course, the temperature of the object to be reproduced, which is included in the data related to the object to be reproduced, may be converted to absolute temperature in advance.

[0036] i in formula (2) ０ As mentioned above, the exchange current is the current inside the battery that occurs when a secondary battery such as a lithium ion battery is not being charged or discharged and is unloaded, and the current is generated by the intercalation and deintercalation of reactants in the electrolyte solution between the positive and negative electrodes and the electrolyte solution. In the case of a lithium ion battery, the reactants are lithium ions. ０ The value of indicates the magnitude of the exchange current.

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

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

[0039] Among the various values ​​in the formulas (2) and (3), the above-mentioned F and R are constants, and θ is determined based on data related to the object to be reproduced. ０ Once this is determined, V ＮＬ (t) is also determined. ０ By appropriately determining α, the tendency of the electrical characteristics of the object to be reproduced by the equivalent circuit model 1, that is, the secondary battery such as a lithium ion battery, can be reproduced with higher accuracy.

[0040] V ＮＬ (t) can be obtained by using numerical analysis. ＮＬ As a numerical analysis algorithm for obtaining (t), the Newton-Raphson method or the secant method is used, but other algorithms may also be used. ０ Define V as the solution of equation (3) ＮＬ (t) may be calculated sequentially, or α and i ０ A two-dimensional lookup table (LUT) showing a solution according to V is created in advance, and V is calculated by referring to the LUT. ＮＬ (t) may be found analytically.

[0041] From the formulas (2) and (3), V ＮＬ It is also possible to derive an inverse function for finding (t). The inverse function can be expressed as in the following equation (4). By using equation (4), it is possible to find V without using analytical methods such as the numerical analysis described above. ＮＬ (t) can also be calculated.

[0042] Next, the voltage V Ｌ As described with reference to FIG. Ｌ is the voltage across the linear resistor 13 depending on the current flowing through the linear resistor 13, and the current is proportional to the voltage. Since the current at a certain point in time (t) is i(t), V Ｌ (t) can be expressed as the following formula (5). Ｌ As described above, R represents the electrical resistance of the linear resistance portion 13. That is, R represents the electrical resistance of the linear resistance portion 13. ＬBy appropriately defining V according to i(t) from equation (5), Ｌ (t) can be calculated. Ｌ (t) = i(t) × R Ｌ ...(5)

[0043] Next, the voltage V Ｔ As described with reference to FIG. Ｔ indicates the voltage drop due to the voltage drop across the CPE 21.

[0044] When a certain current profile is applied to the equivalent circuit model 1, the voltage drop across the CPE 21 at any given time differs between charging and discharging. The charging period refers to the time when a current is applied from the first terminal 15 side, flows through the equivalent circuit model 1, and flows toward the second terminal 16 side. The discharging period refers to the time when a current is applied from the first terminal 15 side, and the voltage V ＯＣ This refers to the time when the current from the power source V flows toward the first terminal 15, that is, when the current flows from the second terminal 16 through the equivalent circuit model 1 toward the first terminal 15. If the current profile is the predetermined current profile described above, then V during charging Ｔ [nΔt] can be expressed as the following equation (6). Ｔ [nΔt] can be expressed as the following equation (7).

[0045] In equations (6) and (7), [nΔt] represents the product of n, which indicates the data number, and Δt, which indicates the sampling time. For example, as described above, if the sampling time is 0.1 seconds, Δt = 0.1. Therefore, by setting nΔt = t, V Ｔ [nΔt] = V Ｔ In a similar way, [kΔt] represents the product of k, which represents a data number less than n, and Δt, which represents the sampling time. For example, i[kΔt] represents the current flowing through the equivalent circuit model 1 at time kΔt.

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

[0047] To further explain, in the electrode reaction during charging and discharging of a secondary battery such as a lithium-ion battery, i.e., the electrochemical reaction between the electrode and the electrolyte solution, an electron transfer reaction and diffusion occur in parallel. The electron transfer reaction is a reaction that causes the transfer of electrons between the electrode and the reactant in the electrolyte solution. Diffusion is a reaction in which the reactant moves toward the electrode in the electrolyte solution. Here, the rate of the electrode reaction is determined by the slower rate (rate-determining) of the electron transfer reaction or diffusion. The electrical characteristics of the secondary battery change depending on whether the electron transfer reaction is relatively slow or the diffusion is relatively slow. For example, the Warburg impedance described above indicates the diffusion resistance when diffusion is slower (diffusion-determining). The p and T of the CPE21 are determined to reproduce the electrical characteristics of such a secondary battery.

[0048] Depending on p and T of the CPE 21, a portion of the current flowing through the transient response unit 20 may flow through the charging resistor 32 or the discharging resistor 42. Specifically, for example, when p = 1, the CPE behaves as a capacitor, so similar to an RC parallel circuit, at the beginning of the current flow, most of the current flows through the CPE 21, and almost none flows through the charging resistor 32 or the discharging resistor 42. As time passes, the current flowing through the CPE approaches 0, and most of the current flows through the charging resistor 32 or the discharging resistor 42. When p = 0, the CPE 21 behaves as a resistor, so current flows in parallel depending on the values ​​of the CPE 21 and the resistors (32, 42). When p is between 0 and 1, the CPE behaves as both a capacitor and a resistor, so the current flowing through the CPE 21 and the charging resistor 32 or the discharging resistor 42 varies depending on their respective values ​​and time.

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

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

[0051] R in formula (6) Ｔ，ｃｈ As described above, R represents the electrical resistance of the charging resistor 32. Ｔ，ｄｉｓ As described above, R represents the electrical resistance of the discharge resistor 42. Ｔ，ｃｈ , R Ｔ，ｄｉｓ By appropriately defining p and T, V can be obtained from equations (6) and (7). Ｔ (t) can be calculated.

[0052] As described above, by calculation based on the formulas (1) to (9), R Ｌ , i ０ ,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 the first embodiment, the voltage response V ｓｉｍ And the voltage response V ＭＥＡＳ Therefore, the voltage response V at a certain point in time (t) is ＭＥＡＳ V ＭＥＡＳ (t), then V ＭＥＡＳ (t) and V ｓｉｍ It is desirable that an evaluation value indicating the result of comparing and evaluating (t) using a predetermined comparison evaluation algorithm satisfies a predetermined evaluation standard. Examples of the predetermined comparison evaluation algorithm for deriving the evaluation value include root mean squared error (RMSE), mean square error, mean absolute error, etc., but other comparison evaluation algorithms may also be used.

[0054] For example, a case where RMSE is used as a method for deriving an evaluation value will be described. Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ A combination of V is adopted, and calculations based on equations (1) to (9) are performed. ｓｉｍ (t) is calculated. ｓｉｍ (t) and V ＭＥＡＳ If the evaluation value indicating the comparison result with (t) is greater than the threshold, it is determined that the criteria are not met, and R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ Another combination in which at least one of the above has been changed is adopted, and V is ｓｉｍ If the evaluation value becomes smaller (for example, below a threshold), V ｓｉｍ (t) by V ＭＥＡＳ (t) is considered to have been reproduced, and the V ｓｉｍ R when (t) is calculated Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The combination of these gives the voltage response V ｓｉｍ The threshold is determined as a parameter necessary for the calculation of V ｓｉｍ V by (t) ＭＥＡＳIt is set in advance so that the reproduction accuracy of (t) is sufficiently ensured.

[0055] R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ For the combination of the above, at least one, preferably a plurality of combination patterns are prepared in advance as data. Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ If the criteria are not met, R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ At least one of the above has been changed and V ｓｉｍ (t) and the evaluation value is calculated, where R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ As a mechanism for changing at least one of the above, for example, an evolutionary algorithm such as a genetic algorithm may be used, but this is not limiting and other mechanisms that function in a similar manner may be employed.

[0056] 2 and 3 show the voltage response V ＭＥＡＳ and an appropriately defined R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The voltage response V calculated according to ｓｉｍ 4 is a graph showing a comparison between the voltage response V ＭＥＡＳ 2 and 3 are graphs showing time-series changes in current due to a current profile given when the above-mentioned predetermined current profile is obtained. The horizontal axis in the graphs of Fig. 2 and Fig. 3 represents time, and the vertical axis represents voltage. That is, the graphs shown in Fig. 2 and Fig. 3 show the time when the above-mentioned predetermined current profile is given on the horizontal axis, and the voltage due to the voltage response occurring at that time on the vertical axis. Fig. 3 is an enlarged view of the graph shown in Fig. 2 from 1025 seconds to 1250 seconds.

[0057] The solid line "experiment" in the graphs shown in FIGS. 2 and 3 represents the voltage response V ＭＥＡＳ The dashed line "simulation" shows the voltage response V ｓｉｍ As shown in Figs. 2 and 3, the voltage response V ｓｉｍ is the voltage response V ＭＥＡＳ In this way, the appropriate R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ and the voltage response V calculated by calculation based on equations (1) to (9). ｓｉｍ is the voltage response V ＭＥＡＳ can be reproduced with high precision.

[0058] The voltage response V ｓｉｍ Calculation of and R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The flow of processing related to determining the combination will be described with reference to the flowchart of FIG.

[0059] 5 is a flowchart showing the flow of processing performed in the first embodiment. First, data relating to the object to be reproduced, including true values, is acquired (step S1). Specifically, as described above, the voltage response V ＭＥＡＳ , the voltage response V ＭＥＡＳ The condition when the voltage response V ＭＥＡＳ When the above is obtained, the predetermined current profile given to the object to be reproduced, the SOC-OCV data of the object to be reproduced, etc. are associated with each other and treated as data related to the object to be reproduced.

[0060] Next, the voltage response V of the equivalent circuit model 1 ｓｉｍ The candidate values ​​of the parameters required for the calculation of R are set (step S2). Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ At least one combination of the above is prepared in advance as candidate values.

[0061] Next, the calculation of the voltage drop of the nonlinear resistance unit 12 (step S3), the calculation of the voltage drop of the linear resistance unit 13 (step S4), the calculation of the voltage drop of the transient response unit 20 (step S5), and the calculation of the OCV (step S6) are performed in this order. The processing from step S3 to step S6 may be performed in any order, in parallel, or by changing part or all of the order shown in FIG. 5 . By the processing of step S3, the above-mentioned voltage V ＮＬ is calculated. By the process of step S4, the voltage V Ｌ is calculated. By the process of step S5, the voltage V Ｔ is calculated. By the process of step S6, the voltage V ＯＣ is derived through calculation.

[0062] After the processes of steps S3 to S6 are completed, the voltage response V ｓｉｍ That is, based on the above-mentioned equation (1), the voltage V ＮＬ , voltage V Ｌ , voltage V Ｔ , voltage V ＯＣ Voltage response V ｓｉｍ is calculated.

[0063] After the process of step S7, an evaluation value is derived as a comparison evaluation between the calculated value and the true value (step S8). Specifically, the voltage response V obtained by the calculation process of step S7 is ｓｉｍ is used as a calculated value, and an evaluation value is derived that indicates the result of comparing and evaluating the calculated value and the true value using the above-mentioned predetermined comparison evaluation algorithm.

[0064] After the process of step S8, it is determined whether the evaluation value satisfies the criterion (step S9). For example, if the predetermined comparison evaluation algorithm is RMSE as described above, if the evaluation value is equal to or less than the threshold, it is determined that the evaluation value satisfies the criterion (step S9; Yes), and if the evaluation value is greater than the threshold, it is determined that the criterion is not satisfied (step S9; No).

[0065] If it is determined in the process of step S9 that the evaluation value does not satisfy the criteria (step S9; No), the process proceeds to the process of step S2. In the process of step S2 from the second time onwards, the candidate values ​​are reset. In the resetting of the candidate values, R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ A process of changing at least one of the above is performed.

[0066] If it is determined in the process of step S9 that the evaluation value satisfies the criteria (step S9; Yes), the R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ is the voltage response V ｓｉｍ are determined as parameters necessary for the calculation (step S10).

[0067] Next, an example of a configuration for performing the process described with reference to FIG. 5 will be described with reference to FIGS. 6 and 7. FIG.

[0068] 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 the outside and data output by the voltage comparison unit 54. The data input to the simulation device 50 from the outside includes the data related to the object to be reproduced described above and the data stored in the R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The parameter input unit 52 reads out the data stored in the data storage unit 51 and outputs it to the voltage calculation unit 60.

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

[0071] The nonlinear resistor voltage calculation unit 61 calculates the voltage V ＮＬ The linear resistor 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 calculates the voltage V ＯＣ In the calculations performed by the nonlinear resistor voltage calculation unit 61, the linear resistor voltage calculation unit 62, the transient response voltage calculation unit 63, and the OCV calculation unit 64, the R indicated by the candidate value data input from the parameter input unit 52 to the voltage calculation unit 60 is calculated as necessary. Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The values ​​of i(t) and i(t) indicated by a predetermined current profile included in the data related to the object to be reproduced are referenced, and the SOC-OCV data is referenced.

[0072] The voltage response calculation unit 65 calculates the voltage V ＮＬ and the voltage V calculated by the linear resistor 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 calculated by the OCV calculation unit 64. ＯＣ Adding these together gives the voltage response V ｓｉｍ The voltage response calculation unit 65 calculates the derived voltage response V ｓｉｍ and the voltage response V included in the data relating to the object to be reproduced. ＭＥＡＳ The voltage response V ＭＥＡＳ The data indicating the above is transferred to the voltage response calculation unit 65 via at least one of the nonlinear resistance unit voltage calculation unit 61, the linear resistance unit voltage calculation unit 62, the transient response unit 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 comparison unit 54 compares and evaluates the voltage response V ｓｉｍ The R used to calculate Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ voltage response V ｓｉｍ It is determined whether the voltage response V ｓｉｍ The R used to calculate Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ voltage response V ｓｉｍ When it is determined that the voltage response V is a parameter necessary for calculating the voltage response V, the voltage comparison unit 54 outputs data indicating this to the data storage unit 51. ｓｉｍ R determined as a parameter necessary for the calculation Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ is stored in a manner that can be distinguished from the candidate value. ｓｉｍ The R used to calculate Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ voltage response V ｓｉｍ If a decision is made not to confirm the parameter as necessary for the calculation of R, the data indicating this and the latest R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The parameter recalculator 55 outputs data indicating the above.

[0074] The parameter recalculation unit 55 calculates R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ The parameter recalculation unit 55 resets R Ｌ , i０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ After the parameter recalculation unit 55 resets the parameter input unit 52, Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ is output to the voltage calculation unit 60.

[0075] Of the processes described with reference to FIG. 5 , the process of step S1 and the initial process of step S2 are performed by inputting data to the data storage unit 51. The process of step S3 is performed by the nonlinear resistor unit voltage calculation unit 61. The process of step S4 is performed by the linear resistor unit voltage calculation unit 62. The process of step S5 is performed by the transient response unit voltage calculation unit 63. The process of step S6 is performed by the OCV calculation unit 64. The process of step S7 is performed by the voltage response calculation unit 65. The processes of steps S8 and S9 are performed by the voltage comparison unit 54. The process of step S2, which is performed when it is determined in the process of step S9 that the evaluation value does not satisfy the criterion (step S9; No), is performed by the parameter recalculation unit 55. The process of step S10 is performed by the voltage comparison unit 54 and the data storage unit 51.

[0076] The data storage unit 51, the parameter input unit 52, the voltage calculation unit 60, the voltage comparison unit 54, and the parameter recalculation unit 55 may be realized by individual circuits or a combination of multiple circuits, or may be realized by a single circuit that integrates some or all of the functions thereof. Furthermore, as shown in Fig. 13 described later, functions similar to those of the configuration shown in Fig. 7 may be realized 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 necessary for the calculation Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓis assumed to have been determined in advance by the first embodiment. That is, the second embodiment is premised on the premise that an environment has already been established in which the equivalent circuit model 1 can reproduce the object to be reproduced. The second embodiment uses the equivalent circuit model 1 to simulate a voltage response under any conditions.

[0078] 8 is a block diagram showing the configuration of the simulation device 70. The simulation device 70 includes an input unit 71, an SOC acquisition unit 72, a data holding unit 80, a nonlinear resistor voltage calculation unit 61, a linear resistor 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 accepts input of data to be stored in the data storage unit 80. The data to be stored in the data storage unit 80 is SOC-OCV data 81 and parameters 82, which will be described later. The input unit 71 also accepts input of data relating to simulation conditions, which are given to the equivalent circuit model 1 in the second embodiment.

[0080] 9 is a diagram showing an example of data related to simulation conditions. The data related to simulation conditions includes initial conditions and variable conditions that change in units of sampling time.

[0081] In the example of FIG. 9 , the data regarding the simulation conditions is data in a table format having four columns ("time," "current," "voltage," and "temperature"). The multiple records included in the data regarding the simulation conditions each have a different value set in the "time" field. A record with a value of "0" set in the "time" field indicates an initial condition. A record with a value other than "0" set in the "time" field indicates a change condition. In the example of FIG. 9 , the sampling time is 0.1 seconds, the same as that used in the example of the first embodiment.

[0082] The value "0" set in the "time" field is synonymous with t=0 in the first embodiment. In other words, the value of "time" in the table shown in FIG. 9 indicates the value of t in the first embodiment. Therefore, the initial condition indicates the state of t=0. The initial condition is that values ​​are set in the fields of "current," "voltage," and "temperature."

[0083] The "current" value in the table shown in FIG. 9 indicates a current externally applied to the equivalent circuit model 1. In other words, the "current" value indicates the value of i(t) in the first embodiment. Therefore, the "current" value in the data related to the simulation conditions functions as a current profile in the second embodiment. It can be said that the predetermined current profile in the first embodiment is substantially the same data. The predetermined current profile functions as current information. For example, in the example of FIG. 9, the "current" value in the initial condition, i.e., i(0), is 0 amperes. The "voltage" value indicates the voltage response of the equivalent circuit model 1, i.e., V ｓｉｍ The value of "voltage" in the initial condition functions as voltage information indicating the initial voltage of the secondary battery. In the example shown in FIG. 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 FIG. 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 the predetermined current profile in embodiment 1. In the example of FIG. 9, the current is 0.5 amperes when "time" is 0.1 seconds, and the current is 0.6 amperes when "time" is 0.2 seconds. Therefore, the change conditions indicated by the data in FIG. 9 are i(0.1) = 0.5, i(0.2) = 0.6. Although FIG. 9 omits illustration of "time" after 0.3, in reality, the current after 0.3 seconds may also be included in the change conditions.

[0085] It is desirable that the "current" in the data related to the simulation conditions has opposite signs for charging and discharging, such as setting the charging current as positive and the discharging current as negative, or vice versa. Furthermore, it is desirable that the "temperature" is a temperature assumed as the battery surface temperature of the secondary battery reproduced by the equivalent circuit model 1. In the explanation with reference to FIG. 9 , "temperature" is set only as an initial condition, but when a simulation is performed taking into consideration that a temperature change occurs within a time period when a predetermined current profile is given, "temperature" may be set in some or all of the records included in the change conditions.

[0086] The SOC acquisition unit 72 references 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 the secondary battery. Therefore, if the OCV of the secondary battery or the equivalent circuit model 1 that reproduces the secondary battery is specified, the SOC corresponding to the OCV can be specified. The SOC acquisition unit 72 regards the "voltage" value under the initial conditions as the OCV of the equivalent circuit model 1 at time t=0, and specifies 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 reproduction target in the first embodiment.

[0087] The nonlinear resistor unit voltage calculation unit 61, the linear resistor unit voltage calculation unit 62, the transient response unit voltage calculation unit 63, the OCV calculation unit 64, and the voltage response calculation unit 65 of the second embodiment are similar to the nonlinear resistor unit voltage calculation unit 61, the linear resistor unit voltage calculation unit 62, the transient response unit voltage calculation unit 63, the OCV calculation unit 64, and the voltage response calculation unit 65 described with reference to FIG. 7 in the description of the first embodiment. However, the voltage response calculation unit 65 of the second embodiment outputs to an output unit 75. Furthermore, the nonlinear resistor unit voltage calculation unit 61, the linear resistor unit voltage calculation unit 62, and the transient response unit voltage calculation unit 63 of the second embodiment refer to parameters 82 corresponding to the value of “temperature” included in the initial conditions and the value of SOC identified by the SOC acquisition unit 72 from data stored in the data holding unit 80. Hereinafter, the term “initial temperature” refers to the value of “temperature” included in the initial conditions. The OCV calculation unit 64 functions as a first calculation unit. The linear resistor section voltage calculation unit 62 functions as a second calculation unit. The nonlinear resistor section voltage calculation unit 61 functions as a third calculation unit. The transient response section voltage calculation unit 63 functions as a fourth calculation unit. The voltage response calculation unit 65 functions as a fifth calculation unit.

[0088] FIG. 10 shows the electrical resistance R of the linear resistor 13. Ｌ 10 and 11 are graphs showing the relationship between p, which is one of the values ​​that determine the characteristics of the CPE 21, and the initial temperature and SOC. FIG. 11 is a graph showing the relationship between p, which is one of the values ​​that determine the characteristics of the CPE 21, and the initial temperature and SOC. The vertical variable parameter "temperature" in FIGS. 10 and 11 corresponds to the initial temperature. Also, the vertical variable parameter "SOC" in FIGS. 10 and 11 corresponds to the SOC value identified by the SOC acquisition unit 72.

[0089] The data shown in Fig. 10 and Fig. 11 is data included in the parameters 82, and is a so-called LUT. It shows that the parameters 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%, the linear resistor section voltage calculation unit 62 calculates the value of the field where "temperature" is 25 and "SOC" is 50 in the LUT shown in Fig. 10 as R ＬIn this case, the transient response section voltage calculation section 63 adopts the value of the field where "Temperature" is 25 and "SOC" is 50 in the LUT shown in FIG. 11 as the value of p.

[0090] R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ 10 and 11, R Ｌ Although the above description has been given with respect to p and p, parameter values ​​corresponding to the initial temperature and SOC are similarly adopted for the other parameters. The parameter values ​​corresponding to the different initial temperatures and SOCs are determined by acquiring data related to the object to be reproduced corresponding to the different initial temperatures and SOCs in the first embodiment. The data acquired in advance in this manner is input as parameters 82 via the input unit 71 together with the above-described SOC-OCV data 81 and stored in the data holding unit 80.

[0091] The output unit 75 outputs the voltage response V ｓｉｍ The data indicating the above is output as a simulation result corresponding to the data regarding the simulation conditions.

[0092] In addition, the nonlinear resistor voltage calculation unit 61 of the second embodiment uses the previously specified α and i ０ Voltage V according to ＮＬ Find the solution of in advance, and then calculate α and i ０ The corresponding voltage V ＮＬ The two-dimensional LUT indicating the voltage V ＮＬ can be analytically determined.

[0093] The input unit 71, the SOC acquisition unit 72, the data holding unit 80, the nonlinear resistor unit voltage calculation unit 61, the linear resistor unit voltage calculation unit 62, the transient response unit voltage calculation unit 63, the OCV calculation unit 64, the voltage response calculation unit 65, and the output unit 75 may be realized by individual circuits or a combination of multiple circuits, or may be realized by a single circuit that integrates some or all of the functions thereof. Furthermore, as shown in FIG. 13 , which will be described later, functions similar to those of the configuration shown in FIG. 7 may be realized by so-called software processing.

[0094] The flow of the processing performed in the second embodiment described above will be described with reference to the flowchart of FIG.

[0095] 12 is a flowchart showing the flow of processing performed 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 storage unit 80.

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

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

[0098] After the process of step S23, the processes of steps S3, S4, S5, S6, and S7 are performed as in the first embodiment. As a result, a voltage response V corresponding to the combination of the model-related parameters input in the process of step S21 and the data related to the simulation conditions input in the process of step S22 is calculated. ｓｉｍ is calculated.

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

[0100] As described above, according to the second embodiment, the voltage response of the secondary battery (voltage response V ｓｉｍ ) is calculated using the parameter (R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ ), and current information indicating currents (i(t)) at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times (Δt), and an initial voltage (V ｓｉｍ (0)) and temperature information indicating the temperature of the secondary battery (for example, the initial temperature described above), a step of specifying the SOC of the secondary battery from the voltage information, and a step of calculating the OCV (voltage V ＯＣ ) by the linear resistance component (linear resistance unit 13) included in the equivalent circuit model 1 using the current information and the parameters; Ｌ ) by the nonlinear resistance component (nonlinear resistance unit 12) included in the equivalent circuit model 1 using the current information, the temperature information, and the parameters; ＮＬ ) by the transient response component (transient response unit 20) included in the equivalent circuit model 1 using the current information and the parameters; Ｔ ), 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 a Butler-Volmer equation (Equation (3) or Equation (4)), and the third voltage drop is calculated based on time domain equations (Equations (6) and (7)) applied 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 when a predetermined current profile is given using the equivalent circuit model 1, the time domain voltage response of the secondary battery can be obtained. Furthermore, since the transient response unit 20 is a circuit model including 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 the second embodiment, the time domain voltage response of the secondary battery can be simulated with higher accuracy.

[0102] In addition, the transient response component (transient response unit 20) is a circuit model including linear resistances (charging resistance 32, discharging resistance 42), and is set to a state in which current also flows through the linear resistances depending on the state of CPE 21, thereby making it possible to reproduce with high accuracy the asymmetry between the current in the charging direction and the current in the discharging direction that can occur in a secondary battery.

[0103] In addition, the transient response component (transient response unit 20) includes a first element 30 in which a charging resistor 32 representing a charging resistance component and a first diode 31 are connected in series, and a second element 40 in which a discharge resistor 42 representing a discharging resistance component and a second diode 41 are connected in series, and is a circuit model in which CPE 21, the first element 30, and the second element 40 are connected in parallel, and under conditions in which a charging current is applied to equivalent circuit model 1, the second diode 41 does not allow current to flow to the second element 40, and under conditions in which a discharging current is applied to equivalent circuit model 1, the first diode 31 does not allow current to flow to the first element 30, thereby making it possible to reproduce with higher accuracy the asymmetry between the current in the charging direction and the current in the discharging direction that can occur in a secondary battery.

[0104] Also, the second voltage drop (voltage V ＮＬ ) is the coefficient representing the exchange current in the Butler-Volmer equation (i ０ ) and the charge transfer coefficient (α), the second voltage drop can be analytically determined.

[0105] Also, the second voltage drop (voltage V ＮＬ) is calculated using an equation with the current as a variable, which is expressed by the inverse function of the Butler-Volmer equation (see equation (4)), so that V ＮＬ (t) can be calculated.

[0106] According to the first embodiment, the OCV (voltage V) is calculated based on the true value indicating the voltage response of the 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 original data indicating the temperature of the secondary battery. ＯＣ ), the first voltage drop (voltage V Ｌ ), the second voltage drop (voltage V ＮＬ ) and a third voltage drop (voltage V Ｔ ) the voltage response (V ｓｉｍ ) is the parameter (R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ ) is identified. This allows the simulation of the secondary battery using the equivalent circuit model 1 to be performed with higher accuracy.

[0107] Furthermore, the parameter (R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ ) is specified in advance, the voltage response (V ｓｉｍ ) can be reduced. In other words, the voltage response when an arbitrary current profile is applied to the secondary battery reproduced by the equivalent circuit model 1 can be obtained more quickly. In addition, the voltage response (V ｓｉｍ (t)) can be simulated in more real time.

[0108] Furthermore, the parameter (R Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ ) in advance, V ｓｉｍ (t) = V ＭＥＡＳ Therefore, the V of the secondary battery to be simulated with the equivalent circuit model 1 can be treated as ＯＣEven if (t) is unknown, V in Eq. (1) ＯＣ As a target for which V is sought, ｓｉｍ , V Ｌ , V ＮＬ , V Ｔ By calculating backwards, V ＯＣ The V obtained in this way can be calculated. ＯＣ Therefore, the response of the SOC of the secondary battery according to the current profile can also be simulated.

[0109] A configuration for performing simulation by so-called software processing will be described below with reference to FIG.

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

[0111] The storage unit 91 stores software programs read by the calculation unit 92 and data referenced in connection with the execution of the software programs. Hereinafter, the term "program" refers to a software program executed by the calculation unit 92. Specifically, the storage unit 91 shown in FIG. 13 stores a 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 the second embodiment. That is, the simulation module 101 is a program for enabling the information processing device 90 to perform the same function as the simulation device 70 described with reference to FIG. 9, and virtually sets the equivalent circuit model 1, and calculates the voltage response V ｓｉｍ Output.

[0113] The simulation condition data 102 is similar to the data relating to the simulation conditions in the second embodiment, and is data indicating the initial conditions and the change conditions.

[0114] The SOC-OCV data 103 is similar to the SOC-OCV data included in the data related to the reproduction target in the first embodiment and the SOC-OCV data 81 in the second embodiment, and is data indicating the correspondence between the SOC and OCV of the secondary battery to be simulated.

[0115] The parameter specifying data 104 is the same as the parameter 82 in the second embodiment, and the voltage response V ｓｉｍ R as a parameter necessary for the calculation Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ This is data showing:

[0116] The parameter specifying module 105 is a program for performing processing corresponding to the first embodiment. That is, the simulation module 101 is a program for enabling the information processing device 90 to perform the same function as the simulation device 50 described with reference to FIGS. 6 and 7, and virtually sets the equivalent circuit model 1 and calculates R based on the processing flow described with reference to FIG. Ｌ , i ０ ,α,p,T,R Ｔ，ｃｈ and R Ｔ，ｄｉｓ Confirm the above.

[0117] The calculation unit 92 includes a calculation circuit that reads out a program from the storage unit 91 and executes the program. The calculation unit 92 references simulation condition data 102, SOC-OCV data 103, and parameter identification data 104 in association with the execution of the simulation module 101. The calculation unit 92 also references data related to the object to be reproduced that is input via the input unit 93 in association with the execution of the parameter identification module 105. The parameter identification data 104 may reflect the output result of the execution of the parameter identification module 105. In other words, the information processing device 90 may be configured to be able to execute the simulation module 101 via the execution of the parameter identification module 105. Of course, the information processing device 90 may be configured to be able to execute the simulation module 101 by storing the parameter identification data 104 that has been determined in advance in the storage unit 91.

[0118] The input unit 93 accepts input to the information processing device 90. Specifically, the input unit 93 includes a human interface, such as a keyboard or a mouse, that can accept input from an operator. The input unit 93 functions as the input unit 71 of the second embodiment. The input unit 93 also accepts input of data related to the object to be reproduced.

[0119] The output unit 94 performs output according to the processing content performed by the information processing device 90. Specifically, the output unit 94 includes a display device such as an image display. Note that a configuration that communicates with an external information processing device, such as a configuration that functions as a NIC (Network Interface Controller), or an interface that can connect to an external storage device that can store various data such as data related to the object to be reproduced, can function as both the input unit 93 and the output unit 94.

[0120] For ease of understanding, the above description does not refer to the number of SOC-OCV data sets. However, if there are multiple secondary batteries to be simulated, SOC-OCV data corresponding to each secondary battery is prepared. Furthermore, for a single secondary battery, if the correspondence between the SOC and OCV changes depending on the temperature of the secondary battery, SOC-OCV data corresponding to the temperature may be prepared. This allows for more accurate simulation.

[0121] The above-described embodiment is intended to facilitate understanding of the present invention, and is not intended to limit the present invention. The present invention may be modified or improved without departing from the spirit and scope of the present invention, and equivalents thereof are also included in the present invention.

[0122] The present disclosure can have the following configurations as described above or instead of the above.

[0123] (1) A simulation method according to one aspect of the present invention is a simulation method for calculating a voltage response of a secondary battery using an equivalent circuit model, the simulation method including the steps of: acquiring parameters indicating electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; acquiring voltage information indicating an initial voltage of the secondary battery; and acquiring temperature information indicating a temperature of the secondary battery; specifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; and calculating a line included in the equivalent circuit model using the current information and the parameters. the step of calculating a first voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters; the step of 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 the step of 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 constant phase element (CPE).

[0124] (2) In the simulation method of (1) above, the transient response component is a circuit model including a linear resistor, and is set to a state in which a current also 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 in which a charging resistor representing a charging resistance component and a first diode are connected in series, and a second element in which a discharge resistor representing a discharging resistance component and a second diode are connected in series, and the constant phase element CPE, the first element, and the second element are connected in parallel to form a circuit model, and the second diode is set to prevent current from flowing through the second element under conditions in which a charging current is applied to the equivalent circuit model, and the first diode is set to prevent current from flowing through the first element under conditions in which a discharging current is applied to the equivalent circuit model.

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

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

[0128] (6) In the simulation methods of (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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery.

[0129] (7) A simulation device according to another aspect of the present invention is a simulation device that sets an equivalent circuit model and calculates a voltage response of a secondary battery, the simulation device including: an acquisition unit that acquires parameters indicating electrical characteristics of the equivalent circuit model; current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; voltage information indicating an initial voltage of the secondary battery; and temperature information indicating a temperature of the secondary battery; an identification unit that identifies an SOC of the secondary battery from the voltage information; a first calculation unit that calculates an OCV using the SOC and the current information; and a second calculation unit that calculates an OCV based on a linear resistance component included in the equivalent circuit model using the current information and the parameters. a second calculation unit that calculates a first voltage drop; a third calculation unit that calculates 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; a fourth calculation unit that calculates a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; and 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, 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 constant phase element CPE.

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

[0131] (9) In the simulation device of (7) above, the transient response component includes a first element in which a charging resistance representing a charging resistance component and a first diode are connected in series, and a second element in which a discharge resistance representing a discharging resistance component and a second diode are connected in series, and the constant phase element CPE, the first element, and the second element are connected in parallel to form a circuit model, and the second diode is set so that under conditions in which a charging current is applied to the equivalent circuit model, no current flows through the second element, and under conditions in which a discharging current is applied to the equivalent circuit model, the first diode does not flow through the first element.

[0132] (10) In the simulation device of (7) to (9) above, the second voltage drop is derived by referring to an 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 device of (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 device according to any one of (7) to (11) above, the parameters are acquired 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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery.

[0135] (13) A program according to another aspect of the present invention is a program for setting an equivalent circuit model and calculating a voltage response of a secondary battery, the program including the steps of: acquiring parameters indicating electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period in which a predetermined current profile is given by a plurality of sampling times; acquiring voltage information indicating an initial voltage of the secondary battery; and acquiring temperature information indicating a temperature of the secondary battery; specifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; and calculating an OCV based on a linear resistance component included in the equivalent circuit model using the current information and the parameters. a step of calculating a first voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, the temperature information, and the parameters; a step of calculating a second voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; and a step of 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 constant phase element CPE.

[0136] (14) In the program of (13) above, the transient response component is a circuit model including a linear resistor, and is set to a state in which a current also 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 resistance representing a charging resistance component and a first diode in series, and a second element formed by connecting a discharge resistance representing a discharging 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 to form a circuit model, and the second diode is set so that under conditions in which a charging current is applied to the equivalent circuit model, no current flows through the second element, and under conditions in which a discharging current is applied to the equivalent circuit model, the first diode does not flow through the first element.

[0138] (16) In the programs (13) to (15) above, the second voltage drop is derived by referring to an LUT that corresponds 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 (13) to (15) 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.

[0140] (18) In the programs (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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery.

[0141] REFERENCE SIGNS LIST 1 equivalent circuit model 11 power supply section 12 nonlinear resistance section 13 linear resistance section 20 transient response section 30 first element 31 first diode 32 charging resistance 40 second element 41 second diode 42 discharging resistance 50, 70 simulation device 81 SOC-OCV data 82 parameters 90 information processing device 100 voltage response calculation program

Claims

1. A simulation method for calculating a voltage response of a secondary battery using an equivalent circuit model, comprising: obtaining parameters that indicate electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period during which a predetermined current profile is provided by a plurality of sampling times, voltage information indicating an initial voltage of the secondary battery, and temperature information indicating a temperature of the secondary battery; Identifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; calculating a first voltage drop due to a linear resistance component included in the equivalent circuit model using the current information and the parameters; calculating 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; calculating a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop; and the second voltage drop is calculated based on the Butler-Volmer 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 a circuit model including a linear resistor, and is set to a state in which a current also flows through the linear resistor depending on the state of the constant phase element CPE. The simulation method according to claim 1 .

3. The transient response component is a first element in which a charging resistor representing a charging resistance component and a first diode are connected in series; a second element in which a discharge resistor representing a discharge resistance component and a second diode are connected in series, and the constant phase element CPE, the first element, and the second element are connected in parallel; A second diode prevents a current from flowing through the second element under a condition where a charging current is given to the equivalent circuit model; a first diode is set to a state in which no current flows through the first element under a condition in which a discharge current is applied to the equivalent circuit model; The simulation method according to claim 1 .

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

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

6. the parameters are identified such that a 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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery; The simulation method according to any one of claims 1 to 3.

7. A simulation device that sets an equivalent circuit model and calculates a voltage response of a secondary battery, an acquisition unit that acquires parameters indicating electrical characteristics of the equivalent circuit model, current information indicating currents at multiple time points obtained by dividing a period in which a predetermined current profile is given by multiple sampling times, voltage information indicating an initial voltage of the secondary battery, and temperature information indicating a temperature of the secondary battery; an identification unit that identifies an SOC of the secondary battery from the voltage information; a first calculation unit that calculates an OCV using the SOC and the current information; a second calculation unit that 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 that calculates 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; a fourth calculation unit that calculates a third voltage drop due to a 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-Volmer 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 a circuit model including a linear resistor, and is set to a state in which a current also flows through the linear resistor depending on the state of the constant phase element CPE. The simulation device according to claim 7.

9. The transient response component is a first element in which a charging resistor representing a charging resistance component and a first diode are connected in series; a second element in which a discharge resistor representing a discharge resistance component and a second diode are connected in series, and the constant phase element CPE, the first element, and the second element are connected in parallel; A second diode prevents a current from flowing through the second element under a condition where a charging current is given to the equivalent circuit model; a first diode is set to a state in which no current flows through the first element under a condition in which a discharge current is applied to the equivalent circuit model; The simulation device according to claim 7.

10. the second voltage drop is derived by referring to a look-up table corresponding to a coefficient representing an exchange current and a charge transfer coefficient among the coefficients included in the Butler-Volmer equation; The simulation device according to any one of claims 7 to 9.

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

12. the parameters are acquired such that a 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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery; The simulation device according to any one of claims 7 to 9.

13. A program for setting an equivalent circuit model and calculating a voltage response of a secondary battery, obtaining parameters that indicate electrical characteristics of the equivalent circuit model; acquiring current information indicating currents at a plurality of time points obtained by dividing a period during which a predetermined current profile is provided by a plurality of sampling times, voltage information indicating an initial voltage of the secondary battery, and temperature information indicating a temperature of the secondary battery; Identifying an SOC of the secondary battery from the voltage information; calculating an OCV using the SOC and the current information; calculating a first voltage drop due to a linear resistance component included in the equivalent circuit model using the current information and the parameters; calculating 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; calculating a third voltage drop due to a transient response component included in the equivalent circuit model using the current information and the parameters; calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop; causing an information processing device to execute the above; the second voltage drop is calculated based on the Butler-Volmer 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 a circuit model including a linear resistor, and is set to a state in which a current also flows through the linear resistor depending on the state of the constant phase element CPE. The program according to claim 13.

15. The transient response component is a first element in which a charging resistor representing a charging resistance component and a first diode are connected in series; a second element in which a discharge resistor representing a discharge resistance component and a second diode are connected in series, and the constant phase element CPE, the first element, and the second element are connected in parallel; A second diode prevents a current from flowing through the second element under a condition where a charging current is given to the equivalent circuit model; a first diode is set to a state in which no current flows through the first element under a condition in which a discharge current is applied to the equivalent circuit model; The program according to claim 13.

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

17. The second voltage drop is calculated by an equation expressed by the inverse function of the Butler-Volmer equation, with current as a variable.

16. The program according to any one of claims 13 to 15.

18. the parameters are identified such that a 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 original data indicating a true value indicating a voltage response of a secondary battery to which a predetermined current profile has been applied, an SOC before the predetermined current profile was applied to the secondary battery, and a temperature of the secondary battery; 16. The program according to any one of claims 13 to 15.