CN110286325A - A kind of local sensitivity degree analysis method of lithium ion battery - Google Patents
A kind of local sensitivity degree analysis method of lithium ion battery Download PDFInfo
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- CN110286325A CN110286325A CN201910688791.4A CN201910688791A CN110286325A CN 110286325 A CN110286325 A CN 110286325A CN 201910688791 A CN201910688791 A CN 201910688791A CN 110286325 A CN110286325 A CN 110286325A
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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
- G01R31/005—Testing of electric installations on transport means
- G01R31/006—Testing of electric installations on transport means on road vehicles, e.g. automobiles or trucks
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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
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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
- G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
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Abstract
The invention discloses a kind of local sensitivity degree analysis methods of lithium ion battery comprising following steps: S1, the circuit equation that target charge states of lithium ion battery estimation electrical equivalent model is established according to Kirchhoff's law;S2, the parameter value for obtaining circuit element in equivalent-circuit model is tested by HPPC;S3, the local sensitivity degree that circuit element parameter in equivalent-circuit model estimates state-of-charge the local sensitivity degree and circuit element parameter of equivalent-circuit model accuracy accuracy is obtained by control variate method.The present invention provides unified, clear, clear, quantitative local sensitivity degree analysis methods come influence when measuring different circuit element parameter variations in equivalent-circuit model to model accuracy and SOC estimation accuracy.
Description
Technical field
The present invention relates to battery analysis fields, and in particular to a kind of local sensitivity degree analysis method of lithium ion battery.
Background technique
Since 21 century, people expect that automobile more cleans, is environmentally friendly, and electric car receives extensive attention.Compare biography
System fuel-engined vehicle, electric car is pollution-free, noise is small, accelerating ability is excellent, receives national governments and the favor of consumer.Electricity
Pond is the kernel component of electric car.Battery management system is essential for battery.Battery management system (battery
Management system, BMS) most important function is to complete estimating for battery charge state (State of Charge, SOC)
Meter.
In a variety of lithium ion battery SOC algorithm for estimating, equivalent-circuit model is all the basis of estimation.Common equivalent electricity
Road model has Rint model, Thevenin model, Order RC model, PNGV model etc..Estimate in the SOC based on equivalent-circuit model
The ultimate challenge faced in meter method is that circuit element parameter has different values, such as discharge-rate, electricity in different situations
Pond degree of aging, environment temperature difference etc..
Standard is estimated to model accuracy and SOC in order to quantitatively analyze the circuit element parameter of equivalent-circuit model and change
True property influences, and needs a unification, clear, quantitative sensitivity analysis method.
Summary of the invention
For above-mentioned deficiency in the prior art, a kind of local sensitivity degree analysis side of lithium ion battery provided by the invention
Method gives a quantitative local sensitivity degree analysis method.
In order to achieve the above object of the invention, the technical solution adopted by the present invention are as follows:
There is provided a kind of local sensitivity degree analysis method of lithium ion battery comprising following steps:
S1, the circuit that target charge states of lithium ion battery estimation electrical equivalent model is established according to Kirchhoff's law
Equation;
S2, the parameter value for obtaining circuit element in equivalent-circuit model is tested by HPPC;
S3, by control variate method obtain equivalent-circuit model in circuit element parameter to equivalent-circuit model accuracy
Local sensitivity degree and circuit element parameter estimate state-of-charge the local sensitivity degree of accuracy.
Further, the specific method of step S3 includes following sub-step:
S3-1, using the parameter value for obtaining circuit element in step S2 as a reference value, and arbitrarily choose a kind of fortune of battery
Row operating condition;Wherein a reference value of first of circuit element isL=1,2,3 ..., L;L is the sum of circuit element;
S3-2, respectively according to formula
Obtain the root-mean-square error E of equivalent-circuit model end voltage under a reference valueU,baseIt is square with state-of-charge estimated value
Root error ESOC,base;Wherein m is the duration of entire cell operating status;Uk,ModelBy equivalent-circuit model when for the k moment
The end voltage estimated value being calculated;Uk.RefThe end voltage true value that actual measurement obtains when for the k moment;SOCk,EstFor the k moment
When the estimated value of state-of-charge that is calculated by equivalent-circuit model;SOCk.RefFor the true value of state-of-charge;
S3-3, n random number m equally distributed in [0,1] are generated using linear congruential method1,m2,m3,...,
mj,...,mn, j=1,2..., n;
S3-4, by 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, according to the random number of generation obtain
Circuit element XlThe equally distributed n value in parameter value variation section;
S3-5, one by one selecting circuit element XlN value, using method identical with step S3-2 obtain circuit element
XlUsing j-th of valueWhen equivalent-circuit model end voltage root-mean-square error EU,l,jIt is square with state-of-charge estimated value
Root error ESOC,l,j;
S3-6, according to formula
Obtain circuit element XlTo the local sensitivity degree of equivalent-circuit model accuracy
S3-7, according to formula
Obtain circuit element XlTo the local sensitivity degree of state-of-charge estimation accuracy
Further, the specific method of the estimated value for the state-of-charge being calculated in step S3-2 by equivalent-circuit model
Including following sub-step:
The output side of S3-2-1, the state space equation for converting circuit equation to nonlinear system and state space equation
Journey:
xk=f (xk-1,uk-1)+wk-1
yk=g (xk,uk)+vk
Wherein xkFor the state of k moment nonlinear system;xk-1For the state of k-1 moment nonlinear system;uk-1When for k-1
Carve the output of nonlinear system;wk-1For the white Gaussian noise at k-1 moment;F () is the state equation of nonlinear system, is non-
Linear function;vkFor white Gaussian noise, vkWith wkIndependently of each other;G () is the output equation of nonlinear system, is non-linear letter
Number;ukFor the output of k moment nonlinear system;ykFor the shape of the output equation of the state space equation of k moment nonlinear system
State;
S3-2-2, according to formula
Respectively to the system state estimation value of nonlinear system initial timeWith error covariance estimated valueIt carries out just
Beginningization;Wherein E [] is statistical expection operator;x0For the original state of nonlinear system;(·)TFor the transposition of matrix;
S3-2-3, according to formula
Obtain the system mode predicted value at k momentWith error covariance predicted valueWhereinFor the k-1 moment
System state estimation value;For the error covariance estimated value at k-1 moment;For Ak-1Transposition, Ak-1For centre ginseng
Number;Q is wkCorresponding covariance matrix, wkFor the white Gaussian noise at k moment;
S3-2-4, according to formula
Obtain kalman gain Kk;Wherein CkFor intermediate parameters, Ck TFor CkTransposition;R is vkCovariance matrix;
S3-2-5, according to formula
Obtain the system state estimation value of k moment nonlinear system after correctingWith error covariance estimated valueTo be
System state estimationEstimated value as the state-of-charge that state-of-charge obtains;Wherein I is unit matrix.
Further, step S3-4 method particularly includes:
By 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, by the constant interval Linear Mapping to section
In [0,1], make circuit element XlValue and step S3-3 in the n that generates equally distributed random numbers correspond, obtain
Circuit element XlThe equally distributed n value in parameter value variation section;Wherein circuit element XlJ-th of value
The invention has the benefit that the present invention provides unified, clear, clear, quantitative local sensitivity degree analysis sides
Method estimates model accuracy and SOC the shadow of accuracy to measure when different circuit element parameters change in equivalent-circuit model
It rings.This method can analyze the circuit element parameter of a variety of equivalent-circuit models, and such as Rint model wears Vernam model, Order RC
Model etc..After obtaining susceptibility sequence, for can only estimate that susceptibility is high in the SOC algorithm for estimating of parameter On-line Estimation
Parameter reduces operand, estimates to obtain balance between accuracy and computing overhead in SOC.
Detailed description of the invention
Fig. 1 is flow diagram of the invention;
Fig. 2 is Order RC equivalent-circuit model figure.
Specific embodiment
A specific embodiment of the invention is described below, in order to facilitate understanding by those skilled in the art this hair
It is bright, it should be apparent that the present invention is not limited to the ranges of specific embodiment, for those skilled in the art,
As long as various change is in the spirit and scope of the present invention that the attached claims limit and determine, these variations are aobvious and easy
See, all are using the innovation and creation of present inventive concept in the column of protection.
As shown in Figure 1, the local sensitivity degree analysis method of the lithium ion battery the following steps are included:
S1, the circuit that target charge states of lithium ion battery estimation electrical equivalent model is established according to Kirchhoff's law
Equation;
S2, the parameter value for obtaining circuit element in equivalent-circuit model is tested by HPPC;
S3, by control variate method obtain equivalent-circuit model in circuit element parameter to equivalent-circuit model accuracy
Local sensitivity degree and circuit element parameter estimate state-of-charge the local sensitivity degree of accuracy.
The specific method of step S3 includes following sub-step:
S3-1, using the parameter value for obtaining circuit element in step S2 as a reference value, and arbitrarily choose a kind of fortune of battery
Row operating condition;Wherein a reference value of first of circuit element isL=1,2,3 ..., L;L is the sum of circuit element;
S3-2, respectively according to formula
Obtain the root-mean-square error E of equivalent-circuit model end voltage under a reference valueU,baseIt is square with state-of-charge estimated value
Root error ESOC,base;Wherein m is the duration of entire cell operating status;Uk,ModelBy equivalent-circuit model when for the k moment
The end voltage estimated value being calculated;Uk.RefThe end voltage true value that actual measurement obtains when for the k moment;SOCk,EstFor the k moment
When the estimated value of state-of-charge that is calculated by equivalent-circuit model;SOCk.RefFor the true value of state-of-charge;
S3-3, n random number m equally distributed in [0,1] are generated using linear congruential method1,m2,m3,...,
mj,...,mn, j=1,2..., n;
S3-4, by 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, according to the random number of generation obtain
Circuit element XlThe equally distributed n value in parameter value variation section;
S3-5, one by one selecting circuit element XlN value, using method identical with step S3-2 obtain circuit element
XlUsing j-th of valueWhen equivalent-circuit model end voltage root-mean-square error EU,l,jIt is square with state-of-charge estimated value
Root error ESOC,l,j;
S3-6, according to formula
Obtain circuit element XlTo the local sensitivity degree of equivalent-circuit model accuracy
S3-7, according to formula
Obtain circuit element XlTo the local sensitivity degree of state-of-charge estimation accuracy
The specific method of the estimated value for the state-of-charge being calculated in step S3-2 by equivalent-circuit model includes following
Sub-step:
The output side of S3-2-1, the state space equation for converting circuit equation to nonlinear system and state space equation
Journey:
xk=f (xk-1,uk-1)+wk-1
yk=g (xk,uk)+vk
Wherein xkFor the state of k moment nonlinear system;xk-1For the state of k-1 moment nonlinear system;uk-1When for k-1
Carve the output of nonlinear system;wk-1For the white Gaussian noise at k-1 moment;F () is the state equation of nonlinear system, is non-
Linear function;vkFor white Gaussian noise, vkWith wkIndependently of each other;G () is the output equation of nonlinear system, is non-linear letter
Number;ukFor the output of k moment nonlinear system;ykFor the shape of the output equation of the state space equation of k moment nonlinear system
State;
S3-2-2, according to formula
Respectively to the system state estimation value of nonlinear system initial timeWith error covariance estimated value P0 +It carries out just
Beginningization;Wherein E [] is statistical expection operator;x0For the original state of nonlinear system;(·)TFor the transposition of matrix;
S3-2-3, according to formula
Obtain the system mode predicted value at k momentWith error covariance predicted valueWhereinFor the k-1 moment
System state estimation value;For the error covariance estimated value at k-1 moment;For Ak-1Transposition, Ak-1For centre ginseng
Number;Q is wkCorresponding covariance matrix, wkFor the white Gaussian noise at k moment;
S3-2-4, according to formula
Obtain kalman gain Kk;Wherein CkFor intermediate parameters, Ck TFor CkTransposition;R is vkCovariance matrix;
S3-2-5, according to formula
Obtain the system state estimation value of k moment nonlinear system after correctingWith error covariance estimated valueTo be
System state estimationEstimated value as the state-of-charge that state-of-charge obtains;Wherein I is unit matrix.Acquisition can
For calculating k+1 moment corresponding value, each moment is non-thread after repeating step S3-2-2 to step S3-2-5 and can obtaining correction
Property system system state estimation value to get to each moment state-of-charge estimated value.
Step S3-4's method particularly includes: by 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, by this
In constant interval Linear Mapping to section [0,1], make circuit element XlValue and step S3-3 in the n that generates be uniformly distributed
Random number correspond, obtain circuit element XlThe equally distributed n value in parameter value variation section;Wherein circuit elements
Part XlJ-th of value
In the specific implementation process, the process of HPPC experiment is as follows:
A) fully charged battery standing is after 1 hour, with 1C multiplying power discharging 6 minutes to SOC=90%;
B) 1 hour is stood;
C) with 3C multiplying power discharging 10 seconds, 40 seconds are stood, then with 2.25C multiplying power charging 10 seconds, stands 40 seconds;
D) with 1C multiplying power discharging 352.5 seconds, so that total discharge capacity of step c and d are the 10% of battery capacity;
E) circulation step b~d totally 9 times.
In the SOC estimation using expanded Kalman filtration algorithm combination equivalent-circuit model, the input of system is electric current
I, the output of system are equivalent-circuit model end voltage U, and the state of system is SOC, if there is RC capacitance-resistance ring in equivalent-circuit model
Section, quantity of state are further added by the end voltage at RC capacitance-resistance link both ends.
In susceptibility of the analyzing equivalent circuit precircuit component parameters to equivalent-circuit model accuracy, become in analysis
Dynamic input parameter is the parameter value of equivalent-circuit model circuit element, and output is that the root mean square of equivalent-circuit model end voltage misses
Poor EU;In susceptibility of the analyzing equivalent circuit precircuit component parameters to SOC estimation accuracy, the input that changes in analysis
Parameter is the parameter value of equivalent-circuit model circuit element, and output is the root-mean-square error E of SOCSOC。
In one embodiment of the invention, as described in Figure 2, with 5 circuit element R of Order RC equivalent-circuit model0、
R1、R2、C1、C2For, the circuit side of lithium ion battery SOC estimation electrical equivalent model is established based on Kirchhoff's law
Journey are as follows:
UOC=f (SOC)
5 circuit element parameter R can be obtained in the step of passing through this method0、R1、R2、C1、C2Respectively to model accuracy EU
Accuracy E is estimated with SOCSOCSusceptibilityWithAnd the susceptibility sequence of 5 circuit element parameters.
In conclusion the present invention provides unified, clear, clear, quantitative local sensitivity degree analysis methods to measure
Influence when imitating different circuit element parameter variations in circuit model to model accuracy and SOC estimation accuracy.This method can
To analyze the circuit element parameter of a variety of equivalent-circuit models, such as Rint model, wear Vernam model, Order RC model.?
To after susceptibility sequence, for can only the high parameter of estimation susceptibility, reduction transport in the SOC algorithm for estimating of parameter On-line Estimation
Calculation amount is estimated to obtain balance between accuracy and computing overhead in SOC.
Claims (4)
1. a kind of local sensitivity degree analysis method of lithium ion battery, which comprises the following steps:
S1, the circuit side that target charge states of lithium ion battery estimation electrical equivalent model is established according to Kirchhoff's law
Journey;
S2, the parameter value for obtaining circuit element in equivalent-circuit model is tested by HPPC;
S3, circuit element parameter is obtained in equivalent-circuit model to the part of equivalent-circuit model accuracy by control variate method
Susceptibility and circuit element parameter estimate state-of-charge the local sensitivity degree of accuracy.
2. the local sensitivity degree analysis method of lithium ion battery according to claim 1, which is characterized in that the step S3
Specific method include following sub-step:
S3-1, using the parameter value for obtaining circuit element in step S2 as a reference value, and arbitrarily choose a kind of operation work of battery
Condition;Wherein a reference value of first of circuit element isL is the sum of circuit element;
S3-2, respectively according to formula
Obtain the root-mean-square error E of equivalent-circuit model end voltage under a reference valueU, baseIt is missed with the root mean square of state-of-charge estimated value
Poor ESOC, base;Wherein m is the duration of entire cell operating status;UK, ModelTo be calculated when the k moment by equivalent-circuit model
Obtained end voltage estimated value;Uk.RefThe end voltage true value that actual measurement obtains when for the k moment;SOCK, EstWhen for the k moment by
The estimated value for the state-of-charge that equivalent-circuit model is calculated;SOCk.RefFor the true value of state-of-charge;
S3-3, n random number m equally distributed in [0,1] are generated using linear congruential method1, m2, m3..., mj..., mn, j
=1,2..., n;
S3-4, by 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, according to the random number of generation obtain circuit
Element XlThe equally distributed n value in parameter value variation section;
S3-5, one by one selecting circuit element XlN value, using method identical with step S3-2 obtain circuit element XlIt adopts
With j-th of valueWhen equivalent-circuit model end voltage root-mean-square error EU, l, jWith the root mean square of state-of-charge estimated value
Error ESOC, l, j;
S3-6, according to formula
Obtain circuit element XlTo the local sensitivity degree of equivalent-circuit model accuracy
S3-7, according to formula
Obtain circuit element XlTo the local sensitivity degree of state-of-charge estimation accuracy
3. the local sensitivity degree analysis method of lithium ion battery according to claim 2, which is characterized in that the step
The specific method of the estimated value for the state-of-charge being calculated in S3-2 by equivalent-circuit model includes following sub-step:
The output equation of S3-2-1, the state space equation for converting circuit equation to nonlinear system and state space equation:
xk=f (xk-1, uk-1)+wk-1
yk=g (xk, uk)+vk
Wherein xkFor the state of k moment nonlinear system;xk-1For the state of k-1 moment nonlinear system;uk-1It is non-for the k-1 moment
The output of linear system;wk-1For the white Gaussian noise at k-1 moment;F () is the state equation of nonlinear system, is non-linear
Function;vkFor white Gaussian noise, vkWith wkIndependently of each other;G () is the output equation of nonlinear system, is nonlinear function;uk
For the output of k moment nonlinear system;ykFor the state of the output equation of the state space equation of k moment nonlinear system;
S3-2-2, according to formula
Respectively to the system state estimation value of nonlinear system initial timeWith error covariance estimated valueIt is initialized;
Wherein E [] is statistical expection operator;x0For the original state of nonlinear system;(·)TFor the transposition of matrix;
S3-2-3, according to formula
Obtain the system mode predicted value at k momentWith error covariance predicted valueWhereinFor the system at k-1 moment
State estimation;For the error covariance estimated value at k-1 moment;For Ak-1Transposition, Ak-1For intermediate parameters;Q
For wkCorresponding covariance matrix, wkFor the white Gaussian noise at k moment;
S3-2-4, according to formula
Obtain kalman gain Kk;Wherein CkFor intermediate parameters, Ck TFor CkTransposition;R is vkCovariance matrix;
S3-2-5, according to formula
Obtain the system state estimation value of k moment nonlinear system after correctingWith the anti-estimate of variance of errorBy system shape
State estimated valueEstimated value as the state-of-charge that state-of-charge obtains;Wherein I is unit matrix.
4. the local sensitivity degree analysis method of lithium ion battery according to claim 2, which is characterized in that the step
S3-4's method particularly includes:
By 0.5 times of a reference value to 1.5 times of constant intervals as parameter value, by the constant interval Linear Mapping to section [0,
1] in, make circuit element XlValue and step S3-3 in the n that generates equally distributed random numbers correspond, obtain circuit
Element XlThe equally distributed n value in parameter value variation section;Wherein circuit element XlJ-th of value
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