CN113868934B - A method for identifying electrochemical parameters of parallel lithium-ion batteries - Google Patents
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- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 title claims abstract description 87
- 229910001416 lithium ion Inorganic materials 0.000 title claims abstract description 87
- 238000000034 method Methods 0.000 title claims abstract description 20
- 239000002245 particle Substances 0.000 claims abstract description 111
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 10
- 238000002922 simulated annealing Methods 0.000 claims abstract description 10
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 claims description 61
- 229910052744 lithium Inorganic materials 0.000 claims description 61
- 238000009830 intercalation Methods 0.000 claims description 58
- 230000002687 intercalation Effects 0.000 claims description 58
- 239000007791 liquid phase Substances 0.000 claims description 44
- 239000007790 solid phase Substances 0.000 claims description 25
- 238000009792 diffusion process Methods 0.000 claims description 21
- 238000004088 simulation Methods 0.000 claims description 19
- 238000007599 discharging Methods 0.000 claims description 15
- 238000004364 calculation method Methods 0.000 claims description 13
- 238000003411 electrode reaction Methods 0.000 claims description 9
- 230000004907 flux Effects 0.000 claims description 9
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- 239000007774 positive electrode material Substances 0.000 claims description 9
- 238000006243 chemical reaction Methods 0.000 claims description 8
- 239000007772 electrode material Substances 0.000 claims description 6
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Abstract
本发明提供一种并联锂离子电池电化学参数辨识方法，将电池的正负极分别等效为单个粒子，建立电池的单粒子电化学模型；根据单粒子电化学模型确定需要辨识的电化学参数；根据电池组的出厂信息，给定充放电电流I总对电池组进行充放电，获得电池组中每个单体电池的实验电压曲线，得到不同时刻并联电池的端电压Vcell；确定并联锂离子电池的优化目标误差函数f；根据电池的电压曲线以及误差函数f，采用模拟退火算法，在仿真软件中对并联电池组中单体电池的电化学参数进行辨识。该发明对通过辨识并联锂离子电池中每个单体电池的电化学参数，分析电池一致性，为判断电池是否还能继续并联使用提高依据。
The present invention provides a method for identifying electrochemical parameters of parallel lithium-ion batteries, which respectively equates the positive and negative electrodes of the battery to single particles, establishes a single-particle electrochemical model of the battery; determines the electrochemical parameters to be identified based on the single-particle electrochemical model; charges and discharges the battery pack with a given charge and discharge current Itotal according to the factory information of the battery pack, obtains the experimental voltage curve of each single cell in the battery pack, and obtains the terminal voltage Vcell of the parallel batteries at different times; determines the optimized target error function f of the parallel lithium-ion batteries; and uses a simulated annealing algorithm based on the voltage curve and error function f of the battery to identify the electrochemical parameters of the single cells in the parallel battery pack in the simulation software. The invention provides a basis for determining whether the battery can continue to be used in parallel by identifying the electrochemical parameters of each single cell in the parallel lithium-ion battery and analyzing the battery consistency.
Description
Technical Field
The invention relates to the technical field of lithium ion batteries, in particular to a method for identifying electrochemical parameters of parallel lithium ion batteries.
Background
The teachings of 1933 Doyle and Numan have proposed a physical-based quasi-two-dimensional (P2D, pseudo two dimention model) electrochemical model describing cell internal coupling relationships by partial differential equations such as solid-phase diffusion equations, liquid-phase diffusion equations, bulter Volumer, etc. Meanwhile, the electrochemical model can be coupled with a thermal model, so that lithium precipitation, thermal runaway and the like of the battery are analyzed, and therefore, the improvement of the identification accuracy of the electrochemical parameters is of great significance.
The P2D electrochemical model has large calculated amount, the single particle model respectively equivalent the anode and the cathode to single particles, and the concentration of particles in the battery is neglected to be uneven, so that the calculation is simplified. In the prior art, the calculated amount of the P2D electrochemical model is large, the anode and the cathode are respectively equivalent to single particles by a single particle model, the concentration of particles in the battery is neglected to be uneven, and the calculation is simplified.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects in the prior art, and provides a method for identifying electrochemical parameters of parallel lithium ion batteries.
The technical scheme adopted for solving the technical problems is that the method for identifying the electrochemical parameters of the parallel lithium ion batteries comprises the following steps:
S1, respectively and equivalently converting the anode and the cathode of a battery into single particles, and establishing a single-particle electrochemical model of the battery;
s2, determining electrochemical parameters to be identified according to a single-particle electrochemical model;
S3, according to factory information of the battery pack, charging and discharging the battery pack by giving a charging and discharging current I Total (S) to obtain an experimental voltage curve of each single battery in the battery pack, namely determining the voltage of the battery terminal under different charging and discharging time to obtain terminal voltage V cell of the parallel batteries at different moments;
s4, determining an optimization objective error function f of the parallel lithium ion batteries;
and S5, identifying electrochemical parameters of the single batteries in the parallel battery pack in simulation software by adopting a simulated annealing algorithm according to the voltage curve and the error function f of the batteries.
Further, the step S1 of establishing an electrochemical model of the battery specifically includes the following steps:
When current with a certain magnitude is introduced into the two ends of the battery, the interaction of lithium ions, active particles and electrons in the electrolyte maintains the stability of external current, and the current density i j of the active surface of the electrode is as follows:
Wherein I j represents the current density of the active surface of the electrode, the unit is A/m 2, the unit is A when the current is introduced into the two ends of the battery, S j represents the equivalent active particle surface area of the electrode material, the unit is m 2, and j represents the positive electrode p or the negative electrode n;
The pore wall flux of lithium ions at the interface of the active particles and the electrolyte is j j:
Wherein j j represents pore wall flux in mol/(m 2. Multidot. S), n represents lithium ion nuclear charge number, i.e., n= 1;F represents Faraday constant 96487C/mol;
meanwhile, the pore wall flux j j can also be expressed by the Butler-Fu Erma (Butler-Volmer) electrochemical reaction equation:
Wherein K j represents liquid phase conductivity, η j represents surface overpotential, c e represents liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents active particle theoretical maximum lithium intercalation lithium ion concentration, c s,j,surf represents active particle surface lithium ion concentration, T is current battery temperature, and R represents gas constant 8.31441 (J/(mol×k));
The surface overpotential η j in the formula (3) is:
ηj＝φs,j-φl,j-Uj (4)
Wherein phi s,j represents a solid phase potential, phi l,j represents a liquid phase potential, and U j represents an equilibrium potential;
The terminal voltage V cell of a known battery can be expressed as:
Vcell＝φs,p-φs,n (5)
Wherein phi s,p represents the solid phase potential of the positive electrode, and phi s,n represents the solid phase potential of the negative electrode;
The difference η p-ηn in positive and negative electrode surface overpotential is deduced:
wherein m j is an intermediate variable, j represents positive electrode p or negative electrode n, and m j is:
Wherein k j represents a reaction rate constant, j is a positive electrode p or a negative electrode n, i.e., k n represents a negative electrode reaction rate constant, and k p represents a positive electrode reaction rate constant;
The derivation of equation (6) is described in the literature "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)".
Bringing equations (4) and (6) into equation (5) derives the terminal voltage V cell of the battery:
Vcell＝Up(xp,surf)-Un(xn,surf)+ηp-ηn+Ul (8)
Wherein U p(xp,surf) represents a positive equilibrium potential, U n(xn,surf) represents a negative equilibrium potential, U l represents a liquid phase potential, x p,surf and x n,surf are both dimensionless quantities related to the lithium ion concentration at the surface of the active particles;
The calculation formula of the liquid phase potential U l in the formula (8) is:
Wherein t + lithium ion liquid phase transfer coefficient, c eL represents the liquid phase lithium ion concentration at the interface of the positive electrode material and the current collector, c e0 represents the liquid phase lithium ion concentration at the interface of the negative electrode material and the current collector, A cell represents the surface area of the battery, L p represents the thickness of the positive electrode material, L n represents the thickness of the negative electrode material, L S represents the thickness of the diaphragm, k p represents the positive liquid phase conductivity, k n represents the negative liquid phase conductivity, k s represents the diaphragm liquid phase conductivity, ε p represents the positive liquid phase volume fraction, ε n represents the negative liquid phase volume fraction, ε s represents the diaphragm liquid phase volume fraction;
positive electrode equilibrium potential U p(xp,surf) is a function of the lithium intercalation concentration on the surface of the positive electrode active particles, negative electrode equilibrium potential U n(xn,surf) is a function of the lithium intercalation concentration on the surface of the negative electrode active particles, and x j,surf is expressed as the state SOL (State of Lithium) of the lithium intercalation on the surface of the electrode material by referring to the material properties to obtain the material properties of the positive and negative electrodes:
Wherein j is positive electrode p or negative electrode n, c s,j,max represents the theoretical maximum lithium intercalation lithium ion concentration of the active particles, and c s,j,surf represents the lithium ion concentration on the surfaces of the active particles;
the state of charge SOC of the battery is expressed as:
Wherein SOL n (t) represents the lithium intercalation state of the negative electrode at the current time, SOL n (0%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium intercalation state of the positive electrode at the current time, SOL p (0%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully discharged, and SOL p (100%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully charged;
The solid-phase diffusion equation is used for describing the diffusion process of lithium ions in the electrode active particles, and is usually described by Fick's second law, so as to calculate the concentration of lithium ions on each position of the active particles, but the open-circuit voltage of the electrode is only related to the concentration of lithium ions on the surfaces of the active particles, and the calculation of the concentration of lithium ions on the surfaces of the active particles is complex by adopting Fick's law. The lithium intercalation state on the surface of the active particles under constant current and isothermal conditions is simplified into:
Wherein SOL ini,j represents an initial lithium intercalation state, delta j represents an intermediate variable, j is positive electrode p or negative electrode n, namely SOL ini,n represents a negative electrode initial lithium intercalation state, SOL ini,p represents a positive electrode initial lithium intercalation state, delta n represents a negative electrode intermediate variable, delta p represents a positive electrode intermediate variable, lambda k is an array which can be obtained through calculation by a known characteristic equation and takes the first 10 values, and the characteristic equation of lambda k calculated by λk＝[0.0148611613482230;4.49340945790908;7.72525183693785;10.9041216594292;14.0661939128319;17.2207552719312;20.3713029592880;23.5194524986894;26.6660542588130;29.8115987908931], is shown in the specification "Meng,Guo,Godfrey.Single-Particle Model for a Lithium-Ion Cell:Thermal Behavior[J].Journal of the Electrochemical Society,2011.";
Wherein, the intermediate variables δ p and δ n are respectively expressed as:
wherein D s,p represents a solid-phase diffusion coefficient of positive electrode active particles, D s,n represents a solid-phase diffusion coefficient of negative electrode active particles, S p represents an equivalent active particle surface area of a positive electrode material, unit m 2;Sn represents an equivalent active particle surface area of a negative electrode material, c s,p,max represents a theoretical maximum lithium intercalation lithium ion concentration of the positive electrode active particles, c s,n,max represents a theoretical maximum lithium intercalation lithium ion concentration of the negative electrode active particles, R p represents a radius of the positive electrode active particles, and R n represents a radius of the negative electrode active particles;
the electrochemical model of the lithium ion battery can calculate the terminal voltage of the battery only by knowing the magnitude of the current flowing through the battery and various parameters of the battery.
Further, the electrochemical parameters to be identified include a negative electrode active particle solid phase diffusion coefficient D s,n, a positive electrode active particle solid phase diffusion coefficient D s,p, a negative electrode reaction rate constant k n, a positive electrode reaction rate constant k p, a negative electrode initial lithium intercalation state SOL ini,n, and a positive electrode initial lithium intercalation state SOL ini,p.
Further, the battery error function f in step S4 is formulated as:
Wherein V i represents a cell terminal voltage measurement value with a number i, i represents a cell number i=1, 2.
Further, the process of parameter identification in step S5 specifically includes the following steps:
s5.1 determining the standard deviation threshold value as S 0
Setting a standard deviation threshold of a voltage curve as s 0 according to the performance requirement of the battery pack;
s5.2 determining the simulation current C (i)
For a parallel circuit, the total current of the parallel cells I Total (S) :
Wherein I i represents the current flowing through the parallel unit cells I, i=1, 2, &.. n is the total number of parallel batteries;
terminal voltage V cell of battery:
Vcell＝V1＝V2＝......＝Vn (18)
wherein n is the total number of the unit batteries connected in parallel, and V 1、V2、V3……Vn is the voltage at two ends of each unit battery;
Given the total current I Total (S) of the parallel cells, the current C (I) of the cell I in the n branches is:
Wherein, sigma is randn (1, n) represents that the current I i which takes the standard deviation as sigma and the average value as I Total (S) /n as n branches is randomly generated;
s5.3, obtaining a simulation voltage curve
In simulation software, an initial value of an electrochemical parameter is given to a single battery i, and then the single battery i is charged and discharged by taking a current C (i) as a charging and discharging current, so that a simulation voltage curve of each single battery is obtained;
s5.4 calculating errors
Then calculating the error f opz (i) of each single battery according to the simulated battery terminal voltage and the experimental battery terminal voltage of the corresponding points in the simulated voltage curve and the experimental voltage curve and the formula (19) of the error function f:
the total error f total of the battery pack is calculated according to equation (20):
Wherein V ij represents the terminal voltage of the unit cell i at the time j, i=1, 2. J=1, 2, once again, m; n represents the number of single batteries, m represents the total number of different moments on each single battery voltage curve;
S5.5 calculating standard deviation
Calculating standard deviation s i of the simulated terminal voltage according to the terminal voltage V ij on the simulated voltage curve, and s i is:
Wherein, Representing the average value of m simulation terminal voltages of the single battery i;
Judging the sizes of a standard deviation s i and a standard deviation threshold s 0, when s i＜s0, the corresponding electrochemical parameter value is the optimal value, otherwise, judging the sizes of a total error f total and a current error minimum value f, when f total is smaller than f, reducing the standard deviation sigma between current distribution I i to ensure sigma=0.9sigma, and recording the total error f total as the error minimum value f, and when f total is larger than f, increasing the standard deviation sigma between current distribution I i to ensure sigma=1.1sigma, and keeping the error minimum value f unchanged;
And then returning to the step S5.2, updating the electrochemical parameters, and continuing to identify until the parameter identification of all the single batteries in the battery pack is completed.
Further, in step S5.1, the standard deviation threshold S 0 is set according to the battery type and the number of data points to be collected
Wherein m is the number of battery voltage points acquired through experiments, V max is the charging cut-off voltage specified by the battery, V min is the discharging cut-off voltage specified by the battery, and the voltage difference between the charging cut-off voltage and the discharging cut-off voltage of the lithium ion battery is usually between 0.5 and 1.5V.
Further, the battery terminal voltage V cell represents the battery terminal voltage across the battery as the battery passes through the total current I Total (S) , and therefore Vcell is a data set related to the time interval, V 1 is a data set of the battery 1 simulating the battery terminal voltage across the battery as it passes through the current C 1I Total (S) under a set of electrochemical parameters;
Introducing a uniformity index, quantifying the uniformity among the parallel lithium ion battery monomers, and the expression is as follows:
Wherein j max、jmin、javg is one of six electrochemical parameters of each single cell, respectively, it can be seen that the smaller the uniformity index is, the smaller the difference between the single cells is, wherein the uniformity index of the current distribution ratio C comprehensively reflects the non-uniformity inside the cell.
The method has the beneficial effects that the solid-phase diffusion is simplified into two-parameter and three-parameter approximation, the electrochemical parameters are identified by adopting a single particle model, the liquid-phase potential change is added on the basis of the single particle model, and the local volume current density is adopted to replace the change of the lithium ion flow along the thickness direction, so that a plurality of electrochemical parameters are identified.
Drawings
The invention is further described below with reference to the drawings and examples.
Fig. 1 is a schematic diagram of a parallel battery pack of the present invention.
Fig. 2 is a schematic diagram illustrating parameter identification of a single battery according to the present invention.
FIG. 3 is a flow chart of electrochemical parameter identification for parallel lithium ion batteries according to the present invention.
Fig. 4 is a parameter identification flow of the single battery i based on the simulated annealing algorithm.
Fig. 5 is a schematic diagram of the experimental data and simulation data of the present invention to calculate the total error.
Detailed Description
The present invention will now be described in detail with reference to the accompanying drawings. The figure is a simplified schematic diagram illustrating the basic structure of the invention only by way of illustration, and therefore it shows only the constitution related to the invention.
As shown in fig. 1-5, the method for identifying electrochemical parameters of parallel lithium ion batteries of the invention comprises the following steps:
S1, respectively and equivalently converting the anode and the cathode of a battery into single particles, and establishing a single-particle electrochemical model of the battery;
the method for establishing the electrochemical model of the battery specifically comprises the following steps:
When current with a certain magnitude is introduced into the two ends of the battery, the interaction of lithium ions, active particles and electrons in the electrolyte maintains the stability of external current, and the current density i j of the active surface of the electrode is as follows:
Wherein I j represents the current density of the active surface of the electrode, the unit is A/m 2, the unit is A when the current is introduced into the two ends of the battery, S j represents the equivalent active particle surface area of the electrode material, the unit is m 2, and j represents the positive electrode p or the negative electrode n;
The pore wall flux of lithium ions at the interface of the active particles and the electrolyte is j j:
Wherein j j represents pore wall flux in mol/(m 2. Multidot. S), n represents lithium ion nuclear charge number, i.e., n= 1;F represents Faraday constant 96487C/mol;
meanwhile, the pore wall flux j j can also be expressed by the Butler-Fu Erma (Butler-Volmer) electrochemical reaction equation:
Wherein K j represents liquid phase conductivity, η j represents surface overpotential, c e represents liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents active particle theoretical maximum lithium intercalation lithium ion concentration, c s,j,surf represents active particle surface lithium ion concentration, T is current battery temperature, and R represents gas constant 8.31441 (J/(mol×k));
The surface overpotential η j in the formula (3) is:
ηj＝φs,j-φl,j-Uj (4)
Wherein phi s,j represents a solid phase potential, phi l,j represents a liquid phase potential, and U j represents an equilibrium potential;
The terminal voltage V cell of a known battery can be expressed as:
Vcell＝φs,p-φs,n (5)
Wherein phi s,p represents the solid phase potential of the positive electrode, and phi s,n represents the solid phase potential of the negative electrode;
The difference η p-ηn in positive and negative electrode surface overpotential is deduced:
wherein m j is an intermediate variable, j represents positive electrode p or negative electrode n, and m j is:
Wherein k j represents a reaction rate constant, j is a positive electrode p or a negative electrode n, i.e., k n represents a negative electrode reaction rate constant, and k p represents a positive electrode reaction rate constant;
The derivation of equation (6) is described in the literature "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)".
Bringing equations (4) and (6) into equation (5) derives the terminal voltage V cell of the battery:
Vcell＝Up(xp,surf)-Un(xn,surf)+ηp-ηn+Ul (8)
Wherein U p(xp,surf) represents a positive equilibrium potential, U n(xn,surf) represents a negative equilibrium potential, U l represents a liquid phase potential, x p,surf and x n,surf are both dimensionless quantities related to the lithium ion concentration at the surface of the active particles;
The calculation formula of the liquid phase potential U l in the formula (8) is:
Wherein t + lithium ion liquid phase transfer coefficient, c eL represents the liquid phase lithium ion concentration at the interface of the positive electrode material and the current collector, c e0 represents the liquid phase lithium ion concentration at the interface of the negative electrode material and the current collector, A cell represents the surface area of the battery, L p represents the thickness of the positive electrode material, L n represents the thickness of the negative electrode material, L S represents the thickness of the diaphragm, k p represents the positive liquid phase conductivity, k n represents the negative liquid phase conductivity, k s represents the diaphragm liquid phase conductivity, ε p represents the positive liquid phase volume fraction, ε n represents the negative liquid phase volume fraction, ε s represents the diaphragm liquid phase volume fraction;
positive electrode equilibrium potential U p(xp,surf) is a function of the lithium intercalation concentration on the surface of the positive electrode active particles, negative electrode equilibrium potential U n(xn,surf) is a function of the lithium intercalation concentration on the surface of the negative electrode active particles, and x j,surf is expressed as the state SOL (State of Lithium) of the lithium intercalation on the surface of the electrode material by referring to the material properties to obtain the material properties of the positive and negative electrodes:
Wherein j is positive electrode p or negative electrode n, c s,j,max represents the theoretical maximum lithium intercalation lithium ion concentration of the active particles, and c s,j,surf represents the lithium ion concentration on the surfaces of the active particles;
the state of charge SOC of the battery is expressed as:
Wherein SOL n (t) represents the lithium intercalation state of the negative electrode at the current time, SOL n (0%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium intercalation state of the positive electrode at the current time, SOL p (0%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully discharged, and SOL p (100%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully charged;
The solid-phase diffusion equation is used for describing the diffusion process of lithium ions in the electrode active particles, and is usually described by Fick's second law, so as to calculate the concentration of lithium ions on each position of the active particles, but the open-circuit voltage of the electrode is only related to the concentration of lithium ions on the surfaces of the active particles, and the calculation of the concentration of lithium ions on the surfaces of the active particles is complex by adopting Fick's law. The lithium intercalation state on the surface of the active particles under constant current and isothermal conditions is simplified into:
Wherein SOL ini,j represents an initial lithium intercalation state, delta j represents an intermediate variable, j is positive electrode p or negative electrode n, namely SOL ini,n represents a negative electrode initial lithium intercalation state, SOL ini,p represents a positive electrode initial lithium intercalation state, delta n represents a negative electrode intermediate variable, delta p represents a positive electrode intermediate variable, lambda k is an array which can be obtained through calculation by a known characteristic equation and takes the first 10 values, and the characteristic equation of lambda k calculated by λk＝[0.0148611613482230;4.49340945790908;7.72525183693785;10.9041216594292;14.0661939128319;17.2207552719312;20.3713029592880;23.5194524986894;26.6660542588130;29.8115987908931], is shown in the specification "Meng,Guo,Godfrey.Single-Particle Model for a Lithium-Ion Cell:Thermal Behavior[J].Journal of the Electrochemical Society,2011.";
Wherein, the intermediate variables δ p and δ n are respectively expressed as:
wherein D s,p represents a solid-phase diffusion coefficient of positive electrode active particles, D s,n represents a solid-phase diffusion coefficient of negative electrode active particles, S p represents an equivalent active particle surface area of a positive electrode material, unit m 2;Sn represents an equivalent active particle surface area of a negative electrode material, c s,p,max represents a theoretical maximum lithium intercalation lithium ion concentration of the positive electrode active particles, c s,n,max represents a theoretical maximum lithium intercalation lithium ion concentration of the negative electrode active particles, R p represents a radius of the positive electrode active particles, and R n represents a radius of the negative electrode active particles;
the electrochemical model of the lithium ion battery can calculate the terminal voltage of the battery only by knowing the magnitude of the current flowing through the battery and various parameters of the battery.
S2, determining electrochemical parameters to be identified according to a single-particle electrochemical model;
The electrochemical parameters to be identified include a cathode active particle solid phase diffusion coefficient D s,n, a cathode active particle solid phase diffusion coefficient D s,p, a cathode reaction rate constant k n, a cathode reaction rate constant k p, a cathode initial lithium intercalation state SOL ini,n, and a cathode initial lithium intercalation state SOL ini,p.
S3, according to factory information of the battery pack, charging and discharging the battery pack by giving a charging and discharging current I Total (S) to obtain an experimental voltage curve of each single battery in the battery pack, namely determining the voltage of the battery terminal under different charging and discharging time to obtain terminal voltage V cell of the parallel batteries at different moments;
s4, determining an optimization objective error function f of the parallel lithium ion batteries;
The battery error function f is formulated as:
Wherein V i represents a cell terminal voltage measurement value with a number i, i represents a cell number i=1, 2.
And S5, identifying electrochemical parameters of the single batteries in the parallel battery pack in simulation software by adopting a simulated annealing algorithm according to the voltage curve and the error function f of the batteries.
The method specifically comprises the following steps:
s5.1 determining the standard deviation threshold value as S 0
Setting a standard deviation threshold of a voltage curve as s 0 according to the performance requirement of the battery pack;
The standard deviation threshold s 0 is determined according to the battery type and the number of the collected data points
Wherein m is the number of battery voltage points acquired through experiments, V max is the charging cut-off voltage specified by the battery, V min is the discharging cut-off voltage specified by the battery, and the voltage difference between the charging cut-off voltage and the discharging cut-off voltage of the lithium ion battery is usually between 0.5 and 1.5V.
S5.2 determining the simulation current C (i)
For lithium ion batteries used In parallel, the single difference causes uneven current distribution inside the battery, as shown In fig. 1, n lithium ion batteries are used In parallel, and due to the difference between the batteries, the current I 1、I2 and the In between the lithium ion batteries are different, but the voltage at the two ends of the battery is V 1＝V2＝……＝Vn at any time. When the batteries are used in parallel, the current flowing through each parallel branch cannot be measured usually due to cost, circuit structure and the like, so that the batteries used in parallel can only measure the total current and I Total (S) flowing through the batteries and the voltage V cell at two ends of the batteries.
Thus, for a parallel circuit, the total current of the parallel cells, I Total (S) :
Wherein I i represents the current flowing through the parallel unit cells I, i=1, 2, &.. n is the total number of parallel batteries;
terminal voltage V cell of battery:
Vcell＝V1＝V2＝......＝Vn (18)
wherein n is the total number of the unit batteries connected in parallel, and V 1、V2、V3……Vn is the voltage at two ends of each unit battery;
Given the total current I Total (S) of the parallel cells, the current C (I) of the cell I in the n branches is:
Wherein, sigma is randn (1, n) represents that the current I i which takes the standard deviation as sigma and the average value as I Total (S) /n as n branches is randomly generated;
therefore, the method for identifying electrochemical parameters of parallel lithium ion batteries in this embodiment identifies electrochemical parameters of each branch battery of the battery under the condition of knowing experimental data of total current and voltage of parallel batteries, and the flow is shown in fig. 2.
S5.3, obtaining a simulation voltage curve
In simulation software, an initial value of an electrochemical parameter is given to a single battery i, and then the single battery i is charged and discharged by taking a current C (i) as a charging and discharging current, so that a simulation voltage curve of each single battery is obtained;
s5.4 calculating errors
As shown in fig. 5, the error f opz (i) of each unit cell is calculated from 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:
the total error f total of the battery pack is calculated according to equation (20):
Wherein V ij represents the terminal voltage of the unit cell i at the time j, i=1, 2. J=1, 2, once again, m; n represents the number of single batteries, m represents the total number of different moments on each single battery voltage curve;
S5.5 calculating standard deviation
Calculating standard deviation s i of the simulated terminal voltage according to the terminal voltage V ij on the simulated voltage curve, and s i is:
Wherein, Representing the average value of m simulation terminal voltages of the single battery i;
Judging the standard deviation s i and the standard deviation threshold s 0, when s i＜s0, the corresponding electrochemical parameter value is the optimal value, otherwise, judging the total error f total and the current error minimum value f, when f total < f, reducing the standard deviation sigma between the current distribution I i to enable sigma=0.9sigma, recording the total error f total as the error minimum value f, when f total > f, increasing the standard deviation sigma between the current distribution I i to enable sigma=1.1sigma, and keeping the error minimum value f unchanged, wherein the initial values of the total error f total and the error minimum value f are required to be initialized before the judgment is entered, and in the embodiment, the initial values of the total error f total and the error minimum value f are 0.
And then returning to the step S5.2, updating the electrochemical parameters, and continuing to identify until the parameter identification of all the single batteries in the battery pack is completed.
In this embodiment, the battery terminal voltage V cell represents the voltage across the battery as the battery passes through the total current I Total (S) , and therefore Vcell is a data set related to the time interval, V 1 is a data set of the battery 1 that emulates the voltage across the battery as it passes through the current C 1I Total (S) under a set of electrochemical parameters;
Introducing a uniformity index, quantifying the uniformity among the parallel lithium ion battery monomers, and the expression is as follows:
Wherein j max、jmin、javg is one of six electrochemical parameters of each single cell, respectively, it can be seen that the smaller the uniformity index is, the smaller the difference between the single cells is, wherein the uniformity index of the current distribution ratio C comprehensively reflects the non-uniformity inside the cell.
In this embodiment, the current flowing in the branch of the battery I is I i, and six electrochemical parameters of the battery I are identified. The basic ideas of identification are shown in fig. 2, the simulation voltage under the given electrochemical parameters is calculated, the square error between the simulation voltage and the parallel battery experimental voltage curve is calculated, six electrochemical parameters to be identified are changed, and when the parameter updating conditions are met, the battery parameters are updated.
The parameter update adopts a simulated annealing algorithm. The principle of the simulated annealing is that the theory of thermodynamics is applied to statistics, each point in the search space is imagined as a molecule in air, and the energy of the molecule is the kinetic energy of the molecule. And each point within the search space also carries "energy" like an air molecule to indicate how appropriate the point is to 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 existing location. The simulated annealing algorithm can be decomposed into three parts, namely a solution space, an objective function and an initial solution.
As shown in fig. 4, the specific steps of the simulated annealing algorithm for electrochemical model parameter identification are as follows:
(1) And initializing parameters. The initial parameters of the cell, param, which is a struct variable including the chemical parameters of cell diffusion coefficient, reaction rate constant, active particle radius, etc., were first obtained by reference. Let the optimized parameter be opz _param, the next state of the parameter be next_param, and assign param to both parameters. The parameter T is set to an empirical value of 10000.
(2) And acquiring the next state of the parameter. next_parallel=next_parallel [ -step+2 x step x rand (1, 1) ], step is a parameter update step, step includes a positive and negative electrode reaction rate change step, a diffusion coefficient change step, an initial lithium intercalation concentration change step, and total six steps, and an empirical value sets the step as 1/20 of the parameter initial value, and t=t-0.01. Wherein T itself does not have any meaning. And only represents the calculation step length and the calculation times, and when the simulation result error of the next state of the parameter is larger than the optimal minimum error along with the reduction of T, the current parameter is accepted with a certain probability, and the optimal parameter is updated.
(3) And judging the temperature. When the temperature T <0, the simulation ends, and when T >0, the next step is entered.
(4) And obtaining the voltage of the simulated battery terminal. Parameters opz _param and next_param are respectively input into the electrochemical model to obtain simulation output terminal voltages Vsim_next and Vsim_ opz of the model.
(5) And (5) comparing errors. And the battery terminal voltage obtained through simulation is respectively calculated with the experimental Vcell data to obtain the square errors, fnext and fopz. fnext < = fopz, accepting parameter change, opz _param = nxet _param, returning to step 2, and when fnext > fopz, entering step 6.
(6) And judging whether to accept the next state of the parameters. The next state of the battery parameters is accepted with a certain probability, dE= fnext-fopz, P=exp (-dE/T/K), the random parameters are a number Rand (1, 1) of 0-1, when Rand (1, 1) > P, the change of the parameters is accepted, opz _parameter= nxet _parameter, the step 2 is returned, and when Rand (1, 1) < P, the step 2 is directly returned. k is a constant and is set to 2, exp represents a natural exponent.
Parameter identification is carried out based on simulated annealing algorithm, and two conditions exist for parameter updating
1. The simulated voltage of the next state parameter next_param is smaller than the error of the current parameter opz _param simulated voltage compared with the experimental voltage, namely fnext < fopz, the updated battery electrochemical parameter fopz = fnext
2. Fnext > fopz, the next state parameter next_parameter of the parameter is accepted with a certain probability, which decreases with increasing number of calculations.
The least squares error fopz (i) of the battery i is finally obtained by the flow shown in fig. 3. The error after the completion of the identification of all n cells is shown in fig. 5.
The electrochemical model in the invention adopts an improved single-particle electrochemical model, the anode and the cathode of the battery are respectively regarded as an active particle, and the electrochemical parameter identification method based on the single-particle electrochemical model is not only suitable for single batteries, but also suitable for lithium ion batteries after parallel connection, and the method is used for improving the basis for judging whether the batteries can be continuously used in parallel connection or not by identifying the electrochemical parameters of each single battery in the parallel lithium ion batteries and analyzing the consistency of the batteries.
While the foregoing is directed to the preferred embodiment of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.
Claims (6)
1. The method for identifying the electrochemical parameters of the parallel lithium ion batteries is characterized by comprising the following steps of:
S1, respectively and equivalently converting the anode and the cathode of a battery into single particles, and establishing a single-particle electrochemical model of the battery;
s2, determining electrochemical parameters to be identified according to a single-particle electrochemical model;
S3, according to factory information of the battery pack, charging and discharging the battery pack by giving a charging and discharging current I Total (S) to obtain an experimental voltage curve of each single battery in the battery pack, and obtaining terminal voltage V cell of the parallel batteries at different moments;
s4, determining an optimization objective error function f of the parallel lithium ion batteries;
S5, identifying electrochemical parameters of the single batteries in the parallel battery pack in simulation software by adopting a simulated annealing algorithm according to a voltage curve and an error function f of the batteries;
the step S1 of establishing the electrochemical model of the battery specifically comprises the following steps:
When current with a certain magnitude is introduced into the two ends of the battery, the interaction of lithium ions, active particles and electrons in the electrolyte maintains the stability of external current, and the current density i j of the active surface of the electrode is as follows:
Wherein I j represents the current density of the active surface of the electrode, the unit is A/m 2, the unit is A when the current is introduced into the two ends of the battery, S j represents the equivalent active particle surface area of the electrode material, the unit is m 2, and j represents the positive electrode p or the negative electrode n;
The pore wall flux of lithium ions at the interface of the active particles and the electrolyte is j j:
Wherein j j represents pore wall flux in mol/(m 2. Multidot. S), n represents lithium ion nuclear charge number, i.e., n= 1;F represents Faraday constant 96487C/mol;
Or pore wall flux j j is represented by the butler-Fu Erma electrochemical reaction equation:
Wherein K j represents liquid phase conductivity, η j represents surface overpotential, c e represents liquid phase lithium ion concentration at all points inside the battery, c s,j,max represents active particle theoretical maximum lithium intercalation lithium ion concentration, c s,j,surf represents active particle surface lithium ion concentration, T is current battery temperature, and R represents gas constant 8.31441 (J/(mol×k));
The surface overpotential η j in the formula (3) is:
ηj＝φs,j-φl,j-Uj (4)
Wherein phi s,j represents a solid phase potential, phi l,j represents a liquid phase potential, and U j represents an equilibrium potential;
The terminal voltage V cell of a known battery can be expressed as:
Vcell＝φs,p-φs,n (5)
Wherein phi s,p represents the solid phase potential of the positive electrode, and phi s,n represents the solid phase potential of the negative electrode;
The difference η p-ηn in positive and negative electrode surface overpotential is deduced:
wherein m j is an intermediate variable, j represents positive electrode p or negative electrode n, and m j is:
Wherein k j represents a reaction rate constant, j is a positive electrode p or a negative electrode n, i.e., k n represents a negative electrode reaction rate constant, and k p represents a positive electrode reaction rate constant;
Bringing equations (4) and (6) into equation (5) derives the terminal voltage V cell of the battery:
Vcell＝Up(xp,surf)-Un(xn,surf)+ηp-ηn+Ul (8)
Wherein U p(xp,surf) represents a positive equilibrium potential, U n(xn,surf) represents a negative equilibrium potential, U l represents a liquid phase potential, x p,surf and x n,surf are both dimensionless quantities related to the lithium ion concentration at the surface of the active particles;
The calculation formula of the liquid phase potential U l in the formula (8) is:
Wherein t + lithium ion liquid phase transfer coefficient, c eL represents the liquid phase lithium ion concentration at the interface of the positive electrode material and the current collector, c e0 represents the liquid phase lithium ion concentration at the interface of the negative electrode material and the current collector, A cell represents the surface area of the battery, L p represents the thickness of the positive electrode material, L n represents the thickness of the negative electrode material, L S represents the thickness of the diaphragm, k p represents the positive liquid phase conductivity, k n represents the negative liquid phase conductivity, k s represents the diaphragm liquid phase conductivity, ε p represents the positive liquid phase volume fraction, ε n represents the negative liquid phase volume fraction, ε s represents the diaphragm liquid phase volume fraction;
Positive electrode equilibrium potential U p(xp,surf) is a function of the lithium intercalation concentration on the surface of the positive electrode active particles, negative electrode equilibrium potential U n(xn,surf) is a function of the lithium intercalation concentration on the surface of the negative electrode active particles, and x j,surf is expressed as the state SOL of intercalation of lithium on the surface of the electrode material by referring to the material properties:
Wherein j is positive electrode p or negative electrode n, c s,j,max represents the theoretical maximum lithium intercalation lithium ion concentration of the active particles, and c s,j,surf represents the lithium ion concentration on the surfaces of the active particles;
the state of charge SOC of the battery is expressed as:
Wherein SOL n (t) represents the lithium intercalation state of the negative electrode at the current time, SOL n (0%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully discharged, SOL n (100%) represents the lithium intercalation state of the negative electrode active particles when the battery is fully charged, SOL p (t) represents the lithium intercalation state of the positive electrode at the current time, SOL p (0%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully discharged, and SOL p (100%) represents the lithium intercalation state of the positive electrode active particles when the battery is fully charged;
the lithium intercalation state on the surface of the active particles under constant current and isothermal conditions is simplified into:
Wherein SOL ini,j represents an initial lithium intercalation state, delta j represents an intermediate variable, j is positive electrode p or negative electrode n, namely SOL ini,n represents a negative electrode initial lithium intercalation state, SOL ini,p represents a positive electrode initial lithium intercalation state, delta n represents a negative electrode intermediate variable, delta p represents a positive electrode intermediate variable, lambda k is an array which can be obtained through calculation by a known characteristic equation and takes the first 10 values, and λk＝[0.0148611613482230;4.49340945790908;7.72525183693785;10.9041216594292;14.0661939128319;17.2207552719312;20.3713029592880;23.5194524986894;26.6660542588130;29.8115987908931];
Wherein, the intermediate variables δ p and δ n are respectively expressed as:
wherein D s,p represents a solid-phase diffusion coefficient of positive electrode active particles, D s,n represents a solid-phase diffusion coefficient of negative electrode active particles, S p represents an equivalent active particle surface area of a positive electrode material, unit m 2;Sn represents an equivalent active particle surface area of a negative electrode material, c s,p,max represents a theoretical maximum lithium intercalation lithium ion concentration of the positive electrode active particles, c s,n,max represents a theoretical maximum lithium intercalation lithium ion concentration of the negative electrode active particles, R p represents a radius of the positive electrode active particles, and R n represents a radius of the negative electrode active particles;
the electrochemical model of the lithium ion battery can calculate the terminal voltage of the battery only by knowing the magnitude of the current flowing through the battery and various parameters of the battery.
2. The method for identifying electrochemical parameters of parallel lithium ion batteries according to claim 1, wherein the electrochemical parameters to be identified comprise a cathode active particle solid phase diffusion coefficient D s,n, a cathode active particle solid phase diffusion coefficient D s,p, a cathode reaction rate constant k n, a cathode reaction rate constant k p, a cathode initial lithium intercalation state SOL ini,n and a cathode initial lithium intercalation state SOL ini,p.
3. The method for identifying electrochemical parameters of parallel lithium ion batteries according to claim 2, wherein the battery error function f in step S4 is formulated as:
Wherein V i represents a cell terminal voltage measurement value with a number i, i represents a cell number i=1, 2.
4. The method for identifying electrochemical parameters of parallel lithium ion batteries of claim 3, wherein the step S5 of identifying the parameters comprises the following steps:
s5.1 determining the standard deviation threshold value as S 0
Setting a standard deviation threshold of a voltage curve as s 0 according to the performance requirement of the battery pack;
s5.2 determining the simulation current C (i)
For a parallel circuit, the total current of the parallel cells I Total (S) :
Wherein I i represents the current flowing through the parallel unit cells I, i=1, 2, &.. n is the total number of parallel batteries;
terminal voltage V cell of battery:
Vcell＝V1＝V2＝......＝Vn(18)
wherein n is the total number of the unit batteries connected in parallel, and V 1、V2、V3……Vn is the voltage at two ends of each unit battery;
Given the total current I Total (S) of the parallel cells, the current C (I) of the cell I in the n branches is:
Wherein, sigma is randn (1, n) represents that the current I i which takes the standard deviation as sigma and the average value as I Total (S) /n as n branches is randomly generated;
s5.3, obtaining a simulation voltage curve
In simulation software, an initial value of an electrochemical parameter is given to a single battery i, and then the single battery i is charged and discharged by taking a current C (i) as a charging and discharging current, so that a simulation voltage curve of each single battery is obtained;
s5.4 calculating errors
Then calculating the error f opz (i) of each single battery according to the simulated battery terminal voltage and the experimental battery terminal voltage of the corresponding points in the simulated voltage curve and the experimental voltage curve and the formula (19) of the error function f:
the total error f total of the battery pack is calculated according to equation (20):
Wherein V ij represents the terminal voltage of the unit cell i at the time j, i=1, 2. J=1, 2, once again, m; n represents the number of single batteries, m represents the total number of different moments on each single battery voltage curve;
S5.5 calculating standard deviation
Calculating standard deviation s i of the simulated terminal voltage according to the terminal voltage V ij on the simulated voltage curve, and s i is:
Wherein V i represents an average value of m simulation terminal voltages of the unit battery i;
Judging the sizes of a standard deviation s i and a standard deviation threshold s 0, when s i＜s0, the corresponding electrochemical parameter value is the optimal value, otherwise, judging the sizes of a total error f total and a current error minimum value f, when f total is smaller than f, reducing the standard deviation sigma between current distribution I i to ensure sigma=0.9sigma, and recording the total error f total as the error minimum value f, and when f total is larger than f, increasing the standard deviation sigma between current distribution I i to ensure sigma=1.1sigma, and keeping the error minimum value f unchanged;
And then returning to the step S5.2, updating the electrochemical parameters, and continuing to identify until the parameter identification of all the single batteries in the battery pack is completed.
5. The method of claim 4, wherein the standard deviation threshold S 0 is set in step S5.1 according to the type of battery and the number of data collected
Wherein m is the number of battery voltage points acquired through experiments, V max is the charge cut-off voltage specified by the battery, and V min is the discharge cut-off voltage specified by the battery.
6. The method of claim 4, wherein the battery terminal voltage V cell represents the battery terminal voltage when the battery pack passes through the total current I Total (S) , and Vcell is therefore a data set related to time intervals, V 1 is a data set of the battery 1 simulating the battery terminal voltage when the battery passes through the current C 1I Total (S) under a set of electrochemical parameters;
Introducing a uniformity index, quantifying the uniformity among the parallel lithium ion battery monomers, and the expression is as follows:
Wherein j max、jmin、javg is one of six electrochemical parameters of each single cell, respectively.
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