CN104392080B - A kind of lithium battery fractional order becomes rank equivalent-circuit model and its discrimination method - Google Patents

A kind of lithium battery fractional order becomes rank equivalent-circuit model and its discrimination method Download PDF

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CN104392080B
CN104392080B CN201410797302.6A CN201410797302A CN104392080B CN 104392080 B CN104392080 B CN 104392080B CN 201410797302 A CN201410797302 A CN 201410797302A CN 104392080 B CN104392080 B CN 104392080B
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fractional order
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electric capacity
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张承慧
商云龙
张奇
崔纳新
李泽元
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Shandong University
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Abstract

The electric capacity become the invention discloses a kind of lithium battery fractional order in rank equivalent-circuit model and its discrimination method, including run time circuit and battery I V characteristic circuits, battery I V characteristic circuits uses the fractional order electric capacity for becoming rank.Order RC circuit model is generalized to non-integral order by the present invention, and based on the model parameter and fractional order exponent number at least squares identification difference SOC, so as to obtain a fractional order equivalent-circuit model for becoming rank according to SOC.The introducing of fractional order realizes the consecutive variations of model order so that model is more stablized, dynamic property is more excellent, precision is higher;The change rank of fractional order realizes the more frees degree of model, bigger flexibility and new meaning.Due to not increasing the number of RC network, the fractional model of the present invention efficiently solves the contradiction between model accuracy and practicality, suitable for the various operating modes of battery, with higher practical value, a battery model that is accurate and easily realizing is provided for SOC accurate estimation.

Description

A kind of lithium battery fractional order becomes rank equivalent-circuit model and its discrimination method
Technical field
Become rank equivalent-circuit model and its discrimination method the present invention relates to a kind of lithium battery fractional order.
Background technology
In order to tackle energy crisis and environmental pollution, electric automobile arises at the historic moment and as whole world focus of attention. Vehicle mounted dynamic battery is as the critical component of electric automobile, and its performance is to the dynamic property, economy and security of vehicle to closing weight Will, it is the key factor for restricting electric automobile scale development.Lithium battery tool energy density height, long service life, cost performance it is good and The advantages of monomer voltage is high, the progressively dynamic origin as hybrid vehicle or pure electric automobile.Accurate battery model Reasonable design and safe operation to onboard power lithium battery is significant, is battery SOC (state-of-charge), SOH (health State) evaluation method basis.
However, it is by no means easy to set up an accurate and simple in construction battery model, because the change of lithium battery interior Learn the complicated conversion that reaction is related to electric energy, chemical energy, heat energy, the non-linear and uncertainty with height.At present, conventional electricity Pool model can be following five class by the difference of modeling mechanism:1. electrochemical model, 2. analysis model, 3. stochastic model, 4. neural Network model and 5. equivalent-circuit model.Wherein, equivalent-circuit model because its simple, intuitive form and be suitable for electrically setting The advantages of meter is with emulation turns into a kind of new model being widely used.In equivalent-circuit model, Order RC model compares it His equivalent-circuit model physical significance is clear, identification of Model Parameters experiment is easily performed, parameter identification method system, model accuracy It is higher, can more accurate, intuitively simulated battery dynamic characteristic.But, Order RC model at battery charging and discharging initial stage and In latter stage, because model order is relatively low, there is larger error of fitting, it is impossible to the accurately static and dynamic performance of simulated battery.Increase Although RC series connection exponent number can improve the accuracy of battery model, the charge-discharge characteristic of electrokinetic cell can be preferably simulated, It is that, if the exponent number of electrokinetic cell model is too high, will be unfavorable for obtaining the parameter in model, and can also greatly increase model Amount of calculation, results even in system concussion, so on the other hand should also limit RC exponent number.Therefore, fixed structure equivalent circuit Model be difficult to describe lithium battery two ends it is steep in the middle of flat non-linear voltage characteristic, it is impossible to solve model accuracy and practicality it Between contradiction.
Therefore, Chinese invention patent application (application number 201410185885.7) and the utility model (patent No. ZL201420226360.9 a kind of change rank RC equivalent-circuit models based on AIC criterion) are proposed, by being slightly increased model Complexity, can more accurately describe the steep middle flat non-linear voltage characteristic in lithium battery two ends, and error has within 0.04V Effect solves the contradiction between model complexity and practicality, with higher practical value.But, the model is integer rank Battery model, the switching of model can only be the change of integer rank, therefore model order fluctuation is big, does not meet gradual change in nature The rule of development, therefore model accuracy is very restricted.In fact, inside battery electrochemical reaction process is extremely complex, bag Conductive ion transfer, internal electrochemical reaction, discharge and recharge hesitation and concentration difference diffusion effect etc. are included, is shown stronger non- Linear characteristic, is more suitable for being simulated with fractional model.Integer model is contrasted, fractional order battery model has more in design The many free degree, bigger flexibility and new meaning.Meanwhile, their introducing also increases many new phenomenons and rule, with normal It is superior that regular several rank battery models can not be realized.
The content of the invention
To solve the deficiency that prior art is present, rank equivalent-circuit model is become the invention discloses a kind of lithium battery fractional order And its discrimination method, according to the principle of electrochemical reaction of lithium ion battery, traditional Order RC equivalent-circuit model is whole using two The RC network of number rank describes the polarity effect and concentration difference effect of battery, and two integer rank RC networks of model are generalized to by the present invention Non-integral order (fractional order), and based on the model parameter and order at least squares identification difference SOC, so as to obtain one Become the fractional order equivalent-circuit model of rank according to SOC.The introducing of fractional order realizes the consecutive variations of model order so that model More stablize, dynamic property is more excellent, precision is higher.Become rank parameter due to adding fractional order, model obtains more freedom Degree, bigger flexibility and new meaning.The model is realized on the basis of traditional Order RC model, does not increase model RC network Number, the contradiction between model accuracy and simplicity is efficiently solved, with higher practical value.
To achieve the above object, concrete scheme of the invention is as follows:
A kind of lithium battery fractional order becomes rank equivalent-circuit model, including run time circuit and cell I-V characteristic circuit, institute State run time circuit and cell I-V characteristic circuit and signal biography is carried out by CCCS and VCVS It is defeated;The run time circuit includes the self discharge resistance R of batterydAnd electric capacity CQ, resistance RdWith electric capacity CQIt is connected in parallel on current control The two ends of current source, one end ground connection of CCCS;The VCVS of the cell I-V characteristic circuit is just One end extremely with two branch roads being in parallel is connected, and negative pole end is connected with the negative pole end of battery model, described two to be in parallel Each branch road of RC network branch road include two the fractional order RC loops and an internal resistance R that are in serieso, described two phases The other end of branch road in parallel is connected with the positive terminal of battery model.
In the RC network branch road that two are in parallel in the cell I-V characteristic circuit, discharge paths include what is be sequentially connected in series Diode Dd, fractional order electric capacity FOE1dWith resistance R1dThe fractional order RC loops of composition, fractional order electric capacity FOE2dWith resistance R2dComposition Fractional order RC loops and resistance Rod
Charging paths include the reversal connection diode D being sequentially connected in seriesd, fractional order electric capacity FOE1cWith resistance R1cThe fractional order of composition RC loops, fractional order electric capacity FOE2cWith resistance R2cThe fractional order RC loops of composition and resistance Roc
The run time circuit and I-V characteristic circuit are built by a CCCS and VCVS Vertical contact, when carrying out discharge and recharge to battery, load current ibatBy CCCS to electric capacity CQCarry out discharge and recharge, Change CQThe electricity of storage, characterizes the change of battery SOC, CQBoth end voltage OCV also changes therewith, the controlled electricity of I-V characteristic circuit Potential source OCV changes with SOC change.
The electric capacity CQRepresent the active volume of battery, CQ=3600CAh·f1·f2, wherein, CAhTo be single with ampere-hour The battery capacity of position, f1And f2It is the modifying factor of battery cycle life and temperature respectively.
The electric current of the CCCS is the end electric current i of batterybat, the load current when battery carries out discharge and recharge ibatBy CCCS to electric capacity CQDischarge and recharge is carried out, changes electric capacity CQThe electricity of middle storage, so as to characterize battery SOC Change.
The voltage at the two ends of the CCCS is battery open circuit voltage OCV.
Two RC network branch roads being in parallel are RC network discharge paths and RC network charging paths, two RC networks respectively Electric capacity in branch road is fractional order electric capacity.
The RC network discharge paths fractional order element FOE1dAnd FOE2dExponent number α, β it is different and become with battery SOC state Change, and meet 0≤αd, βd≤1.Work as αd, βdWhen=0, fractional order element FOE is equivalent to a resistance, works as αd, βdWhen=1, fractional order Element FOE is equivalent to an integer rank electric capacity;When 0<αd, βd<When 1, fractional order element FOE is a fractional order electric capacity;
The RC network charging paths fractional order element FOE1cAnd FOE2cExponent number α, β it is different and become with battery SOC state Change, and meet 0≤αc, βc≤1.Work as αc, βcWhen=0, fractional order element FOE is equivalent to a resistance, works as αc, βcWhen=1, fractional order Element FOE is equivalent to an integer rank electric capacity;When 0<αc, βc<When 1, fractional order element FOE is a fractional order electric capacity.
A kind of lithium battery fractional order becomes the discrimination method of rank equivalent-circuit model, comprises the following steps:
Step one:Write out the discharge process of lithium battery and the fractional order mathematics model expression of static condition;
Step 2:Constant current charge-discharge is carried out to lithium battery, the active volume C of battery model is obtainedQWith self discharge resistance Rd
Step 3:Pulsed discharge test is carried out to lithium battery, battery-end electricity when battery at different SOC starts electric discharge is obtained The moment that the moment drop-out value of pressure, electric discharge terminate rear battery terminal voltage rises to the zero defeated of value, discharge current and battery terminal voltage Enter the data such as response;
Step 4:The data obtained according to step 3, parameter and exponent number based on least squares identification model;
Step 5:Obtained battery model parameter is calculated according to step 4 and calculates open-circuit voltage OCV at different SOC, Europe Nurse internal resistance R0d, activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dAnd concentration polarization Fractional order electric capacity FOE2d
Step 6:The model parameter obtained according to step 5, based in least squares identification open-circuit voltage OCV, ohm Hinder R0d, activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dWith concentration polarization fraction Rank electric capacity FOE2dRelation between SOC;
Step 7:The parameter obtained according to step 2 to six, lithium battery fractional order is built in Matlab and becomes rank equivalent electric Road model.
The terminal voltage of lithium battery is represented by discharge process:
In formula, UbatFor battery terminal voltage;R0dFor ohmic internal resistance;OCVdFor electric discharge open-circuit voltage;α, β are fractional order element FOE1dAnd FOE2dExponent number, meet 0<α, β≤1;idisFor discharge current;τ1d2dThe time constant of respectively two RC networks.
Work as α, during β=0, fractional order element FOE is equivalent to a resistance, work as α, during β=1, fractional order element FOE is equivalent to one Electric capacity;
U1d(0+) and U2d(0+) terminates the terminal voltage initial value of two fractional order RC branch roads of moment for battery discharge, and its value can It is expressed as:
U1d(0+)=idis·R1d (2)
U2d(0+)=idis·R2d (3)
After battery discharge terminates, the terminal voltage of battery is represented by:
In formula, the polarizing voltage of batteryWithGrowth over time and gradually subtract It is small, as t → ∞,WithTend to 0, now battery terminal voltage UbatEqual to the open circuit of battery Voltage OCV.
The detailed process of the step 5 is:Due to the presence of battery ohmic internal resistance, when the cell is discharged, battery terminal voltage It can fall moment, its value is designated as Δ U1;When battery stops discharging, battery terminal voltage can rise to moment, and its value is designated as Δ U2, because This, the ohmic internal resistance R of battery0It can be obtained by following formula:
Activation polarization internal resistance R1dIt can be obtained by following formula:
Concentration polarization internal resistance R2dIt can be obtained by following formula:
Activation polarization fractional order electric capacity FOE1dIt can be obtained by following formula:
Concentration polarization fractional order electric capacity FOE2dIt can be obtained by following formula:
In the step 6:There is non-linear relation in open-circuit voltage OCV and SOC, physical relationship formula is:
In formula, a0-a4For constant, obtained by experimental data based on least squares identification.
Battery ohmic internal resistance RodRelational expression with SOC is:
Ro(SOC)=b0·e-SOC+b1+b2·SOC-b3·SOC2+b4·SOC3 (11)
In formula, b0-b4For constant, obtained by experimental data based on least squares identification.
Activation polarization internal resistance R1dRelational expression with SOC is:
R1d(SOC)=c0·e-SOC+c1+c2·SOC-c3·SOC2+c4·SOC3 (12)
In formula, c0-c4For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order electric capacity FOE1dRelational expression with SOC is:
FOE1d(SOC)=d0·SOC5+d1·SOC4+d2·SOC3+d3·SOC2+d4·SOC+d5 (13)
In formula, d0-d5For constant, obtained by experimental data based on least squares identification.
Concentration polarization internal resistance R2dRelational expression with SOC is:
R2d(SOC)=e0·e-SOC+e1+e2·SOC-e3·SOC2+e4·SOC3 (14)
In formula, e0-e4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order electric capacity FOE2dRelational expression with SOC is:
FOE2d(SOC)=f0·SOC5+f1·SOC4+f2·SOC3+f3·SOC2+f4·SOC+f5 (15)
In formula, f0-f5For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order electric capacity FOE1dExponent number and SOC relational expression is:
α (SOC)=g0·SOC4+g1·SOC3+g2·SOC2+g3·SOC+g4 (16)
In formula, g0-g4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order electric capacity FOE2dExponent number and SOC relational expression is:
β (SOC)=h0·SOC4+h1·SOC3+h2·SOC2+h3·SOC+h4 (17)
In formula, h0-h4For constant, obtained by experimental data based on least squares identification.
Beneficial effects of the present invention:
1. traditional Order RC equivalent-circuit model is generalized to fractional order, and based on least squares identification difference SOC The model parameter and order at place, obtain a fractional order equivalent-circuit model for becoming rank according to SOC;
2. lithium battery has shown fractional order dynamic behavior because of its special material and chemical characteristic, retouched with integer rank Battery behavior its precision is stated to be very restricted, and Bian describes those with fractional calculus per se with fractional order characteristic , can the preferably intrinsic propesties of description object and its behavior during object;
3. due to adding fractional order exponent number this unknown parameter, model obtains more frees degree, bigger flexibility And new meaning;
4. because fractional calculus has certain memory function, and more meet the universal continuous simple philosophy of nature Viewpoint, fractional order becomes rank equivalent-circuit model to obtain higher precision, more preferable dynamic property and stability;
5. contrast and traditional Order RC model, due to not increasing the number of RC network, it is accurate that the present invention efficiently solves model Really the contradiction between property and practicality, with higher practical value, and is applied to the constant current charge-discharge of battery, pulse discharge and recharge With UDDS state of cyclic operations, a battery model that is accurate and easily realizing is provided for SOC accurate estimation.
Brief description of the drawings
Fig. 1 is that lithium battery fractional order of the present invention becomes rank equivalent-circuit model structural representation, and wherein c marks represent charging, d Mark represents electric discharge;
Fig. 2 is the response process figure of battery cell voltage under pulse charge of the invention;
Fig. 3 is the response process figure of battery cell voltage under pulsed discharge of the invention;
Fig. 4 is battery-end electricity after the change rank fractional order of the present invention, integer rank and fixed fraction rank modeling pulsed discharge The recovery response comparison diagram of pressure, wherein (a) is overall diagram, (b) is partial enlarged drawing;
Fig. 5 is the graph of a relation of open-circuit voltage OCV and SOC under pulse charge of the invention;
Fig. 6 is ohmic internal resistance R under the pulse charge of the present invention0With SOC graph of a relation;
Fig. 7 is activation polarization internal resistance R under the pulse charge of the present invention1cWith SOC graph of a relation;
Fig. 8 is activation polarization fractional order electric capacity FOE under the pulse charge of the present invention1cWith SOC graph of a relation;
Fig. 9 is concentration polarization internal resistance R under the pulse charge of the present invention2dWith SOC graph of a relation;
Figure 10 is concentration polarization fractional order electric capacity FOE under the pulse charge of the present invention2cWith SOC graph of a relation;
Figure 11 is activation polarization fractional order electric capacity FOE under the pulse charge of the present invention1cThe graph of a relation of exponent number and SOC;
Figure 12 is concentration polarization fractional order electric capacity FOE under the pulse charge of the present invention2cThe graph of a relation of exponent number and SOC;
Figure 13 is the graph of a relation of open-circuit voltage OCV and SOC under pulsed discharge of the invention;
Figure 14 is ohmic internal resistance R under the pulsed discharge of the present invention0With SOC graph of a relation;
Figure 15 is activation polarization internal resistance R under the pulsed discharge of the present invention1dWith SOC graph of a relation;
Figure 16 is activation polarization fractional order electric capacity FOE under the pulsed discharge of the present invention1dWith SOC graph of a relation;
Figure 17 is concentration polarization internal resistance R under the pulsed discharge of the present invention2dWith SOC graph of a relation;
Figure 18 is concentration polarization fractional order electric capacity FOE under the pulsed discharge of the present invention2dWith SOC graph of a relation;
Figure 19 is activation polarization fractional order electric capacity FOE under the pulsed discharge of the present invention1dThe graph of a relation of exponent number and SOC;
Figure 20 is concentration polarization fractional order electric capacity FOE under the pulsed discharge of the present invention2dThe graph of a relation of exponent number and SOC;
Figure 21 is change rank fractional order cell equivalent-circuit model voltage output figure under the pulsed discharge of the present invention;
Figure 22 is change rank fractional order cell equivalent-circuit model voltage output figure under the pulse charge of the present invention;
Figure 23 is change rank fractional order cell equivalent-circuit model voltage output figure under the constant-current discharge of the present invention;
Figure 24 is change rank fractional order cell equivalent-circuit model voltage output figure under the constant-current charge of the present invention.
Embodiment:
The present invention is described in detail below in conjunction with the accompanying drawings:
Build battery model and refer to theoretical response characteristic and the inside for comprehensively going to describe actual battery as far as possible of applied mathematics Characteristic.So-called response characteristic refers to the terminal voltage of battery and the corresponding relation of load current;Bulk properties refer to the inside of battery Relation between variable ohmic internal resistance, polarization resistance and polarizing voltage and SOC, temperature.
Become rank equivalent-circuit model, including run time circuit as shown in Figure 1 for lithium battery fractional order disclosed by the invention With I-V characteristic circuit, wherein, I-V characteristic circuit includes two-way branch road, and each branch road includes two groups of fractional order electric capacity FOE With the fractional order RC loops of a resistor coupled in parallel composition.The run time circuit includes the self discharge resistance R of batteryd, electric capacity CQ With CCCS circuit, resistance RdWith electric capacity CQThe controlled source two ends of CCCS are connected in parallel on, independent current source One end is grounded.
I-V characteristic circuit includes ohmic internal resistance R0, activation polarization internal resistance R1, activation polarization fractional order electric capacity FOE1, it is dense Poor polarization resistance R2, concentration polarization fractional order electric capacity FOE2With CCCS, VCVS circuit, wherein:
The positive pole connection two-way of the controlled source of VCVS circuit, connects diode D all the waydAfter connect resistance R1d, resistance R2d, resistance RodThe positive pole of battery model is connected afterwards, all the way reversal connection diode DcResistance R is connected afterwards1c, resistance R2c, electricity Hinder RocThe positive pole of battery model is connected afterwards.Fractional order electric capacity FOE1dIt is connected in parallel on resistance R1dTwo ends;Fractional order electric capacity FOE1cIt is in parallel In resistance R1cTwo ends;Fractional order electric capacity FOE2dIt is connected in parallel on resistance R2dTwo ends;Fractional order electric capacity FOE2cIt is connected in parallel on resistance R2c Two ends;Voltage between the controlled source positive and negative electrode of VCVS circuit is battery open circuit voltage OCV.
Run time circuit and I-V characteristic circuit control current source and a voltage controlled voltage source foundation contact by a stream, When carrying out discharge and recharge to battery, load current ibatBy flowing control current source to electric capacity CQDischarge and recharge is carried out, changes CQStorage Electricity, characterizes the change of battery SOC, CQBoth end voltage OCV also changes therewith, the controlled voltage source OCV of I-V characteristic circuit with SOC change and change.
Electric capacity CQRepresent the active volume of battery, CQ=3600CAh·f1·f2, wherein, CAhFor with units of ampere-hour Battery capacity, f1And f2It is the modifying factor of battery cycle life and temperature respectively.
The electric current of the controlled source of CCCS is the end electric current i of batterybat, the load when battery carries out discharge and recharge Electric current ibatBy CCCS to electric capacity CQDischarge and recharge is carried out, changes electric capacity CQThe electricity of middle storage, so as to characterize electricity Pond SOC change.
The voltage at the controlled source two ends of the CCCS is battery open circuit voltage OCV.
A kind of discrimination method for applying above-mentioned lithium battery fractional order to become rank equivalent-circuit model, by taking battery discharge as an example, fills Electric discrimination method is identical with electric discharge, will not be repeated here.Comprise the following steps:
Step one:Write out the discharge process of lithium battery and the fractional order mathematics model expression of static condition;
Step 2:Constant current charge-discharge is carried out to lithium battery, the active volume C of battery model is obtainedQWith self discharge resistance Rd
Step 3:Pulsed discharge test is carried out to lithium battery, battery-end electricity when battery at different SOC starts electric discharge is obtained The moment that the moment drop-out value of pressure, electric discharge terminate rear battery terminal voltage rises to the zero defeated of value, discharge current and battery terminal voltage Enter the data such as response;
Step 4:The data obtained according to step 3, parameter and exponent number based on least squares identification model;
Step 5:Obtained battery model parameter is calculated according to step 4 and calculates open-circuit voltage OCV at different SOC, Europe Nurse internal resistance R0d, activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dAnd concentration polarization Fractional order electric capacity FOE2d
Step 6:The model parameter obtained according to step 5, based in least squares identification open-circuit voltage OCV, ohm Hinder R0d, activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dWith concentration polarization fraction Rank electric capacity FOE2dRelation between SOC;
Step 7:The parameter obtained according to step 2 to six, lithium battery fractional order is built in Matlab and becomes rank equivalent electric Road model.
It is illustrated in figure 2 the response process figure of battery cell voltage under the pulse charge of the present invention;It is illustrated in figure 3 this hair The response process figure of battery cell voltage under bright pulsed discharge;The terminal voltage of battery is represented by process of pulse discharge:
In formula, UbatFor battery terminal voltage;R0dFor ohmic internal resistance;OCVdFor electric discharge open-circuit voltage;α, β are fractional order element FOE1dAnd FOE2dExponent number, meet 0<α, β≤1.Work as α, during β=0, fractional order element FOE is equivalent to a resistance, works as α, β=1 When, fractional order element FOE is equivalent to an electric capacity.U1d(0+) and U2d(0+) terminates two fractional order RC branch of moment for battery discharge The terminal voltage initial value on road, its value can be expressed as:
U1d(0+)=idis·R1d (2)
U2d(0+)=idis·R2d (3)
After battery discharge terminates, the terminal voltage of battery is represented by:
In formula, the polarizing voltage of batteryWithGrowth over time and gradually subtract It is small, as t → ∞,WithTend to 0, now battery terminal voltage UbatEqual to opening for battery Road voltage OCV.
The specific method of the step 5 is:Due to the presence of battery ohmic internal resistance, when the cell is discharged, battery terminal voltage It can fall moment, its value is designated as Δ U1;When battery stops discharging, battery terminal voltage can rise to moment, and its value is designated as Δ U2.Cause This, the ohmic internal resistance R of battery0It can be obtained by following formula:
Activation polarization internal resistance R1dIt can be obtained by following formula:
Concentration polarization internal resistance R2dIt can be obtained by following formula:
Activation polarization fractional order electric capacity FOE1dIt can be obtained by following formula:
Concentration polarization fractional order electric capacity FOE2dIt can be obtained by following formula:
The specific method of the step 6 is:There is non-linear relation in open-circuit voltage OCV and SOC, physical relationship formula is:
In formula, a0-a4For constant, obtained by experimental data based on least squares identification.
Battery ohmic internal resistance RodRelational expression with SOC is:
Ro(SOC)=b0·e-SOC+b1+b2·SOC-b3·SOC2+b4·SOC3 (11)
In formula, b0-b4For constant, obtained by experimental data based on least squares identification.
Activation polarization internal resistance R1dRelational expression with SOC is:
R1d(SOC)=c0·e-SOC+c1+c2·SOC-c3·SOC2+c4·SOC3 (12)
In formula, c0-c4For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order electric capacity FOE1dRelational expression with SOC is:
FOE1d(SOC)=d0·SOC5+d1·SOC4+d2·SOC3+d3·SOC2+d4·SOC+d5 (13)
In formula, d0-d5For constant, obtained by experimental data based on least squares identification.
Concentration polarization internal resistance R2dRelational expression with SOC is:
R2d(SOC)=e0·e-SOC+e1+e2·SOC-e3·SOC2+e4·SOC3 (14)
In formula, e0-e4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order electric capacity FOE2dRelational expression with SOC is:
FOE2d(SOC)=f0·SOC5+f1·SOC4+f2·SOC3+f3·SOC2+f4·SOC+f5 (15)
In formula, f0-f5For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order electric capacity FOE1dExponent number and SOC relational expression is:
α (SOC)=g0·SOC4+g1·SOC3+g2·SOC2+g3·SOC+g4 (16)
In formula, g0-g4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order electric capacity FOE2dExponent number and SOC relational expression is:
β (SOC)=h0·SOC4+h1·SOC3+h2·SOC2+h3·SOC+h4 (17)
In formula, h0-h4For constant, obtained by experimental data based on least squares identification.
1. experiment is set up
Tested and emulated for the extra large string of spy 10 and 16 lithium iron phosphate dynamic battery of cylindrical type 26650, nominal capacity is 23Ah, nominal voltage is 51.2V.Battery testing platform is by advanced AVL batteries simulation/test cabinet, AVL InMotion hardware In ring test platform, AVL switch boards, temperature control box and and AVL Lynx control softwares composition.The voltage of experimental record battery, electricity The operating mode value such as stream and SOC, sample frequency is set to 1Hz.
In view of the difference of charge-discharge parameter, HPPC mixed pulses are tested into (Hybrid Pulse Power Characterization Test, HPPC) in mixed pulses experiment make unidirectional pulse experiment into, i.e. electrokinetic cell pulse fills Electric test and pulsed discharge experiment.So-called pulsed discharge, i.e., under 25 degree of room temperature, the battery that will be filled with electricity is put with 0.2C electric current Electricity is 95% to SOC, stops electric discharge and stands 45min, then using same current discharge to SOC as 90%, by that analogy, until SOC terminates when being 0%.Pulse charge process is similar with process of pulse discharge, will not be repeated here.
2. model order and parameter identification
As shown in figure 4, being electricity after change rank fractional order, integer rank and the fixed fraction rank modeling pulsed discharge of the present invention The recovery response comparison diagram of pond terminal voltage.It can be seen that fractional order becomes rank equivalent-circuit model simulation precision highest.
(1) open-circuit voltage OCV models
The battery open circuit voltage measured according to different SOC (3.45%, 5%, 10% ... 90%, 95%, 98.89%) place, The charging open-circuit voltage for obtaining battery and electric discharge open-circuit voltage OCV can be fitted respectively, as shown in Fig. 5 and Figure 13.And according to formula (10) parameter a can, be picked out using Matlab cftool tool boxes0-a4, as shown in table 1.
The open-circuit voltage OCV parameters that table 1 is obtained using Matlab cftool Fitting Toolboxes
Parameter a0 a1 a2 a3 a4
Charge identifier -1.015 1.915 -0.02047 -0.006009 0.03582
Discharge identifier 2.588 -1.499 -0.007343 -0.01424 0.04207
(2) ohmic internal resistance R0Model
The battery ohmic internal resistance measured according to different SOC (3.45%, 5%, 10% ... 90%, 95%, 98.89%) place, The charging ohmic internal resistance for obtaining battery and electric discharge ohmic internal resistance R can be fitted respectively0, as shown in Fig. 6 and Figure 14.And according to formula (11) parameter b can, be picked out using Matlab cftool tool boxes0-b4, as shown in table 2.
The ohmic internal resistance R that table 2 is obtained using Matlab cftool Fitting Toolboxes0Parameter
Parameter b0 b1 b2 b3 b4
Charge identifier 0.5612 -0.5588 0.5546 -0.2568 0.05642
Discharge identifier -0.638 0.6397 -0.634 0.2967 -0.0663
(3) activation polarization internal resistance R1Model
The battery electrochemical polarization resistance measured according to different SOC (3.45%, 5%, 10%, 15% ..., 95%) place, can The rechargeable electrochemical polarization resistance and electrochemical polarization resistance R of the battery obtained with being fitted respectively1, such as Fig. 7 and Figure 15 institutes Show.And according to formula (12), parameter c can be picked out using Matlab cftool tool boxes0-c4, as shown in table 3.
The activation polarization internal resistance R that table 3 is obtained using Matlab cftool Fitting Toolboxes1Parameter
Parameter c0 c1 c2 c3 c4
Charge identifier 3.891 -3.887 3.87 -1.835 0.4279
Discharge identifier 10.26 -10.24 10.1 -4.607 0.9788
(4) activation polarization fractional order electric capacity FOE1Model
The activation polarization fraction measured according to different SOC (3.45%, 5%, 10% ... 90%, 95%, 98.89%) place Rank electric capacity, the rechargeable electrochemical polarization fractional order electric capacity for obtaining battery and electrochemical polarization fractional order electricity can be fitted respectively Hold FOE1, as shown in Fig. 8 and Figure 16.And according to formula (13), parameter d can be picked out using Matlab cftool tool boxes0-d5, As shown in table 4.
The activation polarization fractional order electric capacity FOE that table 4 is obtained using Matlab cftool Fitting Toolboxes1Parameter
Parameter d0 d1 d2 d3 d4 d5
Charge identifier -3.775e6 8.913e6 -7.623e6 2.976e6 -5.542e5 9.351e4
Discharge identifier 1.387e8 -5.26e8 7.008e8 -4.023e8 9.138e7 -3.683e6
(5) concentration polarization internal resistance R2Model
The battery concentration polarization internal resistance measured according to different SOC (3.45%, 5%, 10%, 15% ..., 95%) place, can be with Charging concentration polarization internal resistance and the electric discharge concentration polarization internal resistance R of obtained battery are fitted respectively2, as shown in Fig. 9 and Figure 17.And root According to formula (14), parameter e can be picked out using Matlab cftool tool boxes0-e4, as shown in table 5.
The concentration polarization internal resistance R that table 5 is obtained using Matlab cftool Fitting Toolboxes2Parameter
Parameter e0 e1 e2 e3 e4
Charge identifier 3.267 -3.265 3.271 -1.594 0.3971
Discharge identifier -4.582 4.584 -4.535 2.102 -0.4632
(6) concentration polarization fractional order electric capacity FOE2Model
The battery concentration polarization fractional order electricity measured according to different SOC (3.45%, 5%, 10%, 15% ..., 95%) place Hold, the charging concentration polarization fractional order electric capacity and electric discharge concentration polarization fractional order electric capacity of obtained battery can be fitted respectively FOE2, as shown in Figure 10 and Figure 18.And according to formula (12), parameter f can be picked out using Matlab cftool tool boxes0-f5, such as Shown in table 6.
The concentration polarization fractional order electric capacity FOE that table 6 is obtained using Matlab cftool Fitting Toolboxes2Parameter
Parameter f0 f1 f2 f3 f4 f5
Charge identifier -1.842e5 4.507e5 -4.116e5 1.704e5 -2.857e4 4.572e4
Discharge identifier -4.529e5 1.188e6 -1.153e6 5.072e5 -9.649e4 8.68e4
(7) activation polarization fractional order electric capacity FOE1Exponent number model
The battery electrochemical polarization fractional order measured according to different SOC (3.45%, 5%, 10%, 15% ..., 95%) place Electric capacity exponent number, the rechargeable electrochemical polarization fractional order electric capacity FOE of obtained battery can be fitted respectively1Exponent number and electrochemical Polarize fractional order electric capacity FOE1Exponent number, as shown in Figure 11 and Figure 19.And according to formula (16), using Matlab cftool tool boxes Parameter g can be picked out0-g4, as shown in table 7.
The activation polarization fractional order electric capacity FOE that table 7 is obtained using Matlabcftool Fitting Toolboxes1Order parameter
Parameter g0 g1 g2 g3 g4
Charge identifier 21.24 -46.26 33.74 -8.854 0.9861
Discharge identifier -15.45 27.57 -14.44 1.862 0.6595
(8) concentration polarization fractional order electric capacity FOE2Exponent number model
For the battery concentration polarization fractional order electricity measured according to different SOC (3.45%, 5%, 10%, 15% ..., 95%) place Hold exponent number, the charging concentration polarization fractional order electric capacity FOE of obtained battery can be fitted respectively2Exponent number and electric discharge concentration polarization point Number rank electric capacity FOE2Exponent number, as shown in Figure 12 and Figure 20.And according to formula (17), can be picked out using Matlabcftool tool boxes Parameter h0-h4, as shown in table 8.
The concentration polarization fractional order electric capacity FOE that table 8 is obtained using Matlab cftool Fitting Toolboxes2Order parameter
Parameter h0 h1 h2 h3 h4
Charge identifier 2.752 -6.434 5.085 -1.319 0.4986
Discharge identifier 4.813 -10.91 8.4 -2.468 0.6779
3. emulation and experimental verification
In order to verify the accuracy of battery model, constant current charge-discharge and pulse charge-discharge test are carried out to battery.Such as Figure 21- It is the contrast of the battery terminal voltage experimental result and model emulation result obtained under pulse charge and discharge shown in 22.Can from figure To find out, fractional order proposed by the present invention become rank equivalent-circuit model can preferably reaction cell pulse charge and discharge process, say The bright model is accurate.Wherein, it is bigger than the error produced in the constant current charge-discharge stage by one in the error of quiescent phase generation A bit.
As shown in figs. 23-24, it is the battery terminal voltage experimental result that is obtained under constant current charge and discharge and model emulation result Contrast.It can be seen that at the initial stage and latter stage of charge and discharge, model error is larger;And in the mid-term of charge and discharge, mould Type output valve is almost overlapped with experiment value.This fits like a glove with the steep middle flat non-linear voltage characteristic in two ends of lithium battery.
In summary, the simulation result obtained by change rank fractional order equivalent-circuit model disclosed by the invention substantially conforms to reality Data are tested, model worst error is applied to the works such as pulse discharge and recharge and the constant current charge-discharge of electric automobile within 0.05V Condition.Demonstrate the validity for becoming rank fractional model.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, not to present invention protection model The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need to pay various modifications or deform still within protection scope of the present invention that creative work can make.

Claims (9)

1. a kind of lithium battery fractional order becomes the discrimination method of rank equivalent-circuit model, it is equivalent that a kind of lithium battery fractional order becomes rank Circuit model, including run time circuit and cell I-V characteristic circuit, the run time circuit and cell I-V characteristic circuit Signal transmission is carried out by CCCS and VCVS;The run time circuit includes putting certainly for battery Resistance RdAnd electric capacity CQ, resistance RdWith electric capacity CQIt is connected in parallel on the two ends of CCCS, one end of CCCS Ground connection;The one of the RC network branch road that the positive terminal of the VCVS of the cell I-V characteristic circuit and two are in parallel End is connected, and negative pole end is connected with the negative pole end of battery model, and each branch road of described two RC network branch roads being in parallel is equal Including two fractional order being in series RC loops and an internal resistance Ro, the other end and the battery mould of described two branch roads being in parallel The positive terminal of type is connected;It is characterized in that, comprise the following steps:
Step one:Write out the discharge process of lithium battery and the fractional order mathematics model expression of static condition;
Step 2:Constant current charge-discharge is carried out to lithium battery, the active volume C of battery model is obtainedQWith self discharge resistance Rd
Step 3:Pulsed discharge test is carried out to lithium battery, battery terminal voltage when different SOC place battery starts to discharge is obtained Moment drop-out value, electric discharge terminate rear battery terminal voltage moment rise to value, discharge current and battery terminal voltage zero input sound Data should be waited;
Step 4:The data obtained according to step 3, parameter and exponent number based on least squares identification model;
Step 5:Obtained battery model parameter is calculated according to step 4 and calculates open-circuit voltage OCV at different SOC, in ohm Hinder R0d, activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dWith concentration polarization fraction Rank electric capacity FOE2d
Step 6:The model parameter obtained according to step 5, based on least squares identification open-circuit voltage OCV, ohmic internal resistance R0d、 Activation polarization internal resistance R1d, activation polarization fractional order electric capacity FOE1d, concentration polarization internal resistance R2dWith concentration polarization fractional order electric capacity FOE2dRelation between SOC;
Step 7:The parameter obtained according to step 2 to six, builds lithium battery fractional order and becomes rank equivalent-circuit model.
2. a kind of lithium battery fractional order as claimed in claim 1 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, two The individual RC network branch road that is in parallel is the electricity in RC network discharge paths and RC network charging paths, two RC network branch roads respectively Appearance is fractional order electric capacity.
3. a kind of lithium battery fractional order as claimed in claim 2 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, it is described RC network discharge paths fractional order element FOE1dAnd FOE2dExponent number α, β it is different and change with battery SOC state, and meet 0≤αd, βd≤ 1, work as αd, βdWhen=0, fractional order element FOE1dAnd FOE2dA resistance is equivalent to, works as αd, βdWhen=1, fractional order element FOE1d And FOE2dIt is equivalent to an integer rank electric capacity;When 0<αd, βd<When 1, fractional order element FOE1dAnd FOE2dIt is a fractional order electric capacity;
The RC network charging paths fractional order element FOE1cAnd FOE2cExponent number α, β it is different and change with battery SOC state, And meet 0≤αc, βc≤1;Work as αc, βcWhen=0, fractional order element FOE1cAnd FOE2cA resistance is equivalent to, works as αc, βc=1 When, fractional order element FOE1cAnd FOE2cIt is equivalent to an integer rank electric capacity;When 0<αc, βc<When 1, fractional order element FOE1cWith FOE2cIt is a fractional order electric capacity.
4. a kind of lithium battery fractional order as claimed in claim 1 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, institute State in the RC network branch road that two are in parallel in cell I-V characteristic circuit, discharge paths include the diode D being sequentially connected in seriesd, point Number rank electric capacity FOE1dWith resistance R1dThe fractional order RC loops of composition, fractional order electric capacity FOE2dWith resistance R2dThe fractional order RC of composition Loop and resistance Rod
Charging paths include the reversal connection diode D being sequentially connected in seriesc, fractional order electric capacity FOE1cWith resistance R1cThe fractional order RC of composition is returned Road, fractional order electric capacity FOE2cWith resistance R2cThe fractional order RC loops of composition and resistance Roc
5. a kind of lithium battery fractional order as claimed in claim 1 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, institute State run time circuit and cell I-V characteristic circuit and set up by a CCCS and VCVS and joined System, when carrying out discharge and recharge to battery, load current ibatBy CCCS to electric capacity CQDischarge and recharge is carried out, changes CQ The electricity of storage, characterizes the change of battery SOC, CQBoth end voltage OCV also changes therewith, the controlled voltage source of I-V characteristic circuit OCV changes with SOC change.
6. a kind of lithium battery fractional order as claimed in claim 1 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, institute The voltage for stating the two ends of CCCS is battery open circuit voltage OCV.
7. a kind of lithium battery fractional order as claimed in claim 1 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, put The terminal voltage of lithium battery is represented by electric process:
In formula, UbatFor battery terminal voltage;R0dFor ohmic internal resistance;OCVdFor electric discharge open-circuit voltage;α, β are fractional order element FOE1d And FOE2dExponent number, meet 0<α, β≤1;idisFor discharge current;τ1d2dThe time constant of respectively two RC networks;
U1d(0+) and U2d(0+) terminates the terminal voltage initial value of two fractional order RC branch roads of moment for battery discharge.
8. a kind of lithium battery fractional order as claimed in claim 7 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, U1d (0+) and U2d(0+) its value can be expressed as:
U1d(0+)=idis·R1d (2)
U2d(0+)=idis·R2d (3)
After battery discharge terminates, the terminal voltage of battery is represented by:
In formula, the polarizing voltage of batteryWithGrowth over time and be gradually reduced, work as t During → ∞,WithTend to 0, now battery terminal voltage UbatEqual to the open-circuit voltage OCV of battery.
9. a kind of lithium battery fractional order as claimed in claim 8 becomes the discrimination method of rank equivalent-circuit model, it is characterized in that, institute The detailed process for stating step 5 is:Due to the presence of battery ohmic internal resistance, when the cell is discharged, battery terminal voltage can fall moment Fall, its value is designated as Δ U1;When battery stops discharging, battery terminal voltage can rise to moment, and its value is designated as Δ U2, therefore, battery Ohmic internal resistance R0It can be obtained by following formula:
Activation polarization internal resistance R1dIt can be obtained by following formula:
Concentration polarization internal resistance R2dIt can be obtained by following formula:
Activation polarization fractional order electric capacity FOE1dIt can be obtained by following formula:
Concentration polarization fractional order electric capacity FOE2dIt can be obtained by following formula:
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