CN110412471A - A kind of construction method of Li-ion batteries piles composite electrochemical polarization model - Google Patents

A kind of construction method of Li-ion batteries piles composite electrochemical polarization model Download PDF

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CN110412471A
CN110412471A CN201910727790.6A CN201910727790A CN110412471A CN 110412471 A CN110412471 A CN 110412471A CN 201910727790 A CN201910727790 A CN 201910727790A CN 110412471 A CN110412471 A CN 110412471A
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ion batteries
batteries piles
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CN110412471B (en
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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 Product Quality Supervision And 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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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367Software therefor, e.g. for battery testing using modelling or look-up tables
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385Arrangements for measuring battery or accumulator variables
    • G01R31/387Determining ampere-hour charge capacity or SoC
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/396Acquisition or processing of data for testing or for monitoring individual cells or groups of cells within a battery

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Abstract

The invention discloses a kind of construction methods of Li-ion batteries piles composite electrochemical polarization model, comprising: S1 establishes the equivalent-circuit model of Li-ion batteries piles;S2 is based on Kirchhoff's laws of electric circuit, constructs the state space equation formula of the equivalent-circuit model;S3 calculates Li-ion batteries piles in the closed circuit voltage U at k moment according to the state space equation formula of the equivalent-circuit modelL(k) discrete formula;S4 solves Li-ion batteries piles in the closed circuit voltage U at k moment using least square methodL(k) parameter for needing to recognize in discrete formula.The present invention realizes the accurate description of Li-ion batteries piles working condition in conjunction with the advantages of different equivalent circuit model by comprehensively considering characterization accuracy and computation complexity.

Description

A kind of construction method of Li-ion batteries piles composite electrochemical polarization model
Technical field
The present invention relates to the state of charge estimating techniques field of Li-ion batteries piles, especially a kind of Li-ion batteries piles are multiple Close the construction method of activation polarization model.
Background technique
Electrokinetic cell system be in one of most important component part, it is very big to overall performance and safety effects, lithium from Sub- battery relies on excellent performance, becomes the most commonly used machine power battery of current application;For lithium ion battery, no Only need to continually look for the core material of function admirable, it is also necessary to battery management system (Battery Management System, BMS) it is managed, to prevent the hair of the dangerous situations such as lithium ion battery spontaneous combustion, self-destruction under certain limiting conditions It is raw;State-of-charge (State of Charge, the SOC) estimation of battery is the basis of BMS, and estimated accuracy is to judge cell tube The important evidence of reason system superiority and inferiority, accurate SOC estimation are conducive to abundant, the reasonable employment of battery, extend the service life of battery, and Improve the safety of battery;Accurate Li-ion battery model is the premise for improving SOC estimation precision, therefore, battery model Accurate establish is the key that battery management system;Battery is a nonlinear system, and common battery model can be divided into electrification Model and two kinds of equivalent-circuit model are learned, electrochemical model is modeled according to electrochemical reaction mechanism, is retouched by mathematical relationship It states inside battery and acts through pure mathematics and describe the internal action of battery to fully describe the characteristic of battery, but traditional pure electrification Learn the dynamic property that model is difficult simulated battery;Equivalent-circuit model utilizes electricity according to the dynamic characteristic and working principle of battery Resistance, capacitor and voltage source built-up circuit network, establish equivalent-circuit model;However, for most of equivalent-circuit models, open circuit Voltage (OCV) is direct measurement or the several specified SOC values for measuring estimation in an experiment, therefore in equivalent-circuit model, it is single Pure is not only time-consuming and laborious as the function of SOC using OCV, or even is easy error;What is worse, OCV is discrete on multiple SOC Indicate not intuitive for Kalman filtering or SOC estimation technique based on Kalman filtering.
Summary of the invention
The technical problems to be solved by the present invention are: causing for existing Li-ion battery model because precision is inadequate The problem of SOC value cannot be estimated accurately provides a kind of construction method of Li-ion batteries piles composite electrochemical polarization model.
The technical solution adopted by the invention is as follows:
A kind of construction method of Li-ion batteries piles composite electrochemical polarization model, comprising:
S1 establishes the equivalent-circuit model of Li-ion batteries piles;
S2 is based on Kirchhoff's laws of electric circuit, constructs the state space equation formula of the equivalent-circuit model;
S3, according to the state space equation formula of the equivalent-circuit model, calculating Li-ion batteries piles are closed circuit the k moment Voltage UL(k) discrete formula;
S4 solves Li-ion batteries piles in the closed circuit voltage U at k moment using least square methodL(k) it is needed in discrete formula The parameter to be recognized calculates the state space equation formula of the equivalent-circuit model using the parameter that the needs that solution obtains recognize In parameter, obtain Li-ion batteries piles composite electrochemical polarization model.
Further, the composition of the equivalent-circuit model are as follows: polarization resistance RPWith polarization capacity CPConstitute single order RC electricity Road;Internal charging resistance RcWith electric discharge internal resistance RdDifferential concatenation diode D respectivelycWith diode DdIt is in parallel afterwards, then it is sequentially connected in series single order RC The open-circuit voltage U of circuit, ohmic internal resistance Ro and Li-ion batteries pilesOC;The closed circuit voltage of the equivalent-circuit model is UL
Further, the S2 is based on Kirchhoff's laws of electric circuit, constructs the state space side of the equivalent-circuit model Formula are as follows:
In formula, R0For the ohmic internal resistance of Li-ion batteries piles;RPFor the polarization resistance of Li-ion batteries piles;CPFor lithium ion The polarization capacity of battery pack;RcdFor the charge and discharge internal resistance of Li-ion batteries piles, the R in chargingcd=Rc, the R in electric dischargecd=Rd;k At the time of locating for the SOC estimation of Li-ion batteries piles;ULIt (k) is closed circuit voltage of the Li-ion batteries piles at the k moment;IL(k) it is Output electric current of the Li-ion batteries piles at the k moment;UPIt (k) is polarization resistance RPVoltage of the both ends at the k moment;Li-ion batteries piles Open-circuit voltage UOCEquivalent, K is carried out by Nernst model1、K2、K3For three constants selected by Nernst model, SOC (k) is SOC estimated value of the Li-ion batteries piles at the k moment;
Further, in the step S3, according to the state space equation formula of the equivalent-circuit model, lithium ion is calculated Closed circuit voltage U of the battery pack at the k momentL(k) process of discrete formula are as follows:
S3-1, by polarization resistance R in state space equation formulaPVoltage U of the both ends at the k momentP(k) differential formula, with one Rank backward difference replaces, and obtains UP(k) the equivalent differential formula of discretization:
In formula, UP(k) and UPIt (k-1) is respectively polarization resistance RPVoltage of the both ends at k moment and k-1 moment, T be lithium from Sub- battery parameter detection cycle, that is, signal sampling time interval;
S3-2, in conjunction with equivalent UP(k) differential formula and UP(k) the equivalent differential formulas of discretization, obtains polarization resistance RPVoltage U of the both ends at the k momentP(k) discrete formula:
In formula, IL(k) and ILIt (k-1) is respectively output electric current of the Li-ion batteries piles at k moment and k-1 moment;
S3-3, by polarization resistance RPVoltage U of the both ends at the k momentP(k) discrete type filial generation enters the state space equation Formula obtains Li-ion batteries piles in the closed circuit voltage U at k momentL(k) discrete formula:
UL(k)=a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)
In formula, the parameter a that needs to recognize1、a2、a3、a4、a5、a6Expanded form it is as follows:
Further, in the step S4, Li-ion batteries piles are solved in the closed circuit voltage at k moment using least square method UL(k) parameter for needing to recognize in discrete formula calculates the equivalent circuit using the parameter that obtained needs recognize is solved Parameter in the state space equation formula of model, obtains the process of Li-ion batteries piles composite electrochemical polarization model are as follows:
S4-1, by Li-ion batteries piles the k moment closed circuit voltage UL(k) discrete formula regard as one by independent variable and Six element sets of dependent variable composition, include N number of unit in each element, N=1,2,3 ..., k:
{UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}
Wherein, the matrix of dependent variable are as follows: Y=[UL(1)UL(2)…UL(N)]T;The matrix of independent variable are as follows: X=[β (1) β (2)…β(N)]T
S4-2, according to UL(k) discrete formula can obtain:
β (k)=[1UL(k-1)ln(SOC(k))ln(1-SOC(k))IL(k)IL(k-1)]
The then parameter matrix of identification in need: A=[a1a2a3a4a5a6]T
S4-3 is estimated using least square method, solves the parameter matrix A=(X for needing to recognizeTX)-1XTY=X-1Y, can be with Obtain the parameter a for needing to recognize1、a2、a3、a4、a5、a6
S4-4, the parameter a recognized as needed1、a2、a3、a4、a5、a6Expanded form further deform and obtain equivalent electricity Parameter in the state space equation formula of road model calculates formula:
The parameter a that the needs that solution obtains are recognized1、a2、a3、a4、a5、a6The state for substituting into the equivalent-circuit model is empty Between parameter in equation calculate formula, calculated result is substituted into the state space equation formula of equivalent-circuit model, obtains lithium Ion battery group composite electrochemical polarization model.
In conclusion by adopting the above-described technical solution, the beneficial effects of the present invention are:
The present invention comprehensively considers characterization accuracy and the computation complexity of Li-ion batteries piles, in conjunction with different equivalent circuit mould The advantages of type, is proposed using mode of the electrochemistry in conjunction with equivalent circuit and constructs the polarization of Li-ion batteries piles composite electrochemical Model;The Li-ion batteries piles composite electrochemical polarization model proposed by inside cascade Li-ion batteries piles in groups not With the simulation of effect, the accurate mathematical expression of Li-ion batteries piles operating condition and the course of work is realized;And it gives based on lithium ion The lithium ion battery parameter identification method based on least square method of battery pack composite electrochemical polarization model;For electrochemical model Beneficial reference and reference are provided with use in conjunction of the equivalent-circuit model in battery management.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below will be to needed in the embodiment attached Figure is briefly described, it should be understood that the following drawings illustrates only certain embodiments of the present invention, therefore is not construed as pair The restriction of range for those of ordinary skill in the art without creative efforts, can also be according to this A little attached drawings obtain other relevant attached drawings.
Fig. 1 is the flow diagram of the construction method of Li-ion batteries piles composite electrochemical polarization model of the invention.
Fig. 2 is the equivalent-circuit model schematic diagram of Li-ion batteries piles of the invention.
Specific embodiment
Feature and performance of the invention are described in further detail with reference to embodiments.
A kind of Li-ion batteries piles composite electrochemical polarization model (Splice- provided in this embodiment Electrochemical Polarization Model, S-EPM model) construction method, as shown in Figure 1, comprising:
S1 establishes the equivalent-circuit model of Li-ion batteries piles;As shown in Fig. 2, the composition of the equivalent-circuit model are as follows: Polarization resistance RPWith polarization capacity CPConstitute First-order Rc Circuit;Internal charging resistance RcWith electric discharge internal resistance RdDifferential concatenation diode D respectivelyc With diode DdIt is in parallel afterwards, then it is sequentially connected in series the open-circuit voltage U of First-order Rc Circuit, ohmic internal resistance Ro and Li-ion batteries pilesOC;It should The closed circuit voltage of equivalent-circuit model is UL
S2 is based on Kirchhoff's laws of electric circuit, constructs the state space equation formula of the equivalent-circuit model:
In formula, R0For the ohmic internal resistance of Li-ion batteries piles, Li-ion batteries piles can be characterized in charge and discharge process Central Europe Positive and negative end voltage drop caused by nurse effect;RPFor the polarization resistance of Li-ion batteries piles, CPFor the polarization of Li-ion batteries piles Capacitor, RPAnd CPRelaxation effect in the First-order Rc Circuit characterization Li-ion batteries piles charge and discharge process of composition, and then realize to lithium The expression of ion battery group transient response;RcdFor the charge and discharge internal resistance of Li-ion batteries piles, the R in chargingcd=Rc, in electric discharge Rcd=Rd;At the time of k is that the SOC estimation of Li-ion batteries piles is locating;ULIt (k) is closed circuit electricity of the Li-ion batteries piles at the k moment Pressure;ILIt (k) is output electric current of the Li-ion batteries piles at the k moment;UPIt (k) is polarization resistance RPVoltage of the both ends at the k moment;Lithium The open-circuit voltage U of ion battery groupOCEquivalent by the progress of Nernst model, Nernst model can be in the entire of Li-ion batteries piles Preferable fitting effect, K are provided in charge and discharge process1、K2、K3For three constants selected by Nernst model, can by lithium from Sub- battery pack works present particular job situation in groups, passes through various combination test and determines;SOC (k) is lithium ion battery SOC estimated value of the group at the k moment.
S3, according to the state space equation formula of the equivalent-circuit model, calculating Li-ion batteries piles are closed circuit the k moment Voltage UL(k) discrete formula;
S3-1, by polarization resistance R in state space equation formulaPVoltage U of the both ends at the k momentP(k) differential formula, with one Rank backward difference replaces, and obtains UP(k) the equivalent differential formula of discretization:
In formula, UP(k) and UPIt (k-1) is respectively polarization resistance RPVoltage of the both ends at k moment and k-1 moment, T be lithium from Sub- battery parameter detection cycle, that is, signal sampling time interval;
S3-2, in conjunction with equivalent UP(k) differential formula and UP(k) the equivalent differential formulas of discretization, obtains polarization resistance RPVoltage U of the both ends at the k momentP(k) discrete formula:
In formula, IL(k) and ILIt (k-1) is respectively output electric current of the Li-ion batteries piles at k moment and k-1 moment;
S3-3, by polarization resistance RPVoltage U of the both ends at the k momentP(k) discrete type filial generation enters the state space equation Formula obtains Li-ion batteries piles in the closed circuit voltage U at k momentL(k) discrete formula:
UL(k)=a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)
In formula, the parameter a that needs to recognize1、a2、a3、a4、a5、a6Expanded form it is as follows:
S4 solves Li-ion batteries piles in the closed circuit voltage U at k moment using least square methodL(k) it is needed in discrete formula The parameter to be recognized calculates the state space equation formula of the equivalent-circuit model using the parameter that the needs that solution obtains recognize In parameter, obtain Li-ion batteries piles composite electrochemical polarization model:
S4-1, by Li-ion batteries piles the k moment closed circuit voltage UL(k) discrete formula regard as one by independent variable and Six element sets of dependent variable composition, include N number of unit in each element, N=1,2,3 ..., k:
{UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}
Wherein, the matrix of dependent variable are as follows: Y=[UL(1)UL(2)…UL(N)]T;The matrix of independent variable are as follows: X=[β (1) β (2)…β(N)]T
S4-2, according to UL(k) discrete formula can obtain:
β (k)=[1UL(k-1)ln(SOC(k))ln(1-SOC(k))IL(k)IL(k-1)]
The then parameter matrix of identification in need: A=[a1a2a3a4a5a6]T
S4-3 is estimated using least square method, solves the parameter matrix A=(X for needing to recognizeTX)-1XTY=X-1Y, can be with Obtain the parameter a for needing to recognize1、a2、a3、a4、a5、a6
S4-4, the parameter a recognized as needed1、a2、a3、a4、a5、a6Expanded form further deform and obtain equivalent electricity Parameter in the state space equation formula of road model calculates formula:
The parameter a that the needs that solution obtains are recognized1、a2、a3、a4、a5、a6The state for substituting into the equivalent-circuit model is empty Between parameter in equation calculate formula, calculated result is substituted into the state space equation formula of equivalent-circuit model, obtains lithium Ion battery group composite electrochemical polarization model.
In conclusion the present invention comprehensively considers characterization accuracy and the computation complexity of Li-ion batteries piles, in conjunction with difference The advantages of equivalent-circuit model, is proposed using mode of the electrochemistry in conjunction with equivalent circuit and to construct Li-ion batteries piles compound Activation polarization model;The Li-ion batteries piles composite electrochemical polarization model proposed passes through to cascade lithium-ion electric in groups The simulation of different effect inside the group of pond, realizes the accurate mathematical expression of Li-ion batteries piles operating condition and the course of work, by experiment Show can by control errors 0.5% within, precision is higher;And it gives based on Li-ion batteries piles composite electrochemical pole Change the lithium ion battery parameter identification method based on least square method of model;It is electrochemical model and equivalent-circuit model in electricity Use in conjunction in the management of pond provides beneficial reference and reference.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.

Claims (5)

1. a kind of construction method of Li-ion batteries piles composite electrochemical polarization model characterized by comprising
S1 establishes the equivalent-circuit model of Li-ion batteries piles;
S2 is based on Kirchhoff's laws of electric circuit, constructs the state space equation formula of the equivalent-circuit model;
S3 calculates Li-ion batteries piles in the closed circuit voltage at k moment according to the state space equation formula of the equivalent-circuit model UL(k) discrete formula;
S4 solves Li-ion batteries piles in the closed circuit voltage U at k moment using least square methodL(k) it needs to distinguish in discrete formula The parameter of knowledge is calculated in the state space equation formula of the equivalent-circuit model using the parameter that obtained needs recognize is solved Parameter obtains Li-ion batteries piles composite electrochemical polarization model.
2. the construction method of Li-ion batteries piles composite electrochemical polarization model according to claim 1, which is characterized in that The composition of the equivalent-circuit model are as follows: polarization resistance RPWith polarization capacity CPConstitute First-order Rc Circuit;Internal charging resistance RcAnd electric discharge Internal resistance RdDifferential concatenation diode D respectivelycWith diode DdIt is in parallel afterwards, then it is sequentially connected in series First-order Rc Circuit, ohmic internal resistance Ro and lithium The open-circuit voltage U of ion battery groupOC;The closed circuit voltage of the equivalent-circuit model is UL
3. the construction method of Li-ion batteries piles composite electrochemical polarization model according to claim 2, which is characterized in that The S2 is based on Kirchhoff's laws of electric circuit, constructs the state space equation formula of the equivalent-circuit model are as follows:
In formula, R0For the ohmic internal resistance of Li-ion batteries piles;RPFor the polarization resistance of Li-ion batteries piles;CPFor lithium ion battery The polarization capacity of group;RcdFor the charge and discharge internal resistance of Li-ion batteries piles, the R in chargingcd=Rc, the R in electric dischargecd=Rd;K is lithium At the time of the SOC estimation of ion battery group is locating;ULIt (k) is closed circuit voltage of the Li-ion batteries piles at the k moment;IL(k) for lithium from Output electric current of the sub- battery pack at the k moment;UPIt (k) is polarization resistance RPVoltage of the both ends at the k moment;Li-ion batteries piles are opened Road voltage UOCEquivalent, K is carried out by Nernst model1、K2、K3For three constants selected by Nernst model, SOC (k) be lithium from SOC estimated value of the sub- battery pack at the k moment.
4. the construction method of Li-ion batteries piles composite electrochemical polarization model according to claim 3, which is characterized in that In the step S3, according to the state space equation formula of the equivalent-circuit model, Li-ion batteries piles closing at the k moment is calculated Road voltage UL(k) process of discrete formula are as follows:
S3-1, by polarization resistance R in state space equation formulaPVoltage U of the both ends at the k momentP(k) differential formula, with single order to Difference replaces afterwards, obtains UP(k) the equivalent differential formula of discretization:
In formula, UP(k) and UPIt (k-1) is respectively polarization resistance RPVoltage of the both ends at k moment and k-1 moment, T are lithium-ion electric Pond group parameter detecting period, that is, signal sampling time interval;
S3-2, in conjunction with equivalent UP(k) differential formula and UP(k) the equivalent differential formulas of discretization, obtains polarization resistance RPTwo Hold the voltage U at the k momentP(k) discrete formula:
In formula, IL(k) and ILIt (k-1) is respectively output electric current of the Li-ion batteries piles at k moment and k-1 moment;
S3-3, by polarization resistance RPVoltage U of the both ends at the k momentP(k) discrete type filial generation enters the state space equation formula, obtains To Li-ion batteries piles the k moment closed circuit voltage UL(k) discrete formula:
UL(k)=a1+a2UL(k-1)+a3ln(SOC(k))+a4ln(1-SOC(k))+a5IL(k)+a6IL(k-1)
In formula, the parameter a that needs to recognize1、a2、a3、a4、a5、a6Expanded form it is as follows:
5. the construction method of Li-ion batteries piles composite electrochemical polarization model according to claim 4, which is characterized in that In the step S4, Li-ion batteries piles are solved in the closed circuit voltage U at k moment using least square methodL(k) in discrete formula The parameter for needing to recognize calculates the state space equation of the equivalent-circuit model using the parameter that the needs that solution obtains recognize Parameter in formula obtains the process of Li-ion batteries piles composite electrochemical polarization model are as follows:
S4-1, by Li-ion batteries piles the k moment closed circuit voltage UL(k) discrete formula regards one as by independent variable and because becoming Six element sets for measuring composition, include N number of unit in each element, N=1,2,3 ..., k:
{UL(k)UL(k-1)SOC(k)SOC(k-1)IL(k)IL(k-1)}
Wherein, the matrix of dependent variable are as follows: Y=[UL(1) UL(2) … UL(N)]T;The matrix of independent variable are as follows: X=[β (1) β (2) … β(N)]T
S4-2, according to UL(k) discrete formula can obtain:
β (k)=[1UL(k-1) ln(SOC(k)) ln(1-SOC(k))IL(k)IL(k-1)]
The then parameter matrix of identification in need: A=[a1a2a3a4a5a6]T
S4-3 is estimated using least square method, solves the parameter matrix A=(X for needing to recognizeTX)-1XTY=X-1Y, it is available The parameter a for needing to recognize1、a2、a3、a4、a5、a6
S4-4, the parameter a recognized as needed1、a2、a3、a4、a5、a6Expanded form further deform and obtain equivalent circuit mould Parameter in the state space equation formula of type calculates formula:
The parameter a that the needs that solution obtains are recognized1、a2、a3、a4、a5、a6Substitute into the state space side of the equivalent-circuit model Parameter in formula calculates formula, calculated result is substituted into the state space equation formula of equivalent-circuit model, obtains lithium ion Battery pack composite electrochemical polarization model.
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CN112733479B (en) * 2020-12-29 2023-06-13 华人运通(江苏)技术有限公司 Model parameter calculation method, device and medium for single battery

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