A method for designing electrode structure based on cellular automaton model

Abstract

The application relates to an electrode structure design method based on a cellular automaton model, which comprises the following steps: establishing a lithium ion reaction diffusion model of a battery charging process based on a cellular automaton; obtaining a reaction quantity space distribution of the model based on a finite difference method; applying the obtained reaction quantity space distribution to a lithium ion concentration updating process of each position in the model according to an interaction rule of the model; verifying the model based on a P2D model to determine an applicable current range of the model; and designing a layered structure of a battery electrode based on the model, and simulating and evaluating the electrode structure based on the model. The application can simulate a dynamic evolution process of lithium ions in an electrolyte and electrode particles in a charging process at a low calculation cost, has an intuitive visual effect, avoids equation solving under a complex solid-liquid boundary, can effectively improve simulation efficiency, and can design an electrode structure capable of improving battery charging efficiency through the model.

Description

Technical Field

[0001] This application relates to the field of electrode structure design technology using mathematical models and dynamic simulations, and in particular to an electrode structure design method based on a cellular automata model. Background Technology

[0002] Battery technology, due to its high energy conversion efficiency and long cycle life, is widely used in various portable devices and electric vehicles. Meanwhile, the battery's fast-charging capability is considered a key factor in further improving product performance. During fast charging, the large current applied often leads to a rapid voltage increase, resulting in only a small amount of charge being delivered by the cutoff voltage, i.e., low charging efficiency. This phenomenon is essentially caused by the difference in speed between electron movement and ion diffusion within the electrode. Electrons move quickly, while reactants diffuse slowly; the accumulation of electrons causes the potential to deviate from the equilibrium potential, forming a high potential difference, a phenomenon also known as concentration polarization. The rate of ion diffusion is strongly correlated with the morphology of electrode particles. Therefore, optimizing the ion diffusion path by changing the electrode morphology to alleviate concentration polarization is an effective method to improve battery charging efficiency. Traditional research uses experimental methods to construct electrodes with different morphologies and then tests the battery's charge-discharge performance. However, the electrode manufacturing process involves multiple steps such as solution preparation, coating, and drying, which are expensive in terms of both time and cost. Therefore, using mathematical models and numerical simulations to design and evaluate electrode structures, and then guiding experimental research, is a more efficient research approach.

[0003] The establishment of battery models requires consideration of both computational efficiency and accuracy. Depending on the model's focus, its application range varies. For example, the equivalent circuit model, widely used in SOC prediction, simplifies the complex internal structure of the battery into a combination of circuit elements, achieving efficient model operation and solving problems such as operating condition optimization and long-cycle lifetime prediction. However, the equivalent circuit model cannot consider the spatiotemporal distribution of concentration within the electrodes and cannot provide a microscopic process explanation for the simulation results of macroscopic variables; therefore, it cannot be used for electrode morphology design. The SP (singleparticle) model, as the simplest electrochemical mechanism model, simplifies both the positive and negative electrodes into single spherical particles. It uses Fick's diffusion law to calculate the ion concentration diffusion inside the sphere and the BV equation to calculate the reaction amount on the particle surface, thus obtaining the evolution process of concentration within the spherical particle while maintaining high computational efficiency. However, because the influence of the liquid electrolyte is ignored, the computational accuracy of this model rapidly decreases under high current conditions, making it difficult to apply to electrode morphology design for fast charging. The MP (multi-particles) model, an improved version of the SP model, calculates the reaction and diffusion processes within multiple particles of different sizes, thus considering combinations of electrode particles with varying diameters, i.e., particle size distribution. However, this model still cannot account for the influence of the positional distribution of electrode particles on battery performance. The P2D (pseudo two-dimensional) model, based on concentrated solution theory and porous electrode theory, assumes uniform distribution and size of electrode particles. Variables in the electrolyte are solved only in the one-dimensional x-direction, while variables in the electrode particles are solved only in the direction of the spherical radius r. It also considers the correction of model parameters such as diffusion coefficient and conductivity based on porosity. The P2D model can obtain the spatial distribution of concentration and potential within the electrode during charge and discharge. The electrode morphology is described by two lumped parameters: particle size and porosity, which can, to some extent, account for the influence of electrode morphology on battery performance. However, the non-uniform distribution and irregular shape of electrode particles have been proven to have a significant impact on battery performance, which the P2D model cannot consider when designing electrode morphology. The MSMD (multi-scale multi-domain) model divides the entire battery space into particle domains, electrode domains, and battery domains based on different length scales. Adjacent domains interact only through regional averages. This modeling method effectively balances computational efficiency while considering the interactions of variables across multiple length scales. However, the use of averages causes the model to lose spatial distribution information of concentration, which is crucial for electrode morphology design. The models described above, through simplification of the actual process to achieve efficient operation, are all computationally efficiency-oriented, sacrificing computational accuracy. Therefore, they cannot consider the irregular morphology and non-uniform spatial distribution of electrode particles.If computational efficiency is not a concern, and only computational accuracy and close resemblance to actual electrodes are desired, CFD (computational fluid dynamics) models are a good choice. They can visualize the concentration evolution inside electrode particles of arbitrary shape and spatial distribution, and can be implemented in both two-dimensional and three-dimensional spaces. However, these models often consist of a large number of coupled partial differential equations, resulting in slow computation speeds and limitations in the optimization of batch electrode structures.

[0004] In summary, existing models, when considering the impact of electrode morphology on battery performance, overemphasize either efficiency or accuracy, failing to simulate the spatiotemporal evolution of ion concentration in irregular and non-uniform electrode particles during charging and discharging at a relatively low computational cost. However, electrode structure design is becoming increasingly refined and diverse, and non-uniform arrangements of electrode particles can exhibit better performance in certain situations. Therefore, a new model framework is needed to assist in the design of novel electrode structures. Summary of the Invention

[0005] This application provides an electrode structure design method based on a cellular automata model. By combining the cellular automata model with the finite difference method and setting simple local interaction rules, it simulates the dynamic evolution of lithium ions in the electrolyte and electrode particles during charging at a low computational cost. It has an intuitive visualization effect, avoids solving equations under complex solid-liquid boundaries, and can effectively improve simulation efficiency. The model can consider the non-uniform distribution and irregular shape of electrode particles, and has greater flexibility in electrode structure design. Within a certain porosity range, the layered structure can effectively alleviate concentration polarization compared with the uniform structure. Electrode structures that can improve battery charging efficiency can be designed using this model.

[0006] In a first aspect, this application provides an electrode structure design method based on a cellular automata model. The method includes: establishing a lithium-ion reaction-diffusion model for the battery charging process based on a cellular automata; obtaining the spatial distribution of the reaction amount in the model based on the finite difference method; applying the obtained spatial distribution of the reaction amount to the lithium-ion concentration update process at each position in the model according to the interaction rules of the model; validating the model based on a P2D model to determine the applicable current range of the model; performing a layered structure design for the battery electrode structure based on the model; and simulating and evaluating the electrode structure based on the model.

[0007] Optionally, the lithium-ion reaction-diffusion model for the battery charging process based on cellular automata includes: dividing the lithium-ion reaction-diffusion process for battery charging into two parts: the diffusion of lithium ions in the solid and liquid phases and the reaction of lithium ions at the solid-liquid boundary.

[0008] The cellular automaton consists of a grid, states, neighbors, and rules, and can be represented as MCA1 = {G, N, S, R}.

[0009] The cellular automaton's grid can be represented as G = {(i,j), i = 1, 2, ..., I, j = 1, 2, ..., J}, where (i,j) represents the cell's coordinate position, and I and J are the total number of rows and columns of the grid, respectively. The cellular automaton's neighbors can be represented as N(i,j) = {(i-1,j), (i,j-1), (i,j+1), (i+1,j)}, where the value and state of each cell are only affected by its four neighbors (up, down, left, and right). The cellular automaton's state can be represented as S = {A,C}, where matrix A records the phase state of each cell, 0 represents the electrolyte phase, 1 represents the solid phase at the non-boundary, and 2 represents the solid phase boundary. Matrix C records the ion concentration of each cell. The interaction rules R between the cellular automata include two diffusion rules and two reaction rules, with different implementation conditions, described by formula (1):

[0010]

[0011] In the formula, rule 1 is the solid-phase diffusion rule, rule 2 is the rule governing the effect of the reaction on the solid-phase boundary cell, rule 3 is the rule governing the effect of the reaction on the liquid-phase cell, rule 4 is the liquid-phase diffusion rule, and Δt s Δt represents the time step of solid-phase diffusion. e Δt represents the time step of liquid-phase diffusion. r Let t represent the time step of the reaction, and let t represent time. The update step of time is Δt, and Δt is a common factor of the other three time steps.

[0012] Optionally, the interaction rule R between cells includes two diffusion rules and two reaction rules, with different implementation conditions for each rule, including: when t / Δt s When the integer is used, rule 1 is applied. The specific form of rule 1 is shown in formula (2):

[0013]

[0014] In the formula, c s D represents the solid-phase lithium-ion concentration. s Let F be the solid-phase diffusion coefficient, Δx be the cell side length, and F be the 0-1 matrix. s The setting is to prevent the exchange of matter between the liquid phase cell and the solid phase cell, where the value of the position of the solid phase cell is 1 and the value of the position of the liquid phase cell is 0.

[0015] When t / Δt r When the integer is an integer, rules 2 and 3 are executed, specifically described by formulas (3) and (4):

[0016] rule 2: c s (i, j, t+Δt) r ) = c s (i, j, t) + (J Li (j) / D s )×Δx×Δt r (3)

[0017] rule 3: c e (i, j, t+Δt) r ) = c e (i, j, t) + (J Li (j) / D s )×Δx×Δt r ×V A＝2 (j) / V A＝0 (j) (4)

[0018] In the formula, J Li (j) represents the reaction amount in column j, which will be calculated using the finite difference method in the next step. V A＝2 (j) represents the volume occupied by the solid boundary cell in column j, V A＝0 (j) represents the volume occupied by the liquid phase cell in column j.

[0019] When t / Δt e When the integer is used, rule 4 is applied, which is specifically described by formula (5):

[0020]

[0021] In the formula, c e D represents the concentration of lithium ions in the liquid phase. e Let F be the liquid phase diffusion coefficient, and F be the 0-1 matrix. e The value of the solid phase cell is 0, and the value of the liquid phase cell is 1.

[0022] Optionally, obtaining the spatial distribution of the reaction amount of the model based on the finite difference method includes: setting the initial reaction amount, the initial value of the solid phase reference potential, and the initial value of the liquid phase reference potential at each location, denoted as the initial value, and the initial reaction amount is described by (19):

[0023]

[0024] The initial reference potentials for both the solid and liquid phases are set to 0.

[0025] Based on the set initial values ​​and using the finite difference method, the solid-phase potential and liquid-phase potential at each location are obtained. Based on the obtained solid-phase potential and liquid-phase potential at each location, the reaction quantity distribution is described using the BV equation, resulting in newly calculated reaction quantity values, solid-phase reference potential values, and liquid-phase reference potential values, which are recorded as data values. The initial values ​​are compared with the data values ​​to obtain the difference. If the difference is within a preset range, the calculated data value is output as the reaction quantity distribution at this moment. If it is not within the preset range, the data value is used as a new initial value to calculate the solid-phase potential and liquid-phase potential at each location using the finite difference method. The above steps are repeated until the difference reaches the preset range, thus obtaining the reaction quantity distribution. The preset range can be set to less than 1*10^-10 mol / (m 2 ·s).

[0026] Optionally, the step of obtaining the solid-phase potential and liquid-phase potential at each location based on the set initial reaction amount, initial value of solid-phase reference potential, and initial value of liquid-phase reference potential using the finite difference method includes: calculating the solid-phase potential distribution, which is described by formulas (6)-(9):

[0027]

[0028]

[0029]

[0030]

[0031] In the formula, φ s Let J be the solid-state potential, σ be the solid-state conductivity, and J be the solid-state conductivity. Li V represents the amount of reaction. - and V + L represents the solid-state reference potential of the negative electrode and the solid-state reference potential of the positive electrode, respectively. n L s and L p These represent the thicknesses of the negative electrode, the separator, and the positive electrode, respectively, where F is the Faraday constant, and a s Let be the specific surface area of ​​the electrode; calculate the liquid phase potential distribution, which is described by formulas (10)-(12):

[0032]

[0033]

[0034]

[0035] In the formula, φ eLet κ be the liquid phase potential, and κ be the liquid phase conductivity. D For diffusion conductivity, t + The transference number of the cation. The average molar activity coefficient is used; the solid-state potential is discretized using the finite difference method and described by equation 16-17:

[0036]

[0037]

[0038] In the formula, the subscripts n and p represent the negative electrode and the positive electrode, respectively, and the subscripts N and P represent the number of discrete points in the positive electrode region and the negative electrode region, respectively; the liquid phase potential is discretized according to the finite difference method and described by formula (18):

[0039]

[0040] In the formula, the subscript N e This indicates the number of discrete points in the electrolyte region within the entire battery.

[0041] Optionally, the step of describing the reaction quantity distribution based on the obtained solid-phase potential and liquid-phase potential at each location using the BV equation to obtain newly calculated reaction quantity values, solid-phase reference potential values, and liquid-phase reference potential values, which are recorded as data values, specifically includes: describing the reaction quantity distribution based on the obtained solid-phase potential and liquid-phase potential at each location using the BV equation to obtain newly calculated reaction quantity values, described by formula 13:

[0042]

[0043] In the formula, the oxidation transfer coefficient, α c Here, E0 is the reduction transfer coefficient, R is the equilibrium potential, and T is the gas constant; the solid-phase reference potential and the liquid-phase reference potential are described by Equation 14:

[0044]

[0045] In the formula, V ± V is the solid-state reference potential. e Here is the liquid phase reference potential. The sum of the reaction amounts at each location is limited by the total number of electrons supplied by the external circuit per unit time, as described by Equation 15:

[0046]

[0047] In the formula, I is the current passing through a unit cross-sectional area, and J Li The values ​​represent the reaction amounts; the subscript n indicates the negative electrode, and the subscript p indicates the positive electrode.

[0048] Optionally, the process of applying the spatial distribution of the reaction amount obtained according to the interaction rules of the model to update the lithium ion concentration at various locations in the model includes: calculating t / Δt r Whether the result is an integer determines whether a reaction has occurred. If it is an integer, a reaction has occurred. The reaction amount at each location is then calculated using the finite difference method, ignoring the effect of diffusion on concentration during the reaction calculation. Then, rules 2 and 3 of the cellular automata model are executed. Based on the calculated t / Δt... s Whether the result is an integer determines whether solid-state diffusion has occurred. If it is an integer, a reaction has occurred, and rule 1 of the cellular automata model is executed, allowing the diffusion process to evolve within the solid-state cell for a certain period of time; based on the calculated t / Δt... e Whether it is an integer determines whether liquid-phase diffusion has occurred. If it is an integer, a reaction has occurred, and rule 4 of the cellular automata model is executed, allowing the diffusion process to evolve in the liquid-phase cell for a period of time.

[0049] Optionally, the verification of the model based on the P2D model to determine the applicable current range of the model includes: simulating the charging of the battery under 1C to 4C charging conditions with the P2D model and the model respectively under the same parameters, comparing the state of charge change curves and voltage change curve variables of the negative and positive electrodes; and verifying the simulation effect based on the average relative error evaluation index of the voltage curve.

[0050] Optionally, the step of designing a layered structure for the battery electrode based on the model, and simulating and evaluating the electrode structure based on the model, includes: maintaining a constant positive electrode morphology and applied current, designing three layered electrode structures for the battery negative electrode, simulating the charging performance of the electrodes with different morphologies of the three layered electrode structures based on the P2D model and the cellular automata model; evaluating the charging performance of the electrodes with different morphologies of the three layered electrode structures based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode; wherein, the three battery structures are: the first layered structure is a porosity layered structure, with high porosity in the part near the positive electrode to ensure unobstructed liquid phase channels and reduce liquid phase diffusion resistance, while low porosity is used in the part away from the positive electrode; the second layered structure is a particle size layered structure, with larger particle size in the part near the positive electrode to reduce liquid phase diffusion resistance, and smaller particle size in the part away from the positive electrode to reduce solid phase diffusion resistance; the third layered structure is a particle size layered structure, with small particle size in the part near the positive electrode and large particle size in the part away from the positive electrode.

[0051] Optionally, the evaluation of the charging performance of the three layered electrode structures with different morphologies based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode includes: based on the porosity layered structure setting, based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, it is found that when the porosity is low, the liquid phase diffusion resistance is the main limiting factor, and porosity layering or particle size layering design can be adopted; based on the particle size layered structure setting, based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, it is found that when the porosity is high, the solid phase diffusion resistance is the main limiting factor, and in this case, small particles can be used in the entire electrode area instead of a layered design.

[0052] This application has at least the following advantages:

[0053] According to the technical content provided in the embodiments of this application, a lithium-ion reaction-diffusion model for the battery charging process is established based on cellular automata. The spatial distribution of the reaction quantity in the model is calculated using the finite difference method, and then the calculated reaction quantity is returned to the cellular automata model. This enables the simulation of the dynamic evolution of lithium ions in the electrolyte and electrode particles during charging at a lower computational cost. By comparing the results with the classic P2D model, the applicability of the model in a large current range is verified. Compared with traditional battery models, this model can consider the non-uniform distribution and irregular shape of electrode particles, and has greater flexibility in electrode structure design. Based on this model and the understanding of the dominant mass transfer resistance at different locations, two layered electrode structures, porosity layering and particle size layering, are designed. Simulations have demonstrated that within a certain porosity range, the layered structure can effectively alleviate concentration polarization compared to the uniform structure. Furthermore, an electrode structure that can improve battery charging efficiency can be designed using this model. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating an electrode structure design method based on a cellular automata model in one embodiment;

[0055] Figure 2 Here is a flowchart illustrating an electrode structure design method based on a cellular automata model in one embodiment;

[0056] Figure 3 This is a flowchart illustrating different rule enforcement conditions based on a cellular automata model in one embodiment;

[0057] Figure 4 This is a schematic diagram illustrating the process of obtaining the spatial distribution of the reaction quantity of the model based on the finite difference method in one embodiment;

[0058] Figure 5This is a schematic diagram illustrating the process of calculating the solid-phase potential and liquid-phase potential at various locations in one embodiment.

[0059] Figure 6 This is a schematic diagram illustrating the process of updating the model based on the corresponding rules of the model according to the reaction amount at each location in one embodiment;

[0060] Figure 7 This is a schematic diagram illustrating the concentration information transfer between the cellular automata model and the finite difference method in one embodiment;

[0061] Figure 8 This is a flowchart illustrating a process for validating a cellular automata model based on a P2D model to determine the applicable current range of the model in one embodiment.

[0062] Figure 9 This is a schematic diagram showing a comparison of simulation results between the P2D model and the cellular automata model under condition 1C in one embodiment;

[0063] Figure 10 This is a schematic diagram showing the spatial distribution of the electrode phase concentration when the cutoff voltage is reached under conditions 1C (a) and 4C (b) in one embodiment;

[0064] Figure 11 This is a schematic diagram illustrating the process of designing a layered structure for a battery electrode structure based on a model and simulating and evaluating the electrode structure in one embodiment.

[0065] Figure 12 This is a schematic diagram showing the structure of three types of layered electrodes in one embodiment;

[0066] Figure 13 This is a flowchart illustrating the evaluation of the charging performance of three different morphological electrodes with three layered electrode structures in one embodiment.

[0067] Figure 14 This is a schematic diagram showing the reaction amount curves and terminal voltage curves of a porosity-layered electrode and a uniform electrode in one embodiment.

[0068] Figure 15 This is a schematic diagram showing the spatial concentration distribution of a porosity-layered electrode and a uniform electrode in one embodiment;

[0069] Figure 16 This is a schematic diagram showing the reaction amount curves of a particle size-stratified electrode and a uniform electrode in one embodiment;

[0070] Figure 17 This is a schematic diagram showing the spatial concentration distribution of a particle size-stratified electrode and a uniform electrode in one embodiment;

[0071] Figure 18This is a flowchart of an electrode structure design system based on a cellular automata model in one embodiment;

[0072] Figure 19 This is a schematic structural diagram of a computer device in one embodiment. Detailed Implementation

[0073] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the scope of the present application.

[0074] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when used in this specification, the words “comprising” and / or “including” indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0075] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the various embodiments of this application to facilitate a better understanding of the application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the various embodiments below is for ease of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0076] Figure 1 A flowchart illustrating an electrode structure design method based on a cellular automata model, as provided in this application embodiment, is shown below. Figure 1 As shown, the method may include the following steps:

[0077] S201. Establish a lithium-ion reaction-diffusion model for the battery charging process based on cellular automata;

[0078] S202. The spatial distribution of the reaction quantity in the model is obtained based on the finite difference method;

[0079] S203. Apply the obtained spatial distribution of reaction amount to the lithium ion concentration update process at each location in the model according to the interaction rules of the model.

[0080] S204. Validate the model based on the P2D model to determine the applicable current range of the model;

[0081] S205. Based on the model, a layered structure design for the battery electrode structure is carried out, and the electrode structure is simulated and evaluated based on the model.

[0082] The following is a detailed explanation of each step:

[0083] S201. Establish a lithium-ion reaction-diffusion model for the battery charging process based on cellular automata;

[0084] like Figure 1 As shown in this embodiment, it should be noted that cellular automata (CA) enables the system to achieve an evolutionary process that follows natural laws by setting simple local interaction rules, while also providing intuitive visualization. This avoids solving equations under complex solid-liquid boundaries, effectively improving simulation efficiency. During battery charging and discharging, ions diffuse from the electrolyte to the particle boundaries, react, and then enter the solid particles to continue diffusing. Cellular automata can describe this process through simple cellular interaction rules. A lithium-ion reaction-diffusion model (CA-FD) for the battery charging process is established based on cellular automata. This model can describe different states of lithium-ion reaction-diffusion, visualize the two-dimensional evolution of ion concentration during charging and discharging, and thus evaluate the performance of different electrode morphologies based on the established model.

[0085] S202. The spatial distribution of the reaction quantity in the model is obtained based on the finite difference method;

[0086] In this embodiment, it should be noted that the finite difference method is an important discrete mathematics method. Its idea is to replace partial derivatives or derivatives with difference quotients, discretizing partial differential equations or systems of differential equations into a system of difference equations for solution. Specifically, the diffusion process of ions is simulated using the simple local evolution rules of cellular automata, and then the finite difference method (FD) can be used to solve for the reaction quantities and potentials at each location, so that the calculated reaction quantities and potentials can be returned to the corresponding cells later.

[0087] S203. Based on the interaction rules of the model, the obtained spatial distribution of reaction amount is applied to the lithium ion concentration update process at each location in the model.

[0088] In this embodiment, it should be noted that after the reaction quantity and potential at each position can be solved using the finite difference method (FD), the calculated reaction quantity is returned to the cellular automata model, and the reaction quantity value is added or subtracted at the corresponding position to complete the hybrid modeling, so as to facilitate subsequent battery topography research and effectively reduce the computational cost.

[0089] S204. Validate the model based on the P2D model to determine the applicable current range of the model;

[0090] In this embodiment, it should be noted that the P2D model has been widely used in battery simulation research. Here, the P2D model, which has been maturely applied in battery simulation research, is used as a verification and comparison model to accurately verify the current applicability of the model.

[0091] S205. Based on the model, a layered structure design for the battery electrode structure is carried out, and the electrode structure is simulated and evaluated based on the model.

[0092] In this embodiment, it is important to explain the electrode structure design based on the model, i.e., the application research of the model. The main advantage of the established model is that it can consider the influence of arbitrary electrode morphology on charging performance. As long as the constructed electrode morphology image is used as the positive or negative electrode for simulation, the electrode structure can be simulated. Through the simulation results, the battery structure design can be determined, thereby effectively alleviating concentration polarization and designing an electrode structure that can improve battery charging efficiency.

[0093] Reference Figure 1 , Figure 2 As shown, in some embodiments, in S201, a lithium-ion reaction-diffusion model for the battery charging process is established based on a cellular automaton, including: dividing the lithium-ion reaction-diffusion process into two parts: the diffusion of lithium ions in the solid and liquid phases and the reaction of lithium ions at the solid-liquid boundary; the cellular automaton consists of a grid, states, neighbors, and rules, and can be represented as MCA1 = {G, N, S, R}; where the grid of the cellular automaton can be represented as G = {(i, j), i = 1, 2, ..., I, j = 1, 2, ..., J}, (i, j) represents the coordinate position of the cell, and I and J are the total number of rows and columns of the grid, respectively. The neighbors of a cellular automaton can be represented as N(i,j)={(i-1,j),(i,j-1),(i,j+1),(i+1,j)}. The value and state of each cellular automaton are only affected by its four neighbors (up, down, left, and right). The state of a cellular automaton can be represented as S={A,C}. Matrix A is used to record the phase state of each cell, where 0 represents the electrolyte phase, 1 represents the solid phase at the non-boundary, and 2 represents the solid phase boundary. Matrix C is used to record the ion concentration of each cell. The interaction rule R between cellular automata includes two diffusion rules and two reaction rules. The implementation conditions of different rules are different and can be described by formula (1):

[0094]

[0095] In the formula, rule 1 is the solid-phase diffusion rule, rule 2 is the rule governing the effect of the reaction on the solid-phase boundary cell, rule 3 is the rule governing the effect of the reaction on the liquid-phase cell, rule 4 is the liquid-phase diffusion rule, and Δt s Δt represents the time step of solid-phase diffusion.e Δt represents the time step of liquid-phase diffusion. r Let t represent the time step of the reaction, and let t represent time. The update step of time is Δt, and Δt is a common factor of the other three time steps.

[0096] In this embodiment, it should be noted that a model framework is established based on the grid, state, neighbors, and rules of the cellular automaton to determine the lithium-ion reaction diffusion state during the battery charging process. Then, according to the preset rules, corresponding calculations are performed to simulate the lithium-ion reaction diffusion state based on the cellular automaton, so as to simulate the battery charging process in the future.

[0097] Reference Figure 2 , Figure 3 As shown, in some embodiments, in S201, the interaction rule R between cells includes two diffusion rules and two reaction rules, with different implementation conditions for each rule, including:

[0098] S2011, when t / Δt s When the integer is used, rule 1 is applied. The specific form of rule 1 is shown in formula (2):

[0099]

[0100] In the formula, c s D represents the solid-phase lithium-ion concentration. s Let F be the solid-phase diffusion coefficient, Δx be the cell side length, and F be the 0-1 matrix. s The setting is to prevent the exchange of matter between the liquid phase cell and the solid phase cell, where the value of the position of the solid phase cell is 1 and the value of the position of the liquid phase cell is 0.

[0101] S2012, when t / Δt r When the integer is an integer, rules 2 and 3 are executed, specifically described by formulas (3) and (4):

[0102] rule 2: c s (i, j, t+Δt) r ) = c s (i, j, t)-(J) Li (j) / D s )×Δx×Δt r (3)

[0103] rule 3: c e (i, j, t+Δt) r ) = c e (i, j, t) + (J Li (j) / D s )×Δx×Δt r ×V A＝2 (j) / VA＝0 (j) (4)

[0104] In the formula, J Li (j) represents the reaction amount in column j, which will be calculated using the finite difference method in the next step. V A＝2 (j) represents the volume occupied by the solid boundary cell in column j, V A＝0 (j) represents the volume occupied by the liquid phase cell in column j;

[0105] S2013, when t / Δt e When the integer is used, rule 4 is applied, which is specifically described by formula (5):

[0106]

[0107] In the formula, c e D represents the concentration of lithium ions in the liquid phase. e Let F be the liquid phase diffusion coefficient, and F be the 0-1 matrix. e The value of the solid phase cell is 0, and the value of the liquid phase cell is 1.

[0108] In this embodiment, it should be noted that formulas (2) and (5) are derived from Fick's diffusion law, which is consistent with the spatial location and time of Fick's diffusion law. Its first law describes the relationship between diffusion flux and concentration gradient, i.e., "diffusion driving force". The second law describes the change of species concentration with time during diffusion. If only one-dimensional diffusion is considered, it can be expressed as gas as diffusion flux, i.e., the amount of substance P passing through a unit cross section along the x-axis per unit time, and is the diffusion coefficient, i.e., the diffusion flux under a unit concentration gradient. In electrochemical research, Fick's law is the starting point for dealing with diffusion overpotential and calculating diffusion current. Formula (3) is derived from the solid boundary conditions in the P2D model, and formula (4) is derived from the law of conservation of mass. Different diffusion states correspond to different calculation rules, thereby constructing an accurate model. In addition, in the cellular automata model, the upper and lower boundaries adopt periodic boundaries, which means that the simulation results can be easily extended to a larger region with similar electrode morphology. The left and right boundaries adopt zero flux boundaries to ensure that no external substances enter the system.

[0109] Reference Figure 1 , Figure 4 As shown, in some embodiments, in S202, the spatial distribution of the model's reaction quantity is obtained based on the finite difference method, including:

[0110] S2021. Set the initial reaction amount, the initial value of the solid phase reference potential, and the initial value of the liquid phase reference potential at each location, and record them as the initial values. The initial reaction amount is described by (19):

[0111]

[0112] The initial reference potentials for both the solid and liquid phases are set to 0.

[0113] S2022. Based on the set initial values ​​and the finite difference method, obtain the solid phase potential and liquid phase potential at each position;

[0114] S2023. Based on the obtained solid-phase potential and liquid-phase potential at each position, describe the reaction amount distribution based on the BV equation to obtain the newly calculated reaction amount value, solid-phase reference potential value and liquid-phase reference potential value, which are recorded as data values.

[0115] S2024. Compare the initial value with the data value to obtain the difference. If the difference is within the preset range, output the calculated data value as the reaction quantity distribution at this moment.

[0116] S2025. If the data value is not within the preset range, the solid phase potential and liquid phase potential at each position are calculated using the finite difference method, and the above steps are repeated until the difference reaches the preset range to obtain the reaction amount distribution.

[0117] The preset range can be set to the difference being less than 1*10^-10 mol / (m 2 ·s).

[0118] In this embodiment, it should be noted that the Poisson equation has wide applications in physics, engineering, computer science, and other fields. In physics, it is used to describe physical phenomena such as electric fields, magnetic fields, and gravitational fields. Solving the Poisson equation is an important mathematical problem. Because this equation is a partial differential equation, its solution requires the use of advanced mathematical tools, such as analysis and partial differential equation theory. In practical applications, numerical methods are usually used to solve this equation, such as the finite element method and the finite difference method. The BV equation is used to calculate the rate of change of the potential on the electrode with respect to ion concentration.

[0119] Specifically, in the electrochemical model, the potential distribution and the reaction amount distribution influence each other. The potential distribution is generally described by the Poisson equation, and the reaction amount distribution is generally described by the BV equation. At the same time, these two partial differential equations are coupled and cannot be solved independently. The Poisson equation described by formula (6) has the potential φ on the left and the reaction amount J on the right. The BV equation described by formula (13) has the reaction amount J on the left and the potential φ on the right. These two equations must be satisfied at every position.

[0120] Here, the solid-phase potential and liquid-phase potential distribution are first described by the Poisson equation, and the reaction quantity distribution is obtained by the BV equation. Then, the finite difference method is used to solve the problem, ensuring that both equations are satisfied at every position, to obtain the final reaction quantity distribution, which can then be used to interactively update the model.

[0121] In some embodiments, refer to Figure 4 , Figure 5 As shown in S2022, based on the set initial reaction amount, initial value of solid-phase reference potential, and initial value of liquid-phase reference potential, the solid-phase potential and liquid-phase potential at each position are obtained using the finite difference method, including:

[0122] S20221. Calculate the solid-state potential distribution, which is described by formulas (6)-(9):

[0123]

[0124]

[0125]

[0126]

[0127] In the formula, φ s Let J be the solid-state potential, σ be the solid-state conductivity, and J be the solid-state conductivity. Li V represents the amount of reaction. - and V + L represents the solid-state reference potential of the negative electrode and the solid-state reference potential of the positive electrode, respectively. n L s and L p These represent the thicknesses of the negative electrode, the separator, and the positive electrode, respectively, where F is the Faraday constant, and a s The specific surface area of ​​the electrode;

[0128] S20222. Calculate the liquid phase potential distribution. The liquid phase potential distribution is described by formulas (10)-(12):

[0129]

[0130]

[0131]

[0132] In the formula, φ e Let κ be the liquid phase potential, and κ be the liquid phase conductivity. D For diffusion conductivity, t + The transference number of the cation. The mean molar activity coefficient;

[0133] S20223. The solid-state potential is discretized using the finite difference method, and described by Equation 16-17:

[0134]

[0135]

[0136] In the formula, the subscripts n and p represent the negative pole and the positive pole, respectively, and the subscripts N and P represent the number of discrete points in the positive pole region and the negative pole region, respectively.

[0137] S20224. The liquid phase potential is discretized according to the finite difference method, and described by Equation 18:

[0138]

[0139] In the formula, the subscript N e This indicates the number of discrete points in the electrolyte region within the entire battery.

[0140] In this embodiment, it should be noted that the solid-phase potential and liquid-phase potential are calculated using the Poisson formula, and then the solid-phase potential and liquid-phase potential calculated by the Poisson formula are solved separately using the finite difference method to obtain the final solid-phase potential and liquid-phase potential for subsequent calculation and analysis.

[0141] In some embodiments, refer to Figure 4 As shown in S2023, based on the obtained solid-phase potential and liquid-phase potential at each location, the reaction quantity distribution is described using the BV equation, resulting in newly calculated reaction quantity values, solid-phase reference potential values, and liquid-phase reference potential values, which are denoted as data values. Specifically, these include:

[0142] Based on the obtained solid-phase and liquid-phase potentials at various locations, the reaction quantity distribution is described using the BV equation, resulting in newly calculated reaction quantity values, which are described by Equation 13:

[0143]

[0144] In the formula, the oxidation transfer coefficient, α c Here, E0 is the reduction transfer coefficient, R is the equilibrium potential, and T is the gas constant.

[0145] The solid-phase reference potential and the liquid-phase reference potential are described by Equation 14:

[0146]

[0147] In the formula, V ± V is the solid-state reference potential. e This is the reference potential for the liquid phase.

[0148] The sum of the reaction amounts at each location is limited by the total number of electrons supplied by the external circuit per unit time, as described by Equation 15:

[0149]

[0150] In the formula, I is the current passing through a unit cross-sectional area, and J Li The values ​​represent the reaction amounts; the subscript n indicates the negative electrode, and the subscript p indicates the positive electrode.

[0151] In this embodiment, it should be noted that the distribution of each reaction quantity is obtained through the BV formula. At the same time, it should be considered that in addition to the reaction quantity distribution obtained by the Poisson equation and the BV equation, the sum of the reaction quantities at each position is limited by the total number of electrons supplied by the external circuit per unit time. Based on the calculation, further restrictions are imposed to finally obtain an accurate reaction quantity distribution for subsequent calculation and analysis.

[0152] Under this total constraint, we then use the Poisson equation and the BV equation to calculate which site has more reaction and which site has less reaction.

[0153] In some embodiments, refer to Figure 2 , Figure 6 As shown in S203, the obtained spatial distribution of reaction amounts is applied to the lithium-ion concentration update process at various locations in the model according to the interaction rules of the model, including:

[0154] S2031, Based on the calculation of t / △t r If the result is an integer, determine whether the reaction has occurred. If it is an integer, the reaction has occurred. Then, calculate the reaction amount at each position using the finite difference method, ignoring the effect of diffusion on concentration when calculating the reaction, and then execute rules 2 and 3 of the cellular automata model.

[0155] S2032, Based on the calculation of t / △t s Whether it is an integer determines whether solid-phase diffusion has occurred. If it is an integer, a reaction has occurred, and rule 1 of the cellular automata model is executed, allowing the diffusion process to evolve within the solid-phase cell for a period of time.

[0156] S2033, Based on the calculation of t / △t e Whether it is an integer determines whether liquid-phase diffusion has occurred. If it is an integer, a reaction has occurred, and rule 4 of the cellular automata model is executed, allowing the diffusion process to evolve in the liquid-phase cell for a period of time.

[0157] In this embodiment, it should be noted that the established computational framework has three time steps, namely the solid-phase diffusion time step Δt. s Liquid phase diffusion time step Δt e and reaction time step Δt r .

[0158] In one example, the step length of t is 0.001 seconds, and Δt e For 0.001 seconds, Δt r For 0.005 seconds, Δt s If the time step is 0.01 seconds, then liquid-phase diffusion needs to be calculated for each increment of t, a reaction for every 5 increments, and solid-phase diffusion for every 10 increments. In reality, all processes occur at each time step; only slower processes are calculated at longer intervals, which doesn't introduce error and can even improve calculation speed. Therefore, at each moment, first, based on the calculated t / Δt... r Whether it is an integer determines whether a reaction has occurred. If a reaction has occurred, the finite difference method is used to calculate the reaction amount at each position, and the effect of diffusion on concentration is ignored when calculating the reaction. Then, rules 2 and 3 of the established cellular automata model are executed. Then, the reaction diffusion state is determined, and the corresponding interaction rule is executed according to the corresponding reaction diffusion state.

[0159] In addition, the three time steps can be selected based on the balance between computational efficiency and computational accuracy. If computational accuracy is pursued, the three time steps should all be small, and the concentration change caused by each reaction should be immediately taken into account for its impact on diffusion. Different physicochemical processes have different time scales. Calculating them all with the smallest time step would result in a huge computational load, while using a longer time step for slower processes can effectively improve computational efficiency while maintaining accuracy. Secondly, the partial differential equations used here are all in one-dimensional form, while the cellular automata model is in two-dimensional form. The purpose is to minimize the number of equations that need to be solved, while also considering the influence of the two-dimensional electrode morphology on the diffusion process. Finally, based on the concentration information transfer of the cellular automata model and the finite difference method, as shown in formula (20) and Figure 7 As shown,

[0160]

[0161] That is, the average solid / liquid concentration of each column of the cellular automaton is input to the corresponding position of the finite difference method, and the reaction amount calculated by the finite difference method is uniformly returned to the boundary cells of each column in the cellular automaton model according to rules 2 and 3, thereby realizing the interaction between the finite difference method and the model and realizing the updating of the model.

[0162] In some embodiments, refer to Figure 1 , Figure 8 As shown in S204, the model is validated based on the P2D model to determine the applicable current range of the model, including:

[0163] S2041. Simulate the charging of the battery under 1C to 4C charging conditions using the P2D model and the model respectively under the same parameters, and compare the state of charge change curves and voltage change curves of the negative and positive electrodes.

[0164] S2042. Verify the simulation effect by evaluating the average relative error of the voltage curve.

[0165] In this embodiment, it should be noted that since the P2D model has been widely used in battery simulation research, it is used to verify the proposed computational framework. The P2D model is established under the assumption of uniform particle size distribution; therefore, a similar model is also constructed here. Figure 9 The uniformly distributed electrode particles shown have graphite as the negative electrode material on the left and lithium manganese oxide as the positive electrode material on the right. The equilibrium potentials of the two materials are calculated using formulas (21) and (23). The state of charge (SOC) of the negative and positive electrodes are defined using formulas (22) and (24), respectively, where c s,n and c s,p c represents the solid-phase ion concentrations at the negative and positive electrodes, respectively. smax,n and c smax,p These represent the maximum solid-phase ion concentrations at the negative and positive electrodes, respectively. The values ​​of the remaining parameters are shown in Table 1, ensuring that the parameter values ​​are the same for both models.

[0166]

[0167]

[0168]

[0169]

[0170] Table 1. Parameter values ​​for the P2D model and the CA-FD model.

[0171]

[0172] To test the applicability of the proposed model, the 1C charging current of the simulated battery, i.e., the theoretical current for a full charge in one hour, was calculated using formula (25). The calculated result is approximately 10 A·m. -2 Therefore, the applied current was set to 10 A·m. -2 20A·m -2 30A·m -2 40A·m -2 Simulations were performed in two models to correspond to charging conditions at 1C, 2C, 3C, and 4C charging rates. The simulation results under the 1C condition are as follows: Figure 9As shown, the three macroscopic variables of positive and negative SOC change curves and voltage change curves are selected for comparison. It can be seen that the simulation results of the two models show good consistency. The mean relative deviation (MRD) of the voltage curve is used as a quantitative comparison index and is calculated by formula (26). The mean relative error of the two models under 1C to 4C charging conditions is shown in Table 2. It can be seen that although the mean relative error increases with the increase of current, it remains within 1%. That is, when charging with 4C and below current, the mean relative error of the simulation results of the proposed model and the P2D model can be kept within 1%.

[0173] I 1C = (1-ε)×L×c s max ×|SOC max -SOC min |×F / 3600 (25)

[0174]

[0175] Table 2 shows the average relative error of the calculation results of the CA-FD model and the P2D model.

[0176] 1 10 0.21％ 2 20 0.46％ 3 30 0.70％ 4 40 0.92％

[0177] In addition to the time series of variables, the evolution of the two-dimensional concentration distribution in the electrode particles is also recorded using the proposed CA-FD model, which is something the P2D model cannot achieve. The spatial distribution of the electrode phase concentration at the cutoff voltage is shown below. Figure 10 As shown, the concentration range displayed is set to 0–23000 mol / m³. 3 The closer the color is to red, the higher the concentration; the closer it is to blue, the lower the concentration. It can be seen that as the applied current increases, the gradient effect within the electrode particles intensifies, and under high current conditions, the concentration differences between particles of different sizes and locations become more pronounced. However, in the P2D model, due to the homogenization assumption, all electrode particles exhibit the same concentration distribution. Therefore, this difference is due to the different model assumptions, while the cellular automata model can consider the non-uniform characteristics of particles. Thus, the increased difference in simulation results between the two models is likely caused by the enhanced differences in particle transport properties at high currents, which can further determine the simulation accuracy of the cellular automata-based model (CA-FD).

[0178] In some embodiments, refer to Figure 1 , Figure 11 As shown in S205, the layered structure design of the battery electrode structure is performed based on the model, and the electrode structure is simulated and evaluated based on the model, including:

[0179] S2051. To maintain a constant positive electrode morphology and applied current, three layered electrode structures are designed for the negative electrode of the battery. The charging performance of the electrodes with different morphologies of the three layered electrode structures is simulated based on the P2D model and the cellular automata model.

[0180] S2052. The charging performance of three layered electrode structures with different morphologies is evaluated based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode.

[0181] Among them, reference Figure 12 As shown, the three battery structures are: the first layered structure is a porosity layered structure, where the part near the positive electrode uses high porosity to ensure unobstructed liquid phase channels and reduce liquid phase diffusion resistance, while the part away from the positive electrode uses low porosity; the second layered structure is a particle size layered structure, where the part near the positive electrode uses larger particle size to reduce liquid phase diffusion resistance, while the part away from the positive electrode uses smaller particle size to reduce solid phase diffusion resistance; and the third layered structure is a particle size layered structure, where the part near the positive electrode uses small particle size, while the part away from the positive electrode uses large particle size.

[0182] In this embodiment, it should be noted that the layered structure design of the battery electrode structure is based on the model, which is an application study of the model. The main advantage of the established model is that it can consider the influence of arbitrary electrode morphology on charging performance, as long as the constructed electrode morphology image is used as the positive or negative electrode for simulation. Most existing models are established under the assumption of uniform distribution of electrode particles, and can only change the overall porosity or average particle size of the electrode region to obtain the influence of changes in lumped morphology parameters on the simulation results. However, when using lower porosity or larger particle size in the entire electrode region, although the energy density is higher, it often leads to higher diffusion resistance, causing the system to enter the diffusion-limited stage. When the electrode particles are waiting for diffusion to transport reactants, the electron transport of the external circuit is continuous. The accumulation of electrons will cause the voltage to rise rapidly to the cutoff voltage, resulting in lower charging efficiency, that is, less actual charge is delivered when the cutoff voltage is reached. This phenomenon is also known as concentration polarization. To alleviate concentration polarization without reducing electrode energy density, three layered electrode structures were designed based on a model for the battery anode. The charging performance of the three layered electrode structures with different morphologies was evaluated based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode.

[0183] In some embodiments, refer to Figure 11 , Figure 13 As shown in S2052, the charging performance of three different morphologies of layered electrode structures is evaluated based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, including:

[0184] S20521. Based on the porosity stratification structure, and using the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode as evaluation indicators, it was found that when the porosity is low, the liquid phase diffusion resistance is the main limiting factor. Porosity stratification or particle size stratification design can be adopted to design an electrode structure that can improve battery charging efficiency.

[0185] S20522. Based on the particle size stratification structure setting, and based on the evaluation indicators of cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, it was found that when the porosity is high, the solid phase diffusion resistance is the main limiting factor. At this time, small particles can be used in the entire electrode area instead of stratification design to design an electrode structure that can improve battery charging efficiency.

[0186] In this embodiment, it should be noted that the first evaluation index is the cumulative reaction amount (CRA), which is calculated using formula (27).

[0187] CRA(t)=(SOC n (t)-SOC n，0 )×c s max，n ×L n ×(1-ε n (27)

[0188] Among them, SOC n,0 This represents the initial SOC of the negative electrode. n (t) represents the negative SOC at time t, c smax,n L represents the maximum solid-phase ion concentration at the negative electrode. n For the negative electrode thickness, ε n This represents the negative porosity.

[0189] The second evaluation index is the charging efficiency η, which is calculated by formula (28). It means the ratio of the effective absorption of the negative electrode to the total amount of reactants that the positive electrode can provide.

[0190]

[0191] The third evaluation index is the lithium-ion storage capacity Q of the electrode, which is calculated by formula (29), where F is the Faraday constant.

[0192] Q = c s max，n ×L n ×(1-ε n )×F (29)

[0193] In one example, to demonstrate the superior performance of the designed electrode, an electrode with uniformly distributed particles was used as a control electrode. This was achieved by ensuring that the overall porosity and average particle size of the layered electrode and the control electrode with uniform particle distribution were identical, meaning they had the same storage capacity, differing only in particle location. Furthermore, the applied current was 40 A·m in all simulation cases. -2 The negative and positive electrode regions are both 50 μm × 50 μm in size, and the separator region is 50 μm × 20 μm in size. The charging simulation results of the porosity-layered electrode are presented below. Figure 14 , Figure 15 And as shown in Table 3. When the overall porosity is around 0.55, from Figure 14 As can be seen, through the porosity stratification design, the cumulative reaction curve rises from the green line to the red line, and the voltage curve becomes more stable with a longer voltage plateau. Figure 15 (a) shows the spatial distribution of concentration when the uniform electrode reaches the cutoff voltage. Figure 15 (c) This shows the spatial distribution of concentration at the cutoff voltage for the porosity-layered electrode. A comparison reveals that the porosity-layered design effectively alleviates concentration polarization, allowing more electrode particles in the negative electrode, even those farther from the positive electrode, to effectively absorb lithium ions. Table 3 shows that when the porosity is around 0.55, the porosity-layered design improves charging efficiency by 35%, while the electrode's storage capacity remains almost unchanged. When the porosity is around 0.61, a comparison... Figure 15 (b) and Figure 15 (d) As can be seen, concentration polarization can also be alleviated through porosity stratification design. However, as shown in Table 3, the charging efficiency only increased by 5%, which is not significant. This indicates that with higher porosity, the liquid phase channel is more unobstructed, and the main limiting factor for mass transport is no longer liquid phase diffusion, but solid phase diffusion within the electrode particles. However, adjusting the porosity alone cannot alleviate solid phase diffusion resistance, which is mainly determined by particle size. Therefore, it is necessary to study the positional distribution of particles of different sizes.

[0194] Table 3 Charging efficiency and storage capacity of porosity-layered electrodes and uniform electrodes

[0195]

[0196] The charging simulation results for the particle size-stratified electrode are presented below. Figure 16 , Figure 17 And in Table 4. For easy distinction... Figure 12 (b) and Figure 12 (c) represents two types of particle size stratification structures, which will be discussed later. Figure 12 (b) represents a structure called particle size stratification structure 1. Figure 12(c) represents a structure called particle size stratification 2. When the overall porosity is around 0.55, from Figure 16 (a) It can be seen that using larger particle sizes near the positive electrode effectively increases the cumulative reaction amount, with the cumulative reaction amount curve rising from the green line to the red line. However, using smaller particle sizes near the positive electrode does not significantly improve the reaction amount, and its cumulative reaction amount is almost the same as that of a uniform electrode. Figure 16 (b) As can be seen, using larger particle sizes near the positive electrode effectively extends the voltage plateau, corresponding to higher charging efficiency in Table 3, with a 28% increase in charging efficiency compared to a uniform electrode, while using smaller particle sizes near the positive electrode only improves charging efficiency by 5%. Figure 17 The concentration distribution diagram also shows the performance differences of electrodes with different morphologies. Through comparison... Figure 17 (a) and Figure 17 (c) shows that the particle size stratification structure 1 alleviates concentration polarization, as can be seen through comparison. Figure 17 (a) and Figure 17 (e) shows that the concentration polarization of the particle size stratified structure 2 is similar to that of the uniform structure. This indicates that when the porosity is low, the main limiting factor in the region near the positive electrode is liquid phase diffusion. Using large-diameter particles in this region to reduce liquid phase transport resistance while sacrificing some solid phase diffusion rate is beneficial to improving charging efficiency. However, using small-diameter particles in this region to reduce solid phase transport resistance is not very meaningful.

[0197] When the porosity is around 0.61, neither of the two particle size-related stratification designs can effectively improve the charging efficiency, as shown in the cumulative reaction amount curve and voltage curve. Figure 16 (c) and Figure 16 As shown in (d), the cumulative reaction amount of the layered electrode is lower than that of the uniform electrode. Although the voltage plateau is prolonged, the overall charging efficiency of the two particle size layered structures decreases by 22% and 30%, respectively. Through observation... Figure 17 The concentration distribution diagrams shown in (b,d,f) can explain this phenomenon. At this porosity, the particles are sparse and the liquid phase channels are unobstructed. The main limiting factor is the solid phase diffusion resistance. The use of large-diameter particles, whether near or far from the positive electrode, further increases this main limiting resistance. A significant concentration gradient is formed inside the large-diameter particles, causing the particle surface to be in a saturated state for a long time. The internal volume of the particles is difficult to be effectively utilized. Therefore, the cumulative reaction amount and charging efficiency of the two particle size stratified structures both show a decreasing trend.

[0198] Therefore, at the electrode structure design level, the simulation results of this model lead to the conclusion that when the porosity is low, the liquid phase diffusion resistance is the main limiting factor, and porosity stratification or particle size stratification design can be adopted to design an electrode structure that can improve battery charging efficiency; when the porosity is high, the solid phase diffusion resistance is the main limiting factor, and it is recommended to use the smallest possible particles in the entire electrode area, rather than a stratified design, to design an electrode structure that can improve battery charging efficiency.

[0199] The above steps primarily involve establishing a lithium-ion reaction-diffusion model for the battery charging process based on cellular automata. The spatial distribution of the reaction quantities in the model is calculated using the finite difference method. The calculated reaction quantities are then fed back into the cellular automata model, thus simulating the dynamic evolution of lithium ions in the electrolyte and electrode particles during charging at a relatively low computational cost. Comparison with the results of the classic P2D model verifies the applicability of this model over a wide current range. Compared to traditional battery models, this model can consider the non-uniform distribution and irregular shape of electrode particles, offering greater flexibility in electrode structure design. Based on this model and an understanding of the dominant mass transfer resistance at different locations, two layered electrode structures—porosity layering and particle size layering—were designed. Simulations demonstrate that within a certain porosity range, layered structures can effectively alleviate concentration polarization compared to uniform structures. Furthermore, this model allows for the design of electrode structures that improve battery charging efficiency.

[0200] Reference Figure 18 As shown, this application also provides an electrode structure design system based on a cellular automata model. This system may include: a model framework construction module, a reaction quantity acquisition module, a model construction module, a verification module, and a battery structure simulation module. The main functions of each component module are as follows:

[0201] Module 301 is used to build a model framework module for establishing a lithium-ion reaction-diffusion model of the battery charging process based on cellular automata.

[0202] The reaction quantity acquisition module 302 is used to obtain the spatial distribution of the reaction quantity of the model based on the finite difference method;

[0203] Model module 303 is constructed to apply the obtained spatial distribution of reaction amount to the lithium ion concentration update process at various locations in the model according to the interaction rules of the model.

[0204] The verification module 304 is used to verify the model based on the P2D model in order to determine the applicable current range of the model.

[0205] The battery structure simulation module 305 is used to perform layered structural design of battery electrode structure based on the model, and to simulate and evaluate the electrode structure based on the model.

[0206] According to embodiments of this application, this application also provides a computer device and a computer-readable storage medium.

[0207] like Figure 19 The diagram shown is a block diagram of a computer device according to an embodiment of this application. The term "computer device" is intended to represent various forms of digital computers or mobile devices. The digital computer may include a desktop computer, a portable computer, a workbench, a personal digital assistant, a server, a mainframe computer, and other suitable computers. The mobile device may include a tablet computer, a smartphone, a wearable device, etc.

[0208] like Figure 19 As shown, device 600 includes a computing unit 601, a ROM 602, a RAM 603, a bus 604, and an input / output (I / O) interface 605. The computing unit 601, ROM 602, and RAM 603 are interconnected via the bus 604. The input / output (I / O) interface 605 is also connected to the bus 604.

[0209] The computing unit 601 can execute various processes in the method embodiments of this application according to computer instructions stored in the read-only memory (ROM) 602 or computer instructions loaded from the storage unit 608 into the random access memory (RAM) 603. The computing unit 601 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. The computing unit 601 can include, but is not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. In some embodiments, the methods provided in the embodiments of this application can be implemented as computer software programs, which are tangibly contained in a computer-readable storage medium, such as the storage unit 608.

[0210] RAM 603 may also store various programs and data required for the operation of device 600. Part or all of the computer program may be loaded and / or installed on device 600 via ROM 602 and / or communication unit 609.

[0211] The input unit 606, output unit 607, storage unit 608, and communication unit 609 in device 600 can be connected to I / O interface 605. The input unit 606 can be, for example, a keyboard, mouse, touchscreen, or microphone; the output unit 607 can be, for example, a display, speaker, or indicator light. Device 600 can exchange information and data with other devices through the communication unit 609.

[0212] It should be noted that the device may also include other components necessary for normal operation. It may also include only the components necessary for implementing the solution of this application, without necessarily including all the components shown in the figures.

[0213] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SOCs), payload programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof.

[0214] The computer instructions used to implement the methods of this application may be written in any combination of one or more programming languages. These computer instructions may be provided to the computing unit 601 such that when executed by the computing unit 601, such as a processor, the computer instructions cause the execution of the steps involved in the embodiments of the methods of this application.

[0215] The computer-readable storage medium provided in this application can be a tangible medium that can contain or store computer instructions for performing the steps involved in the method embodiments of this application. The computer-readable storage medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, and other forms of storage media.

[0216] The specific embodiments described above do not constitute a limitation on the scope of protection of this application. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. An electrode structure design method based on a cellular automata model, characterized in that, Includes the following steps: A lithium-ion reaction-diffusion model for the battery charging process was established based on cellular automata. The spatial distribution of the reaction quantity in the model is obtained based on the finite difference method; The obtained spatial distribution of reaction amount is applied to the lithium ion concentration update process at each location in the model according to the interaction rules of the model. The model was validated based on the P2D model to determine the applicable current range of the model; Based on the model, a layered structure design for the battery electrode structure is performed, and the electrode structure is simulated and evaluated based on the model. The lithium-ion reaction-diffusion model for the battery charging process based on cellular automata includes: The lithium-ion reaction diffusion during battery charging is divided into two parts: the diffusion of lithium ions in the solid and liquid phases and the reaction of lithium ions at the solid-liquid boundary. The cellular automaton consists of a grid, states, neighbors, and rules, and can be represented as MCA1 = {G, N, S, R}. The cellular automaton's grid can be represented as G = {(i,j), i = 1,2,…,I, j = 1,2,…,J}, where (i,j) represents the cell's coordinate position, and I and J are the total number of rows and columns of the grid, respectively. The neighbors of the cellular automaton can be represented as N(i,j) = {(i-1, j), (i, j-1), (i, j+1), (i+1, j)}, where the value and state of each cell are only affected by its four neighbors (up, down, left, and right). The state of the cellular automaton can be represented as S = {A,C}, where matrix A records the phase state of each cell, 0 represents the electrolyte phase, 1 represents the solid phase at non-boundary locations, and 2 represents the solid phase boundary. Matrix C records the ion concentration of each cell. The interaction rules R between the cellular automata include two diffusion rules and two reaction rules. The implementation conditions of the different rules are different, and they are described by formula (1): In the formula, rule 1 is the solid-phase diffusion rule, rule 2 is the rule governing the effect of the reaction on the solid-phase boundary cell, rule 3 is the rule governing the effect of the reaction on the liquid-phase cell, rule 4 is the liquid-phase diffusion rule, and Δt s Δt represents the time step of solid-phase diffusion. e Δt represents the time step of liquid-phase diffusion. r The time step represents the reaction, t represents time, and the update step of time is Δt, where Δt is the common factor of the other three time steps; The spatial distribution of the reaction quantity of the model obtained based on the finite difference method includes: The initial reaction amount, the initial solid phase reference potential, and the initial liquid phase reference potential are set at each location and denoted as the initial value. The initial reaction amount is described by (19): The initial reference potentials for both the solid and liquid phases are set to 0. Based on the initial values ​​set, the solid-phase potential and liquid-phase potential at each position are obtained using the finite difference method. Based on the obtained solid-phase potential and liquid-phase potential at each location, the reaction quantity distribution is described based on the BV equation, and the newly calculated reaction quantity value, solid-phase reference potential value and liquid-phase reference potential value are obtained, which are recorded as data values. The initial value is compared with the data value to obtain the difference. If the difference is within a preset range, the calculated data value is output as the reaction quantity distribution at this moment. If the value is not within the preset range, the data value is used as a new initial value to calculate the solid phase potential and liquid phase potential at each position according to the finite difference method. The above steps are repeated until the difference reaches the preset range to obtain the reaction amount distribution. The preset range can be set to less than 1*10^-10 mol / (m 2 ·s); The process of applying the obtained spatial distribution of reaction amount to the lithium ion concentration update at various locations in the model according to the interaction rules of the model includes: Based on the calculation t / △t r Whether it is an integer determines whether the reaction has occurred. If it is an integer, the reaction has occurred. Then, the reaction amount at each position is calculated according to the finite difference method, and the effect of diffusion on concentration is ignored when calculating the reaction. Then, rules 2 and 3 of the cellular automata model are executed. Based on the calculation t / △t s Whether it is an integer determines whether solid-phase diffusion has occurred. If it is an integer, a reaction has occurred, and rule 1 of the cellular automata model is executed, allowing the diffusion process to evolve within the solid-phase cell for a period of time. Based on the calculation t / △t e Whether it is an integer determines whether liquid-phase diffusion has occurred. If it is an integer, a reaction has occurred, and rule 4 of the cellular automata model is executed, allowing the diffusion process to evolve in the liquid-phase cell for a period of time.

2. The electrode structure design method based on a cellular automata model according to claim 1, characterized in that, The interaction rules R between the cellular automata include two diffusion rules and two reaction rules, with different implementation conditions for each rule, including: When t / △t s When the integer is used, rule 1 is applied. The specific form of rule 1 is shown in formula (2): In the formula, c s The solid-phase lithium-ion concentration is represented by Ds, the solid-phase diffusion coefficient is Δx, the cell side length is Δx, and the 0-1 matrix is ​​F. s The setting is to prevent the exchange of matter between the liquid phase cell and the solid phase cell, where the value of the position of the solid phase cell is 1 and the value of the position of the liquid phase cell is 0. When t / △t r When the integer is an integer, rules 2 and 3 are executed, specifically described by formulas (3) and (4): In the formula, J Li (j) represents the reaction amount in column j, which will be calculated using the finite difference method in the next step. V A=2 (j) represents the volume occupied by the solid boundary cell in column j, V A=0 (j) represents the volume occupied by the liquid phase cell in column j; When t / △t e When the integer is used, rule 4 is applied, which is specifically described by formula (5): In the formula, c e D represents the concentration of lithium ions in the liquid phase. e Let F be the liquid phase diffusion coefficient, and F be the 0-1 matrix. e The value of the solid phase cell is 0, and the value of the liquid phase cell is 1.

3. The electrode structure design method based on a cellular automata model according to claim 1, characterized in that, The process of obtaining the solid-phase potential and liquid-phase potential at each location based on the set initial reaction amount, initial solid-phase reference potential, and initial liquid-phase reference potential using the finite difference method includes: The solid-state potential distribution is calculated and described by formulas (6)-(9): In the formula, s Let J be the solid-state potential, σ be the solid-state conductivity, and J be the solid-state conductivity. Li V represents the amount of reaction. - and V + L represents the solid-state reference potential of the negative electrode and the solid-state reference potential of the positive electrode, respectively. n L s and L p These represent the thicknesses of the negative electrode, the separator, and the positive electrode, respectively, where F is the Faraday constant, and a s The specific surface area of ​​the electrode; The liquid phase potential distribution is calculated and described by formulas (10)-(12): In the formula, e Let κ be the liquid phase potential, and κ be the liquid phase conductivity. D For diffusion conductivity, t + The transference number of the cation. lnf ± / lnc e The mean molar activity coefficient; The solid-state potential is discretized using the finite difference method and described by formulas (16)-(17): In the formula, the subscripts n and p represent the negative pole and the positive pole, respectively, and the subscripts N and P represent the number of discrete points in the positive pole region and the negative pole region, respectively. The liquid phase potential is discretized using the finite difference method and described by formula (18): In the formula, the subscript N e This indicates the number of discrete points in the electrolyte region within the entire battery.

4. The electrode structure design method based on a cellular automata model according to claim 3, characterized in that, The step involves describing the reaction quantity distribution based on the obtained solid-phase potential and liquid-phase potential at each location using the BV equation, and obtaining newly calculated reaction quantity values, solid-phase reference potential values, and liquid-phase reference potential values, which are denoted as data values. Specifically, this includes: Based on the obtained solid-phase potential and liquid-phase potential at each location, the reaction quantity distribution is described using the BV equation, and the newly calculated reaction quantity values ​​are obtained, which are described by formula (13): In the formula, α represents the oxidation transfer coefficient. c Here, E0 is the reduction transfer coefficient, R is the equilibrium potential, and T is the gas constant. The reference potential values ​​for the solid phase and the liquid phase are described by formula (14): In the formula, V ± V is the solid-state reference potential. e The reference potential for the liquid phase; The sum of the reaction amounts at each location is limited by the total number of electrons supplied by the external circuit per unit time, and is described by formula (15): In the formula, I is the current passing through a unit cross-sectional area, and J Li The values ​​represent the reaction amounts; the subscript n indicates the negative electrode, and the subscript p indicates the positive electrode.

5. The electrode structure design method based on a cellular automata model according to claim 1, characterized in that, The verification of the model based on the P2D model to determine the applicable current range of the model includes: The P2D model and the aforementioned model were used to simulate the charging of the battery under charging conditions from 1C to 4C under the same parameters. The state of charge change curves and voltage change curves of the negative and positive electrodes were selected for comparison. The simulation effect was verified by evaluating the average relative error of the voltage curve.

6. The electrode structure design method based on a cellular automata model according to claim 1, characterized in that, The step of designing a layered structure for the battery electrode based on the model, and simulating and evaluating the electrode structure based on the model, includes: To maintain a constant positive electrode morphology and applied current, three layered electrode structures were designed for the negative electrode of the battery. The charging performance of the electrodes with different morphologies of the three layered electrode structures was simulated based on the P2D model and the cellular automata model. The charging performance of the three layered electrode structures with different morphologies was evaluated based on the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode. The three layered electrode structures are as follows: the first layered structure is a porosity layered structure, where the part near the positive electrode has high porosity to ensure unobstructed liquid phase channels and reduce liquid phase diffusion resistance, while the part away from the positive electrode has low porosity; the second layered structure is a particle size layered structure, where the part near the positive electrode has a larger particle size to reduce liquid phase diffusion resistance, while the part away from the positive electrode has a smaller particle size to reduce solid phase diffusion resistance; and the third layered structure is a particle size layered structure, where the part near the positive electrode has a small particle size, while the part away from the positive electrode has a large particle size.

7. The electrode structure design method based on a cellular automata model according to claim 6, characterized in that, The evaluation of the charging performance of the three layered electrode structures with different morphologies is based on the evaluation indicators of cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, including: Based on the porosity stratification structure, and using the cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode as evaluation indicators, it was found that when the porosity is low, the liquid phase diffusion resistance is the main limiting factor, and porosity stratification or particle size stratification design can be adopted. Based on the particle size stratification structure, and using evaluation indicators such as cumulative reaction amount, charging efficiency η, and lithium-ion storage capacity Q of the electrode, it was found that when the porosity is high, solid-phase diffusion resistance is the main limiting factor. In this case, small particles can be used throughout the electrode area instead of a stratified design.

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