RU2714888C1 - Accumulator battery system and a method for evaluating the internal state of an accumulator battery - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to electrical engineering, namely to a storage battery system and a method for evaluating the internal state of an accumulator battery, and can be used, for example, in an electrified vehicle with an accumulator battery. System includes a storage battery having a positive electrode, which includes an active substance of a positive electrode, and a negative electrode, which includes first and second active substances of the negative electrode, and a control device which evaluates the internal state of the battery based on the battery active material model. Control device calculates the number of charge carriers in the first active substance of the negative electrode based on the model of the first active substance, under such condition that the first and second active substances of the negative electrode have identical potential, calculates a value of variation of potential of the open circuit of the first active substance of the negative electrode on the basis of surface mechanical stress of the first active substance of the negative electrode and calculates open circuit potential of negative electrode from potential of open circuit and value of open active circuit potential of first active substance of negative electrode.

EFFECT: high accuracy of estimating the internal state of a storage battery is the technical result of the invention.

9 cl, 25 dwg

Description

Technical field

[0001] The present disclosure relates to a battery system and a method for evaluating an internal state of a battery.

State of the art

[0002] An electrified vehicle (eg, a hybrid vehicle, an electric vehicle, and the like) with a mounted battery is widely used. In the battery, a system is provided in which the “charging curve” as the curve of the state of charge (SOC) versus open circuit voltage (OCV), which should be obtained when the battery is charged from a fully discharged state, and the “discharge curve” as the curve SOC-OCV, which should be obtained when the battery is discharged from a fully charged state, noticeably deviate from each other. If the charging curve and the discharge curve deviate from each other in this way, it is considered that “hysteresis” occurs in the battery. For example, Japanese Patent Application Publication No. 2015-166710 (JP 2015-166710 A) discloses a technology that evaluates SOC from OCV with regard to battery hysteresis.

SUMMARY OF THE INVENTION

[0003] In the present disclosure, the internal state of the battery is evaluated. Assessing the internal state of the battery includes calculating various potential components, such as a positive electrode open circuit potential, a positive electrode potential, a negative electrode open circuit potential, and a negative electrode potential of a battery. For example, a battery OCV may be calculated from a positive electrode open circuit potential and a battery negative electrode open circuit potential, and a battery SOC may be estimated from a calculated OCV. If the potential of the positive electrode of the battery becomes lower than a predetermined lower limit potential or becomes higher than a predetermined upper limit potential, a side reaction in the positive electrode is caused, and the characteristics of the positive electrode may deteriorate. Similarly, if the potential of the negative electrode is outside the specified range of potentials, the characteristics of the negative electrode may deteriorate. Thus, the accuracy of calculating the potential of one electrode (the potential of the positive electrode or the potential of the negative electrode) of the battery increases, due to which it is possible to suppress the deterioration of the characteristics of the positive electrode and the negative electrode of the battery.

[0004] In order to improve the various characteristics of the battery, a technology is analyzed that uses a negative electrode (a so-called composite negative electrode) including a plurality of active substances of the negative electrode. For example, the negative electrode of a lithium-ion battery disclosed in a publication that has not passed the examination of patent application (Japan) No. 2015-167127 (JP 2015-167127 A) includes carbon-based material (in more detail, such a carbon-based material, like nanocarbon or carbon nanotube) and silicon-based material.

[0005] In a lithium ion secondary battery, a negative electrode including a silicon-based material is used, whereby the total charge capacity can be increased compared to a case in which a negative electrode that does not include a silicon-based material is used. If the silicon-based material is included in the negative electrode, it is known that the hysteresis of the SOC-OCV curve is increased compared to the case in which the silicon-based material is not included in the negative electrode (for example, see the publication of the unexamined patent application Japan No. 2014-139521 (JP 2014-139521 A)).

[0006] When evaluating the internal state of a battery having a composite negative electrode, a case is considered in which a method for evaluating the internal state of the prior art is applied. However, in the prior art estimation method, since the hysteresis of the battery is not taken into account, the accuracy of estimating the internal state of the battery can be relatively reduced. For this reason, in a battery having a composite negative electrode, it is desirable to evaluate the internal state of the battery with regard to hysteresis.

[0007] The present disclosure provides a technology capable of improving the accuracy of evaluating the internal state of a battery having a negative electrode including a plurality of active substances of the negative electrode.

[0008] A first aspect of the present disclosure relates to a battery system. The battery system includes a battery and a control device. The battery has a positive electrode and a negative electrode. The positive electrode includes the active substance of the positive electrode. The negative electrode includes the first and second active substances of the negative electrode. The control device is configured to evaluate the internal state of the battery based on a model of the active substances of the battery. The amount of change in the volume of the first active substance of the negative electrode with a change in the number of charge carriers in the first active substance of the negative electrode exceeds the amount of change in the volume of the second active substance of the negative electrode with a change in the number of charge carriers in the second active substance of the negative electrode. The control device is configured to, provided that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential, calculate the number of charge carriers in the first active substance of the negative electrode based on the model of the first active substance. The control device is configured to calculate a change in the open-circuit potential of the first active substance of the negative electrode based on the surface mechanical stress of the first active substance of the negative electrode, which should be determined according to the number of charge carriers in the first active substance of the negative electrode. The control device is configured to calculate the open-circuit potential of the negative electrode from the open-circuit potential and the magnitude of the change in the open-circuit potential of the first active substance of the negative electrode in a state in which surface mechanical stress is not generated in the first active substance of the negative electrode.

[0009] The amount of change in the volume of the first active substance of the negative electrode with a change in the number of charge carriers in the first active substance of the negative electrode (for example, in a silicon-based material) exceeds the amount of change in the volume of the second active substance of the negative electrode with a change in the number of charge carriers in the second active substance of the negative electrode (e.g., carbon based material). For this reason, the effect of hysteresis in the first active substance of the negative electrode exceeds the effect of hysteresis in the second active substance of the negative electrode. With this in mind, according to the first aspect, the number of charge carriers (e.g., the amount of lithium) in the first active substance of the negative electrode is calculated based on the model of the first active substance, and the number of charge carriers in the second active substance of the negative electrode is calculated based on the model of the second active substance. Thus, since the number of charge carriers is calculated separately for each active substance of the negative electrode, it is possible to accurately reflect the influence of hysteresis as a result of evaluating the internal state of the battery (the details are described below). Therefore, it is possible to improve the accuracy of estimating the internal state of the battery.

[0010] In the battery system according to the first aspect of the present disclosure, the control device can be configured so that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential to separately calculate the current flowing in the first active material of the negative electrode, and the current flowing in the second active substance of the negative electrode, through the processing of convergence calculation in such a way that setting tsya predetermined convergence condition. The control device can be configured to calculate the distribution of carrier concentrations in the first active substance of the negative electrode and in the second active substance of the negative electrode by solving the diffusion equation under the boundary condition associated with the current flowing in the first active substance of the negative electrode and in the second active substance of the negative electrode. The control device can be configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode from the distribution of the concentrations of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode.

[0011] The battery system according to the first aspect of the present disclosure may further include a voltage sensor configured to detect a voltage between the positive electrode and the negative electrode. The control device can be configured to calculate the distribution of the concentrations of charge carriers in the active substance of the positive electrode by solving the diffusion equation under the boundary condition associated with the current flowing in the active substance of the positive electrode. The control device can be configured to calculate the number of charge carriers in the active substance of the positive electrode from the distribution of concentrations of charge carriers in the active substance of the positive electrode. The control device may be configured to calculate the potential of the positive electrode based on the open-circuit potential of the active substance of the positive electrode, which should be determined according to the number of charge carriers in the active substance of the positive electrode. The control device may be configured to calculate the potential of the negative electrode based on the potential of the open circuit of the negative electrode. The control device can be configured to calculate the current flowing in the first active substance of the negative electrode, with the condition that the potential difference between the potential of the positive electrode and the potential of the negative electrode coincides with the voltage detected by the voltage sensor as a condition for convergence.

[0012] According to the first aspect, the current flowing in the first active substance of the negative electrode and the current flowing in the second active substance of the negative electrode are separately calculated. As a result, the distribution of carrier concentrations in the first active substance of the negative electrode based on the diffusion equation under the boundary condition associated with the current flowing in the first active substance of the negative electrode, and the distribution of carrier concentrations in the second active substance of the negative electrode based on the diffusion equation for the boundary conditions associated with the current flowing in the second active substance of the negative electrode are obtained with greater accuracy. Since the internal state (open circuit potential or surface mechanical stress) of the battery is calculated based on the distribution of charge carrier concentrations (described below), according to the first aspect, it is possible to improve the accuracy of estimating the internal state of the battery.

[0013] In the battery system according to the first aspect of the present disclosure, the control device may be configured to separate the current flowing in the first active substance of the negative electrode into a reaction current provided for introducing and desorbing charge carriers and a capacitor current not provided in the introduction and desorption of charge carriers, and to calculate the overvoltage during the reaction of the first active substance of the negative electrode by substituting the reaction current into the expression I Butler-Volmer. The control device may be configured to calculate the potential of the negative electrode from the open-circuit potential of the negative electrode and overvoltage during the reaction of the first active substance of the negative electrode.

[0014] According to the first aspect, the influence of the electric double layer that is to be formed on the surface of the active substance is taken into account, and the overvoltage in the reaction of the first active substance of the negative electrode is calculated based on the reaction current as a current component provided for in the introduction and desorption of charge carriers. The capacitor current, not provided for in the introduction and desorption of charge carriers, is removed, thereby increasing the accuracy of calculating the overvoltage during the reaction. For this reason, it is possible to increase the accuracy of calculating the potential of the negative electrode (= potential of the open circuit of the negative electrode + overvoltage during the reaction).

[0015] In the battery system according to the first aspect of the present disclosure, the control device may be configured to calculate the total number of charge carriers in the first and second active substances of the negative electrode from the number of charge carriers in the active substance of the positive electrode according to an expression of a relationship in which the relationship , which should be established between the number of charge carriers in the active substance of the positive electrode and the total number of charge carriers the first and second active materials of the negative electrode is set using the ratio of capacitances on positive electrode capacity to the negative electrode capacity. The control device can be configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode using the law of conservation of charge, which must be set between the value of the temporary change in the total number of charge carriers in the first and second active substances of the negative electrode and current flowing in the active substance of the positive electrode.

[0016] According to the first aspect, the expression of the relation is used, due to which the diffusion equations in the first and second active substances of the negative electrode need not be solved. In addition, you can reduce the parameters that should be used when processing the convergence calculation. Therefore, it is possible to further reduce the amount of computation (computational load, storage capacity, etc.) of the control device (details are described below).

[0017] In the battery system according to the first aspect of the present disclosure, the control device may be configured to calculate the total number of charge carriers in the first and second active substances of the negative electrode from the number of charge carriers in the active substance of the positive electrode according to an expression of a relationship in which the relationship , which should be established between the number of charge carriers in the active substance of the positive electrode and the total number of charge carriers the first and second active materials of the negative electrode is set using the ratio of capacitances on positive electrode capacity to the negative electrode capacity. The control device can be configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode from the value of the temporary change in the total number of charge carriers in the first and second active substances of the negative electrode according to a given relation expression approximating that the potential of the first active substance of the negative electrode varies linearly with the number of charge carriers in the first ac active substance of the negative electrode, and approximating that the potential of the second active substance of the negative electrode varies linearly with the number of charge carriers in the second active substance of the negative electrode.

[0018] According to a first aspect, a predetermined relationship expression is used using linear approximation, whereby the amount of control device calculations can be further reduced (details are described below).

[0019] In the battery system according to the first aspect of the present disclosure, the battery may be a lithium-ion battery. The control device can be configured to, if the potential of the negative electrode, which is to be calculated from the potential of the open circuit of the negative electrode, falls below a predetermined potential above the potential of lithium metal, to more suppress the electric power of the charge in the battery than if the potential of the negative electrode exceeds a given potential.

[0020] According to the first aspect, the electric charge power in the secondary battery is controlled based on the potential of the negative electrode estimated with high accuracy. As a result, the negative electrode can be appropriately protected from degradation (deposition of lithium, described below) of the negative electrode.

[0021] In the battery system according to the first aspect of the present disclosure, the first active substance of the negative electrode may be a silicon-based material, and the second active substance of the negative electrode may be a carbon-based material.

[0022] A second aspect of the present disclosure relates to a method for evaluating an internal state of a battery. The battery has a positive electrode and a negative electrode. The positive electrode includes the active substance of the positive electrode. The negative electrode includes the first and second active substances of the negative electrode. The amount of change in the volume of the first active substance of the negative electrode with a change in the number of charge carriers in the first active substance of the negative electrode exceeds the amount of change in the volume of the second active substance of the negative electrode with a change in the number of charge carriers in the second active substance of the negative electrode. The method is a method for assessing the internal state of a battery based on an active substance model. The method includes, provided that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential, calculating the number of charge carriers in the first active substance of the negative electrode based on the model of the first active substance, calculating the magnitude of the change in the open circuit potential of the first active substances of the negative electrode based on the surface mechanical stress of the first active substance of the negative electrode, which e must be determined according to the number of charge carriers in the first active substance of the negative electrode, and the calculation of the open circuit potential of the negative electrode from the open circuit potential and the magnitude of the change in the open circuit potential of the first active substance of the negative electrode in a state in which surface mechanical stress is not formed in the first active substance negative electrode.

[0023] According to the second aspect, similarly to the first aspect, the accuracy of estimating the internal state of the battery can be improved.

[0024] According to aspects of the present disclosure, in a battery having a negative electrode including a plurality of active substances of the negative electrode, it is possible to improve the accuracy of estimating the internal state of the battery.

Brief Description of the Drawings

[0025] The following describes the features, advantages and technical and industrial significance of exemplary embodiments of the invention with reference to the accompanying drawings, in which like numbers denote like elements, and in which:

FIG. 1 is a diagram schematically showing the general configuration of an electrified vehicle in which a battery system according to Embodiment 1 is mounted;

FIG. 2 is a diagram illustrating in more detail the configuration of each galvanic cell;

FIG. 3 is a graph showing an example of a SOC-OCV curve of a battery in Embodiment 1;

FIG. 4 is a graph schematically showing a change in the potential of an open circuit of a negative electrode with a charge and discharge of a battery when a simple silicon substance is used as the negative electrode;

FIG. 5 is a diagram illustrating a three-particle model;

FIG. 6 is a diagram illustrating a method for calculating lithium concentration distributions in a positive electrode particle, a silicon particle, and a graphite particle;

FIG. 7A is a table illustrating parameters (variables and constants) to be used in a battery model;

FIG. 7B is a table illustrating parameters (variables and constants) to be used in a battery model;

FIG. 8 is a table illustrating additional features (subscripts) to be used in a battery model;

FIG. 9 is a functional block diagram of an ECU related to potential calculation processing and SOC estimation processing in Embodiment 1;

FIG. 10A is a conceptual diagram illustrating a state transition of a battery in a characteristic diagram of a dependence of a quantity of lithium on a surface in a silicon negative electrode on an open circuit potential of a silicon negative electrode;

FIG. 10B is a conceptual diagram illustrating a state transition of a battery in a characteristic diagram of a dependence of the amount of lithium on a surface in a silicon negative electrode on the open potential of a silicon negative electrode;

FIG. 10C is a conceptual diagram illustrating a state transition of a battery in a characteristic diagram of a dependence of the amount of lithium on a surface in a silicon negative electrode on the open potential of a silicon negative electrode;

FIG. 10D is a conceptual diagram illustrating a state transition of a battery in a characteristic diagram of the dependence of the amount of lithium on a surface in a silicon negative electrode on the open potential of a silicon negative electrode;

FIG. 10E is a conceptual diagram illustrating a state transition of a battery in a characteristic diagram of a dependence of the amount of lithium in a negative electrode on the potential of an open circuit of a negative electrode;

FIG. 11 is a graph illustrating a method for calculating surface mechanical stress;

FIG. 12 is a flowchart showing a processing sequence for estimating a battery SOC in Embodiment 1;

FIG. 13 is a flowchart showing a convergence calculation processing in Embodiment 1;

FIG. 14 is a flowchart showing surface stress calculation calculation processing;

FIG. 15 is a conceptual diagram illustrating a change in negative electrode potential when lithium deposition occurs;

FIG. 16 is a flowchart showing a processing sequence for estimating a battery SOC in Embodiment 2;

FIG. 17 is a flowchart showing convergence calculation processing in Embodiment 2;

FIG. 18 is a flowchart showing lithium amount calculation processing in Embodiment 2;

FIG. 19 is a flowchart showing surface mechanical stress calculation processing in Embodiment 2; and

FIG. 20 is a flowchart showing lithium amount calculation processing in Embodiment 3.

Detailed Description of Embodiments

[0026] An embodiment of the present disclosure will now be described in detail with reference to the drawings. In the drawings, identical or similar parts are represented by identical reference numbers, and their description is not repeated.

[0027] In the description below, an example is described of a configuration in which a battery system according to an embodiment of the present disclosure is mounted in an electrified vehicle. The electrified vehicle may be a hybrid vehicle (including a hybrid vehicle with a plug connection for charging from an external source) or may be an electric vehicle. An electrified vehicle may be a hybrid vehicle in which a fuel cell and a battery are combined. A “battery system” according to an embodiment of the present disclosure is not limited to being applied to a vehicle or may be stationary.

Option 1 implementation

Battery System Configuration

[0028] FIG. 1 is a diagram schematically showing the general configuration of an electrified vehicle in which a battery system according to Embodiment 1 is mounted. Referring to FIG. 1, the vehicle 9 is a hybrid vehicle and includes electric generators 91, 92, an engine 93, a power sharing device 94, a drive shaft 95, drive wheels 96, and a battery system 10. The battery system 10 includes a battery 4, a monitoring unit 6, a power control unit (PCU) 8, and an electronic control unit 100 (ECU).

[0029] Each of the electric motor generators 91, 92 is a rotating electric alternating current machine and, for example, is a three-phase alternating current synchronous electric motor in which a permanent magnet is built into the rotor. The electric motor generator 91 is mainly used as a power generator, which is driven by an engine 93 through a power sharing device 94. The electric power generated by the electric motor generator 91 is supplied to the electric motor generator 92 or the battery 4 through the PCU 8.

[0030] The electric motor generator 92 mainly operates as an electric motor and drives the drive wheels 96. The electric motor generator 92 is driven by receiving at least one of the electric power from the battery 4 and the generated electric power of the electric motor generator 91 , and the driving power of the electric motor-generator 92 is transmitted to the drive shaft 95. During braking of the vehicle or to reduce acceleration on the descent, the electric motor-generator 92 operates as a generator power to generate regenerative electric power. The electric power generated by the electric motor-generator 92 is supplied to the battery 4 through the PCU 8.

[0031] The engine 93 is an internal combustion engine that outputs power by converting combustion energy, which is to be generated by burning an air-fuel mixture of air and fuel, into kinetic energy of a motion element such as a piston or rotor.

[0032] The power sharing device 94 includes, for example, a planetary gear mechanism (not shown) having three rotational shafts of a sun gear, a carrier and a ring gear. A power dividing device 94 divides the power delivered from the engine 93 into power for driving the electric motor generator 91 and power for driving the drive wheels 96.

[0033] Battery 4 is an assembled battery including a plurality of galvanic cells 5 (single batteries). In an embodiment, each of the cells 5 is a lithium ion secondary battery. The configuration of each cell 5 is described below with reference to FIG. 2.

[0034] Battery 4 stores electrical power to drive electric motor generators 91, 92 and supplies electric power to electric motor generators 91, 92 via PCU 8. Battery 4 receives and charges generated electric power through PCU 8 during power generation of electric motors- generators 91, 92.

[0035] The monitoring module 6 includes a voltage sensor 71 and a temperature sensor 72. The voltage sensor 71 senses the voltage of each of the galvanic cells 5 included in the battery 4 as an assembled battery. The temperature sensor 72 determines the temperature of each galvanic cell 5. Each sensor displays the result of the determination in the ECU 100.

[0036] The voltage sensor 71 may detect a voltage VB, for example, with a plurality of galvanic cells 5 connected in parallel as a monitoring module. The temperature sensor 72 may detect a temperature TB with a plurality of cells 5 located adjacent to each other as a monitoring module. Thus, in an embodiment, the monitoring module is not particularly limited. Thus, in the description below, to simplify the description, it is simply described that “the voltage VB of the battery 4 is determined”, or “the temperature TB of the battery 4 is determined”. In terms of potential, OCV and SOC, likewise, battery 4 is described as a module for performing each kind of processing.

[0037] The PCU 8 performs bi-directional conversion of electrical power between the battery 4 and the electric motor generators 91, 92 in response to a control signal from the ECU 100. The PCU 8 is configured to separately control the states of the electric motor generators 91, 92 and, for example, can translate an electric motor a generator 92 to a state of power supply when the electric motor-generator 91 is transferred to a recovery state (power generation state). The PCU 8 includes, for example, two inverters, which are provided according to the electric motor generators 91, 92, and a converter that increases the constant voltage supplied to each of the inverters, so that it is equal to or higher than the output voltage of the battery 4 (all not shown) .

[0038] The ECU 100 includes a central processing unit 100A (CPU), a storage device 100B (more specifically, read-only memory (ROM) and random access memory (RAM)) and an input / output port (not shown) for input and output of various signals. The ECU 100 evaluates the state of the battery 4 based on the signals received from the sensors of the monitoring unit 6 and the programs and cards stored in the memory 100B. As the main processing to be performed by the ECU 100, the "potential calculation processing" for calculating various potential components including the potential V _{1 of the} positive electrode and potential V _{2 of the} negative electrode of battery 4 is approximately illustrated. ECU 100 evaluates the SOC of battery 4 or controls by charging and discharging the battery 4 according to the result of the “potential calculation processing”.

[0039] The positive electrode potential V ₁ represents the potential of the positive electrode (see FIG. 2) when the battery 4 is in a state of electrical conductivity. The negative electrode potential V ₂ represents the negative electrode potential when the battery 4 is in a state of electrical conductivity. When the battery 4 is in the no-conductivity state (in the no-load state), the potential of the positive electrode is called the “open circuit potential U ₁ (OCP) of the positive electrode”. The potential of the negative electrode is called the "potential U _{2 of the} open circuit of the negative electrode." Although a potential may be optionally specified that should be reference for these potentials (and other potentials described below), in an embodiment, the potential of lithium metal is determined as a reference potential.

[0040] FIG. 2 is a diagram illustrating in more detail the configuration of each galvanic cell 5. In FIG. 2, the cell 5 is shown in perspective view.

[0041] Referring to FIG. 2, the cell 5 has a square (in the form of an almost rectangular parallelepiped) battery case 51. The upper surface of the battery case 51 is sealed by a cap 52. The first end of each of the positive electrode terminal 53 and the negative electrode terminal 54 protrudes from the cover 52 to the outside. The second ends of the terminal terminal 53 of the positive electrode and the terminal 54 of the negative electrode are connected to the internal terminal of the positive electrode and the internal terminal of the negative electrode (both not shown) in the battery case 51, respectively. An electrode assembly 55 is housed in the battery case 51. The electrode assembly 55 is formed by layering a positive electrode and a negative electrode through a separator and windings of the multilayer material. The electrolyte is stored by means of a positive electrode, negative electrode, separator, etc.

[0042] For a positive electrode, a separator and an electrolyte, known configurations and materials are related such that a positive electrode, a separator and an electrolyte of a lithium-ion battery can be used, respectively. As an example, for a positive electrode, a ternary material can be used in which a portion of lithium and cobalt oxide is replaced by nickel and manganese. For the separator, a polyolefin (e.g., polyethylene or polypropylene) may be used. The electrolyte contains an organic solvent (e.g., a mixed solvent of dimethyl carbonate (DMC), ethyl methyl carbonate (EMC) and ethylene carbonate (EC)), a lithium salt (e.g. LiPF ₆ ), an additive (e.g. bis (oxalate) borate line (LiBOB) or Li [PF ₂ (C2O4) ₂ ]) and the like.

[0043] The configuration of the cell is not particularly limited, and the cell may have a configuration in which the electrode assembly has a multilayer structure instead of a wound structure. The battery case is not limited to a square battery case, and a cylindrical or multilayer battery case may be used.

SOC-OCV curve hysteresis

[0044] In the prior art, a typical negative electrode active substance of a lithium ion secondary battery is a carbon based material such as graphite. In contrast, in an embodiment, a composite material of a material based on silicon (Si or SiO) and graphite is used as the active substance of the negative electrode. This is because if the silicon-based material is turned on, the energy density of the battery 4 increases, thereby increasing the full charging capacity of the battery 4. On the other hand, if the silicon-based material is turned on, hysteresis appears noticeably in the battery 4 .

[0045] FIG. 3 is a graph showing an example SOC-OCV curve of a battery 4 in Embodiment 1. In FIG. 3 and FIG. 10A-FIG. 11, described below, the horizontal axis represents the SOC of the battery 4, and the vertical axis represents the OCV of the battery 4. In this detailed description, OCV means a voltage in a state in which the battery voltage is sufficiently attenuated, i.e. in a state in which the concentration distribution (in an embodiment, the distribution of lithium concentration) of charge carriers in the active substance is attenuated.

[0046] FIG. 3, the charging curve CHG and the discharge curve DCH of the battery 4 are shown. The charging curve CHG is obtained by repeating the charge and pausing (cessation of charge) after the battery 4 has been fully discharged. The discharge curve DCH is obtained by repeating the discharge and pausing (terminating the discharge) after the battery 4 is transferred to a fully charged state.

[0047] In detail, the charging curve of CHG can be obtained as follows. Firstly, the battery 4 in a fully discharged state is prepared and charged, for example, with an electricity value corresponding to an SOC of 5%. After the amount of electricity is charged, the charge stops, and the battery 4 remains in this state for a period of time (for example, 30 minutes) until the polarization caused by the charge is excluded. After the leaving time has expired, the OCV of battery 4 is measured. Then, the combination of (SOC and OCV) SOC (= 5%) after the charge and the measured OCV is illustrated in the drawing.

[0048] After that, the charge (charge from SOC = 5-10%) of battery 4 begins with an electricity value corresponding to SOC with the next 5%. In the event that the charge is completed, similarly, the OCV of the battery 4 is measured after the remaining time has expired. Then, the state (combination of SOC and OCV) of the battery 4 is illustrated again from the OCV measurement result. After that, the identical procedure is repeated until the battery 4 reaches a fully charged state. The CHG charging curve can be obtained by performing such a measurement.

[0049] Similarly, until the battery 4 reaches the fully discharged state from the fully charged state, the OCV of the battery 4 in the SOC at 5% intervals is measured when the discharge is repeated and the discharge of the battery 4 is stopped in turn. A DCH bit curve can be obtained by performing such a measurement. The obtained CHG charging curve and the DCH discharge curve are stored in the memory 100B of the ECU 100.

[0050] An OCV on the CHG charge curve is referred to as a “charge OCV”, and an OCV on the DCH charge curve is referred to as a “charge OCV”. The charging OCV indicates the highest OCV at each SOC, and the discharge OCV indicates the lowest OCV at each SOC. The state of the battery 4 is illustrated on a charging OCV, a discharge OCV or a region (hereinafter referred to as “intermediate region A”) surrounded by a charging OCV and a discharge OCV (see FIGS. 10A-11, described below). The deviation between the charging OCV and the discharge OCV (for example, the occurrence of a voltage difference of approximately 100 mV) represents the presence of hysteresis in the battery 4.

[0051] In the case where a composite material including both silicon-based material and graphite is used as the active substance of the negative electrode, as shown in FIG. 3, the SOC region in which significant hysteresis of the battery 4 occurs is limited to the partial SOC region (in FIG. 3, the SOC region is less than Sc). The value of Sc can be obtained by performing the above measurement in advance.

The surface mechanical stress of the active substance of the negative electrode

[0052] As a factor for which hysteresis occurs in the battery 4, a change in the volume of the active substance of the negative electrode with charge and discharge is considered. The active substance of the negative electrode expands with the introduction of lithium (charge carriers) and contracts with the desorption of lithium. Such a change in the volume of the active substance of the negative electrode leads to mechanical stress on the surface and in the active substance of the negative electrode, and even in a state in which the lithium concentration in the active substance of the negative electrode is weakened, the mechanical stress remains on the surface of the negative electrode. The mechanical stress remaining on the surface of the negative electrode is considered mechanical stress in a state in which the mechanical stress formed in the active substance of the negative electrode is balanced, and various types of force, including the reaction force, which must be applied from the peripheral element (binder, conductive auxiliary means, etc.) of the active substance of the negative electrode to the active substance of the negative electrode, with a change in the volume of the active substance tritsatelnogo electrode. Further in this document, mechanical stress is described as “surface tensile stress σ _surf ”.

[0053] The amount of change in the volume of the silicon-based material with the incorporation or desorption of lithium exceeds the amount of change in the volume of graphite. In particular, if the minimum volume in the state in which lithium is not embedded is used as a reference, while the volume change (expansion rate) of graphite with lithium incorporation is approximately 1.1 times, the material volume change based on silicon maximum is approximately four times. For this reason, if the active substance of the negative electrode includes silicon-based material, the surface mechanical stress σ _surf increases compared to the case in which the active substance of the negative electrode does not include silicon-based material (in the case where the active negative electrode substance is graphite).

[0054] The surface mechanical stress σ _surf can be measured (evaluated) through a thin-film assessment. In the following, a simple example of a method for measuring surface mechanical stress σ _{surf is} described. First, the change in the curvature κ of the negative electrode is measured as a thin film deformed by surface _surfacing σ _surf . For example, the curvature κ can be measured optically using a commercially available radius of curvature measurement system. Then, the surface mechanical stress σ _surf can be calculated by substituting the measured curvature κ and the constant (Young's modulus, Poisson's ratio, thickness, etc.) determined according to the material and shape of the negative electrode (active substance of the negative electrode and peripheral element), in the Stoney formula (for details of measuring mechanical stress, for example, see "In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon", authors VA Sethuraman et al., Journal of The Electrochemical Society, 157 (11) A1253-A1261 (2010) )

[0055] The potential V _{2 of the} negative electrode is determined by the surface state of the active substance of the negative electrode. In more detail, the potential V _{2 of the} negative electrode is determined by the amount of lithium (θ ₂ described below) on the surface of the active substance of the negative electrode and the surface mechanical stress σ _surf (see expression (20) described below). If a material is used that can lead to a large change in the volume with charge and discharge, such as a silicon-based material, as described below, the surface mechanical stress σ _surf changes with an increase or decrease in the amount of lithium in the active substance of the negative electrode, due to which the potential _{of the} open circuit U _{2 of} the negative electrode may increase or decrease.

[0056] FIG. 4 is a graph schematically showing a change in the potential of an open circuit of a negative electrode with a charge and discharge of a battery when a simple silicon substance is used as the negative electrode. In FIG. 4, the horizontal axis represents the amount θ _{Si of} lithium on the surface of the negative electrode silicon active substance, and the vertical axis represents the open electrode potential U _{Si of} the negative electrode. The same applies to FIG. 10A-11 described below.

[0057] FIG. 4, a diagram illustrates an example of a change in the open-circuit potential U _{Si of} the negative electrode of a simple silicon substance in the case if, firstly, the charge and cessation of charge are repeated for each SOC in a few% of the state of lithium quantity θ _{Si_SOC0} corresponding to SOC = 0%, to the state of the quantity θ _{Si_SOC100 of} lithium corresponding to SOC = 100%, and then, discharge and cessation of discharge are repeated for each SOC in a few% from the state of the number θ _{Si_SOC100 of} lithium to the state of the quantity θ _{Si_SOC0 of} lithium.

[0058] The result shown in FIG. 4 can be obtained by evaluating for a galvanic cell including a positive electrode and a negative electrode formed from a simple silicon substance, by providing a reference electrode in the galvanic cell. Alternatively, the result shown in FIG. 4 can be obtained by evaluating for a galvanic half cell including a silicon negative electrode and a lithium metal counter electrode.

[0059] Under conditions of continuous charging on the surface of the active material of the silicon negative electrode, mainly the compressive yield stress σ _{com is} generated (surface stress σ _surf becomes the compressive yield stress σ _com ). In this case, the open-loop potential of the silicon negative electrode decreases compared to the ideal (virtual) state in which the surface stress σ _{surf is} not created. In the following description, an ideal state in which a surface stress σ _{surf is} not generated is called an “ideal state”. The continuous discharge conditions on the surface of the silicon active material of the negative electrode is mainly generated limit σ _ten tensile stress (σ _surf surface tension becomes shallow limit σ _ten tensile yield). In this case, the open-loop potential of the silicon negative electrode increases compared to the ideal state.

[0060] In the case where the negative electrode open circuit potential U _Si decreases compared to the ideal state, OCV as the difference (= U ₁ -U _Si ) between the positive electrode open circuit potential U ₁ and the negative electrode open circuit potential U _Si increases, and in the event that the potential U _{SI of the} open circuit of the negative electrode increases, the OCV decreases. Thus, in the case where the active substance of the negative electrode is a silicon-based material, the charging OCV and the discharge OCV deviate from each other, with a change in the potential U _{Si of the} open circuit of the negative electrode due to surface surfacing stress σ _surf . For this reason, the potential U _{Si of the} open circuit of the negative electrode is calculated taking into account the influence of surface mechanical stress σ _surf , due to which it is possible to calculate OCV with high accuracy and thereby increase the accuracy of SOC estimation for a battery using a silicon-based material as a negative electrode .

Battery model

[0061] The following describes in detail a battery model (active substance model) that is used to evaluate the internal state of the battery 4 in Embodiment 1. In Embodiment 1, a three-particle model is used in which the positive electrode is typically represented by one active substance (one particle), and the negative electrode is typically represented by two particles by the active substance material of the negative electrode.

[0062] FIG. 5 is a diagram illustrating a three-particle model. Referring to FIG. 5, in the three-particle model of Embodiment 1, the positive electrode of battery 4 is represented as one particle formed from the active substance of the positive electrode (eg, ternary material). A particle is described as a “positive electrode particle 1” for simplicity. The negative electrode is represented as two particles. The first particle (model of the first active substance) is formed from silicon-based material in the active substance of the negative electrode, and the second particle (model of the second active substance) is formed from graphite in the active substance of the negative electrode. For simplicity, the first particle is referred to as "silicon particle 21" and the second particle is referred to as "graphite particle 22". The potential of the silicon particle 21 is described as the "potential V _{Si of} silicon", and the potential of the graphite particle 22 is described as the "potential V _{gra of} graphite".

[0063] FIG. 5 shows the shape during the discharge of the battery 4. During the discharge of the battery 4, lithium ions (indicated by Li ⁺⁾ are released at the interface between the silicon particle 21 and the electrolyte and the interface between the graphite particle 22 and the electrolyte. The current flowing in the silicon particle 21 with the release of lithium ions is referred to as the "current I _Si silicon", and the current flowing in the graphite particle 22 with the release of lithium ions is referred to as the "current I _gra graphite". The total current flowing in the battery 4 is represented by I _T. As should be understood from FIG. 5, in the three-particle model of the embodiment, the total current I _{T is} distributed to the current I _{Si of} silicon and the current I _{gra of} graphite.

[0064] During charging of the battery 4, while the direction of the current is reversed with respect to the direction shown in FIG. 5 (not shown), the relationship of the distribution of the total current I _T to the current I _{Si of} silicon and the current I _{gra of} graphite is identical. In this detailed description, the current during charging is shown as negative, and the current during discharge is shown as positive.

[0065] As described below, in the three-particle model of Embodiment 1, the distribution of lithium concentrations in each particle from the positive electrode particle 1, the silicon particle 21, and the graphite particle 22 is calculated.

[0066] FIG. 6 is a diagram illustrating a method for calculating lithium concentration distributions in a positive electrode particle 1, a silicon particle 21, and a graphite particle 22. Referring to FIG. 6, in the three-particle model, in the spherical particle 1 of the positive electrode, it is assumed that the distribution of lithium concentrations in the peripheral direction of the polar coordinates is uniform, and only the distribution of lithium concentrations in the radial direction of the polar coordinates is taken into account. In other words, the internal mode of the positive electrode particle 1 is a one-dimensional model in which the direction of lithium movement is limited by the radial direction.

[0067] The positive electrode particle 1 is virtually divided into N (where N: a natural number equal to or greater than 2) regions in the radial direction. The regions differ from each other by the additional symbol k (where k = 1-N). The lithium concentration c _1k in region k is represented as a function of the position r _{1k of} region k in the radial direction of the positive electrode particle 1 and time t (see expression (1) described below).

[0068] Although a detailed calculation method is described _below , in an embodiment, the lithium concentration c _{s1k of} each region k is calculated (ie, the distribution of lithium concentrations is calculated), and the calculated lithium concentration c _1k is normalized. In particular, as shown in expression (2), the ratio of the calculated lithium concentration c _1k to the maximum value c _{1, max} (hereinafter referred to as the "limiting lithium concentration") lithium concentration is calculated for each region k. The limit concentration c _{1, max} lithium is the concentration determined according to the type of active substance of the positive electrode, and is known through documents.

[0069] Hereinafter, θ _1k is referred to as the "local amount of lithium" of the region k as a value after normalization. The local amount θ _{1k of} lithium assumes a value in the range from 0 to 1 according to the amount of lithium included in the region k of the positive electrode particle 1. The local lithium quantity θ _1N in the extreme outer peripheral region N (i.e., on the surface of the positive electrode particle 1), where k = N is referred to as the “surface lithium quantity θ _{1_surf} ". As shown in expression (3) described below, we obtain the sum of the products of the volume ν1k and the local lithium quantity θ _{1k of the} lithium region k (where k = 1-N), and the value obtained by dividing the sum by the volume of particle 1 of the positive electrode (volume of active substance positive electrode), referred to as the “average amount of lithium” and is represented by θ _{1_ave} .

[0070] Although the particle (positive electrode particle 1) representing the active substance of the positive electrode is described as an example in FIG. 6, a method for calculating the distributions of lithium concentrations and (distributions) of local amounts of lithium in the particles (silicon particle 21 and graphite particle 22) representing the active substance of the negative electrode is identical. Although the number of divided regions between the positive electrode particle 1 and the silicon particle 21 and the number of divided regions between the positive electrode particle 1 and the graphite particle 22 may differ from each other, in an embodiment, both of the divided region numbers may be N.

[0071] FIG. 7A and 7B are tables illustrating the parameters (variables and constants) that should be used in the battery model. FIG. 8 is a table illustrating additional characters (subscripts) to be used in a battery model. As shown in FIG. 7A-8, the additional symbol i serves to distinguish between three particles, and i = 1, Si or gra. The case in which i = 1 means that the parameters are values in particle 1 of the positive electrode, the case in which i = Si means that the parameters are values in silicon particle 21, and the case in which i = gra, means that the parameters are values in the graphite particle 22. Of the parameters to be used in the battery model, the parameters with the additional symbol e attached mean the values in the electrolyte, and the parameters with the additional symbol s attached mean the values in the active substance.

Function blocks

[0072] Although various potential components that are calculated through potential calculation processing can be used for various types of processing or control, in Embodiment 1, a configuration in which “SOC evaluation processing” for evaluating SOC of battery 4 is performed based on the result of potential calculation processing . In an embodiment, prior to evaluating the SOC of the battery 4, a processing sequence (computational processing using an iterative method) is repeatedly performed to determine how the total current I _{T is} distributed between the current (current I _Si silicon) flowing in the silicon particle 21 and the current ( current I _gra graphite) flowing in a graphite particle 22.

[0073] FIG. 9 is a functional block diagram of an ECU 100 related to potential calculation processing and SOC estimation processing in Embodiment 1. Referring to FIG. 9, the ECU 100 includes a parameter setting module 110, an exchange current density calculation module 121, a reaction overvoltage calculation module 122, a concentration distribution calculation module 131, a lithium quantity calculation module 132, a surface stress calculation module 133, a change amount calculation module 134 open circuit potential, open circuit potential calculation module 135, salt concentration difference calculating module 141, salt concentration overvoltage calculation module 142, determination module 151 convergence conditions, current distribution module 152 and SOC evaluation module 160.

[0074] The parameter setting module 110 outputs parameters to be used in the calculation in other function blocks. In particular, the parameter setting module 110 receives the voltage VB of the battery 4 from the voltage sensor 71 and receives the temperature TB of the battery module (not shown) from the temperature sensor 72. The parameter setting module 110 sets the voltage VB as the measured voltage V _{meas of the} battery 4 and converts the temperature TB absolute temperature T (units: degrees Kelvin). The measured voltage V _meas and the absolute temperature T (or temperature TB) are output to other function blocks. Since the absolute temperature T is derived from a plurality of function blocks in order to avoid complicating the drawings, arrows indicating the transmission of the absolute temperature T are omitted.

[0075] In addition, the parameter setting module 110 outputs diffusion coefficients D _s1 , D _{s_Si} , D _{s_gra} to the concentration distribution calculating module 131. As diffusion coefficients D _s1 , D _{s_Si} , D _{s_gra} , it is desirable if different values (these values can be average amounts of lithium or surface amounts of lithium) can be specified according to local amounts of lithium θ ₁ , θ _Si , θ _gra , respectively.

[0076] Although the details are described below, in computational processing using an iterative method, which must be performed by the convergence condition determination module 151 and the current distribution module 152, the current I _{Si of} silicon, the current I _{gra of} graphite and the total current I _T. The parameter setting module 110 receives the currents (I _Si , I _gra , I _T ) set by the current distribution module 152 during the previous calculation, and outputs these currents as parameters to be used in the present calculation to other function blocks.

[0077] The exchange current density calculating module 121 receives the absolute temperature T from the parameter setting module 110 and receives the surface lithium quantity θ _{1_surf of} lithium of the positive electrode particle 1, the surface quantity of lithium θ _{Si_surf} for the silicon particle 21 and the surface quantity of lithium θ _{gra_surf} for the graphite particle 22 of module 132 calculating the amount of lithium. The exchange current density calculating _section 121 calculates the exchange current density i _{0_1} of the positive electrode particle 1, the exchange current density i _{0_Si} of the silicon particle 21 and the exchange current density i _{0_gra} of the graphite particle 22 based on parameters received from other function blocks.

[0078] In more detail, the exchange current density i _{0_1 is the} current density when the anode current density corresponding to the oxidation reaction in the positive electrode particle 1 and the cathode current density corresponding to the reduction reaction in the positive electrode particle 1 become equal to each other. The exchange current density i _{0_1} has a characteristic depending on the surface quantity of lithium θ _{1_surf} of the positive electrode particle 1 and the absolute temperature T. Accordingly, a map (not shown) showing the relationship between the correspondence of the exchange current density i _{0_1} , surface quantity of lithium θ _{1_surf} and the absolute temperature T , prepared in advance, whereby the density of the i _{0_1} exchange current can be calculated from the surface amount θ _{1_surf} lithium (described later) calculated by the module 132 calculating the amount of lithium And the absolute temperature T. The same applies to the density of exchange current i _{0_Si} silicon particles 21 and the density of the exchange current i _{0_gra} graphite particles 22, and therefore description is not repeated.

[0079] The reaction overvoltage calculation unit 122 receives the absolute temperature T from the parameter setting unit 110 and receives the silicon current I _Si , the graphite current I _gra and the total current I _T from the parameter setting unit 110. The reaction overvoltage calculation _section 122 also receives the exchange current densities i _{0_1} , i _{0_Si} , i _{0_gra from the} exchange current density calculating _section 121. Then, the reaction overvoltage calculation unit 122 calculates the overvoltage η ₁ during the reaction (overvoltage of the positive electrode) of the positive electrode particle 1, the overvoltage η _Si during the reaction (overvoltage of silicon) of the silicon particle 21 and the overvoltage η _gra during the reaction (overvoltage of graphite) of the graphite particle 22 according to the expressions (4) - (6), described below, which should be extracted from the expression of the Butler-Volmer relation, respectively. Overvoltage during the reaction is also referred to as overvoltage during activation polarization and is an overvoltage associated with the charge transfer reaction (lithium incorporation and desorption reaction). The calculated overvoltage η ₁ , η _Si , η _gra during the reaction is output to the current distribution module 152.

[0080] The concentration distribution calculation unit 131 receives the lithium diffusion coefficient D _s1 in the positive electrode particle 1 from the parameter setting unit 110. The concentration distribution calculation unit 131 calculates the distribution of lithium concentrations in the positive electrode particle 1 by solving the expression (7) described below as the diffusion equation of the polar coordinate system treating the active substance of the positive electrode (the positive electrode particle 1) as a sphere based on time evolution . Since the magnitude of the change in lithium concentration on the surface (positioning r ₁ = R ₁ ) of the positive electrode particle 1 is proportional to the total current I _T , the boundary condition of the diffusion equation (7) is specified as expression (8).

[0081] With respect to the graphite particle 22, likewise, the concentration distribution calculation module 131 calculates the distribution of lithium concentrations in the graphite particle 22 by solving the expression (9) under the boundary condition shown in the expression (10) described below based on the development over time.

[0082] The diffusion equation of the polar coordinate system relative to the silicon particle 21 is represented as expression (11). Expression (11) differs from the diffusion equations (expressions (7) and (9)) with respect to the other two particles (particle 1 of the positive electrode and graphite particle 22) in that the diffusion term for taking into account the diffusion of lithium in silicon particle 21 due to surface mechanical stress σ _{surf is} included in the second term on the right side.

[0083] In more detail, the diffusion term resulting from the surface mechanical stress σ _sur is represented as expression (12) using the hydrostatic mechanical stress σ _h (r) of the silicon particle 21 in the electrolyte. In expression (12), it is assumed that the active substance of the negative electrode (in the battery model, silicon particle 21) does not plastically deform, the Young's modulus and Poisson's ratio of silicon particle 21 in the range of elastic limits are represented by E and ν, respectively. The total mechanical stress applied to the silicon particle 21 from the peripheral element is represented by F _ex .

[0084] In the case where expression (12), representing the hydrostatic mechanical stress σ _h (r), is substituted into expression (11) as a diffusion equation, expression (11) is modified as follows (see expression (13) described below) .

[0085] Expression (13) is deformed as expression (15) described below using the effective diffusion coefficient D _{s_Si} ^eff , which must be specified by expression (14). Since the effective diffusion coefficient D _{s_Si} ^eff has a positive value, it should be understood from expression (15) that the surface mechanical stress σ _{surf is} applied in the direction of promoting lithium diffusion in the silicon particle 21. It should also be understood that the effect of surface mechanical stress σ _surf is determined according to the concentration c _{s_Si} lithium at each point (at each point of the lattice at which the diffusion equation is calculated) in the silicon particle 21.

[0086] The boundary condition of the diffusion equation (expression (14)) is presented in such a way that it further includes a term depending on the hydrostatic mechanical stress σ _h (r) as expression (16) described below in comparison with the boundary conditions ( see expressions (8) and (10)) with respect to the other two particles (particles 1 of the positive electrode and graphite particles 22).

[0087] Thus, the concentration distribution calculation unit 131 calculates the distribution of lithium concentrations in three particles (in the positive electrode particle 1, the silicon particle 21, and the graphite particle 22). The calculated distributions of lithium concentrations are output to the lithium amount calculation unit 132.

[0088] The lithium quantity calculation module 132 receives the distributions (c _s1 , c _{s_Si} , c _{s_gra} ) of lithium concentrations in three particles from the concentration distribution calculator 131, calculates various amounts of lithium, and outputs the amounts of lithium to other function blocks.

[0089] In particular, the lithium amount calculating unit 132 calculates a surface lithium quantity θ _{1_surf} of the positive electrode particle 1 based on the distribution c _s1 of lithium concentrations of the positive electrode particle 1 (see expression (2)). Similarly, module 132 calculating lithium amount calculates the surface amount θ _{Si_surf} lithium to silicon particle 21 on the basis of the distribution of c _{s_Si} lithium concentrations for silicon particles 21 and calculates the surface amount θ _{gra_surf} lithium for graphite particles 22 on the basis of the distribution of c _{s_gra} lithium concentrations for graphite particle 22 The calculated surface quantities θ _{1_surf} , θ _{Si_surf} , θ _{gra_surf of} lithium are output to the open circuit potential calculating unit 135.

[0090] The lithium quantity calculation unit 132 calculates an average lithium quantity θ _{1_ave} based on the distribution c _s1 of lithium concentrations of the positive electrode particle 1 according to expression (3). Similarly, module 132 calculating lithium amount calculates the average amount θ _{Si_ave} lithium to silicon particle 21 on the basis of the distribution of c _{s_Si} lithium concentrations for silicon particles 21, and calculates the average amount θ _{gra_ave} lithium for graphite particles 22 on the basis of the distribution of c _{s_gra} lithium concentrations for graphite particle 22 The calculated average lithium quantity θ _{Si_ave} is output to the surface mechanical stress calculation unit 133.

[0091] The surface mechanical stress calculation unit 133 calculates a surface mechanical stress σ _surf based on the average lithium quantity θ _{Si_ave} from the lithium amount calculation unit 132. The method for calculating the surface mechanical stress σ _{surf is} described in detail below. The calculated surface mechanical stress σ _surf is output to module 134 calculating the magnitude of the change in the potential of the open circuit. The calculated total mechanical stress F _ex is output to the concentration distribution calculation unit 131.

[0092] The open-circuit potential change amount calculating unit 134 calculates an open-circuit potential change amount ΔV _stress based on the surface stress σ _surf from the surface stress calculating unit 133. The magnitude ΔV _{stress of the} open-circuit potential change is the magnitude of the change in the open-circuit potential of the silicon particle 21 due to surface tensile stress σ _surf . In the case where the state in which the surface mechanical stress σ _surf is not formed is referred to as the “ideal state” and the open circuit potential of the silicon particle 21 in the ideal state is referred to as the “ideal open circuit potential U _{Si_sta} ”, the value ΔV _{stress of the} change in the open circuit potential is replaced by the deviation of the open circuit potential of the silicon particle 21 due to surface mechanical stress σ _surf based on the ideal open circuit potential U _{Si_sta} . The value ΔV _{stress of the} change in the open circuit potential is calculated from the surface mechanical stress σ _surf according to expression (17) using the value Ω of the change in the volume of the silicon-based compound per mol of lithium and the F Faraday constant. The calculated value ΔV _{stress of the} change in the open circuit potential is output to the open circuit potential calculating unit 135.

[0093] The open circuit potential calculating unit 135 calculates an open circuit potential U ₁ of the positive electrode particle 1 based on the surface lithium quantity θ _{1_surf of the} lithium of the positive electrode particle 1 from the lithium quantity calculating unit 132. More specifically, although the positive electrode particle 1 is virtually divided into regions N in the radial direction, the open circuit potential U ₁ of the positive electrode particle 1 is determined according to the local lithium quantity θ _1N (surface lithium quantity θ _{1_surf} ) on the surface of the positive electrode particle 1 as the outermost peripheral region N (see expression (18) described below). For this reason, a map (not shown) indicating the relationship between the open circuit potential U ₁ and the surface lithium quantity θ _{1_surf} is created by a preliminary experiment, whereby the open circuit potential U ₁ can be calculated from the surface lithium quantity θ _{1_surf} . With respect to the graphite particle 22, likewise, the open-circuit potential calculation unit 135 calculates the open-circuit potential U _gra from the surface amount of lithium θ _{gra_surf} for the graphite particle 22 by referring to a predetermined map (not shown) (see expression (19) described below) .

[0094] When calculating the open-loop potential U _{Si of} the silicon particle 21, the influence of surface mechanical stress σ _{surf is} taken into account. The open circuit potential U _Si is calculated by summing the ΔV _stress value of the change in the open circuit potential with the open circuit potential U _{Si_sta of} the silicon particle 21 in a state in which surface tensile stress σ _{surf is} not formed, as shown in expression (20) described below. The open circuit potentials U ₁ , U _Si , U _gra calculated according to expressions (18) - (20) are output to the current distribution unit 152.

[0095] The concentration c _{e of} lithium salt in the electrolyte may vary with the charge and discharge of the battery 4, and a gradient in the concentration of lithium salt in the electrolyte may occur. When this happens, an overvoltage ΔV _e of the salt concentration is formed between the active substance of the positive electrode (particle 1 of the positive electrode) and the active substance of the negative electrode (silicon particle 21 and graphite particle 22) due to the concentration gradient of lithium salt and is likely to affect the potential V _{1 of the} positive electrode and potential V _{2 of the} negative electrode.

[0096] The salt concentration difference calculator 141 calculates a difference Δ _ce of lithium salt concentrations between the active substance of the positive electrode and the active substance of the negative electrode. Since the difference Δ _ce of lithium salt concentrations depends on the electrolyte diffusion coefficient De, the volume fraction ε _{e of the} electrolyte, the transport number t + ⁰ of lithium ions and current (total current I _T ), for example, the difference Δ _ce of lithium salt concentrations can be calculated according to expressions (21) - (23) described below. Since expression (21) as a recurrence equation is repeatedly solved in each given calculation cycle in expressions (21) - (23), the calculation cycle is represented by Δτ. The parameter with t attached on the shoulder (in the upper right side) indicates the parameter during the present calculation, and the parameter with attached (t-Δτ) on the shoulder indicates the parameter during the previous calculation. The calculated difference Δ _{ce of the} concentrations is output to the salt concentration overvoltage calculation unit 142.

[0097] The salt concentration overvoltage calculation module 142 calculates a salt concentration overvoltage ΔV _e from the difference Δ _ce of lithium salt concentrations calculated by the salt concentration difference calculator 141 according to expression (24). The calculated overvoltage ΔV _e of the salt concentration is output to the current distribution module 152.

[0098] The convergence condition determination module 151 and the current distribution module 152 perform computational processing using an iterative method to calculate various components of the battery potential 4. In an embodiment, Newton's law is used as one of the characteristic iterative methods. It should be noted that the type of the iterative method is not limited to this; a solution of a nonlinear equation, such as a method of bisecting or a method based on secants, can be used.

[0099] When calculating the above function blocks, currents (I _T , I _Si , I _gra ) flowing in three particles specified by the current distribution unit 152 during the previous calculation are used. The convergence condition determination unit 151 receives the calculation result based on the currents set during the previous calculation from other function blocks. In more detail, the convergence condition determination module 151 receives the overvoltage η ₁ , η _Si , η _gra during the reaction from the reaction overvoltage calculation module 122 (see expressions (4) - (6)), takes the potentials U ₁ , U _Si , U _gra open the circuit from the open-circuit potential calculation unit 135 (see expressions (18) - (20)), receives the measured voltage V _meas (the measured value of the battery voltage 4) from the parameter setting unit 110 and receives the salt concentration overvoltage ΔV _e from the overvoltage calculation unit 142 salt concentration (see expression (24)). The convergence condition determination unit 151 (not shown) receives the DC resistance Rd from the parameter setting unit 110 (details are described below).

[0100] The module 151 determining convergence conditions calculates voltage battery 4 from the potential V ₁ of the positive electrode potential V ₂ of the negative electrode, the magnitude of voltage drop (= I _T R _d) due Rd DC resistance and overvoltage ΔV _e salt concentration according to the relational expression ( 25), described above, which must be installed between voltage and current. The calculated voltage is described as "calculated voltage V _calc " to distinguish from the measured voltage V _meas (measured value of the voltage sensor 71).

[0101] In expression (25), the potential V _{1 of the} positive electrode is calculated by expression (26). The negative electrode potential V _{2 is} calculated as equal to the silicon potential V _Si shown in expression (27) and the graphite potential V _gra shown in expression (28) (V ₂ = V _Si = V _gra ).

[0102] Then, the convergence condition determination unit 151 determines whether or not the convergence condition of the iterative method is satisfied by comparing the calculated voltage V _calc with the measured voltage V _meas and comparing the potential V _{Si of} silicon with the potential V _{gra of} graphite. In particular, the convergence condition determination module 151 determines whether or not the calculated voltage V _calc and the measured voltage V _{meas coincide} with each other (the error between these voltages is less than the first predetermined value PD1), and the silicon potential V _Si and the potential practically coincide V _gra graphite with each other (the error between these voltages is less than the second setpoint PD2). If the error (= | V _calc -V _meas |) between the calculated voltage V _calc and the measured voltage V _meas is equal to or higher than the first setpoint PD1, or if the error (= | V _Si -V _gra |) between the silicon potential V _Si and the graphite potential V _gra is equal to or higher than the second predetermined value PD2, the convergence condition determination unit 151 outputs, to the current distribution module 152, a determination result that the convergence condition of the iterative method is not satisfied.

[0103] If the determination result that the convergence condition is not satisfied is received from the convergence condition determination unit 151, the current distribution unit 152 updates the currents (I _T , I _Si , I _gra ) flowing in three particles by the values for use during the next calculation. In more detail, the current distribution module 152 sets the silicon current I _Si and the total current I _T to be used during the next calculation from the silicon currents I _Si and the total currents I _T used during the previous calculation and during the present calculation using the algorithm based on Newton’s law (or a method of halving, a method based on secants, etc.). The remaining graphite current I _gra is calculated from the silicon current I _Si and the total current I _T according to the relationship between the currents shown in expression (29). The calculated currents are output to the parameter setting module 110. The current values after the update are then used during the next calculation.

[0104] Thus, the convergence condition determination module 151 and the current distribution module 152 perform computational processing iteratively until the error between the calculated voltage V _calc and the measured voltage V _meas becomes less than the first predetermined value PD1 and the error between the potential V _Si silicon and the potential V _{gra of} graphite will not become less than the second setpoint PD2. If both of the two errors become smaller than the corresponding set values (PD1, PD2), a determination is made as to whether the iterative computation converges, and the convergence condition determination module 151 outputs the parameters (positive electrode open circuit potential U ₁ , surface quantity θ lithium _{i_surf} and the ΔV _stress value of the change in open-circuit potential) required for SOC assessment in SOC assessment module 160.

[0105] The SOC estimator 160 estimates the SOC of the battery 4 based on various amounts (θ _{1_ave} , θ _{1_SOC0} , θ _{1_SOC100} ) of lithium of the positive electrode particle 1. The following describes a method for evaluating SOC.

Calculation of surface stress

[0106] A method for calculating a surface mechanical stress σ _{surf of} an active substance from silicon is described in detail below. In the description below, the state shown in the characteristic diagram of the dependence of the amount of lithium in the silicon substance on the potential of the open circuit of the negative electrode as a combination of (θ _Si , U _Si ) the amount of θ _Si lithium (for example, the average number θ _{Si_ave of} lithium) of the silicon substance and the potential U _Si open-circuit silicon substance, is described as the "state P". In particular, the state P during the mth (m is a natural number) calculation is represented as "P (m)". In an embodiment, the surface stress σ _{surf is} calculated with emphasis on the state transition P.

[0107] FIG. 10A-10E are conceptual diagrams illustrating a state transition P of a battery in a characteristic diagram of the dependence of the amount of lithium on a surface in a silicon negative electrode on the open potential of a silicon negative electrode. In FIG. 10A, an example is shown in which the state P (m) is illustrated on a charging curve (indicated by a dashed line).

[0108] If the charge continues from the state P (m), the state P (m + 1) in the (m + 1) -th calculation cycle is maintained on the charging curve, as shown in FIG. 10B.

[0109] In the event that the discharge is performed from the state P (m) shown in FIG. 10A, as shown in FIG. 10C, the state P (m + 1) in the (m + 1) -th calculation cycle deviates from the charge curve and is illustrated in the region between the charge curve and the discharge curve (indicated by a dash-dot line with one dot). If the discharge continues, for example, in the (m + 2) -th calculation cycle, the state P (m + 2) reaches the discharge curve (see Fig. 10D). If the discharge continues after this, the state P (m + 3) is maintained on the discharge curve (see Fig. 10E).

[0110] FIG. 11 is a graph illustrating a method for calculating a surface mechanical stress σ _{surf of} an active substance from silicon. In FIG. 11, an example in which charge and discharge are performed in the state order P (1) -P (8).

[0111] In more detail, firstly, the discharge starts from the state P (1) on the discharge curve, and the discharge continues to the state P (3). The states P (2), P (3) are supported on the discharge curve. Then, in state P (3), switching from discharge to charge is performed. The states P (4), P (5) after the charge begin a transition in the region between the charge curve and the discharge curve. After that, state P (6) is illustrated on the charging curve. Although the charge continues, the state P is maintained on the charging curve (see states P (7), P (8)).

[0112] In the states P (1) -P (3), which are illustrated in the discharge curve, the surface mechanical stress σ _surf passes the yield strength and is equal to the tensile yield stress σ _ten , as shown in expression (30) described below.

[0113] In the states P (6) -P (8) on the charge curve, the surface mechanical stress σ _surf passes the yield strength at the compressive yield stress σ _com (see expression (31) described below).

[0114] In contrast, in the case where the state P is not illustrated on the charge curve and the discharge curve, ie if the state P is illustrated in the region between the charge curve and the discharge curve (see states P (4), P (5)), then how to calculate the surface mechanical stress σ _surf becomes a problem. In an embodiment, the average concentration c _{Si_ave of} lithium in the silicon particle 21 when the direction of charge or discharge is switched and the surface stress σ _surf at this time is used to calculate the surface stress σ _surf in the region. In the description below, the average concentration c _{Si_ave of} lithium in state P when the direction of charge or discharge is switched is described as “reference concentration c _{REF of} lithium” and surface stress σ _surf in state P is described as “reference surface stress σ _REF ”.

[0115] In the example shown in FIG. 11, the state P, when the charge or discharge is switched, is the state P (3) during the switching from the discharge to the charge. When calculating the states P (4), P (5), the average concentration of lithium _{Si_ave} during the state P (3) has already been calculated using expressions (8) - (10) described above. Accordingly, the average lithium concentration c _{Si_ave} calculated in state P (3) becomes the reference lithium concentration c _REF . The reference surface mechanical stress σ _REF in the state P (3) is the tensile yield stress σ _ten (see expression (30) described above).

[0116] In state P, in the region between the charge curve and the discharge curve, there is a linear relationship represented as expression (32) described below between the difference (c _{s2_ave} -c _REF ) of lithium concentrations obtained by subtracting the reference lithium concentration c _REF from the average concentration of lithium _{Si_ave} , and surface _surfacing σ _surf .

[0117] It should be understood that the linear relationship represents that the magnitude of the change in surface mechanical stress σ _surf is proportional to the magnitude of the change in lithium content in silicon particle 21 (the amount of lithium embedded in silicon particle 21 or the amount of lithium stripped from silicon particle 21) in case the state P, when the direction of charge or discharge is switched, is used as a reference.

[0118] The proportional constant α _c is a parameter that is determined according to the mechanical characteristics of the silicon-based compound as one of the active substance of the negative electrode and the peripheral element and can be obtained by experiment. In more detail, the proportional constant α _c can vary according to the temperature (≅ temperature TB of battery 4) of the active substance of the negative electrode electrode and the lithium content (average concentration of lithium _{Si_ave} c) in the active substance of the negative electrode. For this reason, a proportional constant α _{c is} obtained for various combinations of temperature TB and average lithium concentration c _{Si_ave} , and a map (or ratio expression) is prepared indicating the correlation between the temperature TB, average lithium concentration c _{Si_ave} and proportional constant α _c . A map _{showing the} correlation between one of the temperature TB and the average lithium concentration c _{Si_ave} and the proportional constant α _c can be prepared.

[0119] Since lithium concentration and lithium amount can be replaced as expression (2) described above, expression (32) described above can be modified as expression (33) described below using an average lithium particle quantity θ _{Si_ave of} particle 21 silicon.

[0120] A map indicating the correlation of the temperature TB and the average lithium quantity θ _{Si_ave} and the proportional constant α _c (or the proportional constant α _θ ) is prepared and stored in advance in the ECU 100B 100B. For this reason, the proportional constant α _c can be calculated from the temperature TB (measured value of the temperature sensor 72) and the average lithium quantity θ _{Si_ave} (estimated value during the previous calculation) by accessing the map. Then, the surface stress σ _surf in the above region can be calculated by substituting the proportional constant α _c , the average lithium quantity θ _{Si_ave} , the reference lithium quantity θ _REF and the reference surface stress σ _REF in expression (33) described above. The following describes in detail the flowchart of calculating the surface mechanical stress σ _surf with reference to FIG. 14.

SOC Assessment Flow

[0121] FIG. 12 is a flowchart showing a processing sequence for evaluating an SOC of a battery 4 in Embodiment 1. The flowcharts shown in FIG. 12 and FIG. 17 and 16, described below, are called from the main procedure (not shown), for example, each time a given cycle has expired and repeatedly performed by the ECU 100. Although the steps (hereinafter referred to as abbreviated as "S") included in the flowchart, the flowcharts are essentially implemented through software processing in the ECU 100, the steps can be implemented using specialized hardware (electrical circuitry) manufactured in the ECU 100.

[0122] Referring to FIG. 12, the processing of S101-S106 described below corresponds to the potential calculation processing of one electrode according to Embodiment 1. Firstly, in S101, the ECU 100 receives the voltage VB of the battery 4 from the voltage sensor 71 and obtains the temperature TB of the battery 4 from the temperature sensor 72. The voltage VB is used as the measured voltage V _meas , and the temperature TB is converted to the absolute temperature T. The absolute temperature T can be calculated from the temperature TB at a given point in time (during the present calculation) or can be calculated from the weighted average temperature TB in the last predetermined period (for example, within 30 minutes) determined in advance.

[0123] In S102, the ECU 100 calculates an exchange current density i _{0_1} of the positive electrode particle 1. As described with reference to FIG. 9, the exchange current density i _{0_1} depends on the surface quantity of lithium θ _{1_surf} of the positive electrode particle 1 and the absolute temperature T. Accordingly, the ECU 100 calculates the exchange current density i _{0_1} from the surface amount of lithium θ _{1_surf} (see S303 of FIG. 13) calculated during the previous calculation, and the absolute temperature T by referring to a map (not shown) indicating a correspondence relationship of density i _{0_1} exchange current, the surface amount θ _{1_surf} lithium and absolute temperature T. Similarly, ECU 100 calculates a tighter st i _{0_Si} exchange current of the silicon particles 21 and the density of the exchange current i _{0_gra} graphite particles 22 by referring to the corresponding card (not shown).

[0124] In S103, the ECU 100 calculates the DC resistance Rd of the battery 4. The DC resistance Rd is a resistive component when lithium ions and electrons move between the active substance of the positive electrode and the active substance of the negative electrode, or the resistive component of a metal fragment. The DC resistance Rd has a characteristic that varies depending on the absolute temperature T and the quantity θ ₁ . Accordingly, the direct current resistance Rd can be calculated from the absolute temperature T by preparing a map (not shown) indicating the relationship of the correspondence between the direct current resistance Rd and the absolute temperature T in advance based on the measurement result of the direct current resistance Rd at each temperature.

[0125] In S104, the ECU 100 calculates the difference Δ _ce of lithium salt concentrations between the active substance of the positive electrode and the active substance of the negative electrode in the electrolyte (see expressions (21) to (23) described above). In addition, the ECU 100 calculates the overvoltage ΔV _e of the salt concentration from the difference Δ _ce of the lithium salt concentrations according to the expression (24) described above (S105). These types of processing are described in detail with reference to FIG. 9, and therefore, the description is not repeated.

[0126] In S106, the ECU 100 performs convergence calculation processing for distributing the current (total current I _T ) flowing in the active substance of the negative electrode in the three-particle model to the current (current I _Si silicon) flowing in the silicon particle 21 and the current ( current I _gra graphite) flowing in a graphite particle 22.

[0127] In S200, the ECU 100 estimates the SOC of the battery 4 based on the result of the potential calculation processing (SOC evaluation processing). The following describes the processing of the SOC score.

[0128] FIG. 13 is a flowchart showing convergence calculation processing (processing according to S106 of FIG. 12) in Embodiment 1. Referring to FIG. 13, in S301, the ECU 100 calculates an overvoltage η ₁ during the reaction of the positive electrode particle 1 from the exchange current density i _{0_1} of the positive electrode particle 1 and the absolute temperature T according to expression (4) described above. In addition, the ECU 100 calculates the overvoltage η _Si during the reaction of the silicon particle 21 from the density i _{0_Si of the} exchange current of the silicon particle 21 and the absolute temperature T according to expression (5) described above, and calculates the overvoltage η _gra during the reaction of the graphite particle 22 from the density i _{0_gra} the exchange current of the graphite particle 22 and the absolute temperature T according to the expression (6) described above.

[0129] In S302, with respect to the positive electrode particle 1, the ECU 100 calculates a distribution of lithium concentrations in the positive electrode particle 1 by substituting the lithium diffusion coefficient D _s1 in the positive electrode particle 1 into expression (7) described above as the diffusion equation, and solving the expression (7) under the boundary condition (see expression (8) described above), determined according to the total current I _T. The diffusion coefficient D _s1 depends _{on the} lithium quantity θ ₁ of the positive electrode particle 1 and the absolute temperature T. Thus, the diffusion coefficient D _s1 can be calculated from the lithium quantity θ ₁ during the previous calculation and the absolute temperature T using a map (not shown) prepared in advance.

[0130] With respect to the graphite particle 22, similarly, the ECU 100 calculates the distribution of lithium concentrations in the graphite particle 22 by solving the diffusion equation (9) under the boundary condition (see expression (10) described above). In addition, the ECU 100 calculates the distribution of lithium concentrations in the silicon particle 21 by solving the diffusion equation (15) into which the effective diffusion coefficient D _{s_Si} ^eff is substituted (see expression (14)), under the boundary condition (see expression (16)) .

[0131] In S303, the ECU 100 calculates a surface lithium quantity θ _{1_surf} of the positive electrode particle 1 based on the distribution of lithium concentrations in the positive electrode particle 1 calculated in S302 (see expression (2) described above). Similarly, ECU 100 calculates the amount of surface θ _{Si_surf} lithium to silicon particles 21 and calculates the amount of surface for θ _{gra_surf} lithium graphite particles 22.

[0132] In S304, the ECU 100 calculates an open circuit potential U ₁ from the surface lithium quantity θ _{1_surf} calculated in S303 by referring to a map (not shown) indicating the relationship between the open circuit potential U ₁ and the lithium quantity θ _{1 of} particle 1 positive electrode (see expression (18)). Similarly, the ECU 100 calculates an open circuit potential U _gra from the surface lithium quantity θ _{gra_surf} by referring to a map (not shown) indicating the relationship between the correspondence between the open circuit potential U _gra and lithium θ _gra for graphite particle 22 (see expression (19) )

[0133] In S305, the ECU 100 calculates an open circuit potential U _{Si_sta} from a surface lithium quantity θ _{Si_surf} by referring to a map (not shown) indicating a correlation relationship between an open circuit potential U _Si and a lithium quantity θ _Si for a silicon particle 21 in perfect condition , in which the surface mechanical stress σ _surf = 0.

[0134] In S306, the ECU 100 performs surface stress calculation processing of the silicon particle 21 to calculate the surface stress σ _surf .

[0135] FIG. 14 is a flowchart showing a calculation process of the surface mechanical stress of a silicon particle 21 (processing according to S306 of FIG. 13). Referring to FIG. 14, in S401, the ECU 100 calculates the average amount θ _{Si_ave of} lithium in the silicon particle 21. The average amount θ _{Si_ave of} lithium can be calculated identical to expression (3) described above with respect to the positive electrode particle 1.

[0136] In S402, the ECU 100 reads the reference lithium quantity θ _REF and the reference surface stress σ _REF stored in the memory 100B until the previous calculation (see processing according to S413 described below).

[0137] In S403, the ECU 100 calculates a proportional constant α _θ from the temperature TB of the battery 4 and the average lithium concentration c _{Si_ave} (c _{Si_ave} during the previous calculation) by accessing a card (not shown). The proportional constant α _θ can be calculated (modeling predicted) from the physical properties (Young's modulus, etc.) of the active substance of the negative electrode and the peripheral element. It should be noted that the proportional constant α _θ does not have to be a variable, and a fixed value defined in advance can be used as the proportional constant α _θ .

[0138] In S404, the ECU 100 calculates a surface mechanical stress σ _surf from the proportional constant α _θ and the average lithium quantity θ _{Si_ave} according to expression (33) described above. The surface mechanical stress σ _{surf is} tentatively calculated without taking into account the fluidity of the active substance from silicon and the surface mechanical stress σ _surf , taking into account that the fluidity of the substance from silicon is determined (mainly calculated).

[0139] In S405, the ECU 100 compares the surface tensile stress σ _surf , tentatively calculated on S404, with the compressive yield stress σ _com . If the surface mechanical stress σ _surf , taking into account the sign of the surface mechanical stress σ _surf shown in FIG. 4 is equal to or less than the compressive yield stress σ _com , i.e. in the event that the absolute value of the surface mechanical stress σ _surf is equal to or higher than the absolute value of the compressive yield stress σ _com (at S405, “Yes”), the ECU 100 determines that the active substance of the negative electrode passes through the yield strength, and that the surface mechanical stress σ _surf is equal to the compressive yield stress σ _com (σ _surf = σ _com ) (S406). Thus, the surface mechanical stress σ _surf , tentatively calculated on S404, is not used, and the compressive yield stress σ _{com is} used instead. Then, the ECU 100 updates the reference surface mechanical stress σ _REF by setting the compressive yield stress σ _com as the new reference surface mechanical stress σ _REF . In addition, the ECU 100 updates the lithium reference amount θ _REF by setting the average lithium quantity θ _{Si_ave} calculated in S401 as the lithium reference amount θ _REF (S407).

[0140] If, taking into account the sign, the surface mechanical stress σ _surf exceeds the yield stress σ _com with compression (if the absolute value of the surface mechanical stress σ _{surf is} less than the absolute value of the compressive strength σ _com ) (in S405, " No "), the ECU 100 transfers the process to S408 and compares the surface tensile stress σ _surf with the tensile strength σ _ten .

[0141] If the surface mechanical stress σ _surf is equal to or higher than the tensile yield stress σ _ten (in S408, “Yes”), the ECU 100 determines that the active substance of the negative electrode passes the yield stress and that the surface mechanical the stress σ _surf is equal to the tensile stress σ _ten (S409). Then, the ECU 100 updates the reference surface mechanical stress σ _REF with tensile strength σ _ten and updates the reference lithium quantity θ _REF with the average lithium quantity θ _{Si_ave} calculated in S401 (S410).

[0142] In S408, if the surface mechanical stress σ _{surf is} less than the tensile stress σ _ten (in S408, “No”), the surface mechanical stress σ _surf is in an intermediate region A between the compressive yield stress σ _com and the σ limit _ten tensile yield strength (σ _com <σ _surf <σ _ten ), and the active substance of the negative electrode does not go over the yield strength. Thus, the surface mechanical stress σ _surf , tentatively calculated on S404, is used (S411). In this case, the reference surface mechanical stress σ _{REF is} not updated, and the reference surface mechanical stress σ _REF set at the time of the previous calculation (or during the calculation before the previous calculation) is maintained. The update of the reference lithium quantity θ _REF is also not performed (S412).

[0143] If one of the processing S407, S410 and S412 is performed, the reference lithium quantity θ _REF and the reference surface mechanical stress σ _REF are stored in the storage device 100B (S413). After that, the process returns to S307 (see FIG. 13) of the convergence calculation processing.

[0144] Referring to FIG. 13 again, in S307, the ECU 100 calculates the ΔV _stress value of the change in the open circuit potential from the surface mechanical stress σ _surf according to expression (17) in order to take into account the effect of the surface mechanical stress σ _surf on the open circuit potential U _{Si of} the silicon particle 21.

[0145] In S308, the ECU 100 calculates the sum of the overvoltage η ₁ upon the reaction of the positive electrode particle 1 and the positive electrode open circuit potential U _{1 as} the positive electrode potential V ₁ according to expression (26) described above. In addition, the ECU 100 calculates the _silicon open circuit potential U _Si by summing the ΔV _stress value of the change in the open circuit potential with the ideal open circuit potential U _{Si_sta of} the silicon particle 21 (see expression (20) described above), and further calculates the sum of the overvoltage η _Si in the reaction of a silicon particle 21 and an open silicon potential U _Si as a silicon potential V _Si (see expression (27) described above). In addition, the ECU 100 calculates the sum of the overvoltage η _gra during the reaction of the graphite particle 22 and the potential U _{gra of the} open graphite chain as the potential V _{gra of} graphite (see expression (28) described above).

[0146] In S309, the ECU 100 calculates the calculated voltage V _calc from the potential V _{1 of the} positive electrode, potential V _{2 of the} negative electrode (potential V _Si silicon or potential V _gra graphite), the magnitude of the voltage drop (= I _T R _d ) due to resistance Rd direct current and overvoltage ΔV _e salt concentration according to the expression (25) described above.

[0147] In S310, the ECU 100 determines whether or not a condition (a convergence condition) is established under which iterative calculation converges in the convergence calculation processing. In particular, the convergence condition includes the first and second conditions. The first condition is a condition as to whether or not the absolute value (= | V _calc -V _meas |) of the difference between the calculated voltage V _calc calculated in S309 and the measured voltage V _meas obtained from the voltage sensor 71 on S101, the first specified PD1 values (| V _calc -V _meas | <PD1). The second condition is a condition as to whether the absolute value (= | V _Si -V _gra |) of the difference between the potential V _{Si of} silicon and the potential V _{gra of} graphite calculated in S308 of the second set value PD2 (| V _Si -V _gra | <PD2).

[0148] The ECU 100 determines that the convergence condition is established if both of the first and second conditions are established, and determines that the convergence condition is not established if either of the first and second conditions is not established. If the convergence condition is not established (on S310, “No”), the ECU 100 updates the currents I _T , I _Si , I _gra according to an algorithm based on Newton's law (S311) and returns the process to S301. If the convergence condition is established (at S310, “Yes”), the ECU 100 returns the process to S200 of FIG. 12.

[0149] Referring to FIG. 12 again, in S200, the ECU 100 performs SOC evaluation processing for evaluating the SOC of battery 4 based on the result of the potential component calculation processing. SOC evaluation processing includes, for example, processing according to S201 and S202.

[0150] In S201, the ECU 100 obtains the average amount θ _{1_ave of} lithium (a value calculated by processing S302 at which the convergence condition is established) of the positive electrode particles 1, and reads the known amounts θ _{1_SOC0} , θ _{1_SOC100 of} lithium stored in the memory 100B. The lithium quantity θ _{1_SOC0 is the} lithium amount of the positive electrode particle 1 corresponding to SOC = 0%, and the lithium quantity θ _{1_SOC0 is the} lithium quantity θ _{1_SOC0} of the positive electrode corresponding to SOC = 100%.

[0151] Then, in S202, the ECU 100 estimates the SOC of the battery 4 based on the above three amounts of lithium. In particular, the SOC of battery 4 may be calculated using expression (34) described below.

[0152] As described above, in Embodiment 1, a “three-particle model” is used. In a three-particle model, a positive electrode is typically represented by a positive electrode particle 1, and a negative electrode is typically represented by two particles of a silicon particle 21 and a graphite particle 22. In this case, a current (current I _Si silicon) flowing in the silicon particle 21, and the current (current I _{gra of} graphite) flowing in the graphite particle 22 is different from each other, and the total current I _T flowing in the active substance of the negative electrode is distributed to the current I _{Si of} silicon and the current I _{gra of} graphite.

[0153] Thus, in Embodiment 1, the current distribution between the silicon particle 21 and the graphite particle 22 is taken into account, whereby the accuracy of the calculation of the parameters depending on the current is improved compared to the case in which the current distribution is not taken into account. In particular, in an embodiment, the overvoltage η _{Si of} silicon (see expression (5)), which must be determined according to the current I _{Si of} silicon, and the overvoltage η _{gra of} graphite (see expression (6)), which must be determined according to the current I _gra graphite calculated separately. As a result of this, it is possible to accurately calculate the overvoltage, which is formed according to the reaction during charge transfer (lithium incorporation and desorption reactions), as compared with the case in which the currents do not differ from each other.

[0154] In addition, the accuracy of calculating the distributions of lithium concentrations in particles, which are calculated by solving the diffusion equations shown in expressions (7) to (16), is improved. For this reason, the accuracy of calculating the average concentration c _{s_Si_ave of} lithium (or the average amount θ _{Si_ave of} lithium) in the silicon particle 21 is increased. Accordingly, the accuracy of calculating the surface mechanical stress σ _surf depending on the average concentration c _{s_Si_ave of} lithium (or the average number θ _{Si_ave of} lithium) (see expression (32) or (33) described above). As a result, the ΔV _stress value of the change in the potential of the open circuit can be calculated, indicating the deviation of the potential of the open circuit (potential U _{Si of the} open silicon circuit) of the silicon particle 21 due to the surface mechanical stress σ _surf with high accuracy (see expression (17)). As a result, since it is possible to accurately reflect the influence of surface mechanical stress σ _surf in the potential U _{2 of the} open circuit of the negative electrode (see expression (20) described above), it is also possible to calculate the potential V _{2 of the} negative electrode with high accuracy. In addition, it is also possible to evaluate the SOC of the battery 4 with high accuracy (SOC evaluation processing). As described above, according to Embodiment 1, it is possible to evaluate the internal state of the battery 4 with high accuracy.

Modification Example 1 of Embodiment 1

[0155] In the modification example 1 of the embodiment 1, a configuration is described in which the convergence calculation processing is performed taking into account the influence of an electric double layer that must be formed on the surface of the active substance. In the modification example, the total current I _{T is} additionally distributed to the current component provided for in the manufacture of lithium (incorporation and desorption of lithium ions) and the current component not provided for in the manufacture of lithium. In particular, with respect to the positive electrode particle 1, in the case where the current provided in the manufacture of lithium in the full current I _T is described as a “reaction current I ₁ ^EC ” and the current not provided in the manufacture of lithium is described as “current I ₁ ^C capacitor ", the expression (35) is set, described below.

[0156] The electrostatic capacitance of an electric double layer to be formed in a positive electrode particle 1 is described as C ₁ . The electrostatic capacitance C _{1 is} known through a preliminary assessment. The capacitor current I ₁ ^C is represented as expression (36) described below.

[0157] A relationship identical to that of expression (26) described above is established between the positive electrode potential V _{1, the} positive electrode open circuit potential U ₁ and overvoltage η ₁ during the reaction (see expression (37) described above). It should be noted that in the overvoltage η _{1 of the} positive electrode, as shown in expression (38) described below, the reaction current I ₁ ^EC is used instead of the total current I _T.

[0158] Regarding the side of the negative electrode, the current (current I _Si silicon) flowing in the silicon particle 21 is divided into the current I _Si ^{EC of the} reaction and the current I _Si ^{C of the} capacitor. In addition, the current (current I _gra graphite) flowing in the graphite particle 22 is divided into the current I _gra ^{EC of the} reaction and the current I _gra ^{C of the} capacitor. Then the expression (39) described below is established between these currents.

[0159] The current I _Si ^{C of the} capacitor is represented as expression (40) described below using the electrostatic capacitance C _Si to be formed in the silicon particle 21 and the potential V _{2 of the} negative electrode. The capacitor current I _gra ^C is represented as expression (41) described below using the electrostatic capacitance C _gra to be formed in the graphite particle 22 and the negative electrode potential V ₂ .

[0160] Furthermore, expression (42) is established, which is identical to expressions (27) and (28) described above. Here, the current I _Si silicon in the overvoltage η _Si silicon is replaced by the current I _Si ^{EC of the} capacitor, and the current I _{gra of} graphite in the overvoltage η _{gra of} graphite is replaced by the current I _gra ^{EC of the} capacitor (see expressions (43) and (44) described below )

[0161] As described above, in the modification example 1 of the embodiment 1, the current (total current I _T ) flowing in the positive electrode particle 1 is divided into a capacitor current I ₁ ^C and a reaction current I ₁ ^EC taking into account the influence of the electric double layer, which should be formed on the surface of the active substance of the positive electrode. Regarding the side of the negative electrode, similarly, taking into account the influence of the electric double layer that must be formed on the surface of the active substance of the negative electrode, the current I _Si silicon is divided into the current I _Si ^{C of the} capacitor and the current I _Si ^{EC of the} reaction, and the current I _{gra of} graphite is divided into capacitor current I _gra ^C and reaction current I _gra ^EC . After that, when calculating the overvoltages (η ₁ , η _Si , η _gra ) during the reaction, the corresponding currents (I _T ^EC , I _Si ^EC , I _gra ^EC ) of the reaction are used. Thus, when calculating the overvoltage during the reaction as the voltage that should be formed according to the lithium intercalation and desorption reaction, the influence of the current component (capacitor current) not provided for in the lithium intercalation and desorption is eliminated only by the charge and discharge of the electric double layer. Because of this, while the computational load of the ECU 100 may increase, the accuracy of the calculation of the overvoltage during the reaction can be further improved as compared to Embodiment 1.

Modification Example 2 of Embodiment 1

Negative electrode potential change

[0162] In general, in a lithium ion secondary battery, it is known that charge and discharge performance or thermal resistance of the secondary battery is likely to deteriorate due to “lithium deposition” in which lithium metal is deposited on the negative electrode. In the modification example 2 of Embodiment 1, this restriction applies to the input power of the battery (electric charge power to the battery 4), whereby “lithium deposition suppression control” is performed to protect the battery 4 from lithium deposition.

[0163] FIG. 15 is a conceptual diagram illustrating a change in potential _{of a} negative electrode V ₂ when lithium deposition occurs. In FIG. 15, the horizontal axis represents elapsed time, and the vertical axis represents the potential V _{2 of the} negative electrode based on lithium metal.

[0164] As shown in FIG. 15, the potential V _{2 of the} negative electrode decreases during charging of the battery 4. The greater the electric power of the charge in the battery 4, the greater the decrease in potential V _{2 of the} negative electrode. If the potential V _{2 of the} negative electrode falls below the lithium deposition potential (0 V based on lithium metal), lithium deposition can occur. Accordingly, in the modification example 2 of embodiment 1, the electric charge power in the battery 4 is suppressed from the moment when the negative electrode potential V ₂ reaches a predetermined potential above the lithium deposition potential, so that the negative electrode potential V ₂ is not equal to or less than 0 IN.

[0165] As described above, in modification example 2 of embodiment 1, since the negative electrode potential V ₂ can be calculated with high accuracy, lithium metal deposition on the surface of the negative electrode can be reliably suppressed and battery 4 can be adequately protected even in a battery system in which there is an effect of hysteresis.

Option 2 implementation

[0166] In Embodiment 1, a three-particle model for calculating various components of the potential of battery 4 with high accuracy is described (see FIGS. 5 and 6). In Embodiment 2, in order to reduce the computational load and storage capacity of the ECU 100, a configuration is described which uses a battery model that is more simplified than a three-particle model. In the battery model, as described below, the expressions for calculating the overvoltage (η ₁ , η _Si , η _gra ) during the reaction are simplified, and the diffusion equations are simplified. The general configuration of the battery system according to Embodiment 2 is identical to the general configuration (see FIG. 1) of the battery system 10 according to Embodiment 1.

Simplification of the three-particle model

[0167] With respect to the positive electrode particle 1, the diffusion equation (expression identical to expression (7) described above) shown in expression (45) described below is solved under the boundary condition (see expression (8)), due to which calculates the distribution of lithium concentrations in particle 1 of the positive electrode. Then, the surface lithium quantity θ _{1_surf} of the positive electrode particle 1 is calculated from the distribution of lithium concentrations in the positive electrode particle 1 (see expression (2) described above).

[0168] On the other hand, in Embodiment 2, diffusion of lithium in the silicon particle 21 is simplified. The same applies to graphite particle 22 (the diffusion equation for the silicon particle 21 and the diffusion equations (see expressions (9) - (16) described above) of the graphite particle 22 are omitted). In other words, it is assumed that the distribution of lithium concentrations for the silicon particle 21 is uniform, and it is assumed that the distribution of lithium concentrations for the graphite particle 22 is also uniform.

[0169] As described above, the open circuit potential ( _silicon open chain potential U _Si ) of the silicon particle 21 is determined according to the surface amount of lithium θ _{Si_surf} for the silicon particle 21 (see expression (18) described above). If the formulation of the diffusion equation is omitted provided that the distribution of lithium concentrations for the silicon particle 21 is uniform, then how to calculate the potential U _{Si of the} open silicon chain becomes a problem.

[0170] In general, the concentration of lithium in the active substance of the positive electrode and the concentration of lithium in the active substance of the negative electrode have such a relationship that if one of the concentrations of lithium increases, the other concentration of lithium decreases. In the battery model of Embodiment 2, the lithium concentration in the active substance of the negative electrode is calculated from the concentration of lithium in the active substance of the positive electrode (amount θ _{1 of} lithium of the particle 1 of the positive electrode) using the relationship.

[0171] In detail, in the battery model of Embodiment 2, a silicon particle 21 and a graphite particle 22 are considered as one mixed negative electrode particle 2. The mixed particle 2 of the negative electrode is not virtually divided into many regions, in contrast to the particle 1 of the positive electrode, and the distribution of lithium concentrations in the mixed particle 2 of the negative electrode is not taken into account. For this reason, the surface of the mixed negative electrode particle 2 and other fragments (inside the mixed negative electrode particle 2) do not differ, and the value obtained by normalizing the lithium concentration in the mixed negative electrode particle 2 is described as the amount θ _{2 of} lithium.

[0172] In case the ratio (ratio of capacity) regarding the capacitance of the particle 1 of the positive electrode to the mixed particles of the container 2 of the negative electrode is described as θ _rate, attitude θ _rate capacity is a fixed value and may be represented as the expression (46) described below, using the amount of θ ₁ lithium particles 1 of the positive electrode and the number θ _{2 of} lithium mixed particles 2 of the negative electrode. The values during the present calculation are joined by t in the upper right side (on the right shoulder), and the values during the previous calculation are joined by t (t-Δt) in the upper right side, thereby distinguishing between the values during the present calculation and the values during the previous calculation.

[0173] Then, the lithium quantity θ ₂ ^{t of the} mixed negative electrode particle 2 is calculated. The lithium quantity θ ₂ ^{t of the} mixed negative electrode particle 2 can be calculated using the lithium quantity θ ₁ ^t of the positive electrode particle 1 and the capacitance ratio θ _rate according to expression (47) described below. In expression (45), θ _{1_fix} is a reference value of a quantity θ _{1 of} lithium, and θ _{2_fix} is a value of a quantity θ _{1 of} lithium corresponding to a reference value (θ _{1_fix} ) θ ₁ . Both of these values are obtained through experiment.

[0174] Thus, while the lithium quantity θ _{2 of the} mixed negative electrode particle 2 is calculated from the lithium quantity θ ₁ of the positive electrode particle 1, the lithium quantity θ ₂ is also calculated using another method described below. Then, if the results of calculating the amount θ _{2 of} lithium of the two methods of calculation coincide with each other, it is assumed that the results of the calculation of the parameters are determined by valid. Further in this document, another method for calculating the amount θ _{2 of} lithium is described.

[0175] Since the silicon particle 21 and the graphite particle 22 have the same potential (V _Si = V _gra ), expression (48) described below is established (see expressions (27) and expression (28)).

[0176] In Embodiment 2, for simplicity, it is assumed that the overvoltage η _{Si of} silicon and the overvoltage η _{gra of} graphite are equal to each other (see expression (49) described below).

[0177] Then, expression (48) described above is simplified as expression (50) described below.

[0178] The _silicon open circuit potential U _Si on the left side of expression (50) is represented by the sum of U _{Si_sta} as the open circuit potential if surface stress σ _surf = 0 and the voltage ΔV _stress changes the open circuit potential due to surface mechanical stress σ _surf (see expressions (17) and (20)). Thus, expression (50) is further modified as expression (51) described below.

[0179] Although the second element on the left side of the expression (51) includes the surface mechanical stress σ _surf , the surface mechanical stress σ _{surf is} calculated according to the expression (52) described below, similarly to Embodiment 1.

[0180] A description is provided in expressions (30) and (31), and therefore, the detailed description is not repeated. On the other hand, if the surface mechanical stress σ _surf passes the yield strength, the surface mechanical stress σ _{surf is} calculated by σ _surf = σ _com or σ _surf = σ _ten instead of expression (52).

[0181] The lithium quantity θ ₂ ^{t of the} mixed negative electrode particle 2 can be calculated by the following method without using the capacitance θ _rate ratio. The total current I _T is introduced and output from the mixed negative electrode particle 2 between the previous calculation and the present calculation (while Δt expires), whereby the electricity value of the mixed negative electrode particle 2 is changed by I _T * Δt, and the lithium amount of the mixed particle 2 of the negative electrode changes from θ ₂ ^t-Δt to θ ₂ ^t . With respect to the magnitude (I _T * Δt) of the change in the amount of electricity of the mixed negative particle 2 and the magnitude (θ ₂ ^t -θ ₂ ^t-Δt ) of the change in the amount of lithium, as shown in expression (53) described below, such a condition (condition convergence), that the magnitude of (I _T * Δt) changes and the magnitude of (θ ₂ ^t -θ ₂ ^t-Δt ) changes coincide. On the left side of expression (53), the volume Vol _{2 of the} mixed particle 2 of the negative electrode, the limit concentration c _{Si, max} lithium for the silicon particle 21 and the limit concentration c _{gra, max} lithium for the graphite particle 22 are used.

[0182] Here, the lithium quantity θ _{2 of the} mixed negative electrode particle 2 is represented as expression (54) described below using the lithium quantity θ _Si and the limiting concentration c _{Si, max} lithium for the silicon particle 21 and the lithium amount θ _gra and the limiting concentration c _{gra, max} lithium for a graphite particle 22. Expression (55) is extracted by substituting expression (54) into expression (52).

[0183] Three parameters from the quantities θ _Si , θ _{gra of} lithium and surface mechanical stress σ _surf can be calculated by simultaneously formulating the above expressions. Then, the lithium quantity θ ₂ of the negative electrode mixed particle 2 calculated from the lithium quantity θ _Si for the silicon particle 21 and the lithium quantity θ _gra for the graphite particle 22 according to expression (54) is compared with the lithium quantity θ _{2 of the} mixed negative electrode particle 2 calculated from amount θ _{1 of} lithium according to expression (47). If the quantities θ _{2 of} lithium calculated using the two methods are in good agreement with each other (if the difference is less than the specified value), it is assumed that the results of calculating the quantities θ _Si , θ _{gra of} lithium and surface mechanical stress σ _surf are used ( for details, see the flowchart described below).

SOC Assessment Flow

[0184] FIG. 16 is a flowchart showing a processing sequence for evaluating an SOC of a battery 4 in Embodiment 2. Referring to FIG. 16, in S601, the ECU 100 receives the voltage VB of the battery 4 from the voltage sensor 71. The ECU 100 obtains the temperature TB of the battery 4 from the temperature sensor 72 and calculates the absolute temperature T from the temperature TB.

[0185] In S602, the ECU 100 calculates an exchange current density i _{0_1} of the positive electrode particle 1. The method for calculating the exchange current density i _{0_1} is identical to the method described in Embodiment 1. Thus, the ECU 100 calculates the exchange current density i _{0_1} from the surface lithium quantity θ _{1_surf} (see S703 of FIG. 17) calculated during the previous calculation and the absolute temperature T calculated on S601 by accessing a card (not shown), indicating the relationship between the correspondence of the density i _{0_1 of the} exchange current of the particle 1 of the positive electrode, the surface quantity θ _{1_surf of} lithium and the absolute temperature T.

[0186] In Embodiment 2, since overvoltages η _Si , η _gra are not calculated during the reaction, the calculation of the exchange current density i _{0_Si} of the silicon particle 21 and the exchange current density i _{0_Si} of the graphite particle 22 is also omitted.

[0187] The processing of S603-S605 is identical to the processing (see FIG. 12) of S103-S105 in Embodiment 1. On the other hand, the convergence calculation processing in S606 is different from the convergence calculation processing in S106 (see FIGS. 12 and 13) in Embodiment 1.

[0188] FIG. 17 is a flowchart showing convergence calculation processing (processing according to S606 of FIG. 16) in Embodiment 2. Referring to FIG. 17, in Embodiment 2, the convergence calculation processing is different from the convergence calculation processing (see processing according to S301-S303 of FIG. 13) in Embodiment 1 in that the following processing according to S701-S703 is performed only for the positive electrode particle 1 and not performed for the silicon particle 21 and the graphite particle 22.

[0189] In S701, the ECU 100 calculates an overvoltage η ₁ during the reaction of the positive electrode particle 1 from the exchange current density i _{0_1} of the positive electrode particle 1 and the absolute temperature T according to expression (4) described above. In addition, in S702, the ECU 100 calculates the distribution of lithium concentrations in the positive electrode particle 1 by solving the diffusion equation (expression (7) described above) under a given boundary condition (see expression (8)). Then, the ECU 100 calculates a surface lithium quantity θ _{1_surf} of the positive electrode particle 1 based on the distribution of lithium concentrations in the positive electrode particle 1 (S703, see expression (2) described above).

[0190] In S704, the ECU 100 calculates the lithium quantity θ ₂ ^{t of the} mixed negative particle 2 in the present calculation cycle from the lithium quantity θ ₁ ^t of the positive electrode particle 1 and the capacitance ratio (known value) θ _rate according to expression (47) described above .

[0191] In S705, the ECU 100 calculates a positive electrode open circuit potential U ₁ from a surface lithium quantity θ _{1_surf} calculated in S703 by referring to a card (not shown) indicating a relationship between a positive electrode open circuit potential U ₁ and a surface quantity θ _{1_surf} lithium.

[0192] In addition, the ECU 100 calculates the negative electrode open circuit potential U ₂ from the lithium quantity θ ₂ calculated in S704 by referring to a card (not shown) indicating the correspondence relationship between the negative electrode open circuit potential U ₂ and the surface quantity θ ₂ lithium.

[0193] In S706, the ECU 100 calculates the calculated voltage V _calc from the positive electrode potential V ₁ (= positive electrode open circuit potential U ₁ + positive electrode overvoltage η ₁ ), negative electrode open circuit potential U ₂ , voltage drop value (= I _T R _d ) due to the resistance Rd to direct current and the overvoltage ΔV _e of the salt concentration according to expression (56) described below. In expression (56), as described above, the overvoltage η _{Si of} silicon and the overvoltage η _{gra of} graphite are set equal to each other (see expression (49) described above). It should be understood that since although three overvoltages η ₁ , η _Si , η _gra during the reaction are separately calculated in Embodiment 1, only one overvoltage during the reaction is considered for battery 4 in Embodiment 2 (in other words, the proportion of overvoltages η _Si , η _gra at the reaction in the negative electrode is included in the overvoltage η ₁ during the reaction in the positive electrode).

[0194] Expression (56) is an expression identical to the expression that is established in the single-particle model in which the active substance of the positive electrode and the active substance of the negative electrode are simply integrated. Thus, in embodiment 2, it can be said that a single-particle model is used, in contrast to the three-particle model in embodiment 1.

[0195] In S707, the ECU 100 determines whether or not a condition (convergence condition) is established under which the total current I _T converges. In particular, the ECU 100 determines whether or not the difference (absolute value) between the calculated voltage V _calc calculated in S706 and the measured voltage V _meas determined by the voltage sensor 71, the set value PD (| V _calc -V _meas | < PD). If the absolute value of the difference between the calculated voltage V _calc and the measured voltage V _{meas is} less than the set value PD (in S707, “Yes”), the ECU 100 transfers the process to S709. If the absolute value of the difference is equal to or higher than the specified PD value (at S707, “No”), the ECU 100 updates the total current I _T according to Newton's law (S708) and returns the process to S701.

[0196] In S709, the ECU 100 performs “lithium amount calculation processing” to calculate the amount θ _{Si of} lithium in the silicon particle 21.

[0197] FIG. 18 is a flowchart showing lithium amount calculation processing (processing according to S709 of FIG. 17) in Embodiment 2. Referring to FIG. 18, in S801, the ECU 100 calculates a lithium change amount Δθ _{2 of the} mixed negative electrode particle 2. More specifically, the lithium change amount Δθ ₂ can be calculated by calculating the lithium quantity θ _{2 of the} mixed negative electrode particle 2 calculated from the lithium quantity θ ₁ of the positive electrode particle 1 and the ratio θ _{rate of the} capacitance according to expression (47) described above, twice during the previous calculation and during the present calculation and calculation of the difference between the quantities θ _{2 of} lithium.

[0198] In S802, the ECU 100 sets the lithium quantity θ _Si ^t for the silicon particle 21 during the present calculation, is set by summing the lithium change quantity Δθ _Si (see S810) updated according to Newton's law with the lithium quantity θ _Si ^t-Δt for the silicon particle 21 during the previous calculation (see expression (57) described below).

[0199] In S803, the ECU 100 calculates U _{Si_sta} as the open potential of the silicon particle 21 in the case of surface mechanical stress σ _surf = 0 from the amount θ _Si ^{t of} lithium by accessing a predetermined card (not shown).

[0200] In S804, the ECU 100 calculates a surface tensile stress σ _surf by performing surface tensile stress calculation processing.

[0201] FIG. 19 is a flowchart showing surface mechanical stress calculation processing in Embodiment 2. Referring to FIG. 19, the flowchart of the method differs from the processing of calculating the surface mechanical stress (see FIG. 14) in Embodiment 1 in that the calculation processing (S401) of the average lithium quantity θ _{Si_ave} for the silicon particle 21 is not included. Other types of processing are identical to the corresponding processing when processing the calculation of surface mechanical stress in option 1 implementation, and therefore, the description is not repeated. After the processing sequence ends, the process returns to the lithium amount calculation processing of FIG. 18.

[0202] Referring to FIG. 18 again, in S805, the ECU 100 calculates an ΔV _stress value of an open circuit potential change from a surface mechanical stress σ _surf according to expression (58) (expression identical to expression (17)) described below.

[0203] In S806, the ECU 100 calculates the _silicon open circuit potential U _Si by summing the ΔV _stress value of the open circuit potential change due to the surface mechanical stress σ _surf with U _{Si_sta} as the open circuit potential of the silicon particle 21 when the surface mechanical stress σ _surf = 0 (see expression (59) described below).

[0204] In S807, the ECU 100 calculates the lithium quantity θ _gra for the graphite particle 22 in such a way that a condition is established (see expression (60) described below) that the _silicon open potential U _Si and the graphite open potential U _gra are equal to each other. In particular, since the value of the left side of expression (60) is known by processing S805 and S806, it can be said that the potential value U _{gra of the} open graphite chain indicated on the right side of expression (60) is calculated. Accordingly, the lithium quantity θ _gra can be calculated from the graphite open circuit potential U _gra by referring to a map (not shown) indicating the relationship between the correspondence between the graphite open circuit potential U _gra and lithium quantity θ _gra .

[0205] In S808, the ECU 100 calculates a lithium quantity θ ₂ ^t from lithium quantities θ _Si , θ _gra according to expression (61) described below, which is set between lithium quantity θ _Si for silicon particle 21, lithium quantity θ _gra for graphite particle 22 and the quantity θ _{2 of} lithium of the mixed particle 2 of the negative electrode.

[0206] In S809, the ECU 100 calculates the difference (θ ₂ ^t -θ ₂ ^t-Δt ) between the lithium quantity θ ₂ ^t of the negative electrode mixed particle 2 during the present calculation and the lithium quantity θ ₂ ^{t-Δt of the} mixed negative electrode particle 2 during time of the previous calculation. The lithium quantity θ ₂ ^t-Δt during the previous calculation is temporarily stored in the storage device 100B for use in the present calculation. Then, the ECU 100 compares the difference (θ ₂ ^t -θ ₂ ^t-Δt ) calculated as described above with the lithium change amount Δθ ₂ calculated in S801.

[0207] If the error between the difference (θ ₂ ^t -θ ₂ ^t-Δt ) and the lithium change Δθ ₂ is equal to or higher than the threshold TH (in S809, "No"), the ECU 100 transfers the process to S810 and updates the value Δθ _Si changes in lithium (see S802) for use in calculating the amount of θ _Si lithium during the next calculation according to Newton's law. In case the error between the difference (θ ₂ ^t -θ ₂ ^t-Δt ) and the magnitude Δθ _{2 of} the lithium change is less than the threshold value TH (by S809, "Yes"), the ECU 100 uses the amount θ _{Si of} lithium for the silicon particle 21, calculated through the processing of calculating the amount of lithium, as the value applicable to the processing of the subsequent stage (when processing the evaluation of SOC) (S811). As a result, the lithium amount calculation processing (S709) is completed. After that, the convergence calculation processing (S606) is completed, and the potential calculation processing (S600) is also completed.

[0208] Returning to FIG. 16, the ECU 100 performs SOC evaluation processing (S200) after the potential calculation processing (S600) is completed. The SOC evaluation processing is identical to the SOC evaluation processing (see FIG. 12) in Embodiment 1, and therefore, the detailed description is not repeated.

[0209] As described above, even in Embodiment 2, similarly to Embodiment 1, the surface mechanical stress σ _{surf is} calculated through the surface mechanical stress calculation processing (S804), and the change amount ΔV _{stress of the} open-circuit potential of the silicon particle 21 is calculated based on the surface mechanical voltage σ _surf (S805). Thus, the negative electrode open-circuit potential U _{2 is} calculated taking into account the influence of hysteresis due to surface surfacing stress σ _surf , due to which it is possible to calculate the negative electrode open-circuit potential U ₂ with high accuracy. As a result, the accuracy of the SOC estimation of the battery 4 can also be improved.

[0210] In Embodiment 2, diffusion of lithium in the silicon particle 21 and the graphite particle 22 is simplified, and for this reason, the diffusion equation for the silicon particle 21 and the diffusion equation (see expressions (9) to (16)) relative to the graphite particle 22 fall. A silicon particle 21 and a graphite particle 22 are integrally regarded as a mixed negative electrode particle 2, the surface and the inner part of the mixed negative electrode particle 2 are not different from each other, and the lithium quantity θ ₂ as a parameter obtained by normalizing the concentration of lithium in the negative mixed particle 2 electrode used. Further, in Embodiment 2, with emphasis on the fact that there is a correlation between the lithium concentration in the positive electrode particle 1 and the lithium concentration in the negative electrode mixed particle 2, the lithium quantity θ _{2 of the} mixed negative electrode particle 2 is calculated from the lithium quantity θ ₁ particles of the positive electrode 1 using the ratio θ _rate containers on the container particles of the positive electrode 1 to the mixed particles of the negative electrode container 2 (see. the expressions (46) described above).

[0211] In Embodiment 2, lithium diffusion in the silicon particle 21 and the graphite particle 22 is not intentionally taken into account, thereby reducing the amount of computation (computational load, storage volume and computation time) of the ECU 100.

Option 3 implementation

[0212] In the lithium amount calculation processing (see FIG. 18) in Embodiment 2, such an advantage is described that the calculation (convergence calculation) for updating Δθ _Si is performed until the difference (θ ₂ ^t -θ ₂ ^{t- Δt} ) of the quantity θ _{2 of} lithium between the previous calculation and the present calculation does not converge on the value Δθ _{2 of the} change in lithium calculated by another method (see processing according to S809 and S810). In Embodiment 3, in order to further reduce the calculation volume of the ECU 100, a configuration is described in which the need for convergence calculation is eliminated by performing a linear approximation in order to calculate the lithium change value Δθ _Si for the silicon particle 21.

[0213] Embodiment 3 differs from Embodiment 2 in that another lithium quantity calculation processing is performed instead of lithium quantity calculation processing shown in FIG. 18. Other types of processing, i.e. potential calculation processing, SOC estimation processing (see FIG. 16), convergence calculation processing (see FIG. 17), and surface stress calculation processing (see FIG. 19) are identical to the corresponding processing in Embodiment 2, and in The strength of this description is not repeated. The general configuration of the battery system according to Embodiment 3 is identical to the general configuration (see FIG. 1) of the battery system 10 according to Embodiment 1.

Linear approximation of the distribution of lithium

[0214] The interval from the previous calculation to the present calculation is of the order of tens of milliseconds to hundreds of milliseconds and is quite short. In other words, the Δθ value of the lithium change (in more detail, the Δθ _Si value of the lithium change for the silicon particle) from the previous calculation to the present calculation is considered quite small. Accordingly, in the case where the Taylor series expansion is subjected to a silicon potential V _Si near a certain amount of lithium θ _Si ′, expression (62) described below is extracted.

[0215] In expression (62), if (θ _Si -θ _Si ') is negligible, terms of the second order and higher (θ _Si -θ _Si ') are negligible. Accordingly, expression (62) is modified as expression (63) described below.

[0216] In expression (63), if V _Si (θ _Si ) -V _Si (θ _Si ') = ΔV _Si and θ _Si -θ' = Δθ _Si , expression (64) is described below.

[0217] Since the open-circuit potential U _{Si (} open-circuit potential of silicon) of the silicon particle 21 is defined by the expression (65) described below, the expression (64) can be represented as the expression (66) described below.

[0218] With respect to the graphite particle 22, while there is no term including the surface mechanical stress σ _surf (the second term on the right side of the expression (65) described above), the magnitude ΔV _{gra of} the potential change of the graphite particle 22 can be represented as the expression ( 67), described below, through an identical calculation.

[0219] Since the silicon particle 21 and the graphite particle 22 constantly have the same potential (V _Si = V _gra ), with respect to the ΔV _Si change in the silicon potential and the ΔV _gra change in the graphite potential, such a relationship is established that both of the ΔV _Si change and the values ΔV _{gra of} change are equal to each other (ΔV _Si = ΔV _gra ). The relationship is represented as expression (68), described below, using expressions (66) and (67) described above.

[0220] Expression (69) described below can be extracted from expression (68) described above by performing appropriate modification of the expression.

[0221] If the Δc ₂ value _{of the} change in lithium concentration in the entire mixed negative electrode particle 2 is known, the Δc _Si value of the change in lithium concentration for the silicon particle 21 and the Δc _gra value of the change in lithium concentration for the graphite particle 22 can be calculated using expression (69) . The value Δc _{2 of the} change in the lithium concentration of the mixed negative electrode particle 2 is set by means of expression (70) described below.

[0222] The magnitude Δθ _{Si of the} change in lithium for the silicon particle 21 can be represented as expression (71) described below from expressions (69) and expression (70).

[0223] In the processing for calculating the amount of lithium (see FIG. 18) in Embodiment 2, the lithium change amount Δθ _Si for the silicon particle 21 is repeatedly updated until the difference (θ ₂ ^t -θ ₂ ^t-Δt ) between the amounts θ _{2 of} lithium of the mixed particle 2 of the negative electrode of two successive calculations does not converge on the value Δθ _{2 of the} change in lithium calculated from the number θ _{1 of} lithium and the ratio θ _{rate of the} capacitance of the particle 1 of the positive electrode. For this reason, a large amount of computation is requested for the ECU 100 to make the final decision regarding the magnitude Δθ _{Si of} lithium changes. In contrast, in Embodiment 3 as will be understood from the expression (71), the value Δθ _Si lithium changes to the silicon particles 21 is calculated from the value Δθ ₂ Lithium change (magnitude Δθ ₂ lithium change calculated from the amount of θ ₁ lithium relationship θ _rate capacity positive electrode particles 1) of the mixed negative electrode particles 2 in one calculation. Therefore, it is possible to significantly reduce the amount of computation in order to determine the magnitude Δθ _{Si of} lithium changes.

Lithium Amount Processing Processing Flow

[0224] FIG. 20 is a flowchart showing lithium amount calculation processing in Embodiment 3. In the flowchart of the method, the initial value of the quantity θ _{Si of} lithium for the silicon particle 21 is shown, and the initial value of the quantity θ _{gra of} lithium for the graphite particle and the quantities θ _Si , θ _{gra of} lithium are updated each time the processing sequence is repeatedly performed.

[0225] Referring to FIG. 20, the processing according to S1002-S1006 is the processing that is performed for the silicon particle 21, and the processing according to S1007-S1009 is the processing that is performed for the graphite particle 22. ECU 100 can change the sequence of these types of processing, can perform processing at S1007- S1009 for graphite particle 22 and thereafter may perform the processing of S1002-S1006 for silicon particle 21.

[0226] In S1001, similar to S801 (see FIG. 18) of the lithium quantity calculation processing in Embodiment 2, the ECU 100 calculates a lithium change amount Δθ _{2 of the} mixed negative electrode particle 2. Thus, the lithium change value Δθ ₂ is calculated by calculating the lithium quantity θ _{2 of the} mixed negative electrode particle 2 calculated from the lithium quantity θ ₁ and the ratio θ _{rate of the} capacitance of the positive electrode particle 1 according to the expression (47) described above twice during the previous computing and during the present calculation and computing the difference between the quantities θ _{2 of} lithium.

[0227] In S1002, a lithium quantity θ _Si ′ (= θ _Si ^t ) is calculated which changes with respect to the lithium quantity θ _Si (= θ _Si ^t-Δt ) of the silicon particle 21 during the previous calculation by a small amount. An insignificant amount is set equal to a sufficiently small amount so that the Taylor series expansion can be exposed to the silicon potential V _Si near the quantity θ _Si ′ of lithium (see expression (62) described above).

[0228] In S1003, the ECU 100 calculates the _silicon open circuit potential U _{Si_sta as the} open circuit potential of the silicon particle 21 when the surface stress σ _surf = 0. In more detail, the ECU 100 calculates the _silicon open circuit potential U _{Si_sta} corresponding to the lithium quantity θ _Si ′ calculated in S1001 by referring to a map (not shown) indicating the relationship between the correspondence between the lithium θ _Si amount for the silicon particle 21 and the open circuit potential U _{Si_sta} silicon.

[0229] In S1004, the ECU 100 performs surface tensile stress calculation processing to calculate a surface tensile stress σ _{surf of the} silicon particle 21. As described above, the surface tensile stress calculation processing is carried out together with the surface tensile stress calculation processing (see FIG. 19) in option 2 implementation.

[0230] In S1005, the ECU 100 calculates an ΔV _stress value of an open circuit potential change (= σ _surf Ω / F) based on a calculation result (surface stress σ _{surf of the} silicon particle 21) of the surface stress calculation calculation processing (see expression (58) described above).

[0231] In S1006, the ECU 100 calculates the _silicon open circuit potential U _Si by summing the voltage ΔV _{stress of the} change in the open circuit potential with the silicon open circuit potential U _{Si_sta} (result of the calculation in processing S1003) (see expression (59) described above).

[0232] In S1007, the ECU 100 calculates the partial differential ∂U _Si / ∂θ _{Si of the} potential U _{Si of the} open silicon circuit with the amount of silicon θ _Si = θ _Si '. The value of the calculated partial differential is used in the second term of the denominator of expression (75).

[0233] In S1008, similarly to the processing of S1001, the ECU 100 calculates the amount θ _gra 'of silicon, which changes relative to the amount θ _{gra of} lithium for the graphite particle 22 during the previous calculation by a small amount.

[0234] In S1009, the ECU 100 calculates an open graphite potential U _gra based on the lithium quantity θ _gra for the graphite particle 22 calculated in S1007. A map (not shown) prepared in advance is used in the calculation.

[0235] In S1010, similarly to processing S1006, the ECU 100 calculates the partial differential ∂U _gra / ∂θ _{gra of the} potential U _{gra of the} open graphite chain with the amount of silicon θ _gra = θ _gra '. The value of the calculated partial differential is used in the first terms of the numerator and the denominator of expression (75).

[0236] In S1011, the ECU 100 calculates a lithium change amount Δθ _Si based on the expression (75) described above. In particular, the magnitude Δθ _{2 of} the lithium change of the mixed negative electrode particle calculated in S1001, the partial differential ∂U _Si / ∂θ _{Si of the} potential U _{Si of the} open silicon circuit calculated in S1007, and the partial differential ∂U _gra / ∂θ _{gra of the} potential U _gra the open graphite circuit calculated in S1010 is substituted into expression (75), whereby the magnitude Δθ _{Si of the} change in lithium is calculated.

[0237] As described above, according to Embodiment 3, similarly to Embodiments 1 and 2, the surface mechanical stress σ _{surf is} calculated through the surface mechanical stress calculation processing (S1004), and the change amount ΔV _{stress of the} open-circuit potential of the silicon particle 21 is calculated based on the surface stress σ _surf (S1005). Thus, the potential _{Si Si of the} open silicon circuit is calculated taking into account the influence of hysteresis due to surface mechanical stress σ _surf , due to which it is possible to increase the accuracy of calculating the potential _{Si Si of the} open silicon chain and, as a result, increase the accuracy of the SOC estimation of the battery 4.

[0238] In Embodiment 3, expression (75) is extracted by modifying the expression using the product (c _{Si, max} * c _{gra, max} ) of the limiting lithium concentrations under such a condition that the silicon potential V _Si (see expression (63), described above) subjected to approximation (i.e., linear approximation), in which terms of the second order and higher are ignored after expansion in the Taylor series, and the graphite potential V _gra subjected to identical approximation are equal to each other (see expression (68), described above). The values are substituted into the terms of expression (75), due to which the calculation of convergence is not required, and the magnitude Δθ _{Si of the} change in lithium can be calculated through simple multiplication and division. Therefore, according to Embodiment 3, it is possible to further reduce the computational load and storage capacity of the ECU 100 compared to the lithium amount calculation processing in Embodiment 2.

[0239] The lithium deposition suppression control described in modification example 2 of Embodiment 1 may be combined with potential calculation processing in Embodiment 2 or may be combined with potential calculation processing in Embodiment 3. Thus, the negative electrode potential V ₂ can be calculated by a method in which the three-particle model in Embodiment 1 is more simplified, and the allowable electric charge power I _win can be calculated according to the calculated negative electrode potential V ₂ according to the flowchart, shown in FIG. 19.

[0240] In embodiments 1-3, (and in modification examples 1 and 2 of embodiment 1), an example is described in which a silicon-based material is used as an active substance of a negative electrode having a large change in volume with charge and discharge, is great. However, the active substance of the negative electrode having a large amount of volume change with charge and discharge is not limited to this. In this detailed description, “negative electrode active substance having a large change in volume” means a material having a large change in volume compared to a change in volume (approximately 10%) of graphite with charge and discharge. As such a negative electrode material of a lithium ion secondary battery, the tin compound (Sn, SnO and the like), the germanium (Ge) compound, or the lead (Pb) compound are approximately illustrated. The lithium-ion battery is not limited to a liquid system and may be a polymer system or a fully solid state system.

[0241] The battery to which the above-described potential calculation processing is applicable is not limited to a lithium-ion battery and may be other batteries (eg, a nickel-hydrogen battery).

[0242] The embodiment disclosed herein should be considered merely illustrative and not limiting in all respects. The scope of the present disclosure is defined by the claims, and not the above description of an embodiment, and is intended to include any modifications within the scope and spirit equivalent to the claims.

Claims (36)

1. A battery system comprising: a battery having a positive electrode including an active substance of a positive electrode, and a negative electrode including a first and second active substance of a negative electrode; and a control device configured to evaluate the internal state of the battery based on the model of the active substance of the battery, while: the amount of change in the volume of the first active substance of the negative electrode with a change in the number of charge carriers in the first active substance of the negative electrode exceeds the amount of change in the volume of the second active substance of the negative electrode with a change in the number of charge carriers in the second active substance of the negative electrode; the control device is configured to, provided that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential, calculate the number of charge carriers in the first active substance of the negative electrode based on the model of the first active substance; the control device is configured to calculate the magnitude of the change in the open circuit potential of the first active substance of the negative electrode based on the surface mechanical stress of the first active substance of the negative electrode, determined according to the number of charge carriers in the first active substance of the negative electrode; and the control device is configured to calculate the open-circuit potential of the negative electrode from the open-circuit potential and the magnitude of the change in the open-circuit potential of the first active substance of the negative electrode in a state in which surface mechanical stress is not generated in the first active substance of the negative electrode. 2. The battery system according to claim 1, in which: the control device is configured to, provided that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential, separately calculating the current flowing in the first active substance of the negative electrode and the current flowing in the second active substance of the negative electrode, through convergence calculation processing such that a predetermined convergence condition is established; the control device is configured to calculate the distribution of concentrations of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode by solving the diffusion equation under the boundary condition associated with the current flowing in the first active substance of the negative electrode and in the second active substance of the negative electrode; and the control device is configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode from the distribution of concentrations of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode. 3. The battery system according to claim 2, further comprising a voltage sensor configured to detect a voltage between the positive electrode and the negative electrode, wherein: the control device is configured to calculate the distribution of concentrations of charge carriers in the active substance of the positive electrode by solving the diffusion equation under the boundary condition associated with the current flowing in the active substance of the positive electrode; the control device is configured to calculate the number of charge carriers in the active substance of the positive electrode from the distribution of concentrations of charge carriers in the active substance of the positive electrode; the control device is configured to calculate the potential of the positive electrode based on the open-circuit potential of the active substance of the positive electrode, which should be determined according to the number of charge carriers in the active substance of the positive electrode; the control device is configured to calculate the potential of the negative electrode based on the potential of the open circuit of the negative electrode; and the control device is configured to calculate the current flowing in the first active substance of the negative electrode, with the condition that the potential difference between the potential of the positive electrode and the potential of the negative electrode coincides with the voltage detected by the voltage sensor as a condition for convergence. 4. The battery system according to claim 2 or 3, in which: the control device is configured to separate the current flowing in the first active substance of the negative electrode into a reaction current provided for in the introduction and desorption of charge carriers, and a capacitor current not provided in the introduction and desorption of charge carriers, and calculate overvoltage during the reaction of the first active substance of a negative the electrode by substituting the reaction current into the expression of the Butler-Volmer ratio; and the control device is configured to calculate the potential of the negative electrode from the potential of the open circuit of the negative electrode and overvoltage during the reaction of the first active substance of the negative electrode. 5. The battery system according to claim 1, in which: the control device is configured to calculate the total number of charge carriers in the first and second active substances of the negative electrode from the number of charge carriers in the active substance of the positive electrode according to the expression of the relationship in which the relationship that must be established between the number of charge carriers in the active substance of the positive electrode and the total number charge carriers in the first and second active substances of the negative electrode, is set using the ratio e bones about the capacity of the positive electrode to the negative electrode capacity; and the control device is configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode using the law of conservation of charge, which must be set between the value of the temporary change in the total number of charge carriers in the first and second active substances of the negative electrode and the current flowing in the active substance of the positive electrode. 6. The battery system according to claim 1, in which: the control device is configured to calculate the total number of charge carriers in the first and second active substances of the negative electrode from the number of charge carriers in the active substance of the positive electrode according to the expression of the relationship in which the relationship that must be established between the number of charge carriers in the active substance of the positive electrode and the total number charge carriers in the first and second active substances of the negative electrode, is set using the ratio e bones about the capacity of the positive electrode to the negative electrode capacity; and the control device is configured to calculate the number of charge carriers in the first active substance of the negative electrode and in the second active substance of the negative electrode from the value of the temporary change in the total number of charge carriers in the first and second active substances of the negative electrode according to a predetermined ratio expression approximating that the potential of the first active of the negative electrode substance varies linearly with the number of charge carriers in the first active ETS negative electrode, and approximating that of the second potential of the negative electrode active material varies linearly with the number of charge carriers in the second negative electrode active material. 7. The battery system according to any one of paragraphs. 1-3, in which: the battery is a lithium-ion battery; and the control device is configured to, if the potential of the negative electrode, which should be calculated from the potential of the open circuit of the negative electrode, falls below a predetermined potential, which is higher than the potential of lithium metal, to a greater extent suppress the electric power of the charge in the battery than if the potential of the negative electrode exceeds a given potential. 8. The battery system according to any one of paragraphs. 1-3, in which: the first active substance of the negative electrode is a silicon-based material; a the second active substance of the negative electrode is a carbon based material. 9. A method for evaluating the internal state of a battery, the battery having a positive electrode including the active substance of the positive electrode and a negative electrode including the first and second active substances of the negative electrode, wherein the amount of change in the volume of the first active substance of the negative electrode c a change in the number of charge carriers in the first active substance of the negative electrode exceeds the amount of change in the volume of the second active substance from a negative electrode with a change in the number of charge carriers in the second active substance of the negative electrode, the method being a method for assessing the internal state of a battery based on a model of the active substance, the method comprising the steps of: provided that the first active substance of the negative electrode and the second active substance of the negative electrode have the same potential, calculate the number of charge carriers in the first active substance of the negative electrode based on the model of the first active substance; calculating a change in the open circuit potential of the first active substance of the negative electrode based on the surface mechanical stress of the first active substance of the negative electrode, determined according to the number of charge carriers in the first active substance of the negative electrode; and the negative electrode open-circuit potential is calculated from the open-circuit potential and the magnitude of the change in the open-circuit potential of the first active substance of the negative electrode in a state in which surface mechanical stress is not generated in the first active substance of the negative electrode.

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