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

Abstract

The invention discloses a method for optimizing electrode design parameters of lithium ion batteries, and relates to the field of internal structure design of lithium ion batteries. The electrode design parameters may include electrode thickness, porosity, active material particle size, compacted density, surface density, and the like. The specific optimization steps are as follows: (1) Select the battery to be optimized, and measure the actual measurable electrode design parameters; (2) Establish an electrochemical-thermal coupling model of the lithium-ion battery based on the measured parameters and estimated parameters, and verify it through experiments Adjust the estimated parameters; (3) Taking the maximization of energy density and the maximization of the product of energy density and power density as the optimization goals, the optimized electrode design parameters are obtained through two optimization methods. The invention can select the optimized electrode design parameters in the battery design stage, reduce the development cost, improve the energy density and power density of the battery, and provide a guiding basis for the design of the electrode.

Description

An optimization method for electrode design parameters of lithium-ion batteries

technical field

The invention belongs to the field of internal structure design of lithium ion batteries, and in particular relates to an optimization method of electrode design parameters of lithium ion batteries.

Background technique

At present, people are pursuing lithium-ion batteries with high energy density and power density, but there is a certain contradiction between the two. In general, the higher the energy density, the lower its power density. For example, for an electric vehicle, the energy density determines its maximum mileage, and the power density determines its maximum driving speed. Therefore, how to achieve both "running fast" and "running far" is also a challenge today. The electrode of a lithium-ion battery is the most important component of the entire battery, and its design determines the final capacity, energy density, power density, and other performance of the battery.

Using traditional experimental methods to design and optimize the electrodes of lithium-ion batteries consumes a lot of manpower, material and financial resources as well as time, while the simulation shows many advantages. Design parameters and materials can be changed arbitrarily for design optimization, which can reduce the electrode design cycle and improve efficiency etc. The electrochemical-thermal coupling model established by Newman et al. has been perfected for many years and has become increasingly mature. For example, the model established by Wenxin Mei et al. (Applied Thermal Engineering, 142(2018) 148-165) based on the COMSOL Multiphysics multiphysics simulation platform The electrochemical-thermal coupling model optimizes the design of the lug size of the lithium-ion battery.

Chinese patent CN 107145629A discloses a method for optimizing the electrode thickness of lithium-ion batteries. The basic design parameters of the battery are obtained through customer requirements, and the electrochemical-thermal coupling model is established. The optimization goal is to maximize the energy density, and finally the optimal the electrode thickness. This patent is only applicable to the optimization of a given battery electrode thickness, not applicable to other electrode design parameters, and this patent is only aimed at maximizing a single energy density as the optimization goal, without comprehensively considering the two factors of energy density and power density, while One should not ignore power density while pursuing high energy density, so it is important to consider energy density and power density comprehensively.

Contents of the invention

The invention provides a method for optimizing electrode design parameters of a lithium-ion battery, by establishing an electrochemical-thermal coupling model and analyzing the electrode design parameters (such as electrode thickness, porosity, compaction density) of a given battery based on energy density and power density and surface density, etc.) to optimize the design, so as to select the optimal electrode design parameters, obtain the maximum energy density and power density, and improve battery performance.

The present invention adopts following technical scheme:

A method for optimizing electrode design parameters of a lithium-ion battery, comprising the following steps:

Step 1: Select the battery to be optimized, measure its measurable electrode design parameters and thermophysical parameters, and obtain other electrode design parameters and electrode kinetic parameters;

Step 2, establishing an electrochemical-thermal coupling model of the lithium-ion battery;

Step 3: Carry out model verification and parameter correction through experiments;

Step 4, obtain the objective function and constraint conditions through the corrected model, and optimize the electrode design parameters according to two optimization algorithms;

In step five, the optimal electrode design parameters are obtained by comparing the results obtained by the two optimization algorithms.

Among them, the electrochemical-thermal coupling model includes a pseudo-two-dimensional (P2D) electrochemical model and a three-dimensional (3D) thermal model;

(1) P2D electrochemical model: The electrochemical model is based on concentrated solution theory and porous electrode theory. The model includes two parts: electrode thickness (L) and active material particle size (r). Since L>>r, in the model geometry Neglecting r, there is only a line segment along the thickness direction of the electrode, so it is called a pseudo-two-dimensional model. The grid is divided according to the finite element idea, and then the partial differential equation in the electrochemical process can be solved to obtain the electrode potential and electrolyte potential , electrolyte concentration and other electrochemical properties;

(2) 3D thermal model Construct a three-dimensional geometric model according to the actual size of the battery, and couple the heat source calculated by the P2D electrochemical model into the 3D thermal model as a whole, which will cause the temperature change in the 3D thermal model, and the temperature change in turn Feedback to the P2D electrochemical model causes changes in the temperature-related parameters in the electrochemical model, and changes in these parameters further trigger changes in the heat source, thereby realizing the coupling between the electrochemical model and the thermal model.

Among them, the model verification and parameter correction are carried out through the experimental method, and the following steps are taken in the experiment: (1) the battery is fully charged by the charging method of constant current and then constant voltage; (2) the constant current discharge is performed on the battery, and the cut-off voltage is set to 2.75V; (3) compare the discharge curve obtained by the experiment with the simulated value; (4) shoot the temperature distribution on the surface of the battery at the end of the battery discharge with an infrared thermal imager, and compare it with the simulated result; (5) according to the above steps (3) ) and (4) were corrected to get the corrected electrochemical-thermal coupling model.

Among them, the optimization method adopts multi-objective optimization, comprehensively considers the two factors of energy density and power density, optimizes the electrode design parameters of lithium-ion batteries, and finally obtains the optimal electrode design parameters.

Wherein, the optimization step adopts two optimization algorithms to improve accuracy, and selects the optimal solution according to the optimization results of the two optimization algorithms.

Advantage of the present invention compared with prior art:

1. Establish an electrochemical-thermal coupling model of lithium-ion batteries, and improve the accuracy of the model through experimental verification and parameter correction;

2. This model is suitable for the cycle charge and discharge of batteries with different capacities at different discharge rates;

3. The electrode design parameters of lithium-ion batteries are optimized by combining the two factors of energy density and power density, and the optimal solution after iteration can be given;

4. This method can optimize the energy density and power density of the battery through numerical simulation, which can not only effectively evaluate the performance of the battery, but also save resources;

5. This method can optimize a variety of electrode design parameters (such as electrode thickness, electrode material surface density, porosity, etc.) to seek the highest energy density and power density, making up for the lack of optimizing a single parameter;

6. It is only necessary to prepare a small amount of required batteries for model verification. On this basis, the electrode design parameters are optimized through simulation methods, and then a large number of batteries are produced according to the optimized parameters, which can save manpower, material and financial resources, and reduce battery costs. The design cycle in turn improves battery performance.

Description of drawings

Fig. 1 is a flow chart of an optimization method of lithium-ion battery electrode design parameters based on energy density and power density in the present invention.

Fig. 2 is a schematic diagram of a pseudo two-dimensional (P2D) electrochemical model in the present invention.

Fig. 3 is the appearance and size of the battery in Embodiment 1 of the present invention, wherein Fig. 3(a) is the appearance of the battery, and Fig. 3(b) is the size of the battery.

Fig. 4 is a schematic diagram of the geometry of the three-dimensional thermal model and its grid in Embodiment 1 of the present invention, wherein Fig. 4(a) is a schematic diagram of the geometry of the three-dimensional thermal model, 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 Example 1 of the present invention.

Fig. 6 is the comparison between the simulated results and the experimental results of the average temperature of the battery surface under four different discharge rates in Example 1 of the present invention, wherein Fig. 6 (a-1) is the simulated result of the average temperature of the battery surface under 0.5C discharge, Figure 6(a-2) is the experimental result of the average temperature of the battery surface under 0.5C discharge; Figure 6(b-1) is the simulation result of the average temperature of the battery surface under 1C discharge, and Figure 6(b-2) is the simulation result of the average temperature of the battery surface under 1C discharge The experimental results of the average battery surface temperature; Figure 6(c-1) is the simulation result of the battery surface average temperature under 1.5C discharge, and Figure 6(c-2) is the experimental result of the battery surface average temperature under 1.5C discharge; Figure 6 (d-1) is the simulation result of the average temperature of the battery surface under 2C discharge, and Fig. 6(d-2) is the experimental result of the average temperature of the battery surface under 2C discharge.

Fig. 7 is a graph showing the variation curve of the entropy coefficient of the positive and negative half-cells with the state of charge in the first embodiment of the present invention.

detailed description

In order to facilitate the understanding of the present invention, the following will describe the present invention more comprehensively and in detail in conjunction with preferred embodiments, but the protection scope of the present invention is not limited to the following specific embodiments.

A method for optimizing electrode design parameters of a lithium-ion battery based on energy density and power density in the present invention comprises the following steps: step 1, selecting a battery to be optimized, measuring its measurable electrode design parameters and thermophysical parameters, etc., and Obtain other electrode design parameters and electrode kinetic parameters, etc.; Step 2, establish an electrochemical-thermal coupling model of lithium-ion batteries; Step 3, perform model verification and parameter correction through experiments; Step 4, obtain the target through the corrected model function and constraint conditions, optimize the electrode design parameters according to the two optimization algorithms; Step 5, obtain the optimal electrode design parameters by comparing the results obtained by the two optimization algorithms.

The model in step 2 is a coupled model of a pseudo-two-dimensional (P2D) electrochemical model and a three-dimensional (3D) thermal model, where the electrochemical model uses Newman et al. (Journal of the Electrochemical Society, 1993, DOI: 10.1149/1.2221597) electrochemical model. The establishment process of the P2D electrochemical model and the 3D thermal model are described below:

(1) P2D electrochemical model

The interior of the lithium-ion pouch battery is a laminated structure, which is composed of the following repeating units: separator, negative electrode active material, negative electrode current collector, negative electrode active material, separator, positive electrode active material, positive electrode current collector, positive electrode active material, separator..., due to The repeatability and equivalence of each unit, so only one unit is selected for modeling in its thickness direction. One of the units contains the following five parts: negative electrode current collector (simplified to one point), negative electrode active material (thickness L _n ), separator (thickness L _s ), positive electrode active material (thickness L _p ), positive electrode current collector (simplified for one point).

The governing equation of the P2D electrochemical model mainly includes the following parts: mass conservation equation, charge conservation equation, electrochemical kinetic equation (Butler-Volmer equation), and the governing equation and boundary conditions for this model are listed in Table 1.

(2) Establishment of thermal model

The thermal model is established based on the energy conservation equation. The heat generation of the battery consists of two parts: reversible heat and irreversible heat. Among them, reversible heat is the heat generated during the electrochemical reaction process, which is caused by the entropy change of the electrode material; irreversible heat can be further divided into polarization heat and ohmic heat, of which the former is due to the polarization heat generated by the overpotential, and the latter It is ohmic heat generation due to ohmic internal resistance. For the boundary conditions in the thermal model, that is, the heat dissipation part, two parts of convective heat transfer and radiation heat transfer 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 and thermal models are coupled via the Arrhenius equation:

Among them, Φ is a parameter related to temperature, and 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, which will cause the temperature change in the 3D thermal model, and the temperature change will be fed back to the P2D electrochemical model, causing the electrochemical The change of the temperature-related parameters in the model, the change of these parameters further triggers the change of the heat source, so as to realize the coupling of the electrochemical model and the thermal model.

Table 1. Governing equations and boundary conditions in the P2D model

Table 2. Governing equations and boundary conditions in the 3D thermal model

The symbols and terminology appearing in the text are listed in Table 3.

Table 3. Symbols and terms appearing in the text

The verification of the model in step 3 is carried out through the following steps:

(1) Fully charge the battery by charging with constant current and then constant voltage; (2) Discharge the battery with constant current, and set the cut-off voltage to 2.75V; (3) Compare the discharge curve obtained from the experiment with the simulated value; (4) Use an infrared thermal imager to shoot the temperature distribution on the surface of the battery at the end of discharge, and compare it with the simulation results; (5) Perform parameter correction according to the results of the above steps (3) and (4), and obtain the corrected electrochemical- thermal coupling model.

Embodiment one

Taking the nickel-cobalt-manganese/graphite (NCM/C) pouch battery of commercial 18.5Ah as an example, the representative electrode design parameter of this lithium-ion battery--electrode thickness is optimized, and the present invention is described comprehensively and in detail. The method is not limited to the optimization of this cell and electrode thickness, but is applicable to other electrode design parameters as well. The appearance and actual measurement dimensions of the battery are shown in Figure 3. The optimization is divided into two parts: (1) The objective function is to maximize the energy density. (2) The objective function is to maximize the product of energy density and power density. And two optimization algorithms are used respectively, and finally 4 groups of optimized electrode thicknesses will be obtained, and then the optimal electrode thickness will be selected.

1. First describe the experimental part:

The experimental method is to charge and discharge the battery, and use an infrared thermal imager to capture the temperature of the battery surface. The experiment was carried out at 4 discharge rates (0.5C, 1C, 1.5C, 2C) and compared with the simulation results to improve the accuracy of the simulation. The following is described by taking 1C as an example: (1) The battery is left on hold for 5 minutes; (2) Charge to 4.2V with a constant current at a rate of 1C (18.5A); (3) Charge with a constant voltage of 4.2V, and set the charging cut-off current to 0.185A; (3) The battery is left on hold for 10 minutes; (4) Constant current discharge is performed at a rate of 1C, and the cut-off voltage is 2.75V; (5) The discharge curve of the battery is obtained, that is, the curve of voltage versus time (6) at the end of discharge The temperature distribution on the surface of the battery is captured with an infrared camera at all times.

2. Then describe the numerical simulation part, which is divided into 5 steps, as follows:

Step 1, parameter acquisition. According to the method of experimental measurement and literature research, the battery electrochemical-thermal coupling model parameters, temperature-related parameters, overall thermal parameters of the battery and thermophysical parameters of the electrode materials are listed in Table 3, Table 4 and Table 5, respectively.

Step two, model establishment. A simplified pseudo two-dimensional (P2D) electrochemical model of the battery is established according to mass conservation, charge conservation, and electrochemical kinetics; then a three-dimensional (3D) thermal model of the battery is established according to the energy conservation equation; the heat source calculated by the P2D electrochemical model is Coupled into the 3D thermal model as a whole, this will cause a change in temperature in the 3D thermal model, and the temperature change will be fed back into the P2D electrochemical model, causing changes in the temperature-related parameters in the electrochemical model, changes in these parameters The change of the heat source is further triggered to realize the coupling of the electrochemical model and the thermal model.

Table 4. Electrochemical-thermal coupled model parameters

Note: "-" indicates that the item does not exist or is not considered

Table 5. Temperature-related parameters and overall thermal parameters of the battery

Table 6. Thermophysical parameters of battery materials

parameter (unit) Density(kg/m3) Specific heat capacity (J/kg/K) 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 Formula (35) Formula (34) Formulas (36) and (37)

Step three, model verification and parameter calibration. Based on the COMSOL Multiphysics multiphysics simulation platform, the electrochemical-thermal coupling model as described in step 2 was established. The model began to think that the battery was fully charged, so it only discharged the battery, which was the same as the experimental condition, still at 4 The discharge rate (0.5C, 1C, 1.5C, 2C) is carried out, and finally the discharge curve and the temperature field distribution of each period are obtained, which are compared with the experimental results. The comparison diagrams are shown in Figure 5 and Figure 6.

Step 4, optimization of electrode thickness of lithium-ion battery based on energy density. The energy density of a lithium-ion battery is determined by formula (38), where M is the mass of the electrode, which only includes positive and negative materials, electrolytes, separators, and current collectors, and other inactive materials such as battery shells and conductive agents are not included. This will result in higher calculated energy densities than they actually are, but since these unaccounted masses are assumed to be constant, they do not affect the optimization results.

In this step, two optimization algorithms are adopted for the optimization of the electrode thickness, one of which is the Nelder-Mead algorithm, proposed by John Nelder and Roger Mead in 1965, which is a nonlinear optimization method that does not need to solve the derivative of the objective function; the second The COBYLA method (constrained optimization method for linear approximation), proposed by Michael J.D. Powell in 1997, is a linear optimization method that does not need to solve the derivative of the objective function, and can be used to solve constrained problems. Both optimization algorithms come from the optimization module in COMSOL Multiphysics, and are solved according to a custom optimization solver.

The optimization in this step needs to adopt certain constraints, and it is considered that there are two constraints: one is that the theoretical capacity of the negative electrode should be slightly larger than the theoretical capacity of the positive electrode to avoid the generation of lithium dendrites. According to the battery design experience, according to formula (40), 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, and the NP ratio of the battery is taken to be between 1.1-1.2; secondly, the optimal operating temperature of the lithium-ion battery is 298K-313K, and its operating temperature is set within this range within.

The optimized parameters in this step are the thickness of the positive electrode and the thickness of the negative electrode. The initial values are 55 μm and 65 μm, respectively, according to the experimental measurement. According to the estimation of the customer’s needs within the volume and capacity limits, and the two parameters that satisfy the sum of the upper and lower limits as the initial value times, the value range obtained accordingly is [30,80] and [30,100], and the unit is μm.

The initial value is first brought into the model for calculation, and the value of the objective function is obtained, and then fed back to the optimization algorithm. The optimization procedure is shown in the figure, and finally the optimization results based on the two optimization algorithms are obtained, which are listed in Table 6. It can be seen that, The results obtained by the two optimization algorithms are basically the same, and the energy density is improved compared with the initial energy density, while the power density is decreased. Therefore, it is necessary to comprehensively consider the energy density and power density to obtain the optimal electrode thickness.

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

Table 7. Electrode Thickness Optimization Results Based on Energy Density

Step 5, optimization of lithium-ion battery electrode thickness based on energy density and power density. The power density of a lithium-ion battery is determined by Equation (41). The objective function in this step is the product of energy density and power density. The optimization algorithm, constraint conditions, and parameter value ranges are all consistent with those in step 4. The final optimization results are listed in Table 7, from which it can be seen that although N-M The objective function value obtained by the algorithm is higher than that of the COBYLA algorithm, but the energy density obtained by the N-M algorithm is relatively low, and the thickness of the positive and negative electrodes is relatively small, which does not meet the principle of redundancy of positive and negative materials in the actual design of the battery, so it does not meet our requirements. The optimization target, and the energy density and power density obtained through COBYLA algorithm optimization are improved, so the COBYLA algorithm suitable for solving constrained problems is more suitable for the optimization of the present invention. Finally, it is considered that the thickness of the positive electrode is 55.335 μm and the thickness of the negative electrode is 63.188 μm is the optimal electrode thickness. The energy density of 244.37Wh/kg is higher than the initial energy density of 239.71Wh/kg, and the power density of 247.11W/kg is higher than the initial power density of 244.46W. /kg has also been improved to meet the optimization requirements, which can provide a certain guiding basis for the electrode design of lithium-ion batteries and shorten the battery design cycle.

Table 8. Electrode Thickness Optimization Results Based on Energy Density and Power Density

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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