Computer program, simulation method, and simulation device

Abstract

To provide a computer program, a simulation method, and a simulation device, which can be applied to an all-solid battery and execute a simulation of an electrochemical phenomenon on the basis of a parameter depending on the internal stress of a battery.SOLUTION: The computer program causes a computer to execute processing for simulating an electrochemical phenomenon of an all-solid battery including a solid electrolyte using a simulation model containing a contact area between an active material particle and the solid electrolyte in parameters. A model in which a spherical active material particle and solid electrolyte are in contact is set as a model of the all-solid battery, and boundary conditions are given. The model of the all-solid battery and the boundary condition may be preset.SELECTED DRAWING: Figure 8

Description

[Technical Field]

[0001] The present invention relates to a computer program, a simulation method, and a simulation device. [Background technology]

[0002] Liquid electrolyte lithium-ion batteries, which use organic solvents as ionic conductors, are becoming increasingly popular. They are used not only as mobile batteries for mobile phones, digital cameras, and camcorders, but also as energy sources for automobiles and trains.

[0003] In recent years, all-solid-state batteries have been developed as an alternative to liquid electrolyte lithium-ion batteries. All-solid-state batteries have advantages such as no restrictions on shape, resistance to internal short circuits, and heat resistance. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2012-154665 [Patent Document 2] Japanese Patent Application Laid-Open No. 2016-065828 [Patent Document 3] Japanese Patent Application Publication No. 2019-148537 Summary of the Invention [Problem to be solved by the invention]

[0005] The development and production of liquid electrolyte lithium-ion batteries is progressing worldwide, 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).

[0006] However, there is currently no simulation model for all-solid-state batteries that can predict the internal behavior of the battery, and it is not possible to use simulation models for liquid electrolyte lithium-ion batteries, which have a different mechanism.

[0007] The present invention has been made in view 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 that can execute a simulation of an electrochemical phenomenon based on parameters that depend on the internal stress of the battery. [Means for solving the problem]

[0008] The computer program causes the computer to execute a process of simulating electrochemical phenomena 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.

[0009] The simulation method uses a simulation model that includes the contact area between active material particles and a solid electrolyte as a parameter, and executes a process of simulating electrochemical phenomena in an all-solid-state battery that includes the solid electrolyte by a computer.

[0010] The simulation device includes a calculation unit that simulates electrochemical phenomena in an all-solid-state battery containing a solid electrolyte using a simulation model that includes a contact area between active material particles and a solid electrolyte as a parameter. [Effects of the Invention]

[0011] The above configuration can be applied to all-solid-state batteries, and allows simulation of electrochemical phenomena to be performed based on parameters that depend on the internal stress of the battery. [Brief explanation of the drawings]

[0012] [Figure 1] 1 is a block diagram showing an internal configuration of an estimation device according to a first embodiment. [Figure 2] FIG. 2 is an explanatory diagram illustrating the configuration of an energy storage element. [Figure 3] FIG. 2 is an explanatory diagram illustrating the internal structure of a solid electrolyte layer. [Figure 4] FIG. 10 is an explanatory diagram illustrating a method for calculating an effective diffusion coefficient. [Figure 5] FIG. 1 is an explanatory diagram illustrating a method for calculating an effective diffusion coefficient in an all-solid-state battery. [Figure 6] FIG. 10 is a diagram showing calculation results of an effective diffusion coefficient in an all-solid-state battery. [Figure 7] 1 is a graph showing the relationship between the contact area ratio and the effective diffusion coefficient. [Figure 8] 4 is a flowchart illustrating the execution procedure of a calculation process executed by the estimation device according to the first embodiment. [Figure 9] 10 is a flowchart illustrating the execution procedure of a calculation process executed by an estimation device according to a second embodiment. [Figure 10] 1 is a graph showing the relationship between internal stress and internal resistance of an energy storage element. [Figure 11] FIG. 11 is a block diagram showing the internal configuration of an estimation device according to a third embodiment. [Figure 12] 10 is a flowchart illustrating a procedure for estimating internal stress. DETAILED DESCRIPTION OF THE INVENTION

[0013] The computer program causes the computer to execute a process of simulating electrochemical phenomena 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. Unlike liquid electrolyte lithium-ion batteries, all-solid-state batteries have a high contact resistance unless the contact area between the active material particles and the solid electrolyte is actively increased. That is, all-solid-state batteries have the characteristic that electricity flows more easily when external pressure is applied 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.

[0014] In the computer program, the simulation model may define a relationship between the contact area and the effective diffusion coefficient of the active material particles, and the computer may be caused to execute a process of estimating the effective diffusion coefficient of the active material particles based on the value of the contact area. According to this configuration, by linking the value of the contact area with the effective diffusion coefficient of the active material particles, it is possible to simulate an electrochemical phenomenon of an all-solid-state battery from the value of the contact area.

[0015] In the computer program, the simulation model may define a relationship between the contact area and the effective ionic conductivity of the active material particles, and the computer may be caused to execute a process of estimating the effective ionic conductivity of the active material particles based on the value of the contact area. According to this configuration, by linking the value of the contact area with the effective ionic conductivity of the active material particles, it is possible to simulate electrochemical phenomena in an all-solid-state battery from the value of the contact area.

[0016] In the computer program, the contact area may be a function of internal stress of the all-solid-state battery, and the computer may be caused to execute a process of simulating an electrochemical phenomenon of the all-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 all-solid-state battery from the value of the internal stress.

[0017] 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 an internal stress of the all-solid-state battery based on the acquired measurement data using a model that represents an 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.

[0018] In the computer program, the internal resistance of the all-solid-state battery may be 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 all-solid-state battery can be estimated by linking the value of the internal stress with the value of the internal resistance.

[0019] The simulation method uses a simulation model that includes the contact area between active material particles and a solid electrolyte as a parameter, and executes a process of simulating electrochemical phenomena in an all-solid-state battery that includes the solid electrolyte by a computer. This configuration makes it possible to simulate the electrochemical phenomena of all-solid-state batteries based on the contact area, which is one of the characteristic parameters of all-solid-state batteries.

[0020] The simulation device includes a calculation unit that simulates electrochemical phenomena in an all-solid-state battery containing a solid electrolyte using a simulation model that includes a contact area between active material particles and a solid electrolyte as a parameter. This configuration makes it possible to simulate the electrochemical phenomena of all-solid-state batteries based on the contact area, which is one of the characteristic parameters of all-solid-state batteries.

[0021] The present invention will now be described in detail with reference to the drawings showing embodiments thereof. (Embodiment 1) 1 is a block diagram showing the 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.

[0022] 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.

[0023] Alternatively, the calculation unit 11 may be any processing circuit or calculation circuit including multiple CPUs, a multi-core CPU, a GPU (Graphics Processing Unit), a microcomputer, a volatile or non-volatile memory, etc. Furthermore, the calculation unit 11 may have functions such as a timer that measures the elapsed time from when an instruction to start measurement is given until when an instruction to end measurement is given, a counter that counts numbers, a clock that outputs date and time information, etc.

[0024] 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 that causes a computer to execute a process of estimating an electrochemical phenomenon in 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 include parameters used in the simulation model MD1, parameters used in the estimation program PG1, data generated by the calculation unit 11, and the like.

[0025] 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++, or Java (registered trademark). The numerical analysis software may be a circuit simulator known as 1D-CAE, or a simulator such as a finite element method or finite volume method that operates on 3D shapes. Alternatively, a reduced-order model (ROM) based on these may be used.

[0026] A computer program including the estimation program PG1 is provided by a non-transitory recording medium M on which the computer program is readably recorded. The recording medium M is a portable memory such as a CD-ROM, a USB memory, or an SD (Secure Digital) card. The calculation unit 11 reads the desired computer program from the recording medium M using a reading device (not shown) and stores the read computer program in the storage unit 12. Alternatively, the computer program may be provided by communication.

[0027] 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, a mouse, and a touch panel. The operation unit 13 outputs operation information accepted through the operation devices to the calculation unit 11.

[0028] The output unit 14 includes a connection interface for connecting an external device. The external device connected to the output unit 14 is a display device 140 including 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 displaying the information on the display device 140. Alternatively, the estimation device 1 may include the display device 140 built therein.

[0029] Furthermore, the output unit 14 may include 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 for a mobile terminal, an electric vehicle, or the like that operates using power supplied from the energy storage element 2.

[0030] The storage element 2 that is the target of 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.

[0031] The positive electrode current collector layer 21 is made of a metal foil, a metal mesh, or the like. The metal constituting the positive electrode current collector layer 21 is a metal with good conductivity, such as aluminum, nickel, titanium, or stainless steel. A coating layer for adjusting contact resistance may be formed on the surface of the positive electrode current collector layer 21. An example of the coating layer is a carbon coating. The thickness of the positive electrode current collector layer 21 is not particularly limited and is, for example, 0.1 μm or more and 1 mm or less.

[0032] The positive electrode active material layer 22 is a layer containing 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, etc. The positive electrode active material layer 22 has a thickness of, for example, 0.1 μm or more and 1 mm or less.

[0033] The cathode active material may be any suitable cathode active material suitable for use in solid-state batteries. Examples of suitable cathode active materials include lithium cobalt oxide, lithium nickel oxide, lithium manganese oxide, and spinel-based lithium compounds. The cathode active material may be particles having an average particle size (D50) of 0.5 μm to 20 μm. The particles constituting the cathode active material may be primary particles or secondary particles. The cathode active material may be in the form of a thin film or a particle. The solid electrolyte contained in the cathode active material layer 22 may be an inorganic solid electrolyte having relatively high ionic conductivity and excellent heat resistance. Examples of suitable inorganic solid electrolytes include oxide solid electrolytes such as lithium lanthanum zirconate and sulfide solid electrolytes such as Li2S-P2S5. Examples of suitable conductive additives include carbon materials such as acetylene black and ketjen black, and metal materials such as nickel, aluminum, and stainless steel. Materials such as butadiene rubber (BR), acrylate butadiene rubber (ABR), and polyvinylidene fluoride (PVdF) are used as binders.

[0034] The solid electrolyte layer 23 is a layer containing at least a solid electrolyte. In addition to the solid electrolyte, the solid electrolyte layer 23 may contain a binder or the like. 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.

[0035] The negative electrode active material layer 24 is a layer containing 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, etc. The negative electrode active material layer 24 has a thickness of, for example, 0.1 μm or more and 1 mm or less.

[0036] The negative electrode active material may be any suitable negative electrode active material suitable for use in solid-state batteries. For example, metal active materials and carbon active materials are used. Examples of metal active materials include Li, In, Al, Si, and Sn. The metal active material may be a metal element or a metal composite oxide. Examples of carbon active materials include mesocarbon microbeads (MCMB), highly oriented graphite (HOPG), hard carbon, and soft carbon. The negative electrode active material may be particles having an average particle size (D50) of 0.5 μm to 20 μm. The particles constituting the negative electrode active material may be primary particles or secondary particles. The negative electrode active material may be in the form of a thin film or not. The solid electrolyte, conductive additive, and binder used in the negative electrode active material layer 24 may be the same as those used in the positive electrode active material layer 22.

[0037] The negative electrode current collector layer 25 is made of a metal foil, a metal mesh, or the like. The metal constituting the negative electrode current collector layer 25 is a metal with good conductivity, such as copper, nickel, titanium, or stainless steel. A coating layer for adjusting contact resistance may be formed on the surface of the negative electrode current collector layer 25. An example of the coating layer is a carbon coating. The thickness of the negative electrode current collector layer 25 is not particularly limited and is, for example, 0.1 μm or more and 1 mm or less.

[0038] The energy storage device 2 is restrained by a restraining member 3. The restraining member 3 includes, for example, a case 31 that houses the energy storage device 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 configured with a bottom portion 311 and side portions 312, and a lid 313 that closes an opening of the case body 310. The case body 310 (bottom portion 311 and side portions 312) and the lid 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 portions 312) and the lid 313 may be formed of resin. After the energy storage device 2 is housed in the case body 310, the case body 310 is sealed by the lid 313.

[0039] The elastic member 32 is disposed in a compressed state between the bottom layer (positive electrode current collector layer 21 in the example of FIG. 2) of the energy storage element 2 and the bottom surface portion 311, and between the top layer (negative electrode current collector layer 25 in the example of FIG. 2) of the energy storage element 2 and the lid 313. The elastic member 32 is, for example, a rubber 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).

[0040] In the example of FIG. 2, a configuration is adopted in which an elastic member 32 is disposed inside the case 31, thereby applying a restraining force to the energy storage element 2. 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 unwanted reactions with the battery materials. For example, an inert gas such as nitrogen or dry air may be used. Alternatively, a configuration may be adopted in which the energy storage element 2 is sandwiched between plate members on both sides in the stacking direction, and the plate members are connected together while a restraining force is applied to the energy storage element 2, thereby applying a restraining force to the energy storage element 2.

[0041] FIG. 3 is an explanatory diagram illustrating the internal structure of the solid electrolyte layer 23. In the example of FIG. 3, active material particles are shown as hatched spheres, and the solid electrolyte is shown as unhatched spheres. For simplification, the conductive additive and binder are omitted from FIG. 3. In an all-solid-state battery containing particulate active material (active material particles), the active material particles and the solid electrolyte are in contact with each other over a small contact area (point), as indicated by the black circles in the figure. The contact area between the solid electrolyte and the active material particles varies depending on the restraining force and internal stress that restrain the energy storage element.

[0042] In conventional liquid electrolyte lithium-ion batteries, the active material particles are surrounded by the 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.

[0043] In contrast, in all-solid-state batteries, ions are exchanged only in the small area where the active material particles and the solid electrolyte 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 the solid electrolyte and the effective diffusion coefficient or effective ionic conductivity.

[0044] The present inventors have found, through numerical calculations (simulations), the relationship between the contact area between the active material particles and the solid electrolyte and the effective diffusion coefficient or effective ionic conductivity. In the present embodiment, a simulation method is proposed that uses these relationships to estimate 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).

[0045] As a reference example, a calculation method for determining the effective diffusion coefficient of an electrolyte solution for a liquid electrolyte lithium ion battery will be described below.

[0046] Figure 4 is an explanatory diagram explaining the method for calculating the effective diffusion coefficient. Figure 4 shows a simplified model of the positive electrode of a liquid electrolyte lithium-ion battery. Figure 4 shows a state in which multiple active material particles exist inside the positive electrode, and the inside and surrounding areas are filled with electrolyte. When the thickness of the positive electrode is L (m) and the length of the conduction path indicated by the dashed line in the figure is l (m), the degree of tortuosity τ due to the gaps and active material particles can be expressed as τ = l / L. In this case, 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 equation, where ε represents the volume fraction of the electrolyte.

[0047]

number

[0048] Similarly, the effective ionic conductivity of the electrolyte, σl,eff (Sm -1 ) and true ionic conductivity σ l (Sm -1 ) is expressed by the following equation:

[0049]

number

[0050] The upper side of the model shown in FIG. 4 is the inlet of the electrolyte, and the lower side is the outlet (observation point). By setting appropriate boundary conditions, the flow rate of the electrolyte at the observation point can be calculated. For example, the boundary conditions are 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 ) is given.

[0051] The flow rate of the electrolyte at the observation point is J l , electrolyte concentration c l When the flow velocity J l and concentration c l The relationship between D and l,eff represents the effective diffusion coefficient. The effective diffusion coefficient of the electrolyte, D l,eff is calculated based on Equation 3.

[0052]

number

[0053] In all-solid-state batteries, some of the active material particles are in contact with the solid electrolyte, and the interior and surrounding areas are not filled with electrolyte. Therefore, the calculation method for the effective diffusion coefficient used in liquid electrolyte lithium-ion batteries cannot be directly applied to all-solid-state batteries. Therefore, the present inventors introduce the concept of the contact area between the active material particles and the solid electrolyte and propose a method for calculating the effective diffusion coefficient, which changes depending on the contact area, through simulation.

[0054] FIG. 5 is an explanatory diagram for explaining a method for calculating 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 sets the surface of the sphere as an inlet, and the surfaces of concentric spheres set inside the sphere as observation points, and calculates the flow velocity J at the observation point when a boundary state is given. AM (mol m -2 s -1 The observation points are set, for example, on the surface of a concentric sphere with a radius half that of the sphere. As a boundary condition, a boundary of, for example, 1000 mol m is set around the sphere. -3 concentration, for example, 0 mol m -3 The concentration of is given by the flow rate J AM and the effective diffusion coefficient D AM,eff The relationship between these two is expressed by Equation 4. Here, c AM is the concentration of the active material. The calculation unit 11 calculates the flow rate J AM Substituting into equation 4, the effective diffusion coefficient D of the active material AM,eff Calculate.

[0055]

number

[0056] Figure 6 shows the calculation results for the effective diffusion coefficient in an all-solid-state battery. Figure 6A shows a sphere created by rotating around the axis of rotation to represent the active material of an all-solid-state battery, which is assumed to be 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 calculations were actually performed, the effective diffusion coefficient D AM,eff is 1.0 x 10 -13 (m 2 s -1 ) and the diffusion coefficient of the active material D AM This proves the validity of the calculation method.

[0057] Figure 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 around the axis of symmetry passing through the center of the sphere, where the surface area included in the sphere surface is in contact with the electrolyte. When the half apex angle is 10 degrees, the effective diffusion coefficient D AM,eff is 3.8 x 10 -15 (m 2 s -1 ) and the diffusion coefficient of the active material D AM The value was about two orders of magnitude smaller than that.

[0058] Figure 6C shows the calculation results for a half apex angle of 5 degrees. For a half apex angle of 5 degrees, the effective diffusion coefficient D AM,eff is 1.9 x 10 -15 (m 2 s -1 ), which is even smaller than the value when the half apex angle is 10 degrees.

[0059] Figure 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 Figure 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 of the sphere to the surface area of ​​the sphere, and is a parameter that indicates 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 that represents the active material. The logarithmic axis plot shown in Figure 7 shows that the relationship between the contact area and the effective diffusion coefficient can be formulated using Equation 5. In addition to being able to practically estimate the contact area by analyzing X-ray CT images, parameters that affect the contact area can also be used. For example, in the case of electrodes obtained by press molding, values ​​such as the residual porosity of the electrode composite can be used.

[0060]

number

[0061] where D AM,effis 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 Figure 7) that passes through each point on the graph. The approximation curve can be found using a known method such as the least squares method.

[0062] The calculation unit 11 calculates the effective diffusion coefficient D AM,eff Based on the value of , the effective ionic conductivity σ AM,eff According to Einstein's equation, the relationship between the ionic conductivity σ and the diffusion coefficient D is expressed by Equation 6.

[0063]

number

[0064] where σ is the ionic conductivity (S m -1 ), z is the charge of the ion (dimensionless), F is the 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 represents temperature (K).

[0065] The calculation unit 11 adds the effective diffusion coefficient D calculated from the contact area to the diffusion coefficient D of Equation 6. AM,eff By substituting the value of , the effective ionic conductivity σ AM,eff The effective ionic conductivity σ can be calculated. AM,eff is a physical quantity that affects the electrical resistance of the energy storage element 2. That is, 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.

[0066] The procedure for executing the calculations performed by the estimation device 1 will be described below. FIG. 8 is a flowchart illustrating 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 as a model of an all-solid-state battery, and assigns 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 simply read out the previously set model and boundary conditions from the storage unit 12. Alternatively, the calculation unit 11 may accept the setting of the model and boundary conditions via the operation unit 13.

[0067] Next, the calculation unit 11 receives 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, an actual value obtained by analyzing an SEM image (SEM: Scanning Electron Microscope) of the energy storage element 2 may be provided. The value of the contact area used in the simulation may be stored in advance in the storage unit 12, or may be provided via the operation unit 13 during calculation.

[0068] Next, the calculation unit 11 calculates the effective diffusion coefficient by calculating the flow velocity from the surface 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 a coefficient of the concentration gradient.

[0069] 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.

[0070] 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.

[0071] Furthermore, the calculation unit 11 may estimate other physical quantities related to the electrochemical phenomenon of the energy storage element 2 from the calculated effective diffusion coefficient or effective ion conductivity. For example, the general conductivity σ(S m -1 ) and internal resistance R ohm (Ω), L is the length (m), A is the cross-sectional area (m 2 ) as R ohm =L / (σ×A), the calculation unit 11 may estimate the internal resistance of the storage element 2 using this relational expression.

[0072] 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 values ​​of the effective diffusion coefficient and effective ionic conductivity, 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.

[0073] As described above, in embodiment 1, it is possible to estimate physical quantities related to the electrochemistry of the energy storage device 2, such as the effective diffusion coefficient and effective ionic conductivity, while taking into account the contact area between the active material particles and the solid electrolyte.

[0074] (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.

[0075] In the first embodiment, the relationship between the contact area between the active material particles and the solid electrolyte and the effective diffusion coefficient and effective ion conductivity has been described. For example, Equation 4 expresses the relationship between the contact area x and the effective diffusion coefficient D AM,eff However, compressive stress may be used instead of contact area. Stress is the resistance force generated within a member against a load, and is the force per unit area obtained by dividing the load by the member's area. Hertz theory can be applied to the stress acting on the contact area between spherical elastic bodies. According to Hertz theory, compressive stress at the contact area is described by equation 7.

[0076]

number

[0077] where 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 effective diffusion coefficient D AM,eff and compressive stress S p The calculation unit 11 of the estimation device 1 calculates the compressive stress S p By giving the effective diffusion coefficient D of the active material particles AM,eff may be calculated.

[0078] Furthermore, the calculation unit 11 calculates the effective diffusion coefficient D AM,eff Substituting into equation 6, the effective ionic conductivity σ AM,eff may be calculated.

[0079] FIG. 9 is a flowchart illustrating 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 and a solid electrolyte are in contact as a model of an all-solid-state battery, and assigns boundary conditions (step S201). 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 simply read out the previously set model and boundary conditions from the storage unit 12. Alternatively, the calculation unit 11 may receive the setting of the model and boundary conditions via the operation unit 13.

[0080] Next, the calculation unit 11 receives 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 storage unit 12, or may be given via the operation unit 13 during the calculation.

[0081] 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. Based on Equation 4, the calculation unit 11 can calculate the effective diffusion coefficient as a coefficient of the concentration gradient.

[0082] 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.

[0083] 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 values ​​of the effective diffusion coefficient and effective ionic conductivity, 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.

[0084] In the flowchart of FIG. 9, the calculation unit 11 is configured to calculate both the effective diffusion coefficient and the effective ion conductivity, but it may be configured to calculate only one of the effective diffusion coefficient and the effective ion conductivity.

[0085] The calculation unit 11 may estimate the internal resistance based on the internal stress of the energy storage element 2. FIG. p and internal resistance R ohm The horizontal axis of the graph represents the internal stress S of the energy storage element 2. p The vertical axis represents the internal resistance R of the storage element 2. ohm As shown in the graph in Figure 10, the higher the compressive stress, the lower the internal resistance. ohm The functional form of is ∂R ohm / ∂S p R is defined to be ≥ 0. ohmmay 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 a sufficiently large value. p is the internal resistance R ohm The function to convert the internal stress S p is the internal resistance R ohm A conversion table for converting the

[0086] The estimation device 1 calculates the internal stress S according to a predetermined function (or table). p The value of the internal resistance R ohm The estimation device 1 converts the internal resistance R obtained after the conversion into ohm The value of may be used to estimate physical quantities related to electrochemical phenomena in the energy storage element 2, including the equilibrium potentials of the positive and negative electrodes and the activation overvoltage. For example, the method described in Japanese Patent Application No. 2020-160971 is used as the estimation method.

[0087] 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 the effective ion conductivity, while taking into account the internal stress of the energy storage element 2.

[0088] (Embodiment 3) In the third embodiment, a method for estimating internal stress will be described.

[0089] 11 is a block diagram showing the internal configuration of an estimation device 1 according to embodiment 3. The estimation device 1 includes an input unit 15 in addition to the calculation unit 11, storage unit 12, operation unit 13, and output unit 14 described above.

[0090] The input unit 15 has an interface for connecting various sensors. A strain sensor S1 that measures 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 strain appears in the energy storage element 2. For example, the strain sensor S1 is attached to a side surface portion 312 of a case 31 that houses the energy storage element 2. Alternatively, the strain sensor S1 may be attached to a bottom surface portion 311 or a lid 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.

[0091] 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 ambient temperature of the energy storage element 2, and the like. The temperature sensor S2 is a sensor that is provided at an appropriate location on the energy storage element 2 or on the case 31 that houses the energy storage element 2, and measures the temperature of the energy storage element 2. The temperature sensor S3 is a sensor that is provided around the energy storage element 2, and measures the ambient temperature (ambient temperature) of the energy storage element 2. Existing sensors such as thermocouples and thermistors are used for the temperature sensors S2 and S3. The calculation unit 11 may obtain ambient temperature data from an external server such as a weather server.

[0092] To the input unit 15, 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.

[0093] 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 functions as a state estimator (observer). The estimation device 1 uses a nonlinear filter to sequentially calculate time updates of a time series model expressed by the state equation of Equation 8 and the observation equation of Equation 9, thereby estimating the internal stress S p The time progression of is derived.

[0094] The equation of state is written as follows:

[0095]

number

[0096] where x k is a vector with state quantities as elements (state vector), v k is a vector (disturbance vector) whose elements are disturbance quantities. k represents the time step. f represents the nonlinear transformation of each state quantity. The disturbance term may be calculated by setting some or all elements to 0.

[0097] ε included in the state quantity iso,e 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 active material particles during charging and discharging, causing expansion and contraction, resulting in cracking of the active material particles. As the active material particles crack, their volume increases, generating inherent strain inside the energy storage element 2.

[0098] ε pre,e represents the inherent strain due to the growth of precipitates. For example, if lithium metal is used in the negative electrode of the energy storage element 2, repeated charging and discharging over a long period of time may cause precipitates to form on the surface of the negative electrode. An example of such a precipitate is sparse lithium metal. The precipitate may also be a passive insulator film (SEI film). The growth of this precipitate causes inherent strain inside the energy storage element 2.

[0099] ε ref represents the strain of the storage element 2. ε ref The measurement value by the strain sensor S1 is used for S p represents the internal stress of the energy storage element 2. p is the inherent strain ε due to isolation, taking into account the internal mechanical state (balance of forces) of the energy storage element 2. iso , the inherent strain due to precipitate growth ε pre , and the strain ε obtained as the measurement value of the strain sensor S1 ref It is expressed as a function of

[0100] The observation equation is written as follows:

[0101]

number

[0102] where y k is the observed value, C T is the observation vector. A disturbance vector can also be added to the observation equation.

[0103] Below, a method of sequentially calculating time updates using an ensemble Kalman filter as an example of a nonlinear filter will be described.

[0104] FIG. 12 is a flowchart illustrating the procedure for estimating internal stress. The calculation unit 11 of the estimation device 1 sets an initial value of k=1 (step S301). The calculation unit 11 calculates the measured value of strain measured in advance using the strain sensor S1 as ε ref k is given as the initial value of , and the eigenstrain due to isolation ε iso,e k , the inherent strain due to precipitate growth ε pre,e k , internal stress S p k A predetermined temporary value may be given as the initial value of

[0105] Next, the calculation unit 11 generates N particles for each state variable (step S302), where N is 10 2 ~10 6 It is about that number.

[0106] Next, the calculation unit 11 calculates v for i=1, 2, ..., N. k A random number corresponding to v is generated (step S303). k is assumed to follow a normal distribution and the variance is known.

[0107] The calculation unit 11 performs calculations based on Equation 10 for all N particles, and updates the states of the particles to the states of the particles in the next time step (step S304).

[0108]

number

[0109] The calculation unit 11 calculates the difference x between the state vector of each particle (i=1, 2, . . . , N) and the average value of the state vectors of all particles. k (i) _bar is calculated (step S305). k (i) _bar is represented by the number 11.

[0110]

number

[0111] The calculation unit 11 calculates the covariance matrix P of the predicted state quantities for all particles. k (Step S306) The covariance matrix P k is expressed by the formula 12.

[0112]

number

[0113] 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 is the observed value y k i Give.

[0114] The calculation unit 11 calculates the observation error r of the i-th particle at time step k. k i is calculated (step S308). k is the observed disturbance. The observation error r k i is expressed by the following equation (13):

[0115]

number

[0116] The calculation unit 11 calculates the Kalman gain K at time step k. k (Step S309). k is expressed by the following equation (14):

[0117]

number

[0118] The calculation unit 11 calculates the estimated value x of the i-th particle. k (i) The estimated value x is calculated (step S310). k (i) hat is expressed by Equation 15. That is, the calculation unit 11 calculates the initial predicted value of Equation 10 by multiplying the observation error r k i and the Kalman gain K in equation 14 k and correct it using

[0119]

number

[0120] The calculation unit 11 calculates the average value x of each particle. k _hat is calculated (step S311). The average value x of each particle is calculated. k _hat represents the state vector estimate obtained by the ensemble Kalman filter and is calculated by the following equation:

[0121]

number

[0122] The estimated value obtained by Equation 16 (average value of each particle x k _hat) contains the internal stress S p Includes estimates of

[0123] Next, the calculation unit 11 determines whether or not to end the calculation (step S312). For example, if an end instruction is given by the user, the calculation unit 11 determines to end the calculation. If it is determined 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.

[0124] When it is determined that the calculation unit is to be terminated (S312: YES), the calculation unit 11 calculates the estimated internal stress S p The information about the internal stress S is output from the output unit 14 (step S313), and the process according to this flowchart is terminated. p The information about the internal stress S may be the value of the internal stress itself, or may be a physical quantity derived based on the internal stress (for example, the internal resistance of the energy storage element 2). p Information about the internal stress S p It may be a graph showing the time progression of stress, or a two-dimensional or three-dimensional graph or contour map showing stress distribution.

[0125] As described above, the estimation device 1 uses the ensemble Kalman filter to estimate the internal stress S p The ensemble Kalman filter is a filter method that targets state space models that have nonlinearity or non-Gaussianity, and can also be used for more general state space models. The ensemble Kalman filter has a relatively simple algorithm and can be easily implemented in the estimation device 1.

[0126] 12, the calculation method using the ensemble Kalman filter has been described as an example. Alternatively, the estimation device 1 may use a nonlinear filter such as a particle filter, an extended Kalman filter, or an unscented Kalman filter to calculate the internal stress σ of the energy storage element 2. in may be estimated.

[0127] In the third embodiment, the isolation of material particles and the growth of precipitates are considered as factors that cause distortion in energy storage element 2. However, inherent distortion due to thermal expansion may also be considered.

[0128] The estimation device 1 estimates the internal stress S p The electrochemical phenomena of the electricity storage element 2, such as the effective diffusion coefficient, the effective ion conductivity, and the internal resistance, can be estimated using the above equation.

[0129] The embodiments disclosed herein should be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims.

[0130] For example, the energy storage device 2 may be a module in which a plurality of cells are connected in series, a bank in which a plurality of modules are connected in series, or a domain in which a plurality of banks are connected in parallel. [Explanation of symbols]

[0131] 1 Estimation device 2. Energy storage element 3 Restraining member 11 Arithmetic section 12 Storage section 13 Control section 14 Output section 15 Input section 21 Positive electrode current collector layer 22 Cathode active material layer 23 Solid electrolyte layer 24 Negative electrode active material layer 25 Negative electrode current collector layer 31 cases 32 Elastic member 310 Case body 311 Bottom part 312 Side part 313 Lid MD1 Simulation Model PG1 Estimation Program

Claims

1. On the computer, Using a simulation model including a parameter of the contact area between active material particles and a solid electrolyte, the electrochemical phenomenon of an all-solid-state battery including the solid electrolyte is simulated. A computer program for executing a process.

2. 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.

3. 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.

4. 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.

5. acquiring measurement data relating to the distortion from a distortion sensor that measures the distortion occurring in the all-solid-state battery; Using a model representing an internal mechanical state of the all-solid-state battery, an internal stress of the all-solid-state battery is estimated based on the acquired measurement data.

5. A computer program product according to claim 4, for causing a computer to carry out a process.

6. 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.

7. Using a simulation model including a parameter of the contact area between active material particles and a solid electrolyte, the electrochemical phenomenon of an all-solid-state battery including the solid electrolyte is simulated. A simulation method in which processing is carried out by a computer.

8. 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 the active material particles and the solid electrolyte as a parameter; A simulation device comprising:

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