CN110412471B - Construction method of composite electrochemical polarization model of lithium ion battery pack - Google Patents

Construction method of composite electrochemical polarization model of lithium ion battery pack Download PDF

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CN110412471B
CN110412471B CN201910727790.6A CN201910727790A CN110412471B CN 110412471 B CN110412471 B CN 110412471B CN 201910727790 A CN201910727790 A CN 201910727790A CN 110412471 B CN110412471 B CN 110412471B
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battery pack
lithium
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王顺利
黄琼
谢东
时浩添
白德奎
于春梅
熊丽英
李建超
邹传云
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Deyang Products Quality Supervision & Inspection Institute
Mianyang Product Quality Supervision And Inspection Institute
Southwest University of Science and Technology
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Mianyang Product Quality Supervision And Inspection Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract

本发明公开了一种锂离子电池组复合电化学极化模型的构建方法，包括：S1，建立锂离子电池组的等效电路模型；S2，基于基尔霍夫电路定律，构建所述等效电路模型的状态空间方程式；S3，根据所述等效电路模型的状态空间方程式，计算锂离子电池组在k时刻的闭路电压UL(k)的离散式子；S4，采用最小二乘法求解锂离子电池组在k时刻的闭路电压UL(k)的离散式子中需要辨识的参数。本发明通过综合考虑表征准确度和计算复杂度，结合不同等效电路模型的优点，实现了锂离子电池组工作状态的准确描述。

Figure 201910727790

The invention discloses a method for constructing a composite electrochemical polarization model of a lithium ion battery pack, comprising: S1, establishing an equivalent circuit model of the lithium ion battery pack; S2, constructing the equivalent circuit model based on Kirchhoff's circuit law The state space equation of the circuit model; S3, according to the state space equation of the equivalent circuit model, calculate the discrete formula of the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k; S4, use the least squares method to solve the lithium Parameters that need to be identified in the discrete formula of the closed-circuit voltage UL (k) of the ion battery pack at time k. The present invention realizes the accurate description of the working state of the lithium ion battery pack by comprehensively considering the characterization accuracy and the computational complexity and combining the advantages of different equivalent circuit models.

Figure 201910727790

Description

Construction method of composite electrochemical polarization model of lithium ion battery pack
Technical Field
The invention relates to the technical field of charge state estimation of lithium ion battery packs, in particular to a construction method of a composite electrochemical polarization model of a lithium ion battery pack.
Background
The power battery system is one of the most important components, and has great influence on the performance and safety of the whole machine, and the lithium ion battery becomes the most widely used power battery for the machine at present by virtue of excellent performance; for a lithium ion Battery, not only a Battery core material with excellent performance needs to be continuously searched, but also a Battery Management System (BMS) needs to manage the Battery core material so as to prevent dangerous conditions such as spontaneous combustion and spontaneous explosion of the lithium ion Battery under certain extreme working conditions; the SOC (State of Charge) estimation of the battery is the basis of the BMS, the estimation precision is an important basis for judging the quality of a battery management system, the accurate SOC estimation is favorable for the full and reasonable use of the battery, the service life of the battery is prolonged, and the safety of the battery is improved; the accurate lithium ion battery model is the premise of improving the SOC estimation precision, so the accurate establishment of the battery model is the key of a battery management system; the battery is a nonlinear system, a common battery model can be divided into an electrochemical model and an equivalent circuit model, the electrochemical model is modeled according to an electrochemical reaction mechanism, the internal action of the battery is described through a mathematical relationship, and the internal action of the battery is described through pure mathematics to fully describe the characteristics of the battery, but the traditional pure electrochemical model is difficult to simulate the dynamic performance of the battery; the equivalent circuit model is established by forming a circuit network by using a resistor, a capacitor and a voltage source according to the dynamic characteristics and the working principle of the battery; however, for most equivalent circuit models, the Open Circuit Voltage (OCV) is directly measured or several estimated specified SOC values are measured in experiments, so that in the equivalent circuit model, simply using OCV as a function of SOC is not only time-consuming and labor-consuming, but is even prone to error; worse yet, the discrete representation of the OCV over multiple SOCs is not intuitive for kalman filtering or kalman filtering-based SOC estimation techniques.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the SOC value cannot be accurately estimated due to insufficient accuracy of the existing lithium ion battery model, the construction method of the composite electrochemical polarization model of the lithium ion battery pack is provided.
The technical scheme adopted by the invention is as follows:
a construction method of a composite electrochemical polarization model of a lithium ion battery pack comprises the following steps:
s1, establishing an equivalent circuit model of the lithium ion battery pack;
s2, constructing a state space equation of the equivalent circuit model based on the kirchhoff circuit law;
s3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit modelL(k) The discrete expression of (1);
s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square methodL(k) The parameters to be identified in the discrete expression are solved to calculate the parameters in the state space equation of the equivalent circuit model, so as to obtain the composite electrochemical polarization model of the lithium ion battery pack.
Further, the equivalent circuit model is composed of: polarization resistance RPAnd a polarization capacitor CPForming a first-order RC circuit; internal resistance to charging RcAnd internal discharge resistance RdRespectively reverse-serially connected with diodes DcAnd a diode DdThen connected in parallel, and then sequentially connected in series with a first-order RC circuit, an ohmic internal resistance Ro and an open-circuit voltage U of the lithium ion battery packOC(ii) a The closed circuit voltage of the equivalent circuit model is UL。
Further, in S2, based on kirchhoff' S circuit law, a state space equation for constructing the equivalent circuit model is:
Figure BDA0002159508730000021
in the formula, R0Ohmic internal resistance of the lithium ion battery pack; rPIs the polarization resistance of the lithium ion battery pack; cPIs the polarization capacitance of the lithium ion battery pack; rcdIs the internal resistance of the lithium ion battery pack during charging and discharging, Rcd＝RcAt discharge time Rcd＝Rd(ii) a k is the time of SOC estimation of the lithium ion battery pack; u shapeL(k) The closed circuit voltage of the lithium ion battery pack at the moment k is obtained; i isL(k) The output current of the lithium ion battery pack at the moment k is obtained; u shapeP(k) Is a polarization resistance RPThe voltage at the moment k at both ends; open circuit voltage U of lithium ion battery packOCEquivalence by Nernst model, K1、K2、K3For the three constants selected by the Nernst model, SOC (k) is the SOC estimate for the lithium ion battery pack at time k;
further, in step S3, the closed-circuit voltage U of the lithium ion battery pack at time k is calculated according to the state space equation of the equivalent circuit modelL(k) The discrete formula of (2) is as follows:
s3-1, polarization resistance R in the state space equationPVoltage U across the terminals at time kP(k) By first order backward difference instead, to obtain UP(k) The discretized equivalent differential equation of (1):
Figure BDA0002159508730000031
in the formula of UP(k) And UP(k-1) are respectively a polarization resistance RPVoltages of two ends at the time k and the time k-1, wherein T is a parameter detection period of the lithium ion battery pack, namely a signal sampling time interval;
s3-2, combined with equivalent UP(k) Is differential expression and UP(k) Obtaining the polarization resistance R by the discretization equivalent differential formulaPVoltage U across the terminals at time kP(k) The discrete equation of (c):
Figure BDA0002159508730000032
in the formula IL(k) And IL(k-1) respectively representing the output current of the lithium ion battery pack at the k moment and the k-1 moment;
s3-3, polarization resistance RPVoltage U across the terminals at time kP(k) Substituting the discrete expression into the state space equation to obtain the closed circuit voltage U of the lithium ion battery pack at the moment kL(k) The discrete equation of (c):
UL(k)＝a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)
in the formula, the parameter a to be identified1、a2、a3、a4、a5、a6The development of (a) is as follows:
Figure BDA0002159508730000041
further, in step S4, the closed-circuit voltage U of the lithium ion battery pack at time k is solved by using a least square methodL(k) The parameters to be identified in the discrete expression are solved to obtain the parameters to be identified, and the parameters in the state space equation of the equivalent circuit model are calculated by using the parameters to be identified, so that the process of obtaining the composite electrochemical polarization model of the lithium ion battery pack is as follows:
s4-1, the closed circuit voltage U of the lithium ion battery pack at the moment k is measuredL(k) The discrete expression of (a) is regarded as a six-element set consisting of independent variables and dependent variables, each element contains N units, and N is 1,2,3, …, k:
{UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}
wherein the matrix of dependent variables is: y ═ UL(1)UL(2)…UL(N)]T(ii) a The matrix of arguments is: x ═ β (1) β (2) … β (N)]T；
S4-2, according to UL(k) The discrete expression of (a) can be obtained:
β(k)＝[1UL(k-1)ln(SOC(k))ln(1-SOC(k))IL(k)IL(k-1)]
then there is a parameter matrix to be identified: a ═ a1a2a3a4a5a6]T；
S4-3, estimating by using a least square method, and solving a parameter matrix A (X) needing to be identifiedTX)-1XTY＝X-1Y, obtaining the parameter a to be identified1、a2、a3、a4、a5、a6；
S4-4, identifying the parameter a according to the requirement1、a2、a3、a4、a5、a6The expansion form of the equivalent circuit model is further deformed to obtain a parameter calculation formula in a state space equation of the equivalent circuit model:
Figure BDA0002159508730000051
solving the obtained parameters a needing to be identified1、a2、a3、a4、a5、a6Substituting the calculation result into the state space equation of the equivalent circuit model to obtain the composite electrochemical polarization model of the lithium ion battery pack.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
according to the method, the representation accuracy and the calculation complexity of the lithium ion battery pack are comprehensively considered, the advantages of different equivalent circuit models are combined, and a lithium ion battery pack composite electrochemical polarization model is provided and constructed in a mode of combining electrochemistry and equivalent circuits; the provided composite electrochemical polarization model of the lithium ion battery pack realizes accurate mathematical expression of working conditions and working processes of the lithium ion battery pack by simulating different effects in the lithium ion battery pack in group cascade connection; a lithium ion battery parameter identification method based on a least square method of a lithium ion battery pack composite electrochemical polarization model is provided; provides a useful reference and reference for the combined application of the electrochemical model and the equivalent circuit model in the battery management.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
Fig. 1 is a flow chart of a method for constructing a composite electrochemical polarization model of a lithium ion battery pack according to the present invention.
Fig. 2 is a schematic diagram of an equivalent circuit model of the lithium ion battery pack according to the present invention.
Detailed Description
The features and properties of the present invention are described in further detail below with reference to examples.
The method for constructing a lithium ion battery pack composite Electrochemical Polarization Model (S-EPM Model) provided in this embodiment, as shown in fig. 1, includes:
s1, establishing an equivalent circuit model of the lithium ion battery pack; as shown in fig. 2, the equivalent circuit model is composed of: polarization resistance RPAnd a polarization capacitor CPForming a first-order RC circuit; internal resistance to charging RcAnd internal discharge resistance RdRespectively reverse-serially connected with diodes DcAnd a diode DdThen connected in parallel, and then sequentially connected in series with a first-order RC circuit, an ohmic internal resistance Ro and an open-circuit voltage U of the lithium ion battery packOC(ii) a The closed circuit voltage of the equivalent circuit model isUL。
S2, constructing a state space equation of the equivalent circuit model based on the Kirchoff circuit law:
Figure BDA0002159508730000061
in the formula, R0The ohmic internal resistance of the lithium ion battery pack can represent the voltage drop of the two ends of the positive electrode and the negative electrode caused by the ohmic effect in the charging and discharging processes of the lithium ion battery pack; rPIs the polarization resistance, C, of a lithium ion battery packPIs the polarization capacitance, R, of a lithium ion battery packPAnd CPThe formed first-order RC circuit represents the relaxation effect in the charge and discharge process of the lithium ion battery pack, and further realizes the expression of the transient response of the lithium ion battery pack; rcdIs the internal resistance of the lithium ion battery pack during charging and discharging, Rcd＝RcAt discharge time Rcd＝Rd(ii) a k is the time of SOC estimation of the lithium ion battery pack; u shapeL(k) The closed circuit voltage of the lithium ion battery pack at the moment k is obtained; i isL(k) The output current of the lithium ion battery pack at the moment k is obtained; u shapeP(k) Is a polarization resistance RPThe voltage at the moment k at both ends; open circuit voltage U of lithium ion battery packOCThe Nernst model is used for equivalence, the Nernst model can provide a good fitting effect in the whole charging and discharging process of the lithium ion battery pack, and K is1、K2、K3The three constants selected by the Nernst model can be determined by different combination tests according to the special working conditions of the grouped work of the lithium ion battery pack; SOC (k) is the SOC estimated value of the lithium ion battery pack at the time k.
S3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit modelL(k) The discrete expression of (1);
s3-1, polarization resistance R in the state space equationPVoltage U across the terminals at time kP(k) By first order backward difference instead, to obtain UP(k) The discretized equivalent differential equation of (1):
Figure BDA0002159508730000071
in the formula of UP(k) And UP(k-1) are respectively a polarization resistance RPVoltages of two ends at the time k and the time k-1, wherein T is a parameter detection period of the lithium ion battery pack, namely a signal sampling time interval;
s3-2, combined with equivalent UP(k) Is differential expression and UP(k) Obtaining the polarization resistance R by the discretization equivalent differential formulaPVoltage U across the terminals at time kP(k) The discrete equation of (c):
Figure BDA0002159508730000072
in the formula IL(k) And IL(k-1) respectively representing the output current of the lithium ion battery pack at the k moment and the k-1 moment;
s3-3, polarization resistance RPVoltage U across the terminals at time kP(k) Substituting the discrete expression into the state space equation to obtain the closed circuit voltage U of the lithium ion battery pack at the moment kL(k) The discrete equation of (c):
UL(k)＝a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)
in the formula, the parameter a to be identified1、a2、a3、a4、a5、a6The development of (a) is as follows:
Figure BDA0002159508730000073
s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square methodL(k) The parameters to be identified in the discrete expression are calculated by utilizing the parameters to be identified obtained by solvingObtaining parameters in a state space equation of the effective circuit model to obtain a lithium ion battery pack composite electrochemical polarization model:
s4-1, the closed circuit voltage U of the lithium ion battery pack at the moment k is measuredL(k) The discrete expression of (a) is regarded as a six-element set consisting of independent variables and dependent variables, each element contains N units, and N is 1,2,3, …, k:
{UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}
wherein the matrix of dependent variables is: y ═ UL(1)UL(2)…UL(N)]T(ii) a The matrix of arguments is: x ═ β (1) β (2) … β (N)]T；
S4-2, according to UL(k) The discrete expression of (a) can be obtained:
β(k)＝[1UL(k-1)ln(SOC(k))ln(1-SOC(k))IL(k)IL(k-1)]
then there is a parameter matrix to be identified: a ═ a1a2a3a4a5a6]T；
S4-3, estimating by using a least square method, and solving a parameter matrix A (X) needing to be identifiedTX)-1XTY＝X-1Y, obtaining the parameter a to be identified1、a2、a3、a4、a5、a6；
S4-4, identifying the parameter a according to the requirement1、a2、a3、a4、a5、a6The expansion form of the equivalent circuit model is further deformed to obtain a parameter calculation formula in a state space equation of the equivalent circuit model:
Figure BDA0002159508730000081
solving the obtained parameters a needing to be identified1、a2、a3、a4、a5、a6Parameter calculation substituted into the state space equation of the equivalent circuit modelAnd substituting the calculation result into a state space equation of the equivalent circuit model to obtain the composite electrochemical polarization model of the lithium ion battery pack.
In conclusion, the invention comprehensively considers the representation accuracy and the calculation complexity of the lithium ion battery pack, combines the advantages of different equivalent circuit models, and provides and constructs the composite electrochemical polarization model of the lithium ion battery pack by combining electrochemistry and equivalent circuits; the provided composite electrochemical polarization model of the lithium ion battery pack realizes accurate mathematical expression of working conditions and working processes of the lithium ion battery pack by simulating different effects in the lithium ion battery pack in group cascade connection, and experiments show that the error can be controlled within 0.5 percent, and the precision is higher; a lithium ion battery parameter identification method based on a least square method of a lithium ion battery pack composite electrochemical polarization model is provided; provides a useful reference and reference for the combined application of the electrochemical model and the equivalent circuit model in the battery management.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (2)

1.一种锂离子电池组复合电化学极化模型的构建方法，其特征在于，包括：1. a construction method of a lithium-ion battery pack composite electrochemical polarization model, is characterized in that, comprises: S1，建立锂离子电池组的等效电路模型；S1, establish the equivalent circuit model of the lithium-ion battery pack; S2，基于基尔霍夫电路定律，构建所述等效电路模型的状态空间方程式；S2, constructing the state space equation of the equivalent circuit model based on Kirchhoff's circuit law; S3，根据所述等效电路模型的状态空间方程式，计算锂离子电池组在k时刻的闭路电压UL(k)的离散式子；S3, according to the state space equation of the equivalent circuit model, calculate the discrete formula of the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k; S4，采用最小二乘法求解锂离子电池组在k时刻的闭路电压UL(k)的离散式子中需要辨识的参数，利用求解得到的需要辨识的参数计算所述等效电路模型的状态空间方程式中的参数，得到锂离子电池组复合电化学极化模型；S4, adopt the least square method to solve the parameters that need to be identified in the discrete expression of the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k, and use the obtained parameters to be identified to calculate the state space of the equivalent circuit model The parameters in the equation, the composite electrochemical polarization model of the lithium-ion battery pack is obtained; 所述等效电路模型的组成为：极化电阻RP和极化电容CP构成一阶RC电路；充电内阻Rc和放电内阻Rd分别反向串联二极管Dc和二极管Dd后并联，再依次串联一阶RC电路、欧姆内阻Ro和锂离子电池组的开路电压UOc；该等效电路模型的闭路电压为UL；The composition of the equivalent circuit model is as follows: the polarization resistance R P and the polarization capacitance C P constitute a first-order RC circuit; the charging internal resistance R c and the discharging internal resistance R d are connected in reverse series with the diode D c and the diode D d respectively. In parallel, the first-order RC circuit, the ohmic internal resistance Ro and the open-circuit voltage U Oc of the lithium-ion battery pack are connected in series in sequence; the closed-circuit voltage of the equivalent circuit model is U L ; 所述S2，基于基尔霍夫电路定律，构建所述等效电路模型的状态空间方程式为：In the S2, based on Kirchhoff's circuit law, the state space equation for constructing the equivalent circuit model is:
Figure FDA0002914025930000011
Figure FDA0002914025930000011
 式中，R0为锂离子电池组的欧姆内阻；RP为锂离子电池组的极化电阻；CP为锂离子电池组的极化电容；Rcd为锂离子电池组的充放电内阻，在充电时Rcd＝Rc，在放电时Rcd＝Rd；k为锂离子电池组的SOC估算所处的时刻；UL(k)为锂离子电池组在k时刻的闭路电压；IL(k)为锂离子电池组在k时刻的输出电流；UP(k)为极化电阻RP两端在k时刻的电压；锂离子电池组的开路电压UOC由Nernst模型进行等效，K1、K2、K3为由Nernst模型选择的三个常数，SOC(k)为锂离子电池组在k时刻的SOC估算值；In the formula, R 0 is the ohmic internal resistance of the lithium-ion battery pack; R P is the polarization resistance of the lithium-ion battery pack; C P is the polarization capacitance of the lithium-ion battery pack; R cd is the charge-discharge internal resistance of the lithium-ion battery pack. resistance, R cd =R c when charging, R cd =R d when discharging; k is the moment at which the SOC of the lithium-ion battery pack is estimated; U L (k) is the closed-circuit voltage of the lithium-ion battery pack at time k ; IL (k) is the output current of the lithium-ion battery pack at time k; U P (k) is the voltage across the polarization resistor R P at time k; the open-circuit voltage U OC of the lithium-ion battery pack is calculated by the Nernst model Equivalently, K 1 , K 2 , and K 3 are three constants selected by the Nernst model, and SOC(k) is the estimated SOC value of the lithium-ion battery pack at time k; 所述步骤S3中，根据所述等效电路模型的状态空间方程式，计算锂离子电池组在k时刻的闭路电压UL(k)的离散式子的过程为：In the step S3, according to the state space equation of the equivalent circuit model, the process of calculating the discrete formula of the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k is: S3-1，将状态空间方程式中极化电阻RP两端在k时刻的电压UP(k)的微分式子，以一阶向后差分代替，得到UP(k)的离散化等效微分式子：S3-1, replace the differential formula of the voltage U P (k) across the polarization resistance R P at time k in the state space equation with the first-order backward differential to obtain the discretized equivalent of U P (k) Differential formula:
Figure FDA0002914025930000021
Figure FDA0002914025930000021
 式中，UP(k)和UP(k-1)分别为极化电阻RP两端在k时刻和k-1时刻的电压，T为锂离子电池组参数检测周期，也就是信号采样时间间隔；In the formula, U P (k) and U P (k-1) are the voltages across the polarization resistor R P at time k and time k-1, respectively, and T is the detection period of the parameters of the lithium-ion battery pack, that is, the signal sampling. time interval; S3-2，结合等效UP(k)的微分式子以及UP(k)的离散化等效微分公式，得到极化电阻RP两端在k时刻的电压UP(k)的离散式子：S3-2, combine the differential formula of equivalent U P (k) and the discretized equivalent differential formula of U P (k) to obtain the discrete voltage U P (k) across the polarization resistance R P at time k formula:
Figure FDA0002914025930000022
Figure FDA0002914025930000022
 式中，IL(k)和IL(k-1)分别为锂离子电池组在k时刻和k-1时刻的输出电流；In the formula, IL (k) and IL (k-1) are the output currents of the lithium-ion battery pack at time k and time k-1, respectively; S3-3，将极化电阻RP两端在k时刻的电压UP(k)的离散式子代入所述状态空间方程式，得到锂离子电池组在k时刻的闭路电压UL(k)的离散式子：S3-3: Substitute the discrete expression of the voltage U P (k) across the polarization resistor R P at time k into the state space equation to obtain the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k Discrete formula: UL(k)＝a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)U L (k)=a 1 +a 2 U L (k-1)+a 3 ln(SOC(k))+a 4 ln(1-SOC(k))+a 5 I L (k)+a 6IL ( k-1) 式中，需要辨识的参数a1、a2、a3、a4、a5、a6的展开形式如下：In the formula, the expanded forms of the parameters a 1 , a 2 , a 3 , a 4 , a 5 , and a 6 to be identified are as follows:
Figure FDA0002914025930000023
Figure FDA0002914025930000023
 2.根据权利要求1所述的锂离子电池组复合电化学极化模型的构建方法，其特征在于，所述步骤S4中，采用最小二乘法求解锂离子电池组在k时刻的闭路电压UL(k)的离散式子中需要辨识的参数，利用求解得到的需要辨识的参数计算所述等效电路模型的状态空间方程式中的参数，得到锂离子电池组复合电化学极化模型的过程为：2. The method for constructing the composite electrochemical polarization model of a lithium-ion battery pack according to claim 1, wherein in the step S4, a least squares method is used to solve the closed-circuit voltage U L of the lithium-ion battery pack at time k The parameters to be identified in the discrete formula of (k), the parameters in the state space equation of the equivalent circuit model are calculated by using the obtained parameters to be identified, and the process of obtaining the composite electrochemical polarization model of the lithium-ion battery pack is as follows: : S4-1，将锂离子电池组在k时刻的闭路电压UL(k)的离散式子看成一个由自变量和因变量组成的六元素集合，每个元素中包含N个单元，N＝1，2，3，...，k：S4-1, regard the discrete expression of the closed-circuit voltage U L (k) of the lithium-ion battery pack at time k as a six-element set composed of independent variables and dependent variables, each element contains N units, N= 1, 2, 3, ..., k: {UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}{UL(k)UL(k-1)SOC(k)SOC(k-1 )IL ( k) IL (k-1) } 其中，因变量的矩阵为：Y＝[UL(1)UL(2)…UL(N)]T；自变量的矩阵为：X＝[β(1)β(2)…β(N)]T；Among them, the matrix of the dependent variable is: Y = [UL (1)UL (2)… UL ( N )] T ; the matrix of the independent variable is: X=[β(1)β(2)…β( N)] T ; S4-2，根据UL(k)的离散式子可得：S4-2, according to the discrete formula of U L (k), we can get: β(k)＝[1UL(k-1) ln(SOC(k)) ln(1-SOC(k))IL(k)IL(k-1)]β(k)=[1U L (k-1) ln(SOC(k)) ln(1-SOC(k)) IL (k) IL (k-1)] 则有需要辨识的参数矩阵：A＝[a1a2a3a4a5a6]T；Then there is a parameter matrix that needs to be identified: A=[a 1 a 2 a 3 a 4 a 5 a 6 ] T ; S4-3，采用最小二乘法估算，求解需要辨识的参数矩阵A＝(XTX)-1XTY＝X-1Y，可以得到需要辨识的参数a1、a2、a3、a4、a5、a6；S4-3, use the least squares method to estimate, solve the parameter matrix A=(X T X) -1 X T Y=X -1 Y to be identified, and obtain the parameters a 1 , a 2 , a 3 , a to be identified 4 , a 5 , a 6 ; S4-4，根据需要辨识的参数a1、a2、a3、a4、a5、a6的展开形式进一步变形得到等效电路模型的状态空间方程式中的参数计算式子：S4-4, according to the expanded form of the parameters a 1 , a 2 , a 3 , a 4 , a 5 , and a 6 to be identified, further deform to obtain the parameter calculation formula in the state space equation of the equivalent circuit model:
Figure FDA0002914025930000031
Figure FDA0002914025930000031
 将求解得到的需要辨识的参数a1、a2、a3、a4、a5、a6代入所述等效电路模型的状态空间方程式中的参数计算式子，将计算结果代入等效电路模型的状态空间方程式中，得到锂离子电池组复合电化学极化模型。Substitute the obtained parameters a 1 , a 2 , a 3 , a 4 , a 5 , a 6 into the parameter calculation formula in the state space equation of the equivalent circuit model, and substitute the calculation results into the equivalent circuit In the state space equation of the model, the composite electrochemical polarization model of the lithium-ion battery pack is obtained.
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