JP7651912B2 - Computer program, simulation method, and simulation device - Google Patents

Description

The present invention relates to a computer program, a simulation method, and a simulation device.

Lithium-ion electrolyte batteries, which use organic solvents as ion conductors, are becoming more and more popular. They are used not only as mobile batteries for mobile phones, digital cameras, and camcorders, but also as energy sources for automobiles, trains, and other vehicles.

In recent years, development of all-solid-state batteries has been progressing as an alternative to these electrolyte-based lithium-ion batteries. All-solid-state batteries have features such as no restrictions on shape, resistance to internal short circuits, and heat resistance.

JP 2012-154665 A JP 2016-065828 A JP 2019-148537 A

The development and production of electrolyte-based lithium-ion batteries is progressing around the world, and there are several proven electrochemical simulation models that represent charge/discharge characteristics such as voltage-current characteristics (see, for example, Patent Documents 1-3).

However, there is currently no simulation model that can predict the internal behavior of solid-state batteries, and it is not possible to use a simulation model for liquid electrolyte lithium-ion batteries, which have a different mechanism.

The present invention has been made in consideration of the above circumstances, and aims to provide a computer program, a simulation method, and a simulation device that can be applied to all-solid-state batteries and can perform simulations of electrochemical phenomena based on parameters that depend on the internal stress of the battery.

The computer program causes the computer to execute a process of simulating the electrochemical phenomenon of an all-solid-state battery containing a solid electrolyte using a simulation model whose parameters include the contact area between the active material particles and the solid electrolyte.

The simulation method uses a simulation model that includes the contact area between active material particles and a solid electrolyte as a parameter to execute a process to simulate the electrochemical phenomenon of an all-solid-state battery that includes the solid electrolyte by a computer.

The simulation device includes a calculation unit that uses a simulation model that includes a parameter for the contact area between active material particles and a solid electrolyte to simulate the electrochemical phenomenon of an all-solid-state battery that includes the solid electrolyte.

The above configuration can be applied to all-solid-state batteries, and electrochemical phenomena can be simulated based on parameters that depend on the internal stress of the battery.

1 is a block diagram showing an internal configuration of an estimation device according to a first embodiment. FIG. FIG. 2 is an explanatory diagram illustrating a configuration of an energy storage element. FIG. 2 is an explanatory diagram illustrating an internal configuration of a solid electrolyte layer. FIG. 11 is an explanatory diagram for explaining a method for calculating an effective diffusion coefficient. FIG. 1 is an explanatory diagram for explaining a method for calculating an effective diffusion coefficient in an all-solid-state battery. FIG. 13 is a diagram showing calculation results of an effective diffusion coefficient in an all-solid-state battery. 1 is a graph showing the relationship between the contact area ratio and the effective diffusion coefficient. 4 is a flowchart illustrating a procedure for executing a calculation process performed by the estimation device according to the first embodiment. 10 is a flowchart illustrating a procedure for executing a calculation process performed by an estimation device according to a second embodiment. 1 is a graph showing the relationship between internal stress and internal resistance of an energy storage element. FIG. 11 is a block diagram showing an internal configuration of an estimation device according to a third embodiment. 11 is a flowchart illustrating a procedure for estimating an internal stress.

The computer program causes the computer to execute a process of simulating an electrochemical phenomenon of an all-solid-state battery including a solid electrolyte, using a simulation model including a contact area between active material particles and a solid electrolyte as a parameter.
Unlike liquid electrolyte lithium ion batteries, all-solid-state batteries have a large contact resistance unless the contact area between the active material particles and the solid electrolyte is actively increased. In other words, all-solid-state batteries have the characteristic that electricity flows easily by applying pressure from the outside to increase the contact area between the active material particles and the solid electrolyte.
According to the above configuration, it is possible to simulate the electrochemical phenomenon of an all-solid-state battery based on the contact area, which is one of the characteristic parameters of the all-solid-state battery.

In the computer program, the simulation model may define the relationship between the contact area and the effective diffusion coefficient of the active material particles, and the computer may execute a process of estimating the effective diffusion coefficient of the active material particles based on the value of the contact area. With this configuration, the electrochemical phenomenon of the all-solid-state battery can be simulated from the value of the contact area by linking the value of the contact area with the effective diffusion coefficient of the active material particles.

In the computer program, the simulation model may define the relationship between the contact area and the effective ion conductivity of the active material particles, and the computer may execute a process to estimate the effective ion conductivity of the active material particles based on the value of the contact area. With this configuration, the electrochemical phenomenon of the all-solid-state battery can be simulated from the value of the contact area by linking the value of the contact area with the effective ion conductivity of the active material particles.

In the computer program, the contact area is a function of the internal stress of the solid-state battery, and the computer may be caused to execute a process of simulating an electrochemical phenomenon of the solid-state battery based on the value of the internal stress. According to this configuration, by linking the value of the contact area with the value of the internal stress, it is possible to simulate an electrochemical phenomenon of the solid-state battery from the value of the internal stress.

The computer program may cause the computer to execute a process of acquiring measurement data related to the strain generated in the all-solid-state battery from a strain sensor that measures the strain, and estimating the internal stress of the all-solid-state battery based on the acquired measurement data using a model that represents the internal mechanical state of the all-solid-state battery. With this configuration, the internal stress can be estimated based on the strain data that can be measured by the sensor, and the electrochemical phenomenon of the all-solid-state battery can be simulated from the value of the estimated internal stress.

In the computer program, the internal resistance of the solid-state battery is a function of the internal stress, and the computer may be caused to execute a process of estimating the value of the internal resistance based on the value of the internal stress. With this configuration, the internal resistance of the solid-state battery can be estimated by linking the value of the internal stress and the value of the internal resistance.

The simulation method uses a simulation model including a contact area between active material particles and a solid electrolyte as a parameter, and executes a process of simulating an electrochemical phenomenon of an all-solid-state battery including the solid electrolyte by a computer.
According to this configuration, the electrochemical phenomenon of an all-solid-state battery can be simulated based on the contact area, which is one of the characteristic parameters of an all-solid-state battery.

The simulation device includes a calculation unit that simulates electrochemical phenomena in an all-solid-state battery that includes a solid electrolyte using a simulation model that includes a contact area between active material particles and a solid electrolyte as a parameter.
According to this configuration, the electrochemical phenomenon of an all-solid-state battery can be simulated based on the contact area, which is one of the characteristic parameters of an all-solid-state battery.

Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof.
(Embodiment 1)
1 is a block diagram showing an internal configuration of an estimation device 1 according to embodiment 1. The estimation device 1 includes, for example, a calculation unit (estimation unit) 11, a storage unit 12, an operation unit 13, and an output unit 14. The estimation device 1 estimates an electrochemical phenomenon of an energy storage element 2 (see FIG. 2 ), which will be described later, based on preset information or information input via the operation unit 13.

The calculation unit 11 is an arithmetic circuit including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), etc. The CPU included in the calculation unit 11 executes various computer programs stored in the ROM and the storage unit 12, and controls the operation of each of the above-mentioned hardware components, thereby causing the entire device to function as a state estimator for estimating the electrochemical phenomenon of the energy storage element 2.

Alternatively, the calculation unit 11 may be any processing circuit or calculation circuit equipped with multiple CPUs, a multi-core CPU, a GPU (Graphics Processing Unit), a microcomputer, a volatile or non-volatile memory, etc. The calculation unit 11 may also have functions such as a timer that measures the elapsed time from when an instruction to start measurement is given to when an instruction to end measurement is given, a counter that counts numbers, and a clock that outputs date and time information.

The memory unit 12 includes a storage device such as a flash memory or a hard disk. Various computer programs and data are stored in the memory unit 12. The computer programs stored in the memory unit 12 include an estimation program PG1 for causing a computer to execute a process for estimating an electrochemical phenomenon of the energy storage element 2 using a simulation model MD1. The simulation model MD1 may be described in the estimation program PG1. The data stored in the memory unit 12 includes parameters used in the simulation model MD1, parameters used in the estimation program PG1, data generated by the calculation unit 11, and the like.

The estimation program PG1 may be written in commercially available numerical analysis software or programming languages such as MATLAB (registered trademark), Amesim (registered trademark), Twin Builder (registered trademark), MATLAB & Simulink (registered trademark), Simplorer (registered trademark), ANSYS (registered trademark), Abaqus (registered trademark), Modelica (registered trademark), VHDL-AMS (registered trademark), C language, C++, Java (registered trademark), etc. The numerical analysis software may be a circuit simulator called 1D-CAE, or a simulator such as the finite element method or finite volume method performed on 3D shapes. Alternatively, a reduced-order model (ROM: Reduced-Order Model) based on these may be used.

A computer program including the estimation program PG1 is provided by a non-transitory recording medium M on which the computer program is recorded in a readable manner. The recording medium M is a portable memory such as a CD-ROM, a USB memory, or a Secure Digital (SD) card. The calculation unit 11 reads the desired computer program from the recording medium M using a reading device not shown in the figure, and stores the read computer program in the memory unit 12. Alternatively, the computer program may be provided by communication.

The operation unit 13 has an interface for connecting various operation devices. The operation devices are devices for accepting user operations, such as a keyboard, mouse, or touch panel. The operation unit 13 outputs operation information accepted through the operation devices to the calculation unit 11.

The output unit 14 has a connection interface for connecting an external device. The external device connected to the output unit 14 is a display device 140 having a liquid crystal display or the like. In this case, the calculation unit 11 outputs information relating to the estimated electrochemical phenomenon of the energy storage element 2 from the output unit 14, thereby causing the information to be displayed on the display device 140. Alternatively, the estimation device 1 may have a built-in display device 140.

Furthermore, the output unit 14 may be provided with a communication interface for communicating with an external device. The external device communicatively connected to the output unit 14 is a monitoring server that monitors the state of the energy storage element 2. Alternatively, the external device communicatively connected to the output unit 14 may be a control device such as a mobile terminal or an electric vehicle that operates using power supplied from the energy storage element 2.

The storage element 2 that is the target of the simulation by the estimation device 1 will be described below.
2 is an explanatory diagram illustrating the configuration of the energy storage element 2. The energy storage element 2 is, for example, an all-solid-state battery including a laminate made of a positive electrode current collector layer 21, a positive electrode active material layer 22, a solid electrolyte layer 23, a negative electrode active material layer 24, and a negative electrode current collector layer 25.

The positive electrode collector layer 21 is composed of a metal foil, a metal mesh, or the like. The metal constituting the positive electrode collector layer 21 is a metal having good electrical conductivity, such as aluminum, nickel, titanium, or stainless steel. A coating layer for adjusting the contact resistance may be formed on the surface of the positive electrode collector layer 21. An example of the coating layer is a carbon coating. The thickness of the positive electrode collector layer 21 is not particularly limited, and is, for example, 0.1 μm or more and 1 mm or less.

The positive electrode active material layer 22 is a layer that contains at least a positive electrode active material. In addition to the positive electrode active material, the positive electrode active material layer 22 may contain a solid electrolyte, a conductive additive, a binder, and the like. The positive electrode active material layer 22 has a thickness of, for example, 0.1 μm or more and 1 mm or less.

The positive electrode active material is an appropriate positive electrode active material that can be used in an all-solid-state battery. For example, various lithium-containing composite oxides such as lithium cobalt oxide, lithium nickel oxide, lithium manganate, and spinel-based lithium compounds are used as the positive electrode active material. The positive electrode active material is, for example, particles having an average particle size (D50) of 0.5 μm or more and 20 μm or less. The particles constituting the positive electrode active material may be primary particles or secondary particles. The positive electrode active material is not limited to particles, and may be in the form of a thin film. For the solid electrolyte contained in the positive electrode active material layer 22, an inorganic solid electrolyte having a relatively high ionic conductivity and excellent heat resistance is used. As such an inorganic solid electrolyte, an oxide solid electrolyte such as lithium lanthanum zirconate or a sulfide solid electrolyte such as Li ₂ S-P ₂ S ₅ can be used. For the conductive assistant, a carbon material such as acetylene black or ketjen black or a metal material such as nickel, aluminum, or stainless steel is used. The binder may be made of a material such as butadiene rubber (BR), acrylate butadiene rubber (ABR), or polyvinylidene fluoride (PVdF).

The solid electrolyte layer 23 is a layer that contains at least a solid electrolyte. In addition to the solid electrolyte, the solid electrolyte layer 23 may contain a binder. The solid electrolyte layer 23 has a thickness of, for example, 0.1 μm or more and 1 mm or less. The solid electrolyte contained in the solid electrolyte layer 23 is an inorganic solid electrolyte such as the above-mentioned oxide solid electrolyte or sulfide solid electrolyte. The binder is the same as the binder used in the positive electrode active material layer 22.

The negative electrode active material layer 24 is a layer that contains at least a negative electrode active material. In addition to the negative electrode active material, the negative electrode active material layer 24 may contain a solid electrolyte, a conductive additive, a binder, and the like. The negative electrode active material layer 24 has a thickness of, for example, 0.1 μm or more and 1 mm or less.

For the negative electrode active material, an appropriate negative electrode active material that can be used in an all-solid-state battery is used. For example, a metal active material and a carbon active material are used as the negative electrode active material. Examples of the metal active material include Li, In, Al, Si, and Sn. The metal active material is not limited to a single metal, but may be a metal composite oxide. Examples of the carbon active material include mesocarbon microbeads (MCMB), highly oriented graphite (HOPG), hard carbon, and soft carbon. The negative electrode active material is, for example, particles having an average particle size (D50) of 0.5 μm or more and 20 μm or less. The particles constituting the negative electrode active material may be primary particles or secondary particles. The negative electrode active material is not limited to particles, but may be a thin film. The solid electrolyte, conductive assistant, and binder used in the negative electrode active material layer 24 are appropriately similar to the solid electrolyte, conductive assistant, and binder used in the positive electrode active material layer 22.

The negative electrode collector layer 25 is made of a metal foil, a metal mesh, or the like. The metal constituting the negative electrode collector layer 25 is a metal having good electrical conductivity, such as copper, nickel, titanium, or stainless steel. A coating layer for adjusting the contact resistance may be formed on the surface of the negative electrode collector layer 25. An example of the coating layer is a carbon coating. The thickness of the negative electrode collector layer 25 is not particularly limited, and is, for example, 0.1 μm or more and 1 mm or less.

The energy storage element 2 is restrained by the restraining member 3. The restraining member 3 includes, for example, a case 31 that houses the energy storage element 2, and an elastic member 32 that is arranged in a compressed state within the case 31. The case 31 is, for example, a rectangular parallelepiped container, and includes a case body 310 that is composed of a bottom portion 311 and a side portion 312, and a lid body 313 that closes the opening of the case body 310. The case body 310 (bottom portion 311 and side portion 312) and the lid body 313 are formed of a weldable metal such as stainless steel, aluminum, or an aluminum alloy. Alternatively, the case body 310 (bottom portion 311 and side portion 312) and the lid body 313 may be formed of resin. The case body 310 is sealed by the lid body 313 after the energy storage element 2 is housed therein.

The elastic member 32 is disposed in a compressed state between the bottom layer of the energy storage element 2 (positive electrode collector layer 21 in the example of FIG. 2) and the bottom surface portion 311, and between the top layer of the energy storage element 2 (negative electrode collector layer 25 in the example of FIG. 2) and the lid body 313. The elastic member 32 is, for example, a rubber-like sheet. The elastic force of the elastic member 32 applies a restraining force to the energy storage element 2 in the stacking direction (the vertical direction in the figure).

In the example of FIG. 2, a configuration is adopted in which a restraining force is applied to the energy storage element 2 by disposing an elastic member 32 inside the case 31. Alternatively, a restraining force may be applied to the energy storage element 2 by filling the case 31 with a high-pressure fluid. In this case, the fluid is preferably one that does not cause unnecessary reactions with the battery material. For example, an inert gas such as nitrogen or dry air is used. Alternatively, a restraining force may be applied to the energy storage element 2 by sandwiching the energy storage element 2 between plate members on both sides in the stacking direction and connecting the plate members together while a restraining force is applied to the energy storage element 2.

Figure 3 is an explanatory diagram illustrating the internal structure of the solid electrolyte layer 23. In the example of Figure 3, active material particles are shown as hatched spheres, and solid electrolyte is shown as unhatched spheres. For simplification, the conductive additive and binder are omitted from Figure 3. In an all-solid-state battery containing particulate active material (active material particles), the active material particles and solid electrolyte are in contact with each other over a small contact area (point), as shown by the black circles in the figure. The contact area between the solid electrolyte and the active material particles changes depending on the restraining force and internal stress that restrain the energy storage element.

In conventional electrolyte-based lithium-ion batteries, the active material particles are surrounded by electrolyte, and the entire surface of the active material particles is in contact with the electrolyte. In this case, the apparent diffusion coefficient (effective diffusion coefficient) and ionic conductivity (effective ionic conductivity) are the same as the true diffusion coefficient and ionic conductivity.

In contrast, in all-solid-state batteries, ions are exchanged only in the small area where the active material particles and solid electrolyte are in contact, so the apparent diffusion coefficient (effective diffusion coefficient) and ionic conductivity (effective ionic conductivity) are predicted to be smaller than the true diffusion coefficient and ionic conductivity. However, there are currently no empirical examples of the relationship between the contact area between the active material particles and solid electrolyte and the effective diffusion coefficient or effective ionic conductivity.

The inventors of the present application have discovered the relationship between the contact area between the active material particles and the solid electrolyte and the effective diffusion coefficient and effective ion conductivity through numerical calculations (simulations). In the embodiment, these relationships are used to propose a simulation method for estimating the electrochemical phenomenon of the energy storage element 2 based on the contact area between the active material particles and the solid electrolyte (or the internal stress of the energy storage element 2).

Below, as a reference example, we explain a calculation method for determining the effective diffusion coefficient of the electrolyte for an electrolyte-based lithium-ion battery.

FIG. 4 is an explanatory diagram for explaining a method of calculating the effective diffusion coefficient. FIG. 4 shows a simplified model of the positive electrode of an electrolyte-based lithium-ion battery. FIG. 4 shows a state in which a plurality of active material particles exist inside the positive electrode, and the inside and the periphery are filled with electrolyte. When the thickness of the positive electrode is L (m) and the length of the conductive path shown by the dashed line in the figure is l (m), the degree of bending τ due to the gaps and active material particles is described as τ = l/L. At this time, the relationship between the effective diffusion coefficient D _l,eff (m ² s ^-1 ) and the true diffusion coefficient D _l (m ² s ^-1 ) is expressed by the following formula. ε represents the volume occupancy rate of the electrolyte.

Similarly, the relationship between the effective ionic conductivity σ _l,eff (Sm ⁻¹ ) and the true ionic conductivity σ _l (Sm ⁻¹ ) of the electrolyte is expressed by the following equation:

4 is the inlet of the electrolyte, and the lower side is the outlet (observation point), and the flow rate of the electrolyte at the observation point is calculated by applying appropriate boundary conditions. As the boundary conditions, for example, the concentration of the electrolyte at the inlet (e.g., 1000 mol m ^-3 ) and the concentration of the electrolyte at the outlet (e.g., 0 mol m ^-3 ) are applied.

When the flow velocity of the electrolyte at the observation point is J _l and the concentration of the electrolyte is c _l , the relationship between the flow velocity J _l and the concentration c _l is expressed by the following equation. _{D l,eff} represents the effective diffusion coefficient. The effective diffusion coefficient D _l,eff of the electrolyte is calculated based on Equation 3.

In all-solid-state batteries, some of the active material particles are in contact with the solid electrolyte, and the inside and surroundings of the active material particles are not filled with electrolyte. Therefore, the method of calculating the effective diffusion coefficient in liquid electrolyte lithium-ion batteries cannot be directly applied to all-solid-state batteries. Therefore, the inventors of the present application introduce the concept of the contact area between the active material particles and the solid electrolyte, and propose a method of calculating the effective diffusion coefficient, which changes depending on the contact area, by simulation.

FIG. 5 is an explanatory diagram for explaining a calculation method of the effective diffusion coefficient in an all-solid-state battery. In the embodiment, the active material particles of the all-solid-state battery are assumed to be spherical. The calculation unit 11 of the estimation device 1 calculates the flow velocity J _AM (mol m ⁻² s −1 ) at the observation point when the boundary state is given, with the spherical surface set as the inlet and the surface of a concentric sphere set inside the sphere set as the observation point. The observation point is set, for example, as the surface of a concentric sphere having a radius half that of the sphere. As the boundary condition, a concentration of, for example ^, 1000 mol m ⁻³ is given around the sphere, and a concentration of, for example, 0 mol m ⁻³ is given inside the sphere. The relationship between the flow velocity J _AM and the effective diffusion coefficient D _AM,eff is expressed by Equation 4. Here, c _AM is the concentration of the active material. The calculation unit 11 substitutes the calculated flow velocity J _AM into Equation 4 to calculate the effective diffusion coefficient D _AM,eff of the active material.

FIG. 6 is a diagram showing the calculation results of the effective diffusion coefficient in an all-solid-state battery. FIG. 6A shows a sphere created by rotating around a rotation axis to represent the active material of an all-solid-state battery assumed as a sphere, and shows the calculation results when the entire surface of the sphere is in contact with the electrolyte. When the entire surface of the sphere is in contact with the electrolyte, a uniform flow occurs at the observation point, so it is predicted that the diffusion coefficient of the active material and its effective diffusion coefficient will be the same. When the calculation was actually performed, the effective diffusion coefficient D _AM,eff was 1.0×10 ⁻¹³ (m ² s ⁻¹ ), which is the same value as the diffusion coefficient D _AM of the active material. This demonstrated the validity of the calculation method.

6B shows the calculation results for a spherical cap cut by a cone created by rotating the sphere at a half apex angle of 10 degrees with respect to the axis of symmetry passing through the center of the sphere, in which the surface area included in the sphere surface is in contact with the electrolyte. For a half apex angle of 10 degrees, the effective diffusion coefficient D _AM,eff was 3.8×10 ^-15 (m ² s ^-1 ), which is about two orders of magnitude smaller than the diffusion coefficient D _AM of the active material.

6C shows the calculation results when the half apex angle is 5 degrees. When the half apex angle is 5 degrees, the effective diffusion coefficient D _AM,eff is 1.9×10 ⁻¹⁵ (m ² s ⁻¹ ), which is smaller than when the half apex angle is 10 degrees.

FIG. 7 is a graph showing the relationship between the contact area ratio and the effective diffusion coefficient. The horizontal and vertical axes of the graph shown in FIG. 7 are both logarithmic axes, with the horizontal axis representing the contact area ratio and the vertical axis representing the effective diffusion coefficient (m ² /s). The contact area ratio is the ratio of the area of the cap included in the surface of the sphere to the surface area of the sphere, and is a parameter representing the degree of contact between the active material and the solid electrolyte. The contact area is obtained by multiplying the contact area ratio on the horizontal axis by the surface area of the sphere assuming the active material. From the logarithmic axis plot shown in FIG. 7, it can be seen that the relationship between the contact area and the effective diffusion coefficient is formulated by Equation 5. The contact area can be actually estimated by analyzing X-ray CT images, etc., and parameters that affect the contact area can also be used. For example, in the case of an electrode obtained by press molding, a value such as the remaining porosity of the electrode mixture may be used.

Here, D _AM,eff is the effective diffusion coefficient, and x is the contact area. a, b, and c are coefficients. The coefficients a, b, and c are calculated by finding an approximation curve (a straight line in the logarithmic plot shown in FIG. 7) that passes through each point on the graph. The approximation curve is found using a known method such as the least squares method.

The calculation unit 11 may calculate the effective ionic conductivity σ AM _{,eff based on the calculated value of the effective diffusion coefficient D AM ,eff} . According to Einstein's relational equation, the relationship between the ionic conductivity σ and the diffusion coefficient D is described by Equation 6.

Here, σ is ionic conductivity (S m ^-1 ), z is the ion charge (dimensionless), F is Faraday constant (C mol ^-1 ), D is the diffusion coefficient (m ² s ^-1 ), c is the lithium concentration (mol m ^-3 ), R is the gas constant (m ² kg s ^-1 K ^-1 mol ^-1 ) and T is temperature (K).

The calculation unit 11 can calculate the effective ion conductivity σ AM _{,eff by substituting the value of the effective diffusion coefficient D AM, eff} calculated from the contact area into the diffusion coefficient D in Equation 6. The effective ion conductivity σ _AM,eff is a physical quantity that affects the electrical resistance of the energy storage element 2. In other words, the estimation device 1 can estimate the electrochemical phenomenon in the energy storage element 2 based on the contact area between the active material particles and the solid electrolyte in the all-solid-state battery.

The procedure for executing the calculations performed by the estimation device 1 will be described below.
8 is a flowchart for explaining the execution procedure of the calculation process executed by the estimation device 1 according to the first embodiment. The calculation unit 11 of the estimation device 1 sets a model in which spherical active material particles and a solid electrolyte are in contact with each other as a model of an all-solid-state battery, and provides boundary conditions (step S101). The model and boundary conditions of the all-solid-state battery may be set in advance and stored in the storage unit 12. In this case, the calculation unit 11 may read out the model and boundary conditions set in advance from the storage unit 12. Alternatively, the calculation unit 11 may accept the setting of the model and boundary conditions through the operation unit 13.

Then, the calculation unit 11 accepts the setting of the contact area (half apex angle) (step S102). The contact area may be set assuming the internal stress of the energy storage element 2. Alternatively, a real value obtained by analyzing an SEM image (SEM: Scanning Electron Microscope) of the energy storage element 2 may be given. The value of the contact area used in the simulation may be stored in advance in the memory unit 12, or may be given via the operation unit 13 during calculation.

Next, the calculation unit 11 calculates the effective diffusion coefficient by calculating the flow velocity from the surface portion of the sphere having the contact area set in step S102 to the observation point (step S103). The relationship between the flow velocity and the effective diffusion coefficient is expressed by Equation 4, and the effective diffusion coefficient is calculated as the coefficient of the concentration gradient.

Next, the calculation unit 11 calculates the effective ion conductivity using the effective diffusion coefficient calculated in step S103 (step S104). The relationship between the effective diffusion coefficient and the effective ion conductivity is expressed by Equation 6.

In the flowchart shown in FIG. 8, the calculation unit 11 is configured to calculate both the effective diffusion coefficient and the effective ionic conductivity, but it may be configured to calculate only one of them.

Furthermore, the calculation unit 11 may estimate, from the calculated effective diffusion coefficient or effective ion conductivity, other physical quantities related to the electrochemical phenomenon of the energy storage element 2. For example, since there is a relationship between a general conductivity σ (S m ^-1 ) and internal resistance R _ohm (Ω) of R _ohm = L/(σ × A), where L is length (m) and A is cross-sectional area ( ^m2 ), the calculation unit 11 may estimate the internal resistance of the energy storage element 2 using this relationship.

Next, the calculation unit 11 outputs information on the calculated effective diffusion coefficient and effective ionic conductivity from the output unit 14 (step S105). The calculation unit 11 may output the calculated effective diffusion coefficient and effective ionic conductivity values, or may output a numerical range. Alternatively, the calculation unit 11 may output a graph in which the effective diffusion coefficient and effective ionic conductivity are plotted against the contact area.

As described above, in the first embodiment, it is possible to estimate physical quantities related to the electrochemistry of the energy storage element 2, such as the effective diffusion coefficient and the effective ionic conductivity, while taking into account the contact area between the active material particles and the solid electrolyte.

(Embodiment 2)
In the second embodiment, a configuration for calculating the effective diffusion coefficient and the effective ion conductivity based on the internal stress of the energy storage element 2 will be described.

In the first embodiment, the relationship between the contact area between the active material particles and the solid electrolyte and the effective diffusion coefficient or effective ion conductivity has been described. For example, although the formula 4 expresses the relationship between the contact area x and the effective diffusion coefficient D _AM,eff , the compressive stress may be used instead of the contact area. The stress is the resistance force generated inside the member against the load, and is the force per unit area obtained by dividing the load by the member area. The Hertz theory can be applied to the stress applied to the part where the spherical elastic bodies contact each other. According to the Hertz theory, the compressive stress of the contact part is described by the formula 7.

Here, S _p is the compressive stress (Pa), F is the load (N), and r is the radius of the contact surface (m). When Equation 5 is rewritten using Equation 7, the relationship between the effective diffusion coefficient D _AM,eff and the compressive stress S _p can be obtained. The calculation unit 11 of the estimation device 1 may calculate the effective diffusion coefficient D _AM,eff of the active material particles by applying the compressive stress S _p instead of the contact area x.

Furthermore, the calculation unit 11 may substitute the calculated effective diffusion coefficient D _AM,eff into Equation 6 to calculate the effective ion conductivity σ _AM,eff .

Figure 9 is a flowchart explaining the execution procedure of the calculation process executed by the estimation device 1 according to the second embodiment. The calculation unit 11 of the estimation device 1 sets a model in which spherical active material particles are in contact with a solid electrolyte as a model of an all-solid-state battery, and gives boundary conditions (step S201). The model and boundary conditions of the all-solid-state battery may be set in advance and stored in the memory unit 12. In this case, the calculation unit 11 may read out the model and boundary conditions set in advance from the memory unit 12. Alternatively, the calculation unit 11 may accept the setting of the model and boundary conditions via the operation unit 13.

Next, the calculation unit 11 accepts the setting of the internal stress (step S202). The value of the internal stress used in the simulation may be stored in advance in the memory unit 12, or may be provided via the operation unit 13 during the calculation.

Next, the calculation unit 11 calculates the effective diffusion coefficient by calculating the flow rate from the contact portion between the active material particles and the solid electrolyte to the observation point (step S203). The relationship between the flow rate and the effective diffusion coefficient is expressed by Equation 4. The calculation unit 11 can calculate the effective diffusion coefficient as the coefficient of the concentration gradient based on Equation 4.

Next, the calculation unit 11 calculates the effective ion conductivity using the effective diffusion coefficient calculated in step S203 (step S204). The relationship between the effective diffusion coefficient and the effective ion conductivity is expressed by Equation 6. The calculation unit 11 can calculate the effective ion conductivity based on Equation 6.

Next, the calculation unit 11 outputs information on the calculated effective diffusion coefficient and effective ionic conductivity from the output unit 14 (step S205). The calculation unit 11 may output the calculated effective diffusion coefficient and effective ionic conductivity values, or may output a numerical range. Alternatively, the calculation unit 11 may output a graph in which the effective diffusion coefficient and effective ionic conductivity are plotted against the contact area.

In the flowchart of FIG. 9, the calculation unit 11 is configured to calculate both the effective diffusion coefficient and the effective ionic conductivity, but it may be configured to calculate only one of the effective diffusion coefficient and the effective ionic conductivity.

The calculation unit 11 may estimate the internal resistance based on the internal stress of the storage element 2. FIG. 10 is a graph showing the relationship between the internal stress S _p of the storage element 2 and the internal resistance R _ohm . The horizontal axis of the graph represents the internal stress S _p of the storage element 2, and the vertical axis represents the internal resistance R _ohm of the storage element 2. As shown in the graph of FIG. 10, the function form of R _ohm is determined so that ∂R _ohm /∂S _p ≧0, taking into consideration the experimental fact that the higher the compressive stress, the lower the internal resistance. R _ohm may be a function bounded both above and below, and it is desirable that the lower limit is greater than 0 and the upper limit is sufficiently large. The memory unit 12 of the estimation device 1 may store a function for converting the internal stress S _p into the internal resistance R _ohm , or a conversion table for converting the internal stress S _p into the internal resistance R _ohm .

The estimation device 1 converts the value of the internal stress S _p into the value of the internal resistance R _ohm according to a predetermined function (or table). The estimation device 1 may estimate a physical quantity related to the electrochemical phenomenon of the energy storage element 2, including the equilibrium potential and activation overvoltage of the positive and negative electrodes, using the value of the internal resistance _R ohm obtained after the conversion. For example, the method described in Japanese Patent Application No. 2020-160971 is used as the estimation method.

As described above, in the second embodiment, it is possible to estimate physical quantities related to the electrochemistry of the energy storage element 2, such as the effective diffusion coefficient and effective ionic conductivity, while taking into account the internal stress of the energy storage element 2.

(Embodiment 3)
In the third embodiment, a method for estimating internal stress will be described.

Figure 11 is a block diagram showing the internal configuration of the estimation device 1 according to embodiment 3. The estimation device 1 includes an input unit 15 in addition to the calculation unit 11, memory unit 12, operation unit 13, and output unit 14 described above.

The input unit 15 has an interface for connecting various sensors. A strain sensor S1 that measures the strain occurring in the energy storage element 2 is connected to the input unit 15. The strain sensor S1 is attached to a location where the strain of the energy storage element 2 appears. For example, the strain sensor S1 is attached to the side portion 312 of the case 31 that houses the energy storage element 2. Alternatively, the strain sensor S1 may be attached to the bottom portion 311 or the lid body 313 of the case 31, or may be attached directly to the energy storage element 2. The calculation unit 11 acquires measurement data of the strain measured by the strain sensor S1 via the input unit 15.

The input unit 15 may be connected to a temperature sensor S2 that measures the temperature of the energy storage element 2, a temperature sensor S3 that measures the environmental temperature of the energy storage element 2, and the like. The temperature sensor S2 is provided at an appropriate location on the energy storage element 2 or the case 31 that houses the energy storage element 2, and is a sensor that measures the temperature of the energy storage element 2. The temperature sensor S3 is provided around the energy storage element 2, and is a sensor that measures the temperature around the energy storage element 2 (environmental temperature). Existing sensors such as thermocouples and thermistors are used for the temperature sensors S2 and S3. The calculation unit 11 may obtain environmental temperature data from an external server such as a weather server.

An ammeter S4 that measures the current flowing through the storage element 2 and a voltmeter S5 that measures the voltage of the storage element 2 may be connected to the input unit 15.

The estimation device 1 according to the third embodiment estimates the internal stress of the energy storage element 2 based on measurement data such as strain. That is, in the third embodiment, a part of the estimation device 1 is caused to function as a state estimator (observer). The estimation device 1 derives the time transition of the internal stress S _p by sequentially calculating the time update of a time series model represented by the state equation of Expression 8 and the observation equation of Expression 9 using a nonlinear filter.

The state equation is written as in Equation 8.

Here, x ^k is a vector (state vector) whose elements are state quantities, and v ^k is a vector (disturbance vector) whose elements are disturbance quantities. k represents a time step. f represents a nonlinear transformation of each state quantity. The disturbance term may be calculated by setting some or all of the elements to 0.

The ε _iso,e included in the state quantity represents the inherent strain due to isolation. Isolation refers to the phenomenon in which charge carriers (e.g., lithium atoms) are inserted into and removed from the active material particles during charging and discharging, causing expansion and contraction, which results in the active material particles cracking. The cracking of the active material particles increases the volume, and an inherent strain is generated inside the energy storage element 2.

ε _pre,e represents the inherent strain due to the growth of precipitates. For example, when lithium metal is used in the negative electrode of the energy storage element 2, precipitates may be formed on the surface of the negative electrode due to repeated charging and discharging over a long period of time. An example of the precipitate is sparse lithium metal. The precipitate may be a passive insulating film (SEI film) or the like. The growth of the precipitates generates inherent strain inside the energy storage element 2.

ε _ref represents the strain of the energy storage element 2. A measurement value by the strain sensor S1 is used for ε _ref . S _p represents the internal stress of the energy storage element 2. Taking into consideration the internal mechanical state (balance of forces) of the energy storage element 2, the internal stress S _p is expressed as a function of the inherent strain ε _iso due to isolation, the inherent strain ε _pre due to the growth of precipitates, and the strain ε _ref obtained as a measurement value by the strain sensor S1.

The observation equation is written as follows:

Here, y ^k is the observation value, and C ^T is the observation vector. A disturbance vector may also be added to the observation equation.

Below, we explain a method for sequentially calculating time updates using an ensemble Kalman filter as an example of a nonlinear filter.

12 is a flow chart for explaining the procedure for estimating the internal stress. The calculation unit 11 of the estimation device 1 provides an initial value of k=1 (step S301). The calculation unit 11 provides a measured value of the strain measured in advance using the strain sensor S1 as the initial value of ε _ref ^k , and provides provisional values set in advance as initial values of the inherent strain ε _iso,e ^k due to isolation, the inherent strain ε _pre,e ^k due to the growth of precipitates, and the internal stress S _p ^k .

Next, the calculation unit 11 generates N particles for each state variable (step S302), where N is a number of about 10 ² to 10 ⁶ .

Next, the calculation unit 11 generates random numbers corresponding to _vk for i = 1, 2, ..., N (step S303). It is assumed that _vk follows a normal distribution and that the variance is known.

The calculation unit 11 performs calculations based on equation 10 for all N particles and updates the particle states to the particle states at the next time step (step S304).

The calculation unit 11 calculates the difference x _k ⁽ⁱ⁾ — bar between the state vector of each particle where i=1, 2, . . . , N and the average value of the state vectors of all the particles (step S305). x _k ⁽ⁱ⁾ — bar is expressed by Equation 11.

The calculation unit 11 calculates a covariance matrix P _k of the state quantity predicted values for all particles (step S306). The covariance matrix P _k is expressed by Equation 12.

The calculation unit 11 acquires the sensor output of the strain sensor S1 through the input unit 15 (step S307). The acquired sensor output of the strain sensor S1 gives the observed value y _k ⁱ of each particle at time step k.

The calculation unit 11 calculates the measurement error r _k ⁱ of the i-th particle at the time step k (step S308), where w _k is the observed disturbance. The measurement error r _k ⁱ is expressed by Equation 13.

The calculation unit 11 calculates the Kalman gain K _k at the time step k (step S309). The Kalman gain K _k is expressed by Equation 14.

The calculation unit 11 calculates an estimate x _k ⁽ⁱ⁾ _hat of the i-th particle (step S310). The estimate x _k ⁽ⁱ⁾ _hat is expressed by Equation 15. That is, the calculation unit 11 corrects the initial prediction value of Equation 10 by using the observation error r _k ⁱ of Equation 13 and the Kalman gain K _k of Equation 14.

The calculation unit 11 calculates the average value x _k _hat of each particle (step S311). The average value x _k _hat of each particle represents a state vector estimate obtained by the ensemble Kalman filter, and is calculated by the following formula.

The estimated value obtained by Equation 16 (average value x _k —hat of each particle) includes an estimated value of the internal stress S _p .

Then, the calculation unit 11 judges whether or not to end the calculation (step S312). For example, if an end instruction is given by the user, the calculation unit 11 judges to end the calculation. If it is judged not to end the calculation (S312: NO), the calculation unit 11 returns the process to step S302 and executes the calculation in the next time step.

When it is determined that the calculation unit 11 should be terminated (S312: YES), the calculation unit 11 outputs information on the estimated internal stress S _p from the output unit 14 (step S313), and terminates the processing according to this flowchart. The information on the internal stress S _p output by the calculation unit 11 may be the value of the internal stress itself, or a physical quantity derived based on the internal stress (e.g., the internal resistance of the energy storage element 2). Furthermore, the information on the internal stress S _p output by the calculation unit 11 may be a graph showing the time progression of the internal stress S _p , or a two-dimensional or three-dimensional graph or contour map showing the stress distribution.

As described above, the estimation device 1 estimates the internal stress S _p of the energy storage element 2 by using the ensemble Kalman filter. The ensemble Kalman filter is a filter method targeted at state space models having nonlinearity and non-Gaussianity, and can be targeted at more general state space models. The ensemble Kalman filter has a relatively simple algorithm and can be easily implemented in the estimation device 1.

In the flowchart of Fig. 12, the calculation method using the ensemble Kalman filter has been described as an example. Alternatively, the estimation device 1 may estimate the internal stress σ _in of the energy storage element 2 using a nonlinear filter such as a particle filter, an extended Kalman filter, or an unscented Kalman filter.

In the third embodiment, the isolation of material particles and the growth of precipitates are considered as factors that cause distortion in the energy storage element 2, but inherent distortion due to thermal expansion may also be considered.

The estimation device 1 may estimate electrochemical phenomena of the energy storage element 2, such as the effective diffusion coefficient, the effective ion conductivity, and the internal resistance, using the estimated internal stress S _p .

The embodiments disclosed herein are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is indicated by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims.

For example, the energy storage element 2 may be a module in which multiple cells are connected in series, a bank in which multiple modules are connected in series, or a domain in which multiple banks are connected in parallel.

REFERENCE SIGNS LIST 1 Estimation device 2 Energy storage element 3 Restraint member 11 Calculation unit 12 Memory unit 13 Operation unit 14 Output unit 15 Input unit 21 Positive electrode current collector layer 22 Positive electrode active material layer 23 Solid electrolyte layer 24 Negative electrode active material layer 25 Negative electrode current collector layer 31 Case 32 Elastic member 310 Case body 311 Bottom surface portion 312 Side surface portion 313 Lid MD1 Simulation model PG1 Estimation program

Claims (8)

On the computer,
A computer program for executing a process of simulating an electrochemical phenomenon of an all-solid-state battery including a solid electrolyte, using a simulation model including a contact area between active material particles and a solid electrolyte as a parameter. the simulation model defines a relationship between the contact area and an effective diffusion coefficient of the active material particles,
The computer program product according to claim 1 , which causes the computer to execute a process of estimating an effective diffusion coefficient of the active material particles based on the value of the contact area. the simulation model defines a relationship between the contact area and an effective ionic conductivity of the active material particles;
The computer program product according to claim 1 , which causes the computer to execute a process of estimating an effective ionic conductivity of the active material particles based on the value of the contact area. the contact area is a function of the internal stress of the solid-state battery;
The computer program according to claim 1 , for causing the computer to execute a process of simulating an electrochemical phenomenon in the all-solid-state battery based on a value of the internal stress. acquiring measurement data relating to the distortion from a distortion sensor that measures the distortion occurring in the all-solid-state battery;
The computer program according to claim 4, for causing the computer to execute a process of estimating an internal stress of the all-solid-state battery based on acquired measurement data by using a model representing an internal mechanical state of the all-solid-state battery. The internal resistance of the solid-state battery is a function of the internal stress,
6. The computer program according to claim 4, for causing the computer to execute a process of estimating a value of the internal resistance based on a value of the internal stress. A simulation method comprising: simulating, by a computer, a process of simulating an electrochemical phenomenon in an all-solid-state battery including a solid electrolyte, using a simulation model including a contact area between active material particles and a solid electrolyte as a parameter. A simulation device comprising: a calculation unit that simulates an electrochemical phenomenon of an all-solid-state battery including a solid electrolyte by using a simulation model including a contact area between active material particles and a solid electrolyte as a parameter.

Images