Secondary battery simulator

Abstract

This invention provides a secondary battery simulator that can suppress the long time required for the prediction accuracy of concentration variables to improve. [Solution] The PU first sets a provisional charging current Ic (S30), and then calculates the predicted cell voltage Vce when the cell is charged for a charging time tc using that charging current Ic (S48). The PU then sets the maximum chargeable current Iin to the charging current Ic corresponding to the largest value of the predicted value Vce that is less than or equal to the termination voltage VcH (S54). In order to calculate the predicted value Vce, the PU uses an equation based on a differential equation based on an electrochemical model in which the value of the diffusion coefficient is fixed. The average lithium ion concentrations Cpave and Cnave in the active material are calculated after a charging time tc has elapsed.

Description

Technical Field

[0001] The present invention relates to a simulator for secondary batteries.

Background Art

[0002] For example, Patent Document 1 below describes an apparatus that calculates the power that can be input to and output from a battery using an equivalent circuit of the battery. The apparatus estimates the parameters of the equivalent circuit based on the detection values of sensors.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the case of the above apparatus, the calculation accuracy of the power that can be input and output is low until the estimated values of the parameters of the equivalent circuit converge.

Means for Solving the Problems

[0005] Hereinafter, means for solving the above problems and their effects will be described. 1. A simulator for a secondary battery, comprising a storage device and an execution device, wherein the storage device stores model variables that define an electrochemical model of the secondary battery, and the execution device is configured to execute a concentration variable prediction process, the concentration variable prediction process including a process of predicting the value of a concentration variable due to a current flowing through the secondary battery using an equation in which values of predetermined ones of the model variables are fixed, the concentration variable being a variable indicating the concentration of a predetermined substance at a predetermined location in the secondary battery, and the equation including an equation that defines the time change of the concentration variable.

[0006] In the above configuration, the value of the concentration variable is predicted using an equation based on an electrochemical model. Since the electrochemical model can be created based on the design information of the secondary battery, it is not necessary to collect a large amount of data on various physical quantities associated with the actual charging and discharging of the secondary battery in order to optimize the values ​​of the model variables that define the equation. Therefore, it is possible to suppress the time required for the prediction accuracy of the concentration variable to improve through the concentration variable prediction process.

[0007] Incidentally, predicting concentration variables based on electrochemical models usually requires discretizing differential equations to calculate the changes in model variables and various physical quantities of the secondary battery at minute time intervals. Therefore, predicting concentration variables based on electrochemical models can be computationally intensive. In the above configuration, however, the value of the concentration variable is predicted using an equation in which the values ​​of predetermined model variables are fixed. This reduces the computational load.

[0008] 2. The simulator for a secondary battery according to paragraph 1, wherein the predetermined model variable includes the diffusion coefficient of the diffusion equation for the predetermined substance, and the concentration variable prediction process includes a process of predicting the value of the concentration variable due to current flowing through the secondary battery using the equation with a fixed value for the diffusion coefficient.

[0009] The diffusion coefficient depends on temperature and the concentration of a given substance. Therefore, in predicting concentration variables using electrochemical models, it is natural to update the diffusion coefficient value each time the concentration variable value is calculated. However, in that case, the computational load required to calculate the concentration variable value after the predicted time period may become excessively large. For this reason, there is a particular advantage to using an equation with a fixed diffusion coefficient value.

[0010] 3. The simulator for a secondary battery according to 1 or 2 above, wherein the concentration variable is a variable indicating the ion concentration on the surface of the active material, the memory device stores relational data that defines the relationship between the value of the concentration variable and the open-circuit potential, the execution device is configured to perform a voltage prediction process, the equation includes an expression that relates the average concentration of ions in the active material to its first-order time derivative, the concentration variable prediction process includes a process of predicting the value of the average concentration using the expression, and a process of predicting the value of the concentration variable from the predicted value of the average concentration, and the voltage prediction process includes a process of predicting the terminal voltage of the secondary battery according to the value of the concentration variable using the relational data.

[0011] In the above configuration, the open-circuit potential is predicted by predicting the ion concentration on the surface of the active material. Therefore, the open-circuit potential can be predicted with high accuracy even when the secondary battery is not in a steady state. Based on the open-circuit potential, the terminal voltage can then be predicted with high accuracy.

[0012] 4. The execution device is configured to perform a diffusion coefficient setting process, the diffusion coefficient setting process includes setting the value of the diffusion coefficient as a predetermined model variable to a value corresponding to a predetermined voltage for discharge, the concentration variable prediction process includes predicting the value of the concentration variable using the value of the diffusion coefficient corresponding to the predetermined voltage for discharge, and the predetermined voltage for discharge is a voltage on the terminal voltage side of the secondary battery due to discharge, which is higher than the current terminal voltage of the secondary battery. This is the simulator of the secondary battery described in 3 above.

[0013] The inventors have found that when predicting the value of a concentration variable due to discharge while fixing the value of the diffusion coefficient, the prediction accuracy can be improved by fixing the value of the diffusion coefficient to the value on the termination voltage side due to the discharge. Therefore, with the above configuration, the value of the concentration variable can be predicted with high accuracy while fixing the value of the diffusion coefficient.

[0014] 5. The execution device is configured to perform a diffusion coefficient setting process, the diffusion coefficient setting process includes setting the value of the diffusion coefficient as a predetermined model variable to a value corresponding to a predetermined voltage for charging, the concentration variable prediction process includes predicting the value of the concentration variable using the value of the diffusion coefficient corresponding to the predetermined voltage for charging, and the predetermined voltage for charging is a voltage on the terminal voltage side of the secondary battery due to charging, which is higher than the current terminal voltage of the secondary battery, the simulator for a secondary battery according to 3 or 4 above.

[0015] The inventors have found that when predicting the value of the concentration variable due to charging while fixing the value of the diffusion coefficient, the prediction accuracy can be improved by fixing the value of the diffusion coefficient to the value on the terminal voltage side due to charging. Therefore, in the above configuration, the value of the concentration variable can be predicted with high accuracy while fixing the value of the diffusion coefficient.

[0016] 6. The execution device is configured to perform a current value setting process and a determination process, wherein the current value setting process is a process of setting various currents of the secondary battery as conditions for predicting the value of the concentration variable by the concentration variable prediction process, and the determination process includes a process of determining the value of a constraint variable based on the terminal voltage corresponding to the value of the concentration variable predicted using each of the currents set by the current value setting process, wherein the constraint variable is a variable that indicates a constraint on the current of the secondary battery, as described in any one of claims 3 to 5.

[0017] In the above configuration, by predicting the terminal voltage corresponding to each of the variously set currents, it is possible to find an appropriate value for the constraint on the current. 7. The secondary battery simulator according to any one of 3 to 6 above, wherein the equation includes, in addition to a first equation relating the average concentration of the ions to its first-order time derivative, a second equation relating the degree of diffusion variable to its first-order time derivative, and a third equation relating the average concentration and the degree of diffusion variable to the concentration variable, wherein the degree of diffusion variable is a variable indicating the degree of diffusion of the ions in the active material, and the concentration variable prediction process includes a process of predicting the value of the average concentration and the value of the degree of diffusion variable using the first and second equations, and a process of predicting the value of the concentration variable using the third equation based on the value of the average concentration and the value of the degree of diffusion variable as input variables.

[0018] When calculating the ion concentration on the surface of the active material using only the average concentration and the ion flow rate of the active material determined from the current of the secondary battery, the calculation accuracy tends to decrease when the charge and discharge rates of the secondary battery are high. Therefore, in the above configuration, the ion concentration on the surface of the active material is calculated based on the average concentration and the value of the degree of diffusion variable. This improves the accuracy of calculating the ion concentration on the surface of the active material.

[0019] 8. The execution device is configured to repeatedly perform a diffusion coefficient calculation process, an acquisition process, and a concentration variable calculation process, wherein the diffusion coefficient calculation process is a process of calculating a diffusion coefficient based on the average concentration, the acquisition process is a process of acquiring the current flowing through the secondary battery, the concentration variable calculation process includes a process of calculating the average concentration of ions in the active material using an equation defined by the diffusion coefficient calculated by the diffusion coefficient calculation process, based on the current as an input variable, and the concentration variable prediction process is a process of predicting future values ​​for a time interval longer than the execution cycle of the diffusion coefficient calculation process, the acquisition process, and the concentration variable calculation process, wherein the value calculated by the concentration variable calculation process is used as the initial value of the average concentration, as a simulator for a secondary battery according to any one of 3 to 7 above.

[0020] In the above configuration, since the initial value of the average concentration as an input variable for the concentration variable prediction process is the value of the concentration variable calculated each time by the concentration variable calculation process, the prediction accuracy of the average concentration can be improved.

Brief Description of Drawings

[0021] [Figure 1] It is a system configuration diagram of a drive system of a vehicle according to an embodiment. [Figure 2] It is a flowchart showing the procedure of the process executed by the battery ECU shown in FIG. 1. [Figure 3] It is a diagram illustrating map data used by the battery ECU shown in FIG. 1. [Figure 4] It is a diagram illustrating map data used by the battery ECU shown in FIG. 1. [Figure 5] It is a flowchart showing the procedure of the process executed by the battery ECU shown in FIG. 1. [Figure 6] It is a flowchart showing the procedure of the process executed by the battery ECU shown in FIG. 1.

Modes for Carrying Out the Invention

[0022] Hereinafter, an embodiment will be described with reference to the drawings. FIG. 1 shows the configuration of the drive system of a vehicle. The in-vehicle battery 10 is a series connection body of battery cells 12(1), 12(2),... 12(n). The terminal voltage of the in-vehicle battery 10 may be, for example, several tens of volts to several hundreds of volts. The numbers in parentheses in the battery cells 12(1), 12(2),... 12(n) are numbers for identifying the individual. Hereinafter, when summarizing the battery cells 12(1), 12(2),... 12(n), they will be described as battery cells 12. The battery cell 12 is a lithium-ion secondary battery.

[0023] The terminals of the vehicle battery 10 are connected to the power conversion circuit 22 via the system main relay 20. The power conversion circuit 22 is a circuit that supplies power from the vehicle battery 10 to the motor generator 24. The power conversion circuit 22 is also a circuit that supplies power generated by the motor generator 24 to the vehicle battery 10. The motor generator 24 is mechanically connected to the drive wheels of the vehicle.

[0024] The monitoring unit 30 is a circuit that monitors the status of the battery cells 12(1), 12(2), ... 12(n) of the vehicle battery 10. The battery ECU 40 is a device that monitors the status of the onboard battery 10. The battery ECU 40 can communicate with the higher-level ECU 60 via the in-vehicle network 50. The higher-level ECU 60 is a device that manages the power of the vehicle's drive system. The higher-level ECU 60 controls the driving force of the motor generator 24 by outputting commands to the MGECU 70 via the in-vehicle network 50. The amount of power charged and discharged from the onboard battery 10 is also controlled by the control of the driving force. Therefore, the amount of power charged and discharged from the onboard battery 10 is controlled by the higher-level ECU 60 outputting commands to the MGECU 70 via the in-vehicle network 50.

[0025] The MGECU70 controls the motor generator 24. The MGECU70 operates the power conversion circuit 22 to control the torque and other parameters of the motor generator 24.

[0026] The battery ECU 40 refers to the charge / discharge current I of the onboard battery 10 detected by the current sensor 80. For the purposes of this explanation, it is assumed that the charge / discharge current I is positive when the onboard battery 10 is being charged, and negative when the onboard battery 10 is being discharged. The battery ECU 40 also refers to the cell temperatures Tc(1), Tc(2), ... of the battery cells 12(1), 12(2), ... 12(n), detected by the monitoring unit 30.

[0027] The battery ECU 40 includes a PU 42 and a storage device 44. The PU 42 is a software processing unit such as a CPU. The storage device 44 may be an electrically rewritable non-volatile memory and a storage medium such as a disk medium.

[0028] "Battery cell status calculation process" The battery ECU 40 performs a process to sequentially calculate the state of the battery cell 12 based on an electrochemical model. In particular, the battery ECU 40 sequentially calculates the ion concentration in the active material as the state of the battery cell 12. The electrochemical model used for this purpose is, for example, a mathematical model based on the porous electrode theory of Newman et al. Here, the active material is assumed to be spherical. Also, in this embodiment, for example, it is assumed that the lithium ion concentration in the active material is isotropic. Therefore, the lithium ion concentration cp in the positive electrode active material is expressed as a function with radial distance rp from the center of the positive electrode active material and time t as independent variables. Similarly, the lithium ion concentration cn in the negative electrode active material is expressed as a function with radial distance rn from the center of the negative electrode active material and time t as independent variables. The battery ECU 40 sequentially calculates the lithium ion concentration on the surface of the active material. The lithium ion concentration on the surface of the positive electrode active material can be quantified, for example, by the value of the partial derivative of the lithium ion concentration cp with respect to distance rp at the particle size Rp of the positive electrode active material. Similarly, the lithium ion concentration on the surface of the negative electrode active material can be quantified, for example, by the value of the partial derivative of the lithium ion concentration cn with respect to distance rn at the particle size Rn of the negative electrode active material.

[0029] Figure 2 shows the procedure for calculating the state of the battery cell 12. The process shown in Figure 2 is achieved by the PU 42 repeatedly executing a program stored in the memory device 44, for example, at a predetermined cycle. In the following, the step number of each process is represented by a number preceded by "S".

[0030] In the series of processes shown in Figure 2, the PU42 first acquires the charge / discharge current I and the cell temperature Tc (S10). The cell temperature Tc is the temperature of one of the multiple battery cells 12 that make up the vehicle battery 10. Next, the PU42 acquires the previous value of the average lithium ion concentration Cpave in the positive electrode active material and the previous value of the average lithium ion concentration Cnave in the negative electrode active material (S12). Here, the previous value means the value calculated at the previous execution timing of the series of processes shown in Figure 2. The average lithium ion concentration Cpave in the positive electrode active material is the value obtained by dividing the volume integral of the lithium ion concentration cp in the positive electrode active material by the volume of the active material. The average lithium ion concentration Cnave in the negative electrode active material is the value obtained by dividing the volume integral of the lithium ion concentration cn in the negative electrode active material by the volume of the active material. The variable "n-1" in parentheses after the average concentrations Cpave and Cnave indicates the previous value.

[0031] PU42 calculates the reference temperature coefficient Dpref for the positive electrode based on the previous value of the average concentration Cpave as an input variable, and calculates the reference temperature coefficient Dnref for the negative electrode based on the previous value of the average concentration Cnave as an input variable (S14). The reference temperature coefficients Dpref and Dnref are the diffusion coefficients of lithium ion concentration at a reference temperature. Specifically, PU42 performs a map calculation on the reference temperature coefficients Dpref and Dnref using the map data 44b shown in Figure 1, which is stored in the memory device 44. Here, the map data 44b includes data where the average concentration Cpave is the input variable and the reference temperature coefficient Dpref is the output variable, and data where the average concentration Cnave is the input variable and the reference temperature coefficient Dnref is the output variable.

[0032] Map data is a set of data consisting of discrete values ​​of input variables and corresponding values ​​of output variables for each of the input variable values. A map operation is a process in which, if the value of an input variable matches any of the input variable values ​​in the map data, the corresponding value of the output variable in the map data is the result of the operation. Alternatively, if the value of an input variable does not match any of the input variable values ​​in the map data, the result of the map operation is a value obtained by interpolating the values ​​of multiple output variables included in the map data. Or, instead, if the value of an input variable does not match any of the input variable values ​​in the map data, the result of the map operation may be the value of the output variable in the map data that corresponds to the closest value among the multiple input variable values ​​included in the map data.

[0033] Next, PU42 calculates the diffusion coefficient Dp of the positive electrode based on the reference temperature coefficient Dpref and the cell temperature Tc as input variables using the following equation (c1) (S16). Also, PU42 calculates the diffusion coefficient Dn of the negative electrode based on the reference temperature coefficient Dnref and the cell temperature Tc as input variables using the following equation (c2) (S16).

[0034] Dp=Dpref·exp{Eap / R(1 / Tc-1 / Tref)} …(c1) Dn=Dnref·exp{Ean / R(1 / Tc-1 / Tref)} …(c2) Here, Eap and Ean are the activation energies of the electrodes. Eap and Ean are defined by the model data 44a stored in the memory device 44. The model data 44a is data that defines the model variables that define the electrochemical model described above. R is the ideal gas constant. "Tref" is the reference temperature. The reference temperature coefficients Dpref and Dnref described above are the diffusion coefficients Dp and Dn at the reference temperature Tref.

[0035] PU62 performs the process of calculating the lithium ion flow velocity Jp at the positive electrode based on the charge / discharge current I as an input variable using the following equation (c3) (S18). Also, PU62 performs the process of calculating the lithium ion flow velocity Jn at the negative electrode based on the charge / discharge current I as an input variable using the following equation (c4) (S18).

[0036] Jp = I / (ap·F·Lp·A) …(c3) Jn = I / (an·F·Ln·A) …(c4) Here, F is the Faraday constant, A is the cross-sectional area, Lp is the thickness of the positive electrode, Ln is the thickness of the negative electrode, ap is the surface area of ​​the positive electrode active material per unit volume, and an is the surface area of ​​the negative active material per unit volume. Note that A, Lp, Ln, ap, and an are defined by model data 44a.

[0037] PU42 calculates the current values ​​of the average concentrations Cpave and Cnave, and the current values ​​of the volume-average concentration velocities Qp and Qn (S20). The input variables for this process are the lithium-ion flow velocities Jp and Jn, and the previous values ​​of the average concentrations Cpave and Cnave, and the previous values ​​of the volume-average concentration velocities Qp and Qn. This process is executed based on the differential equations expressed in equations (c5) and (c6) below, where j=p and n, and converted into difference equations.

[0038]

number

[0039] Here, the volume-average concentration velocity Qp and Qn are qualitatively variables that indicate the degree of ion diffusion in the active material. As an example, the volume-average concentration velocity Qp and Qn are quantified by the volume-average value of the lithium ion flow velocity in the active material. That is, the volume-average concentration velocity Qp is the value obtained by dividing the integral of the divergence of the lithium ion concentration cp(rp,t) in the positive electrode active material from the center to the surface of the active material by the volume of the active material. Similarly, the volume-average concentration velocity Qn is the value obtained by dividing the integral of the divergence of the lithium ion concentration cn(rn,t) in the negative electrode active material from the center to the surface of the active material by the volume of the active material. The above equations (c5) and (c6) are derived from the diffusion equation expressed in the following equation (c7) for lithium ion concentrations cp and cn.

[0040]

number

[0041] However, the model used consists of a term where the lithium ion concentration cj(rj,t) depends only on time, a term proportional to the square of the distance rj, and a term proportional to the fourth power of the distance rj. The average concentrations Cpave and Cnave calculated in the S20 process will be acquired by the S12 process at the next execution timing of the series of processes shown in Figure 2.

[0042] Next, the surface concentrations Cps and Cns of PU42 are calculated based on the following formula (c8) (S22). Cjs=Cjave+{Rj / (35Dj)}·(8Dj·Qj-Jj) …(c8) Furthermore, when PU42 completes the process in S22, it temporarily terminates the series of processes shown in Figure 2.

[0043] Using the map data shown in Figure 3 from the aforementioned map data 44b, the open-circuit potential OCP(p) of the positive electrode can be calculated from the surface concentration Cps of the positive electrode. Similarly, using the map data shown in Figure 4 from the same map data 44b, the open-circuit potential OCP(n) of the negative electrode can be calculated from the surface concentration Cns of the negative electrode. Then, the open-circuit voltage of the battery cell 12 can be calculated from the open-circuit potentials OCP(p) and OCP(n). The PU42 may also calculate the open-circuit voltage of the battery cell 12 using the calculated surface concentrations Cps and Cns each time the process shown in Figure 2 is executed. "Determination of the maximum rechargeable current Iin" The battery ECU40 performs a process to search for the maximum chargeable current Iin by predicting the surface concentration Cjs when the charging current Ic is set to various values ​​using the electrochemical model described above.

[0044] Figure 5 shows the procedure for determining the maximum chargeable current Iin. The process shown in Figure 5 is achieved by the PU 42 repeatedly executing a program stored in the memory device 44, for example, at a predetermined cycle.

[0045] In the series of processes shown in Figure 5, PU42 first sets the charging current Ic, termination voltage VcH, and charging time tc (S30). Here, the termination voltage VcH is the cell voltage after the charging time tc has elapsed. For example, the termination voltage VcH is set to the upper limit of the cell voltage Vc. The charging time tc has a time interval longer than the execution cycle of the process in Figure 2. The charging time tc may be several tens to several thousand times longer than the execution cycle of the process in Figure 2. Note that the charging time tc and termination voltage VcH are set only once until the maximum chargeable current Iin is determined. In contrast, the charging current Ic is set to various values ​​for the search. For example, the initial value of the charging current Ic at the start of the search is set to a value that is assumed to be smaller than the maximum chargeable current Iin.

[0046] PU42 calculates the reference temperature coefficients Dpref and Dnref based on the terminal voltage VcH as an input variable (S32). Here, PU42 first calculates the average concentrations Cpave and Cnave from the terminal voltage VcH, assuming that the charging current Ic is constant zero. That is, when the charge / discharge current I is constant zero, the lithium-ion flow velocity Jj and the volume average concentration flow velocity Qj in the above equation (c8) become zero, so the surface concentrations Cps and Cns can be considered equal to the average concentrations Cpave and Cnave, respectively. Therefore, based on the map data shown in Figures 3 and 4, PU42 sets the surface concentrations Cps and Cns corresponding to the terminal voltage VcH to the average concentrations Cpave and Cnave, respectively. Then, PU42 performs a map calculation on the reference temperature coefficients Dpref and Dnref based on the average concentrations Cpave and Cnave as input variables, in the same manner as in the process of S14.

[0047] PU42 obtains the cell temperature Tc and the current values ​​of the average concentrations Cpave and Cnave calculated by the process shown in Figure 2, as well as the current values ​​of the volume-average concentration flow rates Qp and Qn (S34). Then, PU42 calculates the diffusion coefficients Dp and Dn based on the cell temperature Tc obtained by the process in S34 and the reference temperature coefficients Dpref and Dnref calculated by the process in S32 (S36). Furthermore, PU42 calculates the lithium-ion flow rates Jp and Jn based on the charging current Ic as an input variable (S38). The lithium-ion flow rates Jp and Jn obtained by this process are values ​​obtained by substituting the charge / discharge current I with the charging current Ic in the above equations (c3) and (c4).

[0048] Next, PU42 predicts the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn after a charging time tc has elapsed (S40). The input variables for this process are the lithium-ion flow velocities Jp and Jn calculated by the process in S38, the diffusion coefficients Dp and Dn calculated by the process in S36, and the current values ​​of the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn. The process in S40 is a process in which PU42 calculates the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn after a charging time tc has elapsed by fixing the diffusion coefficient Dj in the above equations (c5) and (c6). Specifically, PU42 calculates the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn after a charging time tc has elapsed using the following equations (c9) and (c10).

[0049] Cjave=-3·Jj·tc / Rj+Cjave(n) …(c9) Qj={Qj(n)+3·Jj / (4·Dj)}·exp{-30·Dj·tc / (Rj·Rj)} -3·Jj / (4·Dj) …(c10) Next, PU42 predicts the surface concentrations Cps and Cns after a charging time tc, based on the input variables: the average concentrations Cpave and Cnave and the volume-average concentration flow velocities Qp and Qn (S42). This process, like the process in S22, uses the above equation (c8).

[0050] Next, PU42 calculates the open-circuit potentials OCP(p) and OCP(n) at the time of charging tc based on the surface concentrations Cps and Cns, which are input variables (S44). The process in S44 includes a mapping operation for the open-circuit potential OCP(p) at the time of charging tc based on the surface concentration Cps, which is an input variable. The process in S44 also includes a mapping operation for the open-circuit potential OCP(n) at the time of charging tc based on the surface concentration Cns at the time of charging tc. Map data 44b is used here.

[0051] Next, PU42 subtracts the open-circuit potential OCP(n) from the open-circuit potential OCP(p) and substitutes this value into the open-circuit voltage OCV (S46). Then, PU42 calculates the predicted value Vce of the terminal voltage of the battery cell 12 based on the input variables, the charge / discharge current I, the cell temperature Tc, and the open-circuit voltage OCV (S48). The process in S48 includes a process to calculate the overpotential based on the input variables, the charge current Ic and the cell temperature Tc. The process to calculate the overpotential may also be a process that calculates the overpotential using the Botra-Valma formula based on the surface concentrations Cps and Cns in addition to the input variables, the charge current Ic and the cell temperature Tc.

[0052] Then, PU42 determines whether the predicted value Vce is greater than the termination voltage VcH (S50). This process determines whether the magnitude of the charging current Ic set in the S30 process is excessively large. If PU42 determines that the predicted value Vce is less than or equal to the termination voltage VcH (S50: NO), it adds a predetermined amount ΔI to the charging current Ic and substitutes this value into the charging current Ic (S52), then returns to the S30 process. As a result, PU42 executes the processes from S32 to S50 with a charging current Ic that has been increased by a predetermined amount ΔI.

[0053] On the other hand, if PU42 determines that the predicted value Vce is greater than the termination voltage VcH (S50: YES), it sets the maximum chargeable current Iin to a value that is smaller by a predetermined amount ΔI than the current charging current Ic (S54).

[0054] Furthermore, when PU42 completes the process in S54, it temporarily terminates the series of processes shown in Figure 5. "Determination of the maximum dischargeable current Iout" The battery ECU40 performs a process to search for the maximum dischargeable current Iout by predicting the surface concentration Cjs when the discharge current Id is set to various values ​​using the electrochemical model described above.

[0055] Figure 6 shows the procedure for determining the maximum dischargeable current Iout. The process shown in Figure 6 is achieved by the PU 42 repeatedly executing a program stored in the memory device 44, for example, at a predetermined period.

[0056] In the series of processes shown in Figure 6, PU42 first sets the discharge current Id, termination voltage VdL, and discharge time td (S60). Here, the termination voltage VdL is the cell voltage after the discharge time td has elapsed. For example, the termination voltage VdL is set to the lower limit of the cell voltage Vc. The discharge time td has a time interval longer than the execution cycle of the process in Figure 2. For example, the discharge time td may be several tens to several thousand times longer than the execution cycle of the process in Figure 2. Note that the discharge time td and the termination voltage VdL are set only once until the maximum dischargeable current Iout is determined. In contrast, the discharge current Id is set to various values ​​for the search. For example, the initial value of the discharge current Id at the start of the search is set to a value that is assumed to have an absolute value smaller than the maximum dischargeable current Iout.

[0057] Next, PU42 calculates the reference temperature coefficients Dpref and Dnref based on the termination voltage VdL as an input variable, using the same process as in S32 (S62). PU42 also obtains the cell temperature Tc, the current values ​​of the average concentrations Cpave and Cnave calculated by the process in Figure 2, and the current values ​​of the volume-average concentration velocities Qp and Qn (S64). Then, PU42 calculates the diffusion coefficients Dp and Dn based on the cell temperature Tc obtained in S64 and the reference temperature coefficients Dpref and Dnref calculated in S62 (S66). The process in S66 is the same as the process in S36. Furthermore, PU42 calculates the lithium-ion velocities Jp and Jn based on the discharge current Id as an input variable, using the same process as in S38 (S68).

[0058] Next, PU42 predicts the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn after a discharge time td by a process similar to that of S40 (S70). The input variables for this process are the lithium-ion flow velocities Jp and Jn calculated by the process of S68, the diffusion coefficients Dp and Dn calculated by the process of S66, and the current values ​​of the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn. The process of S70 is a process in which PU42 calculates the average concentrations Cpave and Cnave and the volume-average concentration velocities Qp and Qn after a discharge time td by fixing the diffusion coefficient Dj in the above equations (c5) and (c6).

[0059] Next, PU42 predicts the surface concentrations Cps and Cns at a discharge time td based on the input variables, the average concentrations Cpave and Cnave and the volume-average concentration flow rates Qp and Qn, using a process similar to that in S42 (S72).

[0060] Next, PU42 calculates the open-circuit potentials OCP(p) and OCP(n) at the time of discharge td, based on the surface concentrations Cps and Cns at the time of discharge td, which are input variables, using a process similar to that in S44 (S74).

[0061] Next, PU42 subtracts the open-circuit potential OCP(n) from the open-circuit potential OCP(p) and substitutes this value into the open-circuit voltage OCV (S76). Then, PU42 calculates the predicted value Vce of the terminal voltage of the battery cell 12 based on the input variables, the charge / discharge current I, the cell temperature Tc, and the open-circuit voltage OCV, using the same process as in S48 (S78).

[0062] Then, PU42 determines whether the predicted value Vce is less than the termination voltage VdL (S80). This process determines whether the magnitude of the discharge current Id set in the S60 process is excessively large. If PU42 determines that the predicted value Vce is greater than or equal to the termination voltage VdL (S80: NO), it subtracts a predetermined amount ΔI from the discharge current Id and substitutes the result into the discharge current Id, then returns to the S60 process. As a result, PU42 performs the S62-S80 processes with the discharge current Id, whose absolute value has been increased by a predetermined amount ΔI.

[0063] On the other hand, if PU42 determines that the predicted value Vce is smaller than the termination voltage VdL (S80: YES), it sets the maximum dischargeable current Iout to the value obtained by adding a predetermined amount ΔI to the discharge current Id at that time (S84).

[0064] Furthermore, when PU42 completes the processing in S84, it temporarily terminates the series of processes shown in Figure 5. "The operation and effects of this embodiment" The PU42 first sets a provisional charging current Ic, then calculates a predicted cell voltage Vce when charging for a charging time tc using that charging current Ic. It then sets the maximum possible charging current Iin to the maximum charging current Ic corresponding to the highest value of the predicted Vce that is less than or equal to the termination voltage VcH. This allows for the maximum amount of charging within the charging time tc.

[0065] Furthermore, PU42 first sets a provisional discharge current Id, and then calculates a predicted cell voltage Vce when discharged for a discharge time td using that discharge current Id. Then, it sets the discharge current Id corresponding to the smallest value of the predicted Vce that is greater than or equal to the termination voltage VdL as the maximum dischargeable current Iout. This makes it possible to discharge the maximum amount within the discharge time td.

[0066] Here, the predicted value Vce is predicted based on an electrochemical model. The electrochemical model is determined by model variables defined by model data 44a. Model data 44a is data generated from the design information of the battery cell 12. Therefore, the generation of model data 44a does not require the collection of a large amount of data by performing multiple charge and discharge cycles of the battery cell 12. This suppresses the need for a long time to improve the accuracy of the predicted value Vce.

[0067] Incidentally, the calculation of the predicted value Vce is performed based on the differential equations expressed in the above equations (c5) and (c6), which are defined by the model variables. The diffusion coefficients Dp and Dn in these differential equations are functions of the average concentrations Cpave and Cnave, which are solutions to the differential equations. The average concentrations Cpave and Cnave can fluctuate significantly within a period of charging time tc and discharge time td. However, if the period of charging time tc and discharge time td is divided into small time intervals, and the above differential equations are discretized and the difference equations are solved for each of these time intervals, the computational load for calculating the predicted value Vce becomes excessively large.

[0068] Therefore, in this embodiment, by fixing the diffusion coefficients Dp and Dn, the cell voltage at the time when the charging time tc and the discharging time td have elapsed can be predicted in a single calculation. This reduces the computational load.

[0069] Incidentally, if the battery cell 12 deteriorates, an appropriate predicted value Vce for the deteriorated battery cell 12 can be calculated by changing the open-circuit potential OCP(p) and OCP(n) profiles shown in Figures 3 and 4. In contrast, when using an equivalent circuit model of an electrochemical model and fitting its circuit parameters with time-series data of detected physical quantities associated with the charging and discharging of the battery cell 12, the fitting process needs to be redone to accommodate the deterioration.

[0070] According to the embodiment described above, the following effects and benefits can be obtained. (1) The diffusion coefficients Dp and Dn for calculating the predicted value Vce after charging time tc were set based on the average concentrations Cpave and Cnave corresponding to the termination voltage VcH. The average concentrations Cpave and Cnave thus set are close to the actual average concentrations Cpave and Cnave that occur as the cell voltage approaches the termination voltage VcH during the charging process. Therefore, the terminal voltage can be predicted with high accuracy when using a charging current Ic that brings the cell voltage Vc close to the termination voltage VcH after charging time tc.

[0071] (2) The diffusion coefficients Dp and Dn for calculating the predicted value Vce after discharge time td were set based on the average concentrations Cpave and Cnave corresponding to the terminal voltage VdL. The average concentrations Cpave and Cnave thus set are close to the actual average concentrations Cpave and Cnave that occur as the cell voltage approaches the terminal voltage VdL due to the discharge process. Therefore, the terminal voltage can be predicted with high accuracy when using a discharge current Id that brings the cell voltage Vc close to the terminal voltage VdL after discharge time td.

[0072] <Correspondence> The correspondence between the matters in the above embodiment and the matters described in the "Means for Solving the Problems" section is as follows. Below, the correspondence is shown for each number of the solution means described in the "Means for Solving the Problems" section. [1,2] The execution device corresponds to PU42. The storage device corresponds to storage device 44. The model variables correspond to the reference temperature coefficients Dpref, Dnref, diffusion coefficients Dp, Dn, particle size Rp, Rn, active material thickness Lp, Ln, and electrode activation energies Eap, Ean. The model variables correspond to the cross-sectional area A, positive electrode thickness Lp, negative electrode thickness Ln, positive electrode active material surface area ap per unit volume, and negative active material surface area an per unit volume. The concentration of a predetermined substance corresponds to the lithium ion concentration. The concentration variable prediction process corresponds to the processes in S34-S42 and S64-S72. The predetermined model variables correspond to the reference temperature coefficients Dpref, Dnref and diffusion coefficients Dp, Dn. [3] The related data corresponds to the data shown in Figures 3 and 4 of the map data 44b. The degree of diffusion variables correspond to the volume-average concentration and flow velocity Qp and Qn. The voltage prediction process corresponds to the processes in S44-S48 and S64-S68. The values ​​of the concentration variables on the surface of the active material correspond to the surface concentrations Cps and Cns. [4] The diffusion coefficient setting process corresponds to the processes in S62-S66. The predetermined voltage for charging corresponds to the termination voltage VcH. [5] The diffusion coefficient setting process corresponds to the processes in S32-S36. The predetermined voltage for discharge corresponds to the termination voltage VdL. [6] The current value setting process corresponds to the processes in S30 and S60. The determination process corresponds to the processes in S54 and S84. The constraint variables correspond to the maximum chargeable current Iin and the maximum dischargeable current Iout. [7] The diffusion coefficient calculation process corresponds to the processes in S12-S16. The first equation corresponds to equation (c5). The second equation corresponds to equation (c6). The third equation corresponds to equation (c8). [8] The acquisition process corresponds to the process in S10. The concentration variable calculation process corresponds to the processes in S18 to S22.

[0073] <Other Embodiments> Furthermore, this embodiment can be implemented with the following modifications. This embodiment and the following modifications can be combined with each other to the extent that they do not contradict each other technically.

[0074] "Regarding the diffusion coefficient" The input variables for the process of calculating the reference temperature coefficients Dpref and Dnref must be average concentrations Cpave and Cnave. These input variables could also be, for example, surface concentrations Cps and Cns, and volume-average concentration flow velocities Qp and Qn.

[0075] The calculation process for diffusion coefficients Dp and Dn is not limited to calculating the product of a temperature-dependent function and reference temperature coefficients Dpref and Dnref. For example, the calculation process may involve mapping the diffusion coefficients Dp and Dn using map data where average concentrations Cpave and Cnave and cell temperature Tc are input variables and diffusion coefficients Dp and Dn are output variables.

[0076] "About electrochemical models" • The diffusion degree variables are not limited to volume-average concentration and flow velocity Qp and Qn. For example, they may be Cps-Cpave or Cns-Cnave.

[0077] In the above embodiment, a model is illustrated in which the concentration of the active material consists of a term that does not depend on the radial distances rp,rn from the origin of the active material, a term that is proportional to the square of the distances rp,rn, and a term that is proportional to the fourth power of the distances rp,rn. However, the model is not limited to this. If the equation based on the electrochemical model is a nonlinear equation, the value of the concentration variable can be predicted using a linearized equation. Even in that case, the value of the concentration variable can be predicted in a single calculation by linearizing and fixing the values ​​of predetermined model variables in the linearized equation.

[0078] "Regarding the diffusion coefficient setting process" The predetermined discharge voltage used to calculate the reference temperature coefficients Dpref and Dnref does not necessarily have to be the termination voltage VdL. The predetermined discharge voltage can be any value that is greater than the termination voltage VdL than the current cell voltage Vc, such as the average value of the current cell voltage Vc and the termination voltage VdL.

[0079] The predetermined charging voltage used to calculate the reference temperature coefficients Dpref and Dnref does not necessarily have to be the termination voltage VcH. The predetermined charging voltage can be any value that is closer to the termination voltage VcH than the current cell voltage Vc, such as the average value of the current cell voltage Vc and the termination voltage VcH.

[0080] "Regarding the designated location where the concentration of a specified substance is a concern." The predetermined location in a secondary battery where the concentration of a given substance changes over time is not limited to the location of the active material. For example, it may be the location of the electrolyte in the secondary battery. In this case, the concentration variable may be, for example, a variable indicating the salt concentration in the electrolyte. In this case, when predicting the change in salt concentration over time using the diffusion equation of the liquid phase, the computational load can be reduced by fixing the value of a predetermined model variable. In this case, the predetermined model variable may be the diffusion coefficient in the diffusion equation of the liquid phase.

[0081] "Regarding constraint variables" In the above embodiment, the maximum rechargeable current Iin and the maximum dischargeable current Iout were set as constraint variables based on the predicted terminal voltage Vce of one of the multiple battery cells 12 constituting the vehicle battery 10, but this is not limited to this. For example, the average values ​​of the maximum rechargeable current Iin and the maximum dischargeable current Iout, which are set based on the predicted terminal voltage Vce of each of the multiple battery cells 12, may be set as the final maximum rechargeable current Iin and maximum dischargeable current Iout.

[0082] "About the simulator" The simulator is not limited to one that performs various processes using a PU. The simulator may include, for example, a dedicated hardware circuit such as an ASIC that performs at least a part of the processes performed in the above embodiment. That is, the simulator may include any of the following processing circuits (a) to (c): (a) A processing circuit comprising a processing unit that performs all of the above processes according to a program, and a program storage device such as a memory device that stores the program. (b) A processing circuit comprising a processing unit and a program storage device that perform a part of the above processes according to a program, and a dedicated hardware circuit that performs the remaining processes. (c) A processing circuit comprising a dedicated hardware circuit that performs all of the above processes. Here, there may be multiple software execution devices comprising a processing unit and a program storage device, or multiple dedicated hardware circuits.

[0083] "Regarding rechargeable batteries" • It is not necessary for the secondary battery to be a battery installed in a vehicle. • The secondary battery is not limited to lithium-ion secondary batteries. The secondary battery may also be, for example, a nickel-metal hydride secondary battery. [Explanation of symbols]

[0084] 10…Car battery 12…Battery cell 20... System Main Relay 22... Power conversion circuit 24…Motor Generator 30… Surveillance Unit 40…Battery ECU 44…Storage device

Claims

1. It comprises a storage device and an execution device, The aforementioned memory device stores model variables that define the electrochemical model of the secondary battery. The execution device is configured to perform concentration variable prediction processing, The concentration variable prediction process includes a process of predicting the value of the concentration variable due to the flow of current in the secondary battery using an equation in which the value of a predetermined model variable is fixed, The aforementioned concentration variable is a variable that indicates the concentration of a predetermined substance at a predetermined location in the secondary battery. The aforementioned equation is a simulator for a secondary battery that includes an equation defining the time change of the concentration variable.

2. The predetermined model variables include the diffusion coefficient of the diffusion equation for the predetermined substance, The simulator for a secondary battery according to claim 1, wherein the concentration variable prediction process includes a process of predicting the value of the concentration variable due to current flowing through the secondary battery using the equation with a fixed value of the diffusion coefficient.

3. The aforementioned concentration variable is a variable that indicates the ion concentration on the surface of the active material. The memory device stores relational data that defines the relationship between the value of the concentration variable and the open-circuit potential. The execution device is configured to perform voltage prediction processing, The aforementioned equation includes an expression relating the average concentration of ions in the active material to its first-order time derivative, The concentration variable prediction process includes a process for predicting the average concentration value using the formula, and a process for predicting the value of the concentration variable from the predicted average concentration value. The secondary battery simulator according to claim 1, wherein the voltage prediction process includes a process of predicting the terminal voltage of the secondary battery according to the value of the concentration variable using the relational data.

4. The execution device is configured to perform a diffusion coefficient setting process, The diffusion coefficient setting process includes setting the value of the diffusion coefficient, which is a predetermined model variable, to a value corresponding to a predetermined voltage for discharge. The concentration variable prediction process includes a process of predicting the value of the concentration variable using the value of the diffusion coefficient corresponding to a predetermined voltage for discharge, The simulator for a secondary battery according to claim 3, wherein the predetermined voltage for discharge is a voltage on the terminal voltage side of the secondary battery due to discharge, which is higher than the current terminal voltage of the secondary battery.

5. The execution device is configured to perform a diffusion coefficient setting process, The diffusion coefficient setting process includes setting the value of the diffusion coefficient, which is a predetermined model variable, to a value corresponding to a predetermined voltage for charging. The concentration variable prediction process includes a process of predicting the value of the concentration variable using the value of the diffusion coefficient corresponding to the predetermined voltage for charging, The simulator for a secondary battery according to claim 3, wherein the predetermined voltage for charging is a voltage on the terminal voltage side of the secondary battery after charging, which is higher than the current terminal voltage of the secondary battery.

6. The execution device is configured to perform current value setting and determination processes. The current value setting process is a process of setting various currents of the secondary battery as conditions for predicting the value of the concentration variable by the concentration variable prediction process. The determination process includes a process for determining the value of a constraint variable based on the terminal voltage corresponding to the value of the concentration variable predicted using each of the currents set by the current value setting process, The secondary battery simulator according to claim 3, wherein the constraint variable is a variable indicating a constraint on the current of the secondary battery.

7. The aforementioned equation includes, in addition to a first equation relating the average concentration of the ion to its first-order time derivative, a second equation relating the degree of diffusion variable to its first-order time derivative, and a third equation relating the average concentration and the degree of diffusion variable to the concentration variable. The aforementioned diffusion degree variable is a variable that indicates the degree of diffusion of the ions in the active material, The simulator for a secondary battery according to claim 3, wherein the concentration variable prediction process includes a process of predicting the average concentration value and the diffusion degree variable value using the first and second equations, and a process of predicting the concentration variable value using the third equation based on the average concentration value and the diffusion degree variable value as input variables.

8. The execution device is configured to repeatedly perform the diffusion coefficient calculation process, acquisition process, and concentration variable calculation process. The diffusion coefficient calculation process is a process that calculates the diffusion coefficient based on the average concentration. The acquisition process described above is a process for acquiring the current flowing through the secondary battery, The concentration variable calculation process includes a process of calculating the average concentration of ions in the active material based on the current as an input variable, using an equation defined by the diffusion coefficient calculated by the diffusion coefficient calculation process, The secondary battery simulator according to claim 3, wherein the concentration variable prediction process is a process that predicts future values ​​for a time interval longer than the execution cycle of the diffusion coefficient calculation process, the acquisition process, and the concentration variable calculation process, and includes a process that uses the value calculated by the concentration variable calculation process as the initial value of the average concentration.

Images