A method for sorting consistency of retired batteries based on electrode multi-particle potential model

Abstract

The application discloses a retired battery consistency sorting method based on an electrode multi-particle potential model and belongs to the technical field of retired battery step-by-step utilization. The method takes a simplified P2D model as a basic framework, improves an empirical open-circuit potential item by constructing an electrode multi-particle potential model, forms a non-uniformity compensation simplified P2D model, further extracts external characteristic parameters, simplified P2D model parameters and characteristic parameters representing non-uniformity of the electrode, constructs a fusion feature vector, realizes retired battery consistency sorting in combination with an equalization mixed clustering algorithm on the basis and meets the engineering requirement of equalization of the number of battery groups for step-by-step utilization. Compared with a sorting method only relying on external characteristic parameters, the application can more accurately represent internal state differences of the retired battery, improves the consistency of the sorting result and the real internal state, and provides technical support for reliable step-by-step utilization of the retired battery.

Description

Technical Field

[0001] This invention belongs to the field of retired battery cascade utilization technology, specifically relating to a method for consistent sorting of retired batteries based on an electrode multi-particle potential model. Background Technology

[0002] With the rapid development of the new energy vehicle industry, the scale of power lithium-ion batteries installed in vehicles continues to expand. A large number of power batteries, after meeting vehicle usage requirements, are gradually being phased out of vehicle applications, forming a growing group of retired batteries. Retired batteries can still be reused in energy storage, backup power, and low-speed power applications. Consistency sorting is a crucial step affecting the effectiveness of subsequent battery pack applications. Because batteries experience differences in charge / discharge regimes, workloads, temperature environments, and state of charge ranges during their initial service, even batteries manufactured in the same batch often exhibit significant differences in capacity, internal resistance, and internal aging at retirement. Directly packing retired batteries with significant state differences can easily lead to performance mismatch within the pack, affecting system stability, cycle life, and safety reliability. Therefore, consistency evaluation and sorting of retired batteries are usually required before reuse. Existing methods for consistent sorting of retired batteries mostly use external characteristic parameters such as capacity, internal resistance, and open-circuit voltage as sorting criteria. While these methods are relatively simple to test, external characteristic parameters mainly reflect the apparent performance of the battery and are difficult to reveal intrinsic differences such as active material degradation and internal transport capacity deterioration. For retired batteries with similar external characteristics, their internal aging paths may be different. If only external characteristic parameters are used for sorting, the grouping and matching results may not match the actual state of the batteries.

[0003] To improve the characterization of internal state differences in retired batteries, it is typically necessary to extract characteristic parameters reflecting internal degradation processes using mechanistic models. Simplified P2D models can describe solid-phase diffusion, liquid-phase diffusion, and interfacial electrochemical reaction processes, providing a mechanistic basis for characterizing the internal state of retired batteries. However, existing simplified P2D models usually treat electrode active materials as equivalent to uniform single particles and express the electrode open-circuit potential as an empirical fitting function for a single state of charge. While this approach reduces modeling complexity, it is difficult to incorporate differences in active particle size distribution, effective active surface area, and lithium intercalation state distribution as explicit variables into the electrode potential expression. Therefore, it is difficult to accurately reflect the impact of non-uniformity of the internal particle population on potential behavior and sorting characteristics. When the differences in the internal particle population are significant, particle size distribution and particle population state differences further affect the electrode potential plateau morphology and capacity response. Furthermore, existing methods do not adequately consider the requirement for equal-quantity grouping in cascade utilization projects, making it difficult to directly meet practical application requirements. Therefore, there is an urgent need to propose a method for sorting retired batteries that can improve the expression of open-circuit potential of traditional electrodes, enhance the ability to characterize the non-uniformity inside the electrodes, and meet the quantitative grouping requirements of battery pack quantity in the cascade utilization project. Summary of the Invention

[0004] The purpose of this invention is to address the problems that existing methods for consistent sorting of retired batteries mainly rely on external characteristic parameters, making it difficult to accurately characterize internal state differences, and that the open-circuit potential of electrodes in existing simplified P2D models cannot reflect the differences in the particle population within the electrodes. This invention proposes a method for consistent sorting of retired batteries based on an electrode multi-particle potential model.

[0005] To achieve the above objectives, the present invention provides the following solution: a method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model, comprising the following steps: S1: The P2D model describing the solid-state diffusion behavior of lithium ions inside electrode material particles is simplified to obtain the simplified P2D model. S2: Construct an electrode equilibrium potential model based on the electrode multi-particle structure, and perform non-uniformity compensation on the simplified P2D model based on the electrode equilibrium potential model to obtain a non-uniformly compensated simplified P2D model. S3: Perform feature fusion on the basic external characteristic parameters, the parameters of the non-uniform compensation simplified P2D model, and the multi-particle non-uniformity parameters to obtain fused feature parameters; S4: Perform equal-quantized SK-means clustering on the fused feature parameters, and complete the consistency sorting of retired batteries based on the clustering results; S5: Evaluate the consistency sorting results of retired batteries based on evaluation indicators to obtain evaluation results.

[0006] More preferably, in S1, the simplified P2D model includes: ; In the formula, or p This represents the electrochemical reaction overpotential at the positive electrode. or n This represents the electrochemical reaction overpotential at the negative electrode. e,p This represents the liquid phase potential of the electrolyte phase in the positive electrode region; e,n This represents the liquid phase potential of the electrolyte phase in the negative electrode region; U OCV,p This represents the open-circuit potential of the positive electrode active material; U OCV,n This represents the open-circuit potential of the negative electrode active material; R SEI The equivalent resistance of the SEI film; I For current; or er Indicates the overpotential of an electrochemical reaction; or lpd Indicates the overpotential of an electrochemical reaction; or lpcd Indicates the overpotential of the liquid phase concentration difference; or ohm This represents the lumped ohmic overpotential; or OCV This indicates the open-circuit potential of the electrode.

[0007] More preferably, in S2, the non-uniform compensation simplified P2D model includes: ; in, ; In the formula, This represents the equivalent equilibrium potential of the positive electrode under the multi-particle electrode model. U ref Indicates the reference equilibrium potential. e 0 represents elementary charge; m Li Indicates the mass of a lithium atom; N p Indicates the number of particles in the electrode; Hey E Indicates the effective active surface area; m Li ( y i () represents the chemical potential of intercalated lithium within the particle; m ref Li indicates the reference chemical potential; A EThis represents the total effective active surface area of ​​all particles in the electrode. This represents the equivalent equilibrium potential under the multi-particle electrode model.

[0008] More preferably, the external characteristic basic parameters include: capacity parameters and ohmic internal resistance parameters; the multi-particle non-uniformity parameters include: mean particle size distribution, particle size distribution dispersion, overall effective active surface area ratio, and particle swarm lithium intercalation dispersion.

[0009] More preferably, in S3, the fusion feature parameters include: ; In the formula, Q Indicates the capacity of the retired battery; i ohm Represents the lumped ohmic parameter; i c This represents a parameter characterizing the electrolyte concentration; i D This indicates the diffusion capacity of lithium ions in the electrolyte; i t Indicates the solid-phase diffusion time constant; Indicates the negative electrode capacity; Indicates the mean particle size distribution; Indicates the proportion of effective active surface area; H y This represents the dispersion of lithium intercalation in the particle swarm.

[0010] More preferably, in S4, the process of performing equal-quantization SK-means clustering on the fused feature parameters includes: ① Initialize the number of clusters and cluster centers using the SOM algorithm; ② Based on the initial number of clusters and cluster centers determined by the SOM algorithm, the K-means algorithm is used to perform the initial division of clusters based on the minimum distance rule; ③ The number of clusters is determined based on the SK-means algorithm, and the number of samples in each cluster is made the same according to the intra-group sample equalization rule; ④ Inter-group sample exchange; Step 1: Set up a primary cluster and a secondary cluster, and determine the nearest samples of each cluster; Step 2: Randomly select one nearest sample from each of the primary and secondary clusters as a candidate for exchange; According to the judgment conditions of the inter-group sample exchange rules, if the requirements are met, the sample exchange is performed; if not, continue to select another near-primary sample from the secondary cluster as a candidate for exchange with the near-primary sample of the primary cluster; This process continues until all near-primary samples have been traversed once; Step 3: Select another near-secondary sample from the primary cluster as a candidate for exchange, and repeat the process of Step 2 until all near-secondary samples of the primary cluster have been traversed; Step 4: Select another cluster as the secondary cluster, and repeat the process of Step 2 and Step 3 until all clusters except the primary cluster have been selected as secondary clusters once; Step 5: Select another cluster as the primary cluster, and repeat the process of Step 2, Step 3 and Step 4 until all clusters have been selected as primary clusters once. ⑤ Based on ①-④, recalculate the cluster center of each cluster according to the updated feature parameter distribution; ⑥ Repeat steps ④ and ⑤ until the cluster center no longer changes.

[0011] More preferably, the intra-group sample equalization rule includes: firstly, using the SK-means algorithm to cluster the retired batteries to obtain an initial number of clusters. K and cluster center C c The target sample size for each cluster is set to M. Then, within the cluster with the largest sample size, the samples are sorted according to the distance from the battery in the cluster to the cluster center. Battery samples exceeding M are then assigned to other clusters with a sample size less than M, with priority given to the cluster with the smallest distance to the sample. This process is repeated until the sample size in each cluster is M.

[0012] More preferably, the inter-group sample exchange rule includes: the cluster that actively initiates the battery sample exchange is called the main cluster. G m Cluster center and battery samples within the cluster i They are respectively C m and z m,i Correspondingly, clusters that passively accept exchanges are denoted as secondary clusters. G d The cluster center is C d , the first in the cluster j One battery sample z d,j If a sample in the main cluster is closer to the center of the subcluster, the sample is called a sample that is closer to the center of the main cluster than to the subcluster; if a sample in the subcluster is closer to the center of the main cluster than to the center of the main cluster, the sample is called a sample that is closer to the center of the subcluster than to the main cluster. Main cluster samplei with secondary cluster samples j The following conditions must be met: .

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention, based on a simplified P2D model, introduces a multi-particle structure for the electrode and constructs a non-uniformity-compensated simplified P2D model based on the multi-particle potential model of the electrode. This improves upon the traditional empirical electrode open-circuit potential term and enhances the characterization ability of the non-uniformity of the particle population within the electrode and its potential behavior. Based on the non-uniformity-compensated simplified P2D model, external characteristic parameters, simplified P2D model parameters, and feature parameters characterizing the internal non-uniformity of the electrode are extracted to construct a fusion feature vector for consistent sorting of retired batteries, comprehensively reflecting the internal / external state differences of retired batteries. Combined with an equal-quantization hybrid clustering algorithm, consistent sorting of retired batteries is achieved, meeting the practical requirement of equalizing the number of battery packs in cascade utilization projects. Compared with sorting methods that rely solely on external characteristic parameters, this invention has better overall performance in terms of consistency characterization and engineering applicability. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are 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 these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the overall framework of a method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model, provided in an embodiment of the present invention. Detailed Implementation

[0016] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Example 1: like Figure 1As shown in the figure, this embodiment provides a method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model. The sorting method is explained in detail in the following steps.

[0019] S1: The P2D model describing the solid-state diffusion behavior of lithium ions inside electrode material particles is simplified to obtain the simplified P2D model.

[0020] The P2D model describes the solid-phase diffusion behavior of lithium ions within electrode material particles, while also considering the liquid-phase diffusion process of lithium ions in the electrolyte. Furthermore, it encompasses the electrochemical reactions occurring at the solid-liquid interface where the active electrode particles and the electrolyte meet, thus providing a more comprehensive reflection of the multi-physics coupling mechanism during battery operation. In this model, key physical processes can be characterized by corresponding mathematical equations, specifically including the following aspects: 1. Solid-phase diffusion process.

[0021] The diffusion process of lithium ions within the active materials of the positive or negative electrode is described by the second law, in the form of: (1) In the formula, c s,k Indicates the concentration of lithium ions in the solid phase; r Indicates the radial coordinates within the active particles; t Indicates charging and discharging time; D s,k Indicates the lithium-ion solid-phase diffusion coefficient; p and n These represent the positive and negative electrodes, respectively.

[0022] The boundary conditions are: (2) In the formula, R s,k Indicates the radius of the solid-phase active particles. j k This represents the molar flux of lithium ions at the solid / liquid interface.

[0023] 2. Liquid phase diffusion process.

[0024] (3) In the formula, e e,l Indicates the liquid volume fraction; e s,k It represents the volume fraction of the solid phase. c e,l Indicates the concentration of lithium ions in the liquid phase; x Indicates the coordinates along the battery thickness direction; D e,lIndicates the effective diffusion coefficient of lithium-ion liquid phase; a s,k Indicates the specific surface area of ​​the electrode active particles; Indicates the lithium-ion liquid phase transfer coefficient; September It refers to a diaphragm.

[0025] The boundary conditions are: (4) In the formula, c e,n This indicates the lithium-ion concentration in the electrolyte in the negative electrode region; c e,p This indicates the lithium-ion concentration in the electrolyte in the positive electrode region; c e,sep This indicates the lithium ion concentration in the electrolyte within the diaphragm region; D e,n This represents the effective diffusion coefficient of the electrolyte in the negative electrode region; D e,sep This represents the effective diffusion coefficient of the electrolyte in the diaphragm region; D e,p This represents the effective diffusion coefficient of the electrolyte in the positive electrode region; Indicates the location of the right boundary of the positive electrode active layer; This indicates the location of the left boundary of the positive electrode active layer; This indicates the location of the right boundary of the negative electrode active layer; This indicates the location of the left boundary of the negative electrode active layer; L c This indicates the total thickness of the battery's positive and negative electrodes and the separator.

[0026] 3. Electrochemical reaction process.

[0027] The interfacial electrochemical reaction satisfies the Butler-Volmer kinetic relationship: (5) In the formula, j 0,k Indicates the exchange molar flux; F Denotes Faraday's constant; α a Indicates the anode transfer coefficient; α c The cathode transfer coefficient; R Represents the universal gas constant; T Indicates ambient temperature; or k Indicates the overpotential of an electrochemical reaction; k Indicates the electrochemical reaction constant; c s,max,k Indicates the maximum lithium intercalation concentration within the active material; cs,surf,k This indicates the concentration of solid-phase lithium ions on the surface of the active particles.

[0028] The overpotential of an electrochemical reaction depends not only on the difference between the solid-phase and liquid-phase potentials, but also on the equilibrium potential of the electrode at a specific surface lithium concentration. Furthermore, the SEI film at the solid-liquid interface impedes ion transport, thus introducing a voltage drop across the SEI film. These relationships can be expressed as: (6) In the formula, s,k Represents solid-state potential; e,k Represents the liquid phase potential; U OCV,k Indicates open-circuit potential; Δ SEI,k This indicates the potential drop of the SEI film on the electrode surface; R A SEI, k This represents the area resistivity of the SEI film on the electrode surface. i k This represents the reaction current density.

[0029] 4. Lithium battery terminal voltage.

[0030] In the model, the battery terminal voltage is determined by the solid-state potential difference between the current collectors on the positive and negative sides, and its mathematical expression is: (7) In the formula, U t Indicates the battery terminal voltage; s,p This represents the solid-state potential at the positive current collector; s,n This represents the solid-phase potential at the negative electrode current collector.

[0031] Combining formula (6), the expression for the terminal voltage can be obtained as follows: (8) In the formula, or p This represents the electrochemical reaction overpotential at the positive electrode. or n This represents the electrochemical reaction overpotential at the negative electrode. e,p This represents the liquid phase potential of the electrolyte phase in the positive electrode region; e,n This represents the liquid phase potential of the electrolyte phase in the negative electrode region; U OCV,p This represents the open-circuit potential of the positive electrode active material; UOCV,n This represents the open-circuit potential of the negative electrode active material; R SEI The equivalent resistance of the SEI film; I It represents electric current.

[0032] The P2D model contains a large number of coupled partial differential equations, and direct solution involves significant computational costs. Therefore, this embodiment simplifies the model using the Padé approximation method. For the solid-phase diffusion process, the simulation results of the third-order Padé approximation have high accuracy at low frequencies. Considering that this invention does not require high-frequency sampling signals for parameter identification, the third-order Padé approximation is used to describe the dynamic changes in lithium-ion concentration on the surface of active particles. For the liquid-phase diffusion process, to balance computational efficiency and model accuracy, this invention uses the first-order Padé approximation for simplification. Thus, the battery terminal voltage in the simplified P2D model is further expressed as: (9) In the formula, or er Indicates the overpotential of an electrochemical reaction; or lpd Indicates the overpotential of an electrochemical reaction; or lpcd Indicates the overpotential of the liquid phase concentration difference; or ohm This represents the lumped ohmic overpotential; or OCV This indicates the open-circuit potential of the electrode.

[0033] S2: Construct an electrode equilibrium potential model based on the electrode multi-particle structure, and perform non-uniformity compensation on the simplified P2D model based on the electrode equilibrium potential model to obtain a non-uniformly compensated simplified P2D model.

[0034] Traditional P2D models typically treat electrode active materials as equivalent to uniform single particles and express the electrode open-circuit potential as an empirical fitting function for a single state of charge. While this approach can reduce modeling complexity to some extent, it fails to reflect the impact of differences in active particle size distribution, effective active surface area, and lithium intercalation state distribution within the particle population on the electrode potential in actual electrodes. For electrode materials with phase separation characteristics, such as lithium iron phosphate, particle size distribution affects the order of phase transitions within the particle population, further influencing the voltage plateau morphology, rate capacity, and voltage drop location. Simultaneously, changes in the effective active surface area also affect the battery's usable capacity under rate conditions. Therefore, this invention, based on the simplified P2D model established in S1, introduces a multi-particle structure for the electrode and constructs an electrode equilibrium potential model based on this multi-particle structure to replace the empirical electrode open-circuit potential term in the original model, thus forming a non-uniformity-compensated simplified P2D model.

[0035] First, a multi-particle structure for the electrode is constructed. This invention represents the electrode to be modeled as a collective system composed of multiple particle subgroups. Each particle subgroup corresponds to a representative active particle within a certain particle size range, and it is assumed that particles within the same subgroup have similar geometric scales and similar kinetic response characteristics. This approach can characterize the differences in particle size distribution within the electrode while avoiding the excessive computational complexity of modeling each individual particle individually.

[0036] Assuming the number of particles in the electrode is N p For the first i A particle, whose representative particle size is defined as . R i The particle volume is V i The geometric surface area is A i The effective active surface area is Hey E The molar fraction of lithium intercalation is y i .

[0037] The molar fraction of lithium intercalation is: (10) In the formula, Indicates the first i The number density of intercalated lithium within each active particle; n host This represents the number density of lattice sites available for lithium to occupy per unit volume of active material.

[0038] Unlike traditional simplified P2D models that use a single average state of charge to characterize the entire electrode, this embodiment uses the set of all lithium-intercalated states of the particles { y 1 , y 2 ,…, y Np These elements collectively characterize the internal state of the electrode, thus providing a state basis for describing the non-uniformity of the particle population. Under the assumption of approximately spherical particles, the... i The volume and geometric surface area of ​​each particle are expressed as follows: (11) (12) Considering that not all areas of the particle surface can effectively participate in the lithium-ion intercalation reaction, the first i The effective active surface area of ​​each particle is: (13) In the formula, x i Indicates the firsti The effective active surface area ratio of each particle satisfies 0 < x i ≤1.

[0039] The total volume and total effective active surface area of ​​all particles in the electrode are as follows: (14) (15) The particle size distribution of active particles can be discretized based on the statistical results of material microscopic images, and described using a log-normal distribution to obtain the representative particle size of each particle. R i and their corresponding proportions.

[0040] Next, multi-particle dynamics relationships were established. In the electrode multi-particle structure, different particles exhibit different response rates to external charge-discharge perturbations due to variations in particle size and effective active surface area. Based on the lithium conservation relationship within the particles, and considering that the intercalation process is driven by the difference between the chemical potential of the particle surface and the chemical potential of intercalated lithium within the particle, the state evolution relationship of the lithium intercalation mole fraction for each particle was established as follows: (16) In the formula, t i Indicates the first i The size-dependent relaxation time of each particle; m Li Indicates the mass of a lithium atom; k B Represents the Boltzmann constant; m s,Li Indicates the lithium chemical potential at the particle surface; m Li ( y i () represents the chemical potential of intercalated lithium within the particle; k Li Indicates dynamic parameters.

[0041] because t i The kinetic response speed is related to the particle volume and effective active surface area, therefore particles of different sizes have different kinetic response speeds. The smaller the particle volume and the larger the effective active surface area, the faster its lithium intercalation response; the larger the particle volume and the smaller the effective active surface area, the slower its lithium intercalation response. Thus, formula (16) can characterize the non-uniform lithium intercalation behavior of the particle population.

[0042] For electrode materials exhibiting phase separation characteristics, the intercalation potential of lithium within the particles is expressed as: (17) In the formula, m ref Li indicates the reference chemical potential; L These are the parameters for heat of solution.

[0043] Next, a mapping relationship between the overall state of charge and the multi-particle states is constructed. In the multi-particle structure, the overall state of charge of the electrode is not determined by a single average particle state, but rather by a weighted average of the lithium intercalation states of each particle according to their volume fraction. Therefore, the overall state of charge of the electrode... q ( t )for: (18) The above equation shows that under the same overall state of charge, different particle size distributions and different particle group lithium intercalation state distributions can correspond to different internal states of the electrode, thus leading to different electrode equilibrium potential and voltage behaviors.

[0044] Next, a multi-particle electrode equilibrium potential model is constructed. Based on the aforementioned multi-particle structure and dynamic relationship, this invention constructs a multi-particle electrode equilibrium potential model. The electrode equilibrium potential is: (19) In the formula, U ref Indicates the reference equilibrium potential. e 0 represents elementary charge; A E This represents the total effective active surface area of ​​all particles in the electrode. This represents the equivalent equilibrium potential under the multi-particle electrode model.

[0045] As can be seen from formula (19), when the particle size distribution or effective active surface area distribution changes, the contribution weight of each particle to the electrode equilibrium potential changes, thereby changing the voltage plateau height, plateau slope, and voltage drop position. Therefore, this model can not only characterize the non-uniformity of the particle population, but also provide a basis for the subsequent extraction of mechanistic characteristic parameters related to the non-uniformity inside the electrode.

[0046] Finally, a simplified P2D model with non-uniformity compensation is constructed. In the simplified P2D basic model established in S1, assuming that the positive electrode is the main phase-separated electrode, the improved terminal voltage expression is: (20) In the formula, This represents the equivalent equilibrium potential of the positive electrode in the multi-particle electrode model.

[0047] The above equation is a simplified P2D model for non-uniformity compensation based on the multi-particle structure of electrodes.

[0048] Through S2, this invention completes the transformation from "uniform single-particle empirical electrode potential" to "mechanistic electrode equilibrium potential driven by multi-particle structure," and further embeds this electrode equilibrium potential into a simplified P2D basic model, forming a non-uniformity-compensated simplified P2D model. While retaining the original simplified P2D model's basic framework of solid-liquid phase transport and interfacial reaction, this model introduces information on particle size distribution differences, effective active surface area differences, and inconsistencies in lithium intercalation within particle populations, providing a new mechanistic basis for subsequent extraction of fusion feature parameters and consistent sorting of retired batteries.

[0049] S3: Perform feature fusion on the external characteristic basic parameters, the parameters of the non-uniform compensation simplified P2D model, and the multi-particle non-uniformity parameters to obtain fused feature parameters.

[0050] Building upon the simplified P2D model for non-uniformity compensation based on the multi-particle structure of electrodes constructed in S2, this invention further constructs fused feature parameters for consistent sorting of retired batteries. Unlike traditional sorting methods that rely solely on external characteristic parameters such as capacity and internal resistance, the fused feature parameters employed in this invention consist of three parts: basic external characteristic parameters, simplified P2D basic parameters, and multi-particle non-uniformity parameters. By constructing a multi-level fused feature vector, the apparent performance level, mechanistic degradation information, and non-uniformity differences of the internal particle population of retired batteries can be simultaneously reflected, thereby improving the consistency between the consistent sorting results and the actual internal state of the battery.

[0051] Specifically, the basic external characteristic parameters include: capacity parameters and ohmic internal resistance parameters; the capacity of retired batteries. Q Obtained through constant current charge-discharge experiments, it reflects the remaining usable capacity of retired batteries and is one of the most fundamental external characteristic parameters in consistent sorting. Ohmic internal resistance can be calculated using voltage jumps during charging or under pulsed conditions, characterizing the overall impedance level of the battery's internal current collector, electrodes, electrolyte, and interfacial conductive paths. The lumped ohmic parameters in the simplified P2D model will be... i ohm As a characteristic of the Ohmic response, its expression is: ;(twenty one) In the formula, U 1 indicates the voltage at the moment before charging begins; U 2 indicates the voltage at the start of charging.

[0052] Parameters for the simplified P2D model with non-uniform compensation: In the process of simplifying the P2D model, internal health characteristic parameters characterizing changes in electrolyte performance, such as parameters characterizing electrolyte concentration, can be extracted mainly based on constant current charging data. i c The diffusion capacity of lithium ions in the electrolyte iD ; and internal health characteristics parameters that characterize changes in the performance of electrode active materials, such as the solid-phase diffusion time constant. i t .

[0053] Multi-particle non-uniformity parameters include: mean particle size distribution, particle size distribution dispersion, overall effective active surface area ratio, and particle swarm lithium intercalation dispersion.

[0054] In this embodiment, the average particle size distribution is: ;(twenty two) In the formula, w i Indicates the first i The volume fraction weight of each active particle.

[0055] Different retired batteries may differ in their internal particle structure and effective reaction particle size distribution. Therefore, the mean particle size distribution can be used as an important parameter to reflect the average characteristics of the particle population.

[0056] Particle size distribution dispersion is used to characterize the degree of dispersion in particle size distribution, and its variance expression is: .(twenty three) When the variance is large, it indicates that the particle population size varies more and the dynamic response of different particles varies more significantly, which makes it easier to cause differences in the electrode equilibrium potential and macroscopic voltage curve.

[0057] The overall effective active surface area ratio is: .(twenty four) This parameter characterizes the overall proportion of the actual intercalation reaction area in the electrode, and it can reflect the influence of factors such as surface coverage, local deactivation, and poor contact on the effective reaction area.

[0058] To characterize the consistency of the lithium intercalation state within a particle swarm at a given moment, the lithium intercalation dispersion of the particle swarm is: (25) It reflects the degree of deviation of the lithium-intercalated state of the particles from the overall average state. H y The larger the value, the more inconsistent the lithium insertion state of the particle population, and the stronger the non-uniformity inside the electrode.

[0059] Therefore, the fusion feature vector used in this embodiment to construct the consistency sorting of retired batteries is: (26) In the formula, This indicates the negative electrode capacity.

[0060] S4: Perform equal-quantization SK-means clustering on the fused feature parameters, and complete the consistency sorting of retired batteries based on the clustering results.

[0061] The SK-means algorithm process includes: K-means is an unsupervised machine learning algorithm. Its basic idea is to perform clustering by minimizing the distance between a sample point and the center of its cluster. The main steps are: ① Selecting the number of clusters. K ① Predetermine the number of clusters into which the fused feature parameters will be divided; ② Initialize the cluster center set. C c ={ c 1,…, c K}: Randomly select from the dataset K ① Select each sample point as a cluster center; ② Assign each sample point to the nearest cluster: Calculate the distance of each sample point to each cluster center, and then assign it to the cluster with the shortest distance. (27) In the formula, c i Indicates the first i Cluster center, This indicates Euclidean distance.

[0062] ④ Update the cluster centers c i For clusters i First, all sample points within the cluster are counted; then, the mean of these points is calculated; finally, this mean is designated as the new cluster center. (28) In the formula, n i Indicates the first i The number of sample points in each cluster; z ij Indicates the first i The th cluster j The fusion feature vector of each sample.

[0063] ⑤ Continue iterating through steps ③ and ④ until the cluster center converges or the preset number of iterations is reached.

[0064] Because the K-means clustering algorithm has a low initial cluster size... K and the initial cluster center C c The selection of clustering methods is highly sensitive. This problem can be solved by introducing the Self-Organizing Map Neural Network (SOM) algorithm, which can improve clustering efficiency.

[0065] The SOM algorithm is an unsupervised learning neural network that maps high-dimensional input data to a low-dimensional output space while preserving the topological structure of the input data. It features strong generalization ability, no need for data labels, no need to be informed of the number of categories in advance, and strong fault tolerance. The SOM algorithm consists of two key phases: a competition phase and an adaptation phase. In the competition phase, neurons compete by calculating the distance to the input vector, expressed as: (29) In the formula, d i Represents neurons i The distance; w ij Represents neurons i The j The weight of each component; z j Indicates the first j Dimensional fusion feature vector.

[0066] The neuron with the smallest distance is selected as the winning neuron. (30) During the adaptation phase, the winning neuron and its neighboring neurons gradually adapt to the distribution of the input data through weight updates. The weight update expression is as follows: (31) In the formula, α Indicates the learning rate. h ( i * , i , t ) represents the neighborhood function, which is used to control the range of neuron updates.

[0067] After clustering using the SK-means algorithm, retired batteries can be grouped. However, this method cannot guarantee that the number of retired batteries in each cluster is the same. For the needs of cascade utilization scenarios of retired batteries, it is necessary to group them into equal-quantity groups so that they can be directly applied to cascade utilization scenarios. Therefore, this invention proposes an equal-quantity SK-means clustering algorithm based on the SK-means algorithm. Its main feature is the introduction of rules for equalizing samples within groups and exchanging samples between groups into the SK-means algorithm.

[0068] The intra-group sample equalization rules include: first, using the SK-means algorithm to cluster retired batteries to obtain the initial number of clusters. K and cluster center C cAt this point, the target sample size for each cluster can be set to M. Then, within the cluster with the largest sample size, the samples are sorted according to the distance from the cells within that cluster to the cluster center. Cell samples exceeding M are then sequentially assigned to other clusters with a sample size less than M, prioritizing the cluster with the smallest distance to the assigned sample. This process is repeated until the sample size in each cluster is also M.

[0069] The inter-group sample exchange rules include: The above rules only guarantee that each cluster has M samples, but cannot guarantee the attribution of battery samples. Therefore, an inter-group sample exchange mechanism is introduced to further optimize and standardize the attribution of samples between different clusters. Assume that the cluster that actively initiates the battery sample exchange is called the main cluster. G m Its cluster center and battery samples within the cluster i They are respectively C m and z m,i Correspondingly, clusters that passively accept exchanges are denoted as secondary clusters. G d Its cluster center is C d , the first in the cluster j One battery sample z d,j Under this definition, if a sample in the main cluster is closer to the center of the subcluster, it is called a sample closer to the main cluster than to the subcluster center; correspondingly, if a sample in the subcluster is closer to the center of the main cluster, it is called a sample closer to the subcluster center than to the main cluster center. Specifically, the discrimination method is as follows: if a sample in the main cluster is closer to the center of the subcluster than to the center of the main cluster... i With the main cluster center vector With the main-subcluster center vector If the product of the two factors is greater than 0, then this sample is a primary-near-secondary cluster sample. Similarly, if the secondary cluster sample... j Vector with the center of the subcluster With the secondary-primary cluster center vector If the product of the two is greater than 0, then this sample is a secondary near-center sample.

[0070] If the inter-group sample exchange rule is executed, then samples from the main cluster are required. i with secondary cluster samples j The following conditions must be met: (32) Therefore, the main steps of the equal-quantization SK-means clustering algorithm are as follows: ① Determining the initial number of clusters and cluster centers. The SOM algorithm is used to initialize the number of clusters and cluster centers.

[0071] ② Preliminary cluster division. Based on the initial number of clusters and cluster centers determined by the SOM algorithm, the K-means algorithm is used to perform preliminary cluster division based on the minimum distance rule.

[0072] ③ Equal sample size within each group. Based on the SK-means algorithm described above, the number of clusters was determined, and according to rule 1, the sample size in each cluster was made equal.

[0073] ④ Inter-group sample exchange. 1) Set up a primary cluster and a secondary cluster, and determine the nearest samples of each cluster; 2) Randomly select one nearest sample from each of the primary and secondary clusters as a candidate for exchange. According to the judgment condition of rule 2, if the requirement is met, the sample exchange is performed; if not, continue to select another near-primary sample from the secondary cluster as a candidate for exchange with the near-primary sample of the primary cluster. This process continues until all near-primary samples have been traversed once; 3) Select another near-secondary sample from the primary cluster as a candidate for exchange, and repeat process 2) until all near-secondary samples of the primary cluster have been traversed; 4) Select another cluster as the secondary cluster, and repeat processes 2) and 3) until all clusters except the primary cluster have been selected as secondary clusters once; 5) Select another cluster as the primary cluster, and repeat processes 2), 3), and 4) until all clusters have been selected as primary clusters once.

[0074] ⑤ Based on the above steps, recalculate the cluster center of each cluster according to the updated feature parameter distribution.

[0075] ⑥ Repeat steps ④ and ⑤ until the cluster center no longer changes or changes very little.

[0076] S5: Evaluate the consistency sorting results of retired batteries based on evaluation indicators to obtain evaluation results.

[0077] Based on the extracted fusion features and an equal-quantity hybrid clustering algorithm, retired batteries are sorted for consistency, and the results are compared with those using only external characteristic parameters such as capacity and internal resistance as features. To effectively evaluate the consistency of retired batteries after grouping, this embodiment establishes the standard deviation and coefficient of variation of multi-dimensional health features as evaluation indicators, the mathematical expressions of which are as follows: (33) In the formula, S X Indicates standard deviation, CV X Represents the coefficients of variation. X F This represents multidimensional health characteristic parameters, i.e., multidimensional health characteristic parameters. ; n Indicates the sample size (number of retired batteries); Indicates the first i The value of a battery in a certain health characteristic dimension; This represents the mean of the health characteristic across all samples.

[0078] To reveal the contribution of each health characteristic to the consistency sorting results of retired batteries, the Shapley Additive Explanations (SHAP) method was used to conduct interpretability analysis on the characteristic parameters.

[0079] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model, characterized in that, Includes the following steps: S1: The P2D model describing the solid-state diffusion behavior of lithium ions inside electrode material particles is simplified to obtain the simplified P2D model. S2: Construct an electrode equilibrium potential model based on the electrode multi-particle structure, and perform non-uniformity compensation on the simplified P2D model based on the electrode equilibrium potential model to obtain a non-uniformly compensated simplified P2D model. S3: Perform feature fusion on the basic external characteristic parameters, the parameters of the non-uniform compensation simplified P2D model, and the multi-particle non-uniformity parameters to obtain fused feature parameters; S4: Perform equal-quantized SK-means clustering on the fused feature parameters, and complete the consistency sorting of retired batteries based on the clustering results; S5: Evaluate the consistency sorting results of retired batteries based on evaluation indicators to obtain the evaluation results; In S1, the simplified P2D model includes: ； In the formula, η p This represents the electrochemical reaction overpotential at the positive electrode. η n This represents the electrochemical reaction overpotential at the negative electrode. e,p This represents the liquid phase potential of the electrolyte phase in the positive electrode region; e,n This represents the liquid phase potential of the electrolyte phase in the negative electrode region; U OCV,p This represents the open-circuit potential of the positive electrode active material; U OCV,n This represents the open-circuit potential of the negative electrode active material; R SEI The equivalent resistance of the SEI film; I For current; η er Indicates the overpotential of an electrochemical reaction; η lpd Indicates the liquid phase overpotential; η lpcd Indicates the overpotential of the liquid phase concentration difference; η ohm This represents the lumped ohmic overpotential; η OCV Indicates the open-circuit potential of the electrode; In S2, the non-uniform compensation simplified P2D model includes: ； in, ； In the formula, This represents the equivalent equilibrium potential of the positive electrode under the multi-particle electrode model. U ref Indicates the reference equilibrium potential. e 0 represents elementary charge; m Li Indicates the mass of a lithium atom; N p Indicates the number of particles in the electrode; Indicates the effective active surface area; μ Li ( y i () represents the chemical potential of intercalated lithium within the particle; Indicates the reference chemical potential; A E This represents the total effective active surface area of ​​all particles in the electrode. This represents the equivalent equilibrium potential under the multi-particle electrode model. In S4, the SK-means algorithm process includes: ① Initialize the number of clusters and cluster centers using the SOM algorithm; ② Based on the initial number of clusters and cluster centers determined by the SOM algorithm, the K-means algorithm is used to perform the initial division of clusters based on the minimum distance rule; ③ The number of clusters is determined based on the SK-means algorithm, and the sample size in each cluster is the same according to the intra-group sample equalization rule.

2. The method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model according to claim 1, characterized in that, The external characteristic parameters include: capacity parameters and ohmic internal resistance parameters; the multi-particle non-uniformity parameters include: mean particle size distribution, particle size distribution dispersion, overall effective active surface area ratio, and particle swarm lithium intercalation dispersion.

3. The method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model according to claim 1, characterized in that, In S3, the fusion feature parameters include: ； In the formula, Q Indicates the capacity of the retired battery; θ ohm Represents the lumped ohmic parameter; θ c This represents a parameter characterizing the electrolyte concentration; θ D This indicates the diffusion capacity of lithium ions in the electrolyte; θ t Indicates the solid-phase diffusion time constant; Indicates the negative electrode capacity; Indicates the mean particle size distribution; Indicates the proportion of effective active surface area; H y Indicates the dispersion of lithium intercalation in the particle swarm; σ R This indicates the dispersion of particle size distribution.

4. The method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model according to claim 1, characterized in that, In S4, the process of performing equal-quantization SK-means clustering on the fused feature parameters includes: ① Initialize the number of clusters and cluster centers using the SOM algorithm; ② Based on the initial number of clusters and cluster centers determined by the SOM algorithm, the K-means algorithm is used to perform the initial division of clusters based on the minimum distance rule; ③ The number of clusters is determined based on the SK-means algorithm, and the number of samples in each cluster is made the same according to the intra-group sample equalization rule; ④ Inter-group sample exchange; Step 1: Set up a primary cluster and a secondary cluster, and determine the nearest samples of each cluster; Step 2: Randomly select one nearest sample from each of the primary and secondary clusters as a candidate for exchange; According to the judgment conditions of the inter-group sample exchange rules, if the requirements are met, the sample exchange is performed; if not, continue to select another near-primary sample from the secondary cluster as a candidate for exchange with the near-primary sample of the primary cluster; This process continues until all near-primary samples have been traversed once; Step 3: Select another near-secondary sample from the primary cluster as a candidate for exchange, and repeat the process of Step 2 until all near-secondary samples of the primary cluster have been traversed; Step 4: Select another cluster as the secondary cluster, and repeat the process of Step 2 and Step 3 until all clusters except the primary cluster have been selected as secondary clusters once; Step 5: Select another cluster as the primary cluster, and repeat the process of Step 2, Step 3 and Step 4 until all clusters have been selected as primary clusters once. ⑤ Based on ①-④, recalculate the cluster center of each cluster according to the updated feature parameter distribution; ⑥ Repeat steps ④ and ⑤ until the cluster center no longer changes.

5. The method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model according to claim 4, characterized in that, The intra-group sample equalization rule includes: firstly, using the SK-means algorithm to cluster the retired batteries to obtain the initial number of clusters. K and cluster center C c The target sample size for each cluster is set to M. Then, within the cluster with the largest sample size, the samples are sorted according to the distance from the battery in the cluster to the cluster center. Battery samples exceeding M are then assigned to other clusters with a sample size less than M, with priority given to the cluster with the smallest distance from the sample. This process is repeated until the sample size in each cluster is M.

6. The method for consistent sorting of decommissioned batteries based on an electrode multi-particle potential model according to claim 4, characterized in that, The inter-group sample exchange rules include: the cluster that actively initiates the battery sample exchange is called the main cluster. G m Cluster center and battery samples within the cluster i They are respectively C m and z m,i Correspondingly, clusters that passively accept exchanges are denoted as secondary clusters. G d The cluster center is C d , the first in the cluster j One battery sample z d,j If a sample in the main cluster is closer to the center of the subcluster, the sample is called a sample that is closer to the center of the main cluster than to the subcluster; if a sample in the subcluster is closer to the center of the main cluster than to the center of the main cluster, the sample is called a sample that is closer to the center of the subcluster than to the main cluster. Main cluster sample i with secondary cluster samples j The following conditions must be met: 。

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