JP7850918B2 - Simulation method, simulation apparatus, and program - Google Patents

Description

This invention relates to a simulation method, a simulation apparatus, and a program.

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

Japanese Patent Publication No. 2018-40684 Japanese Patent Publication No. 2019-219275 Japanese Patent Publication No. 2019-191029

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

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

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

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

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

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

Figure 1 shows an equivalent circuit model used in the present invention. Figure 2 is a graph showing a comparative example of the voltage response V _MEAS and the voltage response V _sim calculated according to appropriately defined R _L , i ₀ , α, p, _{T, RT, ch} and _{RT, dis} . Figure 3 is a graph showing a comparative example of the voltage response V _MEAS and the voltage response V _sim calculated according to appropriately defined R _L , i ₀ , α, p, _{T, RT, ch} and _{RT, dis} . Figure 4 is a graph showing the time-series change of current based on the current profile given when the voltage response V _MEAS shown in Figures 2 and 3 is obtained. Figure 5 is a flowchart showing the processing flow performed in Embodiment 1. Figure 6 is a block diagram showing the configuration of the simulation device. Figure 7 is a block diagram showing the configuration of the voltage calculation unit and its inputs and outputs. Figure 8 is a block diagram showing the configuration of the simulation device. Figure 9 shows an example of data related to the simulation conditions. Figure 10 shows the relationship between the electrical resistance R/ _L of the linear resistance section, the initial temperature, and the SOC (State of Temperature). Figure 11 shows the relationship between p, one of the values that determine the characteristics of the CPE, the initial temperature, and the SOC. Figure 12 is a flowchart showing the processing flow performed in Embodiment 2. Figure 13 is a block diagram showing the configuration of an information processing device.

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

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

The power supply unit 11 behaves as a secondary battery. The voltage V _OC shown in Figure 1 represents the open-circuit voltage (OCV) of the power supply unit 11.

The nonlinear resistor 12 behaves as an electrical resistance where the relationship between the current flowing through the nonlinear resistor 12 and the voltage _VNL across the nonlinear resistor 12 is not proportional. In Figure 1, Z _BV (i ₀ , α) represents the nonlinear resistance component of the nonlinear resistor 12. This nonlinear resistance component is an impedance that expresses the voltage drop when a certain current flows through the nonlinear resistor 12. The voltage _VNL indicates the voltage that drops due to this voltage drop. This nonlinear resistance component can be determined based on the Butler-Volmer equation described later. _{i 0} represents the exchange current. α represents the charge transfer coefficient.

The linear resistor 13 behaves as an electrical resistance in which the relationship between the current flowing through the linear resistor 13 and the voltage V _L across the ends of the linear resistor 13 is proportional.

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

As shown in Figure 1, the first diode 31 is configured to allow current to flow from the first terminal 15 to the second terminal 16 of the equivalent circuit model 1, but not in the reverse direction. Similarly, the second diode 41 is configured to allow current to flow from the second terminal 16 to the first terminal 15 of the equivalent circuit model 1, but not in the reverse direction. Therefore, the equivalent circuit model 1 is configured such that, under conditions where a charging current is applied, the second diode 41 prevents current from flowing through the second element 40, and under conditions where a discharge current is applied, the first diode 31 prevents current from flowing through the first element 30. The charging resistor 32 and the discharge resistor 42 behave as electrical resistors.

In Figure 1, the value labeled Z _CPE (p, T) represents the impedance that expresses the voltage drop due to CPE 21. The voltage V _T indicates the voltage drop caused by this voltage drop. p and T are values that determine the characteristics of CPE 21. The inclusion of a first element 30 and a second element 40 in equivalent circuit model 1 is useful when the characteristics of the secondary battery simulated by equivalent circuit model 1 differ between discharge and charge.

Equivalent circuit model 1 is not an actual circuit, but is virtually set up by calculations performed by the simulation devices 50 and 70 and the information processing device 90, which will be described later. Equivalent circuit model 1 is set up 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.

An example of a lithium-ion battery configuration reproduced by Equivalent Circuit Model 1 is a lithium-ion battery in which the main positive electrode active material is lithium iron phosphate (LFP: _LiFePO₄ ), lithium cobalt oxide ( _LiCoO₂ ), lithium nickel cobalt manganese oxide (Li(Ni _x Mn _y Co _z ) _O₂ , x+y+z=1, x, y, and z are each between 0 and 1), or lithium nickel cobalt aluminate (Li(Ni _a Co _b Al _c ) _O₂ , a+b+c=1, a, b, and c are each between 0 and 1), and the main negative electrode active material is graphite or a mixture of graphite and silicon oxide. In the following description of Embodiment 1, it is assumed that the voltage response of the lithium-ion battery is reproduced by Equivalent Circuit Model 1. Furthermore, when "reproduced target" is mentioned, it refers to the lithium-ion battery in question. The secondary battery reproduced by equivalent circuit model 1 is not limited to this, and may have other configurations.

Prior to the simulation using Equivalent Circuit Model 1, data on the target of reproduction is acquired. Specifically, the State of Charge (SOC) of the target of reproduction is adjusted within the range of 10% to 90%. The temperature of the target of reproduction is also adjusted within the range of -10°C to 50°C. Preferably, the temperature of the target of reproduction is the battery surface temperature. A predetermined current profile is given to the reproduced target adjusted in this way. This predetermined current profile, as shown in Figure 4 later, for example, represents a current pattern that combines the current that charges the target of reproduction (charging current), the current that causes discharge from the target of reproduction (discharge current), and no current (0 amperes) that does not cause intentional charging or intentional discharge of the target of reproduction, in a time series. The voltage response V _MEAS (see Figures 2 and 3) of the target of reproduction that occurs while this predetermined current profile is given is measured. The voltage response V _MEAS , the conditions under which the voltage response V _MEAS was obtained, and the predetermined current profile are associated and treated as data related to the reproduction target. The conditions under which the voltage response V _MEAS was obtained include the SOC of the reproduction target and the temperature of the reproduction target immediately before the predetermined current profile was applied to the reproduction target. Furthermore, in Embodiment 1, the SOC-OCV data described later is also included in the data related to the reproduction target. The data related to the reproduction target functions as the source data.

Hereinafter, when "true value" is mentioned, it refers to the voltage response V _MEAS . Embodiment 1 is for reproducing the voltage response V MEAS by the voltage response V sim that occurs between the first terminal 15 and the second terminal 16 when the predetermined current profile described above is applied to the equivalent circuit _model 1 via the first terminal 15 and the second terminal 16 under the same conditions as when the true value was obtained. In other words, Embodiment 1 reproduces in the equivalent circuit model 1 substantially the same electrical characteristics as _the target of reproduction.

The voltage response V _sim can be expressed as shown in equation (1) below. That is, the voltage response V _sim is the sum of the voltages V _OC , V _NL , V _L , and V _T shown in Figure 1.
V _sim =V _OC +V _T +V _NL +V _L ...(1)

The specific derivation methods for each of the voltages _VOC , _VNL , _VL , and _VT will be explained sequentially below. In this explanation, the time during which a predetermined current profile is applied will be referred to as the application time. At some point within the application time, the current generated in the reproduction target when the predetermined current profile is applied to the reproduction target will be denoted as i(t). Here, the value of t in i(t) corresponds to the application time. Note that t=0 indicates the time before the application time, i.e., the initial state. Therefore, in Embodiment 1, i(0) is 0 amperes because it is before the predetermined current profile is applied. Also, if the sampling time is 0.1 seconds, i(0.1) indicates the current at the time 0.1 seconds after the predetermined current profile has been applied to the reproduction target. In this case, i(0.2) indicates the current at the time 0.2 seconds after the predetermined current profile has been applied to the reproduction target. The sampling time is not limited to 0.1 seconds but can be arbitrary.

Furthermore, in the description of Embodiment 1, various values other than current may also be shown using (t) to indicate their value at a certain point in time. For example, the changes in voltage _VOC , _VNL , VL, and _VT in response to a change in i( _t ) can be shown as _VOC (t), _VNL (t), _VL (t), and _VT (t). Since the equivalent circuit model 1 is set up for the purpose of reproducing the object to be reproduced, _VOC (t), _VNL (t), VL(t), and _VT (t) are derived so that the current considered to be flowing through the equivalent circuit model 1 becomes _i (t). Therefore, if Vsim(t) is the voltage response _Vsim in response to _i (t), then from equation (1) it can be expressed as _Vsim (t) = _VOC (t) + _VT (t) + _VNL (t) + _VL (t).

In Embodiment 1, seven variable parameters are set in the equivalent circuit model 1 to reproduce the same electrical characteristics as the target of reproduction. These seven variable parameters are R _L , i ₀ , α, p, T, R _{T, ch,} and R _{T, dis} . R _L represents the electrical resistance of the linear resistance section 13. _{R T, ch} represents the electrical resistance of the charging resistance 32. _{R T, dis} represents the electrical resistance of the discharge resistance 42. As mentioned above, i ₀ represents the exchange current. α represents the charge transfer coefficient. p and T are values that determine the characteristics of the CPE 21.

First, let's explain the voltage V _OC . As mentioned above, the voltage V _OC is the OCV of the power supply unit 11. Since the equivalent circuit model 1 is intended to replicate a secondary battery, the power supply unit 11 is set to behave like a secondary battery and is capable of charging and discharging.

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

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

The initial value of the voltage V _OC is the same as the initial voltage response of the reproducible system, as indicated by the data relating to the reproducible system described above. The initial state refers to the state of the reproducible system before a predetermined current profile is applied. That is, V _OC (0) is the same as the OCV of the initial state of the reproducible system and is identified from the data relating to the reproducible system.

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

When a secondary battery is in a charging or discharging state, that is, when current is flowing, the State of Charge (SOC) of the secondary battery changes. The SOC of the secondary battery depends on the amount of current that flows during charging and the amount of current that flows during discharging. As mentioned above, a predetermined current profile includes the charging current and the discharging current. How the SOC of the power supply unit 11 increases or decreases from the start of measurement according to the charging current and discharging current given by the predetermined current profile can be calculated based on the amount of charging current and the amount of discharging current, i.e., i(t). Furthermore, _VOC (t), which shows the OCV of the power supply unit 11 at a certain point (t) after the predetermined current profile has been applied, can be considered to correspond to the SOC of the power supply unit 11 at that point (t). Therefore, VOC(t) can be derived by calculating the SOC of the power _supply unit 11 at a certain 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.

It should be noted that, in obtaining the true value, the OCV is not measured each time a predetermined current profile is given, nor are such measured OCV values included in the data related to the object of reproduction. On the other hand, considering that the equivalent circuit model 1 is a simulation that does not actually perform charging and discharging of a secondary battery, the change in OCV that occurs while a predetermined current profile is given is derived as _VOC (t). That is, _VOC (t) is the OCV corresponding to the SOC of the power supply unit 11 at a specific time (t), and merely corresponds to the SOC-OCV data. In other words, the fact that the "state in which neither charging nor discharging of the secondary battery is performed" does not elapse sufficiently when a predetermined current profile is given to the equivalent circuit model 1, resulting in "conditions that are not suitable for measuring OCV", is ignored when deriving _VOC (t).

Next, we will explain the voltage _VNL . As explained with reference to Figure 1, the voltage _VNL represents the voltage drop caused by the voltage drop that occurs in accordance with the nonlinear resistance component of the nonlinear resistance section 12. Here, the relationship between i(t) and _VNL (t) can be expressed by the following equation (2). That is, _VNL (t) in equation (2) represents the value of the voltage _VNL at a certain time (t).

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

In equation (2), _i₀ represents the exchange current, as described above. The exchange current refers to the internal current generated by the insertion and removal of reactants in the electrolyte solution between the positive and negative electrodes and the electrolyte solution when there is no load, such as when a secondary battery like a lithium-ion battery is neither charging nor discharging. In the case of a lithium-ion battery, the reactant is lithium ions. The value of _i₀ indicates the magnitude of the exchange current.

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

By the way, equation (2) is equivalent to equation (3) below. Using equation (3), _VNL (t) can be derived more easily.

In equations (2) and (3), F and R are constants, and θ is determined based on data relating to the object to be reproduced. Therefore, once α and _i₀ are determined, _VNL (t) is also determined. By appropriately determining _i₀ and α, the trend of the electrical characteristics of the object to be reproduced by the equivalent circuit model 1, i.e., secondary batteries such as lithium-ion batteries, can be reproduced with higher accuracy.

_VNL (t) can be obtained using numerical analysis. Specifically, in Embodiment 1, the Newton-Raphson method or the secant method is used as the numerical analysis algorithm for obtaining _VNL (t), but other algorithms may be used. Alternatively, _VNL (t) may be calculated sequentially as a solution to equation (3) by defining α and _i0 , or a two-dimensional lookup table (LUT) showing solutions corresponding to α and _i0 may be created in advance, and _VNL (t) may be analytically obtained by referring to the LUT.

Furthermore, the inverse function for finding _VNL (t) can be derived from equations (2) and (3). This inverse function can be expressed as shown in equation (4) below. By using equation (4), _VNL (t) can also be calculated without using analytical methods such as the numerical analysis described above.

Next, we will explain the voltage V _L. As explained with reference to Figure 1, the voltage V _L is the voltage across the linear resistor 13 corresponding to the current flowing through the linear resistor 13, and the current and the voltage are proportional. Since the current at a certain point in time (t) is i(t), V _L (t) can be expressed as shown in equation (5) below. As mentioned above, R _L in equation (5) represents the electrical resistance of the linear resistor 13. That is, by appropriately determining R _L which represents the electrical resistance of the linear resistor 13, V _L (t) corresponding to i(t) can be calculated from equation (5).
V _L (t)=i(t)×R _L ...(5)

Next, we will explain the voltage V _t . As explained with reference to Figure 1, the voltage V _t represents the voltage drop due to the voltage drop by CPE21.

When a certain current profile is applied to the equivalent circuit model 1, the voltage drop due to CPE21 at any given time differs between charging and discharging. Charging refers to the time when a current is generated that is supplied from the first terminal 15, flows through the equivalent circuit model 1, and flows toward the second terminal 16. Discharging refers to the time when a current supplied from the first terminal 15, powered by the voltage _VOC of the equivalent circuit model 1, flows toward the first terminal 15, that is, when the direction of the current is from the second terminal 16, passes through the equivalent circuit model 1, and flows toward the first terminal 15. Assuming that the current profile is the predetermined current profile described above, the V _T [nΔt] during charging can be expressed as shown in equation (6) below. Also, the V _T [nΔt] during discharging can be expressed as shown in equation (7) below.

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 mentioned above, when the sampling time is 0.1 seconds, Δt = 0.1. Therefore, by setting nΔt = t, we can consider V _T [nΔt] = V _T (t). Similarly, [kΔt] represents the product of k, which indicates a data number less than n, and Δt, which indicates the sampling time. For example, i [kΔt] represents the current flowing through equivalent circuit model 1 at time kΔt.

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

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

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

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

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

As described above, R _{T, ch} in equation (6) represents the electrical resistance of the charging resistance 32. Also, as described above, R _{T, dis} in equation (7) represents the electrical resistance of the discharge resistance 42. By appropriately determining _{R T, ch} , R _{T, dis} , p, and T, V _T (t) can be calculated from equations (6) and (7).

Based on the calculations from equations (1) to (9) above, R _L , i ₀ , α, p, T, R _{T, ch} and R _{T, dis} can be appropriately determined, and V _sim (t) = V _OC (t) + V _T (t) + V _NL (t) + V _L (t) can be calculated.

As described above, in Embodiment 1, it is required that the voltage response V _MEAS be reproduced by the voltage response V _sim , which shows the result of the simulation using the equivalent circuit model 1. Therefore, if the voltage response V _MEAS at a certain time (t) is V _MEAS (t), it is desirable that the evaluation value, which shows the result of comparing V _MEAS (t) and V _sim (t) using a predetermined comparison evaluation algorithm, satisfies the predetermined evaluation criteria. Examples of predetermined comparison evaluation algorithms for deriving the evaluation value include the root mean square error (RMSE), mean square error, mean absolute error, etc., but other comparison evaluation algorithms may also be used.

For example, let's explain the case where RMSE is used as a method for deriving the evaluation value. First, a certain combination of R _L , i ₀ , α, p, T, R _{T, ch,} and R _{T, dis} is adopted, and V _sim (t) is calculated based on equations (1) to (9). If the evaluation value, which is the result of comparing _{V sim} (t) and V _MEAS (t), is greater than the threshold, the criterion is not met, and another combination in which at least one of R _L , i ₀ , α, p, T, R _{T, ch,} and R _{T, dis} is changed is adopted, and V _sim (t) is calculated again. If the evaluation value becomes smaller (for example, below the threshold), it is considered that V _sim (t) has reproduced V _MEAS (t), and the combinations of R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} at the time V _sim (t) is calculated are determined as parameters necessary for calculating the voltage response V _sim . This threshold is set in advance to ensure sufficient accuracy in reproducing V _MEAS (t) using V _sim (t).

For the combinations of R _L , i ₀ , α, p, T, _{RT, ch,} and RT _{, dis} , at least one, preferably multiple, combination patterns are prepared in advance and provided as data. If the criteria are not met with R _L , i ₀ , α, p, T, RT _{, ch} , and RT _{, dis} using the data prepared in this way, at least one of R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} is changed and V _sim (t) and the evaluation value are recalculated. Here, the mechanism for changing at least one of R _L , i ₀ , α, p, _{T, RT, ch,} and _{RT, dis} can be an evolutionary algorithm such as a genetic algorithm, but it is not limited to this, and other mechanisms that function similarly can be adopted.

Figures 2 and 3 are graphs showing a comparative example of the voltage response V _MEAS and the voltage response V _sim calculated according to appropriately defined R _L , i ₀ , α, p, T, RT _{, ch} and RT _{, dis} . Figure 4 is a graph showing the time-series change of current due to the current profile given when the voltage response V _MEAS shown in Figures 2 and 3 is obtained. In the graphs of Figures 2 and 3, the horizontal axis is time and the vertical axis is voltage. That is, the graphs shown in Figures 2 and 3 show the voltage due to the voltage response that occurs during the time when the predetermined current profile described above is given on the horizontal axis. Figure 3 is an enlarged view of the graph shown in Figure 2, between 1025 seconds and 1250 seconds.

In the graphs shown in Figures 2 and 3, the solid line "experiment" represents the voltage response V _MEAS , and the dashed line "simulation" represents the voltage response V _sim . As shown in Figures 2 and 3, the voltage response V _sim substantially matches the voltage response V _MEAS . Thus, the voltage response V _sim calculated using appropriate R _L , i _O , α, p, T, RT _{, ch} and RT _{, dis} and equations (1) to (9) can reproduce the voltage response V _MEAS with high accuracy.

The process for calculating the voltage response V _sim and determining the combinations of R _L , i ₀ , α, p, T, RT _{, ch,} and _{RT, dis} , as described above, will be explained with reference to the flowchart in Figure 5.

Figure 5 is a flowchart showing the processing flow performed in Embodiment 1. First, data related to the reproduction target, including the true value, is acquired (Step S1). Specifically, as described above, the voltage response V _MEAS , which is treated as the true value, the conditions under which the voltage response V _MEAS was obtained, a predetermined current profile given to the reproduction target when the voltage response V _MEAS was obtained, the SOC-OCV data of the reproduction target, etc., are associated and treated as data related to the reproduction target.

Next, candidate values for the parameters necessary for calculating the voltage response V _sim of the equivalent circuit model 1 are set (step S2). Specifically, at least one combination of R _L , i ₀ , α, p, T, R _{T, ch} and R _{T, dis} described above is prepared in advance as candidate values.

Next, the voltage drop across the nonlinear resistance section 12 is calculated (step S3), the voltage drop across the linear resistance section 13 is calculated (step S4), the voltage drop across the transient response section 20 is calculated (step S5), and the OCV is calculated (step S6) in sequence. The processes from step S3 to step S6 can be performed in any order, in parallel, or with some or all of the order shown in Figure 5 changed. The voltage _VNL described above is derived through calculation in step S3. The voltage _VL described above is derived through calculation in step S4. The voltage _VT described above is derived through calculation in step S5. The voltage _VOC described above is derived through calculation in step S6.

After the processing from step S3 to step S6 is completed, the voltage response V _sim is calculated (step S7). That is, based on equation (1) described above, the voltage response V _sim is calculated by summing the voltages V _NL , V _L , V _T , and V _OC .

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

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

If the evaluation value is determined to not meet the criteria in step S9 (step S9; No), the process proceeds to step S2. In the second and subsequent steps of step S2, the candidate values are reset. In resetting the candidate values, at least one of the following is changed based on the mechanism of the genetic algorithm described above: R _L , i ₀ , α, p, T, _{RT, ch,} and RT _{, dis} .

If the evaluation value is determined to meet the criteria in step S9 (step S9; Yes), the candidate values R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} adopted in the latest step S2 are determined as parameters necessary for calculating the voltage response V _sim (step S10).

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

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

The data storage unit 51 stores data input to the simulation device 50 from an external source and data output by the voltage comparison unit 54. The data input to the simulation device 50 from an external source includes the data related to the object to be reproduced as described above, and candidate value data that shows at least one combination of R _L , i ₀ , α, p, T, _{RT, ch} and _{RT, dis} prepared in advance. The parameter input unit 52 reads the data stored in the data storage unit 51 and outputs it to the voltage calculation unit 60.

Figure 7 is a diagram showing the configuration and input/output of the voltage calculation unit 60. The voltage calculation unit 60 comprises a nonlinear resistance voltage calculation unit 61, a linear resistance voltage calculation unit 62, a transient response voltage calculation unit 63, an OCV calculation unit 64, and a voltage response calculation unit 65.

The nonlinear resistance voltage calculation unit 61 performs calculations to derive the voltage _VNL . The linear resistance voltage calculation unit 62 performs calculations to derive the voltage _VL . The transient response voltage calculation unit 63 performs calculations to derive the voltage _VT . The OCV calculation unit 64 performs calculations to derive the voltage _VOC . In the calculations performed by the nonlinear resistance voltage calculation unit 61, the linear resistance voltage calculation unit 62, the transient response voltage calculation unit 63, and the OCV calculation unit 64, the values of _RL , _i0 , α, p, T, _{RT, ch,} and RT _{, dis} indicated by the candidate value data input from the parameter input unit 52 to the voltage calculation unit 60 are referenced as needed, as well as i(t) indicated by a predetermined current profile included in the data related to the data to be reproduced, and SOC-OCV data.

The voltage response calculation unit 65 calculates the voltage response V sim by adding together the voltage V _NL derived by the calculation of the nonlinear resistance voltage calculation unit 61, the voltage V _L derived by the calculation of the linear resistance voltage calculation unit 62, the voltage V _T derived by the calculation of the transient response voltage calculation unit 63, and the voltage V _OC derived by the calculation of the OCV calculation _unit 64. The voltage response calculation unit 65 outputs data showing the derived voltage response V _sim and data showing the voltage response V _MEAS included in the data related to the reproduction target to the voltage comparison unit 54. The data showing the voltage response V _MEAS is transferred to the voltage response calculation unit 65 via at least one of the nonlinear resistance voltage calculation unit 61, the linear resistance voltage calculation unit 62, the transient response voltage calculation unit 63, and the OCV calculation unit 64.

The voltage comparison unit 54 compares and evaluates the voltage response V _sim and voltage response V _MEAS indicated by the data input from the voltage response calculation unit 65, derives an evaluation value, and makes a decision based on the evaluation value. That is, the voltage comparison unit 54 determines whether R _L , i ₀ , α, p, T, RT _{, ch} and _{RT, dis} used in the calculation of the voltage response V _sim are to be confirmed as parameters necessary for calculating the voltage response V _sim . If the determination is made to confirm R _L , i ₀ , α, p, T, RT _{, ch} and _{RT, dis} used in the calculation of the voltage response V _sim as parameters necessary for calculating the voltage response V _sim , the voltage comparison unit 54 outputs data indicating this to the data storage unit 51. The data storage unit 51 stores R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} , which have been determined as parameters necessary for calculating the voltage response V _sim , in a manner that they can be distinguished from candidate values. On the other hand, if it is determined that R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} , which were used in the calculation of the voltage response V _sim , are not to be determined as parameters necessary for calculating the voltage response V _sim , data indicating this determination and data showing the latest R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} are output to the parameter recalculation unit 55.

The parameter recalculation unit 55 resets R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} . After the parameter recalculation unit 55 resets R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} , the parameter input unit 52 outputs the R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} reset by the parameter recalculation unit 55 to the voltage calculation unit 60.

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

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

(Embodiment 2)
Next, Embodiment 2 will be described. In Embodiment 2, it is assumed that the parameters R _L , i ₀ , α, p, T, R _{T, ch,} and R _{T, dis} , which are necessary for calculating the voltage response _V sim, are predetermined by Embodiment 1. In other words, Embodiment 2 assumes that the equivalent circuit model 1 is already in an environment where it can reproduce the target of reproduction. Embodiment 2 simulates the voltage response under arbitrary conditions using the equivalent circuit model 1.

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

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

Figure 9 shows an example of data related to simulation conditions. The data includes initial conditions and variable conditions that change in units of sampling time.

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

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

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

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

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

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

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

Figure 10 shows the relationship between R _L , which represents the electrical resistance of the linear resistance section 13, the initial temperature, and the SOC. Figure 11 shows the relationship between p, one of the values that determine the characteristics of the CPE 21, the initial temperature, and the SOC. In Figures 10 and 11, the vertical variable parameter "temperature" corresponds to the initial temperature. Also, in Figures 10 and 11, the vertical variable parameter "SOC" corresponds to the SOC value identified by the SOC acquisition unit 72.

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

Of the parameters R _L , i ₀ , α, p, T, _{RT, ch,} and _{RT, dis} , R _L and p have been explained with reference to Figures 10 and 11, but similarly, the values of the parameters corresponding to the initial temperature and SOC are adopted for the other parameters as well. The determination of the parameter values corresponding to different initial temperatures and SOCs is performed in Embodiment 1 by acquiring data related to the reproducible target corresponding to different initial temperatures and SOCs. The data acquired in this way is input as parameter 82 together with the SOC-OCV data 81 described above via the input unit 71 and stored in the data holding unit 80.

The output unit 75 outputs data showing the voltage response V _sim output by the voltage response calculation unit 65 as a simulation result corresponding to the data related to the simulation conditions.

In the second embodiment, the nonlinear resistance voltage calculation unit 61 pre-determines solutions for the voltage _VNL corresponding to predetermined α and _i0 , and stores a two-dimensional LUT representing the voltage _VNL corresponding to the combination of α and _i0 in the nonlinear resistance voltage calculation unit 61 or in a data holding unit 80 that can be referenced from the nonlinear resistance voltage calculation unit 61, thereby enabling the voltage _VNL to be determined analytically.

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

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

Figure 12 is a flowchart showing the processing flow 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 holding unit 80.

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

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

After the processing in step S23, the processing in steps S3, S4, S5, S6, and S7 is performed in the same manner as in Embodiment 1. This calculates the voltage response V _sim according to the combination of the model parameters input in step S21 and the simulation condition data input in step S22.

After the processing in step S7, the output unit 75 outputs the voltage response V _sim calculated by the voltage response calculation unit 65 (step S29).

As described above, according to Embodiment 2, when calculating the voltage response (voltage response V _sim ) of a secondary battery using the equivalent circuit model 1, the steps are: to acquire parameters (R _L , i ₀ , α, p, T, RT _{, ch} and RT _{, dis} ) that indicate the electrical characteristics of the equivalent circuit model 1; to acquire current information indicating the current (i(t)) at multiple time points obtained by dividing the period over which a predetermined current profile is given into multiple sampling times (Δt); to acquire voltage information indicating the initial voltage (V _sim (0)) of the secondary battery; and to acquire temperature information indicating the temperature of the secondary battery (for example, the initial temperature described above); to identify the SOC of the secondary battery from the voltage information; to calculate the OCV (voltage V _OC ) using the identified SOC and the current information; and to calculate the first voltage drop (voltage V _L) due to the linear resistance component (linear resistance section 13) included in the equivalent circuit model 1 using the current information and the parameters. The process includes the steps of: calculating the OCV; calculating a second voltage drop (voltage _VNL ) due to a nonlinear resistance component (nonlinear resistance section 12) included in the equivalent circuit model 1 using the current information, temperature information, and parameters; calculating a third voltage drop (voltage _VT ) due to a transient response component (transient response section 20) included in the equivalent circuit model 1 using the current information and 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 Butler-Volmer's equation (equation (3) or equation (4)), and the third voltage drop is calculated based on time-domain equations (equations (6) and (7)) applicable to the circuit model including CPE 21.

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

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

Furthermore, the transient response component (transient response section 20) includes a first element 30 formed by connecting a charging resistor 32 representing the charging resistance component and a first diode 31 in series, and a second element 40 formed by connecting a discharge resistor 42 representing the discharge resistance component and a second diode 41 in series. The circuit model is such that CPE 21, the first element 30, and the second element 40 are connected in parallel. Under conditions where a charging current is supplied to the equivalent circuit model 1, the second diode 41 prevents current from flowing through the second element 40, and under conditions where a discharge current is supplied to the equivalent circuit model 1, the first diode 31 prevents current from flowing through the first element 30. This allows for a more accurate reproduction of the asymmetry between the charging current and the discharging current that can occur in a secondary battery.

Furthermore, the second voltage drop (voltage V _NL ) can be analytically determined by referring to the LUT corresponding to the coefficients included in the Butler-Volmer equation, namely the coefficient representing the exchange current (i ₀ ) and the charge transfer coefficient (α).

Furthermore, the second voltage drop (voltage _VNL ) can be calculated using an equation with current as a variable, expressed by the inverse function of the Butler-Volmer equation (see equation (4)), thus allowing _VNL (t) to be calculated without using analytical methods.

Furthermore, according to Embodiment 1, based on raw data showing the true value of the voltage response of a secondary battery given a predetermined current profile, the SOC before the secondary battery was given the predetermined current profile, and the temperature of the secondary battery, parameters (R _L , i 0, α, p, T, RT, ch, and _RT , dis) that reproduce the true value of the voltage response (V _sim ) calculated from the OCV (voltage V _OC ), the first voltage drop (voltage V _L ), the second voltage drop ₍ voltage V _NL ), and the third voltage _drop (voltage _{V T} ) are identified. This makes it possible to perform simulations of the secondary battery using the equivalent circuit model 1 with higher accuracy.

Furthermore, by pre-determining the parameters (R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} ) in Embodiment 1, the computational load required to calculate the voltage response (V _sim ) in Embodiment 2 can be reduced. In other words, the voltage response when an arbitrary current profile is applied to the secondary battery reproduced in Equivalent Circuit Model 1 can be obtained more quickly. In addition, the voltage response (V _sim (t)) corresponding to the current (i (t)) at each time point can be simulated in more real time.

Furthermore, by pre-determining the parameters (R _L , i ₀ , α, p, T, RT _{, ch,} and _{RT, dis} ) according to Embodiment 1, V _sim (t) can be treated as effectively V _MEAS (t). Therefore, even if the V _OC (t) of the secondary battery to be simulated in equivalent circuit model 1 is unknown, V _OC can be calculated inversely by determining V _sim , V _L , V _NL , and V _T as targets for determining V _OC in equation (1). From the V _OC obtained in this way, the SOC of the secondary battery can also be calculated. Consequently, the SOC response of the secondary battery according to the current profile can also be simulated.

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

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

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

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

The simulation condition data 102 is the same as the simulation condition data for Embodiment 2, and represents the initial conditions and change conditions.

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

The parameter identification data 104 is the same as the parameter 82 in Embodiment 2, and is data showing R _L , i ₀ , α, p, T, RT _{, ch,} and RT _{, dis} as parameters necessary for calculating the voltage response V _sim .

The parameter identification module 105 is a program for performing the processing corresponding to Embodiment 1. That is, the simulation module 101 is a program for the information processing device 90 to perform the same functions as the simulation device 50 described with reference to Figures 6 and 7, virtually setting up the equivalent circuit model 1 and determining R _L , i ₀ , α, p, T, R _{T, ch} and R _{T, dis} based on the processing flow described with reference to Figure 3.

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

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

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

For the sake of clarity, the above explanation does not mention the number of SOC-OCV data points. However, if there are multiple secondary batteries being simulated, SOC-OCV data corresponding to each secondary battery will be prepared. Furthermore, even for a single secondary battery, if the correspondence between SOC and OCV changes depending on the battery's temperature, SOC-OCV data corresponding to the temperature may be prepared. This will allow for more accurate simulations.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(16) In the programs described in (13) to (15) 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.

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

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

1 Equivalent circuit model 11 Power supply unit 12 Nonlinear resistance unit 13 Linear resistance unit 20 Transient response unit 30 First element 31 First diode 32 Charging resistor 40 Second element 41 Second diode 42 Discharge resistors 50, 70 Simulation device 81 SOC-OCV data 82 Parameters 90 Information processing device 100 Voltage response calculation program

Claims (18)

A simulation method for calculating the voltage response of a secondary battery using an equivalent circuit model,
The steps include obtaining parameters that represent the electrical characteristics of the equivalent circuit model,
The steps include obtaining current information indicating the current at multiple points in time, obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery.
The steps include identifying the State of Control (SOC) of the secondary battery from the voltage information,
A step of calculating the OCV using the SOC and the current information,
A step of calculating a first voltage drop due to the linear resistance component included in the equivalent circuit model using the current information and the parameters,
A step of calculating a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters,
A step of calculating a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters,
A step of calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop,
It has,
The second voltage drop is calculated based on the Butler-Bolmer equation,
The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE.
Simulation method. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well.
The simulation method according to claim 1. The transient response component is,
The first element consists of a charging resistance component and a first diode connected in series,
The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel.
Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element.
Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element.
The simulation method according to claim 1. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation.
The simulation method according to any one of claims 1 to 3. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation.
The simulation method according to any one of claims 1 to 3. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value.
The simulation method according to any one of claims 1 to 3 . A simulation device that sets up an equivalent circuit model and calculates the voltage response of a secondary battery,
An acquisition unit that acquires parameters indicating the electrical characteristics of the equivalent circuit model, current information indicating the current at multiple points in time when a period for which a predetermined current profile is given is divided into multiple sampling times, voltage information indicating the initial voltage of the secondary battery, and temperature information indicating the temperature of the secondary battery.
A unit for identifying the SOC of the secondary battery from the voltage information,
A first calculation unit that calculates the OCV using the SOC and the current information,
A second calculation unit calculates a first voltage drop due to a linear resistance component included in the equivalent circuit model using the current information and the parameters,
A third calculation unit calculates a second voltage drop due to the nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters.
A fourth calculation unit that calculates a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters,
A fifth calculation unit that calculates the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop,
Equipped with,
The second voltage drop is calculated based on the Butler-Bolmer equation,
The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE.
Simulation device. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well.
The simulation apparatus according to claim 7. The transient response component is,
The first element consists of a charging resistance component and a first diode connected in series,
The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel.
Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element.
Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element.
The simulation apparatus according to claim 7. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation.
The simulation apparatus according to any one of claims 7 to 9. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation.
The simulation apparatus according to any one of claims 7 to 9. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are obtained such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value.
The simulation apparatus according to any one of claims 7 to 9 . This is a program for setting up an equivalent circuit model and calculating the voltage response of a secondary battery.
The steps include obtaining parameters that represent the electrical characteristics of the equivalent circuit model,
The steps include obtaining current information indicating the current at multiple points in time, obtained by dividing a period over which a predetermined current profile is given into multiple sampling times; voltage information indicating the initial voltage of the secondary battery; and temperature information indicating the temperature of the secondary battery.
The steps include identifying the State of Control (SOC) of the secondary battery from the voltage information,
A step of calculating the OCV using the SOC and the current information,
A step of calculating a first voltage drop due to the linear resistance component included in the equivalent circuit model using the current information and the parameters,
A step of calculating a second voltage drop due to a nonlinear resistance component included in the equivalent circuit model using the current information, temperature information, and parameters,
A step of calculating a third voltage drop due to the transient response component included in the equivalent circuit model using the current information and the parameters,
A step of calculating the voltage response from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop,
The information processing device is made to execute this,
The second voltage drop is calculated based on the Butler-Bolmer equation,
The third voltage drop is calculated based on a time-domain equation applied to a circuit model including a constant-phase element CPE.
program. The transient response component is represented as a circuit model including a linear resistor, and the state of the constant-phase element CPE is set so that current flows through the linear resistor as well.
The program according to claim 13. The transient response component is,
The first element consists of a charging resistance component and a first diode connected in series,
The circuit model includes a second element formed by connecting a discharge resistor representing the discharge resistance component and a second diode in series, and the constant-phase element CPE, the first element, and the second element are connected in parallel.
Under the condition that a charging current is applied to the equivalent circuit model, the second diode prevents current from flowing through the second element.
Under the condition that a discharge current is applied to the equivalent circuit model, the first diode is set to a state where no current flows through the first element.
The program according to claim 13. The second voltage drop is derived by referring to a lookup table corresponding to the coefficients representing the exchange current and the charge transfer coefficient, which are included in the Butler-Volmer equation.
The program according to any one of claims 13 to 15. The aforementioned second voltage drop is calculated using an equation with current as a variable, which is expressed by the inverse function of the Butler-Volmer equation.
The program according to any one of claims 13 to 15. Based on raw data showing the true value representing the voltage response of a secondary battery to which a predetermined current profile is applied, the SOC before the secondary battery was to which the predetermined current profile was applied, and the temperature of the secondary battery, the parameters are identified such that the voltage response calculated from the OCV, the first voltage drop, the second voltage drop, and the third voltage drop reproduces the true value.
The program according to any one of claims 13 to 15 .