CN114236402B - Lithium battery equivalent circuit model establishment method considering temperature and SOC double factors - Google Patents

Lithium battery equivalent circuit model establishment method considering temperature and SOC double factors Download PDF

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CN114236402B
CN114236402B CN202111243222.2A CN202111243222A CN114236402B CN 114236402 B CN114236402 B CN 114236402B CN 202111243222 A CN202111243222 A CN 202111243222A CN 114236402 B CN114236402 B CN 114236402B
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equivalent circuit
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arrhenius
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CN114236402A (en
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冯飞
谢翌
杨瑞
章治国
李夔宁
柴毅
牟丽莎
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Chongqing University
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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]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E60/10—Energy storage using batteries

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Abstract

The application relates to a method for establishing a lithium battery equivalent circuit model by considering temperature and SOC (system on chip) double factors, which comprises the steps of designing an orthogonal experiment, constructing an ECM (electronic control module) model according to the temperature and SOC factor influence in the orthogonal experiment design, estimating parameters of the ECM model, using an Arrhenius model as a basis, using a polynomial model as a parameter, describing in a form of a piecewise function to obtain an OPPA model, estimating model parameters of the OPPA model by selecting different sections and orders, loading parameters of the best section and order of a prediction result, substituting the parameters into the OPPA model to obtain the parameters of the ECM model, and thus obtaining the OPPA-ECM model. The application designs a double-factor orthogonal test, and establishes an OPPA model based on the form of an Arrhenius equation influenced by temperature and a polynomial model influenced by SOC. Parameters of the ECM model are corrected by using OPPA, so that the ECM model shows good prediction performance on EIS impedance spectrum under unknown temperature and SOC conditions.

Description

Lithium battery equivalent circuit model establishment method considering temperature and SOC double factors
Technical Field
The application belongs to the technical field of battery management, and particularly relates to a method for establishing an equivalent circuit model of a lithium battery by considering temperature and SOC (system on a chip) double factors.
Background
Reasonable experimental design can control test errors, ensure test quality and enable the test to have representativeness, correctness and replay. One of the main effects of test design is to determine the influence of test factors on test indexes. Temperature and SOC are two important factors affecting battery performance, and many documents have studied them. For example, andre et al used a 6.5Ah high power NCM lithium ion battery as the test subject, designed a two-factor test of 7 temperature levels from-30 ℃ to 50 ℃ and 18 SOC levels from 0% to 100%, the entire test containing 119 test points. The temperature level interval gradually decreases from high temperature to low temperature. The SOC level interval is 5% between the high SOC and the low SOC intervals, and 10% between the medium SOC intervals. The predicted performance of the proposed 2 ECM models on electrochemical impedance spectroscopy (Electrochemical Impedance Spectroscopy, EIS) was compared at different temperature levels of 60% soc. Stefan et al used three different, automotive grade high performance lithium ion batteries for evaluation. A two-factor test was designed for 7 temperature levels from-10 ℃ to 40 ℃ and 12 SOC levels from 0% to 100%, the entire test containing 84 test points. The predicted performance of the EIS profile was compared for two different RC quantities of ECM at two temperature levels of 50% soc. Wang et al tested on 20Ah commercial soft pack LiFePO4 cells at 4 levels ranging from 273 to 303K and 13 levels ranging from 0% to 100% SOC, with the entire test containing 52 test points. At different temperatures, model parameters of the ECM are modeled as SOC polynomial functions. And (3) performing comparative analysis on the prediction performance of the SOC polynomial function and the interpolation function by using a cross-validation method.
All of the above documents employ a comprehensive test, which means that the test is performed on all combinations of levels of the selected test factors. The comprehensive test can obtain comprehensive test information, and the influence analysis of each factor and each level interaction on the test index is clear. However, when the number of factors and the number of levels are large, the number of combinations of the levels in the comprehensive test is too large, and the combination of manpower, material resources, financial resources, sites and the like is generally difficult to bear. The interaction of temperature and SOC factors and corresponding models have also been discussed.
Disclosure of Invention
In view of the above, the application aims to overcome the defects of the prior art, and provides a method for establishing a lithium battery equivalent circuit model by considering temperature and SOC (system on chip) double factors, so as to solve the problem that the total test has too many horizontal combinations and is usually difficult to bear in the prior art when the number of factors and the horizontal number are large.
In order to achieve the above purpose, the application adopts the following technical scheme: a method for establishing a lithium battery equivalent circuit model by considering temperature and SOC double factors comprises the following steps:
selecting a sample battery and designing an orthogonal test;
constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating model parameters of the equivalent circuit model by using a complex nonlinear least square method; wherein the model parameters of the equivalent circuit model include a plurality of;
based on the orthogonal test, representing model parameters of the equivalent circuit model by using a piecewise function representation mode by taking an Arrhenius model as a basis and using a polynomial model as parameters to obtain an orthogonal piecewise polynomial Arrhenius model, selecting different segments and different stages, and estimating the model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
obtaining optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
Further, the design orthogonal test includes:
selecting test factors and determining a test level; wherein, the experimental factors include: temperature and SOC; determining a test level as a level of determining a temperature factor and an SOC factor;
selecting an orthogonal table according to factors, test levels and whether interaction needs to be inspected;
the test factors and interactions are arranged into the orthogonal table, and different horizontal numbers of each column in the orthogonal table are replaced by corresponding horizontal values corresponding to each factor to form an orthogonal test.
Further, the constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating parameters of the equivalent circuit model by using a complex nonlinear least squares method, including:
constructing an equivalent circuit model according to the sample battery;
acquiring impedance of the equivalent circuit model according to the equivalent circuit model;
estimating parameters of the equivalent circuit model through experimental impedance and calculated impedance of the equivalent circuit model by using a complex nonlinear least square method.
Further, the equivalent circuit model is a second-order RC equivalent circuit model; the complex impedance calculation formula of the second-order RC equivalent circuit model is as follows:
Z ECM ＝Z Ro +Z Ri +Z Rct +Z W
wherein Z is ECM Is complex impedance Z Ro For ohmic impedance, Z Ri For the migration resistance of lithium ions in the SEI film,for charge transfer impedance, Z W R is the solid diffusion resistance of lithium ions in active material particles O Is the sum of ohmic resistances, R i R is the sum of SEI film migration resistances ct Is the sum of charge transfer resistances, Q i And Q ct Is a generalized capacity; n is n i And n ct Taking real numbers between 0 and 1 as inhibition factors; r is R W For Warburg resistance, τ W N is the diffusion time constant W Varying between 0 and 1.
Further, the model parameters of the equivalent circuit model are estimated by using the complex nonlinear least square method through the experimental impedance and the calculated impedance of the equivalent circuit model, and the calculation formula is as follows:
wherein K is the number of frequencies, Z' exp (ω k ) And Z' exp (ω k ) Omega respectively k The real and imaginary parts of the experimental impedance at Z' cal (ω k ) And Z' cal (ω K ) Respectively calculated omega k A real part and an imaginary part of the impedance;
and determining the model parameters of the equivalent circuit model when the square sum error of the difference between the experimental impedance and the calculated impedance is minimized by using a complex nonlinear least square method.
Further, based on the orthogonal test, the method uses an Arrhenius model as a base and a polynomial model as parameters, obtains an orthogonal piecewise polynomial Arrhenius model by using a piecewise function representation mode, selects different pieces and different stages, estimates model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least squares method, and comprises the following steps:
based on the orthogonal test, establishing an equivalent circuit parameter model considering temperature and SOC double-factor interaction by taking an Arrhenius model with temperature influence as a basis and taking a polynomial model with SOC influence as a parameter;
expressing the equivalent circuit parameter model in a form of a piecewise function to obtain an orthorhombic piecewise polynomial Arrhenius model;
and selecting different segment numbers and different orders, and estimating model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method.
Further, the equation of the equivalent circuit parameter model considering the interaction of the temperature and the SOC is:
wherein R is x (T, SOC) is a function of model parameters of the ECM at different temperatures and SOCs, including: [ R ] o ，R i ，n i ，Q i ，R ct ，n ct ，Q ct ，R W ，τ W ，n W ]；R x，A (SOC) is a polynomial function of the Arrhenius model proportionality constant;a polynomial function of the activation energy of an Arrhenius model;
the expression of the orthogonal piecewise polynomial Arrhenius model obtained by using the piecewise function expression mode is as follows:
selecting different segment numbers and different orders, and estimating a calculation formula of model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method, wherein the calculation formula is as follows:
wherein I is the number of SOC, J is the number of temperature, R x，exp (T j ，SOC i ) Is SOC (State of charge) i And T j Experimental impedance at, R x，cal (T j ，SOC i ) Is the calculated SOC i And T j Impedance at (c).
Further, the method further comprises the following steps:
and obtaining a predicted value of the complex impedance according to the optimal equivalent circuit model.
The embodiment of the application provides a lithium battery equivalent circuit model building device considering temperature and SOC double factors, which comprises:
the selection module is used for selecting a sample battery and designing an orthogonal test;
the first construction module is used for constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating model parameters of the equivalent circuit model by using a complex nonlinear least square method; wherein the model parameters of the equivalent circuit model include a plurality of;
the second construction module is used for expressing the model parameters of the equivalent circuit model by using a piecewise function expression mode based on the Arrhenius model and using a polynomial model as parameters based on the orthogonal test to obtain an orthogonal piecewise polynomial Arrhenius model, selecting different segment numbers and different stages, and estimating the model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
the acquisition module is used for acquiring optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
By adopting the technical scheme, the application has the following beneficial effects:
according to the application, a two-factor orthogonal test is designed, and OPPA is established based on the form of an Arrhenius equation influenced by temperature and by combining an SOC influence polynomial model. Parameters of the ECM model are corrected by using OPPA, so that the ECM model shows good prediction performance on EIS impedance spectrum under unknown temperature and SOC conditions. The method has the specific advantages that:
(1) According to the application, the battery model is constructed on the premise of reasonable test quantity, and the quantity of comprehensive tests can be effectively reduced through the design of the orthogonal test scheme.
(2) The application establishes the OPPA temperature and SOC dual-factor parameter model, and the model can provide satisfactory ECM parameter prediction performance in a large temperature and wide SOC range which almost covers the whole electric automobile operation working condition.
(3) The application provides an establishment framework suitable for OPPA-ECM under unknown temperature and SOC conditions. And a large number of experiments are carried out, and a large number of experimental results prove that the EIS prediction performance of the framework is higher at the temperature of-20 ℃ to 45 ℃ and in the SOC range of 10% -100%.
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In order to more clearly illustrate the embodiments of the application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of the steps of the method for establishing an equivalent circuit model of a lithium battery taking into account temperature and SOC dual factors;
FIG. 2 is a schematic diagram of a second order RC based ECM provided by the present application;
FIG. 3 is a graph comparing predicted impedances using OPPA-ECM and full test piecewise polynomial Arrhenius FPPA-ECM at different temperatures and SOCs provided by the present application;
fig. 4 is a schematic structural diagram of a device for establishing an equivalent circuit model of a lithium battery, which takes into consideration temperature and SOC dual factors.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, based on the examples herein, which are within the scope of the application as defined by the claims, will be within the scope of the application as defined by the claims.
The following describes a specific method for establishing an equivalent circuit model of a lithium battery taking temperature and SOC into consideration in the embodiment of the application with reference to the accompanying drawings.
As shown in fig. 1, the method for establishing the lithium battery equivalent circuit model taking into consideration temperature and SOC double factors provided in the embodiment of the present application includes:
s101, selecting a sample battery and designing an orthogonal test;
specifically, the design orthogonal test includes:
selecting test factors and determining a test level; wherein, the experimental factors include: temperature and SOC; determining a test level as a level of determining a temperature factor and an SOC factor; in this example, the temperature and SOC factors are at 5 levels. For comparison, the temperature factor of the full test was selected to be 5 level and the SOC factor was selected to be 10 level.
Selecting an orthogonal table according to factors, test levels and whether interaction needs to be inspected; the selection principle of the orthogonal table is that a smaller orthogonal table is selected as far as possible under the premise of arranging test factors and interaction so as to reduce test times. The present example looks at a 2 factor 5 level and selects L by looking up the normal orthogonal table 25 (5 6 ) Is a suitable orthogonal table.
The test factors and interactions are arranged into the orthogonal table, and different horizontal numbers of each column in the orthogonal table are replaced by corresponding horizontal values corresponding to each factor to form an orthogonal test.
Wherein the header design is to arrange the trial factors and interactions reasonably into columns of the selected orthogonal table. Based on the design of the header, the test scheme is formed by changing different horizontal numbers of each column in the selected orthogonal table into corresponding horizontal values corresponding to each factor. After the design of the test protocol is completed, the test can be performed according to the test protocol. After the test was performed, the test results were filled in the corresponding positions as shown in table 1.
Table 1 is based on L 25 (5 6 ) Test scheme and results for ECM parameter estimation for orthogonal tables
S102, constructing an equivalent circuit model (Equivalent Circuit Model, ECM) according to the sample battery, measuring an electrochemical impedance spectrum curve (Electrochemical Impedance Spectroscopy, EIS) according to the experimental condition of the orthogonal test, and estimating model parameters of the equivalent circuit model by using a complex nonlinear least squares method (Complex Nonlinear Least Squares, CNLS); wherein the model parameters of the equivalent circuit model include a plurality of;
CNLS is capable of numerically optimizing model parameters in terms of the sum of the least squares error between the test data and the predicted data.
In some embodiments, the constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating the parameters of the equivalent circuit model by using a complex nonlinear least squares method includes:
constructing an equivalent circuit model according to the sample battery;
acquiring impedance of the equivalent circuit model according to the equivalent circuit model;
estimating parameters of the equivalent circuit model through experimental impedance and calculated impedance of the equivalent circuit model by using a complex nonlinear least square method.
It can be appreciated that the equivalent circuit model established herein can only predict the room temperature impedance.
As shown in fig. 2, the present embodiment selects ECM based on 2 nd order RC; the electrochemical impedance spectrum (Electrochemical Impedance Spectroscopy, EIS) curve is measured by performing experiments under the temperature and SOC conditions in the orthogonal experimental design, the parameters of the ECM are estimated by using a complex nonlinear least squares (Complex Nonlinear Least Squares, CNLS) method, and the CNLS can carry out numerical optimization on the model parameters in the sense of least error square sum between experimental data and predicted data. The method specifically comprises the following steps:
taking the ECM of the second order RC as an example, the complex impedance of the EIS-based ECM can be expressed by the equation as follows:
Z ECM ＝Z Ro +Z Ri +Z Rct +Z W
wherein Z is ECM Is complex impedance Z Ro For ohmic impedance, Z Ri For the migration resistance of lithium ions in the SEI film,for charge transfer impedance, Z W R is the solid diffusion resistance of lithium ions in active material particles O Is the sum of ohmic resistances, R i R is the sum of SEI film migration resistances ct Is the sum of charge transfer resistances, Q i And Q ct Is a generalized capacity; n is n i And n ct Taking real numbers between 0 and 1 as inhibition factors; r is R W For Warburg resistance, τ W N is the diffusion time constant W Varying between 0 and 1. It will be appreciated that R O 、R i 、R ct Are model parameters of the equivalent circuit model. The model parameters of the equivalent circuit model can be obtained in a plurality in the experimental process.
Parameters of ECM are then estimated using CNLS method, which minimizes the sum of squares error (Sum of Squares Error, SSE) of the difference between the experimental and calculated impedances, calculated as:
wherein K is the number of frequencies, Z' exp (ω k ) And Z' exp (ω k ) Omega respectively k The real and imaginary parts of the experimental impedance at Z' cal (ω k ) And Z' cal (ω k ) Respectively calculated omega k A real part and an imaginary part of the impedance;
and determining the model parameters of the equivalent circuit model when the square sum error of the difference between the experimental impedance and the calculated impedance is minimized by using a complex nonlinear least square method.
S103, based on the orthogonal test, using an Arrhenius model as a base and using a polynomial model as parameters, using a piecewise function representation mode to represent the model parameters of the equivalent circuit model to obtain an orthogonal piecewise polynomial Arrhenius model, selecting different segments and different stages, and using a nonlinear least square method to estimate the model parameters of the orthogonal piecewise polynomial Arrhenius model; the method specifically comprises the following steps:
based on the orthogonal test, establishing an equivalent circuit parameter model considering temperature and SOC double-factor interaction by taking an Arrhenius model with temperature influence as a basis and taking a polynomial model with SOC influence as a parameter;
expressing the equivalent circuit parameter model in a form of a piecewise function to obtain an orthorhombic piecewise polynomial Arrhenius model;
and selecting different segment numbers and different orders, and estimating model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method.
In the application, based on the form of an Arrhenius model with temperature influence and a polynomial model with SOC influence as parameters, an ECM parameter model considering the interaction of temperature and SOC double factors is established. In order to describe the dominant effect of elements in different temperature intervals in a more detailed way, the two-factor model is further described in a form of a piecewise function, and an orthogonal piecewise polynomial Arrhenius model (Orthogonal Piecewise polynomial Arrhenius, OPPA) is obtained. Different numbers of segments and different orders are selected and nonlinear least squares (Nonlinear Least Squares, NLS) is used to estimate the model parameters of the OPPA. The method specifically comprises the following steps:
the equation of the equivalent circuit parameter model considering the temperature and SOC dual-factor interaction is:
wherein R is x (T, SOC) is a function of model parameters of the ECM at different temperatures and SOCs, including: [ R ] o ，R i ，n i ，Q i ，R ct ，n ct ，Q ct ，R W ，τ W ，n W ]；R x，A (SOC) is a polynomial function of the Arrhenius model proportionality constant;is a polynomial function of the activation energy of an Arrhenius model.
It will be appreciated that R x The (T, SOC) represents model parameters of an equivalent circuit model, and the equivalent circuit parameter model of the temperature and SOC dual-factor interaction is a representation of the model parameters in the equivalent circuit model. The application firstly needs to determine the parameters in the equivalent circuit parameter model of the temperature and SOC double-factor interaction, wherein the parameters are R x (T, SOC); to determine R x The application determines the number of segments and the number of steps according to the number of the selected temperature levels and the number of SOC levels, wherein the temperature is 5 levels, and the SOC is 5 levels, so that the number of segments can be from 1 to 4, the number of steps can be from 1 to 4, and 16 conditions exist for the segments and the steps.
The expression of the orthogonal piecewise polynomial Arrhenius model obtained by using the piecewise function expression mode is as follows:
selecting different segment numbers and different orders, and estimating a calculation formula of model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method, wherein the calculation formula is as follows:
wherein I is the number of SOC, J is the number of temperature, R x，exp (T j ，SOC i ) Is SOC (State of charge) i And T j Experimental impedance at, R x，cal (T j ，SOC i ) Is the calculated SOC i And T j Impedance at (c). And determining the model parameters of the Arrhenius model by using the model parameters of the equivalent circuit model obtained in the experiment.
S104, obtaining optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
Specifically, the optimal equivalent circuit model is the OPPA-ECM. The present application measures 25 EIS curves at 5 temperature levels of-20 ℃, -10 ℃, 5 ℃, 25 ℃ and 45 ℃ and 5 SOC levels of 10%, 30%, 50%, 70% and 100%, with which 25 lines ECM parameters are estimated one by one. To demonstrate that the established OPPA-ECM is well able to predict experimental impedance spectra, FIG. 3 shows comparative data of the predicted impedance of FPPA-ECM using OPPA-ECM and Full test piecewise polynomial Arrhenius (Full-scale Piecewise polynomial Arrhenius, FPPA) at different temperatures and SOCs, respectively, where (a) is 45℃result, (b) is 25℃result, (c) is-10℃result, and (d) is-20℃result. The OPPA-ECM presented in the examples shows good agreement with the experimental impedance spectrum at unknown SOC and temperature, and the predicted performance of the OPPA-ECM and the FPPA-ECM are similar, whereas the OPPA-ECM uses only half the experimental number of the FPPA-ECM.
The working principle of the lithium battery equivalent circuit model building method considering the temperature and the SOC dual factors is as follows: firstly, selecting a sample battery, constructing an ECM model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating model parameters of the ECM model by using a complex nonlinear least squares method; based on the orthogonal test, an Arrhenius model is taken as a basis, a polynomial model is taken as a parameter, an OPPA model is obtained by using a piecewise function representation mode, different segments and different stages are selected, and the model parameter of the OPPA model is estimated by using a nonlinear least square method; obtaining optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an OPPA model with the corresponding segment number and order to obtain an optimal OPPA model; and selecting the temperature and the SOC value to load into the optimal OPPA model to obtain the optimal parameters of the ECM model, and obtaining the OPPA-ECM model.
In some embodiments, finally, loading parameters into the ECM can result in a predicted value Z of the EIS complex impedance ECM 。
As shown in fig. 4, an embodiment of the present application provides a device for establishing an equivalent circuit model of a lithium battery, which considers two factors of temperature and SOC, including:
a selection module 401 for selecting a sample cell, and designing an orthogonal test;
a first construction module 402, configured to construct an equivalent circuit model according to the sample battery, measure an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimate model parameters of the equivalent circuit model by using a complex nonlinear least squares method; wherein the model parameters of the equivalent circuit model include a plurality of;
the second construction module 403 is configured to obtain an orthogonal piecewise polynomial arrhenius model by using a piecewise function representation manner based on the arrhenius model and using a polynomial model as parameters based on the orthogonal test, select different numbers of segments and different phases, and estimate model parameters of the orthogonal piecewise polynomial arrhenius model by using a nonlinear least squares method;
the obtaining module 404 is configured to obtain an optimal model parameter with the best optimal segment number and order prediction effect, and load the optimal model parameter into an orthogonal segmented polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
The working principle of the lithium battery equivalent circuit model building device considering temperature and SOC double factors provided by the embodiment of the application is that a selection module 401 selects a sample battery and designs an orthogonal test; the first construction module 402 constructs an equivalent circuit model according to the sample battery, measures an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimates model parameters of the equivalent circuit model by using a complex nonlinear least squares method; the second construction module 403 uses an Arrhenius model as a basis and a polynomial model as parameters based on the orthogonal test, and uses a piecewise function representation mode to represent the model parameters of the equivalent circuit model to obtain an orthogonal piecewise polynomial Arrhenius model, selects different segment numbers and different stages, and uses a nonlinear least square method to estimate the model parameters of the orthogonal piecewise polynomial Arrhenius model; the acquisition module 404 acquires optimal model parameters with the best optimal segment number and order prediction effect, and loads the optimal model parameters to an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
The embodiment of the application provides computer equipment, which comprises a processor and a memory connected with the processor;
the memory is used for storing a computer program, and the computer program is used for executing the method for establishing the lithium battery equivalent circuit model taking the temperature and the SOC into consideration, which is provided by any one of the embodiments;
the processor is used to call and execute the computer program in the memory.
In summary, the application provides a method for establishing a lithium battery equivalent circuit model by considering temperature and SOC double factors. Parameters of the ECM model are corrected by using OPPA, so that the ECM model shows good prediction performance on EIS impedance spectrum under unknown temperature and SOC conditions. According to the application, the battery model is constructed on the premise of reasonable test quantity, and the quantity of comprehensive tests can be effectively reduced through the design of the orthogonal test scheme. The application establishes the OPPA temperature and SOC dual-factor parameter model, and the model can provide satisfactory ECM parameter prediction performance in a large temperature and wide SOC range which almost covers the whole electric automobile operation working condition. The application provides an establishment framework suitable for OPPA-ECM under unknown temperature and SOC conditions. And a large number of experiments are carried out, and a large number of experimental results prove that the EIS prediction performance of the framework is higher at the temperature of-20 ℃ to 45 ℃ and in the SOC range of 10% -100%.
It can be understood that the above-provided method embodiments correspond to the above-described apparatus embodiments, and corresponding specific details may be referred to each other and will not be described herein.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, magnetic disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (8)

1. A method for establishing a lithium battery equivalent circuit model by considering temperature and SOC double factors is characterized by comprising the following steps:
selecting a sample battery and designing an orthogonal test;
constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating model parameters of the equivalent circuit model by using a complex nonlinear least square method; wherein the model parameters of the equivalent circuit model include a plurality of;
based on the orthogonal test, representing model parameters of the equivalent circuit model by using a piecewise function representation mode by taking an Arrhenius model as a basis and taking a polynomial model as parameters to obtain an orthogonal piecewise polynomial Arrhenius model; selecting different segment numbers and different stages, and estimating model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
based on the orthogonal test, an Arrhenius model is taken as a base, a polynomial model is taken as a parameter, an orthogonal piecewise polynomial Arrhenius model is obtained by using a piecewise function representation mode, different pieces and different stages are selected, and model parameters of the orthogonal piecewise polynomial Arrhenius model are estimated by using a nonlinear least square method, and the method comprises the following steps:
based on the orthogonal test, establishing an equivalent circuit parameter model considering temperature and SOC double-factor interaction by taking an Arrhenius model with temperature influence as a basis and taking a polynomial model with SOC influence as a parameter;
expressing the equivalent circuit parameter model in a form of a piecewise function to obtain an orthorhombic piecewise polynomial Arrhenius model;
selecting different segment numbers and different orders, and estimating model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
obtaining optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
2. The method of claim 1, wherein the designing an orthogonal experiment comprises:
selecting test factors and determining a test level; wherein the test factors include: temperature and SOC; determining a test level as a level of determining a temperature factor and an SOC factor;
selecting an orthogonal table according to factors, test levels and whether interaction needs to be inspected;
the test factors and interactions are arranged into the orthogonal table, and different horizontal numbers of each column in the orthogonal table are replaced by corresponding horizontal values corresponding to each factor to form an orthogonal test.
3. The method according to claim 1 or 2, wherein constructing an equivalent circuit model from the sample cell, measuring an electrochemical impedance spectrum curve from experimental conditions of the orthogonal test, estimating parameters of the equivalent circuit model using a complex nonlinear least squares method, comprises:
constructing an equivalent circuit model according to the sample battery;
acquiring impedance of the equivalent circuit model according to the equivalent circuit model;
estimating parameters of the equivalent circuit model through experimental impedance and calculated impedance of the equivalent circuit model by using a complex nonlinear least square method.
4. A method according to claim 3, wherein the equivalent circuit model is a second order RC equivalent circuit model; the complex impedance calculation formula of the second-order RC equivalent circuit model is as follows:
Z ECM ＝Z Ro +Z Ri +Z Rct +Z W
wherein Z is ECM Is complex impedance Z Ro For ohmic impedance, Z Ri For the migration resistance of lithium ions in the SEI film,for charge transfer impedance, Z W R is the solid diffusion resistance of lithium ions in active material particles O Is the sum of ohmic resistances, R i R is the sum of SEI film migration resistances ct Is the sum of charge transfer resistances, Q i And Q ct Is a generalized capacity; n is n i And n ct Taking real numbers between 0 and 1 as inhibition factors; r is R W For Warburg resistance, τ W N is the diffusion time constant W Varying between 0 and 1.
5. The method according to claim 4, wherein the model parameters of the equivalent circuit model are estimated by using the complex nonlinear least squares method through experimental impedance and calculated impedance of the equivalent circuit model, and the calculation formula is:
wherein K is the number of frequencies, Z' exp (ω k ) And Z' exp (ω k ) Omega respectively k The real and imaginary parts of the experimental impedance at Z' cal (ω k ) And Z' cal (ω k ) Respectively calculated omega k A real part and an imaginary part of the impedance;
and determining the model parameters of the equivalent circuit model when the square sum error of the difference between the experimental impedance and the calculated impedance is minimized by using a complex nonlinear least square method.
6. The method of claim 1, wherein the step of determining the position of the substrate comprises,
the equation of the equivalent circuit parameter model considering the temperature and SOC dual-factor interaction is:
wherein R is x (T, SOC) is a function of equivalent circuit model parameters at different temperatures and SOCs, including: [ R ] o ，R i ，n i ，Q i ，R ct ，n ct ，Q ct ，R W ，τ W ，n W ]；R x，A (SOC) is a polynomial function of the Arrhenius model proportionality constant;a polynomial function of the activation energy of an Arrhenius model;
the expression of the orthogonal piecewise polynomial Arrhenius model obtained by using the piecewise function expression mode is as follows:
selecting different segment numbers and different orders, and estimating a calculation formula of model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method, wherein the calculation formula is as follows:
wherein I is the number of SOC, J is the number of temperature, R x，exp (T j ，SOC i ) Is SOC (State of charge) i And T j Experimental impedance at, R x，col (T j ，SOC i ) Is the calculated SOC i And T j Impedance at (c).
7. The method as recited in claim 1, further comprising:
and obtaining a predicted value of the complex impedance according to the optimal equivalent circuit model.
8. The utility model provides a lithium battery equivalent circuit model establishment device of taking into account temperature and SOC double-factor which characterized in that includes:
the selection module is used for selecting a sample battery and designing an orthogonal test;
the first construction module is used for constructing an equivalent circuit model according to the sample battery, measuring an electrochemical impedance spectrum curve according to the experimental condition of the orthogonal test, and estimating model parameters of the equivalent circuit model by using a complex nonlinear least square method; wherein the model parameters of the equivalent circuit model include a plurality of;
the second construction module is used for expressing the model parameters of the equivalent circuit model by using a piecewise function expression mode based on the Arrhenius model and using a polynomial model as parameters based on the orthogonal test to obtain an orthogonal piecewise polynomial Arrhenius model, selecting different segment numbers and different stages, and estimating the model parameters of the orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
based on the orthogonal test, an Arrhenius model is taken as a base, a polynomial model is taken as a parameter, an orthogonal piecewise polynomial Arrhenius model is obtained by using a piecewise function representation mode, different pieces and different stages are selected, and model parameters of the orthogonal piecewise polynomial Arrhenius model are estimated by using a nonlinear least square method, and the method comprises the following steps:
based on the orthogonal test, establishing an equivalent circuit parameter model considering temperature and SOC double-factor interaction by taking an Arrhenius model with temperature influence as a basis and taking a polynomial model with SOC influence as a parameter;
expressing the equivalent circuit parameter model in a form of a piecewise function to obtain an orthorhombic piecewise polynomial Arrhenius model;
selecting different segment numbers and different orders, and estimating model parameters of an orthogonal piecewise polynomial Arrhenius model by using a nonlinear least square method;
the acquisition module is used for acquiring optimal model parameters with the best optimal segment number and order prediction effect, and loading the optimal model parameters into an orthogonal segmentation polynomial Arrhenius model with the corresponding segment number and order to obtain an optimal Arrhenius parameter model; and selecting the temperature and the SOC value to load into the optimal Arrhenius parameter model to obtain the optimal parameters of the equivalent circuit model, and obtaining the optimal equivalent circuit model.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105304952A (en) * 2014-07-28 2016-02-03 福特全球技术公司 Reduced order electrochemical battery model for vehicle control
CN110068772A (en) * 2019-05-06 2019-07-30 重庆大学 Based on the charge states of lithium ion battery estimation method for improving fractional model

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP6555773B2 (en) * 2014-11-18 2019-08-07 学校法人立命館 Storage power remaining amount estimation device, method for estimating remaining power storage amount of storage battery, and computer program
US10353007B2 (en) * 2015-05-28 2019-07-16 Mitsubishi Electric Corporation Rechargeable battery parameter estimation apparatus and rechargeable battery parameter estimation method for calculating first and second coefficients which are partial derivatives of an estimated value of the battery state-of-charge

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105304952A (en) * 2014-07-28 2016-02-03 福特全球技术公司 Reduced order electrochemical battery model for vehicle control
CN110068772A (en) * 2019-05-06 2019-07-30 重庆大学 Based on the charge states of lithium ion battery estimation method for improving fractional model

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
唐帅帅.基于自适应卡尔曼滤波的磷酸铁锂电池荷电状态估计研究.电子测量技术.2018,全文. *

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