CN109839599A - Lithium ion battery SOC estimation method based on second order EKF algorithm - Google Patents
Lithium ion battery SOC estimation method based on second order EKF algorithm Download PDFInfo
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Abstract
The invention discloses a kind of lithium ion battery SOC estimation methods based on second order EKF algorithm, comprising steps of one, battery Theoretic Analysis, detailed process are as follows: interval charge-discharge test is carried out to battery, the charge and discharge for obtaining the open circuit voltage curve of the hysteretic characteristic of characterization battery and characterizing the rebound characteristics of battery stand voltage curve；Two, the equivalent-circuit model of battery is established；Three, parameter identification is carried out to the parameter of the equivalent-circuit model of battery；Four, estimated using SOC of the second order EKF algorithm to battery, obtain the prediction result of the SOC of battery.The method of the present invention is novel in design rationally, and it is convenient to realize, with higher estimation precision preferable to the static and dynamic performance adaptability of battery is practical, and application value is high.
Description
Technical field
The invention belongs to battery SOC estimation technique fields, and in particular to a kind of lithium-ion electric based on second order EKF algorithm
Pond SOC estimation method.
Background technique
Green economy is being praised highly, is advocating the current era of sustainable development, pure electric automobile is low, pollution-free with its noise,
The advantages such as energy efficiency height become the Main way studied at present.Power accumulator is as the most important power supply system of electric car
The quality of system and power carrier, operating condition is most important for entire electric car.
Since lithium-ion-power cell has the advantages that monomer voltage is high, energy density height, has extended cycle life in performance
First choice as domestic and international many auto vendors.However, existing disposable since lithium-ion-power cell technology is also immature
The disadvantages of mileage travelled that charges is shorter, poor safety performance and battery are short.Therefore, pass through battery management system
(Battery Management System, BMS), which effectively manages and controls it, to be particularly important.And in BMS
In, no matter the accurate SOC working condition for estimating battery pack all has important for BMS system itself or electric car
Meaning.But since electric car operating condition will receive the influence of surroundings, SOC cannot directly measure to obtain, therefore, choosing
Selecting the SOC estimation method suitable for power battery actual motion is the main direction of scholar's research in the industry instantly.The present invention relates to
A kind of power battery remaining capacity (SOC) estimation problem, and in particular to estimation side lithium ion battery SOC based on second order EKF
Method.
In recent years, domestic and foreign scholars are broadly divided into three categories to the research method of battery SOC.
The first kind is the SOC estimation method based on battery electrochemical property, and representative method has: ampere-hour integral
(AH) method and open-circuit voltage (OCV) method.Wherein the SOC of battery is estimated using battery dynamic model combination AH method, in temperature
Still the SOC of battery can be effectively estimated under conditions of degree and curent change, test the error range of SOC as the result is shown
Within 2.5%；Based on single order equivalent-circuit model, OCV method is improved and combines EKF algorithm respectively to battery
Capacity and SOC are estimated that final result shows SOC estimation precision control within ± 5%.The advantage of such method is
Principle is simply easily realized, but it does not have real-time capability for correcting, the SOC estimation error meeting in automobile strong variable working condition state
It significantly increases.
Second class is mainly based upon the emerging intelligent prediction algorithms of artificial neural network.This algorithm uses input time
The neuralnetwork estimating method of delay, is adjusted between neuron using the multilayer perceptron structure of back-propagation learning rule
Weight to realize accurate estimation, simulation result shows: the root-mean-square error of SOC estimation is less than 0.35%.But this method
It is to be influenced big by sample data scale and training algorithm rule based on great amount of samples data, calculation amount is larger, increases
Online cost.
Third class method is mainly based upon Kalman filtering (Kalman Filter) algorithm of battery model.Since KF is calculated
Method is linear system, and the algorithm for power battery nonlinear system is mainly single order EKF algorithm, wherein in battery
Electrochemical model on the basis of combine Extended Kalman filter the SOC of battery is estimated, the experimental results showed that error does not surpass
Cross 5%；Considering to establish dual power supply model under influence of the discharge-rate variation to battery capacity, utilize spreading kalman
Filtering algorithm, which is realized, estimates that, by constant-current discharge experimental verification, final experimental result shows its maximum estimated to the SOC of battery
Within 8%, mean error is maintained within 5% error.Single order EKF algorithm compares other SOC estimation methods, not only has
On-line Estimation ability and be suitable for various types of batteries, become currently widely used evaluation method, but the method pair
The dependence of battery model is strong, and there is a problem of that precision is not high.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of based on two
The lithium ion battery SOC estimation method of rank EKF algorithm, method is novel in design rationally, and it is convenient to realize, to the sound state of battery
Characteristic adaptation is preferable, estimation precision with higher, practical, and application value is high.
In order to solve the above technical problems, the technical solution adopted by the present invention is that: a kind of lithium based on second order EKF algorithm from
Sub- battery SOC estimation method, method includes the following steps:
Step 1: battery Theoretic Analysis, detailed process are as follows: carry out interval charge-discharge test to battery, obtain characterization electricity
The charge and discharge of the rebound characteristics of the open circuit voltage curve and characterization battery of the hysteretic characteristic in pond stand voltage curve；
Step 2: establishing the equivalent-circuit model of battery, detailed process are as follows:
Step 201, the SOC computation model for establishing battery, and equivalent voltage source is established according to the open circuit voltage curve of battery
Model stands voltage curve according to the charge and discharge of battery and establishes equivalent impedance model；
Step 202 combines SOC computation model, equivalent voltage source model and equivalent impedance model three parts, establishes electricity
The equivalent-circuit model in pond；
Step 3: carrying out parameter identification to the parameter of the equivalent-circuit model of battery；
Step 4: estimating using SOC of the second order EKF algorithm to battery, the prediction result of the SOC of battery is obtained.
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm carries out battery described in step 1
The detailed process of interval charge-discharge test are as follows:
Battery is vented by step 101；
Step 102 executes step when cell voltage reaches 3.65V in 20min with 1/3C discharge-rate charging 20min
Rapid 104, it is no to then follow the steps 103；
Step 103, by battery standing 30min, return step 102 later；
Battery is full of by step 104；
Step 105, the 20min that discharged with 1/3C discharge-rate are entered step if cell voltage is lower than 2.0V in 20min
107, otherwise enter step 106；
Step 106, by battery standing 30min, return to step 105 later；
Battery is vented by step 107 with 0.02C low current.
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm, SOC described in step 202 calculate mould
Type includes capacitor CNWith battery eliminator B, the capacitor CNThe anode of one end and battery eliminator B connect, the capacitor CNIt is another
One end is connect with the cathode of battery eliminator B；Equivalent voltage source model described in step 202 includes current source M, inductance Lh, voltage
Source U1With voltage source U2, anode and the inductance L of the current source MhOne end connection, the cathode of the current source M and inductance Lh
The other end connection, the current source M1With current source M2Cathode after series connection is connect with the cathode of current source M；In step 202
The equivalent impedance model includes resistance R0, resistance R1, resistance R2, capacitor C1With capacitor C2, the resistance R0, resistance R1And electricity
Hinder R2Series connection, the capacitor C1With resistance R1Parallel connection, the capacitor C2With resistance R2It is in parallel；The cathode and electricity of the battery eliminator B
The cathode of potential source U connects, the resistance R0, resistance R1With resistance R2Resistance R after series connection0One end and current source M1And current source
M2Anode connection after series connection.
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm, described in step 3 to battery etc.
The parameter for imitating circuit model carries out the detailed process of parameter identification are as follows:
The parameter identification of step 301, equivalent voltage source model: the equilibrium potential EMF of battery is expressed as
EMF=0.5 (EMFc+EMFd) (F1)
By the hysteresis voltage V of batteryhIt is expressed as
Vh=0.5 (EMFc-EMFd) (F2)
Wherein, EMFcFor the equilibrium potential that charges, EMFdFor equilibrium potential of discharging；
The parameter identification of step 302, equivalent impedance model: any time voltage U is expressed as
Wherein, OCVDThe voltage at voltage curve D moment is stood for charge and discharge, the D moment springs back rank to be gone through after battery discharge
At the time of section voltage no longer changes；I is the current value for flowing through battery, R1For resistance R1Resistance value, τ1For with resistance R1It is corresponding
Time constant andR2For resistance R2Resistance value, τ2For with resistance R2Corresponding time constant andWhen t is
Between；
Fitting function is expressed as
F (x)=A-Bexp (- ax)-Cexp (- bx) (F4)
The C-D stage for standing voltage curve to charge and discharge is fitted, and obtains parameter A, B, C, a and b in fitting function
Value；Wherein, the C-D stage that charge and discharge stand voltage curve refers to that the mutation of battery discharge transient voltage starts to battery to put
The stage no longer changed after electricity through going through rebound stage voltage；
It is equal to each other according to formula (F3) and formula (F4), obtains the parameter of equivalent impedance model are as follows:
Wherein, C1For capacitor C1Capacitance, C2For capacitor C2Capacitance.
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm uses second order EKF described in step 4
Algorithm estimates the SOC of battery, obtains the detailed process of the prediction result of the SOC of battery are as follows:
Step 401, the state-space model for establishing battery system: according to the equivalent circuit for the battery established in step 2
Model, with the SOC of battery, capacitor C1The voltage V at both ends1With capacitor C2The voltage V at both ends2As the state variable of system, stream
The current value I for crossing battery is input quantity, and end voltage V is output quantity, and the state space of battery system is derived according to circuit equation
Model equation are as follows:
Output equation are as follows:
V (t)=VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
Wherein, CnFor the rated capacity of battery, VOCVFor voltage source U1With voltage source U2Total voltage；
Step 402 carries out the Nonlinear state space model equation of battery system linearly by the second Taylor series
Change, detailed process are as follows:
The state-space model equation (F6) of battery system is carried out second order Taylor by step 4021 at state estimation point
Expansion, obtains:
Wherein, f (xk,uk) it is state transition function, g (xk,uk) it is measurement functions, xkFor the state variable at k moment, uk
The control input quantity of etching system when for k,For xkEstimated value；
Step 4022, definition Formula (F8) is substituted into the state-space model side of nonlinear discrete systems
JourneyObtain the lienarized equation of battery system are as follows:
Wherein, Dk=R0；R0For
Resistance R0Resistance value, Δ t be the time variable quantity, ωkThe process noise for being zero for mean value, vkThe measurement for being zero for mean value is made an uproar
Sound, and ωkWith vkIt is irrelevant, ωk~N (0, Qk), vk~N (0, Rk)；That is ωkAnd vkObey the Gaussian Profile that mean value is 0；
Step 403 is estimated lithium ion battery SOC using second order EKF algorithm, detailed process are as follows:
Step 4031, initial phase:
Wherein, x0For the initialization value of state variable,For x0Estimated value, P0For the error of state variable predictive estimation
The initialization value of covariance matrix；
Step 4032, forecast period:
The predictive estimation of state variable:
Wherein,For xk-1Estimated value, xk-1For the state variable at k-1 moment, uk-1The control of etching system when for k-1
Input quantity；
The error co-variance matrix of state variable predictive estimation:
Wherein, Qk-1For the covariance matrix and Q of k-1 etching process noisek-1=Qk, QkFor the association of k etching process noise
Variance matrix；
Step 4033, amendment stage:
Kalman filtering gain:
Wherein, R is the covariance matrix of observation noise；
The amendment of state variable is estimated:
The error co-variance matrix of state variable amendment estimation:
Pk=(I-KkCk)Pk|k-1 (F15)
Step 4034 repeats step 4032 and step 4033, until the number of iterations has reached preset iteration ends value.
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm, Q described in step 4032k-1Value
For
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm, the value of R described in step 4033 are
0.1。
The above-mentioned lithium ion battery SOC estimation method based on second order EKF algorithm, it is preset described in step 4034 to change
It is 150 for stop value.
Compared with the prior art, the present invention has the following advantages:
1, the present invention is inaccurate for there is a problem of that SOC estimates in power battery management system, is main with lithium battery
Research object, for current single order expanded Kalman filtration algorithm (Extend Kalman Filter, EKF), there are precision not
High, stability difference disadvantage, proposes the second order EKF algorithm based on battery model on the basis of single order, realizes to battery
SOC estimation, experiment show that second order EKF algorithm when the SOC to battery estimates, has higher compared to single order EKF algorithm
Estimation precision, it is preferable to the static and dynamic performance adaptability of battery.
2, one aspect of the present invention considers the hysteresis voltage phenomenon of battery, on the other hand quasi- by the RC circuit of different orders
The rebound voltage characteristic for closing battery comprehensively considers the ease of model and to establishing band after the degree of approximation of battery behavior
There is the Order RC circuit model of hysteresis voltage characteristic, is capable of the dynamic Static performance characteristic of accurate simulated battery, convenient for obtaining
More accurate SOC estimated result.
3, since nonlinear degree is higher in actual use for power battery, and single order EKF algorithm ignores two because of it
Higher order term more than rank leads to that its nonlinear degree is weaker, estimation precision is not high, and the present invention is by the state of nonlinear discrete systems
Space equation carries out the second Taylor series at state estimation point, is able to maintain battery nonlinear degree, improves estimation precision；
With the progress of discharge process, second order with respect to single order estimation result closer to true value, can preferably track true value.
4, experiment shows in the error of entire discharge regime single order EKF algorithm within 5.5% and second order EKF algorithm
Error is no more than 3%, and being indicated above second order EKF algorithm compared to single order EKF algorithm has preferable estimation precision.
In conclusion method of the invention is novel in design rationally, it is convenient to realize, to the static and dynamic performance adaptability of battery
Preferably, estimation precision with higher, practical, application value is high.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is method flow block diagram of the invention.
Fig. 2 is the equivalent-circuit model figure for the battery that the present invention establishes.
Fig. 3 is the flow diagram that the present invention estimates the SOC of battery using second order EKF algorithm.
Specific embodiment
As shown in Figure 1, the lithium ion battery SOC estimation method of the invention based on second order EKF algorithm, including following step
It is rapid:
Step 1: battery Theoretic Analysis, detailed process are as follows: carry out interval charge-discharge test to battery, obtain characterization electricity
The charge and discharge of the rebound characteristics of the open circuit voltage curve and characterization battery of the hysteretic characteristic in pond stand voltage curve；
In the present embodiment, a kind of detailed process that interval charge-discharge test is carried out to battery of step are as follows:
Battery is vented by step 101；
Step 102 executes step when cell voltage reaches 3.65V in 20min with 1/3C discharge-rate charging 20min
Rapid 104, it is no to then follow the steps 103；
Step 103, by battery standing 30min, return step 102 later；
Battery is full of by step 104；
Step 105, the 20min that discharged with 1/3C discharge-rate are entered step if cell voltage is lower than 2.0V in 20min
107, otherwise enter step 106；
Step 106, by battery standing 30min, return to step 105 later；
Battery is vented by step 107 with 0.02C low current.
In step 103 and step 106, by setting 30min for the time of repose of battery, it can guarantee the company of experiment
Continuous property.
It to be realized using EKF algorithm and the SOC of battery is estimated, it is necessary to accurate battery model established to battery, and battery
The foundation of model is based on the Theoretic Analysis to battery, and therefore, primary work is to carry out Theoretic Analysis to battery.It is different
Battery charging and discharging equilibrium potential is different at SOC point, and this phenomenon is known as the hysteretic characteristic of battery, hysteretic characteristic there is more than in
Lithium iron phosphate dynamic battery still has in other kinds of lithium ion battery.For battery when discharging standing, voltage is gradually
Rise, and charge stand during, voltage is gradually reduced, and this phenomenon is known as the rebound characteristics of battery, this mainly by
The polarization resistance of inside battery and the influence of polarization capacity.
Step 2: establishing the equivalent-circuit model of battery, detailed process are as follows:
Step 201, the SOC computation model for establishing battery, and equivalent voltage source is established according to the open circuit voltage curve of battery
Model stands voltage curve according to the charge and discharge of battery and establishes equivalent impedance model；
Step 202 combines SOC computation model, equivalent voltage source model and equivalent impedance model three parts, establishes electricity
The equivalent-circuit model in pond；
In the present embodiment, as shown in Fig. 2, SOC computation model described in step 202 includes capacitor CNWith battery eliminator B, institute
State capacitor CNThe anode of one end and battery eliminator B connect, the capacitor CNThe other end connect with the cathode of battery eliminator B；Step
Equivalent voltage source model described in rapid 202 includes current source M, inductance Lh, voltage source U1With voltage source U2, the current source M's
Anode and inductance LhOne end connection, the cathode of the current source M and inductance LhThe other end connection, the current source M1With electricity
Stream source M2Cathode after series connection is connect with the cathode of current source M；Equivalent impedance model described in step 202 includes resistance R0, electricity
Hinder R1, resistance R2, capacitor C1With capacitor C2, the resistance R0, resistance R1With resistance R2Series connection, the capacitor C1With resistance R1And
Connection, the capacitor C2With resistance R2It is in parallel；The cathode of the battery eliminator B is connect with the cathode of voltage source U, the resistance R0, electricity
Hinder R1With resistance R2Resistance R after series connection0One end and current source M1With current source M2Anode connection after series connection.
The equivalent-circuit model for the battery that the present invention establishes can not only describe the hysteresis voltage and open-circuit voltage of battery
With the relationship of battery SOC, and can by ampere-hour integrate method directly the SOC of battery is estimated.
Step 3: carrying out parameter identification to the parameter of the equivalent-circuit model of battery；
In the present embodiment, the specific of parameter identification is carried out to the parameter of the equivalent-circuit model of battery described in step 3
Process are as follows:
The parameter identification of step 301, equivalent voltage source model: the equilibrium potential EMF of battery is expressed as
EMF=0.5 (EMFc+EMFd) (F1)
By the hysteresis voltage V of batteryhIt is expressed as
Vh=0.5 (EMFc-EMFd) (F2)
Wherein, EMFcFor the equilibrium potential that charges, EMFdFor equilibrium potential of discharging；
The parameter identification of step 302, equivalent impedance model: any time voltage U is expressed as
Wherein, OCVDThe voltage at voltage curve D moment is stood for charge and discharge, the D moment springs back rank to be gone through after battery discharge
At the time of section voltage no longer changes；I is the current value for flowing through battery, R1For resistance R1Resistance value, τ1For with resistance R1It is corresponding
Time constant andR2For resistance R2Resistance value, τ2For with resistance R2Corresponding time constant andWhen t is
Between；
Fitting function is expressed as
F (x)=A-Bexp (- ax)-Cexp (- bx) (F4)
The C-D stage for standing voltage curve to charge and discharge is fitted, and obtains parameter A, B, C, a and b in fitting function
Value；Wherein, the C-D stage that charge and discharge stand voltage curve refers to that the mutation of battery discharge transient voltage starts to battery to put
The stage no longer changed after electricity through going through rebound stage voltage；
It is equal to each other according to formula (F3) and formula (F4), obtains the parameter of equivalent impedance model are as follows:
Wherein, C1For capacitor C1Capacitance, C2For capacitor C2Capacitance.
Step 4: estimating using SOC of the second order EKF algorithm to battery, the prediction result of the SOC of battery is obtained.
In the present embodiment, as shown in figure 3, the SOC of battery is estimated using second order EKF algorithm described in step 4,
Obtain the detailed process of the prediction result of the SOC of battery are as follows:
Step 401, the state-space model for establishing battery system (nonlinear discrete systems): it is established according in step 2
Battery equivalent-circuit model, with the SOC of battery, capacitor C1The voltage V at both ends1With capacitor C2The voltage V at both ends2As being
The state variable of system, the current value I (electric discharge is negative, and charging is positive) for flowing through battery is input quantity, and end voltage V is output quantity, root
The state-space model equation of battery system is derived according to circuit equation are as follows:
Output equation are as follows:
V (t)=VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
Wherein, CnFor the rated capacity of battery, VOCVFor voltage source U1With voltage source U2Total voltage；
Step 402 carries out the Nonlinear state space model equation of battery system linearly by the second Taylor series
Change, detailed process are as follows:
The state-space model equation (F6) of battery system is carried out second order Taylor by step 4021 at state estimation point
Expansion, obtains:
Wherein, f (xk,uk) it is state transition function, g (xk,uk) it is measurement functions, xkFor the state variable at k moment, uk
The control input quantity of etching system when for k,For xkEstimated value；
Step 4022, definition Formula (F8) is substituted into the state-space model side of nonlinear discrete systems
JourneyIn, obtain the lienarized equation of battery system are as follows:
Wherein, Dk=R0；R0For
Resistance R0Resistance value, Δ t be the time variable quantity, ωkThe process noise for being zero for mean value, vkThe measurement for being zero for mean value is made an uproar
Sound, and ωkWith vkIt is irrelevant, ωk~N (0, Qk), vk~N (0, Rk)；That is ωkAnd vkObey the Gaussian Profile that mean value is 0；
Step 403 is estimated lithium ion battery SOC using second order EKF algorithm, detailed process are as follows:
Step 4031, initial phase:
Wherein, x0For the initialization value of state variable,For x0Estimated value, P0For the error of state variable predictive estimation
The initialization value of covariance matrix；
Step 4032, forecast period:
The predictive estimation of state variable:
Wherein,For xk-1Estimated value, xk-1For the state variable at k-1 moment, uk-1The control of etching system when for k-1
Input quantity；
The error co-variance matrix of state variable predictive estimation:
Wherein, Qk-1For the covariance matrix and Q of k-1 etching process noisek-1=Qk, QkFor the association of k etching process noise
Variance matrix；
In the present embodiment, Q described in step 4032k-1Value be
Step 4033, amendment stage:
Kalman filtering gain:
Wherein, R is the covariance matrix of observation noise；
The amendment of state variable is estimated:
The error co-variance matrix of state variable amendment estimation:
Pk=(I-KkCk)Pk|k-1 (F15)
In the present embodiment, the value of R described in step 4033 is 0.1.
Step 4034 repeats step 4032 and step 4033, until the number of iterations has reached preset iteration ends value.
In the present embodiment, preset iteration ends value described in step 4034 is 150.
In order to verify the technical effect that the present invention can generate, using the 18650 of the limited production of Tianjin Lishen Battery share
Ferric phosphate lithium cell is experimental subjects, and the Specifeca tion speeification of the battery is as shown in table 1.
The Specifeca tion speeification table of 1 battery of table
In order to study the external characteristics of battery, interval charge-discharge test is carried out to battery, the continuity for experiment considers,
30min is set by the time of repose of battery.Experimental procedure is as shown in table 2.
2 interval charge-discharge test step of table
It is tested to obtain the open circuit voltage curve of the hysteretic characteristic of characterization battery and returning for characterization battery by battery charging and discharging
The charge and discharge for playing characteristic stand voltage curve.The SOC computation model of battery is established, and according to the hysteretic characteristic of battery foundation etc.
Voltage source model is imitated, establishes equivalent impedance model according to the rebound characteristics of battery；Carry out the parameter identification of equivalent impedance model
When, different rank RC network fitting result contrast table is as shown in table 3.
The comparison of 3 different rank RC network fitting result of table
In conjunction with table 3 fitting result comparison it is found that second order RC network and the error of fitting of three rank RC networks are not much different,
Single order fitting result is poor compared to the fitting effect of second order and three ranks.Since second order RC network is simple compared to three rank RC networks, side
Parameter identification and the algorithm estimation of phase after an action of the bowels, compared to the external characteristics that single order RC network can preferably describe battery, therefore, this
Invention selection second order RC network.
In the present embodiment, the equivalent-circuit model figure of the battery of foundation is as shown in Figure 2.
Using second order EKF algorithm to the state variable of the SOC estimating system of battery are as follows: xk=[SOC (k), V1(k), V2
(k)]T, the input quantity of system are as follows: uk=I (k).It will be non-thread by second order Taylor's formula by the state-space model equation of system
Property equation linearized, obtain second order EKF algorithm linearisation after matrix parameter.SOC is carried out based on second order EKF algorithm
Estimation.The comparison of the SOC estimated result of single order EKF algorithm and second order EKF algorithm is as shown in table 4 under difference emulation operating condition.
The different emulation operating condition Algorithm Errors of table 4 compare
By carrying out characteristic test analysis to ferric phosphate lithium cell, the second order equivalent circuit mould for having hysteresis voltage is established
Type simultaneously carries out parameter identification；The estimation to battery SOC is realized using single order, second order EKF algorithm on the basis of equivalent model,
It is verified by estimation precision of the simulated battery difference operating condition to algorithm, finally the results showed that second order EKF algorithm exists
Single order EKF algorithm is superior to the evaluated error precision of battery SOC under difference emulation operating condition, it is good to the dynamic adaptable of battery,
Precision is higher.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer journey
Sequence product.Therefore, complete hardware embodiment, complete software embodiment or combining software and hardware aspects can be used in the application
The form of embodiment.Moreover, it wherein includes the calculating of computer usable program code that the application, which can be used in one or more,
The computer program implemented in machine usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that can be realized by computer program instructions each in flowchart and/or the block diagram
The combination of process and/or box in process and/or box and flowchart and/or the block diagram.It can provide these computers
Processor of the program instruction to general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices
To generate a machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute
For realizing the function of being specified in one or more flows of the flowchart and/or one or more blocks of the block diagram
Device.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that instruction stored in the computer readable memory generation includes
The manufacture of command device, the command device are realized in one box of one or more flows of the flowchart and/or block diagram
Or the function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that
Series of operation steps are executed on computer or other programmable devices to generate computer implemented processing, thus calculating
The instruction executed on machine or other programmable devices is provided for realizing in one or more flows of the flowchart and/or side
The step of function of being specified in block diagram one box or multiple boxes.
The aforementioned description to specific exemplary embodiment of the invention is in order to illustrate and illustration purpose.These are retouched
It states and is not wishing to limit the invention to disclosed precise forms, and it will be apparent that according to the above instruction, can carry out very much
Change and changes.The purpose of selecting and describing the exemplary embodiment is that explaining specific principle of the invention and in fact
Border application, so that those skilled in the art can be realized and utilize a variety of different exemplary embodiment party of the invention
Case and various chooses and changes.The scope of the present invention is intended to be limited by claims and its equivalents.
Claims (8)
1. a kind of lithium ion battery SOC estimation method based on second order EKF algorithm, it is characterised in that: this method includes following step
It is rapid:
Step 1: battery Theoretic Analysis, detailed process are as follows: carry out interval charge-discharge test to battery, obtain characterization battery
The charge and discharge of the rebound characteristics of the open circuit voltage curve and characterization battery of hysteretic characteristic stand voltage curve；
Step 2: establishing the equivalent-circuit model of battery, detailed process are as follows:
Step 201, the SOC computation model for establishing battery, and equivalent voltage source model is established according to the open circuit voltage curve of battery,
Voltage curve, which is stood, according to the charge and discharge of battery establishes equivalent impedance model；
Step 202, by SOC computation model, equivalent voltage source model and equivalent impedance model three parts combine, establish battery etc.
Imitate circuit model；
Step 3: carrying out parameter identification to the parameter of the equivalent-circuit model of battery；
Step 4: estimating using SOC of the second order EKF algorithm to battery, the prediction result of the SOC of battery is obtained.
2. the lithium ion battery SOC estimation method described in accordance with the claim 1 based on second order EKF algorithm, it is characterised in that: step
The detailed process of interval charge-discharge test is carried out described in rapid one to battery are as follows:
Battery is vented by step 101；
Step 102, the 20min that charged with 1/3C discharge-rate execute step 104 when cell voltage reaches 3.65V in 20min,
It is no to then follow the steps 103；
Step 103, by battery standing 30min, return step 102 later；
Battery is full of by step 104；
Step 105, the 20min that discharged with 1/3C discharge-rate enter step 107 if cell voltage is lower than 2.0V in 20min, no
Then enter step 106；
Step 106, by battery standing 30min, return to step 105 later；
Battery is vented by step 107 with 0.02C low current.
3. the lithium ion battery SOC estimation method described in accordance with the claim 1 based on second order EKF algorithm, it is characterised in that: step
SOC computation model described in rapid 202 includes capacitor CNWith battery eliminator B, the capacitor CNOne end and battery eliminator B anode
Connection, the capacitor CNThe other end connect with the cathode of battery eliminator B；Equivalent voltage source model described in step 202 includes
Current source M, inductance Lh, voltage source U1With voltage source U2, anode and the inductance L of the current source MhOne end connection, the electric current
The cathode and inductance L of source MhThe other end connection, the current source M1With current source M2Cathode after series connection and current source M's is negative
Pole connection；Equivalent impedance model described in step 202 includes resistance R0, resistance R1, resistance R2, capacitor C1With capacitor C2, the electricity
Hinder R0, resistance R1With resistance R2Series connection, the capacitor C1With resistance R1Parallel connection, the capacitor C2With resistance R2It is in parallel；It is described equivalent
The cathode of battery B is connect with the cathode of voltage source U, the resistance R0, resistance R1With resistance R2Resistance R after series connection0One end and electricity
Stream source M1With current source M2Anode connection after series connection.
4. the lithium ion battery SOC estimation method described in accordance with the claim 3 based on second order EKF algorithm, it is characterised in that: step
The detailed process of parameter identification is carried out described in rapid three to the parameter of the equivalent-circuit model of battery are as follows:
The parameter identification of step 301, equivalent voltage source model: the equilibrium potential EMF of battery is expressed as
EMF=0.5 (EMFc+EMFd) (F1)
By the hysteresis voltage V of batteryhIt is expressed as
Vh=0.5 (EMFc-EMFd) (F2)
Wherein, EMFcFor the equilibrium potential that charges, EMFdFor equilibrium potential of discharging；
The parameter identification of step 302, equivalent impedance model: any time voltage U is expressed as
Wherein, OCVDFor charge and discharge stand the voltage curve D moment voltage, the D moment be battery discharge after gone through rebound stage voltage
At the time of no longer change；I is the current value for flowing through battery, R1For resistance R1Resistance value, τ1For with resistance R1Corresponding time constant
AndR2For resistance R2Resistance value, τ2For with resistance R2Corresponding time constant andT is the time；
Fitting function is expressed as f (x)=A-Bexp (- ax)-Cexp (- bx) (F4), voltage song is stood to charge and discharge
The C-D stage of line is fitted, and obtains the value of parameter A, B, C, a and b in fitting function；Wherein, charge and discharge stand voltage
The C-D stage of curve refer to battery discharge transient voltage mutation start to battery discharge after gone through rebound stage voltage no longer change
Stage；
It is equal to each other according to formula (F3) and formula (F4), obtains the parameter of equivalent impedance model are as follows:
Wherein, C1For capacitor C1Capacitance, C2For capacitor C2Capacitance.
5. the lithium ion battery SOC estimation method described in accordance with the claim 3 based on second order EKF algorithm, it is characterised in that: step
The SOC of battery is estimated using second order EKF algorithm described in rapid four, obtains the specific mistake of the prediction result of the SOC of battery
Journey are as follows:
Step 401, the state-space model for establishing battery system: according to the equivalent-circuit model for the battery established in step 2,
With the SOC of battery, capacitor C1The voltage V at both ends1With capacitor C2The voltage V at both ends2As the state variable of system, battery is flowed through
Current value I be input quantity, end voltage V be output quantity, the state-space model side of battery system is derived according to circuit equation
Journey are as follows:
Output equation are as follows:
V (t)=VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
Wherein, CnFor the rated capacity of battery, VOCVFor voltage source U1With voltage source U2Total voltage；
Step 402 linearizes the Nonlinear state space model equation of battery system by the second Taylor series, specifically
Process are as follows:
The state-space model equation (F6) of battery system is carried out the second Taylor series by step 4021 at state estimation point,
It obtains:
Wherein, f (xk,uk) it is state transition function, g (xk,uk) it is measurement functions, xkFor the state variable at k moment, ukWhen for k
The control input quantity of etching system,For xkEstimated value；
Step 4022, definition Formula (F8) is substituted into the state-space model side of nonlinear discrete systems
JourneyIn, obtain the lienarized equation of battery system are as follows:
Wherein,Dk
=R0；R0For resistance R0Resistance value, Δ t be the time variable quantity, ωkThe process noise for being zero for mean value, vkIt is zero for mean value
Measure noise, and ωkWith vkIt is irrelevant, ωk~N (0, Qk), vk~N (0, Rk)；That is ωkAnd vkObey the Gauss that mean value is 0
Distribution；
Step 403 is estimated lithium ion battery SOC using second order EKF algorithm, detailed process are as follows:
Step 4031, initial phase:
Wherein, x0For the initialization value of state variable,For x0Estimated value, P0For the error association side of state variable predictive estimation
The initialization value of poor matrix；
Step 4032, forecast period:
The predictive estimation of state variable:
Wherein,For xk-1Estimated value, xk-1For the state variable at k-1 moment, uk-1The control input of etching system when for k-1
Amount；
The error co-variance matrix of state variable predictive estimation:
Wherein, Qk-1For the covariance matrix and Q of k-1 etching process noisek-1=Qk, QkFor the covariance square of k etching process noise
Battle array；
Step 4033, amendment stage:
Kalman filtering gain:
Wherein, R is the covariance matrix of observation noise；
The amendment of state variable is estimated:
The error co-variance matrix of state variable amendment estimation:
Pk=(I-KkCk)Pk|k-1 (F15)
Step 4034 repeats step 4032 and step 4033, until the number of iterations has reached preset iteration ends value.
6. according to claim 5 based on the lithium ion battery SOC estimation method of second order EKF algorithm, it is characterised in that: step
Q described in rapid 4032k-1Value be
7. according to claim 5 based on the lithium ion battery SOC estimation method of second order EKF algorithm, it is characterised in that: step
The value of R described in rapid 4033 is 0.1.
8. according to claim 5 based on the lithium ion battery SOC estimation method of second order EKF algorithm, it is characterised in that: step
Preset iteration ends value described in rapid 4034 is 150.
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