CN203825171U - Variable order RC equivalent circuit model based on AIC criterion - Google Patents

Abstract

The utility model discloses a variable order RC equivalent circuit model based on an AIC criterion. An RC model is selected as the base model, the complexity and accuracy of the model at different SOC based on the AIC criterion are fully weighed, the optimal RC order at each SOC is determined, the RC model of variable orders is realized through controlling a shifting switch, the dynamic and static characteristics of a power battery are accurately simulated within all working ranges by means of a model structure as simple as possible,the model is easy in engineering realization and high in precision, and the integrated optimization of the complexity and accuracy of the model is achieved. The variable order RC equivalent circuit model can well simulate the dynamic and static characteristics of the battery, and is suitable for constant-current charging and discharging, pulse charging and discharging and UDDS circulation working conditions of the power battery.

Description

Change exponent number RC equivalent-circuit model based on AIC criterion

Technical field

The utility model relates to a kind of change exponent number RC equivalent-circuit model based on AIC criterion.

Background technology

The factors such as energy crisis, environmental pollution and energy security are pushed to electric automobile the arena of history again, have become the focus that the whole world is paid close attention to.China also classifies ev industry as the novel strategic industry of giving priority to, and wishes to promote by Development of EV structural adjustment and the technical progress of China's automobile industry, " bend is overtaken other vehicles " of finally realizing automobile industry.

Vehicle mounted dynamic battery is as the critical component of electric automobile, and dynamic property, economy and the security of its performance to car load is most important, is the key factor of restriction electric automobile scale development.And it is significant to build appropriate design and the safe operation of accurate battery model to electrokinetic cell, is mainly reflected in: utilize model can carry out the research of electrochemical response character, for the exploitation of electrode material, electrolytic solution is offered help; Battery model is one of important means of battery design reference; There is no enough accurate electrokinetic cell models, can not carry out the dynamic Characteristic Simulation research of power system of electric automobile; Accurate electrokinetic cell model is that the basis of design motivation battery cell monitoring and management system, particularly SOC, SOH estimate; It is the prerequisite that the extensive electric automobile power battery access of analysis electrical network discharges and recharges the impact that electrical network is brought.

But, the chemical reaction of inside battery be one to environment sensitive and extremely complicated non-linear process, and there are coupling, hysteresis effect and time-varying characteristics.Its performance parameter is subject to the impact of the many factors such as SOC, current ratio, temperature, life-span and self discharge, as battery terminal voltage become with discharge current nonlinearities change, battery active volume with discharge current increase reduce, the internal resistance of cell reduces and becomes large etc. with battery temperature.It can be following five types according to the different demarcation of modeling mechanism that battery model develops into present stage: galvanochemistry model, analytical model, probabilistic model, neural network model and equivalent-circuit model.But up to the present go back neither one and can accurately describe the static and dynamic performance parsing mathematical model that is easy to Project Realization simple in structure again of battery within the scope of all working.In other words, traditional battery model can not be obtained compromise on model complexity and model accuracy.Particularly, the deficiency of existing model mainly contains: the relation between voltage source and SOC is clear and definite not; Some model fails to reflect the hysteresis effect of battery; Some model is too simple, can not describe well the dynamic perfromance of battery as voltage rebound characteristics; Some model is too complicated, though degree of accuracy is high, is difficult to realize in engineering.

Equivalent-circuit model is because of the form of its simple, intuitive and be suitable for the advantage such as electrical design and emulation and become a kind of new model being widely used.In equivalent-circuit model, Order RC model compares that other equivalent-circuit model physical significances are clear, easily execution of identification of Model Parameters test, parameter identification method system, model accuracy are higher, can be more accurately, the dynamic perfromance of simulated battery intuitively.But in battery charging and discharging initial stage and latter stage, because model order is lower, there is larger error of fitting, accurately the static and dynamic performance of simulated battery in Order RC model.Although the series connection exponent number that increases RC can improve the accuracy of battery model, can better simulate the charge-discharge characteristic of electrokinetic cell, if but the exponent number of electrokinetic cell model is too high, by the parameter that is unfavorable for obtaining in model, and also can greatly increase the calculated amount of model, even can cause system concussion, so also should limit on the other hand the exponent number of RC.

Utility model content

The utility model is in order to address the above problem, a kind of change exponent number RC equivalent-circuit model based on AIC criterion has been proposed, it is basic model that this model is chosen RC model, fully weigh complexity and the accuracy of model at different SOC place based on AIC criterion, determine the optimum RC exponent number at each SOC place, and realize by controlling change-over switch the RC model that becomes exponent number, within the scope of all working, accurately simulate the static and dynamic performance of electrokinetic cell with the succinct model structure of trying one's best, reach the comprehensive optimum of model complexity and accuracy, be easy to Project Realization and precision is high.

To achieve these goals, the utility model adopts following technical scheme:

A kind of change exponent number RC equivalent-circuit model based on AIC criterion, comprise circuit and I-V characteristic circuit working time, wherein, I-V characteristic circuit comprises two-way branch road, each branch road comprises three groups of electric capacity and a RC loop that resistance composes in parallel, and two groups of RC loops of each branch road are parallel with change-over switch.Described working time, circuit comprised the self discharge resistance R of battery _d, capacitor C _qwith CCCS circuit, resistance R _dwith capacitor C _qbe connected in parallel on the controlled source two ends of CCCS, one end ground connection of independent current source.

Described I-V characteristic circuit comprises ohmic internal resistance R ₀, activation polarization internal resistance R ₁, activation polarization capacitor C ₁, concentration polarization internal resistance R ₂, concentration polarization capacitor C ₂, become exponent number internal resistance R ₃, become exponent number capacitor C ₃, change-over switch Q ₁, S ₁, Q ₂, S ₂with CCCS, Voltage-controlled Current Source circuit, wherein:

The positive pole of the controlled source of Voltage-controlled Current Source circuit connects two-way, and a road connects diode D _drear contact resistance R _1d, resistance R _2d, resistance R _3d, resistance R _odthe positive pole of rear connection battery, a road reversal connection diode D _crear contact resistance R _1c, resistance R _2c, resistance R _3c, resistance R _octhe positive pole of rear connection battery, capacitor C _1dbe connected in parallel on resistance R _1dtwo ends, change-over switch Q ₂and capacitor C _2dbe connected in parallel on resistance R _2dtwo ends, change-over switch Q ₁and capacitor C _3dbe connected in parallel on resistance R _3dtwo ends, capacitor C _1cbe connected in parallel on resistance R _1ctwo ends, change-over switch S ₂and capacitor C _2cbe connected in parallel on resistance R _2ctwo ends, change-over switch S ₁and capacitor C _3cbe connected in parallel on resistance R _3ctwo ends, the voltage between the controlled source positive and negative electrode of Voltage-controlled Current Source circuit is battery open circuit voltage OCV.

Described working time, circuit and I-V characteristic circuit were set up contact by a Flow Control current source and a voltage controlled voltage source, in the time that battery is discharged and recharged, and load current i _batby Flow Control current source to capacitor C _qdischarge and recharge, change C _qthe electric weight of storage, the variation of characterizing battery SOC, C _qboth end voltage OCV also changes thereupon, and the controlled voltage source OCV of I-V characteristic circuit changes with the variation of SOC.

Described change-over switch Q ₁, S ₁and Q ₂, S ₂while all disconnection, becoming exponent number RC model is three rank RC models; Described change-over switch Q ₁, S ₁closure, Q ₂, S ₂when disconnection, becoming exponent number RC model is Order RC model; Described change-over switch Q ₁, S ₁closure, Q ₂, S ₂also, when closed, becoming exponent number RC model is single order RC model.

Described capacitor C _qrepresent the active volume of battery, C _q=3600C _ahf ₁f ₂, wherein, C _ahfor the battery capacity that is unit by ampere-hour, f ₁and f ₂it is respectively the modifying factor of battery cycle life and temperature.

The electric current of the controlled source of described CCCS is the end current i of battery _bat, load current i in the time that battery discharges and recharges _batby CCCS to capacitor C _qdischarge and recharge, change capacitor C _qthe electric weight of middle storage, thereby the variation of characterizing battery SOC.

The voltage at the controlled source two ends of described CCCS is battery open circuit voltage OCV, and described open-circuit voltage OCV and SOC exist nonlinear relationship, and physical relationship formula is:

$\mathrm{OCV}=a_1+a_2\ln \mathrm{SOC}+a_3\ln (1-\mathrm{SOC})+\frac{a_4}{\mathrm{SOC}}+a_5\mathrm{SOC}---\left(1\right)$

In formula, a ₁～a ₅for constant, obtained based on least squares identification by experimental data.

The beneficial effects of the utility model are:

1, proposed the RC model of a kind of change exponent number (change structure), solved conventional batteries model and be difficult to reach this difficult problem of balance in model complexity and estimated accuracy;

2, first AIC criterion is applied in the selection of battery model exponent number, for the Rational choice of the different SOC RC of place exponent number provides theory support;

3, fully weigh complexity and the accuracy of model based on AIC criterion, determine best RC model order under different SOC, set up a RC model that becomes exponent number, realize the comprehensive optimum of model complexity and accuracy, be easy to Project Realization and precision is high, and the constant current charge-discharge, the pulse that are applicable to battery discharge and recharge the state of cyclic operation with UDDS.

Brief description of the drawings

Fig. 1 is that the utility model becomes exponent number RC model structure schematic diagram;

Fig. 2 is the response process figure of battery terminal voltage under step response of the present utility model;

Fig. 3 is that the battery terminal voltage zero of pulsed discharge SOC while being 10% inputted zero state response figure;

Fig. 4 is that the battery terminal voltage zero of pulsed discharge SOC of the present utility model while being 90% inputted zero state response figure;

Fig. 5 is that the battery terminal voltage zero of pulsed discharge SOC of the present utility model while being 50% inputted zero state response figure;

Fig. 6 is AIC value figure corresponding to the different model parameters of different SOC of the present utility model;

Fig. 7 is the graph of a relation of open-circuit voltage OCV of the present utility model and SOC;

Fig. 8 becomes exponent number RC models fitting design sketch under pulsed discharge of the present utility model;

Fig. 9 becomes exponent number RC models fitting design sketch under pulse charge of the present utility model;

Figure 10 becomes exponent number RC models fitting design sketch under constant-current discharge of the present utility model;

Figure 11 becomes exponent number RC models fitting design sketch under constant-current charge of the present utility model;

Figure 12 becomes exponent number RC models fitting design sketch under UDDS dynamic operation condition of the present utility model, wherein figure (b) is the waveform amplification curve of the front 200s of figure (a).

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the utility model is described in further detail.

Build battery model and refer to theoretical response characteristic and the bulk properties of as far as possible removing all sidedly to describe actual battery of applied mathematics.So-called response characteristic refers to the terminal voltage of battery and the corresponding relation of load current; Bulk properties refer to the relation between built-in variable ohmic internal resistance, polarization resistance and the polarizing voltage of battery and SOC, temperature.

Be illustrated in figure 1 the change exponent number RC model the utility model proposes, wherein U _batfor the terminal voltage of battery; i _batrepresent the end electric current of battery; R _drepresent the self discharge resistance of battery; C _crepresent the active volume of battery; R ₀for ohmic internal resistance; R ₁for activation polarization internal resistance; C ₁for activation polarization electric capacity; R ₂for concentration polarization internal resistance; C ₂concentration polarization electric capacity; R ₃for becoming exponent number internal resistance, C ₃for becoming exponent number electric capacity; Q ₁, S ₁, Q ₂, S ₂for becoming the change-over switch of exponent number RC model; OCV is battery open circuit voltage, is the function of SOC.Wherein d is designated course of discharge, and c is designated charging direction.The left-half of model has been used for reference the thought electric capacity Q of execution cost model _ccome characterizing battery capacity SOC and working time with Flow Control current source; The right half part of model is used for the I-V characteristic of simulated battery.

As change-over switch Q ₁, S ₁and Q ₂, S ₂while all disconnection, described change exponent number RC model is three rank RC models; As change-over switch Q ₁, S ₁closure, Q ₂, S ₂when disconnection, described change exponent number RC model is Order RC model; As change-over switch Q ₁, S ₁closure, Q ₂, S ₂also, when closed, described change exponent number RC model is single order RC model.The described change exponent number RC equivalent-circuit model based on AIC criterion is exactly complexity and the accuracy of fully weighing model according to AIC criterion at different SOC place, determines the optimum RC exponent number at each SOC place, and by controlling change-over switch Q ₁, S ₁and Q ₂, S ₂realize any switching of single order, second order, three rank RC models, realize within the scope of all working the accurately dynamic perfromance of simulation electrokinetic cell to try one's best model structure succinct, precision is high and be easy to Project Realization.

1. become the principle of work of exponent number RC model

The principle of work of this change exponent number RC model is described respectively: 1) active volume below from following three aspects; 2) open-circuit voltage; 3) transient response (RC network).

1) active volume

As shown in Fig. 1 left-half, the active volume of battery taking coulomb as unit can be by a capacitor C _qrepresent, its capacity is:

C _Q＝3600·C _Ah·f ₁·f ₂ (1)

In formula: C _ahfor the battery capacity that is unit by ampere-hour, f ₁and f ₂it is respectively the modifying factor of battery cycle life and temperature.

In the time that battery is discharged and recharged, load current i _batby Flow Control current source to capacitor C _qdischarge and recharge, change C _qthe electric weight of middle storage, thereby the variation of characterizing battery SOC, C _qboth end voltage OCV also changes thereupon, and then the voltage controlled voltage source OCV=f (SOC) of control I-V characteristic circuit changes with the variation of SOC.Load current i _batto capacitor C _qdischarge, work as C _qwhen reaching final discharging voltage, both end voltage OCV can obtain battery total working time.Self discharge resistance R _dthe self-discharge characteristics being used for after simulated battery storage certain hour.In theory, self discharge resistance is SOC, temperature, discharges and recharges the function of frequency and cycle index.In practical application, self discharge resistance is generally simplified to a large resistance or ignores.

2) open-circuit voltage OCV

There is stronger nonlinear relationship in the open-circuit voltage OCV of battery and SOC.As shown in Figure 1, adopt a voltage controlled voltage source to simulate the nonlinear relationship between open-circuit voltage OCV and SOC.

For the nonlinear relationship between open-circuit voltage OCV and SOC, in existing document, the general polynomial expression that adopts carrys out matching, but whether choosing of polynomial expression exponent number be suitable, and whether variable quantity is appropriate, directly affects accuracy and the calculated amount of model.Therefore, for can accurate description OCV and SOC between relation, and reduce calculated amount, several simplification galvanochemistry models that can reference battery: Shepherd model, Unnewehr universal model and Nernst model.These models couplings are got up, can obtain a kind of comparatively ideal open-circuit voltage model:

$\mathrm{OCV}=a_1+a_2\ln \mathrm{SOC}+a_3\ln (1-\mathrm{SOC})+\frac{a_4}{\mathrm{SOC}}+a_5\mathrm{SOC}---\left(2\right)$

In formula, a ₁～a ₅for constant, can use least squares identification to obtain by experimental data.

3) transient response

As shown in Figure 2, under step response, the rejuvenation of cell voltage is slowly, mainly comprises three parts: transient voltage falls, fast time constant and slow time constant.Wherein, ohmic internal resistance R ₀represent the moment pressure drop of battery; R ₁c ₁the fast time constant of network description battery, i.e. the activation polarization effect of battery; R ₂c ₂the slow time constant of network description battery, i.e. the concentration difference effect of battery; R ₃c ₃network is the fitting precision in order to improve a model and network increasing does not have concrete meaning.

As shown in Figure 2, after battery discharge finishes, the zero input response of battery model RC branch road can be expressed as:

$R_i{C}_i\frac{d{U}_i}{\mathrm{dt}}+U_i=0\⇒U_i=U_i(0+)e^{-i/{\mathrm{\τ}}_i}---\left(3\right)$

In formula, subscript i is RC network label, and its value is 1,2,3; τ _ibe the time constant of i RC network, i.e. τ _i=R _ic _i; U _i(0+) for battery impulse electric discharge finishes moment R _ic _ithe terminal voltage initial value of branch road, its value can be expressed as:

U _i(0+)＝R _ii _dis (4)

I in formula _disfor discharge current, R _ibe resistance in parallel in i RC branch road.

The polarizing voltage U of battery _i(0+) reduce gradually along with the growth of time, in the time of t → ∞, be tending towards 0, now battery terminal voltage equals the open-circuit voltage OCV of battery, and therefore, the change procedure that electric discharge finishes rear battery terminal voltage can be expressed as:

$U_{\mathrm{bat}}=\mathrm{OCV}-\underset{i=1}{\overset{x}{\mathrm{\Σ}}}{R}_i{i}_{\mathrm{dis}}{e}^{-t/{\mathrm{\τ}}_i}---\left(5\right)$

In formula, U _batfor battery terminal voltage, obtained by experiment; X is the exponent number of RC, and its value has 1,2,3.

As shown in Figure 2, the response process of battery terminal voltage under step response.Therefrom can find out, in the time of battery discharge, the terminal voltage of battery has the decline Δ U of a moment, and this is to be caused by the ohmic internal resistance of battery, and in the time that battery stops discharging, voltage also has the rising of a moment, and rising value equals Δ U, therefore the ohmic internal resistance R of battery ₀can be obtained by following formula:

$R_0=\frac{\mathrm{\ΔU}}{I}---\left(6\right)$

On the basis of model order identification, reference formula (3)～(6), and the zero input response of battery terminal voltage that utilizes pulse charge and discharge process to obtain, use least square method to carry out parameter identification to becoming exponent number RC model, can obtain the ohmic internal resistance R of battery discharge direction ₀, activation polarization internal resistance R ₁, activation polarization capacitor C ₁, concentration polarization internal resistance R ₂, concentration polarization capacitor C ₂, become exponent number internal resistance R ₃, become exponent number capacitor C ₃and electric discharge open-circuit voltage OCV.

All parameters in model are all the functions of SOC, electric current, temperature and cycle index in theory, but can be reduced to constant or linear according to some parameter of different experiment conditions under certain degree of accuracy requires, low for its self-discharge rate of ferric phosphate lithium cell, have extended cycle life, environment temperature is relatively constant, adopts the comparatively accurately performance of simulated battery of model and parameter of simplifying.

2. akaike information criterion (AIC)

Akaike information criterion (AIC) is a kind of standard of weighing statistical model matching Optimality, is founded and development for great time by Japanese statistician Chi Chi.Before AIC criterion occurs, Model Selection is estimated as representative with maximum likelihood, maximum likelihood is estimated sample and is totally connected, carry out judgment models optimum by likelihood function maximum, become the overall tie of sample analysis, but from information theory the principle of information entropy this be not most economical, because the model parameter that the larger representative of likelihood function is more, no matter from economy, or sees it is not optimum from practicality, operability.And AIC criterion is based upon on the conceptual foundation of entropy and in conjunction with K-L distance, realize the balance of model estimated accuracy and number of parameters, for choosing of above-mentioned model order provides theory support.

General in the situation that, AIC can be expressed as:

AIC＝2k-2ln(L) (7)

In formula, K is the number of parameter, and L is likelihood function.

Hypothesized model error is obeyed independent normal distribution.AIC can be rewritten as so:

AIC＝2k+nln(RSS/n) (8)

In formula, RSS is residual sum of squares (RSS).

Described residual sum of squares (RSS) RSS can be expressed as:

$\mathrm{RSS}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(y_j-y_j^{\′})}^2---\left(9\right)$

In formula, y _jbe j experimental data, y ' _jbe j model emulation value, the zero input response data amount check that n is battery terminal voltage.

Concrete, according to formula (5), the residual sum of squares (RSS) RSS of battery terminal voltage can be expressed as:

$\mathrm{RSS}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(U_{\mathrm{bat},j}-U_{\mathrm{bat},j}^{\′})}^2---\left(10\right)$

In formula, U _{bat, j}be j experimental data, U _{bat, j}' be j the estimated value based on least square method, the data amount check of the zero input response that n is battery terminal voltage.

Can be found out by (8), the number that increases model parameter can improve the Optimality of models fitting, and AIC encourages the Optimality of data fitting still to avoid occurring the situation of overfitting as far as possible.So top-priority model should be AIC value minimum that.Akaike information criterion is to find best decryption but the model that comprises minimum free parameter.

3. experiment is set up

Test and emulation for new Taihang 16 and 16 string column type 26650 lithium iron phosphate dynamic batteries in Henan, nominal capacity is 50Ah, and nominal voltage is 51.2V.Battery testing platform is simulated/is tested cabinet, AVL Inmotion hardware by advanced AVL battery and controls software at ring test platform, temperature control box and AVL switch board and AVL Lynx and form.The operating mode values such as voltage, electric current and the SOC of experimental record battery, sample frequency is set to 1Hz.

Consider the difference that discharges and recharges parameter, by HPPC mixed pulses test (Hybrid Pulse Power Characterization Test, HPPC) the mixed pulses test in makes unidirectional pulse test into, i.e. electrokinetic cell pulse charge test and pulsed discharge test.So-called pulsed discharge, under room temperature 25 degree, will be full of electric battery taking the current discharge of 1/3C to SOC as 90%, and stopping discharging leaves standstill 1h, is then 80% taking same current discharge to SOC, by that analogy, until SOC finishes while being 10%.Pulse charge process and process of pulse discharge are similar, do not repeat them here.

4. model order and parameter identification

As shown in Fig. 3～Fig. 5, for the RC network of different rank is simulated the overpotential characteristic comparison of ferric phosphate lithium cell in the time that SOC is respectively 10%, 50% and 90%.Can find out, the exponent number of RC network is higher, matching just better.In the time that SOC is 50%, from Order RC network to three rank RC network, its error of fitting changes little, but in the time that SOC is 10% or 90%, single order and Order RC network error of fitting are larger, and three rank RC network matchings is better.But although single order or the Order RC model accurately static and dynamic performance of simulated battery simple in structure; Though three rank and the more accurately static and dynamic performance of simulated battery of above RC model, but can not be applied to well in practice because of very complicated.In other words, the RC model of fixing exponent number can not reach balance in model complexity and estimated accuracy.Therefore, proposition should take to become the RC model of exponent number.

Can be found out by formula (5), single order, second order, three rank RC models have respectively 3,5,7 unknown parameters.The zero input response of the different SOC place battery terminal voltage obtaining according to experiment calculates the residual sum of squares (RSS) of the RC models fitting of different rank, calculates AIC value corresponding to the different model parameters of different SOC (exponent number), as shown in Figure 6.According to AIC " stingy principle ", should choose minimum AIC value.As can be seen from Table 1, under different SOC, adopt the obtainable minimum AIC value of RC model (46512.9) of different rank as benchmark.Therefore, in the time that being 10%, SOC should select three rank RC models; In the time that being 50%, SOC should select Order RC model; In the time that being 90%, SOC should select three rank RC models.This is also with above consistent to the analysis of Fig. 3～Fig. 5.While more than just getting respectively 10%, 50% and 90% for SOC, analyzing, is 20%, 30% at SOC, 40%, 60%, 70% and analytical approach 80% time similar to the above, do not repeat them here, by can be calculated, SOC is 20%, 30%, and 40%, 60%, 70% and also should select Order RC model 80% time.Can be by described change-over switch Q ₁, S ₁, Q ₂, S ₂closed or turn-off the change exponent number RC model of realizing according to SOC.

AIC value corresponding to the different model parameters of the different SOC of table 1

On the basis of model order identification, utilize formula (3)～(6), can identification obtain becoming all parameters of filling, putting direction of exponent number RC model based on least square method at different SOC place.

5. open-circuit voltage OCV model

According to above different SOC (10%, 20% ..., 90%) locate charging open-circuit voltage and electric discharge open-circuit voltage that matching obtains, averaged under identical SOC, obtains the open-circuit voltage OCV of battery, as shown in Figure 7.And according to formula (2), application Matlabcftool tool box can pick out parameter a ₁～a ₅, as shown in table 2.

Table 2 is applied formula (2) parameter that Matlabcftool Fitting Toolbox obtains

Parameter	a 1	a 2	a 3	a 4	a 5
						Value	3.377	0.06551	-0.0003054	3.468e-06	-0.03636

6. experimental verification

In order to verify the accuracy of battery model, need carry out constant current charge-discharge, pulse to battery and discharge and recharge (simulating/test cabinet by AVL battery completes) and the test of self-defined UDDS state of cyclic operation (simulating/test cabinet and AVL Inmotion hardware completes at ring test platform by AVL battery).As shown in Fig. 8～12, be respectively constant current charge-discharge, pulse discharge and recharge with self-defined UDDS state of cyclic operation under the battery terminal voltage test findings that obtains and the contrast of model emulation result.

Can find out from Fig. 8～9, the change exponent number RC equivalent-circuit model pulse charge and discharge process of reaction cell well based on AIC criterion the utility model proposes, illustrates that this model is accurately.Than the error producing at quiescent phase more greatly, this is that the experimental data using is the zero input response of battery terminal voltage because when model of fit parameter to the error producing in the constant current charge-discharge stage.On the whole, the error that leaves standstill stage battery is almost nil, and the maximum error that discharges and recharges stage battery is less than 0.02V.

As shown in Figure 10～11, in constant current charge-discharge process, electrokinetic cell is discharging and recharging the initial stage, battery equivalent-circuit model terminal voltage and experiment value differ larger, this is because the discharging and recharging from empty battery and full battery of electrokinetic cell, be charged to SOC and be 10% or when being put into SOC and being 90% battery there is larger polarizing voltage, and in this experiment, model is 10% to start when charging or SOC are 90% to start to discharge from SOC, polarizing voltage is zero, therefore produce larger voltage difference.As shown in figure 12, for self-defined UDDS state of cyclic operation drag simulation value, experiment value and relative error thereof, can find out between simulation result and experimental data and have good consistance, the error that little electric current discharged and recharged and left standstill stage battery is less.Increase to some extent at high-multiplying power discharge time error, main cause is that the equivalent circuit parameter of battery, with the variation of electric current, certain change occurs.All in all, maximum error is in 0.04V.

Can be found out by above comparing result, the simulation result that the change exponent number RC equivalent-circuit model the utility model proposes obtains meets experimental data substantially, maximum error is in 0.04V, and the visible realistic model of setting up is that reasonably it is the dynamic and static characteristic of simulated battery well.And be applicable to constant current charge-discharge, pulse discharges and recharges the state of cyclic operation with UDDS.For the emulation of electric automobile and mixed electric automobile is laid a good foundation.

By reference to the accompanying drawings embodiment of the present utility model is described although above-mentioned; but the not restriction to the utility model protection domain; one of ordinary skill in the art should be understood that; on the basis of the technical solution of the utility model, those skilled in the art do not need to pay various amendments that creative work can make or distortion still in protection domain of the present utility model.

Claims (7)

1. the change exponent number RC equivalent-circuit model based on AIC criterion, it is characterized in that: comprise circuit and I-V characteristic circuit working time, wherein, I-V characteristic circuit comprises two-way branch road, each branch road comprises three groups of electric capacity and a RC loop that resistance composes in parallel, and two groups of RC loops of each branch road are parallel with change-over switch; Described working time, circuit comprised the self discharge resistance R of battery _d, capacitor C _qwith CCCS circuit, resistance R _dwith capacitor C _qbe connected in parallel on the controlled source two ends of CCCS, one end ground connection of independent current source.

2. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, is characterized in that: described I-V characteristic circuit comprises ohmic internal resistance R ₀, activation polarization internal resistance R ₁, activation polarization capacitor C ₁, concentration polarization internal resistance R ₂, concentration polarization capacitor C ₂, become exponent number internal resistance R ₃, become exponent number capacitor C ₃, change-over switch Q ₁, S ₁, Q ₂, S ₂with CCCS, Voltage-controlled Current Source circuit, wherein:

The positive pole of the controlled source of Voltage-controlled Current Source circuit connects two-way, and a road connects diode D _drear contact resistance R _1d, resistance R _2d, resistance R _3d, resistance R _odthe positive pole of rear connection battery, a road reversal connection diode D _crear contact resistance R _1c, resistance R _2c, resistance R _3c, resistance R _octhe positive pole of rear connection battery, capacitor C _1dbe connected in parallel on resistance R _1dtwo ends, change-over switch Q ₂and capacitor C _2dbe connected in parallel on resistance R _2dtwo ends, change-over switch Q ₁and capacitor C _3dbe connected in parallel on resistance R _3dtwo ends, capacitor C _1cbe connected in parallel on resistance R _1ctwo ends, change-over switch S ₂and capacitor C _2cbe connected in parallel on resistance R _2ctwo ends, change-over switch S ₁and capacitor C _3cbe connected in parallel on resistance R _3ctwo ends, the voltage between the controlled source positive and negative electrode of Voltage-controlled Current Source circuit is battery open circuit voltage OCV.

3. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, it is characterized in that: described working time, circuit and I-V characteristic circuit were set up contact by a Flow Control current source and a voltage controlled voltage source, in the time that battery is discharged and recharged, load current i _batby Flow Control current source to capacitor C _qdischarge and recharge, change C _qthe electric weight of storage, the variation of characterizing battery SOC, C _qboth end voltage OCV also changes thereupon, and the voltage controlled voltage source OCV of I-V characteristic circuit changes with the variation of SOC.

4. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, is characterized in that: described change-over switch Q ₁, S ₁and Q ₂, S ₂while all disconnection, becoming exponent number RC model is three rank RC models; Described change-over switch Q ₁, S ₁closure, Q ₂, S ₂when disconnection, becoming exponent number RC model is Order RC model; Described change-over switch Q ₁, S ₁closure, Q ₂, S ₂also, when closed, becoming exponent number RC model is single order RC model.

5. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, is characterized in that: described capacitor C _qrepresent the active volume of battery, C _q=3600C _ahf ₁f ₂, C _ahfor the battery capacity that is unit by ampere-hour, f ₁and f ₂it is respectively the modifying factor of battery cycle life and temperature.

6. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, is characterized in that: the end current i that the electric current of the controlled source of described CCCS is battery _bat, load current i in the time that battery discharges and recharges _batby CCCS to capacitor C _qdischarge and recharge, change capacitor C _qthe electric weight of middle storage, thereby the variation of characterizing battery SOC.

7. a kind of change exponent number RC equivalent-circuit model based on AIC criterion as claimed in claim 1, it is characterized in that: the voltage at the controlled source two ends of described CCCS is battery open circuit voltage OCV, there is nonlinear relationship in described open-circuit voltage OCV and SOC, physical relationship formula is:

$\mathrm{OCV}=a_1+a_2\ln \mathrm{SOC}+a_3\ln (1-\mathrm{SOC})+\frac{a_4}{\mathrm{SOC}}+a_5\mathrm{SOC}---\left(1\right)$

In formula, a ₁～a ₅for constant, obtained based on least squares identification by experimental data.