CN109446619B - Optimization method of design parameters of lithium ion battery electrode - Google Patents

Optimization method of design parameters of lithium ion battery electrode Download PDF

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CN109446619B
CN109446619B CN201811215319.0A CN201811215319A CN109446619B CN 109446619 B CN109446619 B CN 109446619B CN 201811215319 A CN201811215319 A CN 201811215319A CN 109446619 B CN109446619 B CN 109446619B
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王青松
梅文昕
孙金华
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University of Science and Technology of China USTC
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Abstract

The invention discloses a method for optimizing design parameters of a lithium ion battery electrode, and relates to the field of design of internal structures of lithium ion batteries. The specific optimization steps are as follows: (1) Selecting a battery to be optimized, and measuring electrode design parameters which can be actually measured; (2) Establishing an electrochemical-thermal coupling model of the lithium ion battery according to the measured parameters and the estimated parameters, and adjusting the estimated parameters through experimental verification; (3) And obtaining optimized electrode design parameters by two optimization methods by taking the maximization of energy density and the maximization of the product of the energy density and the power density as optimization targets. The invention can select optimized electrode design parameters in the battery design stage, reduce the development cost, improve the energy density and the power density of the battery and provide a guidance basis for the design of the electrode.

Description

Optimization method of design parameters of lithium ion battery electrode
Technical Field
The invention belongs to the field of design of internal structures of lithium ion batteries, and particularly relates to a method for optimizing design parameters of electrodes of a lithium ion battery.
Background
At present, people pursue lithium ion batteries with high energy density and power density, but a certain contradiction exists between the two. Generally, the higher the energy density, the lower its power density. For example, for an electric vehicle, the energy density determines its maximum driving range, while the power density determines its maximum driving speed, and therefore it is a challenge today to be able to achieve both "run fast" and "run far". The design of the electrode of a lithium ion battery, which is the most important component of the overall battery, determines the ultimate capacity, energy density, power density, and other performance advantages and disadvantages of the battery.
The traditional experimental method is adopted to design and optimize the electrodes of the lithium ion battery, so that a large amount of manpower, material resources, financial resources and time are consumed, the simulation shows a plurality of advantages, design parameters, materials and the like can be changed randomly for design and optimization, the electrode design period can be shortened, the efficiency is improved, and the like. The electrochemical-Thermal coupling model established by early Newman et al is improved for many years and matured increasingly, for example, the electrochemical-Thermal coupling model established by Wenxin Mei et al (Applied Thermal Engineering,142 (2018) 148-165) based on a COMSOL Multiphysics multi-physics simulation platform optimizes the tab size of the lithium ion battery.
Chinese patent CN 107145629A discloses a method for optimizing the thickness of lithium ion battery electrode, which obtains the basic design parameters of the battery by the customer's request, and finally obtains the optimal thickness of the electrode by establishing an electrochemical-thermal coupling model and taking the energy density maximization as the optimization goal. The patent is only suitable for optimizing the thickness of a given battery electrode and is not suitable for other electrode design parameters, the patent only aims at optimizing single energy density maximization, and does not comprehensively consider two factors of energy density and power density, and people do not neglect the power density while pursuing high energy density, so that the comprehensive consideration of the energy density and the power density is crucial.
Disclosure of Invention
The invention provides an optimization method of electrode design parameters of a lithium ion battery, which is characterized in that an electrochemical-thermal coupling model is established, and the electrode design parameters (such as electrode thickness, porosity, compaction density, surface density and the like) of a given battery are designed and optimized based on energy density and power density, so that the optimal electrode design parameters are selected, the maximized energy density and power density are obtained, and the battery performance is improved.
The invention adopts the following technical scheme:
a method for optimizing design parameters of lithium ion battery electrodes comprises the following steps:
selecting a battery to be optimized, measuring measurable electrode design parameters and thermophysical parameters of the battery, and acquiring other electrode design parameters and electrode kinetic parameters;
establishing an electrochemical-thermal coupling model of the lithium ion battery;
step three, carrying out model verification and parameter correction through experiments;
acquiring a target function and constraint conditions through the corrected model, and optimizing electrode design parameters according to two optimization algorithms;
and step five, obtaining the optimal electrode design parameters by comparing the results obtained by the two optimization algorithms.
Wherein the electrochemical-thermal coupling model comprises a pseudo-two-dimensional (P2D) electrochemical model and a three-dimensional (3D) thermal model;
(1) P2D electrochemical model: the electrochemical model is based on a concentrated solution theory and a porous electrode theory, the model comprises two parts of electrode thickness (L) and active material particle size (r), because L > r, r is ignored in the model geometry, and only one line segment along the electrode thickness direction is needed, so the model is called a pseudo two-dimensional model, a grid is divided according to a finite element idea, then a partial differential equation in the electrochemical process is solved, and the electrochemical properties such as electrode potential, electrolyte concentration and the like can be obtained;
(2) The 3D thermal model constructs a three-dimensional geometric model according to the actual size of the battery, a heat source obtained by calculation of the P2D electrochemical model is coupled into the 3D thermal model as a whole, so that the temperature in the 3D thermal model is changed, the temperature change is fed back to the P2D electrochemical model to cause the temperature-related parameters in the electrochemical model to be changed, and the change of the parameters further causes the change of the heat source, so that the coupling of the electrochemical model and the thermal model is realized.
The method comprises the following steps of carrying out model verification and parameter correction through an experimental method, wherein the experiment comprises the following steps: (1) Fully charging the battery by a constant-current-first and constant-voltage-second charging method; (2) Discharging the battery at constant current, and setting the cut-off voltage to be 2.75V; (3) Comparing the discharge curve obtained by the experiment with a simulation value; (4) Shooting the temperature distribution of the surface of the battery at the end of discharge by using a thermal infrared imager, and comparing the temperature distribution with a simulation result; (5) And (4) performing parameter correction according to the results of the steps (3) and (4) to obtain a corrected electrochemical-thermal coupling model.
The optimization method adopts multi-objective optimization, comprehensively considers two factors of energy density and power density, optimizes electrode design parameters of the lithium ion battery, and finally obtains optimal electrode design parameters.
The optimization step adopts two optimization algorithms to improve the accuracy, and selects an optimal solution according to the optimization results of the two optimization algorithms.
Compared with the prior art, the invention has the advantages that:
1, establishing an electrochemical-thermal coupling model of the lithium ion battery, and improving the accuracy of the model through experimental verification and parameter correction;
2, the model is suitable for the cyclic charge and discharge of batteries with different capacities under different discharge multiplying powers;
3, optimizing electrode design parameters of the lithium ion battery by integrating two factors of energy density and power density, and giving an optimal solution after iteration;
4, the method can optimize the energy density and the power density of the battery in a numerical simulation mode, so that the performance of the battery can be effectively evaluated, and resources can be saved;
5, the method can optimize various electrode design parameters (such as electrode thickness, electrode material surface density, porosity and the like) to seek the highest energy density and power density, and makes up the defect of optimizing a single parameter;
and 6, only a small amount of required batteries are required to be prepared for verifying the model, electrode design parameters are optimized by a simulation method on the basis, and then a large amount of batteries are manufactured according to the optimized parameters, so that the manpower, material resources and financial resources can be saved, the battery design period can be shortened, and the battery performance can be improved.
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Fig. 1 is a flow chart of an optimization method of lithium ion battery electrode design parameters based on energy density and power density according to the present invention.
FIG. 2 is a schematic diagram of a pseudo two-dimensional (P2D) electrochemical model of the present invention.
Fig. 3 shows the appearance and size of a battery according to a first embodiment of the present invention, wherein fig. 3 (a) shows the appearance and fig. 3 (b) shows the size of the battery.
Fig. 4 is a schematic diagram of a three-dimensional thermal model geometry and a grid thereof according to a first embodiment of the present invention, in which fig. 4 (a) is a schematic diagram of the three-dimensional thermal model geometry and fig. 4 (b) is a schematic diagram of the grid.
Fig. 5 is a comparison of simulation and experimental results of battery discharge curves at four different discharge rates in the first embodiment of the present invention.
FIG. 6 is a comparison between the simulation result of the average temperature of the surface of the battery at four different discharge rates and the experimental result, wherein FIG. 6 (a-1) is the simulation result of the average temperature of the surface of the battery at 0.5C discharge, and FIG. 6 (a-2) is the experimental result of the average temperature of the surface of the battery at 0.5C discharge; FIG. 6 (b-1) is a simulation result of the average temperature of the surface of the battery under 1C discharge, and FIG. 6 (b-2) is an experimental result of the average temperature of the surface of the battery under 1C discharge; FIG. 6 (C-1) is a simulation result of the average temperature of the surface of the battery at 1.5C discharge, and FIG. 6 (C-2) is an experimental result of the average temperature of the surface of the battery at 1.5C discharge; FIG. 6 (d-1) is a simulation result of the average temperature of the surface of the battery under 2C discharge, and FIG. 6 (d-2) is an experimental result of the average temperature of the surface of the battery under 2C discharge.
Fig. 7 is a curve of the variation of the entropy coefficients of the positive and negative half-cells with the state of charge according to an embodiment of the present invention.
Detailed Description
In order to facilitate understanding of the invention, the invention will be described in more detail with reference to preferred embodiments, but the scope of the invention is not limited to the following specific embodiments.
The invention relates to a method for optimizing design parameters of a lithium ion battery electrode based on energy density and power density, which comprises the following steps: selecting a battery to be optimized, measuring measurable electrode design parameters, thermophysical parameters and the like of the battery, and acquiring other electrode design parameters, electrode kinetic parameters and the like; establishing an electrochemical-thermal coupling model of the lithium ion battery; step three, carrying out model verification and parameter correction through experiments; acquiring a target function and constraint conditions through the corrected model, and optimizing electrode design parameters according to two optimization algorithms; and step five, obtaining the optimal electrode design parameters by comparing the results obtained by the two optimization algorithms.
The model in the second step is a coupling model of a pseudo two-dimensional (P2D) Electrochemical model and a three-dimensional (3D) thermal model, wherein the Electrochemical model is an Electrochemical model of Newman et al (Journal of the Electrochemical Society,1993, DOI. The following describes the establishment process of the P2D electrochemical model and the 3D thermal model respectively:
(1) P2D electrochemical model
The interior of the lithium ion soft package battery is of a laminated structure and is composed of the following repeating units: the cell structure comprises a diaphragm, a negative electrode active material, a negative electrode current collector, a negative electrode active material, a diaphragm, a positive electrode active material, a positive electrode current collector, a positive electrode active material, a diaphragm of 82308230, a diaphragm of 8230, and a model is built only by selecting one cell in the thickness direction of the cell due to the repeatability and the equivalence of each cell. One unit comprises the following five parts: negative current collector (simplified to one point), negative active material (thickness L) n ) Diaphragm (thickness L) s ) Positive electrode active material (thickness L) p ) And a positive current collector (simplified to one point).
The governing equation of the P2D electrochemical model mainly comprises the following parts: the mass conservation equation, the charge conservation equation, the electrochemical kinetics equation (Butler-Volmer equation), the governing equation for this model, and the boundary conditions are listed in table 1.
(2) Establishment of thermal model
The thermal model is built based on the energy conservation equation. The heat generation of a battery comprises two parts: reversible heat and irreversible heat. Wherein the reversible heat is the heat generation in the electrochemical reaction process, the heat generation caused by entropy change of the electrode material; irreversible heat can be further divided into polarized heat due to overpotential and ohmic heat due to ohmic internal resistance. For the boundary condition in the thermal model, namely the heat dissipation part, two parts of convection heat exchange and radiation heat exchange are considered. The governing equations and boundary conditions in the thermal model are listed in table 2.
(3) Establishment of electrochemical-thermal coupling model
The electrochemical model and the thermal model are coupled by the Arrhenius equation:
Figure BDA0001833405970000041
where Φ is a temperature-dependent parameter, E a Is the activation energy.
The coupling process is as follows: the heat source calculated by the P2D electrochemical model is coupled into the 3D thermal model as a whole, so that the temperature change in the 3D thermal model is caused, the temperature change is fed back to the P2D electrochemical model to cause the temperature-related parameters in the electrochemical model to change, and the change of the parameters further causes the change of the heat source, so that the coupling of the electrochemical model and the thermal model is realized.
TABLE 1 control equations and boundary conditions in P2D models
Figure BDA0001833405970000051
TABLE 2.3 control equations and boundary conditions in the thermal model
Figure BDA0001833405970000061
The symbols and terms appearing herein are shown in Table 3.
TABLE 3. Symbols appearing herein and terms
Figure BDA0001833405970000062
Figure BDA0001833405970000071
Figure BDA0001833405970000081
Figure BDA0001833405970000091
The verification of the model in the third step is carried out by the following steps:
(1) Fully charging the battery by a constant-current-first and constant-voltage-second charging method; (2) Discharging the battery at constant current, and setting the cut-off voltage to be 2.75V; (3) Comparing the discharge curve obtained by the experiment with a simulation value; (4) Shooting the temperature distribution of the surface of the battery at the end of discharge by using a thermal infrared imager, and comparing the temperature distribution with a simulation result; (5) And (4) performing parameter correction according to the results of the steps (3) and (4) to obtain a corrected electrochemical-thermal coupling model.
Example one
Taking a commercial 18.5Ah nickel-cobalt-manganese/graphite (NCM/C) soft package battery as an example, the invention is fully and specifically described by optimizing a representative electrode design parameter, namely electrode thickness, of the lithium ion battery. The cell profile and the actual measured dimensions are shown in figure 3. The optimization is divided into two parts: and (1) maximizing the energy density to be an objective function. (2) The product of the energy density and the power density is maximized as an objective function. And two optimization algorithms are respectively adopted, 4 groups of optimized electrode thicknesses are finally obtained, and the optimal electrode thickness is selected from the optimized electrode thicknesses.
1. The experimental part is described first:
the experimental method comprises the steps of carrying out charge and discharge tests on the battery, and shooting the temperature of the surface of the battery by using a thermal infrared imager. The experiments were performed at 4 discharge rates (0.5C, 1C,1.5C, 2C) in total, and compared with the simulation results to improve the accuracy of the simulation. The following is described by way of example 1C: (1) the battery was left to stand for 5 minutes; (2) charging to 4.2V at 1C rate (18.5A) constant current; (3) Constant voltage charging is carried out at a voltage of 4.2V, and the charging cut-off current is set to be 0.185A; (3) the battery is left for 10 minutes; (4) Constant current discharge is carried out at a rate of 1C, and the cut-off voltage is 2.75V; (5) And obtaining a discharge curve of the battery, namely a voltage-time curve (6) and shooting the temperature distribution on the surface of the battery by using a thermal infrared imager at the moment of finishing discharge.
2. The numerical simulation part is then described, divided into 5 steps, as follows:
step one, parameter acquisition. The parameters of the electrochemical-thermal coupling model of the battery, the temperature-related parameters, the overall thermal parameters of the battery and the thermophysical parameters of the electrode material are obtained according to the experimental measurement and the literature research and study methods and are respectively listed in the tables 3, 4 and 5.
And step two, establishing a model. Establishing a simplified pseudo-two-dimensional (P2D) electrochemical model of the battery according to mass conservation, charge conservation and electrochemical dynamics; then establishing a three-dimensional (3D) thermal model of the battery according to an energy conservation equation; the heat source calculated by the P2D electrochemical model is coupled into the 3D thermal model as a whole, so that the temperature change in the 3D thermal model is caused, the temperature change is fed back to the P2D electrochemical model to cause the temperature-related parameters in the electrochemical model to change, and the change of the parameters further causes the change of the heat source, so that the coupling of the electrochemical model and the thermal model is realized.
TABLE 4 electrochemical-thermal coupling model parameters
Figure BDA0001833405970000101
Note: "-" indicates that the item is not present or is not considered
TABLE 5 temperature-related parameters and Battery Overall thermal parameters
Figure BDA0001833405970000102
Figure BDA0001833405970000111
TABLE 6 thermal Property parameters of Battery materials
Parameter (Unit) Density (kg/m 3) Specific heat capacity (J/kg/K) Coefficient of thermal conductivity (W/m/K)
Negative electrode 1555 1437 1.04
Positive electrode 2895 1270 1.58
Diaphragm 1017 1978 0.34
Electrolyte 1210 1518 0.099
Aluminum foil 2702 903 238
Copper foil 8933 385 398
Battery with a battery cell Formula (35) Formula (34) Formulas (36) and (37)
And step three, verifying the model and correcting the parameters. Based on the COMSOL Multiphysics multi-physics simulation platform, the electrochemical-thermal coupling model is established according to the step two, the model only considers that the battery is in a full-electricity state, and therefore, only the battery is discharged under 4 discharge multiplying factors (0.5C, 1C,1.5C, 2C) as same as the experimental working condition, finally, a discharge curve and temperature field distribution of each time period are obtained, and the comparison graph is shown in fig. 5 and fig. 6 as compared with the experimental result.
And step four, optimizing the thickness of the lithium ion battery electrode based on the energy density. The energy density of a lithium ion battery is determined by equation (38), where M is the electrode mass and contains only positive and negative materials, electrolyte, separator, and current collectors, the battery case, and other inactive materials such as conductive agents, etc. not counted. This will result in a calculated energy density that is higher than it actually is, but does not affect the optimization results since these un-calculated qualities are considered to be constant.
In the step, two optimization algorithms are adopted for optimizing the electrode thickness, one of the two optimization algorithms is a Nelder-Mead algorithm which is proposed by John Nelder and Roger Mead in 1965 and is a nonlinear optimization method, and the derivative of an objective function does not need to be solved; the second method is a COBYLA method (linear approximation constraint optimization method), which is proposed by Michael j.d. powell in 1997 and is a linear optimization method, which does not need to solve the derivative of an objective function and can be used for solving the constraint problem. Both optimization algorithms come from an optimization module in COMSOL Multiphysics and are solved according to a self-defined optimization solver.
In the optimization in this step, certain constraint conditions are adopted, and two constraint conditions are considered: firstly, the theoretical capacity of a negative electrode is slightly larger than that of a positive electrode so as to avoid the generation of lithium dendrites, according to the design experience of the battery, the NP ratio of the battery is defined as the ratio of the theoretical capacity of the negative electrode to the theoretical capacity of the positive electrode according to a formula (40), and the NP ratio of the battery is 1.1-1.2; secondly, the optimal working temperature of the lithium ion battery is 298K-313K, and the working temperature is set within the range.
The optimized parameters in the step are the thickness of the anode and the thickness of the cathode, the initial values of the thicknesses are respectively 55 mu m and 65 mu m through experimental measurement, the estimation is carried out within the limited range of the volume and the capacity according to the requirement of a client, the sum of the upper limit and the lower limit is twice of the initial value, the value ranges obtained according to the method are [30,80] and [30,100], and the unit is mu m.
The initial values are first brought into the model for calculation to obtain the value of the objective function, then the value is fed back to the optimization algorithm, the optimization program is shown in the figure, and finally the optimization results based on the two optimization algorithms are obtained and listed in the table 6. It is therefore necessary to obtain an optimum electrode thickness by taking the energy density and power density into consideration.
Figure BDA0001833405970000131
M＝(L pcc ρ pcc +L ncc ρ ncc +L p ε ps ρ p +L p ε pl ρ l +
L n ε ns ρ n +L n ε nl ρ l +L s ε s ρ l +L s ρ s )×A elec
Figure BDA0001833405970000132
TABLE 7 electrode thickness optimization results based on energy density
Figure BDA0001833405970000133
And fifthly, optimizing the thickness of the lithium ion battery electrode based on the energy density and the power density. The power density of the lithium ion battery is determined by equation (41). The objective function in the step is the product of the energy density and the power density, the optimization algorithm, the constraint condition and the parameter value range are all consistent with those in the fourth step, and the finally obtained optimization result is listed in table 7, so that the N-M algorithm obtains an objective function value higher than that of the COBYLA algorithm, but the N-M algorithm obtains a low energy density and a small thickness of the positive electrode and the negative electrode, and does not meet the positive and negative electrode material redundancy principle of the battery in actual design, so that the optimization target of the battery is not met, and the energy density and the power density obtained by the optimization of the COBYLA algorithm are improved, so that the COBYLA algorithm suitable for solving the constraint problem is more suitable for the optimization of the invention. Finally, the thickness of the positive electrode is 55.335 μm, the thickness of the negative electrode is 63.188 μm, the energy density is 244.37Wh/kg, the initial energy density is 239.71Wh/kg, the power density is 247.11W/kg, the initial power density is 244.46W/kg, the optimization requirements are met, a certain guide basis can be provided for electrode design of the lithium ion battery, and the battery design period is shortened.
Figure BDA0001833405970000134
TABLE 8 electrode thickness optimization results based on energy density and power density
Figure BDA0001833405970000141

Claims (4)

1. A method for optimizing design parameters of lithium ion battery electrodes is characterized by comprising the following steps:
selecting a battery to be optimized, measuring measurable electrode design parameters and thermophysical parameters of the battery, and acquiring other electrode design parameters and electrode kinetic parameters;
establishing an electrochemical-thermal coupling model of the lithium ion battery;
step three, carrying out model verification and parameter correction through experiments;
acquiring a target function and a constraint condition through the corrected model, and optimizing electrode design parameters according to two optimization algorithms;
step five, obtaining optimal electrode design parameters by comparing the results obtained by the two optimization algorithms;
the electrochemical-thermal coupling model comprises a pseudo-two-dimensional (P2D) electrochemical model and a three-dimensional (3D) thermal model;
(1) P2D electrochemical model: the electrochemical model is based on a concentrated solution theory and a porous electrode theory, the model comprises two parts of electrode thickness (L) and active material particle size (r), because L > r, r is ignored in the model geometry, and only one line segment along the electrode thickness direction is needed, so the model is called a pseudo two-dimensional model, a grid is divided according to a finite element idea, then a partial differential equation in the electrochemical process is solved, and the electrochemical properties such as electrode potential, electrolyte concentration and the like can be obtained;
(2) The 3D thermal model constructs a three-dimensional geometric model according to the actual size of the battery, a heat source obtained by calculation of the P2D electrochemical model is coupled into the 3D thermal model as a whole, so that the temperature in the 3D thermal model is changed, the temperature change is fed back to the P2D electrochemical model to cause the temperature-related parameters in the electrochemical model to be changed, and the change of the parameters further causes the change of the heat source, so that the coupling of the electrochemical model and the thermal model is realized.
2. The method for optimizing design parameters of electrodes of lithium ion batteries according to claim 1, wherein: model verification and parameter correction are carried out through an experimental method, and the experiment comprises the following steps: (1) Fully charging the battery by a constant-current-first and constant-voltage-second charging method; (2) Discharging the battery at constant current, and setting the cut-off voltage to be 2.75V; (3) Comparing the discharge curve obtained by the experiment with the simulation value; (4) Shooting the temperature distribution of the surface of the battery at the end of discharge by using a thermal infrared imager, and comparing the temperature distribution with a simulation result; (5) And (5) performing parameter correction according to the results of the steps (3) and (4) to obtain a corrected electrochemical-thermal coupling model.
3. The method for optimizing design parameters of lithium ion battery electrodes according to claim 1, wherein: the optimization method adopts multi-objective optimization, comprehensively considers two factors of energy density and power density, optimizes the electrode design parameters of the lithium ion battery, and finally obtains the optimal electrode design parameters.
4. The method for optimizing design parameters of electrodes of lithium ion batteries according to claim 1, wherein: the optimization step adopts two optimization algorithms to improve the accuracy, and selects an optimal solution according to the optimization results of the two optimization algorithms.
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