CN112924867A - Lithium battery capacity attenuation calculation method under multi-field coupling - Google Patents
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 48
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 48
- 230000008878 coupling Effects 0.000 title claims abstract description 24
- 238000010168 coupling process Methods 0.000 title claims abstract description 24
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 24
- 238000004364 calculation method Methods 0.000 title claims abstract description 17
- 238000000034 method Methods 0.000 claims abstract description 11
- 239000007787 solid Substances 0.000 claims abstract description 7
- 238000007781 pre-processing Methods 0.000 claims abstract description 5
- 238000001228 spectrum Methods 0.000 claims abstract description 5
- 230000005518 electrochemistry Effects 0.000 claims abstract description 4
- 229910001416 lithium ion Inorganic materials 0.000 claims description 42
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 claims description 35
- 230000002441 reversible effect Effects 0.000 claims description 14
- 230000008859 change Effects 0.000 claims description 10
- 239000007772 electrode material Substances 0.000 claims description 9
- 239000007773 negative electrode material Substances 0.000 claims description 9
- 239000012798 spherical particle Substances 0.000 claims description 9
- 239000000463 material Substances 0.000 claims description 8
- 239000000126 substance Substances 0.000 claims description 8
- 238000009792 diffusion process Methods 0.000 claims description 7
- 230000035882 stress Effects 0.000 claims description 7
- 150000002500 ions Chemical class 0.000 claims description 6
- 230000001133 acceleration Effects 0.000 claims description 5
- 230000006355 external stress Effects 0.000 claims description 5
- 239000003792 electrolyte Substances 0.000 claims description 4
- 239000012528 membrane Substances 0.000 claims description 4
- 239000013543 active substance Substances 0.000 claims description 3
- 208000012839 conversion disease Diseases 0.000 claims description 3
- 238000005562 fading Methods 0.000 claims description 3
- 230000004907 flux Effects 0.000 claims description 3
- 230000037427 ion transport Effects 0.000 claims description 3
- 239000007791 liquid phase Substances 0.000 claims description 3
- 239000007774 positive electrode material Substances 0.000 claims description 3
- 239000007790 solid phase Substances 0.000 claims description 3
- 230000032258 transport Effects 0.000 claims description 3
- 238000010998 test method Methods 0.000 claims 1
- 238000006243 chemical reaction Methods 0.000 description 7
- 230000005489 elastic deformation Effects 0.000 description 4
- 238000004088 simulation Methods 0.000 description 3
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 2
- 229910052799 carbon Inorganic materials 0.000 description 2
- 230000003071 parasitic effect Effects 0.000 description 2
- 239000000243 solution Substances 0.000 description 2
- 230000002159 abnormal effect Effects 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 125000004122 cyclic group Chemical group 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000007599 discharging Methods 0.000 description 1
- 238000003487 electrochemical reaction Methods 0.000 description 1
- 239000008151 electrolyte solution Substances 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 239000006260 foam Substances 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
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- 230000004048 modification Effects 0.000 description 1
- 239000002861 polymer material Substances 0.000 description 1
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- 238000006722 reduction reaction Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/385—Arrangements for measuring battery or accumulator variables
- G01R31/386—Arrangements for measuring battery or accumulator variables using test-loads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
Abstract
The invention provides a lithium battery capacity attenuation calculation method under multi-field coupling, which comprises the following steps: s1: establishing a one-dimensional lithium battery model; s2: analyzing the current of the one-dimensional lithium battery model under the driving condition, and acquiring a load signal; s3: preprocessing the load signal by a stress spectrum signal to obtain a preprocessed signal; s4: determining the thermal coupling equations of electrochemistry, laminar flow and solid of the one-dimensional lithium battery model; s5: and establishing a capacity attenuation calculation equation of the one-dimensional lithium battery model. The method for calculating the capacity attenuation of the lithium battery under multi-field coupling can quickly calculate the capacity attenuation of the battery.
Description
Technical Field
The invention relates to the technical field of power batteries, in particular to a lithium battery capacity attenuation calculation method under multi-field coupling.
Background
The power battery is used as the only power source of the electric automobile and determines key indexes of the electric automobile such as power performance, driving range and the like. Among them, lithium ion batteries are widely used in new energy vehicles due to their superior performance. However, as the market share of electric vehicles increases, the problems related to electric vehicles become more and more prominent, and the capacity estimation of new energy vehicle batteries is necessary for the energy management of the whole vehicle.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for calculating the capacity attenuation of a lithium battery under multi-field coupling, which can quickly calculate the capacity attenuation of the battery.
In order to achieve the above object, the present invention provides a method for calculating capacity attenuation of a lithium battery under multi-field coupling, comprising the steps of:
s1: establishing a one-dimensional lithium battery model;
s2: analyzing the current of the one-dimensional lithium battery model under the driving condition, and acquiring a load signal;
s3: preprocessing the load signal by a stress spectrum signal to obtain a preprocessed signal;
s4: determining the thermal coupling equations of electrochemistry, laminar flow and solid of the one-dimensional lithium battery model;
s5: and establishing a capacity attenuation calculation equation of the one-dimensional lithium battery model.
Preferably, in the step S1, the electrode active material of the one-dimensional lithium battery model is a spherical particle with a fixed radius, and the electrochemical model of the one-dimensional lithium battery model adopts a porous electrode model based on ionic charge conservation and material conservation; modeling the conservation of ionic charge and the conservation of substances according to a binary 1:1 electrolyte equation; adopting Fick diffusion to describe the material transport in the spherical particles, and using a diffusion equation to describe the lithium ion transport in the spherical particles under a spherical coordinate system; the charge conservation comprises solid phase charge conservation and liquid phase ion charge conservation, the electron charge conservation is calculated according to ohm law, and the ion charge conservation is calculated according to a concentrated solution theory; the method comprises the steps of carrying out one-dimensional modeling on the lithium battery, and dividing the lithium battery into a negative electrode, a diaphragm and a positive electrode.
Preferably, in the step S2, the main discharging condition in the national standard according to the GBT 31484-.
Preferably, in the step S3, the load signal is preprocessed by Ncode software to perform outlier rejection and signal denoising.
Preferably, in the step S4, the electrochemical, laminar flow and solid thermal coupling equations include a temperature derivative equation, a reversible heat equation, a convective heat transfer equation and a lithium ion conductivity equation of the separator;
the temperature derivative equation is:
wherein, DeltarHmRepresenting the change of the molar gibbs-helmholtz free energy of the reversible cell; z represents the number of changes, F represents the Faraday constant, E represents the potential, T represents the cell temperature,
a temperature derivative representing the electromotive force of the battery;
the reversible thermal equation includes a heat source expression:
wherein W represents a heat source, Q represents heat, V represents volume, t represents time, n represents n mol of a substance,
the convection heat transfer equation is:
where ρ represents the convective density, CpRepresenting the heat transfer coefficient, t representing time, u representing flux,
the backward difference in temperature is represented by,
representing convective heat, QtedRepresents an additional heat source;
the first electrode material thermal conductivity in the normal direction is expressed as:
wherein k isrRepresents the normal thermal conductivity, L _ batt represents the battery thickness, L _ pos represents the positive electrode thickness, kT _ pos represents the thermal conductivity of the positive electrode material, L _ neg represents the negative electrode thickness, kT _ neg represents the thermal conductivity of the negative electrode material, L _ pos _ cc represents the positive electrode current collector thickness, kT _ pos _ cc represents the positive electrode current collector thermal conductivity, L _ neg _ cc represents the negative electrode current collector thickness, kT _ neg _ cc represents the negative electrode current collector thermal conductivity, L _ sep represents the membrane thickness, kT _ sep represents the thermal conductivity of the negative electrode material;
the expression of the thermal conductivity of the second electrode material in the tangential direction is:
wherein k istRepresents the tangential thermal conductivity;
the lithium ion conductivity equation of the diaphragm is as follows:
wherein, kappa represents the lithium ion conductivity in the separator, and kappa1Denotes the initial conductivity,. epsilondDenotes the strain in the collapse zone, alpha denotes the reaction conversion coefficient, epsilonelRepresenting the strain of the plastic deformation zone; chi shapeelDenotes the ratio of plastic deformation,%dShowing the ratio of collapse deformation,. epsilon.showing the strain,. epsilonmaxRepresenting the maximum strain.
Under the driving condition that random external stress is considered, the lithium ion conductivity equation of the diaphragm is as follows:
κt＝κ2(1+εt)；0≤εt＜εel (7)；
wherein, κtDenotes the lithium ion conductivity, κ, as a function of time2Denotes the initial conductivity,. epsilontRepresenting strain over time;
and (4) determining the lithium ion conductivity changing along with time according to a formula (6), and obtaining the lithium ion conductivity change in the battery model by adopting cubic spline interpolation.
Preferably, in the step S5, the capacity fade calculation equation includes an SEI generation equation:
(τ+1)S+Li++e-+(τ-1)Li(s)→τPSEI (8)；
wherein τ represents a time acceleration factor, S represents a negative electrode material, and Li+Represents lithium ion, e-Represents an electron, Li(s) represents an active substance, PSEIIndicates the amount of SEI film produced
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
the stress spectrum acquired by the real vehicle is converted to be used as an input signal of random external stress borne by the lithium battery, and electrochemical simulation of the temperature field of the lithium battery is carried out simultaneously, so that the simulation of the running condition of the existing electric vehicle under electrochemical-laminar flow-solid-external stress coupling is realized; under the above conditions, a method of rapidly calculating the battery capacity fade incorporating a temporal acceleration factor is proposed in consideration of the generation reaction of the SEI. The calculation speed is fast, and the accuracy is high.
Drawings
Fig. 1 is a flowchart of a lithium battery capacity fading calculation method under multi-field coupling according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a diaphragm structure according to an embodiment of the present invention;
FIG. 3 is a graph of battery voltage change during cyclic conditions of an embodiment of the present invention;
FIG. 4 is a graph of capacity versus time for an embodiment of the present invention;
FIG. 5 is a graph of capacity versus cycle number for an embodiment of the present invention.
Detailed Description
The following description of the preferred embodiments of the present invention will be provided in conjunction with the accompanying drawings of fig. 1 to 5, and will make the functions and features of the present invention better understood.
Referring to fig. 1, a method for calculating capacity attenuation of a lithium battery under multi-field coupling according to an embodiment of the present invention includes:
s1: establishing a one-dimensional lithium battery model;
the electrode active material of the one-dimensional lithium battery model is spherical particles with a fixed radius, and the electrochemical model of the one-dimensional lithium battery model adopts a porous electrode model based on ionic charge conservation and material conservation; modeling the conservation of ionic charge and the conservation of substances according to a binary 1:1 electrolyte equation; adopting Fick diffusion to describe the material transport in the spherical particles, and using a diffusion equation to describe the lithium ion transport in the spherical particles under a spherical coordinate system; the charge conservation comprises solid phase charge conservation and liquid phase ion charge conservation, the electron charge conservation is calculated according to ohm law, and the ion charge conservation is calculated according to a concentrated solution theory; the method comprises the steps of carrying out one-dimensional modeling on the lithium battery, and dividing the lithium battery into a negative electrode, a diaphragm and a positive electrode.
S2: analyzing the current of the one-dimensional lithium battery model under the driving condition, and acquiring a load signal;
according to GBT 31484-.
S3: preprocessing the load signal by a stress spectrum signal to obtain a preprocessed signal;
when a test yard collects load signals, due to the influence of the performance of the measuring equipment and the surrounding environment, abnormal phenomena such as burrs, signal loss and the like may occur in the collected signals. These phenomena affect the accuracy of the analysis. And carrying out preprocessing of outlier elimination and signal denoising on the load signal through Ncode software.
S4: determining the thermal coupling equations of electrochemistry, laminar flow and solid of the one-dimensional lithium battery model;
the electrochemical, laminar flow and solid thermal coupling equations comprise a temperature derivative equation, a reversible heat equation, a convective heat transfer equation and a lithium ion conductivity equation of the diaphragm;
1. temperature derivative of battery electromotive force
The temperature derivative equation is:
wherein, DeltarHmRepresenting the change of the molar gibbs-helmholtz free energy of the reversible cell; z represents the number of changes, F represents the Faraday constant, E represents the potential, T represents the cell temperature,
a temperature derivative representing the electromotive force of the battery;
when a chemical reaction occurs, the temperature changes dT, describing the change delta of the molar Gibbs free energy of the reversible cell based on the Gibbs-Helmholtz equationrGmAs shown in equation (1):
will be provided with
Instead of equation (9), the equation can be rewritten as:
2. reversible heat released during cell reaction
The relationship between molar gibbs free energy and molar entropy change is:
under reversible conditions, the molar reversible thermal expression is:
when n mol of substances participate in reversible heat, the generated heat is as follows:
the reversible thermal equation includes a heat source expression of:
wherein W represents a heat source, Q represents heat, V represents volume, t represents time, n represents n mol of a substance,
3. convection heat transfer equation
The heat transfer includes three types, i.e., conduction heat transfer, convection heat transfer, and thermal radiation, and the present embodiment adopts a convection heat transfer mode, and the convection heat transfer equation is as follows:
wherein ρ represents a convective density, CpRepresenting the heat transfer coefficient, t representing time, u representing flux,
the backward difference in temperature is represented by,
representing convective heat, QtedRepresents an additional heat source;
the first electrode material thermal conductivity in the normal direction is expressed as:
wherein k isrRepresents the normal thermal conductivity, L _ batt represents the battery thickness, L _ pos represents the positive electrode thickness, kT _ pos represents the thermal conductivity of the positive electrode material, L _ neg represents the negative electrode thickness, kT _ neg represents the thermal conductivity of the negative electrode material, L _ pos _ cc represents the positive electrode current collector thickness, kT _ pos _ cc represents the positive electrode current collector thermal conductivity, L _ neg _ cc represents the negative electrode current collector thickness, kT _ neg _ cc represents the negative electrode current collector thermal conductivity, L _ sep represents the membrane thickness, kT _ sep represents the thermal conductivity of the negative electrode material;
the expression of the thermal conductivity of the second electrode material in the tangential direction is:
wherein k istRepresents the tangential thermal conductivity;
assuming that the heat conductivity coefficient is related to the position, is influenced by the temperature gradient to a minimum and is ignored, and the heat conductivity coefficient is a diagonal line at the moment;
4. coupling of electrochemical physical field and external stress field
The diaphragm belongs to a polymer material, and the porosity of the diaphragm is changed due to pressure change, so that the electrochemical performance of the lithium ion battery is influenced.
Referring to fig. 2, in order to consider the influence of pressure on the diaphragm, the diaphragm structure is characterized by interconnected tetrahedrons;
the tetrahedron is strained by compression under pressure, and the strain curve can be divided into deformation regions such as elastic strain region, plastic strain region and collapse region, which are described by equations (13), (14) and (15), respectively:
the strain of the diaphragm under pressure influences the diffusion of lithium ions, and when the model is established, the influence of the pressure on the lithium ion conductivity of the diaphragm is simulated by the flow model of liquid in a foam structure.
In the elastic deformation region, the magnitude of lithium ion conductivity in the separator is described by formula (16):
κ＝κ(1+ε)；0≤ε＜εel (16)；
in the plastic deformation and the collapse region, which are superimposed states of the elastic deformation and the collapse deformation, the proportions of the elastic deformation and the collapse deformation are expressed by equations (17), (18), respectively:
substituting equations (17), (18) into equation (16), the lithium ion conductivities in the plastic deformation region and the collapse deformation region can be written as:
wherein, kappa represents the lithium ion conductivity in the separator, and kappa1Denotes the initial conductivity,. epsilondDenotes the strain in the collapse zone, alpha denotes the reaction conversion coefficient, epsilonelRepresenting the strain of the plastic deformation zone; chi shapeelDenotes the ratio of plastic deformation,%dShowing the ratio of collapse deformation,. epsilon.showing the strain,. epsilonmaxRepresenting the maximum strain.
Under the actual driving working condition, after the load signal is preprocessed, the acceleration signal is converted into stress:
σ＝gρ (19)；
the diaphragm only generates elastic deformation, and the strain of the diaphragm is calculated on the basis of the known stress, and the calculation is shown as a formula (20):
under the driving condition that random external stress is considered, the lithium ion conductivity equation of the diaphragm is as follows:
κt＝κ2(1+εt)；0≤εt＜εel (7)；
wherein, κtDenotes the lithium ion conductivity, κ, as a function of time2Denotes the initial conductivity,. epsilontRepresenting strain over time;
and (4) determining the lithium ion conductivity changing along with time according to a formula (6), and obtaining the lithium ion conductivity change in the battery model by adopting cubic spline interpolation.
S5: and establishing a capacity attenuation calculation equation of the one-dimensional lithium battery model.
A solid electrolyte film (SEI film) is formed on the surface of a carbon negative electrolyte solution of a lithium ion battery, and lithium ions in the battery are consumed in the formation process of the SEI film, so that the energy density of the battery is reduced. The SEI film is unstable, and the film is broken continuously during the cycle, and a new SEI film is generated on the surface of the generated new carbon and the electrolyte, resulting in continuous loss of lithium ions.
In summary, based on the parasitic side reaction generated by the SEI film on the negative electrode, the expression is shown in formula (21):
S+Li++e-→PSEI (21)；
the reaction kinetics equation is shown in equation (22):
the capacity attenuation of the lithium battery is discussed under the running working condition, the difference of each cycle is very small, and the obvious capacity attenuation phenomenon can be found after multiple cycles.
Suppose that: each charge-discharge cycle represents the average aging characteristic of a large number of cycles τ; after one charge-discharge cycle, all lithium captured in the SEI layer came from the negative electrode. The chemical equivalent of the SEI generation reaction is rewritten, the operation speed of capacity loss is optimized, and the improved SEI generation reaction formula is shown as a formula (8):
(τ+1)S+Li++e-+(τ-1)Li(s)→τPSEI (8)；
wherein τ represents a time acceleration factor, S represents a negative electrode material, Li+Represents lithium ion, e-Represents an electron, Li(s) represents an active substance, PSEIIndicates the amount of SEI film generated. τ represents the number of actual cycles per cell simulated. In this model, τ was taken to be 250, and 1 cycle corresponded to 250 SEI generation reactions.
The simulation results under the driving conditions of the electric vehicle are shown below.
Referring to fig. 3, the voltage of the battery varies from 2.7V to 3.6V, and the battery operates in a specific voltage range (2.7V to 3.6V) to prolong the service life and improve safety.
The battery and materials are not completely depleted. The positive electrode is within 70-90% and the negative electrode is within 5-20%.
The temperature of the battery core is obtained through the coupling of the flow field and the heat transfer field, and the temperature is averagely acted on the electrochemical reaction of the one-dimensional lithium battery. As can be seen from the temperature profile inside the battery pack, the outlet temperature is significantly higher than the inlet temperature.
Referring to fig. 4 and 5, which are the relationships of capacity with time and cycle number, respectively, the capacity of the battery is lost during charge and discharge cycles, the resistance of the SEI layer is increased due to reduction reaction of parasitic lithium/solvent SEI on the cathode, the film thickness is increased, and the cycle material is decreased. It is known that the capacity decreases with time and the number of cycles.
While the present invention has been described in detail and with reference to the embodiments thereof as illustrated in the accompanying drawings, it will be apparent to one skilled in the art that various changes and modifications can be made therein. Therefore, certain details of the embodiments are not to be interpreted as limiting, and the scope of the invention is to be determined by the appended claims.
Claims (6)
1. A lithium battery capacity attenuation calculation method under multi-field coupling comprises the following steps:
s1: establishing a one-dimensional lithium battery model;
s2: analyzing the current of the one-dimensional lithium battery model under the driving condition, and acquiring a load signal;
s3: preprocessing the load signal by a stress spectrum signal to obtain a preprocessed signal;
s4: determining the thermal coupling equations of electrochemistry, laminar flow and solid of the one-dimensional lithium battery model;
s5: and establishing a capacity attenuation calculation equation of the one-dimensional lithium battery model.
2. The method for calculating the capacity fading of the lithium battery under the multi-field coupling according to claim 1, wherein in the step S1, the electrode active material of the one-dimensional lithium battery model is a spherical particle with a fixed radius, and an electrochemical model of the one-dimensional lithium battery model adopts a porous electrode model based on ionic charge conservation and material conservation; modeling the conservation of ionic charge and the conservation of substances according to a binary 1:1 electrolyte equation; adopting Fick diffusion to describe the material transport in the spherical particles, and using a diffusion equation to describe the lithium ion transport in the spherical particles under a spherical coordinate system; the charge conservation comprises solid phase charge conservation and liquid phase ion charge conservation, the electron charge conservation is calculated according to ohm law, and the ion charge conservation is calculated according to a concentrated solution theory; the method comprises the steps of carrying out one-dimensional modeling on the lithium battery, and dividing the lithium battery into a negative electrode, a diaphragm and a positive electrode.
3. The lithium battery capacity attenuation calculation method under the multi-field coupling as claimed in claim 1, wherein in the step S2, the main discharge condition is used as the discharge current of the driving condition according to the power battery cycle life requirement and test method for electric vehicles in the national standard of GBT 31484 and 2015.
4. The lithium battery capacity attenuation calculation method under the multi-field coupling according to claim 1, wherein in the step S3, the load signal is preprocessed by Ncode software for outlier rejection and signal denoising.
5. The lithium battery capacity fading calculation method under multi-field coupling according to claim 1, wherein in the step S4, the electrochemical, laminar and solid thermal coupling equations comprise a temperature derivative equation, a reversible thermal equation, a convective heat transfer equation and a lithium ion conductivity equation of a membrane;
the temperature derivative equation is:
wherein, DeltarHmRepresenting the change of the molar gibbs-helmholtz free energy of the reversible cell; z represents the number of changes, F represents the Faraday constant, E represents the potential, T represents the cell temperature,
a temperature derivative representing the electromotive force of the battery;
the reversible thermal equation includes a heat source expression:
wherein W represents a heat source, Q represents heat, V represents volume, t represents time, n represents n mol of a substance,
the convection heat transfer equation is:
where ρ represents the convective density, CpRepresenting the heat transfer coefficient, t representing time, u representing flux,
the backward difference in temperature is represented by,
representing convective heat, QtedRepresents an additional heat source;
the first electrode material thermal conductivity in the normal direction is expressed as:
wherein k isrRepresents the normal thermal conductivity, L _ batt represents the battery thickness, L _ pos represents the positive electrode thickness, kT _ pos represents the thermal conductivity of the positive electrode material, L _ neg represents the negative electrode thickness, kT _ neg represents the thermal conductivity of the negative electrode material, L _ pos _ cc represents the positive electrode current collector thickness, kT _ pos _ cc represents the positive electrode current collector thermal conductivity, L _ neg _ cc represents the negative electrode current collector thickness, kT _ neg _ cc represents the negative electrode current collector thermal conductivity, L _ sep represents the membrane thickness, kT _ sep represents the thermal conductivity of the negative electrode material;
the expression of the thermal conductivity of the second electrode material in the tangential direction is:
wherein k istRepresents the tangential thermal conductivity;
the lithium ion conductivity equation of the diaphragm is as follows:
wherein, kappa represents the lithium ion conductivity in the separator, and kappa1Denotes the initial conductivity,. epsilondDenotes the strain in the collapse zone, alpha denotes the reaction conversion coefficient, epsilonelRepresenting the strain of the plastic deformation zone; chi shapeelDenotes the ratio of plastic deformation,%dShowing the ratio of collapse deformation,. epsilon.showing the strain,. epsilonmaxRepresenting the maximum strain.
Under the driving condition that random external stress is considered, the lithium ion conductivity equation of the diaphragm is as follows:
κt＝κ2(1+εt)；0≤εt＜εel (7)；
wherein, κtDenotes the lithium ion conductivity, κ, as a function of time2Denotes the initial conductivity,. epsilontRepresenting strain over time;
and (4) determining the lithium ion conductivity changing along with time according to a formula (6), and obtaining the lithium ion conductivity change in the battery model by adopting cubic spline interpolation.
6. The method according to claim 1, wherein in step S5, the capacity fade calculation equation comprises an SEI generation equation:
(τ+1)S+Li++e-+(τ-1)Li(s)→τPSEI (8)；
wherein τ represents a time acceleration factor, S represents a negative electrode material, Li+Represents lithium ion, e-Represents an electron, Li(s) represents an active substance, PSEIIndicates the amount of SEI film generated.
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Cited By (2)
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| CN116381512A (en) * | 2023-06-06 | 2023-07-04 | 宁德时代新能源科技股份有限公司 | Battery voltage calculation method, battery voltage calculation device, electronic equipment and readable storage medium |
| CN116449223A (en) * | 2023-06-20 | 2023-07-18 | 苏州精控能源科技有限公司 | Energy storage battery capacity prediction method and device based on compressed sensing |
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