A fast charging numerical simulation method, device and medium for a thick electrode of a lithium ion battery

Abstract

The present application relates to the technical field of electrochemistry, and in particular to a fast-charging numerical simulation method, device and medium for thick electrodes of lithium ion batteries, the method comprising: constructing an electrochemical model of a lithium ion battery based on a pseudo two-dimensional model; loading basic parameters of the lithium ion battery, spatially discretizing according to the battery structure, and initializing an array of physical quantities required for simulation; using a Bayesian optimization algorithm, determining the charge-discharge curve of the lithium ion battery based on experiments, and calibrating the kinetic parameters of the battery cell; switching the charge-discharge mode according to the state of the lithium ion battery, performing cycle simulation, outputting simulation data, and completing fast-charging numerical simulation. The method overcomes the problems of the prior art, such as the inability of the pseudo two-dimensional model to accurately simulate the low-temperature fast-charging process of thick electrodes, the lack of an efficient and accurate method for obtaining kinetic parameters, and the difficulty in predicting battery aging caused by SEI growth.

Description

Technical Field

[0001] This invention relates to the field of electrochemical technology, and in particular to a fast-charging numerical simulation method, equipment, and medium for thick electrodes of lithium-ion batteries. Background Technology

[0002] Using thick electrodes is an effective way to improve the energy density of lithium-ion batteries. However, as the electrode thickness increases, the electron / ion transport path lengthens, leading to increased electrode impedance. A well-designed electrode structure (such as low-torsion / gradient porosity electrodes) can effectively improve the performance of thick electrodes. Furthermore, considering the winter usage scenarios of current new energy vehicles, lithium-ion batteries often need to operate at low temperatures. At low temperatures, the discharge voltage and usable capacity of lithium-ion batteries decay rapidly. Moreover, due to intensified polarization at low temperatures, metallic lithium accumulates on the surface of the negative electrode during charging, even promoting lithium dendrite growth, piercing the battery separator, causing short circuits, and resulting in permanent damage to the lithium battery. Designing a stepped charging strategy can effectively avoid anode lithium deposition during low-temperature charging.

[0003] Currently, there is a lack of systematic and in-depth research on the low-temperature fast charging process and the kinetics of thick electrodes in lithium-ion batteries. Furthermore, exploring optimal charging strategies and thick electrode structural parameters using experimental methods is time-consuming and laborious. Therefore, establishing an ion transport model under a wide temperature range and high voltage, and employing numerical simulation methods to describe the voltage and current density changes during the battery's charging and discharging transient processes, while analyzing the battery's internal electrochemical behavior, can help to gain a deeper understanding of the anode lithium plating process and the kinetics of thick electrodes. This is crucial for achieving high-rate performance, high energy density, and excellent cycle life in the fabrication of lithium-ion batteries.

[0004] Therefore, it is necessary to provide a fast-charging numerical simulation method, equipment, and medium for thick electrodes of lithium-ion batteries to solve the above-mentioned technical problems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a numerical simulation method, apparatus, and dielectric for fast charging of thick electrodes in lithium-ion batteries. This method overcomes the limitations of existing pseudo-two-dimensional (P2D) models, which cannot accurately simulate the low-temperature fast charging process of thick electrodes, lack efficient and accurate methods for obtaining kinetic parameters, and struggle to predict battery aging caused by SEI growth.

[0006] In a first aspect, the present invention proposes a fast-charging numerical simulation method for thick electrodes in lithium-ion batteries, comprising the following steps: S1: Constructing an electrochemical model of lithium-ion batteries based on a pseudo-two-dimensional model; S2: Load the basic parameters of the lithium-ion battery, discretize the battery structure in space, and initialize the array of physical quantities required for the simulation. S3: Using a Bayesian optimization algorithm, the dynamic parameters of the battery cell are calibrated based on the experimentally determined charge-discharge curves of the lithium-ion battery. S4: Switch charging and discharging modes according to the state of the lithium-ion battery, perform cyclic simulation, output simulation data, and complete fast charging numerical simulation. The process of cyclic simulation includes: S4.1: Input the kinetic parameters of the battery cell and calculate the interface current density of the lithium-ion battery; S4.2: In the electrochemical model of lithium-ion batteries, the growth simulation of solid electrolyte interface film is introduced, and the main electrochemical reaction and the interface side reaction are coupled to realize the quantitative calculation of solid electrolyte interface film. S4.3: Check if a solid electrolyte interface membrane exists. If a solid electrolyte interface membrane exists, enable the solid electrolyte interface membrane model to batch update the solid electrolyte interface membrane variables, then update the interface current density, and end one loop. If no solid electrolyte interface membrane exists, end one loop after updating the interface current density.

[0007] Preferably, in S2, the basic parameters of the lithium-ion battery include geometric dimensions, material properties, and electrochemical parameters; the battery structure of the lithium-ion battery includes a negative electrode, a separator, and a positive electrode, and spatial numerical discretization is achieved by calculating the number of nodes and grid spacing in each region; the array of physical quantities required for simulation includes voltage, current, electrolyte concentration, and potential.

[0008] Preferably, in S3, the process of calibrating the kinetic parameters of the battery cell includes: The Arrhenius formula is used to construct the relationship between kinetic parameters and temperature, and the parameter values ​​are transformed into temperature dependence coefficients. The kinetic parameters at multiple temperature points are optimized at the same time, and the physical constraints between temperatures are used to improve the optimization stability. Using a Bayesian optimization algorithm, the optimal parameter combination is automatically searched. Based on the charge-discharge curves obtained from experiments, dynamic parameters over a wide temperature range are obtained, and the dynamic parameters of the battery cell are calibrated.

[0009] Preferably, in S3, the expression for the relationship between the kinetic parameters and temperature is as follows: param(T) = param_RT × exp(a × (1 / T – 1 / T_RT)); Where param(T) represents the parameter value at temperature T; param_RT represents the reference parameter value at room temperature; exp represents the natural exponential function; and a represents the activation energy correlation coefficient to be optimized, with each kinetic parameter corresponding to an activation energy correlation coefficient.

[0010] Preferably, in S3, the Bayesian optimization algorithm process includes: Bayesian optimization based on Gaussian model is adopted. The mapping from parameter space to objective function is established through Gaussian process and uncertainty is quantified. The expected improvement is used as the sampling function to guide sampling, balancing exploration and utilization. In each iteration, the most promising point is selected for evaluation and the Gaussian model is updated to gradually approach the optimal solution. The objective function includes root mean square error, capacity penalty, and voltage step penalty, where: The root mean square error is used to reflect the overall fitting accuracy of the simulated and experimental voltage curves. The capacity penalty is used to apply a penalty to the excess portion when the simulated capacity is lower than the experimental capacity; The voltage step penalty is used to detect and penalize abnormal voltage abrupt changes in the simulated curve.

[0011] Preferably, in step S3, the kinetic parameters are further corrected, taking into account the influence of electrode porosity and tortuosity factor on diffusion coefficient and conductivity. The corrected expressions for effective diffusion coefficient and effective conductivity are as follows: ; ; in, , The effective diffusion coefficient and effective conductivity are the corrected values. Electrode porosity, , The intrinsic diffusion coefficient and conductivity are, The electrode tortuosity factor. The determination was performed using the symmetrical electrode method.

[0012] Preferably, in S4, the process of simulating the growth of the solid electrolyte interface film includes: The initial values ​​are set, including the initial lithium ion concentration, potential, initial interface reaction current density, and initial solid electrolyte interface film thickness and impedance. After entering the iterative solution step, the lithium-ion intercalation current density of the main reaction and the side reaction current density of solid electrolyte interface film thickening are calculated based on the current local overpotential. This process includes kinetic constraints or diffusion constraints. Solve the liquid phase potential equation and solid phase potential equation based on the updated current distribution; The calculated total interfacial reaction current density is compared with the total interfacial reaction current density of the previous iteration. If the difference is less than the tolerance, convergence is determined. The thickness, porosity and active lithium loss of the solid electrolyte interfacial film at the next moment are updated according to Faraday's law, and the calculation of the next iteration is performed. If the difference is greater than the tolerance, the interfacial current density value is updated and iterative calculation is performed. During the iteration process, the implicit finite difference algorithm is used to solve this set of partial differential equations coupled with multiphysics.

[0013] Preferably, in S4, the electrochemical model for simulating the growth of the solid electrolyte interface film includes: The growth of solid electrolyte interfacial films is described as an electrochemical consumption process involving solvents, electrons, and lithium ions, with the following reaction equation: ; in, Indicates solvent, Represents electron, Indicates lithium ions. express, Indicates the solid electrolyte interface film; During charging, both the intercalation reduction main reaction and the solid electrolyte interfacial film reaction occur simultaneously on the anode surface, resulting in a local total current density. The expression is as follows: ; in, This represents the exchange current flux of the intercalation reduction main reaction. This represents the exchange current flux of the solid electrolyte interfacial membrane reaction; The exchange current flux of the solid electrolyte interfacial membrane reaction is described using the modified Butler-Volmer form, as shown in the following expression: ; ; in, This represents the exchange current density at the solid electrolyte interface membrane. Denotes Faraday's constant. express, R The gas constant is T Absolute temperature, unit: K , Indicates SEI overpotential. Represents solid-state potential. Represents the liquid phase potential. This represents the open-circuit potential for SEI film growth; The difference between kinetically limited and diffusion-limited reactions lies in the definition of the solid electrolyte interfacial membrane exchange current density. In the kinetically limited model, the solid electrolyte interfacial membrane exchange current density is treated as a constant fitting parameter. In the diffusion-limited model, the solid electrolyte interfacial membrane exchange current density considers the diffusion process of solvent molecules, and in this case, the solid electrolyte interfacial membrane exchange current density is dynamically related to the solvent concentration, as expressed below: ; ; in, This represents the SEI reaction rate constant. This indicates the electrolyte concentration at the SEI / electrolyte interface. Indicates SEI porosity. Indicates the concentration of the liquid electrolyte. Indicates the thickness of the SEI film. This represents the diffusion coefficient of Li in the electrolyte.

[0014] In a second aspect, the present invention also provides a computer device, including a memory and a processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the fast-charging numerical simulation method for thick electrodes of lithium-ion batteries as described above.

[0015] In a third aspect, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the fast-charging numerical simulation method for thick electrodes of a lithium-ion battery as described above.

[0016] The application of the technical solution of the present invention has at least the following beneficial effects: The present invention provides a fast-charging numerical simulation method for thick electrodes of lithium-ion batteries. It adopts a Bayesian optimization algorithm and, based on a small number of experimental measurements of charge-discharge curves, quickly calibrates the relevant dynamic parameters of the battery cell (such as diffusion coefficient, electrode reaction rate constant, conductivity, etc.). Finally, the average relative error between the simulated room temperature charging curve and the experimental value is small, thus achieving accurate simulation of the battery cell charging and discharging process.

[0017] The method of this invention can output the liquid / solid phase lithium concentration distribution and liquid / solid phase potential distribution that vary with time and space, providing guidance for analyzing changes in cell performance: the solid phase potential can be used to determine whether lithium is deposited on the negative electrode during the charging process (when the solid phase potential of the negative electrode is less than 0, lithium dendrites will grow on the surface of graphite particles); the lithium concentration distribution can be used to analyze the concentration polarization of the cell under different operating conditions, and a lower degree of polarization under the same operating conditions indicates that the cell has better rate performance.

[0018] The method of this invention also provides a simulation of the growth of the negative electrode SEI during cycling. The distribution of SEI film thickness and internal resistance is in excellent agreement with the literature results, with a small average relative error. The method of this invention can accurately describe the growth kinetics of the SEI film and can be effectively used to predict the cell capacity decay and internal resistance increase caused by SEI thickening under various operating conditions.

[0019] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the steps of the fast charging numerical simulation method for thick electrodes of lithium-ion batteries in a preferred embodiment of the present invention; Figure 2 The diagram shows a comparison between the positive and negative electrode equilibrium potential curves obtained by the interpolation method used in this invention and the measured values. (a) is the equilibrium potential curve of the lithium iron phosphate positive electrode, and (b) is the equilibrium potential curve of the graphite negative electrode. Figure 3 The figure shows the effect of different initial sampling points on the optimization results of Bayesian method. In this figure, (a) shows the relationship between different sampling points and the error of the final curve, and (b) shows the relationship between the error and the number of iterations under different sampling point conditions. Figure 4 The comparison charts of the optimized charging curves and experimental results are shown below. (a) shows the comparison results of 1C charging, (b) shows the comparison results of 3C charging, (c) shows the comparison results of 0.5C charging, and (d) shows the comparison results of 2C charging. Figure 5 The spatiotemporal distribution diagrams of solid / liquid lithium concentration and potential during the charging and discharging process of the battery cell are shown. (a) shows the solid concentration distribution, (b) shows the liquid concentration distribution, (c) shows the solid potential distribution, and (d) shows the liquid potential distribution. Figure 6 The graph shows the evolution of SEI film concentration and SEI film thickness with time and cycle number. In the graph, (a) shows the distribution of SEI film concentration at the negative electrode, and (b) shows the distribution of SEI film thickness at the negative electrode. Figure 7 The graph shows the volume retention rate measured in the experiment versus the simulation results. Figure 8The graph shows the cumulative growth law and growth rate changes of key SEI parameters with the number of cycles. Among them, (a) shows the change of SEI film concentration with the number of cycles, (b) shows the change of SEI film internal resistance with the number of cycles, (c) shows the change of SEI film thickness with the number of cycles, (d) shows the change rate of SEI film concentration with the number of cycles, (e) shows the change rate of SEI film internal resistance with the number of cycles, and (f) shows the change rate of SEI film thickness with the number of cycles. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0023] Example: like Figure 1 As shown, this embodiment provides a fast-charging numerical simulation method for thick electrodes in lithium-ion batteries, including the following steps (S1 to S4): A numerical simulation method for fast charging of a thick electrode in a lithium-ion battery includes the following steps: S1: Construct an electrochemical model of lithium-ion batteries based on a pseudo-two-dimensional model.

[0024] It should be noted that the pseudo-two-dimensional model (P2D) is a commonly used electrochemical model in lithium-ion batteries. This model ignores side reactions in the battery and considers that the electrode is composed of spherical particles of active material. The mass balance of lithium ions in a single spherical particle is described by Fick's second law. ; in, Represents lithium-ion concentration, subscript Indicates solid phase, Representative electrode ( Indicates the positive electrode. (Indicates the negative electrode). D The diffusion coefficient of lithium ions in the active particles is denoted as . Where is the radius of the particle. This refers to the discharge time.

[0025] Furthermore, the boundary conditions at the center and surface of the spherical particles are as follows: ; ; in, The radius of the electrode active particles. This represents the flux through the pore walls on the particle surface.

[0026] Furthermore, the mass balance of lithium ions in the electrolyte is controlled by the following equation: ; Among them, subscript It is a liquid phase. Porosity denoted as the lithium-ion transfer coefficient. Position in the thickness direction, subscript Indicates electrode or diaphragm ( (Indicates diaphragm) The specific surface area of ​​an electrode per unit volume is expressed as: ; in, This represents the volume fraction of active particles in the electrode.

[0027] The condition at the boundary between the current collector and the electrode is expressed as: ; ; in, L The thickness is the electrode or membrane thickness, ignoring the solubility limit of lithium salt in the liquid phase and the precipitation of lithium salt.

[0028] The charge balance in a solid phase is governed by Ohm's law: ; in, The effective conductivity of the electrode. For solid-state potential, F is Faraday's constant.

[0029] The charge flux at the collector boundary is equal to the applied current density ( ): ; Since the diaphragm is an insulator, the charge flux at the boundary between the electrode and the diaphragm is zero. ; Will The negative electrode potential is set to 0. The positive electrode potential at that point is set as the battery voltage. : ; ; The charge balance in the liquid phase is expressed as: ; The boundary conditions are: ; in, The effective ionic conductivity of the electrolyte in the porous medium. The liquid phase potential, R The gas constant is T For temperature.

[0030] The kinetic equation for the electrochemical reaction uses the Butler-Volmer equation, and the pore wall flux is expressed as: ; in, The reaction rate constant is... This represents the lithium-ion concentration on the surface of the active particles. η The overpotential of an electrochemical reaction is given by the following equation: ; in, U This is the open-circuit voltage.

[0031] The electrochemical model constructed using the pseudo-two-dimensional model (P2D) described above can simulate the charging and discharging process of a battery at different charging rates, and obtain the ionic conductivity of the electrode / electrolyte. It can also simulate the changes in battery performance with electrode material, electrode thickness, and electrode porosity to explore the rate-limiting factors of the charging process.

[0032] S2: Load the basic parameters of the lithium-ion battery, discretize it spatially according to the battery structure, and initialize the array of physical quantities required for the simulation.

[0033] In S2, the basic parameters of a lithium-ion battery include geometric dimensions, material properties, and electrochemical parameters; the battery structure of a lithium-ion battery includes a negative electrode, a separator, and a positive electrode, and spatial numerical discretization is achieved by calculating the number of nodes and grid spacing in each region; the array of physical quantities required for simulation includes voltage, current, electrolyte concentration, and potential.

[0034] Next, initialize the arrays of various physical quantities required for the simulation, including voltage, current, concentration, and potential, to prepare storage space for time-iteration calculations. When the SEI model is enabled, it is also necessary to initialize variables such as SEI thickness, resistance, and concentration. These variables only apply to the negative electrode region because the SEI film is mainly formed on the surface of the graphite particles in the negative electrode.

[0035] S3: Using a Bayesian optimization algorithm, the dynamic parameters of the battery cell are calibrated based on the experimentally determined charge-discharge curves of lithium-ion batteries.

[0036] Specifically, the process of calibrating the dynamic parameters of a battery cell includes: The Arrhenius formula is used to construct the relationship between kinetic parameters and temperature, and the parameter values ​​are transformed into temperature dependence coefficients. The kinetic parameters at multiple temperature points are optimized at the same time, and the physical constraints between temperatures are used to improve the optimization stability. Using a Bayesian optimization algorithm, the optimal parameter combination is automatically searched. Based on the charge-discharge curves obtained from experiments, dynamic parameters over a wide temperature range are obtained, and the dynamic parameters of the battery cell are calibrated.

[0037] Furthermore, the expression for the relationship between the kinetic parameters and temperature is as follows: param(T) = param_RT × exp(a × (1 / T – 1 / T_RT)); Where param(T) represents the parameter value at temperature T; param_RT represents the reference parameter value at room temperature; exp represents the natural exponential function; and a represents the activation energy correlation coefficient to be optimized, with each kinetic parameter corresponding to an activation energy correlation coefficient.

[0038] Furthermore, the process of the Bayesian optimization algorithm includes: Bayesian optimization based on Gaussian model is adopted. The mapping from parameter space to objective function is established through Gaussian process and uncertainty is quantified. The expected improvement is used as the sampling function to guide sampling, balancing exploration and utilization. In each iteration, the most promising point is selected for evaluation and the Gaussian model is updated to gradually approach the optimal solution. The objective function includes root mean square error, capacity penalty, and voltage step penalty, where: The root mean square error is used to reflect the overall fitting accuracy of the simulated and experimental voltage curves. The capacity penalty is used to apply a penalty to the excess portion when the simulated capacity is lower than the experimental capacity; The voltage step penalty is used to detect and penalize abnormal voltage abrupt changes in the simulated curve.

[0039] Furthermore, this embodiment also includes corrections to the kinetic parameters. Considering the influence of electrode porosity and tortuosity factor on the diffusion coefficient and conductivity, the corrected expressions for the effective diffusion coefficient and effective conductivity are as follows: ; ; in, , The effective diffusion coefficient and effective conductivity are the corrected values. Electrode porosity, , The intrinsic diffusion coefficient and conductivity are, The electrode tortuosity factor. The determination was performed using the symmetrical electrode method.

[0040] In this embodiment, the input parameters are summarized in Table 1.

[0041] Table 1 Summary of Input Parameters for LFP-Graphite Cells

[0042] In this embodiment, the liquid-phase diffusion coefficient and solid-phase diffusion coefficient are adopted from literature values; the maximum lithium concentration of the positive and negative electrodes is calculated based on the theoretical specific capacity of lithium iron phosphate and graphite; and the electrode reaction rate constant is calculated based on the electrode exchange current density.

[0043] Furthermore, the electrode equilibrium potential curve input is as follows: Figure 2 As shown, the electrode tortuosity factor was determined based on the eSCM method, and the positive electrode tortuosity factor was determined. The negative tortuosity factor is 1.66. The value was set to 2.75, and the dynamic parameters were corrected before being used as the input parameters for cell simulation.

[0044] It should be noted that this embodiment uses a Bayesian optimization algorithm to calibrate the parameters, and the results are as follows: Figure 3 and Figure 4 As shown, where: When the initial number of sampling points is 25, the final weighted RMSE is the lowest (approximately 0.0223 V), the convergence speed is the fastest, and it reaches stability after about 100 iterations.

[0045] With an initial sampling number of 20, the final error was 0.0230 V, and the convergence speed was relatively fast. With an initial sampling number of 40, the final error was 0.0253 V, and the convergence process showed fluctuations.

[0046] When the initial number of sampling points is 15, the final error is the highest (approximately 0.0246 V), and the convergence is slow.

[0047] In summary, an initial sampling number of 25 achieves a good balance between convergence speed and final accuracy, and can be considered a recommended configuration for optimizing 23 Ah battery cells. Furthermore, optimization results for 23 Ah battery cells at 0.5C, 1.0C, 2.0C, and 3.0C show that the optimized parameters significantly improved the fit with the experimental data.

[0048] At 1.0C, the initial parameter RMSE was 0.0326 V, which was reduced to 0.0230 V after optimization, an improvement of about 29.4%. The optimized curve is closer to the experimental data in both the plateau region and the voltage rise at the end, indicating better capacity matching.

[0049] At 3.0C, the initial parameter RMSE was 0.0382 V, which was reduced to 0.0224 V after optimization, an improvement of about 41.4%. The optimized curve showed a significant improvement in the plateau region and was more accurate in the voltage rise segment at the end.

[0050] At 0.5C, the initial parameter RMSE was 0.0319 V, which was reduced to 0.0204 V after optimization, an improvement of approximately 36.1%; the optimized curve was in high agreement with the experimental data throughout the charging process.

[0051] At 2.0C, the initial RMSE was 0.0337 V, which was reduced to 0.0233 V after optimization, an improvement of approximately 30.9%. At all rates, the optimized curves better matched the capacity range and voltage characteristics of the experimental data, indicating that the optimization method is effective at different rates.

[0052] After optimization, D_neg_s decreased from its initial value of 5.06 × 10⁻⁶. -14 m 2 / s increased to the optimized value of 7.71 × 10 -14 m 2 / s, with a change rate of +52.29%. D_pos_s changed from an initial value of 7.91 × 10 -16 m 2 / s decreased to the optimized value of 4.72×10 -16 m 2 / s, the rate of change is -40.32%. K_0_neg changes from an initial value of 7.36 × 10 -12 m 2.5 / (mol 0.5 The value of ·s) was reduced to the optimized value of 5.61 × 10. -12 m 2.5 / (mol 0.5 The change rate was -23.84% (·s). K_0_pos started from an initial value of 2.02 × 10⁻⁶. -11 m 2.5 / (mol 0.5 The value of ·s was significantly reduced to the optimized value of 7.09 × 10⁻⁶. -12 m 2.5 / (mol 0.5 (·s), with a change rate of -64.97%.

[0053] S4: Switch charging and discharging modes according to the lithium-ion battery state, perform cyclic simulation, output simulation data, and complete the fast charging numerical simulation. In this embodiment, the number of cycles is set to be no less than 50.

[0054] The process of cyclic simulation includes: S4.1: Input the kinetic parameters of the battery cell and calculate the interface current density of the lithium-ion battery.

[0055] In this embodiment, the process of calculating the interface current density includes: The open-circuit voltage of each node is calculated using an interpolation function based on the solid phase concentration of the electrode material. Based on the Butler-Volmer equation, considering the solid phase concentration and liquid phase concentration, the electrode reaction exchange current density is calculated. Depending on whether an SEI model is available, different methods are used to calculate the current density distribution: without an SEI model, the liquid phase concentration and phase potential equations are solved directly to obtain the current density distribution and liquid phase potential; with an SEI model, the influence of SEI resistance is considered, and the corrected current density distribution is solved; in the static state, both the current density and liquid phase potential are zero.

[0056] The outputs of the above process are current density and liquid phase potential.

[0057] S4.2: In the electrochemical model of lithium-ion batteries, the growth simulation of solid electrolyte interface film is introduced, coupling the main electrochemical reaction and the interface side reaction to achieve quantitative calculation of solid electrolyte interface film.

[0058] It should be noted that the solid electrolyte interface film growth simulation in this embodiment includes at least solving for the solid phase potential, solving for the liquid phase concentration, solving for the solid phase concentration, and updating the SEI, wherein: The process of solving for the solid-state potential includes: Using current density, liquid phase potential, and open-circuit voltage, the total overpotential is first calculated. Based on the inverse function of the Butler-Volmer equation, the overpotential of each node is calculated according to the total current density and the exchange current density.

[0059] Depending on whether an SEI model exists, different methods are used to update the solid-state potential: Without an SEI model, the solid-state potential equals the sum of the liquid-state potential and the open-circuit voltage; with an SEI model, the additional voltage drop caused by the SEI resistance needs to be considered, and the solid-state potential equals the sum of the activation overpotential, liquid-state potential, open-circuit voltage, and the SEI resistance voltage drop. When an SEI exists, it is also necessary to calculate the SEI overpotential and the SEI side reaction current density. Calculate the net reaction current density, which is the total current minus the SEI secondary reaction current density, to obtain the actual current density used for lithium insertion / extraction, and update the activation overpotential based on the net reaction current density.

[0060] The process of determining the concentration of the liquid phase includes: Based on the principle of mass conservation, using liquid phase concentration, current density, and physical property parameters, considering the diffusion and migration of lithium ions in the electrolyte, the partial differential equation is discretized using the finite volume method, and the liquid phase concentration distribution of the next time step is obtained by solving it. The output of the above process is the liquid phase concentration for the next time step, which will be used in the calculation of the next time step.

[0061] The process of determining the solid concentration includes: Based on Fick's diffusion law, the radial diffusion process of lithium ions within the electrode material particles is considered using solid phase concentration and current density. For both the negative and positive electrodes, the finite volume method is used to solve the concentration distribution equation of lithium ions in the solid phase, and the concentration distribution inside the particles and the surface concentration are calculated. After the solution is completed, the surface concentrations of the negative electrode and the positive electrode are combined to obtain the solid phase concentration distribution of the entire battery region at the next time step; In addition, the above process also checks the boundary conditions of the state of charge, calculates the maximum and minimum concentration values ​​of the negative and positive electrodes, as well as the minimum concentration value of the liquid phase, for subsequent state control and boundary condition judgment.

[0062] The SEI update process includes: SEI updates are performed only when the SEI model is enabled. Using SEI parameters and SEI side-reaction currents, the appropriate update strategy is selected based on the SEI model type (kinetically restricted or diffusion-restricted). For kinetically restricted SEI models, changes in SEI thickness, resistance, and concentration are directly determined by the SEI side-reaction currents, with the rate of change proportional to the current. This allows for the calculation of SEI parameters for the next time step. For diffusion-restricted models, the diffusion restriction of the solvent within the SEI layer is considered in addition to the kinetic model. Therefore, the solvent concentration distribution for the next time step needs to be updated, and the SEI exchange current needs to be recalculated. After the update, the new SEI parameter values ​​are saved for calculation in the next time step, simulating the dynamic growth of the SEI film over time.

[0063] Based on the optimized input parameters, the spatiotemporal distribution of solid / liquid lithium concentration and potential during the charging and discharging process of the battery cell was simultaneously output, such as... Figure 5 As shown.

[0064] It should be noted that the SEI model in this embodiment includes a kinetically confined SEI model and a diffusion-confined SEI model, wherein: Dynamically constrained SEI model: The kinetically limited SEI model assumes that SEI growth is controlled by reaction kinetics, and changes in SEI parameters are directly determined by the reaction current. Based on the SEI side-reaction current, the kinetically limited SEI model updates SEI parameters using kinetic equations: the rate of change of SEI thickness is proportional to the SEI current, the rate of change of SEI resistance is related to both the SEI current and conductivity, and the change in SEI concentration is related to both specific surface area and SEI current. The kinetically limited SEI model is applicable when SEI growth is primarily limited by the reaction rate.

[0065] Diffusion-limited SEI model: The diffusion-limited SEI model, based on the kinetic model, additionally considers the diffusion-limiting effect of the solvent within the SEI layer, thus more accurately describing the SEI growth process. The diffusion-limited SEI model first updates parameters such as SEI thickness, resistance, and concentration, similar to the kinetic model. Then, it considers solvent diffusion limitation within the SEI layer and updates the solvent concentration distribution. Finally, it recalculates the SEI exchange current based on the updated solvent concentration, forming a complete diffusion-limited SEI growth model.

[0066] S4.3: Check if a solid electrolyte interface membrane exists. If a solid electrolyte interface membrane exists, enable the solid electrolyte interface membrane model to batch update the solid electrolyte interface membrane variables, then update the interface current density, and end one loop. If no solid electrolyte interface membrane exists, end one loop after updating the interface current density.

[0067] Specifically, in S4, the process of simulating the growth of the solid electrolyte interface film includes: The initial values ​​are set, including the initial lithium ion concentration, potential, initial interface reaction current density, and initial solid electrolyte interface film thickness and impedance. After entering the iterative solution step, the lithium-ion intercalation current density of the main reaction and the side reaction current density of solid electrolyte interface film thickening are calculated based on the current local overpotential. This process includes kinetic constraints or diffusion constraints. Solve the liquid phase potential equation and solid phase potential equation based on the updated current distribution; The calculated total interfacial reaction current density is compared with the total interfacial reaction current density of the previous iteration. If the difference is less than the tolerance, convergence is determined. The thickness, porosity and active lithium loss of the solid electrolyte interfacial film at the next moment are updated according to Faraday's law, and the calculation of the next iteration is performed. If the difference is greater than the tolerance, the interfacial current density value is updated and iterative calculation is performed. During the iteration process, the implicit finite difference algorithm is used to solve this set of partial differential equations coupled with multiphysics.

[0068] In this embodiment, the electrochemical model for simulating the growth of a solid electrolyte interface film includes: The growth of solid electrolyte interfacial films is described as an electrochemical consumption process involving solvents, electrons, and lithium ions, with the following reaction equation: ; in, Indicates solvent, Represents electron, Indicates lithium ions. express, Indicates the solid electrolyte interface film; During charging, both the intercalation reduction main reaction and the solid electrolyte interfacial film reaction occur simultaneously on the anode surface, resulting in a local total current density. The expression is as follows: ; in, This represents the exchange current flux of the intercalation reduction main reaction. This represents the exchange current flux of the solid electrolyte interfacial membrane reaction; The exchange current flux of the solid electrolyte interfacial membrane reaction is described using the modified Butler-Volmer form, as shown in the following expression: ; ; in, This represents the exchange current density indicating the thickening reaction of the solid electrolyte interfacial film. Denotes Faraday's constant. α SEI Indicates the transfer coefficient of the SEI reaction. R The gas constant is T Absolute temperature, unit: K , Indicates SEI overpotential. Represents solid-state potential. Represents the liquid phase potential. This represents the open-circuit potential for SEI film growth; The difference between kinetically limited and diffusion-limited reactions lies in the definition of the solid electrolyte interfacial membrane exchange current density. In the kinetically limited model, the solid electrolyte interfacial membrane exchange current density is treated as a constant fitting parameter. In the diffusion-limited model, the solid electrolyte interfacial membrane exchange current density considers the diffusion process of solvent molecules, and in this case, the solid electrolyte interfacial membrane exchange current density is dynamically related to the solvent concentration, as expressed below: ; ; in, k SEI This represents the SEI reaction rate constant. This indicates the electrolyte concentration at the SEI / electrolyte interface. Indicates SEI porosity. Indicates the concentration of the liquid electrolyte. Indicates the thickness of the SEI film. This represents the diffusion coefficient of Li in the electrolyte.

[0069] The method described in this embodiment is applied for simulation, and the model's predictive ability for interface aging characteristic parameters is verified by introducing SEI growth simulation. For example... Figure 6 As shown, the evolution of SEI film thickness (L_SEI), SEI film internal resistance (R_SEI), and SEI film concentration (c_SEI) over time and cycle number is compared in detail. The data indicate that the SEI film thickness and internal resistance calculated by the method in this embodiment agree very well with the literature results, with an average relative error kept within 1%, and the simulation error for solvent concentration changes is also controlled within 6%. This fully verifies that the method in this embodiment can accurately describe the growth kinetics of the SEI film and can be effectively used to predict cell capacity decay and internal resistance increase caused by SEI thickening under various operating conditions.

[0070] like Figure 7 As shown, the method in this embodiment exhibits different SEI reaction exchange current densities ( Sensitivity analysis and experimental verification of battery cycle life under certain parameters. Figure 7 The experimentally measured capacity retention rate was compared with the simulation results. The results show that the battery capacity decreases with the number of cycles. By adjusting the exchange current density in the kinetic constraint model, the method in this embodiment can accurately fit the aging curve. The simulation results under optimal parameters are highly consistent with the linear fitting slope of the experimental data, with an average absolute error of only 0.19% to 0.66%. This proves that the model constructed by the method in this embodiment (P2D-SEI model) can not only reproduce the capacity decay phenomenon, but also accurately quantify the influence of the side reaction kinetic intensity on the lifetime through parameter calibration.

[0071] like Figure 8 As shown, the method in this embodiment quantitatively describes the cumulative growth law and growth rate change of SEI key parameters with the number of cycles. Figure 8 (a)~(c) show that the average lithium concentration, internal resistance and thickness of the SEI exhibit an approximately linear cumulative growth trend with the number of cycles, quantitatively reflecting the degree of irreversible aging in long-cycle cycling. Figure 8 The growth rate analysis in (d)~(f) further reveals the kinetic characteristics within a single cycle: the growth rate of the SEI gradually decreases as the reaction time progresses. This result is consistent with the classic self-limiting growth mechanism, i.e., the formed SEI film hinders subsequent electron tunneling or solvent diffusion, leading to a gradual slowdown in side reaction kinetics, further verifying the physical effectiveness of the method in this embodiment.

[0072] This embodiment also provides a computer device, including a memory and a processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the fast-charging numerical simulation method for thick electrodes of lithium-ion batteries as described above.

[0073] It should be noted that computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0074] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0075] In addition, this embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the fast-charging numerical simulation method for thick electrodes of lithium-ion batteries as described above.

[0076] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., a computer program) for executing the above-described fast-charging numerical simulation method for thick electrodes of lithium-ion batteries. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as the beneficial effects of the fast-charging numerical simulation method for thick electrodes of lithium-ion batteries provided in the above embodiments, and will not be repeated here.

[0077] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.

Claims

1. A numerical simulation method for fast charging of thick electrodes in lithium-ion batteries, characterized in that, Includes the following steps: S1: Constructing an electrochemical model of lithium-ion batteries based on a pseudo-two-dimensional model; S2: Load the basic parameters of the lithium-ion battery, discretize the battery structure in space, and initialize the array of physical quantities required for the simulation. S3: Using a Bayesian optimization algorithm, the dynamic parameters of the battery cell are calibrated based on the experimentally determined charge-discharge curves of the lithium-ion battery. S4: Switch charging and discharging modes according to the state of the lithium-ion battery, perform cyclic simulation, output simulation data, and complete fast charging numerical simulation. The process of cyclic simulation includes: S4.1: Input the kinetic parameters of the battery cell and calculate the interface current density of the lithium-ion battery; S4.2: In the electrochemical model of lithium-ion batteries, the growth simulation of solid electrolyte interface film is introduced, and the main electrochemical reaction and the interface side reaction are coupled to realize the quantitative calculation of solid electrolyte interface film. S4.3: Check if a solid electrolyte interface membrane exists. If a solid electrolyte interface membrane exists, enable the solid electrolyte interface membrane model to batch update the solid electrolyte interface membrane variables, then update the interface current density, and end one loop. If no solid electrolyte interface membrane exists, end one loop after updating the interface current density.

2. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 1, characterized in that, In S2, the basic parameters of a lithium-ion battery include geometric dimensions, material properties, and electrochemical parameters; the battery structure of a lithium-ion battery includes a negative electrode, a separator, and a positive electrode, and spatial numerical discretization is achieved by calculating the number of nodes and grid spacing in each region; the array of physical quantities required for simulation includes voltage, current, electrolyte concentration, and potential.

3. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 1, characterized in that, In S3, the process of calibrating the cell's dynamic parameters includes: The Arrhenius formula is used to construct the relationship between kinetic parameters and temperature, and the parameter values ​​are transformed into temperature dependence coefficients. The kinetic parameters at multiple temperature points are optimized at the same time, and the physical constraints between temperatures are used to improve the optimization stability. Using a Bayesian optimization algorithm, the optimal parameter combination is automatically searched. Based on the charge-discharge curves obtained from experiments, dynamic parameters over a wide temperature range are obtained, and the dynamic parameters of the battery cell are calibrated.

4. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 3, characterized in that, In S3, the expression for the relationship between the kinetic parameters and temperature is as follows: param(T) = param_RT × exp(a × (1 / T – 1 / T_RT)); Where param(T) represents the parameter value at temperature T; param_RT represents the reference parameter value at room temperature; exp represents the natural exponential function; and a represents the activation energy correlation coefficient to be optimized, with each kinetic parameter corresponding to an activation energy correlation coefficient.

5. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 3, characterized in that, In S3, the Bayesian optimization algorithm process includes: Bayesian optimization based on Gaussian model is adopted. The mapping from parameter space to objective function is established through Gaussian process and uncertainty is quantified. The expected improvement is used as the sampling function to guide sampling, balancing exploration and utilization. In each iteration, the most promising point is selected for evaluation and the Gaussian model is updated to gradually approach the optimal solution. The objective function includes root mean square error, capacity penalty, and voltage step penalty, where: The root mean square error is used to reflect the overall fitting accuracy of the simulated and experimental voltage curves. The capacity penalty is used to apply a penalty to the excess portion when the simulated capacity is lower than the experimental capacity; The voltage step penalty is used to detect and penalize abnormal voltage abrupt changes in the simulated curve.

6. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 3, characterized in that, S3 also includes corrections to the kinetic parameters, considering the influence of electrode porosity and tortuosity factor on the diffusion coefficient and conductivity. The corrected expressions for the effective diffusion coefficient and effective conductivity are as follows: ； ； in, , The effective diffusion coefficient and effective conductivity are the corrected values. Electrode porosity, , The intrinsic diffusion coefficient and conductivity are, The electrode tortuosity factor. The determination was performed using the symmetrical electrode method.

7. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 1, characterized in that, In S4, the simulation process for solid electrolyte interface film growth includes: The initial values ​​are set, including the initial lithium ion concentration, potential, initial interface reaction current density, and initial solid electrolyte interface film thickness and impedance. After entering the iterative solution step, the lithium-ion intercalation current density of the main reaction and the side reaction current density of solid electrolyte interface film thickening are calculated based on the current local overpotential. This process includes kinetic constraints or diffusion constraints. Solve the liquid phase potential equation and solid phase potential equation based on the updated current distribution; The calculated total interfacial reaction current density is compared with the total interfacial reaction current density of the previous iteration. If the difference is less than the tolerance, convergence is determined. The thickness, porosity and active lithium loss of the solid electrolyte interfacial film at the next moment are updated according to Faraday's law, and the calculation of the next iteration is performed. If the difference is greater than the tolerance, the interfacial current density value is updated and iterative calculation is performed. During the iteration process, the implicit finite difference algorithm is used to solve this set of partial differential equations coupled with multiphysics.

8. The fast-charging numerical simulation method for thick electrodes of lithium-ion batteries according to claim 7, characterized in that, In S4, the electrochemical model for simulating the growth of a solid electrolyte interface film includes: The growth of solid electrolyte interfacial films is described as an electrochemical consumption process involving solvents, electrons, and lithium ions, with the following reaction equation: ； in, Indicates solvent, Represents electron, Indicates lithium ions. express, Indicates the solid electrolyte interface film; During charging, both the intercalation reduction main reaction and the solid electrolyte interfacial film reaction occur simultaneously on the anode surface, resulting in a local total current density. The expression is as follows: ； in, This represents the exchange current flux of the intercalation reduction main reaction. This represents the exchange current flux of the solid electrolyte interfacial membrane reaction; The exchange current flux of the solid electrolyte interfacial membrane reaction is described using the modified Butler-Volmer form, as shown in the following expression: ； ； in, This represents the exchange current density at the solid electrolyte interface membrane. F Denotes Faraday's constant. Indicates the transfer coefficient of the SEI reaction. R The gas constant is T Absolute temperature, unit: K , Indicates SEI overpotential. Represents solid-state potential. Represents the liquid phase potential. This represents the open-circuit potential for SEI film growth; The difference between kinetically limited and diffusion-limited reactions lies in the definition of the solid electrolyte interfacial membrane exchange current density. In the kinetically limited model, the solid electrolyte interfacial membrane exchange current density is treated as a constant fitting parameter. In the diffusion-limited model, the solid electrolyte interfacial membrane exchange current density considers the diffusion process of solvent molecules, and in this case, the solid electrolyte interfacial membrane exchange current density is dynamically related to the solvent concentration, as expressed below: ； ； in, This represents the SEI reaction rate constant. This indicates the electrolyte concentration at the SEI / electrolyte interface. Indicates SEI porosity. Indicates the concentration of the liquid electrolyte. Indicates the thickness of the SEI film. This represents the diffusion coefficient of Li in the electrolyte.

9. A computer device, characterized in that, Including memory and processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the fast-charging numerical simulation method for thick electrodes of lithium-ion batteries as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the fast-charging numerical simulation method for a thick electrode of a lithium-ion battery as described in any one of claims 1 to 8.

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