Computer program, simulation method, and simulation device

Abstract

To provide a computer program, a method for simulation, and a simulation device.SOLUTION: A computer is caused to calculate a unique distortion of a power storage element on the basis of the amount of generated precipitates and the manner of precipitates regarding a power storage element that generates precipitates in response to charging and discharging and to calculate the distribution of stress or distortion generated in the power storage element on the basis of the calculated unique distortion.SELECTED DRAWING: Figure 5

Description

[Technical field]

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

[0002] In recent years, the demand for batteries has been increasing in various devices and systems such as personal computers, mobile phones, electric vehicles, etc. Batteries used for such applications are required to be lightweight and have high energy density.

[0003] In response to the above demands, lithium metal batteries using lithium metal in the negative electrode have been attracting attention. Because lithium has low density and a very low standard reduction potential, it has been attracting attention as an electrode material for lightweight, high-energy density batteries (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2014-197472 A Summary of the Invention [Problem to be solved by the invention]

[0005] On the other hand, in lithium metal batteries, sparse deposition of lithium on the surface of the negative electrode can cause changes in battery characteristics and battery expansion.

[0006] The morphology of the precipitates varies with the degree of sparseness, such as dendritic, moss-like, granular, dense, etc. Here, dendritic and moss-like precipitates are sparse morphologies.

[0007] In order to suppress the growth of precipitates, it is effective to apply a restraining force from the outside of the battery so that uniform stress is generated inside the battery. However, no method has been proposed so far to estimate the distribution of stress or strain inside the battery.

[0008] The present invention has been made in view of the above circumstances, and has an object to provide a computer program, a simulation method, and a simulation device that are capable of calculating the distribution of stress or strain inside an energy storage element. [Means for solving the problem]

[0009] The computer program causes the computer to execute a process of calculating the inherent strain of an energy storage element in which deposits occur in response to charging and discharging, based on the amount of deposits produced and the precipitation form of the deposits, and calculating the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain.

[0010] The simulation method involves a computer-implemented process in which, for an energy storage element in which deposits occur in response to charging and discharging, the inherent strain of the energy storage element is calculated based on the amount of deposits produced and the precipitation form of the deposits, and the distribution of stress or strain occurring in the energy storage element is calculated based on the calculated inherent strain.

[0011] The simulation device has a calculation unit that calculates the inherent strain of an energy storage element in which deposits occur in response to charging and discharging based on the amount of deposits produced and the precipitation form of the deposits, and calculates the distribution of stress or strain generated in the energy storage element based on the calculated inherent strain. Effect of the Invention

[0012] According to the above configuration, the distribution of stress or strain inside the energy storage element can be calculated. [Brief description of the drawings]

[0013] [Figure 1] 1 is a block diagram showing an internal configuration of an estimation device according to a first embodiment. [Diagram 2] FIG. 2 is an explanatory diagram illustrating a configuration of an energy storage element. [Diagram 3] 1 is a graph showing an example of the relationship between the amount of precipitates formed and the inherent strain. [Figure 4]11 is a graph showing another example of the relationship between the amount of precipitates formed and the inherent strain. [Diagram 5] 1 is a flowchart showing the calculation procedure for stress-strain distribution. [Figure 6] FIG. 2 is a circuit diagram showing an example of an equivalent circuit model. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] The computer program causes the computer to execute a process of calculating the inherent strain of an energy storage element in which deposits occur in response to charging and discharging, based on the amount of deposits produced and the precipitation form of the deposits, and calculating the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain. When an energy storage element is repeatedly charged and discharged, deposits form inside the element. For example, lithium metal batteries, which are expected to have a high energy density, use lithium metal in the negative electrode, but repeated charging and discharging causes sparse deposits (dendrites, etc.) to form on the surface of the negative electrode. It is known that metal deposits form in various forms not only in lithium metal batteries, but also in various other batteries such as lithium ion batteries and all-solid-state batteries. In particular, if there is variation in the internal stress and strain of the battery, the growth of deposits is likely to accelerate locally. The growth of deposits can be a factor that causes changes in battery characteristics and battery expansion. In order to suppress the growth of precipitates, it is effective to apply a restraining force from the outside of the battery so as to generate uniform stress inside the battery. However, no method has been proposed so far for estimating the distribution of stress or strain inside the battery. According to the above configuration, the inherent strain of the energy storage element is calculated, and the distribution of stress or strain can be calculated based on the calculated inherent strain.

[0015] In the computer program, the formation rate of the precipitates may be described as a function of stress generated in the field of the formation reaction, and the computer may be caused to execute a process of calculating the formation amount based on the formation rate of the precipitates calculated by the function. With this configuration, the formation amount is calculated based on the formation rate of the precipitates, and the inherent strain can be calculated based on the calculated formation amount of the precipitates.

[0016] The computer program may cause the computer to execute a process for simulating an electrochemical phenomenon in the energy storage element based on the amount of precipitate generated and the stress field. With this configuration, it is possible to simulate an electrochemical phenomenon including a change in the internal resistance of the energy storage element based on the amount of precipitate generated and the stress field of the energy storage element.

[0017] The computer program may cause the computer to execute a process of simulating a thermal phenomenon in the energy storage element based on the generation amount and precipitation form. With this configuration, it is possible to simulate a thermal phenomenon including a temperature behavior of the energy storage element based on the generation amount and precipitation form of the precipitate.

[0018] The computer program may execute a process of calculating an amount of gas generated inside the energy storage element and calculating a distribution of stress or strain generated in the energy storage element based on the calculated amount of gas generated. With this configuration, the distribution of stress or strain in the energy storage element can be calculated based on the amount of gas generated inside the energy storage element.

[0019] The simulation method includes a process of calculating an inherent strain of an electric storage element in which deposits occur in response to charging and discharging, based on the amount of deposits produced and the precipitation form of the deposits, and calculating a distribution of stress or strain occurring in the electric storage element based on the calculated inherent strain, by a computer. With this configuration, it is possible to calculate the inherent strain of the electric storage element, and to calculate the distribution of stress or strain based on the calculated inherent strain.

[0020] The simulation device includes a calculation unit that calculates an inherent strain of an electric storage element in which deposits are generated in response to charging and discharging based on the amount of deposits generated and the precipitation form of the deposits, and calculates a distribution of stress or strain generated in the electric storage element based on the calculated inherent strain. With this configuration, it is possible to calculate the inherent strain of the electric storage element, and to calculate the distribution of stress or strain based on the calculated inherent strain.

[0021] Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof. (Embodiment 1) Fig. 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 a stress or strain distribution 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 central processing unit (CPU), a read only memory (ROM), a random access memory (RAM), 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 device for estimating the distribution of stress or strain in the energy storage element 2.

[0023] Alternatively, the calculation unit 11 may be any processing circuit or calculation circuit including a plurality of 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 include functions such as a timer that measures the elapsed time from when a measurement start instruction is given to when a measurement end instruction is given, a counter that counts numbers, and a clock that outputs date and time information.

[0024] The storage unit 12 includes a storage device such as a flash memory or a hard disk. Various computer programs and data are stored in the storage unit 12. The computer programs stored in the storage unit 12 include an estimation program PG1 for causing a computer to execute a process of estimating the distribution of stress or strain 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 storage 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.

[0025] The estimation program PG1 may be written in a commercially available numerical analysis software or programming language 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 a finite element method or a finite volume method performed on a 3D shape. 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 a Secure Digital (SD) card. The calculation unit 11 reads a 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 storage unit 12. Alternatively, the computer program may be provided by communication.

[0027] The operation unit 13 includes an interface for connecting various operation devices. The operation devices are devices for receiving user operations, such as a keyboard, a mouse, a touch panel, etc. The operation unit 13 outputs operation information received 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 causing the display device 140 to display the information. 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 such as a mobile terminal or an electric vehicle that operates using power supplied from the energy storage element 2.

[0030] The storage element 2 that is the target of the simulation by the estimation device 1 will now be described. 2 is an explanatory diagram illustrating the configuration of the energy storage element 2. The energy storage element 2 is, for example, a metal lithium battery. The energy storage element 2 includes a laminate of a positive electrode current collector layer 21, a positive electrode active material layer 22, an electrolyte layer 23, and a negative electrode current collector layer 24.

[0031] The positive electrode collector layer 21 is made 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 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.

[0032] The positive electrode active material layer 22 is formed of a lithium-containing compound capable of absorbing and releasing lithium ions.x CoO2, Li x NiO2, Li x Mn2O4, Li x FePO4, etc., is used. The positive electrode active material layer 22 may contain a solid electrolyte, a conductive additive, and a binder in addition to the positive electrode active material.

[0033] The electrolyte layer 23 is a separator impregnated with an electrolytic solution. The electrolytic solution includes, for example, a non-aqueous solvent and a lithium salt dissolved in the non-aqueous solvent. Examples of the non-aqueous solvent include cyclic carbonate solvents, cyclic ether solvents, chain ether solvents, cyclic ester solvents, and chain ester solvents. Examples of the lithium salt include LiPF6, LiBF4, LiN(SO2CF3)2, and LiN(SO2C2F5)2.

[0034] The negative electrode current collector layer 24 is made of a metal foil, a metal mesh, or the like. The metal constituting the negative electrode current collector layer 24 is a metal having good electrical conductivity, such as copper, nickel, titanium, or stainless steel. For example, lithium metal or a lithium alloy dissolves or precipitates on the surface of the negative electrode current collector layer 24. Here, dissolution is not limited to complete dissolution, but includes partial dissolution. That is, the lithium metal or lithium alloy may remain on the surface of the negative electrode current collector layer 24 when the energy storage element 2 is in a discharged state.

[0035] The energy storage element 2 may be restrained by a 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 inside 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 a side portion 312, and a lid body 313 that closes an 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 a resin. The case body 310 is sealed by the lid body 313 after the energy storage element 2 is housed therein.

[0036] 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 bottom surface portion 311, and between the top layer (negative electrode current collector layer 24 in the example of FIG. 2) of the energy storage element 2 and 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).

[0037] 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 binding force to the energy storage element 2. Alternatively, a binding 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 material. For example, an inert gas such as nitrogen or dry air is used. Alternatively, a configuration is adopted in which a binding force is applied to the energy storage element 2 by sandwiching the energy storage element 2 between plate members from both sides in the stacking direction and connecting the plate members together while a binding force is applied to the energy storage element 2.

[0038] FIG. 3 is a graph showing an example of the relationship between the amount of precipitates produced and the inherent strain. The horizontal axis of the graph shown in FIG. 3 represents the amount of precipitates produced, and the vertical axis represents the inherent strain. Repeated charging and discharging over a long period of time may cause precipitates to be deposited inside the energy storage element 2. For example, when 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 lithium metal to be sparsely deposited on the surface of the negative electrode. The deposit form may also be dense.

[0039] As shown in the graph, the inherent strain of the energy storage element 2 is proportional to the amount of precipitates, but the magnitude differs depending on the precipitation form. Even with the same amount of precipitates, when dense metal precipitates, the inherent strain is relatively small, and when sparsely precipitated, the inherent strain is relatively large. When moss-like precipitates precipitate, the inherent strain is intermediate between the two.

[0040] Figure 4 is a graph showing another example of the relationship between the amount of precipitates and the inherent strain. The horizontal axis of the graph shown in Figure 4 represents the amount of precipitates, and the vertical axis represents the inherent strain. The graph shows how dense precipitates precipitate in the early stage of precipitation, followed by sparse precipitates. The inherent strain of the energy storage element 2 is given as a value proportional to the amount of precipitates precipitated, both at the stage where dense precipitates precipitate and at the stage where sparse lithium precipitates precipitate.

[0041] The storage unit 12 of the estimation device 1 stores a function or a table for converting the amount of precipitate generation into the inherent strain of the energy storage element 2. The calculation unit 11 of the estimation device 1 refers to the function or the table stored in the storage unit 12, and calculates the inherent strain of the energy storage element 2 when the amount of precipitate generation is given.

[0042] The calculation unit 11 estimates the distribution of stress or strain in the energy storage element 2 based on the calculated inherent strain.

[0043] For example, the relational expression between stress and strain of a linear elastic body without deformation anisotropy is expressed by the following Equation 1. Alternatively, an equation expressing the characteristics of an elastoplastic body or a brittle material may be used depending on the constituent material of the object.

[0044]

number

[0045] Here, σ ii ,σ ij The tensor with elements σ represents the stress tensor. ii is the normal stress acting on the surface normal to the i direction, σ ij represents the shear stress in the j direction acting on a plane normal to the i direction. The tensor described by the Lamé constants λ and μ represents the elasticity tensor. The Lamé constants λ and μ are expressed in terms of Young's modulus and Poisson's ratio. The Lamé constants λ and μ may be given as a function of the amount of precipitates formed. ε is the strain tensor, and ε ii ,ε ij Contains elements. ii is the normal distortion acting on the surface normal to the i direction, σ ijrepresents the shear strain in the j direction acting on a surface normal to the i direction. ε 0 is the eigenstrain tensor, and ε ii 0 ,ε ij 0 Contains elements. ii 0 is the normal eigenstrain acting on the surface normal to the i direction, ε ij 0 represents the inherent shear strain in the j direction acting on a surface normal to the i direction. ii 0 ,ε ij 0 is given as a function of the amount of precipitate formed.

[0046] The calculation unit 11 of the estimation device 1 applies an inherent strain to a member in which precipitates are formed, and calculates the distribution of stress or strain by solving the stress-strain relational equation (1) and the force and moment balance equation (2) under arbitrary constraint conditions.

[0047]

number

[0048] The procedure of the process executed by the estimation device 1 will be described below. 5 is a flow chart showing the calculation procedure for the stress-strain distribution. The calculation unit 11 provides the amount of precipitates generated for the energy storage element 2 to be simulated (step S101), and calculates the inherent strain of the member in which the precipitates are to be precipitated (step S102). At this time, the calculation unit 11 reads out from the storage unit 12 a function or table for converting the amount of precipitates generated into inherent strain, and converts the amount of precipitates generated into inherent strain according to the read function or table.

[0049] Next, the calculation unit 11 imposes constraint conditions on the energy storage element 2 (step S103), and calculates the distribution of stress or strain based on the stress-strain relational equation and the force and moment balance equation based on Equation 1 and Equation 2 (step S104).

[0050] As described above, in the first embodiment, the distribution of stress or strain in energy storage device 2 can be calculated by taking into account the amount of precipitate formed inside energy storage device 2.

[0051] (Embodiment 2) In the second embodiment, a configuration will be described in which the rate at which precipitates are formed is calculated based on the internal stress of energy storage element 2, and the amount of precipitates formed is calculated based on the calculated rate of formation.

[0052] The formation of precipitates inside the energy storage element 2 is affected by stress occurring at the site of the precipitate formation reaction (for example, the negative electrode surface). The rate of precipitate formation is expressed as a function of stress occurring at the site of the precipitate formation reaction as follows:

[0053]

number

[0054] Here, R p is the rate of precipitate formation (kg / (sm 2 )) and σ is the stress tensor (N / m 2 ).

[0055] The formation of precipitates is affected not only by stress but also by changes in charge / discharge current density and overpotential over time. The formation rate of precipitates may be expressed as follows:

[0056]

number

[0057] where i react is the reaction current density (A / m 2 ) and η is the overpotential (V).

[0058] When the generation rate of the precipitate is given by Equation 3 (or Equation 4), the calculation unit 11 can calculate the generation amount of the precipitate by the calculation of Equation 5.

[0059]

number

[0060] The calculation unit 11 can calculate the inherent strain based on the calculated amount of precipitates generated. The calculation unit 11 can calculate the distribution of stress or strain based on the calculated inherent strain.

[0061] The calculation unit 11 may calculate the distribution of the amount of precipitates generated as an areal density using Equation 6, and may also calculate the inherent strain as a distribution.

[0062]

number

[0063] Below, the generation rate R p An example of the formula will be described. When the reaction of forming a precipitate is regarded as an electrode reaction, the reaction current density is expressed as follows using the Butler-Volmer equation:

[0064]

number

[0065] where i react_p is the reaction current density (A / m 2 ), and i 0_p is the exchange current density (A / m 2 ) α a ,α c are the charge transfer coefficients for the oxidation and reduction reactions, n is the number of electrons involved in the reaction, F is the Faraday constant (C / mol), η is the overpotential (V), R is the gas constant (J / (mol K)), and T is the temperature (K). φ s is the solid-state potential (V), φ l is the liquid phase potential (V), E eq represents the equilibrium potential (V).

[0066] Reaction current density i react_p is given by Equation 7, the formation rate of precipitates R pis expressed as in Equation 8.

[0067]

number

[0068] Here, M Li represents the molar mass (kg / mol) of the precipitate (e.g., lithium metal). At this time, the swelling amount Δl (m) of the electrode is calculated by Equation 9. p is the density of the precipitate (kg / m 3 ).

[0069]

number

[0070] When the amount of precipitate is zero, the dimension of the electrode in the direction perpendicular to the deposition surface is l (m). When a precipitate of Δl is formed on the electrode, ε l is defined as the following equation 10. Equation 10 represents the compressive strain in the precipitation direction that occurs when it is assumed that the electrode portion where the precipitate is generated does not deform at all even if the precipitate precipitates.

[0071]

number

[0072] The unit vector of the direction of the bulging of the mixture due to the formation of precipitates (direction perpendicular to the deposition surface) is n = (n x ,n y ,n z ) the eigenstrain tensor ε 0 is written as in Equation 11.

[0073]

number

[0074] The calculation unit 11 of the estimation device 1 calculates the inherent strain tensor ε 0By deriving the above and using the formulas 1 and 2 described in the first embodiment, the distribution of stress or strain in energy storage element 2 is calculated.

[0075] As described above, in the second embodiment, the amount of precipitates generated and the stress-strain distribution can be calculated in a coupled manner.

[0076] (Embodiment 3) In the third embodiment, a configuration for simulating the electrochemical phenomenon in the energy storage element 2 will be described, taking into consideration the amount of precipitates produced and the stress field.

[0077] The amount of precipitates and stress generated inside the electric storage element 2 affect the battery characteristics of the electric storage element 2. The intrinsic conductivity, liquid phase conductivity, and exchange current density of the electric storage element 2 are expressed as follows as functions of the amount of precipitates, stress, and time.

[0078]

number

[0079] where i0 is the exchange current density (A / m 2 ), σ l is the liquid phase conductivity (S / m), σ s is the solid phase conductivity (S / m), m p is the amount of precipitate (kg) or the areal density of precipitates (kg / m 2 ), σ is the stress tensor, and t is time.

[0080] The calculation unit 11 can simulate the electrochemical phenomenon of the energy storage element 2 taking into account the amount of precipitate generation and the influence of stress by solving an electrochemical model such as the Newman model using Equation 12.

[0081] The Newman model is described by the Nernst-Planck equation, the charge conservation equation, the diffusion equation, the Butler-Volmer equation, and the Nernst equation, which are explained below.

[0082] The Nernst-Planck equation is an equation for solving ion diffusion in electrolytes and electrodes, and is expressed as follows:

[0083]

number

[0084] Here, σ l is the liquid phase conductivity (S / m), φ l is the liquid phase potential (V), R is the gas constant (J / (K mol)), T is the temperature (K), F is the Faraday constant (C / mol), f is the activity coefficient, c l is the ion concentration of the electrolyte (mol / m 3 ), t + is the cation transport number. l tot is the liquid phase current flow (A / m 3 )

[0085] The charge conservation equation represents electronic conduction in active materials and current collector foils, and is expressed by the following equation:

[0086]

number

[0087] where i s is the solid-state current density (A / m 2 ), φ s is the solid-state potential (v), σ s is the solid-phase conductivity (S / m). s tot is the solid-phase current flow (A / m 3 )

[0088] The diffusion equation is an equation that represents the diffusion of an active material in an active particle, and is expressed by the following formula.

[0089]

number

[0090] where c s is the active material concentration in the solid phase (mol / m 3 ), t is time (s), D s is the diffusion coefficient in the solid phase (m 2 / s).

[0091] The Butler-Volmer equation expresses the relationship between the reaction current and activation overvoltage that occurs in the charge transfer reaction at the interface between the solid and liquid phases. The Nernst equation expresses the equilibrium potential, which is a factor that determines the activation overvoltage.

[0092]

number

[0093] where i react is the reaction current density (A / m 2 ), i0 is the exchange current density (A / m 2 ), α a ,α c are the transfer coefficients for the oxidation and reduction reactions, η is the activation overpotential (V), and φ s is the solid-state potential (V), φ l is the liquid phase potential (V), E eq is the equilibrium potential (V), E0 is the standard electrode potential (V), n is the number of electrons contributing to the redox reaction, a Ox ,a Red are the activities of the chemical species before and after the reaction. Alternatively, the Butler-Volmer equation can be modified based on experimental data. For example, the exchange current density can be made a function of the active material concentration or ion concentration, or the Nernst equation can be used to calculate the equilibrium potential E eq Instead of calculating , the open circuit potential may be calculated using actual measurement data of SOC and open circuit potential. Each parameter in the above-mentioned formulas 13 to 16 may be written as a function of other physical quantities.

[0094] In the present embodiment, the Newman model has been shown as an example of a physical model of the energy storage element 2. As long as the charge / discharge characteristics are expressed, a model other than the physical model, such as an equivalent circuit model or a polynomial model, may be used instead.

[0095] FIG. 6 is a circuit diagram showing an example of an equivalent circuit model. The equivalent circuit model of the energy storage element 2 is expressed by a combination of resistors and capacitance components. In the equivalent circuit model shown in FIG. 6, R0 is an ohmic resistance component, R pos is the reaction resistance component of the positive electrode, C pos is the capacitance component of the positive electrode, R neg is the reaction resistance component of the negative electrode, C neg represents the capacitance component of the negative electrode. However, Fig. 6 is merely an example, and there is no limitation on the combination of series and parallel connections or the number and types of electric circuit elements.

[0096] When the estimation device 1 evaluates the electrochemical phenomenon of the energy storage element 2 in 1D using an equivalent circuit model, it is sufficient to estimate each resistance and capacitance based on the following equation (17).

[0097]

number

[0098] where m p is the amount of precipitate (kg) or the areal density of precipitates (kg / m 2 ), σ is stress, and t is time.

[0099] As described above, in the third embodiment, the electrochemical phenomenon in the energy storage element 2 can be simulated based on the amount of precipitates produced and the stress field.

[0100] (Embodiment 4) In the fourth embodiment, a configuration for simulating a thermal phenomenon in an energy storage element 2 based on the amount and form of precipitates will be described.

[0101] The amount and morphology of precipitates generated inside the energy storage element 2 affect the thermal phenomena of the energy storage element 2. The heat generation reaction rate, thermal conductivity, specific heat, and density of the energy storage element 2 are expressed as functions of the amount and morphology of precipitates as follows:

[0102]

number

[0103] Here, Q TR is heat generation (W / m 3 ), C p is the specific heat (J / (kg K)), k is the thermal conductivity (W / (m K)), and ρ is the density (kg / m 3 ) m p is the amount of precipitates (kg), and α is a coefficient set according to the precipitate morphology. The coefficient α is given, for example, as a value proportional to the specific surface area of ​​the precipitates. Alternatively, the coefficient α may be given as a value proportional to (absolute value of inherent strain / amount of precipitates).

[0104] The calculation unit 11 can simulate the thermal phenomenon of the energy storage element 2 taking into consideration the influence of the amount of precipitates produced and the precipitation form by solving the heat conduction equation using the formula 18. The heat conduction equation is expressed by the formula 19.

[0105]

number

[0106] where Q is heat generation (W / m 3 ) and Q in Eq. TR is equivalent to.

[0107] The calculation unit 11 may calculate the Joule heat based on the following formula in combination with the electrochemical model described in the third embodiment.

[0108]

number

[0109] where i l is the liquid phase current density (A / m 2 ), φ l is the liquid phase conductivity (A / m 2 ), i s is the solid-state current density (A / m 2 ), φ s is the solid phase conductivity (A / m 2).

[0110] As described above, in the third embodiment, the thermal phenomenon in the energy storage element 2 can be simulated based on the amount and form of precipitates produced.

[0111] (Embodiment 5) In the fifth embodiment, a configuration for calculating the distribution of stress or strain in energy storage device 2 taking into consideration the amount of gas generated inside energy storage device 2 will be described.

[0112] Repeated charging and discharging may cause gas to be generated inside the energy storage element 2. When gas is generated inside the energy storage element 2, the energy storage element 2 expands, and distortion occurs due to the expansion. In the fifth embodiment, a method for calculating the distribution of stress or distortion in the energy storage element 2 taking into account the amount of gas generated will be described.

[0113] The amount of gas generated in the energy storage element 2 can be calculated by various formulas. For example, when there is reaction unevenness and current concentration, gas generation is likely to progress, and the reaction current density i react Based on this, the amount of gas generated is n gas (mol) is calculated.

[0114]

number

[0115] Here, J is a variable that is 1 when the local reaction current density is higher than the average (when there is current concentration) and is 0 otherwise. react is the average reaction current density (A / m 2 ).

[0116] At this time, the internal pressure p (N / m 2 ) is calculated using the following formula 22.

[0117]

number

[0118] Here, n0 is the initial amount of gas (mol), and v is the volume of the gap inside the storage element (m 3 ) Strictly speaking, the Gibbs-Duhem relationship (Gibbs-Duhem equation) is followed, but equation 22 may be used to simplify the calculation. Also, equation 22 may be used assuming an ideal gas, but the gas equation of state that takes intermolecular forces into account may also be used.

[0119] In this case, the stress tensor σ is expressed as follows using the internal pressure p of the energy storage element 2:

[0120]

number

[0121] The calculation unit 11 calculates the distribution of stress or strain by taking into account the stress shown in Equation 23 and solving the stress-strain relational equation in Equation 1 and the force and moment balance equation in Equation 2.

[0122] As described above, in the fifth embodiment, the distribution of stress or strain in energy storage device 2 can be calculated by taking into account the amount of gas generated inside energy storage device 2.

[0123] The embodiments disclosed herein are illustrative in all respects and should not be considered as limiting. 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.

[0124] For example, the energy storage element 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, a domain in which a plurality of banks are connected in parallel, or the like. [Explanation of symbols]

[0125] 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 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, For an electric storage element in which a precipitate is generated in response to charging and discharging, an inherent strain of the electric storage element is calculated based on the amount and form of the precipitate; Calculating the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain A computer program for executing a process.

2. The formation rate of the precipitate is described as a function of stress generated in the field of the formation reaction, The amount of the precipitate is calculated based on the rate of precipitate formation calculated by the function. The computer program product according to claim 1, for causing a computer to carry out a process.

3. The electrochemical phenomenon of the energy storage element is simulated based on the generated amount and the stress field.

3. A computer program product according to claim 1 or 2, for causing a computer to execute a process.

4. A thermal phenomenon in the electric storage element is simulated based on the amount of generation and the precipitation form.

4. A computer program product according to claim 1, for causing a computer to execute a process.

5. Calculating the amount of gas generated inside the energy storage element; Calculating the distribution of stress or strain occurring in the electric storage element based on the calculated amount of gas generated. A computer program product according to any one of claims 1 to 4 for executing a process.

6. For an electric storage element in which a precipitate is generated in response to charging and discharging, an inherent strain of the electric storage element is calculated based on the amount and form of the precipitate; Calculating the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain A simulation method in which processing is carried out by a computer.

7. For an electric storage element in which a precipitate is generated in response to charging and discharging, an inherent strain of the electric storage element is calculated based on the amount and form of the precipitate; Calculating the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain A simulation device having a calculation unit.

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