CN114280480B - Method for decomposing direct-current internal resistance of lithium ion battery based on numerical model - Google Patents
Method for decomposing direct-current internal resistance of lithium ion battery based on numerical model Download PDFInfo
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Abstract
The embodiment of the disclosure provides a method for decomposing direct current internal resistance of a lithium ion battery based on a numerical model, which belongs to the technical field of electricity and specifically comprises the following steps: the control equation and boundary conditions related to the lithium ion battery numerical model are classified, combined and coupled according to mass conservation, charge conservation and energy conservation; determining electrochemical parameters associated with the decomposition of the internal resistance of the battery in a corresponding control equation aiming at the lithium ion battery to be decomposed to obtain an integrated scheme corresponding to the electrochemical parameters; the lithium ion battery to be decomposed is divided into infinite units according to an integrated scheme, internal resistance generated on each battery unit is subjected to averaging treatment according to ohm law, an internal resistance source is determined according to a battery structure, the average internal resistance is subjected to deformation treatment in a structural interval, and then the internal resistances of different components are obtained through integration. Through the scheme of the present disclosure, the direct current internal resistance of the lithium ion battery can be efficiently and accurately decomposed, and the purpose of predicting the battery performance is achieved.
Description
Technical Field
The embodiment of the disclosure relates to the technical field of electricity, in particular to a method for decomposing direct current internal resistance of a lithium ion battery based on a numerical model.
Background
At present, with the popularization of lithium ion batteries in the fields of new energy automobiles, notebook computers, mobile phones, other wearable devices and the like, the service life, the quick charge performance and the safety performance of the lithium ion batteries are more and more important. The performance is closely related to the internal resistance of the lithium ion battery. The internal resistance is one of important indexes for evaluating the lithium ion battery, the internal resistance of the battery changes in the charging and discharging processes and the storage processes of the battery, and the change rule of the internal resistance is mastered, so that the lithium ion battery has good guiding effect on the structural design and new product development of the lithium ion battery. The existing analysis and research on the internal resistance of the lithium ion battery are less, the potential and current distribution in the battery scale, the generation and transmission of heat, the complex transmission phenomenon in the electrode, and the microstructure of the electrode material are all the causes of the internal resistance. The internal resistance of the battery is not constant, and changes continuously with time and space in the process of charging and discharging. The internal resistance is decomposed into different components according to different working intervals of the battery structure, and the prediction of the battery performance is realized by establishing the relation between each internal resistance component and the battery state. The internal resistance can be accurately described and decomposed by analyzing the electrochemical working principle of the lithium ion battery and numerically modeling the working process and researching the internal lithium ion transmission behavior and the battery transmission condition of the battery through a control equation and boundary conditions.
Therefore, a method for decomposing the direct current internal resistance of the lithium ion battery based on a numerical model, which can effectively and accurately decompose the direct current internal resistance of the lithium ion battery and realize the prediction of the battery performance, is needed.
Disclosure of Invention
In view of the above, the embodiments of the present disclosure provide a method for decomposing a direct current internal resistance of a lithium ion battery based on a numerical model, which at least partially solves the problems in the prior art that the direct current internal resistance of the lithium ion battery is decomposed, and the efficiency and the accuracy of predicting the battery performance are poor.
The embodiment of the disclosure provides a method for decomposing direct current internal resistance of a lithium ion battery based on a numerical model, which comprises the following steps:
the control equation and boundary conditions related to the lithium ion battery numerical model are classified, combined and coupled according to mass conservation, charge conservation and energy conservation;
determining electrochemical parameters associated with the decomposition of the internal resistance of the battery in a corresponding control equation of the lithium ion battery to be decomposed, and obtaining an integrated scheme corresponding to the electrochemical parameters;
dividing the lithium ion battery to be decomposed into infinite units according to the integrated scheme, carrying out averaging treatment on the internal resistance generated on each battery unit according to ohm law, determining an internal resistance source according to a battery structure, carrying out deformation treatment on the average internal resistance in the structural interval, and integrating to obtain the internal resistances of different components.
According to a specific implementation manner of the embodiment of the disclosure, the numerical model of the lithium ion battery is any one or the coupling of several models of a single particle model, a pseudo two-dimensional model, an electrochemical model in a three-dimensional model, a thermal model or a force model;
according to a specific implementation of the disclosed embodiment, the mass conservation relates to a diffusion process of lithium ions in the positive electrode material particles, a diffusion process of lithium ions in the negative electrode material particles and a diffusion process of lithium ions in the electrolyte phase.
According to a specific implementation of an embodiment of the disclosure, the conservation of charge involves an electron current passing through the positive electrode current collector, the positive electrode material, the negative electrode current collector, the negative electrode material, and an ion current in the positive electrode electrolyte, the separator electrolyte, and the negative electrode electrolyte.
According to a specific implementation of an embodiment of the present disclosure, the conservation of energy includes a heat capacity phase, a heat conduction term, and a heat source term.
According to a specific implementation of an embodiment of the present disclosure, the coupling is any one or a combination of more of an electrochemical field, a thermal field, or a force field.
According to a specific implementation manner of the embodiment of the disclosure, the positive electrode material of the lithium ion battery to be decomposed is one or more of lithium cobaltate, lithium manganate, lithium nickelate, lithium nickel cobalt manganate, lithium nickel cobalt aluminate and lithium iron phosphate mixed in any proportion;
the negative electrode material of the lithium ion battery to be decomposed is one or more of graphite, lithium titanate, silicon-based material, phosphorus-based material, tin-based material, germanium-based material or zinc-based material which are mixed in any proportion;
the membrane material of the lithium ion battery to be decomposed is any one or more of a porous polymer membrane, a non-woven fabric membrane and an inorganic composite membrane;
the electrolyte of the lithium ion battery to be decomposed is any one or more of inorganic liquid electrolyte, organic liquid electrolyte, inorganic solid electrolyte, organic liquid electrolyte and molten salt electrolyte.
According to a specific implementation manner of the embodiment of the disclosure, the electrochemical parameter includes any one parameter or a combination of several parameters of available capacity of a battery, initial lithium intercalation amount of anode and cathode materials, maximum lithium intercalation amount of anode and cathode materials, lithium ion diffusion coefficient of anode and cathode materials, balance potential curve of anode and cathode materials, entropy thermal coefficient curve of anode and cathode materials, thickness of anode and cathode and diaphragm, volume fraction of anode and cathode active substances, volume fraction of anode and cathode and diaphragm liquid phase, particle size of anode and cathode materials, tortuosity coefficient of diaphragm, reaction rate constant of anode and cathode materials, solid phase conductivity of anode and cathode materials, conductivity of electrolyte, migration number of lithium ions of diaphragm, cathode transfer coefficient of anode and cathode materials.
According to a specific implementation manner of the embodiment of the disclosure, the battery structure is any one or more of a negative electrode tab, a negative electrode current collector, a negative electrode material, a diaphragm, a positive electrode material, a positive electrode current collector and a positive electrode tab.
According to a specific implementation manner of the embodiment of the disclosure, the internal resistance source is one or more of an adhesive insulating film on the surface of the positive electrode material, an SE I film on the surface of the positive electrode material, damage to the structure of the positive electrode material, a conductive agent between particles of the positive electrode material, failure of the adhesive between particles of the positive electrode material, material shedding between the positive electrode material layer and the aluminum foil, surface resistance of the aluminum foil, polarization of electric potential distribution in the aluminum foil, a conductive agent on the surface of the negative electrode material, an SE I film on the surface of the negative electrode material, damage to the structure of the negative electrode material, failure of the adhesive between particles of the negative electrode material, material shedding between the negative electrode material layer and the copper foil, copper dissolution of the surface of the copper foil, polarization of electric potential distribution in the copper foil, incomplete infiltration of the electrolyte to the positive and negative electrode material porosity effects on the distribution of the electrolyte, conductivity of the electrolyte, distribution of the electrolyte in the separator, and electrolyte allowance.
The scheme for decomposing the direct current internal resistance of the lithium ion battery based on the numerical model in the embodiment of the disclosure comprises the following steps: the control equation and boundary conditions related to the lithium ion battery numerical model are classified, combined and coupled according to mass conservation, charge conservation and energy conservation; determining electrochemical parameters associated with the decomposition of the internal resistance of the battery in a corresponding control equation of the lithium ion battery to be decomposed, and obtaining an integrated scheme corresponding to the electrochemical parameters; dividing the lithium ion battery to be decomposed into infinite units according to the integrated scheme, carrying out averaging treatment on the internal resistance generated on each battery unit according to ohm law, determining an internal resistance source according to a battery structure, carrying out deformation treatment on the average internal resistance in the structural interval, and integrating to obtain the internal resistances of different components.
The beneficial effects of the embodiment of the disclosure are that: according to the scheme, the numerical model control equation and boundary conditions of the lithium ion battery are analyzed, and the accuracy of the model is guaranteed by acquiring key electrochemical parameters involved in the control equation. Dividing the battery into infinite areas by a differentiation method, calculating the average polarization of each area according to ohm law, and integrating the average polarization in different structural interval ranges inside the battery to obtain the internal resistances of different components after the average polarization is deformed according to the difference of electrochemical principles for generating the internal resistances.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present disclosure, and other drawings may be obtained according to these drawings without inventive effort to a person of ordinary skill in the art.
Fig. 1 is a flow chart of a method for decomposing a direct current internal resistance of a lithium ion battery based on a numerical model according to an embodiment of the disclosure;
fig. 2 is a schematic diagram of a dc internal resistance decomposition process according to an embodiment of the disclosure;
FIG. 3 is a schematic diagram of a pseudo two-dimensional model and coordinate conditions provided in an embodiment of the disclosure;
fig. 4 to 7 are schematic diagrams of a G ITT method for testing a lithium ion diffusion coefficient of graphite according to embodiments of the present disclosure;
fig. 8 is a schematic structural view of a battery divided into an infinite number of cells according to an embodiment of the present disclosure;
fig. 9 is a graph of the dc internal resistance according to the component decomposition ratio provided in the embodiment of the present disclosure;
fig. 10 is a diagram of a direct current internal resistance according to a battery structure decomposition ratio provided in an embodiment of the present disclosure.
Detailed Description
Embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.
Other advantages and effects of the present disclosure will become readily apparent to those skilled in the art from the following disclosure, which describes embodiments of the present disclosure by way of specific examples. It will be apparent that the described embodiments are merely some, but not all embodiments of the present disclosure. The disclosure may be embodied or practiced in other different specific embodiments, and details within the subject specification may be modified or changed from various points of view and applications without departing from the spirit of the disclosure. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict. All other embodiments, which can be made by one of ordinary skill in the art without inventive effort, based on the embodiments in this disclosure are intended to be within the scope of this disclosure.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should also be noted that the illustrations provided in the following embodiments merely illustrate the basic concepts of the disclosure by way of illustration, and only the components related to the disclosure are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided in order to provide a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
The embodiment of the disclosure provides a method for decomposing direct current internal resistance of a lithium ion battery based on a numerical model, which can be applied to battery performance prediction processes of scenes such as new energy automobiles, notebook computers and the like.
Referring to fig. 1, a flow chart of a method for decomposing a dc internal resistance of a lithium ion battery based on a numerical model according to an embodiment of the disclosure is provided. As shown in fig. 1, the method mainly comprises the following steps:
s101, classifying, combining and coupling a control equation related to a lithium ion battery numerical model and boundary conditions thereof according to mass conservation, charge conservation and energy conservation;
optionally, the numerical model of the lithium ion battery is any one or the coupling of a plurality of models of a single particle model, a pseudo two-dimensional model, an electrochemical model in a three-dimensional model, a thermal model or a force model;
alternatively, the conservation of mass involves a diffusion process of lithium ions in the particles of the positive electrode material, a diffusion process of lithium ions in the particles of the negative electrode material, and a diffusion process of lithium ions in the electrolyte phase.
Optionally, the conservation of charge involves electron current passing through the positive current collector, the positive material, the negative current collector, the negative material, and ion current in the positive electrolyte, the separator electrolyte, and the negative electrolyte.
Optionally, the conservation of energy includes a thermal capacity phase, a heat conduction term, and a heat source term.
Optionally, the coupling is any one or more of an electrochemical field, a thermal field, or a force field.
For example, in the process of decomposing the direct current internal resistance of the lithium ion battery as shown in fig. 2, the numerical model of the lithium ion battery can be processed as a pseudo two-dimensional model, the schematic diagram and the coordinate condition of the model are shown in fig. 3, and the control equation and the boundary condition related to mass conservation are as follows:
wherein the diffusion process of lithium ions in the solid phase of the anode follows the control equation:
wherein c s Is the solid-phase lithium ion concentration, D s,a The solid phase diffusion coefficient of the negative electrode, and t is time.
Boundary conditions at the sphere center and sphere of the anode material particles:
wherein R is a Radius j of cathode material a Is the negative current density.
Control equation for diffusion and migration processes of lithium ions in the negative electrode liquid phase:
wherein ε a Is the porosity of the cathode material, c is the generalized lithium ion concentration, t + D is the migration number of lithium ions eff,a Is the negative electrode solid phase effective lithium ion diffusion coefficient alpha a Is the anode transfer coefficient.
Boundary conditions on both sides of the diaphragm:
wherein h is a Is the thickness of the negative pole piece, D eff,s Is the effective diffusion coefficient of liquid-phase lithium ions in the diaphragm area, near the membrane side of the membrane-positive interface, +.>Is near the positive side of the separator-positive interface.
The diffusion process of lithium ions in the positive solid phase follows the control equation:
wherein D is s,c Is the solid phase diffusion coefficient of the positive electrode.
Boundary conditions at the sphere center and sphere of the positive electrode material particles:
wherein R is c Radius j of positive electrode material c Is the positive current density.
Control equation for diffusion and migration processes of lithium ions in the negative electrode liquid phase:
wherein ε c Is the porosity of the positive electrode material, t + D is the migration number of lithium ions eff,c Is positive electrode solid phase effective lithium ion diffusion coefficient alpha c Is the cathode transfer coefficient.
Boundary conditions on both sides of the positive electrode material:
wherein h is tot The total thickness of the negative pole piece, the diaphragm and the positive pole piece is as follows.
The diffusion process of lithium ions in the diaphragm region follows the control equation:
wherein ε s Is the membrane porosity.
Boundary conditions for lithium ion concentration on both sides of the separator:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the near negative side of the negative-separator interface, < >>Is the separator-proximal side of the negative electrode-separator interface.
The control equations and boundary conditions related to charge conservation are as follows:
wherein the negative solid phase current follows the control equation:
wherein sigma eff,a Is the effective electrical conductivity of the cathode material,at solid phase potential, F is faraday constant.
Boundary conditions on both sides of the diaphragm:
wherein h is a Is the thickness of the cathode, h s For the thickness of the diaphragm, h c Is the thickness of the positive electrode.
Wherein the negative liquid phase current follows the control equation:
wherein, kappa eff,a For the effective ionic conductivity of the electrolyte in the negative electrode region,is the liquid phase potential, R is the ideal gas constant, T is Kelvin temperature, and I is the current.
Boundary conditions on both sides of the diaphragm:
wherein, kappa eff,s Effective conductivity, κ of electrolyte in diaphragm region eff,c The effective conductivity of the electrolyte is the positive electrode area.
Wherein the diaphragm region liquid phase current follows the control equation:
boundary conditions on both sides of the diaphragm:
the control equation related to energy conservation is as follows:
q＝Q 1 +Q tab
wherein ρ is density, C p Is specific heat capacity, k x ，k y ，k z The heat conductivity coefficients in the x, y and z directions are respectively, Q is the heat generation amount, and Q 1 For electrochemical heating, Q tab,i To generate heat for the tab, q irrev Is irreversible heat, q rev Is reversible heat, E eq Is balanced potential, V is voltage, R is total DC internal resistance value, A tab For the cross-sectional area of the tab, sigma tab,i For the i component tab conductivity, sigma c,i The contact conductivity between the tab and the clamp.
Boundary conditions related to conservation of energy involve heat exchange of the battery with the environment:
Q loss ＝Q conv +Q rad ＝-h(T amb -T)-εσ(T amb 4 -T 4 )
wherein Q is loss Q is the heat loss of the battery conv For heat convection and dissipation, Q rad For heat radiation, h is the convection heat transfer coefficient, T is the battery temperature, T amb Is the external environment temperature (25 ℃), epsilon is the heat emissivity of the battery. Sigma is the Stefin-Boltzmann constant.
According to solid-liquid charge conservation, the current density in the electrolyte, the local current density per unit area of the active material, and the lithium ion flux at the interface between the active particle surface and the electrolyte are coupled by the following equation:
wherein j is L A is the specific area of active material particles in the electrode, j is the liquid phase current density loc For local current density, J n Is the lithium ion flux at the interface between the surface of the active particles and the electrolyte.
S102, determining electrochemical parameters associated with battery internal resistance decomposition in a corresponding control equation of a lithium ion battery to be decomposed to obtain an integrated scheme corresponding to the electrochemical parameters;
optionally, the positive electrode material of the lithium ion battery to be decomposed is one or more of lithium cobaltate, lithium manganate, lithium nickelate aluminate and lithium iron phosphate which are mixed in any proportion;
the negative electrode material of the lithium ion battery to be decomposed is one or more of graphite, lithium titanate, silicon-based material, phosphorus-based material, tin-based material, germanium-based material or zinc-based material which are mixed in any proportion;
the membrane material of the lithium ion battery to be decomposed is any one or more of a porous polymer membrane, a non-woven fabric membrane and an inorganic composite membrane;
the electrolyte of the lithium ion battery to be decomposed is any one or more of inorganic liquid electrolyte, organic liquid electrolyte, inorganic solid electrolyte, organic liquid electrolyte and molten salt electrolyte.
Optionally, the electrochemical parameter includes any one parameter or a combination of several parameters of available capacity of the battery, initial lithium intercalation amount of the anode and cathode materials, maximum lithium intercalation amount of the anode and cathode materials, lithium ion diffusion coefficient of the anode and cathode materials, balance potential curve of the anode and cathode materials, entropy coefficient curve of the anode and cathode materials, thickness of the anode and the cathode and diaphragm, volume fraction of the anode active material, volume fraction of the anode and the cathode and diaphragm liquid phase, particle size of the anode and cathode materials, tortuosity coefficient of the diaphragm, reaction rate constant of the anode and cathode materials, solid phase conductivity of the anode and cathode materials, conductivity of the electrolyte, lithium ion migration number of the diaphragm, cathode transfer coefficient of the anode and cathode materials.
In specific implementation, for the lithium ion battery to be decomposed, electrochemical parameters associated with the decomposition of the internal resistance of the battery in a corresponding control equation can be determined first, and an integrated scheme corresponding to the electrochemical parameters is obtained. For example, the lithium ion battery to be decomposed is a lithium cobaltate-graphite soft package battery, the electrochemical parameters with larger influence on the decomposition of the direct internal resistance of the battery and the acquisition scheme are as follows, and other electrochemical parameters with smaller influence on the decomposition of the direct internal resistance of the battery can be preset and set by an operator according to actual requirements.
First, the battery available capacity test and determination of the amount of lithium intercalation. Constant current charging was performed at 1C up to the battery charge upper limit voltage (4.55V) at 25 ℃; then, constant voltage charging is carried out on the battery at 4.55V until the current is reduced to 0.1C, and the battery is kept stand for 1 hour, so that the polarization effect of the battery is basically reduced; finally, constant-current discharge is carried out at 1C until the lower limit (3V) of battery discharge is reached, and the battery is kept still for 1h; the above charge and discharge process is cycled at least 3 times to ensure capacity results (denoted as C max ) Is accurate and reliable. At full charge, initial lithium ion intercalation concentration (C 0 ) And maximum solid phase lithium ion concentration (C s,max ) Initial lithium intercalation amount (C s,0％ /C s,max ) Maximum lithium intercalation (C s,100％ /C s,max ). The negative and positive lithium intercalation amounts are denoted by x and y, respectively. Maximum lithium intercalation C s,100％ /C s,max Minimum lithium intercalation C s,0％ /C s,max . And respectively measuring and testing the charge-discharge curve of the button cell and the charge-discharge curve of the full cell, and performing differential treatment:
wherein x is 0％ Is the minimum lithium intercalation amount of the positive electrode,is the minimum value of the differential curve of the voltage of the positive electrode charge-discharge curve and the lithium intercalation quantity, +.>For the battery capacity corresponding to the minimum value, Q p,theory Is the theoretical capacity of positive electrode, x 100％ Maximum lithium intercalation amount of positive electrode, Q charge For charging capacity, y 0％ Minimum lithium intercalation for the negative electrode,/->Is the maximum value of the differential curve of the voltage of the charge-discharge curve of the negative electrode and the lithium intercalation quantity, +.>To the maximum corresponding battery capacity, Q n,theory Theoretical capacity of negative electrode, y 100％ Is the maximum lithium intercalation amount of the negative electrode.
Second, OCV-SOC curves at different rates and different temperatures. Lithium cobaltate and graphite button cells were assembled separately. The following tests were completed at 25 ℃):
testing of lithium cobaltate button cell: constant current charging was performed at 1C until the battery charge upper limit voltage (4.55V); then, constant voltage charging is carried out on the battery at 4.55V until the current is reduced to 0.1C, and the battery is kept stand for 1 hour, so that the polarization effect of the battery is basically reduced; finally, constant-current discharge is carried out at 1C until the lower limit (3V) of battery discharge is reached, and the battery is kept still for 1h; the above charge and discharge process is cycled at least 3 times to ensure accurate and reliable capacity results (noted Cmax). Then constant current charging is performed at 0.02C until the battery charge upper limit voltage (4.55V); and finally, constant-current discharge is carried out at 0.02C until the battery discharge lower limit (3V) is reached, an OCV-SOC curve of lithium cobaltate under the 0.02C multiplying power is obtained, 0.02C is replaced by 0.05C, and 0.1C is respectively obtained to obtain OCV-SOC curves under the 0.05C multiplying power and 0.1C multiplying power.
Testing of graphite button cell: constant current discharge is carried out at 1C until the battery discharge lower limit voltage (0.01V); then, constant current charging is carried out on the battery at 1C until the upper limit voltage (2V) of the battery is charged, and the battery is kept stand for 1h; the above charge and discharge process is cycled at least 3 times to ensure accurate and reliable capacity results (noted Cmax). Then constant current discharge is carried out at 0.02C until the battery discharges the lower limit voltage (0.01V); and finally, constant-current charging is carried out at 0.02C until the battery charging upper limit (2V) is reached, an OCV-SOC curve under the 0.02C multiplying power of graphite is obtained, 0.02C is replaced by 0.05C, and 0.1C is respectively obtained to obtain OCV-SOC curves under the 0.05C multiplying power and 0.1C multiplying power.
Thirdly, acquiring a lithium ion diffusion coefficient. And respectively assembling graphite and lithium cobaltate button cells. The following tests were completed at 25 ℃): graphite lithium ion diffusion coefficient D-was measured on Graphite/Li using a constant current intermittent titration method (GITT). The specific test procedure is set as follows: (1) The battery is circulated for 3 circles under the current density of 0.1C to be completely activated, and the charging and discharging range is 2-0.01V; (2) constant-current discharge for 10min at 0.1C, and standing for 50min; (3) If the voltage of the battery is more than or equal to 0.01V, repeating the second step, and if the voltage is less than 0.01V, jumping to the next step; (4) constant-current charging for 10min at 0.1C, and standing for 50min; (5) And repeating the fourth step when the voltage is less than or equal to 2V, otherwise ending the test. The test results are shown in fig. 4 to 7. E-tau 1/2 For polarizing voltage pairsThe curves of the square roots are in a linear relation, so that the simplified lithium ion diffusion coefficient formula can be used for calculation:
where τ is the duration of the current pulse, 600s; m is m B 2.248mg of active material mass of electrode material;and M B The molar volume and the molar mass of the electrode material are 5.333cm3/mol and 12g/mol respectively; s is the surface contact area of the electrode and the electrolyte, and can be approximately replaced by the surface area of the electrode plate, namely 1.5386cm2; ΔE s Is the voltage variation difference caused by the pulse. ΔE τ Is the voltage variation difference of constant current discharge.
The lithium ion diffusion coefficient D+ of lithium cobaltate was measured by a constant current batch titration method (GITT) on LiCoO 2/Li. The charge-discharge range is 4.55-3V, and other testing processes are the same as the graphite testing process.
Calculating the diffusion coefficient of lithium ions in graphite and lithium cobaltate to calculate the migration number t of the diaphragm + ：
Wherein D is + Is the diffusion coefficient of positive lithium ion, D - Is the diffusion coefficient of negative lithium ions.
And S103, dividing the lithium ion battery to be decomposed into infinite units according to the integrated scheme, carrying out averaging treatment on the internal resistance generated on each battery unit according to ohm law, determining an internal resistance source according to a battery structure, carrying out deformation treatment on the average internal resistance in the structural interval, and integrating to obtain the internal resistances of different components.
Optionally, the battery structure is any one or more of a negative electrode tab, a negative electrode current collector, a negative electrode material, a diaphragm, a positive electrode material, a positive electrode current collector and a positive electrode tab.
Optionally, the source of internal resistance is one or more of an adhesive insulating film on the surface of the positive electrode material, an SEI film on the surface of the positive electrode material, damage to the structure of the positive electrode material, a conductive agent between particles of the positive electrode material, failure of the adhesive between particles of the positive electrode material, material shedding between a positive electrode material layer and an aluminum foil, surface resistance of the aluminum foil, polarization of electric potential distribution in the aluminum foil, a conductive agent on the surface of the negative electrode material, SEI film on the surface of the negative electrode material, damage to the structure of the negative electrode material, failure of the adhesive between particles of the negative electrode material, material shedding between the negative electrode material layer and a copper foil, copper dissolution on the surface of the copper foil, polarization of electric potential distribution in the copper foil, incomplete infiltration of the electrolyte to the positive electrode material and the negative electrode material porosity on the distribution of the electrolyte, conductivity of the electrolyte, distribution of the electrolyte in the diaphragm, and electrolyte allowance.
In the specific implementation, as shown in fig. 8. The internal resistance generated at each cell is averaged according to ohm's law:
wherein R is ave,i To average internal resistance, j app To apply the current density, I loc Is the current of each battery cell with increased polarization, I tot Is the total current through the cell and L is the thickness of the electrode or separator.
Determining the source of internal resistance according to the structure of the battery, and deforming and integrating the average internal resistance in the structural interval to obtain the internal resistances of different components.
Wherein for polarization to occur at the electrolyte/electrode interface, the average polarization can be deformed as:
wherein j is tot Is through a unit cross-sectional areaTotal current of j loc Is the local current through the unit cross-sectional area.
Polarization occurring in an electrolyte or solid phase material, the average polarization of which can be deformed into:
wherein, the liquid crystal display device comprises a liquid crystal display device,for local electrochemical potential, j ν Is the local current per unit cross-sectional area in the solid phase material or electrolyte phase.
The following internal resistance components can be obtained by integration in different structural intervals of the battery.
Wherein the diffusion polarization of the electrolyte:
wherein c L Is liquid phase lithium ion concentration, kappa c For electrolyte conductivity, j L Is the liquid phase current density.
Diffusion polarization internal resistance of solid phase:
wherein E is surf For the surface potential of solid phase particles, E ave Is the average potential of the solid phase particles.
Ohmic internal resistance of electrolyte:
wherein, kappa eff Is the effective conductivity of the liquid phase.
Ohmic internal resistance of solid phase:
wherein j is s For solid phase current density, sigma eff Is the effective conductivity of the solid phase.
The electrochemical reaction activates polarized internal resistance:
wherein phi is s Is of solid phase potential phi L Is a liquid phase potential.
The contact internal resistance is R contact
Decomposition of the internal resistance of the battery can be completed in different battery structure intervals according to the above different internal resistance components, and the decomposition results are shown in table 1.
TABLE 1
The symbol descriptions involved in the embodiments of the present disclosure are shown in table 2:
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at 25 ℃, when the battery is discharged at 0.2 ℃ for 5s, the internal resistance of the battery is decomposed according to ohmic internal resistance, diffusion internal resistance, activation internal resistance, SE I film activation internal resistance and other components in a 90% SOC state, and the decomposition is shown in figure 9. The internal resistance of the whole battery is divided into positive electrode area internal resistance, diaphragm area internal resistance and negative electrode area internal resistance according to the battery structure, and the proportion of the area internal resistances is shown in figure 10.
According to the method for decomposing the direct current internal resistance of the lithium ion battery based on the numerical model, the accuracy of the model is guaranteed by analyzing the control equation and the boundary condition of the numerical model of the lithium ion battery and acquiring the key electrochemical parameters involved in the control equation. Dividing the battery into infinite areas by a differentiation method, calculating the average polarization of each area according to ohm law, and integrating the average polarization in different structural interval ranges inside the battery to obtain the internal resistances of different components after the average polarization is deformed according to the difference of electrochemical principles for generating the internal resistances.
The foregoing is merely specific embodiments of the disclosure, but the protection scope of the disclosure is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the disclosure are intended to be covered by the protection scope of the disclosure. Therefore, the protection scope of the present disclosure shall be subject to the protection scope of the claims.
Claims (9)
1. The method for decomposing the direct current internal resistance of the lithium ion battery based on the numerical model is characterized by comprising the following steps of:
the control equation and boundary conditions related to the lithium ion battery numerical model are classified, combined and coupled according to mass conservation, charge conservation and energy conservation;
the control equation comprises a control equation followed by a diffusion process of lithium ions in a solid phase of the anode, a control equation followed by a diffusion and migration process of lithium ions in a liquid phase of the anode, and a control equation followed by a diffusion process of lithium ions in a diaphragm area, wherein the expression of the control equation followed by the diffusion process of lithium ions in the solid phase of the anode is that
Wherein c s Is the solid-phase lithium ion concentration, D s,a The solid phase diffusion coefficient of the negative electrode is represented by t, and the time is represented by t;
the expression of the control equation of the diffusion and migration process of lithium ions in the liquid phase of the anode is
Wherein ε a Is the porosity of the cathode material, c is the generalized lithium ion concentration, t + D is the migration number of lithium ions eff,a Is the negative electrode solid phase effective lithium ion diffusion coefficient alpha a Is the anode transfer coefficient;
the diffusion process of the lithium ions in the diaphragm area follows the expression of a control equation
Wherein ε s Is the diaphragm porosity;
the simultaneous and coupled expression is
Wherein j is L A is the specific area of active material particles in the electrode, j is the liquid phase current density loc For local current density, J n Is the lithium ion flux at the interface between the surface of the active particle and the electrolyte;
determining electrochemical parameters related to internal resistance decomposition of a battery in a corresponding control equation of the lithium ion battery to be decomposed, and obtaining an integrated scheme corresponding to electrochemical parameters matched with each other between the positive electrode and the negative electrode through matching of a positive electrode solid-phase concentration range and a negative electrode solid-phase concentration range, wherein the electrochemical parameters comprise any one parameter or a combination of several parameters of available capacity of the battery, initial lithium intercalation amount of the positive electrode material and the negative electrode material, maximum lithium intercalation amount of the positive electrode material and the negative electrode material, lithium ion diffusion coefficient of the positive electrode material and the negative electrode material, balance potential curve of the positive electrode material and the negative electrode material, entropy coefficient curve of the positive electrode material and the negative electrode and thickness of a diaphragm, volume fraction of positive electrode active substances, volume fraction of positive electrode, negative electrode and diaphragm, particle size of the positive electrode material and the negative electrode material, tortuosity coefficient of the diaphragm, reaction rate constant of the positive electrode material and the negative electrode material, solid-phase conductivity of the electrolyte, migration number of the diaphragm lithium ions of the diaphragm, cathode transfer coefficient of the positive electrode material and anode transfer coefficient of the positive electrode material and the negative electrode material;
dividing the lithium ion battery to be decomposed into infinite units according to the integrated scheme, carrying out averaging treatment on the internal resistance generated on each battery unit according to ohm law, determining an internal resistance source according to a battery structure, carrying out deformation treatment on the average internal resistance in a battery structure interval, and integrating to obtain the internal resistances of different components.
2. The method of claim 1, wherein the lithium ion battery numerical model is a single particle model, a pseudo two-dimensional model, an electrochemical model in a three-dimensional model, a thermal model, or a coupling of any one or more of force models.
3. The method of claim 1, wherein the conservation of mass involves diffusion of lithium ions in the particles of positive electrode material, diffusion of lithium ions in the particles of negative electrode material, and diffusion of lithium ions in the electrolyte phase.
4. The method of claim 1, wherein the conservation of charge involves electron current passing in the positive current collector, positive material, negative current collector, negative material, and ion current in the positive electrolyte, separator electrolyte, and negative electrolyte.
5. The method of claim 1, wherein the conservation of energy comprises a heat capacity phase, a heat conduction term, and a heat source term.
6. The method of claim 1, wherein the coupling is any one or more of an electrochemical field, a thermal field, or a force field.
7. The method according to claim 1, wherein the positive electrode material of the lithium ion battery to be decomposed is one or more of lithium cobaltate, lithium manganate, lithium nickelate, lithium nickel cobalt manganate, lithium nickel cobalt aluminate and lithium iron phosphate mixed in any proportion;
the negative electrode material of the lithium ion battery to be decomposed is one or more of graphite, lithium titanate, silicon-based material, phosphorus-based material, tin-based material, germanium-based material or zinc-based material which are mixed in any proportion;
the membrane material of the lithium ion battery to be decomposed is any one or more of a porous polymer membrane, a non-woven fabric membrane and an inorganic composite membrane;
the electrolyte of the lithium ion battery to be decomposed is any one or more of inorganic liquid electrolyte, organic liquid electrolyte, inorganic solid electrolyte, organic liquid electrolyte and molten salt electrolyte.
8. The method of claim 1, wherein the battery structure is any one or more of a negative electrode tab, a negative electrode current collector, a negative electrode material, a separator, a positive electrode material, a positive electrode current collector, or a positive electrode tab.
9. The method of claim 1, wherein the source of internal resistance is one or more of an adhesive insulating film on a surface of a positive electrode material, an SEI film on a surface of a positive electrode material, a destruction of a structure of a positive electrode material, a conductive agent between particles of a positive electrode material, a failure of an adhesive between particles of a positive electrode material, a material shedding between a positive electrode material layer and an aluminum foil, a surface resistance of an aluminum foil, a polarization of an internal potential distribution of an aluminum foil, a conductive agent on a surface of a negative electrode material, an SEI film on a surface of a negative electrode material, a destruction of a structure of a negative electrode material, a failure of an adhesive between particles of a negative electrode material, a material shedding between a layer of a negative electrode material and a copper foil, a copper dissolution of a copper foil, a polarization of an internal potential distribution of a copper foil, an incomplete wetting of a positive and negative electrode material porosity to an electrolyte distribution, an electrical conductivity of an electrolyte, a distribution of an electrolyte within a separator, or an electrolyte balance.
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