JP7115439B2 - SECONDARY BATTERY SYSTEM AND SECONDARY BATTERY INTERNAL STATE ESTIMATION METHOD - Google Patents

Description

The present disclosure relates to a secondary battery system and a secondary battery internal state estimation method.

In recent years, the spread of electric vehicles (for example, hybrid vehicles, electric vehicles, etc.) equipped with secondary batteries is progressing. In a secondary battery, there is a “charge curve” that is an SOC (State Of Charge)-OCV (Open Circuit Voltage) curve obtained when charging the secondary battery from a completely discharged state, and a “charge curve” that is obtained when the secondary battery is fully charged. There is a system in which the "discharge curve", which is the SOC-OCV curve obtained when the secondary battery is discharged from the discharged state, deviates significantly. Such divergence between the charge curve and the discharge curve is also called the existence of "hysteresis" in the secondary battery. For example, Japanese Patent Laying-Open No. 2015-166710 (Patent Literature 1) discloses a technique of estimating SOC from OCV in consideration of hysteresis of a secondary battery.

JP 2015-166710 A JP 2015-167127 A JP 2014-139521 A WO2010/005079

"In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon", V. A. Sethuraman et al., Journal of The Electrochemical Society, 157 (11) A1253-A1261 (2010)

In the present disclosure, the internal state of the secondary battery is estimated. Estimation of the internal state of the secondary battery includes calculating various potential components such as the positive electrode open-circuit potential, the positive electrode potential, the negative electrode open-circuit potential, and the negative electrode potential of the secondary battery. For example, the OCV of the secondary battery can be calculated from the positive electrode open-circuit potential and the negative electrode open-circuit potential of the secondary battery, and the SOC of the secondary battery can be estimated from the calculated OCV. Further, when the positive electrode potential of the secondary battery becomes lower than the predetermined lower limit potential or higher than the predetermined upper limit potential, a side reaction occurs at the positive electrode, which may deteriorate the positive electrode. Similarly, the negative electrode may deteriorate when the negative electrode potential is outside the predetermined potential range. Therefore, by improving the calculation accuracy of the single electrode potential (positive electrode potential or negative electrode potential) of the secondary battery, deterioration of the positive electrode and the negative electrode of the secondary battery can be suppressed.

In order to improve various characteristics of a secondary battery, the use of a negative electrode containing multiple negative electrode active materials (so-called composite negative electrode) has been studied. For example, the negative electrode of the lithium ion secondary battery disclosed in Japanese Patent Application Laid-Open No. 2015-167127 (Patent Document 2) includes a carbon-based material (more specifically, a carbon-based material such as nanocarbon or carbon nanotube) and a silicon-based material. including.

In a lithium-ion secondary battery, by using a negative electrode containing a silicon-based material, the full charge capacity can be increased compared to a case where a negative electrode that does not contain a silicon-based material is used. On the other hand, it is known that when the negative electrode contains a silicon-based material, the hysteresis of the SOC-OCV curve increases compared to when the negative electrode does not contain a silicon-based material (for example, JP-A-2014. -139521: See Patent Document 3).

In estimating the internal state of a secondary battery having a composite negative electrode, it is also conceivable to apply a conventional internal state estimation method. However, since the conventional estimation method does not consider the hysteresis of the secondary battery, the accuracy of estimating the internal state of the secondary battery may be relatively low. Therefore, in a secondary battery having a composite negative electrode, it is desirable to estimate the internal state of the secondary battery in consideration of hysteresis.

The present disclosure has been made to solve the above problems, and an object thereof is to provide a technique for improving the accuracy of estimating the internal state of a secondary battery having a negative electrode containing a plurality of negative electrode active materials. is.

(1) A secondary battery system according to an aspect of the present disclosure includes a secondary battery and a control device configured to estimate an internal state of the secondary battery based on an active material model of the secondary battery. A secondary battery has a positive electrode containing a positive electrode active material and a negative electrode containing first and second negative electrode active materials. The amount of change in volume of the first negative electrode active material due to the change in the amount of charge carriers in the first negative electrode active material is the volume change of the second negative electrode active material due to the change in the amount of charge carriers in the second negative electrode active material. Greater than the amount of change. The control device calculates the amount of charge carriers in the first negative electrode active material based on the first active material model under the condition that the first negative electrode active material and the second negative electrode active material are equipotential. calculate. The control device calculates the amount of change in open-circuit potential of the first negative electrode active material based on the surface stress of the first negative electrode active material that is determined according to the amount of charge carriers in the first negative electrode active material. The control device calculates the open-circuit potential of the negative electrode from the open-circuit potential of the first negative-electrode active material in a state in which no surface stress is generated in the first negative-electrode active material and the amount of change in the open-circuit potential.

The amount of change in volume of the first negative electrode active material due to the change in the amount of charge carriers in the first negative electrode active material (eg, silicon-based material) is the amount of charge carriers in the second negative electrode active material (eg, carbon-based material). is larger than the amount of change in volume of the second negative electrode active material due to the change in , the effect of hysteresis on the first negative electrode active material is greater than the effect of hysteresis on the second negative electrode active material. Focusing on this point, according to the configuration (1) above, the amount of charge carriers (for example, the amount of lithium) in the first negative electrode active material is calculated based on the first active material model, and the second A charge carrier amount in the second negative electrode active material is calculated based on the active material model. That is, since the amount of charge carriers is calculated separately for each negative electrode active material, it is possible to accurately reflect the influence of hysteresis on the estimation result of the internal state of the secondary battery (details will be described later). Therefore, it is possible to improve the estimation accuracy of the internal state of the secondary battery.

(2) Preferably, the control device controls the first negative electrode active material and the second negative electrode active material so that a predetermined convergence condition is established under the condition that the first negative electrode active material and the second negative electrode active material are equipotential. A current flowing through the material and a current flowing through the second negative electrode active material are separately calculated by convergence arithmetic processing. The controller calculates the concentration distribution of charge carriers in the first and second negative electrode active materials by solving a diffusion equation under boundary conditions for current flowing through the first and second negative electrode active materials, and the calculated The amount of charge carriers in the first and second negative electrode active materials is calculated from the concentration distribution.

(3) Preferably, the secondary battery system further includes a voltage sensor that detects voltage between the positive electrode and the negative electrode. The control device calculates the concentration distribution of charge carriers in the positive electrode active material by solving a diffusion equation under boundary conditions regarding the current flowing through the positive electrode active material, and calculates the amount of charge carriers in the positive electrode active material from the calculated concentration distribution. calculate. The control device calculates the potential of the positive electrode based on the open potential of the positive electrode active material, which is determined according to the amount of charge carriers in the positive electrode active material, and calculates the potential of the negative electrode based on the open potential of the negative electrode. The control device calculates the current flowing through the first negative electrode active material using the condition that the calculated potential difference between the positive electrode and the negative electrode matches the voltage detected by the voltage sensor as a convergence condition.

According to the configurations (2) and (3) above, the current flowing through the first negative electrode active material and the current flowing through the second negative electrode active material are calculated separately. As a result, the concentration distribution of the charge carriers in the first negative electrode active material based on the diffusion equation under the boundary conditions regarding the current flowing through the first negative electrode active material and the boundary conditions regarding the current flowing through the second negative electrode active material The concentration distribution of charge carriers in the second negative electrode active material based on the diffusion equation can be obtained with higher accuracy. Since the internal state (open-circuit potential and surface stress) of the secondary battery is calculated based on the concentration distribution of the charge carriers (described later), according to the above configurations (2) and (3), the internal state of the secondary battery can improve the estimation accuracy of

(4) More preferably, the control device distinguishes the current flowing through the first negative electrode active material into a reaction current involved in the insertion and desorption of charge carriers and a capacitor current not involved in the insertion and desorption of charge carriers. do. The control device calculates the reaction overvoltage of the first negative electrode active material by substituting the reaction current into the Butler-Volmer relational expression, and from the open circuit potential of the negative electrode and the reaction overvoltage of the first negative electrode active material, Calculate the potential of the negative electrode.

According to the above configuration (4), the effect of the electric double layer formed on the surface of the active material is taken into consideration, and the reaction current, which is the current component involved in the insertion and desorption of the charge carrier, A reaction overvoltage of the active material is calculated. By removing the capacitor current that is not involved in the insertion and desorption of charge carriers, the calculation accuracy of the reaction overvoltage is improved, so the calculation accuracy of the negative electrode potential (=negative electrode opening potential + reaction overvoltage) can be improved.

(5) Preferably, the control device establishes a relationship between the amount of charge carriers in the positive electrode active material and the total amount of charge carriers in the first and second negative electrode active materials. The total amount of charge carriers in the first and second negative electrode active materials is calculated from the amount of charge carriers in the positive electrode active material according to a relational expression defined using the ratio of capacity to capacity. The control device calculates the amount of charge carriers in the first and second negative electrode active materials by utilizing the law of conservation of charge amount established between the amount of change in the total amount over time and the current flowing through the positive electrode active material. do.

According to the configuration (5) above, the use of the above relational expression eliminates the need to solve the diffusion equations in the first and second negative electrode active materials. Also, the parameters used for the convergence calculation process can be reduced. Therefore, compared to the configurations (2) and (3) above, it is possible to reduce the amount of computation (computation load, memory size, etc.) of the control device (details will be described later).

(6) Preferably, the control device establishes a relationship between the amount of charge carriers in the positive electrode active material and the total amount of charge carriers in the first and second negative electrode active materials. The total amount of charge carriers in the first and second negative electrode active materials is calculated from the amount of charge carriers in the positive electrode active material according to a relational expression defined using the ratio of capacity to capacity. The control device approximates that the potential of the first negative electrode active material changes linearly according to the change in the amount of charge carriers in the first negative electrode active material, and the change in the amount of charge carriers in the second negative electrode active material. The amount of charge carriers in the first and second negative electrode active materials is calculated from the amount of time change of the total amount according to a predetermined relational expression that approximates that the potential of the second negative electrode active material changes linearly according to .

According to the above configuration (6), by using the above-mentioned predetermined relational expression using linear approximation, it is possible to further reduce the amount of calculation of the control device compared to the above configuration (5) (details are later).

(7) Preferably, the secondary battery is a lithium ion secondary battery. When the potential of the negative electrode calculated from the open-circuit potential of the negative electrode is lower than a predetermined potential higher than the potential of metallic lithium, the controller controls the secondary battery as compared with the case where the potential of the negative electrode exceeds the predetermined potential. Suppress the charging power to

With configuration (7) above, the charging power to the secondary battery is controlled based on the negative electrode potential estimated with high accuracy. Thereby, the negative electrode can be appropriately protected from deterioration of the negative electrode (deposition of lithium, which will be described later).

(8) Preferably, the first negative electrode active material is a silicon-based material. The second negative electrode active material is a carbonaceous material.

(9) A method for estimating the internal state of a secondary battery according to another aspect of the present disclosure estimates the internal state of a secondary battery having a positive electrode containing a positive electrode active material and a negative electrode containing first and second negative electrode active materials. Estimated based on the active material model. The amount of change in volume of the first negative electrode active material due to the change in the amount of charge carriers in the first negative electrode active material is the volume change of the second negative electrode active material due to the change in the amount of charge carriers in the second negative electrode active material. Greater than the amount of change. A secondary battery internal state estimation method includes first to third steps. The first step is to generate charge carriers in the first negative electrode active material based on a first active material model under the condition that the first negative electrode active material and the second negative electrode active material are equipotential. This is the step of calculating the quantity. The second step is a step of calculating the amount of change in open-circuit potential of the first negative electrode active material based on the surface stress of the first negative electrode active material determined according to the amount of charge carriers in the first negative electrode active material. be. The third step is a step of calculating the open circuit potential of the negative electrode from the open circuit potential of the first negative electrode active material in a state where the first negative electrode active material has no surface stress and the amount of change in the open circuit potential.

According to the method (9) above, similarly to the configuration (1) above, it is possible to improve the accuracy of estimating the internal state of the secondary battery.

According to the present disclosure, it is possible to improve the accuracy of estimating the internal state of a secondary battery having a negative electrode containing a plurality of negative electrode active materials.

1 is a diagram schematically showing an overall configuration of an electric vehicle equipped with a secondary battery system according to Embodiment 1; FIG. FIG. 4 is a diagram for explaining the configuration of each cell in more detail; 4 is a diagram showing an example of an SOC-OCV curve of a battery according to Embodiment 1; FIG. FIG. 4 is a diagram for explaining changes in negative electrode open-circuit potential due to charging and discharging when silicon simple substance is used as a negative electrode. It is a figure for demonstrating a three-particle model. FIG. 4 is a diagram for explaining a method of calculating lithium concentration distribution inside positive electrode particles, silicon particles, and graphite particles; FIG. 4 is a diagram for explaining parameters (variables and constants) used in a battery model; FIG. 4 is a diagram for explaining subscripts (subscripts) used in battery models; 4 is a functional block diagram of an ECU relating to potential calculation processing and SOC estimation processing in the first embodiment; FIG. FIG. 4 is a conceptual diagram for explaining the transition of the state of the battery on the silicon negative electrode surface lithium amount-silicon negative electrode open potential characteristic diagram. It is a figure for demonstrating the calculation method of the surface stress of a silicon active material. 4 is a flowchart showing a series of processes for estimating the SOC of a battery in Embodiment 1; 4 is a flowchart showing convergence calculation processing in Embodiment 1. FIG. 4 is a flowchart showing surface stress calculation processing of silicon particles. FIG. 4 is a conceptual diagram for explaining changes in negative electrode potential when lithium deposition occurs. 7 is a flowchart showing a series of processes for estimating the SOC of a battery in Embodiment 2; 10 is a flow chart showing convergence calculation processing in Embodiment 2. FIG. 10 is a flowchart showing lithium amount calculation processing in Embodiment 2. FIG. 10 is a flowchart showing surface stress calculation processing in Embodiment 2. FIG. 10 is a flowchart showing lithium amount calculation processing in Embodiment 3. FIG.

Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. The same or corresponding parts in the drawings are denoted by the same reference numerals, and the description thereof will not be repeated.

A configuration in which a secondary battery system according to an embodiment of the present disclosure is mounted on an electric vehicle will be described below as an example. An electric vehicle may be a hybrid vehicle (including a plug-in hybrid vehicle) or an electric vehicle. Also, the electric vehicle may be a hybrid vehicle in which a fuel cell and a secondary battery are combined. However, the application of the "secondary battery system" according to the present disclosure is not limited to vehicles, and may be stationary.

[Embodiment 1]
<Configuration of secondary battery system>
FIG. 1 is a diagram schematically showing an overall configuration of an electric vehicle equipped with a secondary battery system according to Embodiment 1. FIG. Referring to FIG. 1, vehicle 9 is a hybrid vehicle and includes motor generators 91 and 92, engine 93, power split device 94, drive shaft 95, drive wheels 96, and secondary battery system 10. Prepare. The secondary battery system 10 includes a battery 4 , a monitoring unit 6 , a power control unit (PCU) 8 , and an electronic control unit (ECU) 100 .

Each of motor generators 91 and 92 is an AC rotating electric machine, for example, a three-phase AC synchronous electric motor in which permanent magnets are embedded in the rotor. Motor generator 91 is mainly used as a generator driven by engine 93 via power split device 94 . Electric power generated by the motor generator 91 is supplied to the motor generator 92 or the battery 4 via the PCU 8 .

Motor generator 92 mainly operates as an electric motor to drive drive wheels 96 . Motor generator 92 is driven by receiving at least one of electric power from battery 4 and electric power generated by motor generator 91 , and the driving force of motor generator 92 is transmitted to drive shaft 95 . On the other hand, the motor generator 92 operates as a power generator to perform regenerative power generation when braking the vehicle or reducing acceleration on a downward slope. Electric power generated by the motor generator 92 is supplied to the battery 4 via the PCU 8 .

The engine 93 is an internal combustion engine that outputs power by converting combustion energy generated when a mixture of air and fuel is burned into kinetic energy of motion elements such as pistons and rotors.

The power split device 94 includes, for example, a planetary gear mechanism (not shown) having three rotating shafts of sun gear, carrier, and ring gear. Power split device 94 splits the power output from engine 93 into power for driving motor generator 91 and power for driving drive wheels 96 .

The battery 4 is an assembled battery including a plurality of cells (unit cells) 61 . Each cell 5 in this embodiment is a lithium ion secondary battery. The configuration of each cell 5 will be described with reference to FIG.

Battery 4 stores electric power for driving motor generators 91 and 92 and supplies electric power to motor generators 91 and 92 through PCU 8 . Also, the battery 4 is charged by receiving generated power through the PCU 8 when the motor generators 91 and 92 generate power.

Monitoring unit 6 includes a voltage sensor 71 and a temperature sensor 72 . A voltage sensor 71 detects the voltage of each cell 5 included in the battery 4, which is an assembled battery. A temperature sensor 72 detects the temperature of each cell 5 . Each sensor outputs its detection result to the ECU 100 .

Note that the voltage sensor 71 may detect the voltage VB using, for example, a plurality of cells 5 connected in series as a monitoring unit. Moreover, the temperature sensor 72 may detect the temperature TB by using a plurality of cells 5 arranged adjacent to each other as a monitoring unit. Thus, in this embodiment, the monitoring unit is not particularly limited. Therefore, for the sake of simplification of explanation, it will simply be described as "detecting the voltage VB of the battery 4" or "detecting the temperature TB of the battery 4". Similarly, the potential, OCV (Open Circuit Voltage), and SOC are described using the battery 4 as an execution unit for each process.

PCU 8 performs bidirectional power conversion between battery 4 and motor generators 91 and 92 in accordance with control signals from ECU 100 . PCU 8 is configured to be able to separately control the states of motor generators 91 and 92. For example, motor generator 91 can be in a regenerative state (power generation state) and motor generator 92 can be in a power running state. PCU 8 includes, for example, two inverters provided corresponding to motor generators 91 and 92, and a converter (both not shown) that boosts the DC voltage supplied to each inverter to the output voltage of battery 4 or higher. consists of

The ECU 100 includes a CPU (Central Processing Unit) 100A, memory (more specifically, ROM (Read Only Memory) and RAM (Random Access Memory)) 100B, and input/output ports (not shown) for inputting and outputting various signals. It is configured including ECU 100 estimates the state of battery 4 based on the signals received from each sensor of monitoring unit 6 and the programs and maps stored in memory 100B. A major process executed by the ECU 100 is _a “potential calculation process” for calculating various potential components including the positive electrode potential V1 and the negative electrode potential V2 of the battery ₄ . The ECU 100 "estimates the SOC of the battery 4 and controls charging and discharging of the battery 4 according to the result of the potential calculation process.

The positive electrode potential V1 is the potential of the positive electrode (see FIG. 2) when the battery ₄ is in an energized state. The negative electrode potential V2 is the potential of the negative electrode when the battery ₄ is in an energized state. On the other hand, when the battery 4 is in a non-energized state (no load state), the potential of the positive electrode is referred to as a positive open circuit potential (OCP: Open Circuit Potential) U1, and the potential of the negative electrode is referred to as _a negative open circuit potential _U2 . A potential that serves as a reference for these potentials (and other potentials to be described later) can be arbitrarily set, but in the present embodiment, the potential of metallic lithium is set as the reference potential.

FIG. 2 is a diagram for explaining the configuration of each cell 5 in more detail. The cell 5 in FIG. 2 is shown through its interior.

Referring to FIG. 2, cell 5 has a rectangular (substantially rectangular parallelepiped) battery case 51 . The upper surface of the battery case 51 is sealed with a lid 52 . One end of each of positive electrode terminal 53 and negative electrode terminal 54 protrudes outside from cover 52 . The other ends of the positive terminal 53 and the negative terminal 54 are connected to an internal positive terminal and an internal negative terminal (both not shown) inside the battery case 51, respectively. An electrode body 55 is housed inside the battery case 51 . The electrode body 55 is formed by stacking a positive electrode and a negative electrode with a separator interposed therebetween and winding the stack. The electrolyte is held in the positive electrode, the negative electrode, the separator, and the like.

The positive electrode, the separator and the electrolytic solution can use conventionally known structures and materials for the positive electrode, separator and electrolytic solution of lithium ion secondary batteries, respectively. As an example, the positive electrode can use a ternary material in which a portion of lithium cobaltate is replaced with nickel and manganese. A polyolefin (eg, polyethylene or polypropylene) can be used for the separator. The electrolytic solution contains an organic solvent (for example, a mixed solvent of DMC (dimethyl carbonate), EMC (ethyl methyl carbonate), and EC (ethylene carbonate)), a lithium salt (for example, LiPF ₆ ), and an additive (for example, LiBOB (lithium bis (oxalate)borate) or Li[PF ₂ (C ₂ O ₄ ) ₂ ]) and the like.

The structure of the cell is not particularly limited, and the electrode body may have a laminated structure instead of a wound structure. Moreover, not only the rectangular battery case, but also a cylindrical or laminated battery case can be used.

<Hysteresis of SOC-OCV curve>
Conventionally, a typical negative electrode active material for lithium ion secondary batteries has been a carbonaceous material such as graphite. In contrast, in the present embodiment, a composite material of a silicon-based material (Si or SiO) and graphite is employed as the negative electrode active material. This is because the inclusion of a silicon-based material increases the energy density of the battery 4 , thereby increasing the full charge capacity of the battery 4 . On the other hand, if the silicon-based material is included, the battery 4 may exhibit significant hysteresis.

FIG. 3 is a diagram showing an example of the SOC-OCV curve of the battery 4 according to the first embodiment. 3 and FIGS. 10 and 11, which will be described later, the horizontal axis represents the SOC of the battery 4, and the vertical axis represents the OCV of the battery 4. In FIG. In this specification, OCV refers to a state in which the voltage of the secondary battery is sufficiently relaxed, that is, in a state in which the concentration distribution of charge carriers in the active material (lithium concentration distribution in the present embodiment) is relaxed. means voltage.

FIG. 3 shows the charging curve CHG and the discharging curve DCH of the battery 4 . The charging curve CHG is obtained by repeating charging and resting (stopping charging) after the battery 4 is completely discharged. The discharge curve DCH is obtained by repeating discharge and rest (discharge stop) after the battery 4 is fully charged.

Specifically, the charging curve CHG can be obtained as follows. First, the fully discharged battery 4 is prepared and charged with an amount of electricity corresponding to an SOC of 5%, for example. After charging that amount of electricity, the charging is stopped, and the battery 4 is left for a period of time (for example, 30 minutes) until the polarization caused by the charging is eliminated. After the standing time has elapsed, the OCV of the battery 4 is measured. Then, the combination of the SOC (=5%) after charging and the measured OCV (SOC, OCV) is plotted in the figure.

Subsequently, charging of the battery 4 with an electric quantity corresponding to the next 5% SOC (charging from SOC=5% to 10%) is started. When the charging is completed, the OCV of the battery 4 is similarly measured after the standing time has passed. Then, from the OCV measurement result, the state of the battery 4 (combination of SOC and OCV) is plotted again. After that, the same procedure is repeated until the battery 4 is fully charged. A charging curve CHG can be obtained by performing such a measurement.

Similarly, the OCV of the battery 4 is measured at SOC in 5% increments while repeating the discharging and stopping of the discharging of the battery 4 until the battery 4 reaches the fully discharged state from the fully charged state. A discharge curve DCH can be obtained by performing such a measurement. The obtained charging curve CHG and discharging curve DCH are stored in memory 100B of ECU 100 .

The OCV on the charging curve CHG is also called "charging OCV", and the OCV on the discharging curve DCH is also called "discharging OCV". The charge OCV indicates the maximum value of OCV at each SOC, and the discharge OCV indicates the minimum value of OCV at each SOC. The state of the battery 4 is plotted either on the charge OCV, on the discharge OCV, or in the area surrounded by the charge OCV and the discharge OCV (hereinafter also referred to as "intermediate area A") ( (see FIGS. 10 and 11, which will be described later). The difference between the charge OCV and the discharge OCV (for example, the occurrence of a voltage difference of about 100 mV) indicates the presence of hysteresis in the battery 4 .

When a composite material containing both a silicon-based material and graphite is employed as the negative electrode active material, as shown in FIG. SOC region below). This value of Sc can be obtained by performing the above-described measurement in advance.

<Surface stress of negative electrode active material>
A possible cause of the hysteresis in the battery 4 is the change in volume of the negative electrode active material due to charging and discharging. The negative electrode active material expands as lithium (charge carrier) is inserted and contracts as lithium is desorbed. With such a volume change of the negative electrode active material, stress is generated on the surface and inside of the negative electrode active material, and the stress remains on the surface of the negative electrode even when the lithium concentration in the negative electrode active material is relaxed. The stress remaining on the surface of the negative electrode is the stress generated inside the negative electrode active material and the reaction acting on the negative electrode active material from the surrounding materials (binder, conductive aid, etc.) due to the volume change of the negative electrode active material. The stress is considered to be the state in which various forces including the force and the like are balanced in the whole system. This stress is hereinafter referred to as "surface stress σ _surf ".

The amount of change in volume of the silicon-based material due to the insertion or extraction of lithium is greater than the amount of change in volume of graphite. Specifically, when the minimum volume in a state where lithium is not inserted is used as a reference, the volume change (expansion coefficient) of graphite accompanying lithium insertion is about 1.1 times, The volume change amount of the silicon-based material is about four times at maximum. Therefore, when the negative electrode active material contains a silicon-based material, the surface stress _surf is greater than when the negative electrode active material does not contain a silicon-based material (when the negative electrode active material is graphite).

The surface stress σ _surf can be measured (estimated) through thin film evaluation. An example of a method for measuring the surface stress σ _surf will be briefly described. First, the change in the curvature κ of the negative electrode, which is a thin film deformed by the surface stress σ _surf , is measured. Curvature κ can be optically measured, for example, by using a commercially available radius of curvature measurement system. Then, by substituting the measured curvature κ and constants (Young's modulus, Poisson's ratio, thickness, etc.) determined according to the material and shape of the negative electrode (negative electrode active material and peripheral members) into the Stoney equation, the surface stress σ _surf can be calculated (for details of stress measurements see, for example, Non-Patent Document 1).

_The negative electrode potential V2 is determined by the surface state of the negative electrode active material. More specifically, the negative electrode potential V ₂ is determined by the amount of lithium (θ ₂ described below) on the surface of the negative electrode active material and the surface stress σ _surf (see formula (20) described later). When using a material such as a silicon-based material that can cause a large volume change with charging and discharging, as described below, the surface stress σ _surf changes as the amount of lithium in the negative electrode active material changes. The negative opening potential _U2 can rise or fall.

FIG. 4 is a diagram for explaining changes in the negative electrode open-circuit potential due to charging and discharging when simple silicon is used as the negative electrode. In FIG. 4, the horizontal axis represents the amount of lithium θSi on the surface of the negative electrode active material made of simple _silicon , and the vertical axis represents the negative electrode opening potential _USi . The same applies to FIGS. 10 and 11 to be described later.

First, in FIG. 4, the state of lithium amount θSi_SOC0 corresponding to SOC=0% of the battery using silicon simple substance for the negative electrode to the state of lithium amount _{θSi_SOC100} corresponding to SOC=100% is _shown for each several percent of SOC. An example of a change in the negative electrode open-circuit potential _USi when charging and stopping charging are repeated, and then discharging and stopping discharging are repeated every several percent of SOC from the state of the lithium amount _{θSi_SOC100} to the state of the lithium amount _{θSi_SOC0} is as follows. Schematically shown.

The results shown in FIG. 4 can be obtained by evaluating a cell containing a positive electrode and a negative electrode made of simple silicon with a reference electrode inserted therein. Alternatively, the results shown in FIG. 4 can be obtained by evaluating a half-cell comprising a silicon negative electrode and a lithium metal counter electrode.

During continuous charging, a compressive yield stress σ _com mainly occurs on the surface of the silicon negative electrode active material (the surface stress σ _surf becomes a compressive yield stress), and an ideal (virtual) surface stress σ _surf does not occur. The silicon negative electrode open potential U _Si is lowered compared to the state. An ideal state in which no surface stress σ _surf is generated is hereinafter also referred to as an “ideal state”. On the other hand, during continuous discharge, mainly the tensile yield stress σ _ten occurs on the surface of the silicon negative electrode active material (the surface stress σ _surf becomes the tensile yield stress), and the silicon negative electrode open potential U _Si rises compared to the ideal state. .

When the negative open-circuit potential U _Si decreases compared to the ideal state, OCV, which is the difference (=U ₁ −U _Si ) between the positive open-circuit potential U ₁ and the negative open-circuit potential U _Si , increases, while the negative open-circuit potential As U _Si increases, OCV decreases. As described above, when the negative electrode active material is a silicon-based material, the charge OCV and the discharge OCV diverge due to changes in the negative electrode open-circuit potential U _Si caused by the surface stress σ _surf . Therefore, by calculating the negative electrode open-circuit potential _USi in consideration of the influence of the surface stress σ _surf , it is possible to calculate the OCV with high accuracy. can be improved.

<Battery model>
Next, the battery model (active material model) used for estimating the internal state of the battery 4 in the first embodiment will be described in detail. In Embodiment 1, a "three-particle model" is adopted in which the positive electrode is represented by one active material (one particle) and the negative electrode is represented by two particles for each negative electrode active material.

FIG. 5 is a diagram for explaining the three-particle model. Referring to FIG. 5, in the three-particle model according to the first embodiment, the positive electrode of battery 4 is represented as one particle made of a positive electrode active material (for example, a ternary material). This particle is referred to as "positive electrode particle 1" for simplicity. On the other hand, the negative electrode is represented as two particles. One particle (first active material model) is composed of a silicon-based material in the negative electrode active material, and the other particle (second active material model) is composed of graphite in the negative electrode active material. For simplicity, the former particles are referred to as "silicon particles 21" and the latter particles as "graphite particles 22". The potential of the silicon particles 21 is described as "silicon potential V _Si ", and the potential of the graphite particles 22 is described as "graphite potential V _gra ".

FIG. 5 shows how the battery 4 is discharged. When the battery 4 is discharged, lithium ions (denoted as Li ⁺ ) are released at the interface between the silicon particles 21 and the electrolyte and at the interface between the graphite particles 22 and the electrolyte. The current flowing through the silicon particles 21 due to the release of lithium ions is referred to as "silicon current I _Si ", and the current flowing through the graphite particles 22 due to the release of lithium ions is referred to as "graphite current I _gra ". Also, the total current flowing through the battery 4 is represented by _IT . As can be seen from FIG. 5, in the three-particle model in this embodiment, the total current IT is divided between the _silicon current _ISi and the graphite current _Igra .

When the battery 4 is charged, the direction of the current is opposite to that shown in FIG. 5 (not shown), but the relationship in which the total current I _T is divided between the silicon current I _Si and the graphite current I _gra is equivalent. is. In this specification, the current during charging is negative, and the current during discharging is positive.

As described below, in the three-particle model according to Embodiment 1, the lithium concentration distribution inside each particle of positive electrode particle 1, silicon particle 21, and graphite particle 22 is calculated.

FIG. 6 is a diagram for explaining a method of calculating the lithium concentration distribution inside the positive electrode particles 1, the silicon particles 21, and the graphite particles 22. As shown in FIG. Referring to FIG. 6, in the three-particle model, the lithium concentration distribution in the circumferential direction of the polar coordinates is assumed to be uniform inside the spherical positive electrode particles 1, and only the lithium concentration distribution in the radial direction of the polar coordinates is taken into consideration. In other words, the internal model of the positive electrode particles 1 is a one-dimensional model in which the moving direction of lithium is limited to the radial direction.

The positive electrode particles 1 are virtually divided into N regions (N: a natural number equal to or greater than 2) in the radial direction. Each region is distinguished from each other by a subscript k (k=1 to N). The lithium concentration c _1k in the region k is expressed as a function of the position r _1k of the region k in the radial direction of the positive electrode particles 1 and the time t (see formula (1) below).

A detailed calculation method will be described later, but in the present embodiment, the lithium concentration c _s1k in each region k is calculated (that is, the lithium concentration distribution is calculated), and the calculated lithium concentration c _s1k is normalized. be. Specifically, as shown in formula (2), the ratio of the calculated value of the lithium concentration c _1k to the maximum value of the lithium concentration (hereinafter referred to as the “limit lithium concentration”) c _1,max is calculated for each region k. be done. The critical lithium concentration c _1,max is a concentration determined according to the type of positive electrode active material, and is known from literature.

The normalized value θ _1k is hereinafter referred to as the “local lithium amount” of region k. The local lithium amount θ _1k takes a value within the range of 0 to 1 depending on the lithium amount contained in the region k of the positive electrode particles 1 . Also, the local lithium amount θ _1N in the outermost peripheral region N (that is, the surface of the positive electrode particles 1) where k=N is referred to as “surface lithium amount θ 1 _—surf ”. Furthermore, as shown in the following formula (3), the sum of the products of the volume ν _1k of the region k (k = 1 to N) and the local lithium amount θ _1k is obtained, and the sum is the volume of the positive electrode particles 1 (positive active material The value divided by the volume of the material) is called the "average amount of lithium" and is denoted by θ _{1_ave} .

In FIG. 6, the particles representing the positive electrode active material (positive electrode particles 1) were described as an example, but the lithium concentration distribution and the local lithium amount (distribution) inside the particles representing the negative electrode active material (silicon particles 21 and graphite particles 22) The calculation method for is also the same. Note that the positive electrode particles 1, the silicon particles 21, and the graphite particles 22 may have different division numbers of regions, but in the present embodiment, the division number is N for simplification of explanation. and

FIG. 7 is a diagram for explaining parameters (variables and constants) used in the battery model. FIG. 8 is a diagram for explaining subscripts (subscripts) used in battery models. As shown in FIGS. 7 and 8, the subscript i is for distinguishing the three particles from each other, and is set to i=1, Si, or gra. When i=1, it means the value for the positive electrode particle 1, when i=Si, it means the value for the silicon particle 21, and when i=gra, the value for the graphite particle 22. means that In addition, among the parameters used in the battery model, those with subscript e mean values in the electrolyte, and those with subscript s mean values in the active material. do.

<Functional block>
Various potential components calculated by the potential calculation process can be used for various processes and controls. In the first embodiment, however, an "SOC estimation process" for estimating the SOC of the battery 4 based on the result of the potential calculation process is executed. The configuration for In the present embodiment, prior to estimating the SOC of the battery 4, the total current I _T is compared with the current flowing through the silicon particles 21 (silicon current I _Si ) and the current flowing through the graphite particles 22 (graphite current I _gra ). A series of processing (arithmetic processing by an iterative method) for determining whether to distribute to is repeatedly executed.

FIG. 9 is a functional block diagram of ECU 100 regarding potential calculation processing and SOC estimation processing in the first embodiment. Referring to FIG. 9, ECU 100 includes parameter setting unit 110, exchange current density calculation unit 121, reaction overvoltage calculation unit 122, concentration distribution calculation unit 131, lithium amount calculation unit 132, and surface stress calculation unit 133. , an open-circuit potential change amount calculator 134, an open-circuit potential calculator 135, a salt concentration difference calculator 141, a salt concentration overvoltage calculator 142, a convergence condition determiner 151, a current distributor 152, and an SOC estimator. 160 and .

The parameter setting unit 110 outputs parameters used in calculations by other functional blocks. Specifically, parameter setting unit 110 receives voltage VB of battery 4 from voltage sensor 71 and temperature TB of a battery module (not shown) from temperature sensor 72 . Parameter setting unit 110 sets voltage VB as measured voltage V _meas of battery 4 and converts temperature TB into absolute temperature T (unit: Kelvin). The measured voltage V _meas and absolute temperature T (or temperature TB) are output to other functional blocks. Since the absolute temperature T is output by many functional blocks, an arrow indicating transmission of the absolute temperature T is omitted in order to avoid complication of the drawing.

In addition, parameter setting section 110 outputs diffusion coefficients D _s1 , D _{s_Si} and D _{s_gra} to concentration distribution calculating section 131 . Diffusion coefficients D _s1 , D _{s_Si} , and D _{s_gra} are different values depending on local lithium amounts θ ₁ , θ _Si , and θ _gra (may be average lithium amount or surface lithium amount). is preferably set.

Although the details will be described later, in the arithmetic processing by the iterative method executed by the convergence condition determination unit 151 and the current distribution unit 152, the silicon current I _Si , the graphite current I _gra and the total current I _T are variably set parameters. Used. The parameter setting unit 110 receives the currents (I _Si , I _gra , I _T ) set by the current distribution unit 152 during the previous computation, and outputs these currents to other functional blocks as parameters used during the current computation. .

The exchange current density calculation unit 121 receives the absolute temperature T from the parameter setting unit 110, and also receives the surface lithium amount θ _{1_surf} of the positive electrode particles 1, the surface lithium amount θ _{Si_surf} of the silicon particles 21, and the graphite particles 22 from the lithium amount calculation unit 132. , the surface lithium amount θ _{gra_surf} is received. The exchange current density calculator 121 calculates the exchange current density i _{0_1} of the positive electrode particles 1, the exchange current density i _{0_Si} of the silicon particles 21, and the exchange current density i _{0_gra} of the graphite particles 22 based on parameters received from other functional blocks. calculate.

More specifically, 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 particles 1 and the cathode current density corresponding to the reduction reaction in the positive electrode particles 1 are equal. The exchange current density i _{0_1} has a characteristic that depends on the surface lithium amount θ _{1_surf} and the absolute temperature T of the positive electrode particles 1 . Therefore, by preparing in advance a map (not shown) that defines the correspondence between the exchange current density i _{0_1} , the surface lithium amount θ _{1_surf} , and the absolute temperature T, the surface lithium calculated by the lithium amount calculation unit 132 From the quantity θ _{1_surf} (described later) and the absolute temperature T, the exchange current density i _{0_1} can be calculated. The same applies to the exchange current density i _{0_Si} of the silicon particles 21 and the exchange current density i _{0_gra} of the graphite particles 22, so the description will not be repeated.

Reaction overvoltage calculation unit 122 receives absolute temperature T from parameter setting unit 110 , silicon current I _Si , graphite current I _gra and total current I _T from parameter setting unit 110 . Also, exchange current densities i ₀ — 1 , i 0 — Si and i 0 — _gra are _received from the exchange current density calculator 121 . Then, the reaction overvoltage calculation unit 122 calculates the reaction overvoltage (positive electrode overvoltage) η ₁ of the positive electrode particles 1, the silicon particle The reaction overvoltage (silicon overvoltage) η _Si of 21 and the reaction overvoltage (graphite overvoltage) η _gra of graphite particles 22 are calculated. The reaction overvoltage is also called an activation overvoltage, and is an overvoltage related to charge transfer reaction (insertion/desorption reaction of lithium). Each of the calculated reaction overvoltages η ₁ , η _Si and η _gra is output to the current distributor 152 .

Concentration distribution calculator 131 receives diffusion coefficient D _s1 of lithium in positive electrode particles 1 from parameter setting unit 110 . The concentration distribution calculation unit 131 calculates the lithium concentration distribution inside the positive electrode particles 1 by solving the following equation (7), which is a diffusion equation in a polar coordinate system in which the positive electrode active material (the positive electrode particles 1) is treated as a sphere, in time evolution. Calculate Since the amount of change in the lithium concentration on the surface of the positive electrode particle 1 (position r ₁ =R ₁ ) is _proportional to the total current IT, the boundary condition of diffusion equation (7) is set as shown in equation (8). .

Similarly for the graphite particles 22, the concentration distribution calculator 131 calculates the lithium concentration distribution inside the graphite particles 22 by solving the equation (9) in a time evolution manner under the boundary conditions shown in the following equation (10). do.

On the other hand, the diffusion equation of the polar coordinate system for the silicon particles 21 is expressed as in Equation (11). Equation (11) includes, in the second term on the right side, a diffusion term for considering the diffusion of lithium in the silicon particle 21 caused by the surface stress σ _surf . ) for (Eqs. (7) and (9)).

More specifically, the diffusion term derived from the surface stress σ _surf is expressed by Equation (12) using the hydrostatic stress σ _h (r) of the silicon particles 21 in the electrolyte. In equation (12), it is assumed that the negative electrode active material (silicon particles 21 in the battery model) is not plastically deformed, and the Young's modulus and Poisson's ratio of the silicon particles 21 within the elastic limit are represented by E and ν, respectively. Further, F _ex represents the total stress that the silicon particles 21 receive from the surrounding members.

Substituting Equation (12) representing the hydrostatic stress σ _h (r) into Equation (11), which is a diffusion equation, Equation (11) is transformed as follows (see Equation (13) below).

Equation (13) is transformed into Equation (15) below using the effective diffusion coefficient D _{s_Si} ^eff defined by Equation (14). Since the effective diffusion coefficient D _{s_Si} ^eff is a positive value, it can be seen from equation (15) that the surface stress σ _surf acts to accelerate lithium diffusion within the silicon particles 21 . It can also be seen that the influence of the surface stress σ _surf is determined according to the lithium concentration c _{s_Si} at each point in the silicon particle 21 (each lattice point where the diffusion equation is calculated).

Note that the boundary conditions of the diffusion equation (equation (14)) are also compared with the boundary conditions for the other two particles (positive particle 1 and graphite particle 22) (see equations (8) and (10)), the following equation (16) further includes a term dependent on the hydrostatic stress σ _h (r).

Thus, the concentration distribution calculator 131 calculates the lithium concentration distribution inside each of the three particles (positive electrode particle 1, silicon particle 21, and graphite particle 22). Each calculated lithium concentration distribution is output to the lithium amount calculation unit 132 .

The lithium amount calculation unit 132 receives the lithium concentration distribution (c _s1 , c _{s_Si} , c _{s_gra} ) inside each of the three particles from the concentration distribution calculation unit 131, calculates various lithium amounts, and outputs them to other functional blocks. .

Specifically, the lithium amount calculator 132 calculates the surface lithium amount _{θ1_surf} of the positive electrode particles 1 based on the lithium concentration distribution _cs1 of the positive electrode particles 1 (see formula (2)). Similarly, the lithium amount calculation unit 132 calculates the surface lithium amount θ _{Si_surf} of the silicon particles 21 based on the lithium concentration distribution c _{s_Si} of the silicon particles 21, and the graphite particles based on the lithium concentration distribution c _{s_gra} of the graphite particles 22. 22 surface lithium amount θ _{gra_surf} is calculated. The calculated surface lithium amounts θ _{1 — surf} , θ Si — surf and θ _{gra — surf} are output to the open-circuit potential calculator 135 .

In addition, the lithium amount calculator 132 calculates the average lithium amount _{θ1_ave} based on the lithium concentration distribution c _s1 of the positive electrode particles 1 according to Equation (3). Similarly, the lithium amount calculation unit 132 calculates the average lithium amount θ _{Si_ave} of the silicon particles 21 based on the lithium concentration distribution c _{s_Si} of the silicon particles 21, and the graphite particles based on the lithium concentration distribution c _{s_gra} of the graphite particles 22. 22 average lithium amount _{θgra_ave} is calculated. The calculated average lithium amount θ _{Si_ave} is output to the surface stress calculator 133 .

The surface stress calculator 133 calculates the surface stress σ _surf based on the average lithium amount θ _{Si_ave} from the lithium amount calculator 132 . A method for calculating the surface stress σ _surf will be described later in detail. The calculated surface stress σ _surf is output to the open-circuit potential change amount calculator 134 . The calculated external force F _ex is output to the concentration distribution calculator 131 .

The open-circuit potential change amount calculator 134 calculates the open-circuit potential change amount ΔV _stress based on the surface stress σ _surf from the surface stress calculator 133 . The open-circuit potential change amount ΔV _stress is the change amount of the open-circuit potential of the silicon particles 21 due to the surface stress σ _surf . A state in which no surface _stress σ _surf is generated is called an “ideal state”, and the open circuit potential of the silicon particles 21 in the ideal state is called an “ideal open circuit potential U _{Si — sta} ”. , the deviation amount of the open-circuit potential of the silicon particles 21 due to the surface stress σ _surf with reference to the ideal open-circuit potential U _{Si_sta} . The open-circuit potential change amount ΔV _stress is calculated from the surface stress σ _surf according to equation (17) using the volume change amount Ω of the silicon-based compound per mole of lithium and the Faraday constant F. The calculated open-circuit potential change amount ΔV _stress is output to the open-circuit potential calculator 135 .

The open-circuit potential calculation unit 135 calculates the open-circuit potential U1 of the positive electrode particles 1 based on the surface lithium amount _{θ1_surf} of the positive electrode particles ₁ from the lithium amount calculation unit 132 . More specifically, the positive electrode particle 1 is virtually divided into N regions in its radial direction, and the open potential U1 of the positive electrode particle ₁ is the surface of the positive electrode particle 1, which is the outermost peripheral region N. is determined according to the local lithium amount θ _1N (surface lithium amount θ _{1_surf} ) (see formula (18) below). Therefore, the open-circuit potential _{U1 can be calculated from the surface lithium amount θ1_surf by} preparing _a map (not shown) that defines the correspondence relationship between the open-circuit potential _U1 and the surface lithium amount θ1_surf through preliminary experiments. . Similarly for the graphite particles 22, the open-circuit potential calculation unit 135 calculates the open-circuit potential U _gra from the surface lithium amount θ _{gra_surf} of the graphite particles 22 by referring to a predetermined map (not shown) (the following formula ( 19)).

On the other hand, when calculating the open-circuit potential U _Si of the silicon particles 21, the influence of the surface stress σ _surf is considered. The open-circuit potential U _Si is calculated by adding the open-circuit potential change amount ΔV _stress to the open-circuit potential U _{Si_sta} of the silicon particles 21 in the state where the surface stress σ _surf does not occur, as shown in the following equation (20). be. Open-circuit potentials U ₁ , U _Si and U _gra calculated according to equations (18) to (20) are output to current distributor 152 .

As the battery 4 is charged and discharged, the concentration _ce of the lithium salt in the electrolyte changes, and a concentration gradient of the lithium salt may occur in the electrolyte. Then, a salt concentration overvoltage ΔV _e due to the concentration gradient of the lithium salt is generated between the positive electrode active material (positive electrode particles 1) and the negative electrode active material (silicon particles 21 and graphite particles 22), and the positive electrode potential V ₁ and the negative electrode potential It can affect _V2 .

The salt concentration difference calculator 141 calculates a lithium salt concentration difference ΔC _e between the positive electrode active material and the negative electrode active material. The lithium salt concentration difference Δc _e depends on the diffusion coefficient D _e of the electrolyte, the volume fraction ε _e of the electrolyte, the transport number t ₊ ⁰ of the lithium ion, and the current (total current I _T ). It can be calculated according to formulas (21) to (23). Equation (21), which is a recurrence formula, is repeatedly solved for each predetermined calculation cycle, and in Equations (21) to (23), the calculation cycle is represented by Δτ. Note that the parameters with a superscript (upper right) with t are those at the time of the current calculation, and the parameters with a superscript (t-Δτ) are those with the previous calculation. . The calculated concentration difference _Δce is output to the salt concentration overvoltage calculator 142 .

The salt concentration overvoltage calculator 142 calculates the salt concentration overvoltage ΔV _e from the lithium salt concentration difference _Δce calculated by the salt concentration difference calculator 141 according to the equation (24). The calculated salt concentration overvoltage ΔV _e is output to the current distributor 152 .

The convergence condition determination unit 151 and the current distribution unit 152 execute iterative arithmetic processing for calculating various potential components of the battery 4 . In this embodiment, Newton's method, which is one of representative iterative methods, is used. However, the type of iterative method is not limited to this, and other nonlinear equation solving methods such as the bisection method or the secant method may be used.

The calculations by the functional blocks described above use the currents (I _T , I _Si , I _gra ) flowing through the three particles set by the current distributor 152 at the time of the previous calculation. The convergence condition determination unit 151 receives the calculation result based on the current set at the previous calculation from other functional blocks. More specifically, the convergence condition determination unit 151 receives the reaction overvoltages η ₁ , η _Si , and η _gra from the reaction overvoltage calculation unit 122 (see formulas (4) to (6)), and releases them from the open-circuit potential calculation unit 135. Receives potentials U ₁ , U _Si , and U _gra (see formulas (18) to (20)), receives measured voltage V _meas (measured voltage of battery 4) from parameter setting unit 110, and salt concentration overvoltage calculator It receives the salt concentration overvoltage ΔV _e from 142 (see equation (24)). Although not shown, the convergence condition determination unit 151 receives the DC resistance _Rd from the parameter setting unit 110 (details will be described later).

_The convergence condition determination unit 151 determines the positive electrode potential V1, the negative electrode potential V2, and the voltage drop amount _{( = IT} R _d ) and the salt concentration overvoltage ΔV _e , the voltage of the battery 4 is calculated. The calculated voltage is described as “computed voltage V _calc ” to distinguish it from the measured voltage V _meas (value measured by the voltage sensor 71).

_The positive electrode potential V1 in equation (25) is calculated by equation (26). The negative electrode potential V ₂ is calculated as being equal to the silicon potential V _Si shown in Equation (27) and the graphite potential V _gra shown in Equation (28) (V ₂ =V _Si =V _gra ).

Then, the convergence condition determination unit 151 compares the calculated voltage V _calc and the measured voltage V _meas , and compares the silicon potential V _Si and the graphite potential V _gra to determine whether the convergence condition of the iterative method is satisfied. determine what Specifically, the convergence condition determining unit 151 determines that the calculated voltage V _calc and the measured voltage V _meas are substantially the same (the error between these voltages is less than the first predetermined value PD1), and the silicon potential A determination is made as to whether V _Si and graphite potential V _gra substantially match (whether the error between these voltages is less than a second predetermined value PD2). If the error (=|V _calc −V _meas |) between the calculated voltage V _calc and the measured voltage V _meas is equal to or greater than the first predetermined value PD1, or if the difference between the silicon potential V _Si and the graphite potential V _gra is equal to or greater than the second _{predetermined} value _PD2 , the convergence condition determination unit 151 determines that the convergence condition of the iterative method is not satisfied. Output to unit 152 .

When the current distribution unit 152 receives the determination result indicating that the convergence condition is not satisfied from the convergence condition determination unit 151, the currents (I _T , I _Si , I _gra ) flowing through the three particles are used for the next calculation. value. More specifically, the current distribution unit 152 uses an algorithm of Newton's method (which may be the bisection method, the secant method, etc.) to calculate the silicon current I _Si used in the previous calculation and the current calculation, and the total current Based on _IT , the silicon current _ISi and the total current _IT used in the next calculation are set. The remaining graphite current I _gra is calculated from the silicon current I _Si and the total current I _T by the relationship between the currents shown in equation (29). Each calculated current is output to parameter setting section 110 . Then, each updated current value will be used in the next calculation.

In this manner, convergence condition determination unit 151 and current distribution unit 152 ensure that the error between calculated voltage V _calc and measured voltage V _meas is less than first predetermined value PD1, and that silicon potential V _Si and graphite Arithmetic processing is performed repeatedly until the error with the potential V _gra becomes less than the second predetermined value PD2. When both of the above two errors are less than the corresponding predetermined values (PD1, PD2), it is assumed that the iterative calculation process has converged, and the convergence condition determination unit 151 determines the parameters necessary for SOC estimation (positive electrode open-circuit potential U ₁ , surface The amount of lithium θ _{i_surf} and the amount of change in open circuit potential ΔV _stress ) are output to SOC estimating section 160 .

The SOC estimator 160 estimates the SOC of the battery 4 based on various lithium amounts (θ 1 — _{ave , θ 1 — SOC0 ,} θ _{1 — SOC100} ) of the positive electrode particles 1 . This SOC estimation method will be described later.

<Calculation of surface stress>
Next, a method for calculating the surface stress σ _surf of the silicon active material will be described in detail. In the following, the combination of the lithium content θ _Si (for example, the average lithium content θ _{Si_ave} ) of the silicon material and the silicon open-circuit potential U _Si (θ _Si , U _Si ) is represented on the lithium content-silicon open-circuit potential characteristic diagram of the silicon material. The state in which the In particular, the state P at the time of the m (m is a natural number) computation is expressed as "P(m)". In this embodiment, the surface stress σ _surf is calculated by focusing on the transition of the state P.

FIG. 10 is a conceptual diagram for explaining the transition of the state P on the silicon negative electrode surface lithium amount-silicon negative electrode open potential characteristic diagram. In FIG. 10A, an example is shown where state P(m) is plotted on the charge curve (indicated by the dashed line).

When charging is continued from state P(m), state P(m+1) in the (m+1)th calculation cycle is maintained on the charging curve as shown in FIG. 10B.

On the other hand, when the state P(m) shown in FIG. 10A is discharged, as shown in FIG. plotted in the area between the curves (indicated by the dashed-dotted line). As the discharge continues, the state P(m+2) reaches the discharge curve, for example, in the (m+2)th calculation cycle (see FIG. 10D). If the discharge continues after that, the state P(m+3) is maintained on the discharge curve (see FIG. 10E).

FIG. 11 is a diagram for explaining a method of calculating the surface stress σ _surf of the silicon active material. FIG. 11 shows an example in which charging and discharging are performed in order of states P(1) to P(8).

More specifically, discharge starts from state P(1) on the discharge curve and continues to state P(3). States P(2) and P(3) during this period are maintained on the discharge curve. Then, in state P(3), switching from discharging to charging is performed. States P(4) and P(5) after the start of charging transit within the region between the charge curve and the discharge curve. Then state P(6) is plotted on the charge curve. State P remains on the charge curve while charging continues (see states P(7) and P(8)).

In states P(1) to P(3) plotted on the discharge curve, the surface stress σ _{surf yields} and is equal to the tensile yield stress σ _ten as shown in equation (30) below.

On the other hand, the surface stress σ _surf in states P(6) to P(8) on the charging curve yields at the compressive yield stress σ _com (see formula (31) below).

On the other hand, if state P is plotted neither on the charge curve nor on the discharge curve, i.e. if state P is plotted in the region between the charge and discharge curves (state P(4) , P(5)) is how to calculate the surface stress σ _surf . In the present embodiment, to calculate the surface stress σ _surf in such a region, the average lithium concentration c _{Si_ave} in the silicon particles 21 when the charging/discharging direction is switched, and the surface stress σ _surf at that time is used. Hereinafter, the average lithium concentration c _{Si_ave} in the state P when the charging/discharging direction is switched is described as “reference lithium concentration c _REF ”, and the surface stress σ _surf in the state P is described as “reference surface stress σ _REF ”. do.

In the example shown in FIG. 11, the state P when the charging/discharging direction is switched is the state P(3) when switching from discharging to charging. When calculating the states P(4) and P(5), the average lithium concentration c _{Si_ave} at the time of the state P(3) has already been calculated by the above formulas (8) to (10). Therefore, the calculated average lithium concentration c _{Si_ave} in the state P(3) is taken as the reference lithium concentration c _REF . Also, the reference surface stress σ _REF in the state P(3) is the tensile yield stress σ _ten (see the above formula (30)).

In the state P in the region between the charge curve and the discharge curve, between the lithium concentration difference (c _{Si_ave} −c _REF ), which is the average lithium concentration c _{Si_ave} minus the reference lithium concentration c _REF , and the surface stress σ _surf , There is a linear relationship represented by the following equation (32).

This linear relationship indicates that the amount of change in the surface stress σ _surf is the amount of change in the lithium content in the silicon particles 21 (lithium insertion into the silicon particles 21 or the amount of lithium released from the silicon particles 21).

The constant of proportionality α _c is a parameter that is determined according to the mechanical properties of the silicon-based compound, which is one of the negative electrode active materials, and the peripheral members, and can be obtained through experiments. More specifically, the constant of proportionality α _c can change according to the temperature of the negative electrode active material (≈temperature TB of battery 4) and the lithium content in the silicon active material (average lithium concentration c _{Si_ave} ). Therefore, the proportionality constant αc is obtained for each of various combinations of the temperature TB and the average lithium concentration _{cSi_ave} , and a map (or a relational expression ₎ showing the correlation between the temperature TB, the average lithium concentration _{cSi_ave} , and the proportionality constant _αc is obtained. be prepared. A map showing the correlation between either one of the temperature TB and the average lithium concentration c _{Si_ave} and the constant of proportionality α _c may be prepared.

Since the lithium concentration and the lithium amount can be replaced as in the above formula (2), the above formula (32) is transformed into the following formula (33) using the average lithium amount θ _{Si_ave} of the silicon particles 21. You may

A map showing the correlation between temperature TB and average lithium amount θ _{Si_ave} and proportionality constant α _c (or proportionality constant α _θ ) is prepared and stored in memory 100B of ECU 100 in advance. Therefore, by referring to the map, the constant of proportionality α _c can be calculated from the temperature TB (measured value by the temperature sensor 72) and the average lithium amount θ _{Si_ave} (estimated value at the time of the previous calculation). Then, by substituting the proportional constant α _c , the average lithium amount θ _{Si_ave} , the reference lithium amount θ _REF and the reference surface stress σ _REF into the above equation (33), the surface stress σ _surf in the above region can be calculated. can. Note that the calculation flow of the surface stress σ _surf will be described in detail with reference to FIG. 14 .

<SOC estimation flow>
FIG. 12 is a flow chart showing a series of processes for estimating the SOC of battery 4 in the first embodiment. Flowcharts shown in FIG. 12 and FIGS. 17 and 16, which will be described later, are called from a main routine (not shown) and repeatedly executed by ECU 100, for example, each time a predetermined period elapses. Each step (hereinafter abbreviated as "S") included in these flowcharts is basically realized by software processing by the ECU 100, but is realized by dedicated hardware (electrical circuits) fabricated within the ECU 100. good too.

Referring to FIG. 12, the processing of S101 to S107 described below corresponds to the single electrode potential calculation processing according to the first embodiment. First, in S<b>101 , the ECU 100 acquires the voltage VB of the battery 4 from the voltage sensor 71 and acquires the temperature TB of the battery 4 from the temperature sensor 72 . This voltage VB is used as the measurement voltage V _meas and the temperature TB is converted to absolute temperature T. Note that the absolute temperature T may be calculated from the temperature TB at the current time (at the time of the current calculation), or may be calculated from the weighted average of the temperature TB during the most recent predetermined period (for example, 30 minutes). good.

In S<b>102 , the ECU 100 calculates the exchange current density i _{0_1} of the positive electrode particles 1 . As described with reference to FIG. 9, the exchange current density i _{0_1} depends on the surface lithium amount θ _{1_surf} of the positive electrode particles 1 and the absolute temperature T. As shown in FIG. Therefore, the ECU 100 refers to a map (not shown) that defines the correspondence between the exchange current density i _{0_1} , the surface lithium amount θ _{1_surf} , and the absolute temperature T, so that the surface lithium amount θ _{1_surf} (see S203 in FIG. 13) and the absolute temperature T, the exchange current density _{i0_1} is calculated. The ECU 100 similarly calculates the exchange current density _{i0_Si} of the silicon particles 21 and the exchange current density _{i0_gra} of the graphite particles 22 by referring to the corresponding maps (not shown).

In S< _b >103 , the ECU 100 calculates the DC resistance Rd of the battery 4 . The direct current resistance _Rd is a resistance component when lithium ions and electrons move between the positive electrode active material and the negative electrode active material and the resistance component of the metal portion. _The DC resistance _Rd has characteristics that change depending on the absolute temperature T and the amount of lithium θ1. Therefore, by preparing in advance a map (not shown) that defines the correspondence relationship between the DC resistance _Rd and the absolute temperature T based on the measurement results of the DC resistance _Rd for each temperature, the absolute temperature T can be converted to the DC The resistance _Rd can be calculated.

In S104, the ECU 100 calculates the lithium ion concentration difference ΔC _e between the positive electrode active material and the negative electrode active material in the electrolytic solution (see formulas (21) to (23) above). Further, the ECU 100 calculates the salt concentration overvoltage ΔV _e from the lithium ion concentration difference ΔC _e according to the above equation (24) (S105). Since these processes have been described in detail with reference to FIG. 9, the description will not be repeated.

In S106, the ECU 100 divides the current (total current I _T ) flowing through the negative electrode active material into the current flowing through the silicon particles 21 (silicon current I _Si ) and the current flowing through the graphite particles 22 (graphite current I _gra ) in the three-particle model. Perform a convergence operation to distribute to .

In S200, the ECU 100 estimates the SOC of the battery 4 based on the result of the potential calculation process (SOC estimation process). This SOC estimation processing will be described later.

FIG. 13 is a flow chart showing the convergence calculation process (the process of S106 in FIG. 12) according to the first embodiment. Referring to FIG. 13, in S301, ECU 100 calculates reaction overvoltage η ₁ of positive electrode particles 1 from exchange current density i _{0_1} and absolute temperature T of positive electrode particles 1 according to the above equation (4). Further, the ECU 100 calculates the reaction overvoltage η Si of the silicon particles 21 from the exchange current density i _{0_Si} of the silicon particles 21 and the absolute temperature T according to the above equation (5), and calculates the reaction overvoltage η _Si of the graphite particles 22 according to the above equation (6). From the exchange current density i _{0 — gra} and the absolute temperature T, the reaction overvoltage η _gra of the graphite particles 22 is calculated.

In S302, for the positive electrode particles 1, the ECU 100 substitutes the diffusion coefficient _Ds1 of lithium in the positive electrode particles 1 into the above equation (7), which is the diffusion equation, and _calculates the boundary condition (the above equation (8 )), the lithium concentration distribution inside the positive electrode particles 1 is calculated by solving below. The diffusion coefficient D _s1 depends on the amount of lithium θ ₁ of the positive electrode particles 1 and the absolute temperature T. Therefore, the diffusion coefficient _Ds1 can be calculated from the amount of lithium _θ1 and the absolute temperature T at the time of the previous calculation using a map (not shown) prepared in advance.

For graphite particles 22, ECU 100 similarly calculates the lithium concentration distribution inside graphite particles 22 by solving diffusion equation (9) under boundary conditions (see equation (10) above). Further, the ECU 100 solves the diffusion equation (15) into which the effective diffusion coefficient D _{s_Si} ^eff (see formula (14)) is substituted under boundary conditions (see formula (16)), thereby determining the lithium Calculate the concentration distribution.

In S303, the ECU 100 calculates the surface lithium amount _{θ1_surf} of the positive electrode particles 1 based on the lithium concentration distribution inside the positive electrode particles 1 calculated in S302 (see the above formula (2)). Similarly, the ECU 100 calculates the surface lithium amount θ _{Si_surf} of the silicon particles 21 and calculates the surface lithium amount θ _{gra_surf} of the graphite particles 22 .

In S304, the ECU ₁₀₀ refers to a map (not shown) that defines the correspondence relationship between the open-circuit potential U1 of the positive electrode particles ₁ and the lithium amount θ1, so that the surface lithium amount _{θ1_surf} calculated in S303 is The open circuit potential _U1 is calculated (see formula (18)). Similarly, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the open-circuit potential U _gra of the graphite particles 22 and the lithium amount θ _gra , and calculates the open-circuit potential U _gra from the surface lithium amount θ _{gra_surf} . (See formula (19)).

In S305, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the open potential U _Si of the silicon particles 21 and the amount of lithium θ _Si in an ideal state where the surface stress σ _surf =0. The open-circuit potential U _{Si_sta} is calculated from the amount of lithium θ _{Si_surf} .

In S306, the ECU 100 executes a "surface stress calculation process" of the silicon particles 21 for calculating the surface stress σ _surf .

FIG. 14 is a flow chart showing the surface stress calculation process of the silicon particles 21 (the process of S306 in FIG. 13). Referring to FIG. 14, in S401, ECU 100 calculates average lithium amount θ _{Si_ave} in silicon particles 21 . The average lithium amount θ _{Si_ave} can be calculated in the same manner as the above formula (3) for the positive electrode particles 1 .

In S402, the ECU 100 reads out the reference lithium amount θ _REF and the reference surface stress σ _REF stored in the memory 100B up to the previous calculation (see the processing of S413 to be described later).

In S403, ECU 100 calculates proportionality constant _αθ from temperature TB of battery 4 and average lithium concentration _{cSi_ave} ( _{cSi_ave} at the time of the previous calculation) by referring to a map (not shown). It is also possible to calculate (predict by simulation) the constant of proportionality α _θ from physical properties (Young's modulus, etc.) of the negative electrode active material and peripheral members. However, it is not essential to make the constant of proportionality α _θ variable, and a predetermined fixed value may be used as the constant of proportionality α _θ .

In S404, the ECU 100 calculates the surface stress σ _surf from the proportionality constant α _θ and the average lithium amount θ _{Si_ave} according to the above equation (33) (S105). This surface stress σ _surf is tentatively calculated without considering the yield of the silicon active material, and the subsequent processing determines the surface stress σ _surf considering the yield of the silicon active material (main calculation). .

At S405, the ECU 100 compares the surface stress σ _surf provisionally calculated at S404 with the compressive yield stress σ _com . When the surface stress σ _surf is _equal to or less than the compressive yield stress σ _com after considering the sign of the surface stress σ _surf as shown in _FIG . If it is equal to or greater than the magnitude (YES in S444), the ECU 100 determines that the surface stress σ _surf is equal to the compressive yield stress σ _com (σ _surf =σ _com ), assuming that the negative electrode active material has yielded (S406). . That is, the surface stress σ _surf provisionally calculated in S404 is not used, and the compressive yield stress σ _com is used instead. Then, the ECU 100 updates the reference surface stress σ _REF by setting the compressive yield stress σ _com as a new reference surface stress σ _REF . Furthermore, the ECU 100 updates the reference lithium amount θ _REF by setting the average lithium amount θ _{Si_ave} calculated in S401 as the reference lithium amount θ _REF (S407).

On the other hand, if the surface stress σ _surf after considering the sign is greater than the compressive yield stress σ _com (when the magnitude of the surface stress σ _surf is less than the magnitude of the compressive yield stress σ _com ) (NO in S405) Then, the ECU 100 advances the process to S408 and compares the surface stress σ _surf and the tensile yield stress σ _ten .

When surface stress σ _surf is equal to or greater than tensile yield stress σ _ten (YES in S408), ECU 100 determines that the negative electrode active material has yielded and surface stress σ _surf is equal to tensile yield stress σ _ten . (S409). Then, the ECU 100 updates the reference surface stress σ _REF with the tensile yield stress σ _ten and updates the reference lithium amount θ _REF with the average lithium amount θ _{Si_ave} calculated in S401 (S410).

If the surface stress σ _surf is less than the tensile yield stress σ _ten in S408 (NO in S408), the surface stress σ _surf is within the intermediate region A between the compressive yield stress σ _com and the tensile yield stress σ _ten (σ _com <σ _surf <σ _ten ), and the negative electrode active material has not yielded. Therefore, the surface stress σ _surf tentatively calculated in S404 is adopted (S411). In this case, the reference surface stress σ _REF is not updated, and the reference surface stress σ _REF set at the previous calculation (or at the previous calculation) is maintained. Also, the reference lithium amount θ _REF is not updated (S412).

When one of the processes of S407, S410 and S412 is executed, the reference lithium amount θ _REF and the reference surface stress σ _REF are stored in memory 100B (S413). After that, the process is returned to S307 (see FIG. 13) of the convergence calculation process.

Referring to FIG. 13 again, in S307, the ECU 100 calculates the open-circuit potential change amount from the surface stress σ _surf according to the above equation (17) in order to take into account the effect of the surface stress σ _surf on the open-circuit potential U _Si of the silicon particles 21. ΔV _stress is calculated.

In S308, the ECU ₁₀₀ calculates the sum of the reaction overvoltage _η1 of the positive electrode particles ₁ and the positive electrode open potential U1 as the positive electrode potential V1 according to the above equation (26). Further, the ECU 100 calculates the silicon open-circuit potential U _Si by adding the open-circuit potential change amount ΔV _stress to the ideal open-circuit potential U _{Si_sta} of the silicon particles 21 (see the above formula (20)), and furthermore, the reaction of the silicon particles 21 The sum of the overvoltage η _Si and the silicon open potential U _Si is calculated as the silicon potential V _Si (see equation (27) above). Furthermore, the ECU 100 calculates the sum of the reaction overvoltage η _gra of the graphite particles 22 and the graphite open-circuit potential U _gra as the graphite potential V _gra (see formula (28) above).

In S309, the ECU ₁₀₀ determines the positive electrode potential V1, the negative electrode potential V2 ( _silicon potential _VSi or graphite potential _Vgra ), and the amount of voltage drop due to the DC resistance _Rd (= _{IT Rd} ) according to the above equation (25). ) and the salt concentration overvoltage ΔV _e , the calculated voltage V _calc is calculated.

In S310, the ECU 100 determines whether or not a condition (convergence condition) for convergence of the iterative computation in the convergence computation process is established. Specifically, the convergence condition includes first and second conditions. The first condition is that the absolute value of the difference between the calculated voltage V _calc calculated in S309 and the measured voltage V _meas obtained from the voltage sensor 71 in S101 (=|V _calc −V _meas |) is The condition is whether or not it is less than the first predetermined value PD1 (|V _calc −V _meas |<PD1). The second condition is whether or not the absolute value of the difference (=|V _Si −V _gra |) between the silicon potential V _Si and the graphite potential V _gra calculated in S308 is less than the second predetermined value PD2. (|V _Si −V _gra |<PD2).

The ECU 100 determines that the convergence condition is met when both the first and second conditions are met, and the convergence condition is not met when one of the first and second conditions is not met. I judge. If the convergence condition is not satisfied (NO in S310), ECU 100 updates currents I _T , I _Si and I _gra according to the algorithm of Newton's method (S311), and returns the process to S301. On the other hand, if the convergence condition is satisfied (YES in S310), ECU 100 returns the process to S200 of FIG.

Referring to FIG. 12 again, at S200, ECU 100 executes an SOC estimation process for estimating the SOC of battery 4 based on the result of the potential component calculation process. The SOC estimation process includes, for example, the processes of S201 and S202.

In S201, the ECU 100 acquires the average lithium amount _{θ1_ave} of the positive electrode particles 1 (the value calculated in the process of S302 where the convergence condition is satisfied), and obtains the known lithium amount _{θ1_SOC0} , stored in the memory 100B. _{Read θ1_SOC100} . The lithium amount _{θ1_SOC0} is the lithium amount of the positive electrode particles 1 corresponding to SOC=0%, and the lithium amount _{θ1_SOC100} is the lithium amount of the positive electrode particles 1 corresponding to SOC=100%.

Then, in S202, the ECU 100 estimates the SOC of the battery 4 based on the three amounts of lithium. Specifically, the SOC of the battery 4 can be calculated using the following equation (34).

As described above, the "three-particle model" is adopted in the first embodiment. In the three-particle model, the positive electrode is represented by positive electrode particles 1 and the negative electrode is represented by two particles, silicon particles 21 and graphite particles 22 . Then, the current flowing through the silicon particles 21 (silicon current I _Si ) and the current flowing through the graphite particles 22 (graphite current I _gra ) are distinguished, and the total current _{IT flowing through the negative electrode active material is the silicon current I Si and} the graphite current I _gra .

As described above, in Embodiment 1, by considering the current distribution between the silicon particles 21 and the graphite particles 22, the calculation accuracy of each parameter dependent on the current is improved compared to the case where the current distribution is not considered. do. Specifically, in the present embodiment, the silicon overvoltage η _Si (see equation (5)) determined according to the silicon current I _Si and the graphite overvoltage η _gra determined according to the graphite current I _gra (see equation (6) ) are calculated separately. As a result, the overvoltage generated according to the charge transfer reaction (insertion/desorption reaction of lithium) can be calculated more accurately than when the two are not distinguished.

In addition, the calculation accuracy of the lithium concentration distribution in each particle, which is calculated by solving the diffusion equations shown in Equations (7) to (16), is improved. Therefore, the calculation accuracy of the average lithium concentration c _{s_Si_ave} (or the average lithium amount θ _{Si_ave} ) in the silicon particles 21 is improved. Therefore, the calculation accuracy of the surface stress σ _surf that depends on the average lithium concentration c _{s_Si_ave} (or the average lithium amount θ _{Si_ave} ) is also improved (see formula (32) or (33) above). As a result, it is possible to accurately calculate the open-circuit potential change amount ΔV _stress indicating the amount of deviation of the open-circuit potential (silicon open-circuit potential U _Si ) of the silicon particles 21 due to the surface stress σ _surf (see formula (17)). As a result, the influence of the surface stress σ _surf can be accurately reflected in the negative electrode open _- circuit potential U2 (see the above equation (20)), so that the negative electrode potential V2 can also be calculated with _high accuracy. Furthermore, the SOC of the battery 4 can also be estimated with high accuracy (SOC estimation processing). As described above, according to Embodiment 1, the internal state of battery 4 can be estimated with high accuracy.

[Modification 1 of Embodiment 1]
In Modification 1 of Embodiment 1, a configuration will be described in which convergence arithmetic processing is executed in consideration of the influence of an electric double layer formed on the surface of the active material. In this variant, the total current _IT is further divided into current components involved in lithium production (insertion and extraction of lithium ions) and current components not involved in lithium production. Specifically, for the positive electrode particles 1, the current involved in lithium formation in the total current I _T is indicated as "reaction current I ₁ ^EC ", and the current not involved in lithium formation is indicated as "capacitor current I ₁ ^C ". Then, the following formula (35) is established.

Also, the capacitance of the electric double layer formed on the positive electrode particles ₁ is denoted as C1. _The capacitance C1 is known by prior evaluation. Capacitor current I ₁ ^C is represented by the following equation (36).

_A relationship similar to the above formula (26) is established among the positive electrode potential V1, the positive electrode open potential _U1 , and the reaction overvoltage _η1 (see the following formula (37)). However, in the positive electrode overvoltage η ₁ , a reaction current I ₁ ^EC is used instead of the total current I _T as shown in the following equation (38).

On the negative electrode side, the current (silicon current I _Si ) flowing through the silicon particles 21 is divided into a reaction current I _Si ^EC and a capacitor current I _Si ^C. Also, the current flowing through the graphite particles 22 (graphite current I _gra ) is classified into a reaction current I _gra ^EC and a capacitor current I _gra ^C. Then, the following formula (39) is established between these currents.

Capacitor current I _Si ^C is expressed by the following equation (40) using electrostatic capacitance C _Si formed in silicon particle 21 and negative electrode potential V ₂ . Capacitor current I _gra ^C is expressed by the following equation (41) using capacitance C _gra formed in graphite particles 22 and negative electrode potential V ₂ .

Also, the following equation (42) similar to the above equations (27) and (28) holds. Here too, the silicon current I _Si is replaced by the capacitor current I _Si ^EC in the silicon overvoltage η _Si , and the graphite current I _gra is replaced by the capacitor current I _gra ^EC in the graphite overvoltage η _gra (equation (43) and equation (44) below. )reference).

As described above, in Modification 1 of Embodiment 1, in consideration of the influence of the electric double layer formed on the surface of the positive electrode active material, the current flowing through the positive electrode particles 1 (total current I _T ) is the capacitor current A distinction is made between I ₁ ^C and reaction current I ₁ ^EC . Similarly, on the negative electrode side, considering the influence of the electric double layer formed on the surface of the negative electrode active material, the silicon current I _Si is classified into the capacitor current I _Si ^C and the reaction current I _Si ^EC , and the graphite current I _gra is differentiated into capacitor current I _gra ^C and reaction current I _gra ^EC . Corresponding reaction currents ( _{IT EC , I Si EC , I gra} ^EC ₎ ^are _used ^to calculate each reaction overvoltage (η ₁ , η _Si , η _gra ). In other words, in the calculation of the reaction overvoltage, which is the voltage generated in response to the lithium insertion/desorption reaction, the influence of the current component (capacitor current) that does not contribute to lithium insertion/desorption by simply charging and discharging the electric double layer is excluded. As a result, although the calculation load on the ECU 100 may increase as compared with the first embodiment, the calculation accuracy of each reaction overvoltage can be further improved.

[Modification 2 of Embodiment 1]
<Change in negative electrode potential>
It is generally known that in lithium-ion secondary batteries, there is a possibility that the charging/discharging performance of the secondary battery may deteriorate and the thermal resistance may deteriorate due to "lithium deposition" in which metallic lithium deposits on the negative electrode. It is In Modification 2 of Embodiment 1, "lithium deposition suppression control" for protecting battery 4 from lithium deposition is executed by setting a certain limit on battery input (charging power to battery 4). .

_FIG . 15 is a conceptual diagram for explaining changes in the negative electrode potential V2 when lithium deposition occurs. In FIG. 15, the horizontal axis represents the elapsed time, and the vertical axis represents the negative electrode potential V2 based _on metallic lithium.

As shown in FIG. 15, the negative electrode potential V2 decreases when the battery ₄ is charged. _The amount of decrease in the negative electrode potential V2 increases as the charging power to the battery 4 increases. Lithium deposition can occur when the negative electrode potential V2 is below the lithium deposition potential ( ₀ V relative to metallic lithium). Therefore, in the modification 2 of the first embodiment, charging power to the battery 4 is supplied from the point when the negative electrode potential V2 reaches a predetermined potential higher _than the lithium deposition potential so that the negative electrode potential V2 does not become ₀ V or less. suppress

As described above, in Modification 2 of Embodiment 1, the negative electrode potential V2 can be calculated with high accuracy. Therefore, deposition of metallic lithium on the surface of the negative electrode can be reliably suppressed even in a battery system affected by hysteresis. and the battery 4 can be appropriately protected.

[Embodiment 2]
In Embodiment 1, the three-particle model for calculating the various potential components of the battery 4 with high accuracy has been described (see FIGS. 5 and 6). In the second embodiment, a configuration using a battery model, which is a simplified version of the three-particle model, will be described in order to reduce the calculation load and memory capacity of ECU 100. FIG. In this battery model, the equation for calculating the reaction overvoltage (η ₁ , η _Si , η _gra ) is simplified and the diffusion equation is also simplified, as described below. The overall configuration of the secondary battery system according to Embodiment 2 is the same as the overall configuration of secondary battery system 10 according to Embodiment 1 (see FIG. 1).

<Simplification of the three-particle model>
The lithium concentration distribution in the positive electrode particles 1 is calculated by solving the diffusion equation (similar to the above equation (7)) shown in the following equation (45) for the positive electrode particles 1 under boundary conditions (see equation (8)). be. Then, the surface lithium amount _{θ1_surf} of the positive electrode particles 1 is calculated from the lithium concentration distribution inside the positive electrode particles 1 (see the above formula (2)).

On the other hand, in the second embodiment, the diffusion of lithium inside the silicon particles 21 is simplified. The same applies to the graphite particles 22 (the diffusion equation for the silicon particles 21 and the diffusion equation for the graphite particles 22 (see formulas (9) to (16) above) are omitted). In other words, the silicon particles 21 are assumed to have a uniform lithium concentration distribution, and the graphite particles 22 are assumed to have a uniform lithium concentration distribution.

As described above, the open-circuit potential of the silicon particles 21 (silicon open-circuit potential U _Si ) is determined according to the surface lithium amount θ _{Si_surf} of the silicon particles 21 (see formula (18) above). If the lithium concentration distribution of the silicon particles 21 is assumed to be uniform and the formulation of the diffusion equation is omitted, the problem is how to calculate the _silicon open-circuit potential USi.

In general, there is a relationship between the lithium concentration in the positive electrode active material and the lithium concentration in the negative electrode active material such that one increases and the other decreases. In the battery model according to Embodiment 2, this relationship is used to calculate the lithium concentration in the negative electrode active material from the lithium concentration in the positive electrode active material (the lithium amount θ ₁ in the positive electrode particles 1).

Specifically, in the battery model according to Embodiment 2, silicon particles 21 and graphite particles 22 are regarded as one mixed negative electrode particle 2 . Unlike the positive electrode particles 1, the mixed negative electrode particles 2 are not virtually divided into a plurality of regions, and the lithium concentration distribution inside them is not considered. Therefore, without distinguishing between the surface of the mixed negative electrode particles 2 and the rest (the inside of the mixed negative electrode particles 2), the normalized value of the lithium concentration in the mixed negative electrode particles ₂ is referred to as the lithium amount θ2.

If the ratio (capacity ratio) between the capacity of the positive electrode particles 1 and the capacity of the mixed negative electrode particles 2 (capacity ratio) is described as θ _rate , this capacity ratio θ _rate is a fixed value, but the lithium amount θ ₁ of the positive electrode particles 1 and the mixed negative electrode It can also be expressed by the following formula (46) using the lithium amount θ ₂ of the particles 2 . Note that the values in the current calculation are marked with t in the upper right (right shoulder), and the values in the previous calculation are marked with (t-Δt) in the upper right to distinguish between them.

Next, the lithium amount θ ₂ ^t of the mixed negative electrode particles 2 is calculated. The lithium content θ ₂ ^t of the mixed negative electrode particles 2 can be calculated using the lithium content θ ₁ ^t of the positive electrode particles 1 and the capacity ratio θ _rate according to the following formula (47). _In equation (45), _{θ1_fix} is the reference value of the lithium amount θ1, and _{θ2_fix} is the value of the lithium amount θ2 corresponding to the reference value _{( θ1_fix} ) of _θ1 . All of these values are obtained by experiments.

In this way, while the lithium amount θ2 of the mixed negative electrode particles ₂ is calculated from the lithium amount θ1 of the positive electrode particles ₁ , the lithium amount _θ2 is also calculated by another method described below. Then, if the calculation results of the lithium amount θ2 by the _two methods match, it is determined that the calculation result of each parameter is appropriate. Another method for calculating the amount of lithium θ ₂ will be described below.

Since the silicon particles 21 and the graphite particles 22 have the same potential (V _Si =V _gra ), the following formula (48) holds (see formulas (27) and (28)).

In the second embodiment, for simplification, it is assumed that the silicon overvoltage η _Si and the graphite overvoltage η _gra are equal to each other (see equation (49) below).

Then, the above equation (48) is simplified to the following equation (50).

The silicon open-circuit potential U _Si on the left side of equation (50) is represented by the sum of the open-circuit potential U _{Si_sta} when the surface stress σ _surf =0 and the open-circuit potential variation ΔV _stress due to the surface stress σ _surf . (See equations (17) and (20)). That is, equation (50) is further transformed into equation (51) below.

The second term on the left side of equation (51) includes surface stress σ _surf , and this surface stress σ _surf is calculated according to equation (52) below, as in the first embodiment.

Although detailed description will not be repeated because it has been described with equations (30) and (31), when the surface stress σ _{surf yields} , instead of equation (52), σ _surf =σ _com or The surface stress σ _surf is calculated by σ _surf =σ _ten .

Alternatively, the lithium amount θ ₂ ^t of the mixed negative electrode particles 2 can be calculated by the following method without using the capacity ratio θ _rate . By inputting/outputting the total current I _T to the mixed negative electrode particles 2 between the time of the previous calculation and the time of the current calculation (while Δt elapses), the quantity of electricity of the mixed negative electrode particles 2 changes by I _T ×Δt. Along with this, the amount of lithium in the mixed negative electrode particles 2 changes from θ ₂ ^t−Δt to θ ₂ ^t . Between the amount of change in the amount of electricity (I _T ×Δt) and the amount of change in the amount of lithium (θ ₂ ^t −θ ₂ ^t−Δt ) of the mixed negative electrode particles 2, as shown in the following formula (53), both There is a condition (constraint condition) that In the left side of equation (53), the volume Vol ₂ of the mixed negative electrode particles 2, the critical lithium amount cSi,max of the silicon particles 21, and the critical lithium amount _{cgra,max of} the graphite particles 22 are used.

Here, the lithium amount θ ₂ of the mixed negative electrode particles 2 is obtained by combining the lithium amount θ _Si and the limit lithium concentration c _Si,max of the silicon particles 21 and the lithium amount θ _gra and the limit lithium concentration c _gra,max of the graphite particles 22. It is represented by the following formula (54) using Substituting equation (54) into equation (52) leads to equation (55).

By combining the above equations, the three parameters of the lithium amount θ _Si , θ _gra and the surface stress σ _surf can be calculated. Then, the lithium amount θ ₂ of the mixed negative electrode particles 2 calculated according to the formula (54) from the lithium amount θ _Si of the silicon particles 21 and the lithium amount θ _gra of the graphite particles 22, and the lithium amount θ ₁ calculated according to the formula (47). The lithium amount θ ₂ of the mixed negative electrode particles 2 obtained is compared. When the lithium amounts θ ₂ calculated by these two methods are in good agreement (when the difference is less than a predetermined value), the calculation results of the lithium amounts θ _Si and θ _gra and the surface stress σ _surf shall be adopted. (See flow chart below for details).

<SOC estimation flow>
FIG. 16 is a flow chart showing a series of processes for estimating the SOC of battery 4 in the second embodiment. Referring to FIG. 16 , in S<b>601 ECU 100 acquires voltage VB of battery 4 from voltage sensor 71 . The ECU 100 also obtains the temperature TB of the battery 4 from the temperature sensor 72 and calculates the absolute temperature T from the temperature TB.

In S<b>602 , the ECU 100 calculates the exchange current density i _{0_1} of the positive electrode particles 1 . The method for calculating the exchange current density _{i0_1} is the same as the method described in the first embodiment. That is, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the exchange current density i _{0_1} of the positive electrode particles 1, the surface lithium amount θ _{1_surf} , and the absolute temperature T, so that the surface The exchange current density i _{0_1} is calculated from the amount of lithium θ _{1_surf} (see S703 in FIG. 17) and the absolute temperature T calculated in S601.

In the second embodiment, since the reaction overvoltages η _Si and η _gra are not calculated, the calculation of the exchange current density i _{0_Si} of the silicon particles 21 and the exchange current density i _{0_gra} of the graphite particles 22 is also omitted.

The processing of S603-S605 is equivalent to the processing of S103-S105 (see FIG. 12) in the first embodiment. On the other hand, the convergence calculation process in S606 differs from the convergence calculation process S106 (see FIGS. 12 and 13) in the first embodiment.

FIG. 17 is a flowchart showing convergence calculation processing (processing of S606 in FIG. 16) according to the second embodiment. Referring to FIG. 17, in the second embodiment, the following processing of S701 to S703 is performed only on positive electrode particles 1, and not performed on silicon particles 21 and graphite particles 22. This is different from the convergence calculation process in form 1 (see the processes of S301 to S303 in FIG. 13).

In S701, the ECU 100 calculates the reaction overvoltage _η1 of the positive electrode particles 1 from the exchange current density _{i0_1} and the absolute temperature T of the positive electrode particles 1 according to the above equation (4). Further, in S702, the ECU 100 calculates the lithium concentration distribution inside the positive electrode particles 1 by solving the diffusion equation (equation (7) above) under predetermined boundary conditions (see equation (8)). Then, the ECU 100 calculates the surface lithium amount _{θ1_surf} of the positive electrode particles 1 based on the lithium concentration distribution inside the positive electrode particles 1 (S703, see formula (2) above).

In ^S704 , the _{ECU 100} calculates the mixed negative electrode particle 2 The amount of lithium θ ₂ ^t is calculated.

In S705, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the positive electrode open potential _{U1 and the surface lithium amount θ1_surf ,} thereby determining the positive electrode open potential U1 from the surface lithium amount _{θ1_surf} calculated in S703. Calculate the potential _U1 .

Further, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the negative electrode open _- circuit potential U2 and the surface lithium amount θ2, thereby calculating the negative electrode open _- circuit potential U from the lithium amount _θ2 calculated in S704. ₂ is calculated.

In S706, the ECU 100 controls 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 , and DC resistance R _d The calculated voltage V _calc is calculated from the voltage drop amount (= _IT R _d ) due to and the salt concentration overvoltage ΔV _e . Equation (56) assumes that the silicon overvoltage η _Si and the graphite overvoltage η _gra are equal as described above (see equation (49) above). This is because the three reaction overvoltages η ₁ , η _Si , and η _gra are separately calculated in the first embodiment, whereas in the second embodiment only one reaction overvoltage for the battery 4 is considered. (In other words, the contributions of the reaction overvoltages η _Si and η _gra at the negative electrode are included in the reaction overvoltage η ₁ at the positive electrode).

Note that the formula (56) is similar to the formula that holds in a one-particle model in which the positive electrode active material and the negative electrode active material are simply integrated. In other words, it can be said that the second embodiment adopts the one-particle model in contrast to the three-particle model in the first embodiment.

In _S707 , ECU 100 determines whether or not a condition (convergence condition) for convergence of total current IT is established. Specifically, the ECU 100 determines whether the difference (absolute value) between the calculated voltage V _calc calculated in S706 and the measured voltage V _meas detected by the voltage sensor 71 is less than a predetermined value PD ( | _Vcacl - _Vmeas |<PD). If the absolute value of the difference between calculated voltage V _calc and measured voltage V _meas is less than predetermined value PD (YES in S707), ECU 100 advances the process to S709. On the other hand, if the absolute value of the difference is greater than or equal to predetermined value PD (NO in S707), ECU 100 updates total current IT by Newton's method ( _S708 ), and returns the process to S701.

In S<b>709 , the ECU 100 executes a “lithium amount calculation process” for calculating the lithium amount θ _Si in the silicon particles 21 .

FIG. 18 is a flow chart showing the lithium amount calculation process (the process of S709 in FIG. 17) in the second embodiment. Referring to FIG. 18 , in S801, ECU 100 calculates lithium change amount Δθ2 of mixed negative electrode particles ₂ . More specifically, the lithium content θ 2 of the mixed negative electrode particles 2 calculated from the lithium content θ ₁ of the positive electrode particles 1 and the capacity ratio θ _rate according to the above equation (47) is ₂ between the previous calculation and the current calculation. times and taking the difference between the two, the amount of change in lithium Δθ ₂ can be calculated.

In S802, the ECU 100 adds the amount of lithium change Δθ _Si (see S810) updated by Newton's method to the lithium amount θ _Si ^t−Δt of the silicon particles 21 at the time of the previous calculation, thereby obtaining the silicon particles at the time of the current calculation. 21 lithium amount θ _Si ^t is set (see the following formula (57)).

In S803, the ECU 100 calculates U _{Si_sta} , which is the open potential of the silicon particles 21 when the surface stress σ _surf =0, from the lithium amount θ _Si ^t by referring to a predetermined map (not shown).

In S804, ECU 100 calculates surface stress σ _surf by executing surface stress calculation processing.

FIG. 19 is a flowchart showing surface stress calculation processing according to the second embodiment. Referring to FIG. 19, this flowchart differs from the surface stress calculation process (see FIG. 14) in Embodiment 1 in that the calculation process (S401) of the average lithium amount _{θSi_ave} of silicon particles 21 is not included. Other processing is the same as the processing corresponding to the surface stress calculation processing in Embodiment 1, so description thereof will not be repeated. After completing the series of processes, the process is returned to the lithium amount calculation process of FIG.

Referring to FIG. 18 again, in S805, ECU 100 calculates open-circuit potential change amount ΔV _stress from surface stress σ _surf according to the following equation (58) (the same equation as equation (17)).

In S806, the ECU 100 calculates the silicon open-circuit potential U _Si by adding the open-circuit potential variation ΔV _stress due to the surface stress σ _surf to U _{Si_sta} , which is the open-circuit potential of the silicon particles 21 when the surface stress σ _surf =0. (see formula (59) below).

In S807, the ECU 100 calculates the lithium amount θ _gra of the graphite particles 22 so as to satisfy the condition that the silicon open-circuit potential U _Si and the graphite open-circuit potential U _gra are equal (see formula (60) below). Specifically, since the value of the left side of the equation (60) is known by the processing of S805 and S806, it is assumed that the value of the graphite open-circuit potential U _gra defined on the right side of the equation (60) has already been calculated. I can say Therefore, the lithium amount θ _gra can be calculated from the graphite open-circuit potential U _gra by referring to a map (not shown) that defines the correspondence relationship between the graphite open-circuit potential U _gra and the lithium amount θ _gra .

In S808, the ECU 100 determines the amount of lithium according to the following formula (61) established between the amount of lithium θ _Si of the silicon particles 21, the amount of lithium θ _gra of the graphite particles 22, and the amount of lithium θ ₂ of the mixed negative electrode particles 2. The amount of lithium θ ₂ ^t is calculated from θ _Si and θ _gra .

_In S809, the ECU 100 ^determines the difference _{(θ 2 t} ^- θ ₂ ^{t - Δt} ) is calculated. Note that the lithium amount θ ₂ ^t−Δt at the time of the previous calculation was temporarily stored in the memory 100B for use in the current calculation. The ECU 100 then compares the difference (θ ₂ ^t - θ ₂ ^{t - Δt} ) calculated as described above with the lithium change amount Δθ ₂ calculated in S801.

If the error between the two is equal to or greater than the threshold TH (NO in S809), the ECU 100 advances the process to S810, and _{determines the amount of change in lithium Δθ Si (} S802) is updated. On the other hand, if the error between the two is less than the threshold TH (YES in S809), the ECU 100 uses the lithium amount θ _Si of the silicon particles 21 calculated by the lithium amount calculation process in the subsequent process (SOC estimation process). It is adopted as a possible value (S811). This completes the lithium amount calculation process (S709). Accordingly, the convergence calculation process (S606) ends, and the potential calculation process (S600) ends.

Returning to FIG. 16, the ECU 100 executes the SOC estimation process (S200) after completing the potential calculation process (S600). This SOC estimation process is equivalent to the SOC estimation process (see FIG. 12) in Embodiment 1, and therefore detailed description will not be repeated.

As described above, in the second embodiment, as in the first embodiment, the surface stress σ _surf is calculated by the surface stress calculation process (S804), and the open-circuit potential change amount of the silicon particles 21 is calculated based on the surface stress σ _surf . ΔV _stress is calculated (S805). Thus, by calculating the negative electrode open-circuit potential U2 in consideration of the influence of hysteresis caused by the surface stress _σsurf , it is possible to calculate the negative electrode open _- circuit potential U2 with _high accuracy. As a result, the estimation accuracy of the SOC of the battery 4 can also be improved.

On the other hand, in the second embodiment, the diffusion of lithium inside the silicon particles 21 and the graphite particles 22 is simplified, and therefore the diffusion equation for the silicon particles 21 and the diffusion equation for the graphite particles 22 (equation (9 ) to formula (16) are omitted. In addition, the silicon particles 21 and the graphite particles 22 are integrally regarded as the mixed negative electrode particles 2, the surface and the inside are not distinguished, and the lithium concentration in the mixed negative electrode particles 2 is a standardized parameter. θ ₂ is used. Then, in Embodiment 2, focusing on the fact that there is a correlation between the lithium concentration in the positive electrode particles 1 and the lithium concentration in the mixed negative electrode particles 2, the capacity of the positive electrode particles 1 and the capacity of the mixed negative electrode particles 2 differ. Using the capacity ratio θ _rate , the lithium amount θ 2 of the mixed negative electrode particles ₂ is calculated from the lithium amount θ ₁ of the positive electrode particles 1 (see the above formula (46)).

In addition, in the second embodiment, the diffusion of lithium inside the silicon particles 21 and the graphite particles 22 is intentionally not taken into consideration, thereby reducing the amount of calculation (calculation load, memory amount, and calculation time) of the ECU 100. can.

[Embodiment 3]
In the lithium calculation process (see FIG. 18) in the second embodiment, the difference (θ ₂ ^t - θ ₂ ^{t - Δt} ) in lithium amount θ2 between the previous calculation and the current calculation is calculated by another method. It has been explained that the calculation for updating Δθ _Si (convergence calculation) is executed until the lithium change amount Δθ ₂ converges (see the processing of S809 and S810). In the third embodiment, in order to further reduce the amount of calculation of ECU 100, a configuration will be described in which linear approximation is performed to calculate lithium change amount Δθ _Si of silicon particles 21, thereby eliminating the need for convergence calculation.

Embodiment 3 differs from Embodiment 2 in that another lithium amount calculation process is executed instead of the lithium calculation process shown in FIG. Other processes, that is, potential calculation process, SOC estimation process (see FIG. 16), convergence calculation process (see FIG. 17), and surface stress calculation process (see FIG. 19) are equivalent to the corresponding processes in the second embodiment. Therefore, the description will not be repeated. The overall configuration of the secondary battery system according to Embodiment 3 is also the same as the overall configuration of secondary battery system 10 according to Embodiment 1 (see FIG. 1).

<Linear approximation of lithium distribution>
The interval from the previous calculation to the current calculation is, for example, on the order of several tens of milliseconds to several hundred milliseconds, which is sufficiently short. In other words, the amount of change in lithium Δθ (more specifically, the amount of change in lithium of silicon particles Δθ _Si ) from the previous calculation to the current calculation is considered to be sufficiently small. Therefore, Taylor expansion of the silicon potential V _Si around a certain amount of lithium θ _Si ′ leads to the following equation (62).

If (θ _Si - θ _Si ') in equation (62) is very small, the second or higher terms of (θ _Si - θ _Si ') can be ignored. Therefore, equation (62) is transformed into equation (63) below.

In formula (63), if V _Si (θ _Si )−V _Si (θ _Si ′)=ΔV _Si and θ _Si −θ _Si ′=Δθ _Si , the following formula (64) is obtained. .

Furthermore, since the open-circuit potential (silicon open-circuit potential) U _Si of the silicon particles 21 is given by the following formula (65), the formula (64) can be expressed as the following formula (66).

On the other hand, graphite particles 22 do not have a term containing surface stress σ _surf (the second term on the right side of formula (65) above), but by similar calculations, the amount of potential change ΔV _gra of graphite particles 22 is calculated by the following formula (67): ) can be expressed as

Since the silicon particles 21 and the graphite particles 22 are always at the same potential (V _Si =V _gra ), the change amount ΔV _Si in the silicon potential and the change amount ΔV _gra in the graphite potential are equal (ΔV _si =ΔV _gra ) holds. This relationship is represented by the following equation (68) using the above equations (66) and (67).

By appropriately transforming the formula, the following formula (69) can be derived from the above formula (68).

Once the amount of change in lithium concentration Δc ₂ for the entire mixed negative electrode particles 2 is known, the amount of change in lithium concentration Δc _Si of the silicon particles 21 and the amount of change in lithium concentration Δc _gra of the graphite particles 22 are calculated using equation (69). can do. The amount of lithium concentration change Δc2 of the mixed negative electrode particles ₂ is given by the following formula (70).

From the equations (69) and (70), the lithium change amount Δθ _Si of the silicon particles 21 can be expressed as the following equation (71).

In the lithium calculation process (see FIG. 18) in Embodiment 2, the difference (θ ₂ ^t - θ ₂ ^{t - Δt} ) in the lithium amount θ ₂ of the mixed negative electrode particles 2 between two consecutive calculations is the positive electrode particles 1 The lithium change amount Δθ _Si of the silicon particles 21 is repeatedly updated until it converges to the lithium change amount Δθ ₂ calculated from the lithium amount θ ₁ and the capacity ratio θ _rate of . Therefore, the ECU 100 may be required to perform a large amount of calculations to finally determine the amount of change in lithium Δθ _Si . On the other hand, in Embodiment 3, as can be understood from the formula (71), the amount of lithium change Δθ ₂ of the mixed negative electrode particles 2 (calculated from the lithium amount θ ₁ of the positive electrode particles 1 and the capacity ratio θ _rate The amount of change in lithium Δθ _Si of the silicon particles 21 is calculated by one calculation from the amount of change in lithium Δθ ₂ ). Therefore, it is possible to greatly reduce the amount of calculation for determining the lithium change amount Δθ _Si .

<Lithium amount calculation processing flow>
FIG. 20 is a flowchart showing lithium amount calculation processing according to the third embodiment. In this flowchart, the initial value of the lithium content θ _Si of the silicon particles 21 and the initial value of the lithium content θ _gra of the graphite particles are given, and each time the series of processes is repeatedly executed, each lithium content θ _Si , _θgra is updated.

With reference to FIG. 20, the processes of S1002 to S1006 are performed on silicon particles 21, and the processes of S1007 to S1009 are performed on graphite particles 22. Referring to FIG. The ECU 100 may change the order of these processes so that the processes S1007 to S1009 for the graphite particles 22 are performed first, and then the processes S1002 to S1006 for the silicon particles 21 are performed.

In S1001, the ECU 100 calculates the amount of change in lithium Δθ2 of mixed negative electrode particles ₂ in the same manner as in S801 (see FIG. 18) of the lithium amount calculation process in the second embodiment. That is, the lithium amount θ ₂ of the mixed negative electrode particles 2 calculated from the lithium amount θ ₁ of the positive electrode particles 1 and the capacity ratio θ _rate according to the above formula (47) is calculated twice at the previous calculation and the current calculation, By taking the difference between the _two , the amount of change in lithium Δθ2 is calculated.

In S1002, the lithium amount θ _Si ′ (=θ _Si ^t ) is calculated by slightly changing the lithium amount θ _Si (=θ _Si ^t−Δt ) of the silicon particles 21 in the previous calculation. The minute amount is set to a sufficiently small value so that the silicon potential V _Si can be Taylor-expanded around the lithium amount θ _Si ′ (see formula (62) above).

In S1003, the ECU 100 calculates a silicon open-circuit potential U _{Si_sta} , which is the open-circuit potential of the silicon particles 21 when the surface stress σ _surf =0. More specifically, the ECU 100 refers to a map (not shown) that defines the correspondence relationship between the lithium amount θ _Si of the silicon particles 21 and the silicon open-circuit potential U _{Si_sta} , thereby determining the lithium amount θ calculated in S1001. A silicon open potential U _{Si_sta} corresponding to _Si ′ is calculated.

In S1004, the ECU 100 calculates the surface stress σ _surf of the silicon particles 21 by executing surface stress calculation processing. This surface stress calculation process is common to the surface stress calculation process (see FIG. 19) in the second embodiment, as described above.

In S1005, the ECU 100 calculates the open-circuit potential change amount ΔV _stress (=σ _surf Ω/F) based on the calculation result of the surface stress calculation process (the surface stress σ _surf of the silicon particles 21) (see formula (58) above). ).

In S1006, the ECU 100 calculates the silicon open-circuit potential U Si by adding the open-circuit potential change amount ΔV _stress to the silicon open-circuit potential U _{Si — sta} (calculated result in the process of S1003) (see the above equation (59)).

In S1007, the ECU 100 calculates the partial differential ∂U _Si /∂θ _Si of the silicon open circuit potential U _Si at the silicon amount θ _Si =θ _Si '. The calculated partial differential value is used for the second term in the denominator of equation (75).

In S1008, the ECU 100 calculates the amount of silicon θ _gra ′ by slightly changing the amount of lithium θ _gra of the graphite particles 22 in the previous calculation, as in the processing of S1001.

At S1009, the ECU 100 calculates a graphite open-circuit potential U _gra based on the lithium amount θ _gra of the graphite particles 22 calculated at S1007. A map (not shown) prepared in advance is also used for this calculation.

In S1010, the ECU 100 calculates the partial differential ∂U _gra /∂θ _gra of the graphite open-circuit potential U _gra at the silicon amount θ _gra =θ _gra ', as in the processing of S1006. The calculated partial differential value is used for the numerator and the first term of the denominator of equation (75).

In S1011, the ECU 100 calculates the lithium change amount Δθ _Si based on the above equation (75). Specifically, the lithium change amount Δθ ₂ of the mixed negative electrode particles calculated in S1001, the partial differential ∂U _Si /∂θ _Si of the silicon open-circuit potential U _Si calculated in S1007, and the By substituting the partial differential ∂U _gra /∂θ _gra of the graphite open-circuit potential U _gra obtained, into the equation (75), the lithium change amount Δθ _Si is calculated.

As described above, according to Embodiment 3, similarly to Embodiments 1 and 2, the surface stress σ _surf is calculated by the surface stress calculation process (S1004), and the surface stress σ _surf of the silicon particles 21 is calculated based on the surface stress σ surf. An open circuit potential change amount ΔV _stress is calculated (S1005). By calculating the _silicon open-circuit potential USi in consideration of the influence of hysteresis caused by the surface stress σ _surf in this way, the calculation accuracy of the _silicon open-circuit potential USi is improved. As a result, the SOC of the battery 4 can be estimated. Accuracy can also be improved.

Furthermore, in the third embodiment, the silicon potential V _Si (see the above equation (63)) obtained by approximation (ie, linear approximation) ignoring terms of second order or higher after Taylor expansion, and the graphite potential obtained by similar approximation Equation (75) is derived by transforming the equation using the product of critical lithium concentrations (c _Si,max ×c _gra,max ) under the condition that V _gra is equal to V gra (see higher-order equation (68)). By substituting values for each term in equation (75), the convergence operation becomes unnecessary, and the lithium change amount Δθ _Si can be calculated by simple multiplication and division. Therefore, according to the third embodiment, the calculation load and memory capacity of ECU 100 can be further reduced as compared with the lithium amount calculation process in the second embodiment.

The lithium deposition suppression control described in Modification 2 of Embodiment 1 may be combined with the potential calculation process in Embodiment 2 or may be combined with the potential calculation process in Embodiment 3. That is, the negative electrode potential V2 is calculated by a method that simplifies the three-particle model in Embodiment ₁ , and the allowable charging power _Iwin is calculated according to the calculated negative electrode potential V2 according to the flowchart shown in _FIG . may

Further, in Embodiments 1 to 3 (and Modifications 1 and 2 of Embodiment 1), the example in which a silicon-based material is used as a negative electrode active material that undergoes a large amount of volume change due to charging and discharging has been described. However, the negative electrode active material that undergoes a large volume change due to charging and discharging is not limited to this. In the present specification, the “negative electrode active material with a large volume change” means a material with a large volume change compared to the graphite volume change (approximately 10%) during charging and discharging. Examples of negative electrode materials for such lithium ion secondary batteries include tin-based compounds (Sn, SnO, etc.), germanium (Ge)-based compounds, and lead (Pb)-based compounds. The lithium ion secondary battery is not limited to a liquid system, and may be a polymer system or an all-solid system.

Further, the secondary battery to which the potential calculation process described above can be applied is not limited to the lithium ion secondary battery, and may be another secondary battery (for example, a nickel metal hydride battery).

The embodiments disclosed this time should be considered as examples and not restrictive in all respects. The scope of the present disclosure is indicated by the scope of claims rather than the description of the above-described embodiments, and is intended to include all modifications within the scope and meaning equivalent to the scope of the claims.

1 cathode particles, 2 mixed anode particles, 21 silicon particles, 22 graphite particles, 4
Battery 5 Cell 51 Battery Case 52 Cover 53 Positive Electrode Terminal 54 Negative Electrode Terminal 55 Electrode Body 56 Positive Electrode 57 Negative Electrode 58 Separator 6 Monitoring Unit 71 Voltage Sensor 72 Temperature Sensor 8 PCU 9 Vehicle, 91, 92 Motor generator, 93 Engine, 94 Power split device, 95 Drive shaft, 96 Drive wheel, 10 Secondary battery system, 100 ECU, 100A CPU, 100B Memory, 110 Parameter setting unit, 121 Replacement current density calculation unit , 122 reaction overvoltage calculator, 131 concentration distribution calculator, 132 lithium amount calculator, 133 surface stress calculator, 134 open circuit potential change amount calculator, 135 open circuit potential calculator, 141 salt concentration difference calculator, 142 salt concentration overvoltage Calculation unit, 151 convergence condition determination unit, 152 current distribution unit, 160 SOC estimation unit.

Claims (9)

a secondary battery having a positive electrode containing a positive electrode active material and a negative electrode containing first and second negative electrode active materials;
a control device configured to estimate an internal state of the secondary battery based on the active material model of the secondary battery;
The amount of change in volume of the first negative electrode active material due to the change in the amount of charge carriers in the first negative electrode active material is the amount of change in the volume of the second negative electrode due to the change in the amount of charge carriers in the second negative electrode active material. larger than the volume change of the active material,
The control device is
Under the condition that the first negative electrode active material and the second negative electrode active material are equipotential, the amount of charge carriers in the first negative electrode active material is calculated based on the first active material model. death,
calculating the open-circuit potential change amount of the first negative electrode active material based on the surface stress of the first negative electrode active material determined according to the amount of charge carriers in the first negative electrode active material;
A secondary battery system, wherein the open circuit potential of the negative electrode is calculated from the open circuit potential of the first negative electrode active material in a state in which surface stress is not generated in the first negative electrode active material and the amount of change in the open circuit potential. The control device is
Under the condition that the first negative electrode active material and the second negative electrode active material are equipotential, the current flowing through the first negative electrode active material and the first The current flowing through the negative electrode active material of 2 is separately calculated by convergence arithmetic processing,
calculating the concentration distribution of charge carriers in the first and second negative electrode active materials by solving a diffusion equation under boundary conditions for the current flowing through the first and second negative electrode active materials; 2. The secondary battery system according to claim 1, wherein the amount of charge carriers in said first and second negative electrode active materials is calculated from . Further comprising a voltage sensor that detects a voltage between the positive electrode and the negative electrode,
The control device is
The concentration distribution of the charge carriers in the positive electrode active material is calculated by solving a diffusion equation under boundary conditions regarding the current flowing through the positive electrode active material, and the amount of charge carriers in the positive electrode active material is calculated from the calculated concentration distribution. calculate,
calculating the potential of the positive electrode based on the open potential of the positive electrode active material determined according to the amount of charge carriers in the positive electrode active material;
calculating the potential of the negative electrode based on the open potential of the negative electrode;
3. The current flowing through the first negative electrode active material is calculated using a condition that the calculated potential difference between the positive electrode and the negative electrode matches the voltage detected by the voltage sensor as the convergence condition. 2. The secondary battery system according to 2. The control device is
distinguishing the current flowing through the first negative electrode active material into a reaction current involved in the insertion and desorption of the charge carriers and a capacitor current not involved in the insertion and desorption of the charge carriers;
Calculate the reaction overvoltage of the first negative electrode active material by substituting the reaction current into the Butler-Volmer relational expression,
4. The secondary battery system according to claim 2, wherein the potential of said negative electrode is calculated from the open circuit potential of said negative electrode and the reaction overvoltage of said first negative electrode active material. The control device is
The relationship between the amount of charge carriers in the positive electrode active material and the total amount of charge carriers in the first and second negative electrode active materials is defined as the capacity ratio between the capacity of the positive electrode and the capacity of the negative electrode. calculating the total amount of charge carriers in the first and second negative electrode active materials from the amount of charge carriers in the positive electrode active material according to the relational expression defined using
2. The method according to claim 1, wherein the amount of charge carriers in the first negative electrode active material is calculated using a law of conservation of charge amount that is established between the amount of change in the total amount over time and the current flowing through the positive electrode active material. A secondary battery system as described. The control device is
The relationship between the amount of charge carriers in the positive electrode active material and the total amount of charge carriers in the first and second negative electrode active materials is defined as the capacity ratio between the capacity of the positive electrode and the capacity of the negative electrode. Calculating the total amount of charge carriers in the first and second negative electrode active materials from the amount of charge carriers in the positive electrode active material according to the relational expression defined using
It is approximated that the potential of the first negative electrode active material changes linearly according to the change in the amount of charge carriers in the first negative electrode active material, and the change in the amount of charge carriers in the second negative electrode active material The amount of charge carriers in the first negative electrode active material is calculated from the amount of time change of the total amount according to a predetermined relational expression approximating that the potential of the second negative electrode active material linearly changes according to the 2. The secondary battery system according to 1. The secondary battery is a lithium ion secondary battery,
When the potential of the negative electrode calculated from the open-circuit potential of the negative electrode is below a predetermined potential higher than the potential of metallic lithium, the control device compares the potential of the negative electrode with the potential above the predetermined potential. 7. The secondary battery system according to any one of claims 1 to 6, wherein the secondary battery system suppresses charging power to the secondary battery. The first negative electrode active material is a silicon-based material,
The secondary battery system according to any one of claims 1 to 7, wherein the second negative electrode active material is a carbon-based material. A secondary battery internal state estimation method for estimating the internal state of a secondary battery having a positive electrode containing a positive electrode active material and a negative electrode containing first and second negative electrode active materials based on an active material model, comprising: ,
The amount of change in volume of the first negative electrode active material due to the change in the amount of charge carriers in the first negative electrode active material is the amount of change in the volume of the second negative electrode due to the change in the amount of charge carriers in the second negative electrode active material. larger than the volume change of the active material,
The method for estimating the internal state of the secondary battery includes:
Under the condition that the first negative electrode active material and the second negative electrode active material are equipotential, the amount of charge carriers in the first negative electrode active material is calculated based on the first active material model. and
calculating the amount of change in open-circuit potential of the first negative electrode active material based on the surface stress of the first negative electrode active material determined according to the amount of charge carriers in the first negative electrode active material;
calculating the open circuit potential of the negative electrode from the open circuit potential of the first negative electrode active material in a state where the first negative electrode active material has no surface stress and the amount of change in open circuit potential; A method for estimating the internal state of a next battery.

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