JP7651911B2 - Computer program, simulation method, and simulation device - Google Patents

Description

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

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

In response to the above demands, lithium metal batteries that use lithium metal in the negative electrode have attracted attention. Lithium has a low density and a very low standard reduction potential, so it has attracted attention as an electrode material for lightweight, high-energy density batteries (see, for example, Patent Document 1).

JP 2014-197472 A

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.

There are various types of precipitates, including dendritic, moss-like, granular, and dense, with different degrees of sparseness. Here, dendritic and moss-like are sparse forms.

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, but currently no method has been proposed for estimating the distribution of stress or strain inside the battery.

The present invention was made in consideration of the above circumstances, and aims to provide a computer program, a simulation method, and a simulation device that can calculate the distribution of stress or strain inside an energy storage element.

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

The simulation method involves a computer-implemented process 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 then calculates the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain.

The simulation device includes a calculation unit that calculates the inherent strain of an energy storage element in which precipitates occur in response to charging and discharging, based on the amount of precipitates produced and the precipitation form, and calculates the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain.

The above configuration makes it possible to calculate the distribution of stress or strain inside the energy storage element.

1 is a block diagram showing an internal configuration of an estimation device according to a first embodiment. FIG. FIG. 2 is an explanatory diagram illustrating a configuration of an energy storage element. 1 is a graph showing an example of the relationship between the amount of precipitates formed and the inherent strain. 11 is a graph showing another example of the relationship between the amount of precipitates formed and the inherent strain. 1 is a flowchart showing a calculation procedure for stress/strain distribution. FIG. 2 is a circuit diagram showing an example of an equivalent circuit model.

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 a storage element is repeatedly charged and discharged, deposits are formed inside the storage element. For example, lithium metal batteries, which are expected to have a high energy density, use lithium metal in the negative electrode, but sparse deposits (dendrites, etc.) are formed on the surface of the negative electrode due to repeated charging and discharging. It is known that metal deposits are formed in various forms not only in lithium metal batteries but also in various 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, but 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 stress or strain distribution can be calculated based on the calculated inherent strain.

In the computer program, the formation rate of the precipitates may be described as a function of the stress generated at the site of the formation reaction, and the computer may execute a process to calculate 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.

The computer program may cause the computer to execute a process for simulating electrochemical phenomena in the energy storage element based on the amount of precipitates produced and the stress field. With this configuration, electrochemical phenomena including changes in the internal resistance of the energy storage element can be simulated based on the amount of precipitates produced and the stress field of the energy storage element.

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

The computer program may execute a process to calculate the amount of gas generated inside the storage element, and calculate the distribution of stress or strain generated in the storage element based on the calculated amount of gas generated. With this configuration, the distribution of stress or strain in the storage element can be calculated based on the amount of gas generated inside the storage element.

The simulation method involves a computer executing a process to calculate the inherent strain of an energy storage element in which precipitates occur in response to charging and discharging, based on the amount of precipitates produced and the precipitation form, and to calculate the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain. With this configuration, the inherent strain of the energy storage element can be calculated, and the distribution of stress or strain can be calculated based on the calculated inherent strain.

The simulation device includes a calculation unit that calculates the inherent strain of an energy storage element in which precipitates occur in response to charging and discharging, based on the amount of precipitates produced and the precipitation form, and calculates the distribution of stress or strain occurring in the energy storage element based on the calculated inherent strain. With this configuration, it is possible to calculate the inherent strain of the energy storage element, and to calculate the distribution of stress or strain based on the calculated inherent strain.

Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof.
(Embodiment 1)
1 is a block diagram showing an internal configuration of an estimation device 1 according to embodiment 1. The estimation device 1 includes, for example, a calculation unit (estimation unit) 11, a storage unit 12, an operation unit 13, and an output unit 14. The estimation device 1 estimates 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.

The calculation unit 11 is a calculation 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 device for estimating the distribution of stress or strain in the energy storage element 2.

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

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

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

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

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

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

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

The storage element 2 that is the target of the simulation by the estimation device 1 will be described below.
2 is a diagram illustrating the configuration of the energy storage element 2. The energy storage element 2 is, for example, a metallic 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.

The positive electrode collector layer 21 is composed of a metal foil, a metal mesh, or the like. The metal constituting the positive electrode collector layer 21 is a metal having good electrical conductivity, such as aluminum, nickel, titanium, or stainless steel. A coating layer for adjusting the contact resistance may be formed on the surface of the positive electrode collector layer 21. One example of the coating layer is a carbon coating.

The positive electrode active material layer 22 is formed of _a lithium-containing compound capable of absorbing and releasing lithium ions. Examples of _the lithium _- containing compound include _LixCoO2 , _LixNiO2 , _LixMn2O4 , and _LixFePO4 . The positive electrode active material layer 22 may contain a solid electrolyte, a conductive assistant, and a _binder in addition to the positive _electrode active material.

The electrolyte layer 23 is a separator impregnated with an electrolytic solution. The electrolytic solution contains, for example, a non-aqueous solvent and a lithium salt dissolved in the non-aqueous solvent. Examples of the non-aqueous solvent include a cyclic carbonate solvent, a cyclic ether solvent, a chain _ether solvent, a cyclic _ester solvent, _and a chain ester solvent. Examples of the lithium salt include _LiPF6 , _LiBF4 , LiN( _SO2CF3 ) ₂ , and LiN( _SO2C2F5 ) ₂ .

The negative electrode collector layer 24 is made of a metal foil, a metal mesh, or the like. The metal constituting the negative electrode 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 collector layer 24. Here, dissolution is not limited to complete dissolution, but includes partial dissolution. In other words, the lithium metal or lithium alloy may remain on the surface of the negative electrode collector layer 24 when the energy storage element 2 is in a discharged state.

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

The elastic member 32 is disposed in a compressed state between the bottom layer of the energy storage element 2 (positive electrode collector layer 21 in the example of FIG. 2) and the bottom surface portion 311, and between the top layer of the energy storage element 2 (negative electrode collector layer 24 in the example of FIG. 2) and the lid body 313. The elastic member 32 is, for example, a rubber-like sheet. The elastic force of the elastic member 32 applies a restraining force to the energy storage element 2 in the stacking direction (the vertical direction in the figure).

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

Figure 3 is 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 Figure 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 form inside the energy storage element 2. 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 lithium metal to precipitate sparsely on the surface of the negative electrode. The precipitation form may also be dense.

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, if dense metal precipitates, the inherent strain will be relatively small, and if sparsely precipitated, the inherent strain will be relatively large. If moss-like precipitates precipitate, the inherent strain will be intermediate between the two.

Figure 4 is a graph showing another example of the relationship between the amount of precipitates formed and the inherent strain. The horizontal axis of the graph shown in Figure 4 represents the amount of precipitates formed, and the vertical axis represents the inherent strain. The graph shows how dense precipitates precipitate in the early stages 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 formed, both at the stage where dense precipitates precipitate and at the stage where sparse lithium precipitates precipitate.

The memory unit 12 of the estimation device 1 stores a function or table that converts 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 table stored in the memory unit 12 and calculates the inherent strain of the energy storage element 2 when the amount of precipitate generation is given.

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

For example, the relationship between stress and strain for 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.

Here, the tensor with σ _ii and σ _ij as elements represents the stress tensor. σ _ii represents the normal stress acting on the surface normal to the i direction, and σ _ij represents the shear stress in the j direction acting on the surface 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 by Young's modulus and Poisson's ratio. The Lamé constants λ and μ may be given as a function of the amount of precipitates generated. ε is a strain tensor, and its elements include ε _ii and ε _ij . ε _ii represents the normal strain acting on the surface normal to the i direction, and σ _ij represents the shear strain in the j direction acting on the surface normal to the i direction. ε ⁰ is an inherent strain tensor, and its elements include ε _ii ⁰ and ε _ij ^0. ε _ii ⁰ represents the normal inherent strain acting on the surface normal to the i direction, and ε _ij ⁰ represents the shear inherent strain in the j direction acting on the surface normal to the i direction. In an embodiment, ε _ii ⁰ and ε _ij ⁰ are given as functions of the amount of precipitates formed.

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

The procedure of the process executed by the estimation device 1 will be described below.
5 is a flow chart showing a calculation procedure for stress and strain distribution. The calculation unit 11 is provided with 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 generated (step S102). At this time, the calculation unit 11 reads out a function or table for converting the amount of precipitates generated into inherent strain from the storage unit 12, and converts the amount of precipitates into inherent strain according to the read function or table.

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

As described above, in embodiment 1, the stress or strain distribution of the energy storage element 2 can be calculated by taking into account the amount of precipitates that precipitate inside the energy storage element 2.

(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.

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

Here, R _p is the rate of formation of precipitates (kg/(s m ² )), and σ is the stress tensor (N/m ² ).

The formation of precipitates is affected not only by stress but also by changes in charge/discharge current density and overvoltage over time. The rate of precipitate formation may be described as follows:

Here, i _react is the reaction current density (A/m ² ) and η is the overpotential (V).

When the rate of precipitate formation is given by equation 3 (or equation 4), the calculation unit 11 can calculate the amount of precipitate formation by calculating equation 5.

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

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

An example of an equation expressing the generation rate R _p will be described below.
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:

Here, i _{react_p} is the reaction current density (A/m ² ) in the precipitate formation reaction, and i _{0_p} is the exchange current density (A/m ² ). _{α a} and α _c are the charge transfer coefficients for the oxidation reaction and reduction reaction, respectively, 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-phase potential (V), φ _l is the liquid-phase potential (V), and E _eq is the equilibrium potential (V).

When the reaction current density i _{react_p} is given by Equation 7, the deposition rate R _p is expressed by Equation 8.

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. ρ _p is the density of the precipitate (kg/m ³ ).

When the amount of precipitate is zero, the dimension of the electrode in the direction perpendicular to the precipitate surface is taken as l (m), and when a precipitate of Δl is formed on the electrode, _εl 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 formed does not deform at all even when the precipitate precipitates.

When the unit vector in the direction of the composite material swelling due to the generation of precipitates (direction perpendicular to the precipitate surface) is _n =(nx, _ny , _nz ), the inherent strain tensor ^ε0 is expressed as in Equation 11.

The calculation unit 11 of the estimation device 1 derives the inherent strain tensor ε ⁰ based on, for example, equations 7 to 11, and calculates the stress or strain distribution of the energy storage element 2 by using equations 1 and 2 described in the first embodiment.

As described above, in embodiment 2, the amount of precipitates generated can be calculated in conjunction with the stress and strain distribution.

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

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

Here, _i0 represents the exchange current density (A/ ^m2 ), _σl represents the liquid phase conductivity (S/m), _σs represents the solid phase conductivity (S/m), _mp represents the amount of precipitate produced (kg) or the areal density of the precipitate (kg/ ^m2 ), σ represents the stress tensor, and t represents time.

The calculation unit 11 can simulate the electrochemical phenomenon of the energy storage element 2 taking into account the amount of precipitate formation and the effects of stress by solving an electrochemical model such as the Newman model using equation 12.

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.

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

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 ), and t ₊ is the cation transport number. i ^l _tot in Equation 13 represents the liquid phase current flow (A/m ³ ).

The charge conservation equation represents the electronic conduction in active materials and current collector foils, and is expressed as follows:

Here, i _s is the solid-phase current density (A/m ² ), φ _s is the solid-phase potential (v), and σ _s is the solid-phase conductivity (S/m). In equation 14, i ^s _tot represents the solid-phase current outflow (A/m ³ ).

The diffusion equation describes the diffusion of active material in active particles and is expressed as follows:

Here, c _s is the active material concentration in the solid phase (mol/m ³ ), t is time (s), and D _s is the diffusion coefficient in the solid phase (m ² /s).

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

Here, i _react is the reaction current density (A/m ² ), i ₀ is the exchange current density (A/m ² ), α _a and α _c are the transfer coefficients of the oxidation reaction and reduction reaction, respectively, η is the activation overpotential (V), φ _s is the solid-phase potential (V), φ _l is the liquid-phase potential (V), E _eq is the equilibrium potential (V), E ₀ is the standard electrode potential (V), n is the number of electrons contributing to the oxidation-reduction reaction, and a _Ox and a _Red are the activities of the chemical species before and after the reaction. The Butler-Volmer formula may be modified based on experimental values instead. For example, the exchange current density may be a function of the active material concentration or ion concentration, or the actual measurement data of the SOC and open circuit potential may be used as the open circuit potential instead of calculating the equilibrium potential E _eq using the Nernst formula, and the like. Each parameter in the above formulas 13 to 16 may be described as a function of other physical quantities.

In this embodiment, the Newman model is shown as an example of a physical model of the storage element 2. Alternatively, a model other than a physical model, such as an equivalent circuit model or a polynomial model, may be used to represent the charge/discharge characteristics.

Fig. 6 is a circuit diagram showing an example of an equivalent circuit model. The equivalent circuit model of the storage element 2 is expressed by a combination of resistors and capacitance components. In the equivalent circuit model shown in Fig. 6, _R0 represents an ohmic resistance component, _Rpos represents a positive electrode reaction resistance component, _Cpos represents a positive electrode capacitance component, _Rneg represents a negative electrode reaction resistance component, and _Cneg represents a negative electrode capacitance component. However, Fig. 6 is an example, and there is no limitation on the series and parallel combinations or the number and types of electric circuit elements.

When the estimation device 1 evaluates the electrochemical phenomenon of the 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.

Here, m _p represents the amount of precipitates formed (kg) or the areal density of precipitates (kg/m ² ), σ represents stress, and t represents time.

As described above, in embodiment 3, the electrochemical phenomenon of the energy storage element 2 can be simulated based on the amount of precipitates produced and the stress field.

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

The amount and morphology of precipitates formed 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:

Here, Q _TR is heat generation (W/m ³ ), C _p is specific heat (J/(kgK)), k is thermal conductivity (W/(mK)), and ρ is density (kg/m ³ ). m _p is the amount of precipitates formed (kg), and α is a coefficient set according to the precipitation 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 formed).

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

Here, Q is heat generation (W/m ³ ) and corresponds to Q _TR in Equation 18.

The calculation unit 11 may combine the electrochemical model described in embodiment 3 to calculate the Joule heat based on the following formula:

Here, 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 phase current density (A/m ² ), and φ _s is the solid phase conductivity (A/m ² ).

As described above, in embodiment 3, the thermal phenomenon of the energy storage element 2 can be simulated based on the amount of precipitates produced and the precipitation form.

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

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 embodiment 5, a method for calculating the distribution of stress or distortion in the energy storage element 2 taking into account the amount of gas generated is described.

The amount of gas generated in the energy storage element 2 is given by various formulas. For example, when there is reaction unevenness and current concentration makes it easy for gas generation to proceed, the amount of gas generated n _gas (mol) is calculated based on the above-mentioned reaction current density i _react .

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. ave_i _react is the average reaction current density (A/m ² ).

At this time, the internal pressure p (N/m ² ) of the electric storage element 2 due to gas generation is calculated by the following equation 22.

Here, _n0 is the initial amount of gas (mol), and v is the volume of the gap inside the energy storage element ( ^m3 ). Strictly speaking, the Gibbs-Duhem relationship (Gibbs-Duhem equation) is followed, but equation 22 may be used to simplify the calculation. Furthermore, equation 22 may be used assuming an ideal gas, but the gas state equation considering intermolecular forces may also be used.

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

The calculation unit 11 calculates the stress or strain distribution 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.

As described above, in embodiment 5, the distribution of stress or strain in the storage element 2 can be calculated taking into account the amount of gas generated inside the storage element 2.

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

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

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

Claims (7)

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;
A computer program for executing a process of calculating a distribution of stress or strain generated in the energy storage element based on the calculated inherent strain. The formation rate of the precipitate is described as a function of stress generated in the field of the formation reaction,
The computer program according to claim 1 , which causes the computer to execute a process of calculating the amount of precipitates generated based on the generation rate of the precipitates calculated by the function. The computer program according to claim 1 or 2, which causes the computer to execute a process of simulating an electrochemical phenomenon in the electricity storage element based on the production amount and the stress field. The computer program according to claim 1 , which causes the computer to execute a process of simulating a thermal phenomenon in the energy storage element based on the amount of generation and the precipitation form. Calculating the amount of gas generated inside the energy storage element;
The computer program product according to claim 1 , for executing a process of calculating a distribution of stress or strain generated in the electric storage element based on the calculated amount of gas generated. 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;
A simulation method comprising: calculating, by a computer, a distribution of stress or strain generated in the energy storage element based on the calculated inherent strain. 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;
A simulation device comprising a calculation unit that calculates a distribution of stress or strain generated in the energy storage element based on the calculated inherent strain.

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