CN117930026A - Mechanism-based wide temperature range lithium ion battery life prediction method - Google Patents
Mechanism-based wide temperature range lithium ion battery life prediction method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 63
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 title claims abstract description 40
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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]
- G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
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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]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/04—Ageing analysis or optimisation against ageing
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
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Abstract
The invention belongs to the technical field of power lithium ion batteries, and relates to a wide temperature range lithium ion battery life prediction method based on a mechanism, which is used for obtaining battery product specifications and cell design parameters, measuring intrinsic characteristic parameters, electrochemical parameters, kinetic parameters and thermodynamic parameters of electrode materials, and testing data of multiplying power performance of a battery in a wide temperature range; establishing an electrochemical model and a thermal model, and establishing an electrochemical-thermal coupling model; acquiring accelerated aging test data of the battery at different temperatures; establishing a side reaction model, and establishing an electrochemical-thermal-side reaction coupling model; and verifying the electrochemical-thermal-side reaction coupling model and correcting the aging parameters according to the measured data to obtain the lithium ion battery electrochemical-thermal-side reaction life prediction model. The invention takes into account the internal physical and chemical process of the battery and the external environment variable, can simulate the rule of aging and attenuation of the battery from linear to nonlinear, and meets the requirement on the optimal design of battery products.
Description
Technical Field
The invention belongs to the technical field of power lithium ion batteries, and particularly relates to a wide temperature range lithium ion battery life prediction method based on a mechanism.
Background
The lithium ion battery is used as a main power source of the new energy automobile, and the proportion of the lithium ion battery in the whole automobile cost of the new energy automobile is approximately 40%. The new energy automobile can cause the battery to age to different degrees through some physical, chemical and electrochemical reactions occurring in the lithium ion battery in the process of placing or driving, so that the service life of the battery is shortened, and the purchase cost of consumers is increased. The battery aging is unavoidable, if the battery design can be optimized through the related technical means, the battery aging rate can be slowed down, the service life of the battery can be prolonged, the large-scale popularization and commercial development of new energy automobiles can be facilitated, and the early realization of the double-carbon target can be accelerated.
In the prior art, life prediction methods of lithium ion batteries include an experimental method and a model prediction method. The experimental method needs to carry out a large amount of testing and disassembling work on the finished battery, such as a lithium ion battery capacity degradation prediction method based on chemical degradation and mechanical degradation developed by patent CN115047364A, needs to carry out cyclic testing on a plurality of batteries, disassembles the batteries with different cyclic times, measures the composition and thickness of a solid electrolyte interface on a negative electrode plate, the length and depth of surface cracks of a negative electrode material, and predicts the battery capacity through a mathematical algorithm. The method needs a large amount of experimental tests and battery disassembly work, is time-consuming and labor-consuming, and has a certain danger in battery disassembly.
Model prediction is mainly divided into three categories, namely fitting method prediction based on empirical data, data-driven method prediction based on data driving and mechanism model prediction based on mechanism. The empirical fitting method is simple in that an empirical formula is fitted to limited measured data to predict the service life, but the required test data amount is large, and the prediction error for a long life cycle is large, for example, the patent CN114624604A, CN115291131A, CN115407210A, CN113740752A, CN113125982A predicts the service life of a battery based on the empirical fitting method.
The data driving method is to collect a large amount of test or actual operation information, screen out characteristic factors which can be used for representing the service life of the battery according to a mathematical statistics method, and conduct probability prediction on the service life attenuation condition of the battery. The first two methods all rely on a large number of battery external state parameters (current, voltage, resistance and charge and discharge time) and product test data to predict the service life and estimate the health state, a rule formula is fitted by obtaining a large number of test data through experiments, and the health state and the service life of the battery are predicted by a method similar to probability statistics. The prediction methods directly take the cycle number as an input parameter of a model, and the output parameter is the current capacity loss condition of the battery, but the internal aging condition of the battery cannot be known, and the existing prediction methods are difficult to effectively realize data acquisition and life prediction under the condition that a formed product still exists in a design stage.
A mechanism model is a mathematical model that describes an object or process that is built based on the internal principles or mechanisms of the object under study. The lithium ion battery model based on the mechanism gives consideration to the internal physical and chemical process and the external operation condition of the battery, and different research and development requirements are generally realized by simplifying or expanding the P2D model. Patent CN109446619a discloses an optimization method of electrode design parameters of a lithium ion battery based on electrochemical mechanism, the method takes energy density and power density as evaluation indexes of battery optimization design, and the electrode design parameters (the electrode design parameters comprise electrode thickness, porosity, active material particle size, compaction density and area density, etc.) are optimally designed according to electrochemical performance of a model, but the method is limited to estimation of electrochemical performance of the battery, and cannot simulate aging and service life attenuation processes of the battery. More importantly, the electrochemical performance of the battery changes as the battery ages, and the battery aging trend and cycle life are coupled with the battery design parameters and operating conditions in a nonlinear manner, which are difficult to solve by current patent technology.
In view of the lack of a method for researching and predicting the aging process and life decay of a battery at different temperatures from the mechanism level, it is necessary to develop a life prediction method capable of sufficiently considering the internal mechanism and external state of the battery, so as to accurately and efficiently predict the service life of the battery at different temperatures. By analyzing aging characteristics and key factors causing battery degradation aging, offline optimization design of the battery of the product is assisted, design cost is saved, the whole life design cycle of the battery is shortened, and the design efficiency of the battery product is improved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a mechanism-based wide-temperature range lithium ion battery life prediction method, which can predict the life cycle and life decay law of the battery under specific conditions, and the electrochemical performance and the internal aging performance of the battery in any cycle process with less measured data and limited input parameters.
The technical scheme for realizing the purpose of the invention is as follows:
a wide temperature range lithium ion battery life prediction method based on a mechanism comprises the following steps:
Step one, obtaining battery product specifications and cell design parameters, and measuring intrinsic characteristic parameters, electrochemical parameters, kinetic parameters and thermodynamic parameters of electrode materials;
Step two, acquiring rate performance test data of the battery in a wide temperature range;
Thirdly, respectively establishing an electrochemical model and a thermal model based on a mathematical equation, establishing an electrochemical-thermal coupling model, and endowing parameters in the first step into the electrochemical-thermal coupling model;
Step four, applying initial conditions, boundary conditions and operation conditions of an electrochemical-thermal coupling model, dividing a calculation domain grid, and setting a solver algorithm;
Step five, acquiring accelerated aging test data of the battery at different temperatures;
step six, establishing a side reaction model based on a mathematical equation, establishing an electrochemical-thermal-side reaction coupling model, applying initial conditions, boundary conditions and operation conditions of the electrochemical-thermal-side reaction coupling model, dividing a calculation domain grid, and setting a solver algorithm;
And step seven, verifying the electrochemical-thermal-side reaction coupling model and correcting aging parameters according to measured data to obtain a lithium ion battery electrochemical-thermal-side reaction life prediction model, and judging the life decay condition of the battery based on the capacity, the health state and the aging condition calculated by the model.
Further, the battery product specification in the first step includes a battery nominal capacity, a battery upper and lower limit cutoff voltage and a cutoff current.
The cell design parameters include: the length and width of the positive pole pieces, the number of the positive pole pieces, the composition components and proportion of positive pole materials, the composition components and proportion of negative pole materials, the thicknesses of positive and negative pole current collectors, the thickness of a diaphragm and the porosity of the diaphragm.
The intrinsic characteristic parameters refer to equilibrium potentials of the positive electrode material and the negative electrode material in different lithium intercalation states.
The electrochemical parameters include: positive electrode particle radius, negative electrode particle radius, positive electrode material conductivity, negative electrode material conductivity, positive electrode material maximum lithium intercalation concentration, negative electrode material maximum lithium intercalation concentration.
The kinetic parameters include: reaction rate constant, diffusion coefficient, reaction activation energy, diffusion activation energy.
The thermodynamic parameters include: specific volume, entropy coefficient, heat transfer coefficient.
Further, in the second step, the rate performance test under the wide temperature range is to perform a multi-rate charge and discharge test on the battery at different temperatures. Physical quantities tested included voltage, current, temperature and capacity.
Further, the mutual dependency relationship between the electrochemical model and the thermal model in the third step is described by the two-way coupling through an Arrhenius formula.
And step three, parameters influenced by temperature in the electrochemical model comprise: electrode solid phase reaction rate constant, electrode solid phase diffusion coefficient, electrolyte phase migration number, electrolyte phase activity dependence coefficient, electrolyte phase conductivity.
The mathematical equation of the electrochemical model in the third step comprises solid-phase mass conservation, liquid-phase mass conservation, solid-phase charge conservation and liquid-phase charge conservation, wherein the electrochemical reaction of the electrode/electrolyte interface is described by using a Butler-Volmer equation.
And thirdly, describing a control equation of the thermal model as an energy conservation equation, wherein the thermal gradient between the heat generated by the battery and the heat dissipated by the battery causes the temperature fluctuation of the battery body.
The heat sources in the thermal model include ohmic heat, electrochemical heat, polarized heat, and mixed heat, wherein the electrochemical heat is reversible heat and the polarized heat is irreversible heat.
Setting initial lithium intercalation state of the positive and negative electrodes according to actual conditions or requirements, applying current or voltage boundary conditions to the electrode scale direction, and applying concentration flux boundary conditions to the electrode grain scale.
Step three includes, but is not limited to, using the cutoff voltage as a model termination condition.
Further, in the fourth step, initial conditions include initial lithium intercalation concentrations in the positive electrode and the negative electrode, and after the maximum lithium intercalation concentration of the electrode is fixed, the initial conditions of the positive electrode and the negative electrode are expressed by initial lithium intercalation states.
The boundary conditions include applying current/current density, voltage to the battery.
The operation working condition refers to multiplying power conditions and temperature conditions which are consistent with actual requirements.
In the fourth step, comparing and verifying the calculation result of the electrochemical-thermal coupling model with the charge-discharge data and performing electrochemical-thermal model calibration.
Further, the accelerated aging test method in the fifth step adopts a national standard battery cycle life test flow, or automatically sets a test flow and test conditions according to the actual running environment and running working conditions of the designed battery.
The cycle life test flow is as follows: and (3) performing constant-current discharge, standing for 30 minutes, constant-current charging, constant-voltage charging and standing for 30 minutes, and performing cyclic test, wherein the constant current is 1C, the discharge cutoff voltage is 2.75V, the constant-current charging cutoff potential is 4.2V, and the constant-voltage charging cutoff current is C/20. The above life test method is merely exemplary in the present invention, and the present invention is not limited by the test flow.
In the battery cycle aging test, characteristic quantities such as voltage, current, temperature, charge and discharge capacity and the like are required to be measured.
Further, in the step six, bidirectional coupling between temperature and side reaction is realized between the side reaction model and the thermal model through an Arrhenius formula;
The exchange current density of each side reaction in the side reaction model is constrained by temperature fluctuations in the thermal model.
The heat change in the thermal model is restrained by the generated products of each side reaction in the side reaction model through ohmic heat generation and polarized heat.
The output physical quantity of the side reaction model comprises battery capacity, health state and surface film thickness, wherein the change of the surface film thickness can be used for judging the aging condition of the battery.
The operation working conditions are multiplying power conditions, temperature conditions and circulation conditions which are consistent with actual requirements.
Describing interface parasitic reaction in a side reaction model through a cathode Tafel equation; the side reaction model considers the influence of aging factors such as cathode interface solid electrolyte layer growth (Solid Electrolyte Interphase, SEI) and lithium precipitation on the service life of the battery. The SEI and lithium precipitation side reaction products are attached to the surface of the anode particles, so that the volume fraction of the liquid phase in the electrode is reduced, and the material transportation of the liquid phase is further influenced.
The side reaction model considers that the reduction product attached at the electrode/electrolyte interface causes the increase of interface polarization potential and impedance, thereby affecting ohmic heat and polarization heat of the thermal model. The influence of temperature on the exchange current density of each side reaction is described by an Arrhenius formula in the side reaction model, so that bidirectional coupling between the side reaction model and the thermal model is realized.
The acquisition mode of parameters required by the construction of the electrochemical-thermal-side reaction model is not strictly limited, and the parameters can be obtained by adopting a conventional test method in the field or by adopting the existing theoretical data or literature records and other modes.
Parameters affected by temperature are described by the Arrhenius formula in the electrochemical model: electrode solid phase diffusion coefficient, reaction rate constant, electrolyte phase diffusion coefficient, electrolyte phase conductivity, ion migration number in electrolyte, and electrolyte phase activity dependence coefficient.
Further, the calculation domain grids in the fourth and sixth steps are used for discretizing the model by selecting a structured or unstructured mode according to the dimension and the geometric configuration of the built model.
And step four and step six, in the solver, the model calculation process is regulated and controlled by setting certain termination conditions (upper and lower limit voltages and 80% of nominal capacity). The method comprises the following steps: step four, the solver sets charge-discharge calculation termination conditions as an electrochemical-thermal coupling model when the battery voltage is charged to an upper limit voltage or is reduced to a lower limit voltage; and step six, the solver sets the calculation termination condition of the electrochemical-thermal-side reaction coupling model that the discharge capacity of the battery is reduced to 80% of the nominal capacity.
Further, the physical quantities of the electrochemical-thermal-side reaction coupling model and the measured data verification and judgment in the seventh step include battery capacity, health status and battery aging status (i.e. surface film thickness).
And comparing the cyclic test data with a life model calculation result, calibrating the life model, and performing reverse fitting on unknown parameters in the life model. The unknown parameters include molar mass, mass density, ionic conductivity within the surface film of the side reaction product, and exchange current density and reaction activation energy of the side reaction.
The invention has the advantages and beneficial effects that:
The method of the invention constructs an electrochemical-thermal Model frame based on a P2D Model (Pseudo-Two-Dimension Model), side reactions in the battery simulate the aging process of the battery, the thermal Model, the electrochemical Model and the side reaction Model are coupled through an Arrhenius formula, the full life cycle of the battery in a wide temperature range can be predicted by only needing less test data, and the initial State and the external environmental condition of the battery are used as input in the developed life Model, so that the State of health (SOH) and the cycle life of the aged battery in the full life cycle can be estimated. Compared with the prior art, the method has the advantages that the internal physical and chemical process and external environment variables of the battery are considered, the rule of aging attenuation of the battery from linear to nonlinear can be simulated, in addition, the prediction model can acquire more detailed aging data, and the requirements on optimal design of battery products are met efficiently.
Drawings
Fig. 1 is a simplified hypothetical cell geometry model of a battery.
Fig. 2 shows the balance potential of the positive and negative electrodes as a function of the lithium intercalation state, wherein (a) is the balance potential of the negative electrode of graphite as a function of the lithium intercalation state, and (b) is the balance potential of the positive electrode of LiNi 0.6Co0.1Mn0.3O2 as a function of the lithium intercalation state.
FIG. 3 is a plot of negative entropy coefficient as a function of lithium intercalation state.
Fig. 4 is an expansion function associated with the lithium intercalation state of a graphite negative electrode (the expansion function is used to describe the SEI regeneration reaction caused by the expansion and rupture of the negative electrode graphite particles).
FIG. 5 is a comparison of simulation results and measured data of electrochemical performance of 1C discharge at 25℃and 45 ℃. Wherein, (a) is the change of discharge voltage with discharge time, and (b) is the change of temperature with discharge time.
Fig. 6 is a graph comparing simulated battery cycle process state of health changes with measured data at 25 ℃ and 45 ℃. Wherein, the constant current condition is 1C, the discharge cut-off voltage is 2.75V, the charge cut-off potential is 4.3V, and the cut-off current of constant voltage charge is C/20. Wherein, (a) is the comparison of SOH obtained by simulating the battery cycle at 25 ℃ and the measured data, and (b) is the comparison of SOH obtained by simulating the battery cycle at 45 ℃ and the measured data.
Fig. 7 is a graph of the model predicted battery discharge voltage and temperature change for any cycle at 25 c and 45 c. Wherein (a) and (b) are battery discharge voltage and temperature changes corresponding to cycles 700, 1400 and 2100 at a temperature of 25 ℃, and (c) and (d) are battery discharge voltage and temperature changes corresponding to cycles 700, 1400 and 1700 predicted at 45 ℃.
Fig. 8 shows the predicted change in the negative electrode/separator side surface film thickness (i.e., side reaction product) during the battery cycle aging process according to the life model, wherein (a) and (b) correspond to 25 ℃ and 45 ℃, respectively.
Detailed Description
To facilitate understanding of the present invention, examples are set forth below. It will be apparent to those skilled in the art that the examples are merely to aid in understanding the invention and are not to be construed as a specific limitation thereof.
It is to be noted that the embodiments of the invention and the features of the embodiments may vary in form and in particular number of values without conflict.
The invention constructs a life prediction model of electrochemical-thermal-side reaction, and comprises an electrochemical model, a thermal model and a side reaction model based on P2D. Neglecting the non-uniformity and non-uniformity inside the battery pack, the concentration, current density and voltage distribution in the direction perpendicular to the thickness direction of the pole piece are assumed to be uniform, so that the study object is simplified into a one-dimensional cell model by the example, as shown in fig. 1.
The invention discloses a mechanism-based wide temperature range lithium ion battery life prediction method, which comprises the following specific steps:
Step one, obtaining the cell geometric dimension of the design parameters of the battery product, and measuring the physicochemical characteristic parameters, electrochemical parameters, kinetic parameters and thermodynamic parameters required by the model.
The battery in the example of the present invention was a 78Ah soft pack power lithium ion battery (LiNi 0.6Co0.1Mn0.3O2/Graphite) manufactured by Jieswei power industry Co., ltd. The size of the positive pole pieces in the battery pack is 505mm multiplied by 95.5mm, and the number of the positive pole pieces is 23.
The membrane thickness in this example was 16 μm and the membrane porosity was 0.42. The negative side was a copper current collector 6 μm thick, and the collection was an aluminum current collector 12 μm thick.
The particle size of the positive and negative electrodes in the example of the invention adopts a D50 value measured by a laser particle size distribution instrument.
The remaining parameters in step one are listed in table 1.
The electrode and the diaphragm in the battery sample adopted by the embodiment of the invention are porous composite materials, and the diffusion process of lithium ions in the liquid phase is influenced by considering the uneven distribution of the porosity, so that the diffusion coefficient of the liquid phase in the model is corrected by the porosity and the Bruggeman coefficient:
Dl,eff＝εBruggemanDl
Wherein Dl ,eff is the effective diffusion coefficient of ions in the electrolyte phase in the electrode, ε is the porosity (i.e. the volume fraction of electrolyte in the electrode), D l is the diffusion coefficient of ions in the pure electrolyte, and the Bruggeman coefficients used in the positive electrode, the negative electrode and the separator in this example take values of 2, 1.5 and 2, respectively.
TABLE 1 electrochemical model parameters
| Parameter name | Negative electrode | Positive electrode |
| Pole piece thickness/. Mu.m | 77 | 56 |
| Electrode particle size/. Mu.m | 12.7 | 4 |
| Porosity epsilon | 0.28 | 0.21 |
| Solid phase conductivity sigma/S.m -1 | 460 | 16 |
| Maximum lithium intercalation concentration c s,max/mol·m-3 | 30507 | 47653 |
| Anode charge transfer coefficient alpha a | 0.5 | 0.5 |
| Cathode charge transfer coefficient alpha c | 0.5 | 0.5 |
| Reaction rate constant k/m.s -1 | 3.5E-11 | 2.0E-11 |
| Reaction activation energy/J.mol -1 | 40000 | 30000 |
| Solid diffusion coefficient D s/m2·s-1 | 2.2E-14 | 1E-13 |
| Diffusion activation energy/J.mol -1 | 65000 | 45000 |
In the embodiment of the invention, liPF 6 is used as lithium salt, and Ethylene Carbonate (EC), ethylmethyl carbonate (EMC) and diethyl carbonate (DEC) are used as electrolyte of solvent. The electrolyte concentration was 1.05M. The transport parameters in the electrolyte, including diffusion coefficient, conductivity, activity dependence coefficient and migration number, all vary with the change in electrolyte salt concentration, and the relationship between the transport parameters and electrolyte salt concentration can be expressed by empirical formulas in Table 2 (references ：Nyman,A.,Behm,M.,et al.Electrochemical characterization and modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte[J].Electrochimica Acta,2008,53:6356–6365. and ：Nyman,A.,Behm,M.,et al.Electrochemical characterization and modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte[J].Electrochimica Acta,2008,53:6356–6365. Zavalis,T.G.,Behm,M.,et al.Investigation of short-circuit scenarios in a lithium-ion battery cell[J].Journal ofThe Electrochemical Society.2012,159:A848–A859).
TABLE 2 electrolyte transport parameters
Further, the button cell corresponding to the positive electrode material and the negative electrode material is assembled, and the equilibrium potential under different lithium intercalation states is measured, and the function relationship is shown in fig. 2.
And step two, applying 1C multiplying power to the test battery at 25 ℃ and 45 ℃ to perform charge and discharge performance test. The electrochemical performance of the cells is typically evaluated by discharge capacity, and the change in cell voltage and temperature with capacity during discharge is selected as comparative calibration data for electrochemical-thermal model in the examples of the present invention, as shown in fig. 5.
And thirdly, building an electrochemical-thermal coupling model frame based on design parameters, physical and chemical characteristics and a mathematical equation. The electrochemical model adopts a P2D model based on a porous electrode theory and a concentrated solution theory, which are proposed by Newman et al, and the model comprises two scales of electrode plates and electrode particles.
The electrochemical model adopts a material conservation equation and a charge conservation equation to describe the transportation process of the battery and the inside of electrode particles, and the Butler-Volmer equation describes the electrochemical reaction of an electrode/electrolyte interface, and the control equation is as follows:
Conservation of solid phase species:
Conservation of solid phase charge:
Conservation of liquid phase material:
Conservation of liquid phase charge:
Butler-Volmer equation:
Interface reaction exchange current density:
Interfacial reaction overpotential: η=φ s-φl-Eeq-Δφdiff
Wherein c s represents lithium ion concentration in electrode particles (solid phase), t represents time, D s is diffusion coefficient of lithium ions in solid phase, r represents radial direction in electrode particles, r p is average radius of electrode particles, i s is current density of electrode solid phase, sigma is conductivity of electrode solid phase, phi s is potential of electrode solid phase, c l electrolyte salt concentration, epsilon is porosity of electrode, t + is migration number of lithium ions, z + is charged number of lithium ions, v + is number of particles dissociated by 1mol of electrolyte, r p represents radius of electrode particles, j n is pore wall flux of electrode/electrolyte interface, i l is current density of electrolyte liquid phase, phi l is potential of electrolyte liquid phase, kappa is conductivity of electrolyte,For the activity correlation coefficient, R is the gas constant, 8.314 J.kg -1·K-1, T is the battery temperature, F is the Faraday constant, the exchange current density of 96485 C.mol -1,j0 delithiation reaction, alpha a and alpha c are the anode charge transfer coefficient and the cathode charge transfer coefficient (0.5 in this example) respectively, k is the reaction rate constant, C s,max is the maximum lithium intercalation concentration of the electrode particles, η is the overpotential of the delithiation reaction, E eq is the equilibrium potential of the delithiation reaction, and Deltaphi diff is the potential difference generated by the lithium ions participating in the delithiation reaction through the electrode surface film.
In the electrochemical model, there is no interfacial electrochemical reaction in the membrane, i.e., j n =0.
The thermal model is based on the law of conservation of energy, and the influence of the temperature difference between heat generation in the battery and heat dissipation of the battery on the temperature of the battery body is considered. The heat sources in the thermal model of this example include ohmic heat, polarized heat (also referred to as irreversible heat), and electrochemical heat (also referred to as reversible heat). The heat dissipation process of the battery is described in the thermal model in a heat conduction mode.
The thermal model is expressed as follows:
conservation of energy:
heat generation:
And (3) heat dissipation:
Arrhenius empirical formula:
Where ρ is the mass density of the cell, C p is the isobaric specific heat capacity of the cell (1010 J.kg -1·K-1),qsource is taken as the heat source, a i is the activity (1 in this example), i i and η i are the local current density and overpotential of the ith side reaction, respectively, The entropy coefficient is expressed as the change relation of equilibrium potential along with temperature, lambda is the heat conductivity coefficient, h is the convection heat transfer coefficient (10 W.m -2·K-1 is taken), A is the sectional area of the battery (the area of the positive electrode plate is taken), T ∞ is the ambient temperature, T ref is the reference temperature 298.15K,/>Is the parameter value at the reference temperature,/>For the parameters at the corresponding temperatures calculated by the Arrhenius formula, E a is the activation energy. The thermal model parameters in this example are shown in table 3.
TABLE 3 thermal model parameters
| Parameters (parameters) | Negative electrode | Diaphragm | Positive electrode | Copper current collector | Aluminum current collector |
| Mass density ρ/kg.m -3 | 2240 | 1000 | 4600 | 8960 | 2700 |
| Thermal conductivity lambda/W.m -1·K-1 | 1.2 | 0.6 | 0.6 | 400 | 238 |
The relationship between the entropy coefficient of the negative electrode and the lithium intercalation state is considered in this example, as shown in fig. 3.
And in the fourth step, the initial lithium intercalation states of the positive electrode and the negative electrode under the initial conditions of the electrochemical-thermal model are respectively 0.23 and 0.90, the operation multiplying power is 1C, parameterized scanning calculation is carried out on the temperatures of 25 ℃ and 45 ℃, and the discharge cut-off voltage is set to be 2.75V.
And fifthly, performing accelerated aging test on the battery at 25 ℃ and 45 ℃, recording the discharge capacity of the battery in each cycle, and converting the discharge capacity into the current health state of the battery. The State of Health (SOH) in the present invention is defined as the ratio of the maximum discharge capacity of the current cycle of the battery to the nominal capacity of the battery.
And step six, describing reduction reactions corresponding to SEI and lithium precipitation through a cathode Tafel equation, and fusing the reduction reactions with the electrochemical-thermal coupling model in the step four to build an electrochemical-thermal-side reaction coupling life model.
The occurrence of negative electrode solid electrolyte layers (Solid Electrolyte Interphase, SEI) and lithium evolution consumes the recyclable lithium content inside the battery while increasing the internal resistance of the battery, and numerous studies have shown that SEI and lithium evolution are the main causes of battery aging and life degradation.
The present example mainly considers the effect of SEI and lithium precipitation on battery life in the side reaction model. The SEI comprises an SEI growth process and an SEI regeneration process. The battery forms an initial SEI layer on the surface of the anode particles after the formation process, and the product generated after the electrolyte is oxidized and decomposed and the reduction reaction with the electrode active material in the circulation process promotes the SEI layer to be continuously increased and thickened, which is the growth process of SEI. During the circulation process, cracks and even breakage are generated on the surface of the electrode active particles due to the extraction and intercalation of lithium ions, and a new SEI layer, namely the regeneration process of SEI, is generated on the exposed fresh active particle surface.
The SEI growth process is described by a cathode Tafel equation in the life model, and the equation is as follows:
ηSEI＝φs-φl-Eeq,SEI-Δφdiff
Where I SEI,formation is the local current density of the SEI growth, I0 ,SEI is the exchange current density of the SEI growth reaction, α c,SE I is the charge transfer coefficient of the SEI growth, η SEI represents the overpotential of the SEI growth, and E eq,SEI is the equilibrium potential of the SEI growth.
SEI regeneration process of the cathode under different lithium intercalation states is described by an expansion function, so that the SEI regeneration process can be described by a cathode Tafel equation corrected by the expansion function:
Where i SEI,reformation is the local current density of SEI regeneration and f expansion is the expansion function (as shown in fig. 4).
The lithium precipitation process in the side reaction model is also described by a cathode Tafel equation:
ηlpl＝φs-φl-Eeq,lpl-Δφdiff
Where i lpl is the local current density of the lithium-precipitation reaction, i 0,lpl is the exchange current density of the lithium-precipitation reaction, and η lpl is the overpotential of the lithium-precipitation reaction.
In the life model, the side reaction products are attached to the surfaces of electrode particles and form a surface film. In the circulation process, lithium ions are repeatedly released and intercalated between the electrolyte and the two phases of the electrode particles, and the lithium ions are blocked to a certain extent when passing through the surface film, so that polarization potential delta phi diff is generated at the film, namely: Δφ diff＝i*Rfilm. Where i is the current density of the lithium intercalation reaction and R film is the sheet resistance of the negative electrode surface film.
In this example, the sheet resistance is proportional to the film thickness and inversely proportional to the ionic conductivity within the film:
Where δ 0 is the initial thickness of the film formed on the surface of the electrode particle after the formation step, and σ film is the ionic conductivity in the surface film.
In the model, the surface film consists of an SEI growth layer, an SEI regeneration layer and a lithium precipitation layer, so that the thickness change delta of the surface film is the sum of the changes of three film layers:
wherein the subscript j represents three side reactions of SEI growth, SEI regeneration and lithium precipitation, M represents the molar mass of each side reaction product, ρ represents the mass density of each side reaction product, and c represents the concentration of each side reaction product. Representing the sum of the changes in the volume fractions of the respective side reaction products.
In the life model, the reaction rate of the side reaction changes along with the change of the temperature, and the change rule of the side reaction is considered to be satisfied between the exchange current density and the temperature of the side reaction and can be described by using an Arrhenius formula, so that the bidirectional coupling between the side reaction model and the thermal model is realized.
The parameters in the side reaction model are shown in table 4.
TABLE 4 side reaction model parameters
| Parameter name | Numerical value |
| SEI switching current density i 0,SEI/A·m-2 | 1.8E-7 |
| SEI equilibrium potential E eq,SEI/V | 0.4 |
| SEI molar mass M SEI/g·mol-1 | 26 |
| SEI Density ρ SEI/kg·m-3 | 2640 |
| SEI reaction activation energy E a,SEI/J·mol-1 | 30000 |
| Lithium separation exchange current density i 0,lpl/A·m-2 | 3.7E-3 |
| Lithium precipitation equilibrium potential E eq,lpl/V | 0 |
| Molar mass M of lithium metal Li/g·mol-1 | 6.94 |
| Lithium metal density ρ Li/kg·m-3 | 534 |
| Lithium separation activation energy E a,Li/J·mol-1 | 50000 |
| Initial film thickness delta 0/nm | 5 |
| Ion conductivity sigma in surface film layer film/S·m-1 | 3.8E-6 |
Step six, setting initial lithium intercalation states of the positive electrode and the negative electrode to be 0.23 and 0.90 respectively in the life model, setting constant-current charge-discharge multiplying power to be 1C, and calculating cycle life and health state of the battery at the ambient temperature of 25 ℃ and 45 ℃ respectively.
In the seventh step, the health status of the battery obtained by simulation under different cycle numbers is compared with the measured data, as shown in fig. 6, and the aging parameters and the side reaction activation energy in the side reaction model are reversely fitted.
Preferably, in the step seven, the finally built electrochemical-thermal-side reaction life model predicts and extracts electrochemical performance data (shown in fig. 7) and aging performance change conditions (shown in fig. 8) in any cycle, and provides reference values for life judgment and optimization design of battery products.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is also noted that the terminology used in the application is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments in accordance with the application. The method relies on an electrochemical-thermal-side reaction coupling life model which integrates the nonlinear relation among electrochemistry, side reaction and heat, can predict the health state and cycle life of the battery under the working condition of wide temperature range, can predict the life decay data of any cycle number and the aging degree of the battery with less experimental data, can screen out optimal design according to different battery product requirements, improves the product design efficiency, shortens the whole life design period of the battery, and saves the design cost.
The applicant states that the detailed method of the present invention is illustrated by the above examples, but the present invention is not limited to the detailed method described above, i.e. it does not mean that the present invention must be practiced in dependence upon the detailed method described above. It should be apparent to those skilled in the art that any modification to the present invention, substitution of any product in the present invention, simplification and extension of the model equations, etc., falls within the scope of the present invention and the scope of the disclosure.
Claims (10)
1. The wide temperature range lithium ion battery life prediction method based on the mechanism is characterized by comprising the following steps:
Step one, obtaining battery product specifications and cell design parameters, and measuring intrinsic characteristic parameters, electrochemical parameters, kinetic parameters and thermodynamic parameters of electrode materials;
step two, acquiring rate performance test data of the battery at different temperatures;
Thirdly, respectively establishing an electrochemical model and a thermal model based on a mathematical equation, constructing an electrochemical-thermal coupling model with a bidirectional coupling function, and endowing parameters in the first step into the electrochemical-thermal coupling model;
Step four, applying initial conditions, boundary conditions and operation conditions of an electrochemical-thermal coupling model, dividing a calculation domain grid, and setting a solver algorithm;
Step five, acquiring accelerated aging test data of the battery at different temperatures;
step six, establishing a side reaction model based on a mathematical equation, establishing an electrochemical-thermal-side reaction coupling model, applying initial conditions, boundary conditions and operation conditions of the electrochemical-thermal-side reaction coupling model, dividing a calculation domain grid, and setting a solver algorithm;
And step seven, verifying the electrochemical-thermal-side reaction coupling model and correcting aging parameters according to the measured data to obtain a lithium ion battery electrochemical-thermal-side reaction life prediction model, and judging the battery capacity, the health state and the aging condition based on the model calculation result.
2. The method for predicting the lifetime of a wide temperature range lithium ion battery of claim 1, wherein step one said battery product specifications comprise a nominal battery capacity, upper and lower battery cutoff voltages and cutoff currents;
The cell design parameters include: the length and width of the positive pole pieces, the number of the positive pole pieces, the composition components and proportion of positive pole materials, the composition components and proportion of negative pole materials, the thicknesses of positive and negative pole current collectors, the thickness of a diaphragm and the porosity of the diaphragm;
the intrinsic characteristic parameters refer to equilibrium potentials of the positive electrode material and the negative electrode material in different lithium intercalation states;
The electrochemical parameters include: positive electrode particle radius, negative electrode particle radius, positive electrode material conductivity, negative electrode material conductivity, positive electrode material maximum lithium intercalation concentration, negative electrode material maximum lithium intercalation concentration;
the kinetic parameters include: reaction rate constant, diffusion coefficient, reaction activation energy, diffusion activation energy;
The thermodynamic parameters include: specific volume, entropy coefficient, heat transfer coefficient.
3. The method for predicting the lifetime of a wide temperature range lithium ion battery according to claim 1, wherein the rate performance test under the wide temperature range in the second step is a multi-rate charge and discharge test for the battery under different temperatures, and the physical quantities to be measured in the rate performance test include voltage, current, temperature and capacity.
4. The wide temperature range lithium ion battery life prediction method according to claim 1, wherein in the third step, the temperature change of the battery in the thermal model is related to an electrochemical model parameter by an Arrhenius formula, wherein the parameters affected by the temperature in the electrochemical model include: the electrode solid phase reaction rate constant, the electrode solid phase ion diffusion coefficient, the electrolyte phase ion migration number, the electrolyte phase activity dependence coefficient and the electrolyte phase conductivity.
5. The method for predicting the life of a wide temperature range lithium ion battery according to claim 1, wherein the initial conditions in the fourth step include initial lithium intercalation concentrations in the positive electrode and the negative electrode, and the initial conditions of the positive electrode and the negative electrode are represented by initial lithium intercalation states after the maximum lithium intercalation concentrations of the electrodes are fixed;
the boundary conditions include applying current/current density, voltage to the battery;
the operation working condition refers to multiplying power conditions and temperature conditions which are consistent with actual requirements.
6. The method for predicting the lifetime of a lithium ion battery with a wide temperature range according to claim 1, wherein the accelerated aging test method adopts a national standard battery cycle lifetime test flow or automatically sets a test flow and test conditions according to the actual operation condition of the designed battery product.
7. The method for predicting the service life of a lithium ion battery with a wide temperature range according to claim 1, wherein bidirectional coupling between temperature and side reaction is realized between the side reaction model and the thermal model in the step six through an Arrhenius equation;
the exchange current density of each side reaction in the side reaction model is constrained by temperature fluctuation in a thermal model;
the heat change in the thermal model is restrained by the generated products of each side reaction in the side reaction model through ohmic heat generation and polarized heat;
the output physical quantity of the side reaction model comprises battery capacity, health state and surface film thickness;
the operation working conditions are multiplying power conditions, temperature conditions and circulation conditions which are consistent with actual requirements.
8. The method for predicting the lifetime of a wide temperature range lithium ion battery according to claim 1, wherein the calculation domain grids in the fourth and sixth steps are used for discretizing the model by selecting a structured or unstructured mode according to the dimensions and geometric configuration of the model to be built.
9. The method for predicting the lifetime of a lithium ion battery with a wide temperature range according to claim 1, wherein the solver sets a charge-discharge calculation termination condition of the electrochemical-thermal coupling model when the battery voltage is charged to an upper limit voltage or falls to a lower limit voltage; and step six, the solver sets the calculation termination condition of the electrochemical-thermal-side reaction coupling model that the discharge capacity of the battery is reduced to 80% of the nominal capacity.
10. The method for predicting the lifetime of a lithium ion battery with a wide temperature range as in claim 1, wherein the physical quantities verified by the electrochemical-thermal-side reaction coupling model and the measured data in the seventh step include a battery capacity, a health status and an aging status.
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