CN106872901B - KiBaM- fractional order equivalent circuit comprehensive characteristics battery model and parameter identification method - Google Patents
KiBaM- fractional order equivalent circuit comprehensive characteristics battery model and parameter identification method Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/385—Arrangements for measuring battery or accumulator variables
- G01R31/387—Determining ampere-hour charge capacity or SoC
Abstract
The invention discloses a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model and discrimination methods, battery electrochemical characteristic and nonlinear electrical characteristic are comprehensively considered, organically blending, having complementary advantages between KiBaM electrochemical model and equivalent-circuit model is realized, the non-linear capacity characteristic and dynamic electrical characteristic of power battery can be accurately captured.Wherein, KiBaM electrochemical model considers the recovery Effects and specific volume graded effect of battery, describes the non-linear capacity effect of battery and the bulk properties of runing time well；Fractional order becomes the polarity effect and concentration difference effect that rank RC equivalent-circuit model is used to describe battery, describes the output I-V external behavior of battery well.The present invention provides a battery comprehensive characteristics models that is accurate and easily realizing, realize and accurately simulate to the synthesis of power battery interior feature and external behavior, practical value with higher.
Description
Technical field
The present invention relates to a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model and parameter identification methods.
Background technique
As energy crisis and environmental pollution are got worse, electric car has become whole world focus of attention.Vehicle at present
Carrying power battery is the bottleneck for restricting electric car scale development, most important to vehicle dynamic property, economy and safety.
Accurate battery model is of great significance to component design, safety management and the operation of power battery, is battery
State-of-charge estimation, health status evaluation method basis.However, establish that one accurate and the simple battery model of structure absolutely not
Easy thing, this is because internal chemical reaction is complicated, it is non-linear and uncertain with height.Battery model develops to existing rank
Section, according to the difference of modeling mechanism can be divided into the performance electrochemical models of inside battery feature, simplification electrochemical models,
Thermal model etc., and stochastic model, neural network model, the equivalent-circuit model etc. of description outside batteries feature.Wherein, electrochemical
It learns model and uses complex nonlinear differential equation inside battery chemical process, it is accurately but too abstract；Thermal model is mainly ground
Heat, the diabatic process for studying carefully battery, can couple with electrochemical model；But model above is difficult to characterize the electric parameter of battery,
It should not be used in electrical, control circuit design and emulation etc.；Stochastic model is primarily upon the recovery characteristics of battery, and battery behavior is retouched
It states as a markoff process, the pulse discharge characteristic of battery can be described well, but be unsuitable for time-dependent current load
Situation；Neural network model have good non-linear mapping capability, quick parallel processing capability, stronger self study and from
Organizational capacity etc., but lot of experimental data is needed, and influence of the model error vulnerable to training data and training method.Therefore on
Several models are stated to be greatly limited in actual electrical design and Simulation Application.
Equivalent-circuit model uses different physics components such as voltage source, current source, capacitor according to the physical characteristic of battery
The I-V characteristic for carrying out simulated battery with composition equivalent-circuit models such as resistance because of the form of its simple, intuitive, and is suitable for electrical
A kind of the advantages that design is with emulation, it has also become the model being most widely used.In equivalent-circuit model, other equivalent electricity are compared
Road model, such as Rint model, Thevenin model, PNGV model, GNL model, Order RC equivalent-circuit model physical significance
Clearly, identification of Model Parameters test is relatively easy, model accuracy is higher, can accurate, intuitively simulated battery dynamic characteristic.
But Order RC model, in battery charging and discharging initial stage and latter stage, since model order is lower, there are biggish errors of fitting, no
Can accurately simulated battery static and dynamic performance.The accuracy and preferably of battery model can be improved in the series connection order for increasing RC
The charge-discharge characteristic of power battery is simulated, but order is excessively high will to be unfavorable for obtaining the parameter in model, can also greatly increase mould
The calculation amount of type results even in system concussion, so the order of RC should be limited.Therefore, it is difficult to determine structure equivalent-circuit model
To describe the steep intermediate flat non-linear voltage characteristic in lithium battery both ends, the lance between the accuracy of model and practicability not can solve
Shield.For this purpose, Chinese invention patent application (patent No. ZL201410185885.7) proposes a kind of change rank RC based on AIC criterion
Equivalent-circuit model realizes by being slightly increased the complexity of model and more accurately describes lithium-ion-power cell both ends
Steep intermediate flat non-linear voltage characteristic, error efficiently solve the lance between model complexity and practicability within 0.04V
Shield, practical value with higher.
However, the RC battery model of above-mentioned conventional integer rank, the switching between model order can only be the variation of integer rank,
Model order fluctuation is big, does not meet the rule of development of gradual change in nature, therefore model accuracy is very restricted.It is true
On, lithium battery is because of its special material and chemical characteristic, and inside battery electrochemical reaction process is extremely complex, including conductive ion
Transfer, internal electrochemical reaction, charge and discharge hesitation and concentration difference diffusion effect etc., show stronger nonlinear characteristic,
Fractional order dynamic behavior has been shown, battery behavior its precision has been described with integer rank and is very restricted, and has used score
When rank calculus describes those objects per se with fractional order characteristic, intrinsic propesties and its row of object can be better described
For.
Although traditional equivalent-circuit model can describe the I-V output external characteristic of battery, it is difficult to show the non-of battery
The internal features such as linear capacity effect and runing time, and KiBaM electrochemical model (KiBaM, full name Kinetic
Battery Model) but cleverly solve very much this problem.KiBaM model is the intuitive electrochemical model of comparison, is examined
The recovery Effects and specific volume graded effect for having considered battery characterize the non-linear capacity effect and fortune of battery using a depression of order equation
The internal features such as row time can describe the non-linear discharge characteristic of battery well；But KiBaM model itself cannot but be retouched
State the I-V external characteristics of battery.Therefore KiBaM electrochemical model and equivalent-circuit model, the two naturally form one kind and take long benefit
Relationship that is short, having complementary advantages, but by the two combination not a duck soup.It does not find KiBaM model and the equivalent electricity of fractional order also at present
Road carries out the related research of comprehensive modeling feature, therefore the unique innovation of the present invention, has preferable application value.
Summary of the invention
The present invention to solve the above-mentioned problems, proposes a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model
And parameter identification method, the present invention have comprehensively considered battery electrochemical characteristic and nonlinear electrical characteristic, realize KiBaM electrification
Organically blending, having complementary advantages between model and equivalent-circuit model is learned, the non-linear capacity that can accurately capture power battery is special
Property and dynamic electrical characteristic.
The first object of the present invention is to provide a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model, the model
The recovery Effects and specific volume graded effect for considering battery, describe well battery non-linear capacity effect and runing time it is interior
Portion's characteristic；Fractional order becomes the polarity effect and concentration difference effect that rank RC equivalent-circuit model is used to describe battery, well description electricity
The output I-V external behavior in pond.
The second object of the present invention is to provide the parameter identification method of above-mentioned model, and this method enables to KiBaM- score
Rank equivalent circuit comprehensive characteristics battery model efficiently identifies call parameter during the work time, so that modeling is set up, guarantees
The accurate and easy realization of model is accurately simulated with the synthesis that can be realized to power battery interior feature and external behavior, is had
Higher practical value.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model, including performance battery non-linear capacity characteristic
Fractional order equivalent-circuit model two parts of KiBaM electrochemical model and performance cell I-V characteristic, in which:
The KiBaM electrochemical model includes temporary capacity and available capacity portions, the temporary capacity part table
Show the electricity that can be directly obtained when electric discharge, indicates the state-of-charge of battery；The available capacity portions expression cannot be direct
The electricity of acquisition, two parts are connected, and when the cell is discharged, load current is flowed out from temporary capacity part, while obtaining capacity
Partial electricity through-rate coefficient, using the height ratio of temporary capacity and available capacity portions, in conjunction with battery capacity characteristic
The size of fractional order order expresses the non-linear capacity effect and battery recovery effect of battery；
The fractional order equivalent-circuit model, controlled voltage source and two fractional orders being in parallel including SOC control are dense
Difference polarizes equivalent branch, and the positive terminal of the controlled voltage source of SOC control is connected with one end of two branches that are in parallel, negative pole end and
The negative pole end of battery model is connected, and the other end of described two branches being in parallel is connected with the positive terminal of battery model.
The sum of the temporary capacity part and available capacity portions are the total capacity of battery.
After battery discharges completely, the height of temporary capacity part is zero.
The temporary capacity is denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate battery
State-of-charge SOC；The available capacity is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；Also,
Y1 and y2The sum of be battery total capacity；C represents the allocation proportion of battery capacity between two parts, and there are following relationships:
KiBaM battery model part, temporary capacity y1With available capacity y2With represent battery charge state SOC's
h1And h2Between relationship be expressed as:
In formula, temporary capacity is denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate battery
State-of-charge SOC；The available capacity is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；Also, y1
With y2The sum of be battery total capacity；C represents the allocation proportion of battery capacity between two parts；K is indicated from temporary capacity portion
It is diverted to the velocity coefficient of available capacity.
By the KiBaM battery model of foundation, current battery total surplus capacity y (t), active volume C are obtainedavail(t)、
Unavailable capacity Cunavail(t) and battery charge state SOC, to capture in cell runtime and power battery non-linear capacity
Feature.
The state-of-charge SOC of power battery is indicated are as follows:
Wherein, the unavailable capacity C of batteryunavailIt can further indicate that are as follows:
Take primary condition t0=0, then when discharging battery, the capacity relationship formula of battery be may be expressed as:
Cavail(t)=Cinit-∫ibat(t)dt-Cunavail(t)。
SOC0For initial cells state-of-charge.
The equivalent branch of fractional order concentration polarization being in parallel includes a discharge paths and a charging paths, described
Discharge paths include the diode D being sequentially connected in seriesd, fractional order capacitor FOE1dWith resistance R1dThe circuit fractional order RC of composition, score
Rank capacitor FOE2dWith resistance R2dThe circuit fractional order RC of composition and resistance Rod；Charging paths include two pole of reversal connection being sequentially connected in series
Pipe Dd, fractional order capacitor FOE1cWith resistance R1cThe circuit fractional order RC of composition, fractional order capacitor FOE2cWith resistance R2cPoint of composition
The number circuit rank RC and resistance Roc。
The controlled voltage that the battery KiBaM model and fractional order equivalent circuit is controlled by charging and discharging currents and SOC
Connection is established in source；The controlled voltage source OCV changes with the SOC of KiBaM model and is changed.
Using the discrimination method of above-mentioned model, comprising the following steps:
(1) constant current charge-discharge experiment is carried out to power battery, so that power battery is restored to fully charged state, as battery
Original state；
(2) experiment of low current constant-current discharge is carried out to power battery, obtains the initial capacity of power battery；
(3) fully charged to power battery, carry out the experiment of high current constant-current discharge, since discharge current is very big, very short time
Discharge cut-off voltage is just discharged into, the capacity of power battery under high current is obtained, determines allocation proportion；
(4) constant-current discharge for carrying out two groups of different multiplyings to power battery is tested, and obtains under this discharge-rate battery not
Active volume and discharge time data；It according to the condition for judging that battery discharge terminates, is calculated and can be identified parameter, to obtain
All parameters of tested battery KiBaM model part；
(5) pulsed discharge test is carried out to lithium battery, obtains battery different SOC at and starts battery terminal voltage when discharging
Zero input that the moment of battery terminal voltage rises to value, discharge current and battery terminal voltage after moment drop-out value, electric discharge is rung
Data are answered, determine the device parameter values of the equivalent branch of fractional order concentration polarization；
(6) consider that moment of the battery terminal voltage in battery discharge caused by battery ohmic internal resistance is fallen, confirm fractional order
Relationship between the device parameter values and SOC of the equivalent branch of concentration polarization, to determine tested battery fractional order equivalent-circuit model portion
All parameters divided, and then obtain the KiBaM and fractional order equivalent circuit comprehensive characteristics battery model of tested battery.
Compared with prior art, the invention has the benefit that
1. real the invention discloses a kind of KiBaM and fractional order equivalent circuit comprehensive characteristics battery model and discrimination method
The mutual supplement with each other's advantages between KiBaM electrochemical model and equivalent-circuit model is showed.Wherein, KiBaM electrochemical model considers electricity
The recovery Effects and specific volume graded effect in pond, describe the flash-over characteristics such as non-linear capacity effect and the runing time of battery well；
Fractional order becomes the polarity effect and concentration difference effect that rank RC equivalent-circuit model is used to describe battery, describes the output of battery well
I-V external characteristics.
2. fractional calculus has certain memory function, more meet the universal continuous simple philosophical viewpoint of nature.
The present invention becomes rank concept by introducing fractional order, and battery model is made to obtain more freedom degrees, bigger flexibility and new meaning；Point
The introducing of number rank also increases many new phenomenons and rule, the consecutive variations of model order is realized, so that model is more steady
Fixed and moving state property can it is more excellent, precision is higher, there is conventional integer rank battery model cannot achieve superior.The present invention solves existing
There is deficiency existing for fuel cell modelling technology and methods, provides a battery model that is accurate and easily realizing, reality with higher
With value.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation are not constituted an undue limitation on the present application for explaining the application.
Fig. 1 is structural schematic diagram of the invention, and wherein subscript c mark indicates charging, and d mark indicates electric discharge.
Specific embodiment:
The invention will be further described with embodiment with reference to the accompanying drawing.
It is noted that following detailed description is all illustrative, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
A kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model, including performance battery non-linear capacity characteristic
Equivalent-circuit model two parts of KiBaM electrochemical model and performance cell I-V characteristic；
The KiBaM electrochemical model part includes two parts, for describing the non-linear capacity characteristic of battery,
It is called " temporary capacity " and " available capacity " respectively；The two parts can be regarded as the device of two connections, and such as well is described
" temporary capacity " is denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate the state-of-charge of battery
SOC；" the available capacity " is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；Also, y1With y2It
With the total capacity for being battery；C represents the allocation proportion of battery capacity between two " wells ", it is clear that there are following relationships:
KiBaM battery model part, " temporary capacity " y1" available capacity " y2With represent battery charge state
The h of SOC1And h2Between relationship may be expressed as:
In formula, " temporary capacity " is denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate battery
State-of-charge SOC；" the available capacity " is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；And
And y1With y2The sum of be battery total capacity；C represents the allocation proportion of battery capacity between two " wells "；K is indicated from " interim to hold
Amount " flows to the velocity coefficient of " available capacity ".
Definition represents the difference in height of two " well " as δh(t), it is clear that:
δh(t)=h2(t)-h1(t) (3)
The total capacity of battery, unavailable capacity, active volume can respectively indicate are as follows:
In formula, Cmax、Cavail、CunavailRespectively represent the initial capacity, active volume and unavailable capacity of battery；Wherein
Unavailable capacity CunavailRepresent the non-linear SOC variable of battery influenced due to battery non-linear capacity characteristic；
Assuming that battery " temporary capacity " y1" available capacity " y2The capacity y of original state10And y20It is respectively as follows:
In formula, C indicates the total capacity of battery.
Constant current discharge, and discharge time section t are carried out to battery with electric current I when for the first time0≤t≤td, it is then allowed to stand one section
Time td< t≤tr, then formula (2) is omitted through Laplace transformation and inverse Laplace transformation, conversion process, and arrangement can obtain:
In formula, coefficient
Arrangement can obtain:
In formula, t0、td、trRespectively indicate original state time, electric discharge end time and the recovery time when battery discharge.
The unavailable capacity C of batteryunavailIt can further indicate that are as follows:
If taking primary condition t0=0, then when discharging battery, the capacity relationship formula of battery be may be expressed as:
Cavail(t)=Cinit-∫ibat(t)dt-Cunavail(t) (9)
The state-of-charge SOC of battery may be expressed as:
By front analysis it is found that when battery is discharged completely, height h1=0；The total surplus capacity of battery is equal to not at this time
Active volume, it may be assumed that
Y (t)=Cunavail(t)=(1-c) δh(t) (11)
The KiBaM model part, available current battery total surplus capacity y (t), active volume Cavail(t)、
Unavailable capacity Cunavail(t) and battery charge state SOC cell runtime can be captured, therefore accurately and power battery is non-
Feature in linear capacity.
The KiBaM model part, when the cell is discharged, y of the load current i from expression " temporary capacity "1The lower right corner
Pipeline outflow, " available capacity " y simultaneously2Electricity y is slowly flowed by k1, and the speed flowed out is than from y2Flow into y1
Speed it is fast, y1Decline faster, y1And y2Difference in height increases therewith；When battery stops discharging, y1Electricity can be gone up,
Until y1And y2It is highly equal, it is the embodiment of battery recovery effect；It also illustrates when discharge current is bigger, is released simultaneously
Electricity is just smaller, embodies the non-linear capacity effect of battery；
The fractional order equivalent-circuit model part, for describing the I-V external characteristics of battery, circuit includes SOC control
Controlled voltage source, the diode D of systemd, fractional order activation polarization capacitor FOE1d, activation polarization resistance R1d, fractional order concentration difference
Polarization capacity FOE2d, concentration polarization resistance R2dAnd resistance Rod, it is reversely connected diode Dd, fractional order activation polarization capacitor FOE1c、
Activation polarization resistance R1c, fractional order concentration polarization capacitor FOE2c, concentration polarization resistance R2cAnd resistance Roc。
The positive terminal of the fractional order equivalent-circuit model part, the controlled voltage source of SOC control is in parallel with two
One end of branch is connected, and negative pole end is connected with the negative pole end of battery model, the other end and electricity of described two branches being in parallel
The positive terminal of pool model is connected；
The fractional order equivalent-circuit model part, each branch of two branches being in parallel include two phases
The circuit concatenated fractional order RC and an internal resistance Ro；Discharge paths include the diode D being sequentially connected in seriesd, fractional order capacitor FOE1d
With resistance R1dThe circuit fractional order RC of composition, fractional order capacitor FOE2dWith resistance R2dThe circuit fractional order RC of composition and resistance Rod；
Charging paths include the reversal connection diode D being sequentially connected in seriesd, fractional order capacitor FOE1cWith resistance R1cThe circuit fractional order RC of composition,
Fractional order capacitor FOE2cWith resistance R2cThe circuit fractional order RC of composition and resistance Roc。
The controlled voltage that the battery KiBaM model and fractional order equivalent circuit is controlled by charging and discharging currents and SOC
Connection is established in source；The controlled voltage source OCV changes with the SOC of KiBaM model and is changed；By taking discharge process as an example, battery
Open-circuit voltage OCVd:
Battery terminal voltage can indicate are as follows:
Ubat=OCVd-idis·R0d-U1d(t)-U2d(t)
In formula, UbatFor battery terminal voltage；idisFor discharge current；R0dFor ohmic internal resistance；OCVdFor the open-circuit voltage that discharges；U1d
(t) and U2d(t) terminate the end voltage of two fractional order RC branches of moment for battery discharge, value can be stated are as follows:
In formula, α, β are fractional order element FOE1dAnd FOE2dOrder, meet 0 < α, β < 1；τ1d,τ2dRespectively two RC nets
The time constant of network.
If taking primary condition t0=0, then have:
U1d(0+) and U2d(0+) is the end voltage initial value that battery discharge terminates two fractional order RC branches of moment, and value can
Statement are as follows:
After battery discharge, the end voltage of battery be may be expressed as:
In formula, the polarizing voltage of batteryWithGradually subtract with the growth of time
It is small, as t → ∞,WithTend to 0, at this time battery terminal voltage UbatEqual to opening for battery
Road voltage OCVd。
A kind of discrimination method using above-mentioned KiBaM- fractional order equivalent circuit comprehensive characteristics battery model, with battery discharge
For, the content of parameter identification mainly includes the initial capacity y of battery KiBaM model part0, allocation proportion c, velocity coefficient k；
And the open-circuit voltage OCV of fractional order equivalent-circuit model partd, fractional order activation polarization capacitor FOE1dAnd fractional order order
α, fractional order concentration polarization capacitor FOE2dAnd fractional order order β, activation polarization resistance R1d, concentration polarization resistance R2dAnd resistance
Rod, comprising the following steps:
Step 1: carrying out constant current charge-discharge experiment to power battery, power battery made to be restored to fully charged state, as
The original state of battery；
Step 2: the experiment of low current constant-current discharge is carried out to power battery, obtains the initial capacity C of power batteryinit；
Step 3: it is fully charged to power battery, the experiment of high current constant-current discharge is carried out, it is very short since discharge current is very big
Time just discharges into discharge cut-off voltage, obtains the capacity C of power battery under high current1；The then parameter of battery model
Step 4: the constant-current discharge for carrying out two groups of different multiplyings to power battery is tested, and battery under this discharge-rate is obtained
Unavailable capacity Cunavail, discharge time tdEtc. data；According to formula (8) C for judging that battery discharge terminatesunavail=(1-c)
δh(td), it can be identified parameter k', and then obtain parameter k；
Step 5: by testing and testing above, all parameters of available tested battery KiBaM model part；
Step 6: carrying out pulsed discharge test to lithium battery, obtains battery-end electricity when battery at different SOC starts electric discharge
The moment of battery terminal voltage rises to the zero defeated of value, discharge current and battery terminal voltage after the moment drop-out value of pressure, electric discharge
Enter the data such as response；According to the above data of acquisition, the ohmic internal resistance R at different SOC is calculated0d, activation polarization internal resistance R1d、
Concentration polarization internal resistance R2d, activation polarization fractional order capacitor FOE1dAnd fractional order order α, concentration polarization fractional order capacitor FOE2d
And fractional order order β；
The detailed process of the step six are as follows: due to the presence of battery ohmic internal resistance, when the cell is discharged, battery-end electricity
Pressure can be fallen moment, and value is denoted as Δ U1；When battery stops discharging, battery terminal voltage can be risen to moment, and value is denoted as Δ U2,
Therefore,
Battery ohmic internal resistance R0dIt 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 capacitor FOE1dIt can be obtained by following formula:
Concentration polarization fractional order capacitor FOE2dIt can be obtained by following formula:
Step 7: the model parameter obtained according to step 6 is based on least squares identification battery open circuit voltage OCVd, Europe
Nurse internal resistance R0d, activation polarization internal resistance R1d, concentration polarization internal resistance R2d, activation polarization fractional order capacitor FOE1dAnd fractional order rank
Secondary α, concentration polarization fractional order capacitor FOE2dAnd the relationship between fractional order order β and SOC；It is main involved in this parameter identification process
Formula is wanted, as follows:
When electric discharge, battery open circuit voltage OCVd:
Battery ohmic internal resistance RodWith the relational expression of SOC are as follows:
Rod(SOC)=b0·e-SOC+b1+b2·SOC-b3·SOC2+b4·SOC3 (24)
In formula, b0-b4For constant, obtained by experimental data based on least squares identification.
Activation polarization internal resistance R1dWith the relational expression of SOC are as follows:
R1d(SOC)=c0·e-SOC+c1+c2·SOC-c3·SOC2+c4·SOC3 (25)
In formula, c0-c4For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order capacitor FOE1dWith the relational expression of SOC are as follows:
FOE1d(SOC)=d0·SOC5+d1·SOC4+d2·SOC3+d3·SOC2+d4·SOC+d5 (26)
In formula, d0-d5For constant, obtained by experimental data based on least squares identification.
Concentration polarization internal resistance R2dWith the relational expression of SOC are as follows:
R2d(SOC)=e0·e-SOC+e1+e2·SOC-e3·SOC2+e4·SOC3 (27)
In formula, e0-e4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order capacitor FOE2dWith the relational expression of SOC are as follows:
FOE2d(SOC)=f0·SOC5+f1·SOC4+f2·SOC3+f3·SOC2+f4·SOC+f5 (28)
In formula, f0-f5For constant, obtained by experimental data based on least squares identification.
Activation polarization fractional order capacitor FOE1dThe relational expression of order and SOC are as follows:
α (SOC)=g0·SOC4+g1·SOC3+g2·SOC2+g3·SOC+g4 (29)
In formula, g0-g4For constant, obtained by experimental data based on least squares identification.
Concentration polarization fractional order capacitor FOE2dThe relational expression of order and SOC are as follows:
β (SOC)=h0·SOC4+h1·SOC3+h2·SOC2+h3·SOC+h4 (30)
In formula, h0-h4For constant, obtained by experimental data based on least squares identification.
The parameter that step 8: obtaining according to step 2 to seven and identification obtains, by modeling, available tested battery
KiBaM and fractional order equivalent circuit comprehensive characteristics battery model.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (8)
1. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model, it is characterized in that: including the performance non-linear appearance of battery
The KiBaM electrochemical model of flow characteristic and fractional order equivalent-circuit model two parts of performance cell I-V characteristic, in which:
The KiBaM electrochemical model includes temporary capacity and available capacity portions, and the temporary capacity part indicates to put
The electricity that can be directly obtained when electric indicates the state-of-charge of battery；The available capacity portions expression cannot directly acquire
Electricity, two parts are connected, and when the cell is discharged, load current is flowed out from temporary capacity part, while obtaining capacity portions
Electricity through-rate coefficient, using the height ratio of temporary capacity and available capacity portions, in conjunction with battery capacity characteristic score
The size of rank order expresses the non-linear capacity effect and battery recovery effect of battery；
The fractional order equivalent-circuit model, controlled voltage source and two fractional order concentration polarizations being in parallel including SOC control
Change equivalent branch, the positive terminal of the controlled voltage source of SOC control is connected with one end of two branches that are in parallel, negative pole end and battery
The negative pole end of model is connected, and the other end of described two branches being in parallel is connected with the positive terminal of battery model；
The battery KiBaM model and fractional order equivalent circuit is built by the controlled voltage source that charging and discharging currents and SOC are controlled
Vertical connection；The controlled voltage source OCV changes with the SOC of KiBaM model and is changed, and considers electricity by battery KiBaM model
The recovery Effects and specific volume graded effect in pond, describe the non-linear capacity effect of battery and the bulk properties of runing time, fractional order
Become polarity effect and concentration difference effect that rank RC equivalent-circuit model describes battery, describes the output I-V external behavior of battery.
2. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: described
Temporary capacity part and the sum of available capacity portions be battery total capacity.
3. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: when electricity
After pond is discharged completely, the height of temporary capacity part is zero.
4. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: described
Temporary capacity be denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate the state-of-charge of battery
SOC；The available capacity is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；Also, y1 and y2The sum of
It is the total capacity of battery；C represents the allocation proportion of battery capacity between two parts, and there are following relationships:
5. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: described
KiBaM battery model part, temporary capacity y1With available capacity y2With the h for representing battery charge state SOC1And h2Between close
System indicates are as follows:
In formula, temporary capacity is denoted as y1, indicate the electricity that can be directly obtained when electric discharge, height is denoted as h1, indicate the charged of battery
State SOC；The available capacity is denoted as y2, indicate the electricity that cannot be directly acquired, height is denoted as h2；Also, y1With y2
The sum of be battery total capacity；C represents the allocation proportion of battery capacity between two parts；K indicates to flow from temporary capacity part
To the velocity coefficient of available capacity.
6. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: passing through
The KiBaM battery model of foundation obtains current battery total surplus capacity y (t), active volume Cavail(t), unavailable capacity
Cunavail(t) and battery charge state SOC, to capture feature in cell runtime and power battery non-linear capacity.
7. a kind of KiBaM- fractional order equivalent circuit comprehensive characteristics battery model as described in claim 1, it is characterized in that: described
The equivalent branch of fractional order concentration polarization being in parallel includes a discharge paths and a charging paths, the discharge paths include
The diode D being sequentially connected in seriesd, fractional order capacitor FOE1dWith resistance R1dThe circuit fractional order RC of composition, fractional order capacitor FOE2dWith
Resistance R2dThe circuit fractional order RC of composition and resistance Rod；Charging paths include the reversal connection diode D being sequentially connected in seriesd, fractional order electricity
Hold FOE1cWith resistance R1cThe circuit fractional order RC of composition, fractional order capacitor FOE2cWith resistance R2cThe circuit fractional order RC of composition and
Resistance Roc。
8. it is applied to the discrimination method of model of any of claims 1-7, it is characterized in that: the following steps are included:
(1) constant current charge-discharge experiment is carried out to power battery, power battery is made to be restored to fully charged state, as the first of battery
Beginning state；
(2) experiment of low current constant-current discharge is carried out to power battery, obtains the initial capacity of power battery；
(3) fully charged to power battery, the experiment of high current constant-current discharge is carried out, since discharge current is very big, very short time is just put
Electricity arrives discharge cut-off voltage, obtains the capacity of power battery under high current, determines allocation proportion；
(4) constant-current discharge for carrying out two groups of different multiplyings to power battery is tested, and obtains the unavailable of battery under this discharge-rate
Capacity and discharge time data；It according to the condition for judging that battery discharge terminates, is calculated and can be identified parameter, to be tested
All parameters of battery KiBaM model part；
(5) pulsed discharge test is carried out to lithium battery, obtains the moment for the battery terminal voltage that battery at different SOC starts when discharging
The moment of battery terminal voltage rises to the zero input response number of value, discharge current and battery terminal voltage after drop-out value, electric discharge
According to determining the device parameter values of the equivalent branch of fractional order concentration polarization；
(6) consider that moment of the battery terminal voltage in battery discharge caused by battery ohmic internal resistance is fallen, confirm fractional order concentration difference
Relationship between the device parameter values and SOC of equivalent branch that polarize, to determine tested battery fractional order equivalent-circuit model part
All parameters, and then obtain the KiBaM and fractional order equivalent circuit comprehensive characteristics battery model of tested battery.
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