A method for identifying electrochemical parameters of parallel lithium-ion batteries

Abstract

The present invention provides a method for identifying electrochemical parameters of parallel lithium-ion batteries, which respectively treats the positive and negative electrodes of the battery as single particles and establishes a single-particle electrochemical model of the battery; determines the electrochemical parameters to be identified based on the single-particle electrochemical model; and gives a charge and discharge current I according to the factory information of the battery pack. 总 Charge and discharge the battery pack to obtain the experimental voltage curve of each single cell in the battery pack, and obtain the terminal voltage V of the parallel batteries at different times. cell ; Determine the optimized target error function f of the parallel lithium-ion battery; Based on the battery voltage curve and the error function f, use the simulated annealing algorithm to identify the electrochemical parameters of the single cells in the parallel battery pack in the simulation software. This invention identifies the electrochemical parameters of each single cell in the parallel lithium-ion battery, analyzes the battery consistency, and provides a basis for determining whether the battery can continue to be used in parallel.

Description

Technical Field

[0001] The invention relates to the technical field of lithium ion batteries, and in particular to a method for identifying electrochemical parameters of parallel lithium ion batteries. Background Art

[0002] In 1933, Professors Doyle and Numan proposed a physics-based quasi-two-dimensional (P2D) electrochemical model, which describes the internal coupling relationship of the battery through partial differential equations such as the solid phase diffusion equation, the liquid phase diffusion equation, and the Butler Volumer. Compared with the equivalent circuit model, the electrochemical model is based on the internal electrochemical mechanism of the battery, and the model parameters have more practical physical meanings; at the same time, the electrochemical model can be coupled with the thermal model to analyze the lithium deposition and thermal runaway of the battery, so it is of great significance to improve the identification accuracy of the electrochemical parameters.

[0003] The P2D electrochemical model has a large amount of calculation. The single particle model treats the positive and negative electrodes as single particles, ignoring the uneven concentration of particles inside the battery to simplify the calculation. The P2D electrochemical model in the prior art has a large amount of calculation. The single particle model treats the positive and negative electrodes as single particles, ignoring the uneven concentration of particles inside the battery to simplify the calculation. Summary of the invention

[0004] The technical problem to be solved by the present invention is: in order to overcome the deficiencies in the prior art, the present invention provides a method for identifying electrochemical parameters of parallel lithium-ion batteries.

[0005] The technical solution to be adopted by the present invention to solve the technical problem is: a method for identifying electrochemical parameters of parallel lithium-ion batteries, comprising the following steps:

[0006] S1: The positive and negative electrodes of the battery are equivalent to single particles respectively, and the single particle electrochemical model of the battery is established;

[0007] S2: Determine the electrochemical parameters that need to be identified based on the single particle electrochemical model;

[0008] S3: According to the factory information of the battery pack, the charge and discharge current I is given 总 Charge and discharge the battery pack to obtain the experimental voltage curve of each single cell in the battery pack, that is, determine the size of the battery terminal voltage at different charge and discharge times, and obtain the terminal voltage V of the parallel batteries at different times. cell ;

[0009] S4: Determine the optimization target error function f of the parallel lithium-ion batteries;

[0010] S5: According to the voltage curve of the battery and the error function f, a simulated annealing algorithm is used to identify the electrochemical parameters of the single cells in the parallel battery pack in the simulation software.

[0011] Furthermore, establishing the electrochemical model of the battery in step S1 specifically includes the following steps:

[0012] When a certain current flows through the two ends of the battery, the lithium ions, active particles, and electrons in the electrolyte interact to maintain the stability of the external current. The current density i on the active surface of the electrode is j for:

[0013]

[0014] Among them, i j Indicates the current density of the active surface of the electrode, unit: A / m 2 ; I represents the current flowing into the two ends of the battery, unit: A; S j Indicates the equivalent active particle surface area of ​​the electrode material, in m 2 ; j represents the positive electrode p or the negative electrode n;

[0015] Then the pore wall flux of lithium ions at the interface between active particles and electrolyte is j j for:

[0016]

[0017] Among them, j j Indicates the pore wall flux, unit: mol / (m 2 ·s); n represents the nuclear charge number of lithium ions, that is, n=1; F represents the Faraday constant 96487C / mol;

[0018] At the same time, the pore wall flux j j It can also be expressed by the Butler-Volmer electrochemical reaction equation:

[0019]

[0020] Among them, k j represents the liquid phase conductivity, η j is the surface overpotential, c e represents the liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf represents the lithium ion concentration on the surface of active particles, T is the current battery temperature, and R represents the gas constant 8.31441 (J / (mol*K));

[0021] The surface overpotential η in formula (3) j for:

[0022] η j =φ s,j -φ l,j -U j (4)

[0023] Among them, φ s,j represents the solid phase potential, φ l,j represents the liquid phase potential, U j represents the equilibrium potential;

[0024] The terminal voltage V of the known battery cell It can be expressed as:

[0025] V cell =φ s,p -φ s,n (5)

[0026] Among them, φ s,p represents the solid phase potential of the positive electrode, φ s,n represents the solid phase potential of the negative electrode;

[0027] The difference in overpotential between the positive and negative electrodes is derived as p -η n :

[0028]

[0029] Among them, m j is an intermediate variable, j represents the positive electrode p or the negative electrode n, then m j for:

[0030]

[0031] Among them, k j represents the reaction rate constant, j is the positive electrode p or the negative electrode n, that is, k n represents the negative electrode reaction rate constant, k p represents the positive electrode reaction rate constant;

[0032] The derivation process of formula (6) can be found in the reference “Guo M, Sik Ha G, White R E. Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior (vol 158, pg A122, 2011) [J]. Journal of The Electrochemical Society, 2011, 158 (2)”.

[0033] Substituting formula (4) and formula (6) into formula (5), the terminal voltage V of the battery can be derived: cell :

[0034] V cell =U p (x p,surf )-U n (x n,surf )+η p -η n +U l (8)

[0035] Among them, U p (x p,surf ) represents the positive electrode equilibrium potential, U n (x n,surf ) represents the negative electrode equilibrium potential, U l represents the liquid phase potential; x p,surf and x n,surf All are dimensionless quantities related to the lithium ion concentration on the surface of active particles;

[0036] The liquid potential U in formula (8) l The calculation formula is:

[0037]

[0038] Among them, t + Lithium ion liquid phase transfer coefficient, c eL represents the liquid lithium ion concentration at the interface between the positive electrode material and the current collector, c e0 A represents the concentration of liquid lithium ions at the boundary of the negative electrode material and current collector, cell Represents the battery surface area, L p Indicates the thickness of the positive electrode material, L n Indicates the thickness of the negative electrode material, L S Indicates the thickness of the diaphragm, k p represents the positive electrode liquid conductivity, k n represents the negative electrode liquid conductivity, k s represents the conductivity of the diaphragm liquid phase, ε p represents the volume fraction of the positive electrode liquid phase, ε n represents the volume fraction of the negative electrode liquid phase, ε s represents the volume fraction of the diaphragm liquid phase;

[0039] Positive electrode equilibrium potential U p (x p,surf ) is a function of the lithium concentration on the surface of the positive electrode active particles, and the negative electrode equilibrium potential U n (x n,surf ) is a function of the lithium concentration on the surface of the negative electrode active particles; by consulting the material properties to obtain the material properties of the positive and negative electrodes, then x j,surf The lithium insertion state SOL (State of Lithium) on the surface of the electrode material is expressed as:

[0040]

[0041] Where j is the positive electrode p or the negative electrode n, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf Represents the lithium ion concentration on the surface of active particles;

[0042] The battery state of charge SOC is expressed as:

[0043]

[0044] Among them, SOL n (t) represents the lithium insertion state of the negative electrode at the current moment, SOL n (0%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium insertion state of the positive electrode at the current moment, SOL p (0%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully discharged, SOL p (100%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully charged;

[0045] The solid phase diffusion equation is used to describe the diffusion process of lithium ions inside the active particles of the electrode. It is often described by Fick's second law to calculate the lithium ion concentration at each location of the active particles. However, the electrode open circuit voltage is only related to the lithium ion concentration on the surface of the active particles. The calculation of the lithium ion concentration on the surface of the active particles using Fick's law is complex. The lithium insertion state on the surface of the active particles under constant current and isothermal conditions is simplified to:

[0046]

[0047] Among them, SOL ini,j represents the initial lithium insertion state, δ j Indicates the intermediate variable, j is the positive electrode p or the negative electrode n, that is, SOL ini,n Indicates the initial lithium insertion state of the negative electrode, SOL ini,p Indicates the initial lithium insertion state of the positive electrode, δ n represents the negative intermediate variable, δ p Represents the positive intermediate variable; λ k is an array that can be calculated using the known characteristic equation and the first 10 values ​​are taken. Then λ k=[0.0148611613482230; 4.49340945790908; 7.72525183693785; 10.9041216594292; 14.0661939128319; 17.2207552719312; 20.3713029592880; 23.5194524986894; 26.6660542588130; 29.8115987908931], calculate λ k The characteristic equation of can be found in “Meng, Guo, Godfrey. Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior[J]. Journal of the Electrochemical Society, 2011.”;

[0048] Among them, the intermediate variable δ p and δ n They are expressed as follows:

[0049]

[0050] Among them, D s,p represents the solid phase diffusion coefficient of the positive electrode active particles; D s,n represents the solid phase diffusion coefficient of the negative electrode active particles; S p Indicates the equivalent active particle surface area of ​​the positive electrode material, unit: m 2 ; S n represents the equivalent active particle surface area of ​​the negative electrode material; c s,p,max represents the theoretical maximum lithium ion concentration of the positive electrode active particles; c s,n,max Represents the theoretical maximum lithium ion concentration of the negative electrode active particles; R p Represents the radius of the positive electrode active particles; R n represents the radius of the negative electrode active particles;

[0051] The electrochemical model of lithium-ion batteries only requires the current flowing through the battery and the battery parameters to calculate the battery terminal voltage.

[0052] Furthermore, the electrochemical parameters that need to be identified include the solid phase diffusion coefficient D of the negative electrode active particles. s,n , the solid phase diffusion coefficient D of the positive electrode active particles s,p , negative electrode reaction rate constant k n , positive electrode reaction rate constant k p , initial lithium insertion state of negative electrode SOL ini,n , the initial lithium insertion state of the positive electrode SOL ini,p .

[0053] Further, in step S4, the battery error function f is expressed by the formula:

[0054]

[0055] Among them, V i It represents the terminal voltage measurement value of the single cell with serial number i, i represents the serial number of the single cell, i=1,2...n; n is the total number of single cells connected in parallel in the battery pack.

[0056] Further, the parameter identification process in step S5 specifically includes the following steps:

[0057] S5.1: Determine the standard deviation threshold s0

[0058] According to the performance requirements of the battery pack, the standard deviation threshold of the voltage curve is set to s0;

[0059] S5.2: Determine the simulated current C(i)

[0060] For a parallel circuit, the total current of the parallel batteries is I 总 :

[0061]

[0062] Among them, I i Represents the current flowing through the single battery i in parallel, i = 1, 2, ... n, n is the total number of batteries in parallel;

[0063] Battery terminal voltage V cell :

[0064] V cell =V1=V2=......=V n (18)

[0065] Where n is the total number of single cells connected in parallel, V1, V2, V3...V n is the voltage across each single battery;

[0066] Given the total current I of the parallel connected batteries 总 , then the current C(i) of the single cell i in the n branches is:

[0067]

[0068] Among them, σ*randn(1,n) means random generation with standard deviation σ and mean value I 总 / n are the currents I of the n branches respectively. i ;

[0069] S5.3: Get the simulated voltage curve

[0070] In the simulation software, for single cell i, the initial value of the electrochemical parameter is given first, and then the single cell i is charged and discharged with the current C(i) as the charge and discharge current to obtain the simulation voltage curve of each single cell;

[0071] S5.4: Calculation Error

[0072] Then, the error f of each single cell is calculated based on the simulated battery terminal voltage and the experimental battery terminal voltage at the corresponding points in the simulated voltage curve and the experimental voltage curve, and the formula (19) of the error function f opz (i)

[0073]

[0074] According to formula (20), the total error f of the battery pack is calculated total :

[0075]

[0076]

[0077] Among them, V ij It represents the terminal voltage of single cell i at time j, i = 1, 2, ... n; j = 1, 2, ... m; n represents the number of single cells, and m represents the total number of each single cell voltage curve at different times;

[0078] S5.5: Calculate standard deviation

[0079] According to the terminal voltage V on the simulation voltage curve ij Calculate the standard deviation s of the simulated terminal voltage i , then s i for:

[0080]

[0081] in, represents the average value of the m simulated terminal voltages of single cell i;

[0082] Determine the standard deviation i With the size of the standard deviation threshold s0, when s i <s0, at this time, the corresponding electrochemical parameter value is the optimal value; otherwise, the total error f total The size of the current error minimum value f, when f total <f, reduce the current distribution I i The standard deviation σ between them is set to 0.9σ, and the total error f is recorded. total As the minimum error value f; when f total >f, increase the current distribution Ii The standard deviation σ between them is set to 1.1σ, and the minimum error value f is kept unchanged;

[0083] Then, the process returns to step S5.2, and the electrochemical parameters are updated, and the identification is continued until the parameter identification of all the single cells in the battery pack is completed.

[0084] Furthermore, the setting of the standard deviation threshold s0 in step S5.1 is determined according to the battery type and the number of collected data points.

[0085]

[0086] Where m is the number of battery voltage points collected in the experiment, V max The charging cut-off voltage specified for the battery, V min The discharge cut-off voltage specified for the battery. The difference between the charge cut-off voltage and the discharge cut-off voltage of a lithium-ion battery is usually between 0.5-1.5V.

[0087] Furthermore, the battery terminal voltage V cell Indicates that the total current I 总 When the battery is at the same voltage, Vcell is a data set related to the time interval; V1 is the current C1I of battery 1 under a set of electrochemical parameters. 总 The data set of the terminal voltage of the simulated battery at both ends;

[0088] The uniformity index is introduced to quantify the consistency between parallel lithium-ion battery cells. The expression is as follows:

[0089]

[0090] Among them, j max 、j min 、j avg They are respectively one of the six electrochemical parameters of each single cell. It can be seen that the smaller the uniformity index is, the smaller the difference between the battery cells is. The uniformity index of the current distribution ratio C comprehensively reflects the inconsistency inside the battery.

[0091] The beneficial effects of the present invention are as follows: a method for identifying electrochemical parameters of parallel lithium-ion batteries provided by the present invention simplifies solid-phase diffusion into two-parameter and three-parameter approximations, and uses a single-particle model to identify electrochemical parameters; on the basis of the single-particle model, liquid phase potential changes are added, and local volume current density is used to replace changes in lithium ion flow along the thickness direction to identify multiple electrochemical parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0093] Figure 1 It is a schematic diagram of the principle of the parallel battery pack of the present invention.

[0094] Figure 2 It is a schematic diagram of parameter identification of a single cell of the present invention.

[0095] Figure 3 This is the electrochemical parameter identification process of the parallel lithium-ion battery of the present invention.

[0096] Figure 4 This is the parameter identification process of the single cell i based on the simulated annealing algorithm of the present invention.

[0097] Figure 5 It is a schematic diagram of the total error calculated by the experimental data and simulation data of the present invention. DETAILED DESCRIPTION

[0098] The present invention will now be described in detail with reference to the accompanying drawings. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore only shows the components related to the present invention.

[0099] like Figure 1-Figure 5 As shown, a method for identifying electrochemical parameters of parallel lithium-ion batteries of the present invention comprises the following steps:

[0100] S1: The positive and negative electrodes of the battery are equivalent to single particles respectively, and the single particle electrochemical model of the battery is established;

[0101] Establishing the electrochemical model of the battery specifically includes the following steps:

[0102] When a certain current flows through the two ends of the battery, the lithium ions, active particles, and electrons in the electrolyte interact to maintain the stability of the external current. The current density i on the active surface of the electrode is j for:

[0103]

[0104] Among them, i j Indicates the current density of the active surface of the electrode, unit: A / m 2 ; I represents the current flowing into the two ends of the battery, unit: A; S j Indicates the equivalent active particle surface area of ​​the electrode material, in m 2 ; j represents the positive electrode p or the negative electrode n;

[0105] Then the pore wall flux of lithium ions at the interface between active particles and electrolyte is j j for:

[0106]

[0107] Among them, j jIndicates the pore wall flux, unit: mol / (m 2 ·s); n represents the nuclear charge number of lithium ions, that is, n=1; F represents the Faraday constant 96487C / mol;

[0108] At the same time, the pore wall flux j j It can also be expressed by the Butler-Volmer electrochemical reaction equation:

[0109]

[0110] Among them, k j represents the liquid conductivity, η j is the surface overpotential, c e represents the liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf represents the lithium ion concentration on the surface of active particles, T is the current battery temperature, and R represents the gas constant 8.31441 (J / (mol*K));

[0111] The surface overpotential η in formula (3) j for:

[0112] η j =φ s,j -φ l,j -U j (4)

[0113] Among them, φ s,j represents the solid phase potential, φ l,j represents the liquid phase potential, U j represents the equilibrium potential;

[0114] The terminal voltage V of the known battery cell It can be expressed as:

[0115] V cell =φ s,p -φ s,n (5)

[0116] Among them, φ s,p represents the solid phase potential of the positive electrode, φ s,n represents the solid phase potential of the negative electrode;

[0117] The difference in overpotential between the positive and negative electrodes is derived as p -η n :

[0118]

[0119] Among them, m j is an intermediate variable, j represents the positive electrode p or the negative electrode n, then mj for:

[0120]

[0121] Among them, k j represents the reaction rate constant, j is the positive electrode p or the negative electrode n, that is, k n represents the negative electrode reaction rate constant, k p represents the positive electrode reaction rate constant;

[0122] The derivation process of formula (6) can be found in the reference “Guo M, Sik Ha G, White R E. Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior (vol 158, pg A122, 2011) [J]. Journal of The Electrochemical Society, 2011, 158 (2)”.

[0123] Substituting formula (4) and formula (6) into formula (5), the terminal voltage V of the battery can be derived: cell :

[0124] V cell =U p (x p,surf )-U n (x n,surf )+η p -η n +U l (8)

[0125] Among them, U p (x p,surf ) represents the positive electrode equilibrium potential, U n (x n,surf ) represents the negative electrode equilibrium potential, U l represents the liquid phase potential; x p,surf and x n,surf All are dimensionless quantities related to the lithium ion concentration on the surface of active particles;

[0126] The liquid potential U in formula (8) l The calculation formula is:

[0127]

[0128] Among them, t + Lithium ion liquid phase transfer coefficient, c eL represents the liquid lithium ion concentration at the interface between the positive electrode material and the current collector, c e0 A represents the concentration of liquid lithium ions at the boundary of the negative electrode material and current collector,cell Represents the battery surface area, L p Indicates the thickness of the positive electrode material, L n Indicates the thickness of the negative electrode material, L S Indicates the thickness of the diaphragm, k p represents the positive electrode liquid conductivity, k n represents the negative electrode liquid conductivity, k s represents the conductivity of the diaphragm liquid phase, ε p represents the volume fraction of the positive electrode liquid phase, ε n represents the volume fraction of the negative electrode liquid phase, ε s represents the volume fraction of the diaphragm liquid phase;

[0129] Positive electrode equilibrium potential U p (x p,surf ) is a function of the lithium concentration on the surface of the positive electrode active particles, and the negative electrode equilibrium potential U n (x n,surf ) is a function of the lithium concentration on the surface of the negative electrode active particles; by consulting the material properties to obtain the material properties of the positive and negative electrodes, then x j,surf The lithium insertion state SOL (State of Lithium) on the surface of the electrode material is expressed as:

[0130]

[0131] Where j is the positive electrode p or the negative electrode n, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf Represents the lithium ion concentration on the surface of active particles;

[0132] The battery state of charge SOC is expressed as:

[0133]

[0134] Among them, SOL n (t) represents the lithium insertion state of the negative electrode at the current moment, SOL n (0%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium insertion state of the positive electrode at the current moment, SOL p (0%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully discharged, SOL p (100%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully charged;

[0135] The solid phase diffusion equation is used to describe the diffusion process of lithium ions inside the active particles of the electrode. It is often described by Fick's second law to calculate the lithium ion concentration at each location of the active particles. However, the electrode open circuit voltage is only related to the lithium ion concentration on the surface of the active particles. The calculation of the lithium ion concentration on the surface of the active particles using Fick's law is complex. The lithium insertion state on the surface of the active particles under constant current and isothermal conditions is simplified to:

[0136]

[0137] Among them, SOL ini,j represents the initial lithium insertion state, δ j Indicates the intermediate variable, j is the positive electrode p or the negative electrode n, that is, SOL ini,n Indicates the initial lithium insertion state of the negative electrode, SOL ini,p Indicates the initial lithium insertion state of the positive electrode, δ n represents the negative intermediate variable, δ p Represents the positive intermediate variable; λ k is an array that can be calculated using the known characteristic equation and the first 10 values ​​are taken. Then λ k =[0.0148611613482230; 4.49340945790908; 7.72525183693785; 10.9041216594292; 14.0661939128319; 17.2207552719312; 20.3713029592880; 23.5194524986894; 26.6660542588130; 29.8115987908931], calculate λ k The characteristic equation of can be found in “Meng, Guo, Godfrey. Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior[J]. Journal of the Electrochemical Society, 2011.”;

[0138] Among them, the intermediate variable δ p and δ n They are expressed as follows:

[0139]

[0140] Among them, D s,p represents the solid phase diffusion coefficient of the positive electrode active particles; D s,n represents the solid phase diffusion coefficient of the negative electrode active particles; S p Indicates the equivalent active particle surface area of ​​the positive electrode material, unit: m 2 ; S nrepresents the equivalent active particle surface area of ​​the negative electrode material; c s,p,max represents the theoretical maximum lithium ion concentration of the positive electrode active particles; c s,n,max Represents the theoretical maximum lithium ion concentration of the negative electrode active particles; R p Represents the radius of the positive electrode active particle; R n represents the radius of the negative electrode active particles;

[0141] The electrochemical model of lithium-ion batteries only requires the current flowing through the battery and the battery parameters to calculate the battery terminal voltage.

[0142] S2: Determine the electrochemical parameters that need to be identified based on the single particle electrochemical model;

[0143] The electrochemical parameters that need to be identified include the solid phase diffusion coefficient D of the negative electrode active particles s,n , the solid phase diffusion coefficient D of the positive electrode active particles s,p , negative electrode reaction rate constant k n , positive electrode reaction rate constant k p , initial lithium insertion state of negative electrode SOL ini,n , the initial lithium insertion state of the positive electrode SOL ini,p .

[0144] S3: According to the factory information of the battery pack, the charge and discharge current I is given 总 Charge and discharge the battery pack to obtain the experimental voltage curve of each single cell in the battery pack, that is, determine the size of the battery terminal voltage at different charge and discharge times, and obtain the terminal voltage V of the parallel batteries at different times. cell ;

[0145] S4: Determine the optimization target error function f of the parallel lithium-ion batteries;

[0146] The battery error function f is expressed as:

[0147]

[0148] Among them, V i It represents the terminal voltage measurement value of the single cell with serial number i, i represents the serial number of the single cell, i=1,2...n; n is the total number of single cells connected in parallel in the battery pack.

[0149] S5: According to the voltage curve of the battery and the error function f, a simulated annealing algorithm is used to identify the electrochemical parameters of the single cells in the parallel battery pack in the simulation software.

[0150] The specific steps include:

[0151] S5.1: Determine the standard deviation threshold s0

[0152] According to the performance requirements of the battery pack, the standard deviation threshold of the voltage curve is set to s0;

[0153] The standard deviation threshold s0 is set according to the battery type and the number of collected data points.

[0154]

[0155] Where m is the number of battery voltage points collected in the experiment, V max The charging cut-off voltage specified for the battery, V min The discharge cut-off voltage specified for the battery. The difference between the charge cut-off voltage and the discharge cut-off voltage of a lithium-ion battery is usually between 0.5-1.5V.

[0156] S5.2: Determine the simulated current C(i)

[0157] For lithium-ion batteries used in parallel, differences in cells lead to uneven current distribution inside the battery, such as Figure 1 As shown, n lithium-ion batteries are used in parallel. Due to the differences between the batteries, the currents I1, I2, ...In between the lithium-ion batteries are different, but the voltage across the battery is V1 = V2 = ... = V at any time. n When batteries are used in parallel, it is usually impossible to measure the current flowing through each parallel branch due to cost, circuit structure and other reasons. Therefore, batteries used in parallel can usually only measure the total current flowing through the battery and I 总 , the voltage across the battery V cell .

[0158] Therefore, for a parallel circuit, the total current of the parallel batteries is I 总 :

[0159]

[0160] Among them, I i Represents the current flowing through the single battery i in parallel, i = 1, 2, ... n, n is the total number of batteries in parallel;

[0161] Battery terminal voltage V cell :

[0162] V cell =V1=V2=......=V n (18)

[0163] Where n is the total number of single cells connected in parallel, V1, V2, V3...V n is the voltage across each single battery;

[0164] Given the total current I of the parallel connected batteries 总, then the current C(i) of the single cell i in the n branches is:

[0165]

[0166] Among them, σ*randn(1,n) means random generation with standard deviation σ and mean value I 总 / n are the currents I of the n branches respectively. i ;

[0167] Therefore, the method for identifying the electrochemical parameters of parallel lithium-ion batteries in this embodiment is to identify the electrochemical parameters of each branch battery when the total current and voltage experimental data of the parallel batteries are known. The process is as follows: Figure 2 shown.

[0168] S5.3: Get the simulated voltage curve

[0169] In the simulation software, for single cell i, the initial value of the electrochemical parameter is given first, and then the single cell i is charged and discharged with the current C(i) as the charge and discharge current to obtain the simulation voltage curve of each single cell;

[0170] S5.4: Calculation Error

[0171] like Figure 5 As shown, the error f of each single cell is calculated based on the simulated battery terminal voltage and the experimental battery terminal voltage at the corresponding points in the simulated voltage curve and the experimental voltage curve, and the formula (19) of the error function f opz (i)

[0172]

[0173] According to formula (20), the total error f of the battery pack is calculated total :

[0174]

[0175]

[0176] Among them, V ij It represents the terminal voltage of single cell i at time j, i = 1, 2, ... n; j = 1, 2, ... m; n represents the number of single cells, and m represents the total number of each single cell voltage curve at different times;

[0177] S5.5: Calculate standard deviation

[0178] According to the terminal voltage V on the simulation voltage curve ij Calculate the standard deviation s of the simulated terminal voltage i , then s i for:

[0179]

[0180] in, represents the average value of the m simulated terminal voltages of single cell i;

[0181] Determine the standard deviation i With the size of the standard deviation threshold s0, when s i <s0, at this time, the corresponding electrochemical parameter value is the optimal value; otherwise, the total error f total The size of the current error minimum value f, when f total When <f, reduce the current distribution I i The standard deviation σ between them is set to 0.9σ, and the total error f is recorded. total As the minimum error value f; when f total >f, increase the current distribution I i The standard deviation σ between them is set to 1.1σ, and the minimum error value f is kept unchanged; it should be noted that before entering the judgment, the total error f total and the minimum error value f are initialized. In this embodiment, the initial values ​​of both are 0.

[0182] Then, the process returns to step S5.2, and the electrochemical parameters are updated, and the identification is continued until the parameter identification of all the single cells in the battery pack is completed.

[0183] In this embodiment, the battery terminal voltage V cell Indicates that the total current I 总 When the battery is at the same voltage, Vcell is a data set related to the time interval; V1 is the current C1I of battery 1 under a set of electrochemical parameters. 总 The data set of the terminal voltage of the simulated battery at both ends;

[0184] The uniformity index is introduced to quantify the consistency between parallel lithium-ion battery cells. The expression is as follows:

[0185]

[0186] Among them, j max 、j min 、j avg They are respectively one of the six electrochemical parameters of each single cell. It can be seen that the smaller the uniformity index is, the smaller the difference between the battery cells is. The uniformity index of the current distribution ratio C comprehensively reflects the inconsistency inside the battery.

[0187] In this embodiment, the current flowing through the battery i branch is I i, identify the six electrochemical parameters of battery i. The basic idea of ​​identification is as follows Figure 2 As shown, the simulation voltage under given electrochemical parameters is calculated, the square error between the simulation voltage and the parallel battery experimental voltage curve is calculated, the six electrochemical parameters that need to be identified are changed, and the battery parameters are updated when the parameter update conditions are met.

[0188] The parameter update adopts the simulated annealing algorithm. The principle of "simulated annealing" is: apply the theory of thermodynamics to statistics, imagine each point in the search space as a molecule in the air, and the energy of the molecule is its own kinetic energy. And each point in the search space also carries "energy" like air molecules to indicate the suitability of the point for the proposition. The algorithm starts with an arbitrary point in the search space, selects a "neighbor" at each step, and then calculates the probability of reaching the "neighbor" from the current position. The simulated annealing algorithm can be decomposed into three parts: solution space, objective function and initial solution.

[0189] like Figure 4 As shown in the figure, the specific steps of using the simulated annealing algorithm to identify the electrochemical model parameters are as follows:

[0190] (1) Parameter initialization. First, obtain the initial battery parameter param from the reference. param is a struct variable, which includes chemical parameters such as battery diffusion coefficient, reaction rate constant, and active particle radius. Set the optimized parameter to opz_param and the next state of the parameter to next_param, and assign param to these two parameters. Set the parameter T to the empirical value of 10000.

[0191] (2) Get the next state of the parameter. next_param = next_param + [-step + 2*step*rand(1,1)], step is the parameter update step, step includes the positive and negative electrode reaction rate change step, diffusion coefficient change step, initial lithium insertion concentration change step, a total of six steps, the empirical value is set to 1 / 20 of the initial value of the parameter, T = T-0.01. Among them, T itself has no meaning. It only represents the calculation step and the number of calculations. As T decreases, when the simulation result error of the next state of the parameter is greater than the minimum optimization error, the current parameter is accepted with a certain probability and the optimization parameter is updated.

[0192] (3) Determine the temperature. When the temperature T < 0, the simulation ends, and when T > 0, proceed to the next step.

[0193] (4) Obtaining the simulated battery terminal voltage. Input the two sets of parameters opz_param and next_param into the electrochemical model to obtain the simulated output terminal voltages Vsim_next and Vsim_opz of the model.

[0194] (5) Comparison error. The two - times errors, fnext and fopz, are calculated respectively between the battery terminal voltage obtained by simulation and the experimental Vcell data. When fnext <= fopz, accept the parameter change, opz_param = nxet_param, and return to step 2; when fnext > fopz, go to step 6.

[0195] (6) Determine whether to accept the next state of the parameter. Accept the next state of the battery parameter with a certain probability. dE = fnext - fopz, P = exp(-dE / T / K). Generate a random number rand(1,1) between 0 and 1. When Rand(1,1) > P, accept the parameter change, opz_param = nxet_param, and return to step 2; when Rand(1,1) < P, directly return to step 2. k is a constant, set to 2, and exp represents the natural exponent.

[0196] Parameter identification is carried out based on the simulated annealing algorithm, and there are two cases of parameter update

[0197] 1. The simulated voltage of the next - state parameter next_param is smaller than the error between the simulated voltage of the current parameter opz_param and the experimental voltage, that is, fnext < fopz, and update the battery electrochemical parameter fopz = fnext

[0198] 2. When fnext > fopz, accept the next - state parameter next_param of the parameter with a certain probability, and this probability decreases with the increase of the number of calculations.

[0199] Through Figure 3 The least - squares error fopz(i) of battery i is finally obtained through the process shown. The errors after identifying n batteries are as Figure 5 shown.

[0200] The electrochemical model in the present invention adopts an improved single - particle electrochemical model. The positive and negative electrodes of the battery are regarded as an active particle respectively. The electrochemical parameter identification method based on this single - particle electrochemical model is applicable not only to a single battery but also to lithium - ion batteries after parallel connection. By identifying the electrochemical parameters of each single battery in the parallel - connected lithium - ion batteries, the battery consistency is analyzed, providing a basis for judging whether the battery can continue to be used in parallel.

[0201] Inspired by the ideal embodiments of the present invention described above, through the above - mentioned description, relevant staff can make various changes and modifications completely within the scope not deviating from the present invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for identifying electrochemical parameters of parallel lithium-ion batteries, characterized in that: The following steps are involved: S1: The positive and negative electrodes of the battery are equivalent to single particles respectively, and the single particle electrochemical model of the battery is established; S2: Determine the electrochemical parameters that need to be identified based on the single particle electrochemical model; S3: According to the factory information of the battery pack, the charge and discharge current I is given 总 Charge and discharge the battery pack to obtain the experimental voltage curve of each single cell in the battery pack, and obtain the terminal voltage V of the parallel batteries at different times. cell ; S4: Determine the optimization target error function f of the parallel lithium-ion batteries; S5: According to the voltage curve of the battery and the error function f, a simulated annealing algorithm is used to identify the electrochemical parameters of the single cells in the parallel battery pack in the simulation software; Wherein, establishing the electrochemical model of the battery in step S1 specifically includes the following steps: When a certain current flows through the two ends of the battery, the lithium ions, active particles, and electrons in the electrolyte interact to maintain the stability of the external current. The current density i on the active surface of the electrode is j for: Among them, i j Indicates the current density of the active surface of the electrode, unit: A / m 2 ; I represents the current flowing into the two ends of the battery, unit: A; S j Indicates the equivalent active particle surface area of ​​the electrode material, in m 2 ; j represents the positive electrode p or the negative electrode n; Then the pore wall flux of lithium ions at the interface between active particles and electrolyte is j j for: Among them, j j Indicates the pore wall flux, unit: mol / (m 2 ·s); n represents the nuclear charge number of lithium ions, that is, n=1; F represents the Faraday constant 96487C / mol; Or, the pore wall flux j j It is expressed by the Butler-Volmer electrochemical reaction equation: Among them, k j represents the liquid conductivity, η j is the surface overpotential, c e represents the liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf represents the lithium ion concentration on the surface of active particles, T is the current battery temperature, and R represents the gas constant 8.31441 (J / (mol*K)); The surface overpotential η in formula (3) j for: or j =φ s,j -f l,j -U j (4) Among them, φ s,j represents the solid phase potential, φ l,j represents the liquid phase potential, U j represents the equilibrium potential; The terminal voltage V of the known battery cell It can be expressed as: V cell =φ s,p -f s,n (5) Among them, φ s,p represents the solid phase potential of the positive electrode, φ s,n represents the solid phase potential of the negative electrode; The difference in overpotential between the positive and negative electrodes is derived as p -η n : Among them, m j is an intermediate variable, j represents the positive electrode p or the negative electrode n, then m j for: Among them, k j represents the reaction rate constant, j is the positive electrode p or the negative electrode n, that is, k n represents the negative electrode reaction rate constant, k p represents the positive electrode reaction rate constant; Substituting formula (4) and formula (6) into formula (5), the terminal voltage V of the battery can be derived: cell : V cell =U p (x p,surf )-U n (x n,surf )+η p -η n +U l (8) Among them, U p (x p,surf ) represents the positive electrode equilibrium potential, U n (x n,surf ) represents the negative electrode equilibrium potential, U l represents the liquid phase potential; x p,surf and x n,surf All are dimensionless quantities related to the lithium ion concentration on the surface of active particles; The liquid potential U in formula (8) l The calculation formula is: Among them, t + Lithium ion liquid phase transfer coefficient, c eL represents the liquid lithium ion concentration at the interface between the positive electrode material and the current collector, c e0 A represents the concentration of liquid lithium ions at the boundary of the negative electrode material and current collector, cell Represents the battery surface area, L p Indicates the thickness of the positive electrode material, L n Indicates the thickness of the negative electrode material, L S Indicates the thickness of the diaphragm, k p represents the positive electrode liquid conductivity, k n represents the negative electrode liquid conductivity, k s represents the conductivity of the diaphragm liquid phase, ε p represents the volume fraction of the positive electrode liquid phase, ε n represents the volume fraction of the negative electrode liquid phase, ε s represents the volume fraction of the diaphragm liquid phase; Positive electrode equilibrium potential U p (x p,surf ) is a function of the lithium concentration on the surface of the positive electrode active particles, and the negative electrode equilibrium potential U n (x n,surf ) is a function of the lithium concentration on the surface of the negative electrode active particles; by consulting the material properties to obtain the material properties of the positive and negative electrodes, then x j,surf The lithium insertion state SOL on the surface of the electrode material is expressed as: Where j is the positive electrode p or the negative electrode n, c s,j,max represents the theoretical maximum lithium insertion concentration of active particles, c s,j,surf Represents the lithium ion concentration on the surface of active particles; The battery state of charge SOC is expressed as: Among them, SOL n (t) represents the lithium insertion state of the negative electrode at the current moment, SOL n (0%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) indicates the lithium insertion state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium insertion state of the positive electrode at the current moment, SOL p (0%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully discharged, SOL p (100%) indicates the lithium insertion state of the positive electrode active particles when the battery is fully charged; The lithium embedding state on the surface of active particles under constant current and isothermal conditions is simplified to: Among them, SOL ini,j represents the initial lithium insertion state, δ j Indicates the intermediate variable, j is the positive electrode p or the negative electrode n, that is, SOL ini,n Indicates the initial lithium insertion state of the negative electrode, SOL ini,p Indicates the initial lithium insertion state of the positive electrode, δ n represents the negative intermediate variable, δ p Represents the positive intermediate variable; λ k is an array that can be calculated using the known characteristic equation and the first 10 values ​​are taken. Then λ k =[0.0148611613482230; 4.49340945790908; 7.72525183693785; 10.9041216594292; 14.0661939128319; 17.2207552719312; 20.3713029592880; 23.5194524986894; 26.6660542588130; 29.8115987908931]; Among them, the intermediate variable δ p and δ n They are expressed as follows: Among them, D s,p represents the solid phase diffusion coefficient of the positive electrode active particles; D s,n represents the solid phase diffusion coefficient of the negative electrode active particles; S p Indicates the equivalent active particle surface area of ​​the positive electrode material, unit: m 2 ; S n represents the equivalent active particle surface area of ​​the negative electrode material; c s,p,max represents the theoretical maximum lithium ion concentration of the positive electrode active particles; c s,n,max Represents the theoretical maximum lithium ion concentration of the negative electrode active particles; R p Represents the radius of the positive electrode active particle; R n represents the radius of the negative electrode active particles; The electrochemical model of lithium-ion batteries only requires the current flowing through the battery and the battery parameters to calculate the battery terminal voltage.

2. The method for identifying electrochemical parameters of parallel lithium-ion batteries according to claim 1, characterized in that: The electrochemical parameters that need to be identified include the solid phase diffusion coefficient D of the negative electrode active particles s,n , the solid phase diffusion coefficient D of the positive electrode active particles s,p , negative electrode reaction rate constant k n , positive electrode reaction rate constant k p , initial lithium insertion state of negative electrode SOL ini,n , the initial lithium insertion state of the positive electrode SOL ini,p .

3. The method for identifying electrochemical parameters of parallel lithium-ion batteries according to claim 2, characterized in that: The battery error function f in step S4 is expressed as: Among them, V i It represents the terminal voltage measurement value of the single cell with serial number i, i represents the serial number of the single cell, i=1,2...n; n is the total number of single cells connected in parallel in the battery pack.

4. The method for identifying electrochemical parameters of parallel lithium-ion batteries according to claim 3, characterized in that: The parameter identification process in step S5 specifically includes the following steps: S5.1: Determine the standard deviation threshold s0 According to the performance requirements of the battery pack, the standard deviation threshold of the voltage curve is set to s0; S5.2: Determine the simulated current C(i) For a parallel circuit, the total current of the parallel batteries is I 总 : Among them, I i Represents the current flowing through the single battery i in parallel, i = 1, 2, ... n, n is the total number of batteries in parallel; Battery terminal voltage V cell : V cell =V1=V2=......=V n (18) Where n is the total number of single cells connected in parallel, V1, V2, V3...V n is the voltage across each single battery; Given the total current I of the parallel connected batteries 总 , then the current C(i) of the single cell i in the n branches is: Among them, σ*randn(1,n) means random generation with standard deviation σ and mean value I 总 / n are the currents I of the n branches respectively. i ; S5.3: Get the simulated voltage curve In the simulation software, for single cell i, the initial value of the electrochemical parameter is given first, and then the single cell i is charged and discharged with the current C(i) as the charge and discharge current to obtain the simulation voltage curve of each single cell; S5.4: Calculation Error Then, the error f of each single cell is calculated based on the simulated battery terminal voltage and the experimental battery terminal voltage at the corresponding points in the simulated voltage curve and the experimental voltage curve, and the formula (19) of the error function f opz (i) According to formula (20), the total error f of the battery pack is calculated total : Among them, V ij It represents the terminal voltage of single cell i at time j, i = 1, 2, ... n; j = 1, 2, ... m; n represents the number of single cells, and m represents the total number of each single cell voltage curve at different times; S5.5: Calculate standard deviation According to the terminal voltage V on the simulation voltage curve ij Calculate the standard deviation s of the simulated terminal voltage i , then s i for: Among them, V i represents the average value of the m simulated terminal voltages of single cell i; Determine the standard deviation i With the size of the standard deviation threshold s0, when s i <s0, at this time, the corresponding electrochemical parameter value is the optimal value; otherwise, the total error f total The size of the current error minimum value f, when f total When <f, reduce the current distribution I i The standard deviation σ between them is set to 0.9σ, and the total error f is recorded. total As the minimum error value f; when f total >f, increase the current distribution I i The standard deviation σ between them is set to 1.1σ, and the minimum error value f is kept unchanged; Then, the process returns to step S5.2, and the electrochemical parameters are updated, and the identification is continued until the parameter identification of all the single cells in the battery pack is completed.

5. The method for identifying electrochemical parameters of parallel lithium-ion batteries according to claim 4, characterized in that: The setting of the standard deviation threshold s0 in step S5.1 is determined according to the battery type and the number of collected data points. Where m is the number of battery voltage points collected in the experiment, V max The charging cut-off voltage specified for the battery, V min The discharge cut-off voltage specified for the battery.

6. The method for identifying electrochemical parameters of parallel lithium-ion batteries according to claim 4, characterized in that: The battery terminal voltage V cell Indicates that the total current I 总 When the battery is at the same voltage, Vcell is a data set related to the time interval; V1 is the current C1I of battery 1 under a set of electrochemical parameters. 总 The data set of the terminal voltage of the simulated battery at both ends; The uniformity index is introduced to quantify the consistency between parallel lithium-ion battery cells. The expression is as follows: Among them, j max 、j min 、j avg Each cell is one of the six electrochemical parameters.

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