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Comparison study on the battery models used for the energy management

Comparison study on the battery models used for the energy management
Comparison study on the battery models used for the energy management

Comparison study on the battery models used for the energy management of batteries in electric vehicles

Hongwen He ?,Rui Xiong,Hongqiang Guo,Shuchun Li

National Engineering Laboratory for Electric Vehicles,School of Mechanical Engineering,Beijing Institute of Technology,South No.5Zhongguancun Street,Beijing 100081,China

a r t i c l e i n f o Article history:

Received 10February 2012

Received in revised form 8April 2012Accepted 17April 2012

Available online 24September 2012Keywords:

Battery models

Lithium-ion battery Electric vehicles Experiment

Battery management system

a b s t r a c t

Battery model plays an important role in the simulation of electric vehicles (EVs)and states estimation of the batteries in the development of the model-based battery management system.To build a battery model with enough precision and suitable complexity,?rstly this paper summarizes the seven represen-tative battery models,which belong to the simpli?ed electrochemical models or the equivalent circuit models.Then the model equations are built and the model parameters are identi?ed with an online parameter identi?cation method.The battery test bench is built and the experiment schedule is designed.Finally an evaluation is performed on the seven battery models by an experiment approach from the aspects of the estimation accuracy of the terminal voltages.To evaluate the effect of the number of RC networks on the model’s precision,the battery general equivalent circuit models (GECMs)with different RC networks are also discussed further.The results indicate the equivalent circuit model with two RC net-works,the DP model,has an optimal performance.

ó2012Elsevier Ltd.All rights reserved.

1.Introduction

Energy is the basis of the human survival and development,it’s urgent to develop green energy and use the nonrenewable energy rationally.Since transportation consumes a large part of energy,to develop and apply the electric vehicles (EVs)is necessary in the way of green mobility [1–4].Power battery is the key component of EVs,which include battery electric vehicles (BEVs),hybrid elec-tric vehicles (HEVs)and plug-in hybrid electric vehicles (PHEVs).To ensure the power battery work safely and reliably,which is functioned by the battery management system (BMS)[5–7],the temperature,voltage,current of the batteries should be monitored and the states of the batteries should be estimated precisely in real time.However,it is hard to measure the states of batteries,like state of charge (SoC),state of health (SoH),state of function (SoF)directly for the complicated electrochemical process and various in?uence factors from the practice application,the estimation method based on battery models is used broadly and the battery model plays an important role [8–15].

Many battery models,which are lumped models with relatively few parameters,have been put forward especially for the purpose of vehicle power management control and battery management system development.The most commonly used models can be summarized as two kinds:the electrochemical models and the equivalent circuit models [9,15–21].The electrochemical models utilize a set of coupled non-linear differential equations to describe the pertinent transport,thermodynamic,and kinetic phenomena occurring in the cell.They are relatively straight forward to trans-late the distributions into easily measurable quantities such as cell current and voltage,and build a relationship between the micro-scopic quantities,such as electrode and interfacial microstructure and the fundamental electrochemical studies and cell performance [22].However,they typically deploy partial differential equations (PDEs)with a large number of unknown parameters,which often leads to a large memory requirement and a heavy computation burden,so the electrochemical battery models are not desirable for actual BMS (battery management system)[23]and the simpli-?ed electrochemical models,which ignore the thermodynamic and quantum effects,are proposed to simulate the electrochemical and voltage performance.The Shepherd model,the Unnewehr Universal model,the Nernst model and the Combined model are the typical representatives.The equivalent circuit battery models are devel-oped by using resistors,capacitors and voltage sources to form a circuit network.Typically,a big capacitor or an ideal voltage source is selected to describe the open-circuit voltage (OCV),the remain-der of the circuit simulates the battery’s internal resistance and relaxation effects such as dynamic terminal voltage.The Rint mod-el,the Thevenin model,the DP model and their revisions are widely used.

For the modeling and simulation of EVs and the development of the model-based BMS,the ?rst important thing is to select and build a suitable battery model.How to evaluate and get a compro-mise in the balance of complexity and accuracy of the battery

0196-8904/$-see front matter ó2012Elsevier Ltd.All rights reserved.https://www.doczj.com/doc/861475890.html,/10.1016/j.enconman.2012.04.014

Corresponding author.Tel./fax:+861068914842.

E-mail address:hwhebit@https://www.doczj.com/doc/861475890.html, (H.He).

model is one of the key technologies,and also the problem to be discussed and solved in this paper.

2.Battery models and parameters identi?cation method

2.1.The battery models

The equivalent circuits of the Rint model,the Thevenin model and the DP model are shown in Fig.1.The equations and features of the seven representative battery models mentioned before are summarized and listed in Table1.

Where U t is the terminal voltage;K0,K1,K2,K3,K4are constants chosen to make the model?t the data well;I L is the load current;R o is the internal resistance;z s is the abbreviation for SoC;U oc is the open-circuit voltage;R p is the equivalent polarization resistance and C p is the equivalent polarization capacitance to model the bat-tery relaxation effect during charging and discharging;U p is the voltages across C p;I p is the out?ow current of C p;R1,R2are the effective resistances and C1,C2are the effective capacitances used to model the polarization characteristic in more details;U1and U2 are the voltages across C1and C2respectively.

2.2.Model parameters’identi?cation

The models’parameters identi?ed by the traditional of?ine identi?cation method maybe exit errors inevitably which caused by internal and external factors such as battery operating environ-ment and aging,thus the accuracy will decrease.To solve these problems,we choose an online parameter identi?cation method instead based on the recursive least squares(RLSs)method with an optimal forgetting factor.

2.2.1.The recursive least squares method with an optimal forgetting factor

A model-based method can provide a cheap alternative in esti-mation or it can be used along with a sensor-based scheme to pro-vide some redundancy.The RLS method with an optimal forgetting factor(RLSF)has been widely used in estimation and tracking of time varying parameters in various?elds of engineering.Many successful implementations of RLSF-based adaptive control for time varying parameters estimation are available in the literature [26–28].

We would like to apply the RLSF method in the prediction of battery terminal voltages with an online parameters’identi?cation of the battery models.Consider a single input single output(SISO) process described by the general higher order auto-regressive exogenous(ARX)model:

y

k

?u k h ktn ke1Twhere y is the system output,which denotes the terminal voltage U t in this paper.u and h are the information vector and the unknown parameter vector respectively.The parameters in h can either be constant or subject to infrequent jumps.n is a stochastic noise var-iable(random variable with normal distribution and zero mean), and k denotes the sample interval,k=0,1,2,...

Table1

Battery models and key features.

Classi?cation Models Model equations and Features

Simpli?ed electrochemical battery models[9]1-Shepherd model U t=K0àR o I L+K1/z s

The model describes the electrochemical behavior of the battery directly in terms of voltage and current

2-Unnewehr

Universal Model

U t=K0àR o I L+K2z s

The model simpli?es the Shepherd model and attempts to model the variation in resistance with respect to SoC 3-Nernst model U t=K0àR o I L+K3ln z s+K4ln(1àz s)

The model can be viewed as a modi?cations to the Shepherd model and uses exponential function with respect

to SoC

4-Combined model U t=K0àR o I L+K1/z s+K2z s+K3ln z s+K4ln(1àz s)

The model can be viewed as a combination of the previous three models to obtain the most accurate

performance

Equivalent circuit battery models 5-Rint model[24]U t=U ocàI L R o

6-Thevenin model

[25]

_U

p

?I L

C p

àU p

R p C p

U t?U/àU pàI L R o

(

The model connects a parallel RC network in series based on the Rint model,describing the dynamic

characteristics of the battery[25]

7-DP model[21]_U

1

?àU1

11

tI L

1

_U

2

?àU2

R2C2

tI L

C2

U t?U/àU1àU2àI L R o

8

><

>:

The model connects a parallel RC network in series based on the Thevenin model,in order to re?ne the

description of polarization characteristics and simulate the concentration polarization and the electrochemical

polarization separately which may leads to a more accurate performance

114H.He et al./Energy Conversion and Management64(2012)113–121

Then the system identi?cation is realized as follows [28].

K k ?P k à1u T

k k tu T k P k à1u k P k ?P k à1àK k u T k P k à1

k e k ?y k àu k ^h k à1^

h k ?^

h k à1tK k e k 8

>>>>>><>>>>>>:e2T

where ^h k is the estimate of the parameter vector h k ;e k is the predic-tion error of the terminal voltage;K k is the algorithm gain and P k is the covariance matrix;the constant k is the forgetting factor,typi-cally k e [0.95,1]and is very important to obtain a good estimated parameter set with small error.

2.2.2.Parameters’identi?cation

The simpli?ed electrochemical model in discrete form can be rewritten in the form of the ARX model,and then use the RLSF-based method to carry out parameter identi?cation.While for the equivalent circuit model,there need to get a discrete form of the dynamic equations ?rst,then use the RLSF-based method to carry out parameter identi?cation.

Considering the bilinear transformation method can keep the dynamic characteristics of the system well,we adopt this method to discretize the dynamic equations.

The electrical behavior equation shown in Table 1for the Thevenin model can be rewritten as follows in the frequency domain.

U t es T?U oc es TàI L es TR o t

R p

1tR p C p s

e3T

De?ne E t =U t àU oc ,the transfer function G (s )of Eq.(3)can be written as follows.

G es T?

E t es TI L es T?àR o àR p 1tR p C p s

?àR o tR p tR o R p C p s

1tR p C p s e4T

A bilinear transformation method shown in Eq.(5)is employed for the discretization calculation of Eq.(4)and the result is shown in Eq.(6).

s ?

2T s 1àz à11tz à1

e5T

where z is the discretization operator and T s is the sample interval.Herein,T s is 1s.

G ez à1

T?à

a 2ta 3z à1

1àa 1z à1

e6T

De?ne:

a 1?à1à2R p C p

1t2R p C p a 2?àR o tR p t2R o R p C p

1t

2R p C p

a 3?àR o tR p à2R o R p C p

p p

8>>>>><

>>>>>:e7T

Then the model parameters can be solved according to the uni-ted equations of a 1,a 2and a 3.Ref.[11]concludes the model’s parameters can be viewed as a constant value in limited sample intervals,then:

_U

oc %0)U oc ;k %U oc ;k à1e8T

Similarly,the _R o %0holds since the sampling period is rela-tively small,and then,

U t ;k ?e1àa 1TU oc ;k ta 1U t ;k à1ta 2I L ;k ta 3I L ;k à1e9T

Similarly,the DP model can be discretized with the bilinear method,and then:

U t ;k ?e1àb 1àb 2TU oc ;k tb 1U t ;k à1tb 2U t ;k à2tb 3I L ;k

tb 4I L ;k à1tb 5I L ;k à2

e10T

where b 1,b 2,b 3,b 4and b 5are the coef?cient which contain model’s

parameters,and the detailed recursion solution equations for the above seven models are listed in Table 2.

Where u i ,k is the information matrix and h i ,k is the unknown parameter matrix of the i th model,i =1,2,3,...,7.3.Experiments and data sampling

In order to sample the measurement data from the sensors to perform the model parameters’identi?cation and the performance evaluation on the battery models,the battery test bench is built and the experiment schedule is designed.3.1.Battery test bench

The test bench is shown in Fig.2,which consists of a Digatron battery test system BNT 400-050,a thermal chamber for environ-ment control,a host computer and BTS-600interface for program-ming the BNT 400-050.The host computer is used for the real-time calculation of the model parameters.The BNT 400-050can charge/discharge a battery according to the designed program with max-imum voltage of 50V and maximum charge/discharge current of 400A,and its recorded data include current,voltage,temperature,accumulative amp–hours (A h)and watt–hours (W h),etc.The measured data is transmitted to the host computer through TCP/IP driven by BNT 400-050.The host computer has a low-pass ?ltering function to implement large noise cancellation [15].Furthermore,in order to improve the sampling precision of cell voltage,the Fluke 8846A multimeter,whose measurement accu-racy of DC voltage is up to 0.0024%with a 6.5digit resolution,has been applied for cell voltage measurement [29].A LiFePO 4cell with nominal voltage of 3.2V and nominal capacity of 10A h is selected as the test object.3.2.Battery test schedule

The battery is kept in the thermal chamber and the temperature is controlled within 20±5°C.The battery text schedule is designed

Table 2

The detailed recursive equations of the battery models.Battery models

Recursion equations 1-Shepherd model

y k ?U t ;k

u 1;k ??1àI L ;k 1=z s ;k h 1;k ??E 0;k R o ;k K 1;k T 8

<:

2-Unnewehr Universal Model y k ?U t ;k

u 2;k ??1àI L ;k 1=z s ;k h 2;k ??E 0;k R o ;k K 2;k T 8

<:

3-Nernst model

y k ?U t ;k

u 3;k ??1àI L ;k ln z s ;k ln e1àz s ;k T h 3;k ??E 0;k R o ;k K 3;k K 4;k T 8

<:

4-Combined model

y k ?U t ;k

u 4;k ??1àI L ;k 1=z s ;k z s ;k ln z s ;k ln e1àz s ;k T h 4;k ??E 0;k R o ;k K 1;k K 2;k K 3;k K 4;k T 8

<:

5-Rint model

y k ?U t ;k

u 5;k ??1I L ;k h 5;k ??U oc ;k àR o ;k T 8

<:

6-Thevenin model

y k ?U t ;k

u 6;k ??1U t ;k à1I L ;k I L ;k à1 h 6;k ??e1àa 1TU oc ;k a 1a 2a 3 T 8

<:

7-DP model

y k ?U t ;k

u 7;k à1??1U t ;k à1U t ;k à2I L ;k I L ;k à1I L ;k à2 h 7;k ??e1àb 1àb 2TU oc ;k b 1b 2b 3b 4b 5 T

8

<:

H.He et al./Energy Conversion and Management 64(2012)113–121115

and shown in Fig.3,which includes a characteristic test and an aging cycle test followed.For the characteristic test,the available capacity test is based on the standard of[30]to measure the max-imum available https://www.doczj.com/doc/861475890.html,ually,the available capacity test is re-peated three times.If the error of the experiment results between the maximum and the average is within2%,the available capacity test is effective and the average value is taken as the actual maxi-mum available capacity;however,if the error is more than2%,the available capacity test should be repeated.The HPPC test is from the Battery Test Manual[31]and is the foundation of power bat-tery characteristic test and parameter identi?cation test,which achieves good results in off-line parameter identi?cation and is used widely.The Dynamic Stress Test(DST)and the Federal Urban Dynamic Schedule(FUDS)test are the commonly used test proce-dures of Digatron[32].The FUDS is a standard time-velocity pro?le for urban driving vehicles and has been widely used in the evalu-ation of model accuracy and SoC estimate of battery management system.For the driving-cycle testing of USABC batteries,a simpli-?ed version of the FUDS test is modi?ed into the Dynamic Stress Test(DST).For the FUDS test,the DST test and the HPPC test,the battery SOC is controlled in the range of0.25–1.0,0.2–1.0and 0–1.0respectively.

3.3.Data of the battery experiment

In this paper,the data collected in the characteristic test of a fresh cell are arranged for the model parameters’identi?cation and model evaluation.

For the LiFePO4cell,the available capacity test shows that its actual maximum available capacity is10.78A h,slightly higher than10A h of the nominal capacity.The HPPC test results are shown in Fig.4including a sample HPPC current curve,a sample HPPC voltage curve under SoC=0.8,the current pro?les,the volt-age pro?les and the SoC pro?les.The DST test results are shown in Fig.5including the current vs.time pro?les and the SoC vs.time pro?les.The FUDS test results are shown in Fig.6including the SoC pro?les and one sample current pro?le of one FUDS cycle.

Due to the hard determination of the exact SoC value,here we determine the initial SoC and the terminal SoC of the LiFePO4lith-ium-ion battery according to the de?nition of SoC with a standard charging experiment and a further standard discharging experi-ment after?nishing a test,so the initial SoC and the terminal SoC are accurate.The ampere–hour counting approach is used to calculate the SoC since it can keep track of the accurate SoC with an accurate initial SoC and a compensation of the coulombic ef?-ciency.We also improve the SoC accuracy with a revision method based on the accurate terminal SoC.Considering all the battery experiments are carried out in a temperature chamber;the SoC calculation method is feasible with an acceptable accuracy.

4.Evaluation and discussion on the battery models

To evaluate the battery models rationally and objectively,an evaluation method is built?rst.Then the performances of the seven battery models are compared by the RLSF-based method. And the effect of the different RC networks of the equivalent circuit models are also discussed by a comparison of the terminal voltage estimation accuracy.

4.1.Evaluation method

To evaluate the battery models well,the online voltage estima-tion is performed with the HPPC test,the DST test and the FUDS test.Further,a statistics of the voltage error is analyzed in the as-pects of the maximum,the minimum,the mean,the maximum of the RMSE(the root mean square error)and the mean of the RMSE. The voltage error denotes the difference between the experimental data and online estimated value.The RMSE denotes the deviation degree of the estimated value and the experimental value,which not only shows the present error,but also indicates the conver-gence of the estimation algorithm.

4.2.Evaluation analysis on the battery models

The evaluation results of the seven battery models under the HPPC test are shown in Fig.7,including the statistics results of the voltage errors,the statistics results of the RMSE,the voltage pro?les of model-based estimation with the representatives of the Shepherd model,the Nernst model,the DP model and the HPPC test.Fig.7a shows that6-Thenenin model and7-DP model have smaller voltage errors,the mean of the voltage error of the simpli-?ed electrochemical models are also small.For1-Shepherd model and3-Nernst model,the maximum of voltage errors or the absolute value of the minimum of voltage errors are bigger than others. Fig.7b shows that the RMSE of the seven models is less than 25mV and is within1%of the cell’s nominal voltage,that means the online parameter identi?cation method is effective.Just like the results of Fig.7b,6-Thevenin model and7-DP model have smal-ler RMSE values and is better than the other?ve models under the HPPC test,since they takes the cell’s relaxation effect into account for modeling.The fact,that5-Rint model exists a big estimation er-ror for the ignorance of the battery’s dynamic voltage performance, indicates it is necessary to consider the voltage relaxation effect to

116H.He et al./Energy Conversion and Management64(2012)113–121

improve the precision of the models for lithium-ion battery.Fig.7c shows that the estimated voltages based on1-Shepherd model nearly follow the test data except for the terminals where the SoC is nearly zero and the battery seldom works.Fig.7b shows that 1-Shepherd model has higher precision than3-Nernst model,that can also be veri?ed from the fact,that the estimated voltage based on3-Nernst model is higher than the experimental data at the end of the test and also a bigger voltage error of3-Nernst model exists as shown in Fig.7c.Fig.7d shows that the terminal voltage esti-mated by7-DP model agrees quite well with the experimental value.Based on the above analysis,it can be concluded that the DP model has the best dynamic voltage simulation performance among the seven battery models.

The evaluation results of the seven battery models under the DST test are shown in Fig.8including the statistics results of the voltage errors,the statistics results of the RMSE.Fig.8a shows that 1-Shepherd model,6-Thevenin model and7-DP model have good online estimation precision with small voltage errors.Fig.8b shows that6-Thevenin model and7-DP model have a relatively small RMSE,especially the7-DP model.There can conclude that

H.He et al./Energy Conversion and Management64(2012)113–121117

the DP model is the most outstanding model among the seven models,followed by 6-Thevenin model.This result agrees with the HPPC test.In Fig.9,we choose two pro?les in the DST test to describe the estimate accuracy between the estimated voltage by the DP model and the experiment data.It indicates that the DP model can simulate the battery’s dynamic voltage performance very well under the DST test,which fully satis?es the development requirements of model-based BMS used in the EVs.

The evaluation results of the seven battery models under the FUDS test are shown in Fig.10including the statistics results of the voltage errors,the statistics results of the RMSE,the RMSE pro-?les of the four speci?c battery models,the voltage pro?les of the DP model-based estimation and FUDS test data.Fig.10a shows that the two models,6-Thevenin model and 7-DP model,both of them take the polarization characteristics into consideration,have a smaller voltage error compared with other models.Also,Fig.10b indicates that the mean of the RMSE of 6-Thevenin model and 7-DP model is the smallest.But the maximum of the RMSE of the Thevenin model is bigger than 1-Shepherd model and 2-Unnewehr Universa l https://www.doczj.com/doc/861475890.html,bined Fig.10a and b,we can conclude that the DP model has a higher precision than other six models surely.However,to determine if 6-Thevenin is the second better model de-pends on the RMSE pro?le additionally.Fig.10c intuitively indi-cates that 6-Thevenin model and 7-DP model restrain themselves

to approach the true values faster,so they have smaller mean of

the RMSE,while 1-Shepherd model and 2-Unnewehr Universal mod-el maintain themselves above 10mV without a convergent ten-dency;The maximum of the RMSE of 6-Thevenin model is bigger than that of 1-Shepherd model and 2-Unnewehr Universal model.But for the convergent tendency,6-Thevenin model is more stable,and the voltage error is less than 1-Shepherd model and 2-Unnewehr Universal model,so it can be determined that 6-Thevenin

118H.He et al./Energy Conversion and Management 64(2012)113–121

model is the second better model.Therefore,in the FUDS test,the DP model still has the most outstanding performance,followed by the Thevenin model;we can conclude that it is reasonable to re?ne the lithium-ion battery’s voltage relaxation effect to improve the model-based estimated precision.

The evaluation results of the HPPC test,the DST test,the FUDS test come to one conclusion that the Thevenin model and the DP model are more accurate than the other?ve models ow-ing to their considerations of the voltage relaxation effect to some extent.After re?ning the polarization characteristics,the accuracy of the DP model gets a signi?cant improvement com-pared with the Thevenin model by connecting an additional RC network,does it mean that it will improve the model accuracy by connecting enough RC networks in series?We will discuss this next.

4.3.Discussions

The above evaluation results show that the equivalent circuit models considering the voltage relaxation effect have better per-formance than the other models,and the DP model with two RC networks has better dynamic voltage estimation precision than the Thevenin model with one RC network.In order to give a further study of the RC networks on the model accuracy,the battery gen-eral equivalent circuit model(GECM)with n RC networks is pro-posed as shown in Fig.11.

Where C i is the i th equivalent polarization capacitance and R i is the i th equivalent polarization resistance simulating the transient response during a charge or discharge process,U i is the voltage across C i.i=1,2,3,4,...,n.

The electrical behavior of the GECM model can be expressed by Eq.(11)in the frequency domain.

U tesT?U ocesTàI LesTR ot

R1

1tR1C1s

tááát

R n

1tR n C n s

en?0;1;2;...Te11TSimilarly with the Thevenin model and the DP model,the GECM model can be discretized with the bilinear method[33],and then:U t;k?1à

X n

i?1

c i

!

U oc;ktc1U t;kà1tc2U t;kà2tááátc n U t;kàn tc nt1I L;ktc nt2I L;kà1tááátc2nt1I L;kàne12Twhere c i(i=1,2,...,2n+1)are the coef?cient which contain mod-el’s parameters such as polarization capacitance,polarization resis-tance and open-circuit voltage

De?ne:

u

n;k

??1U t;kà1U t;kà2áááU t;kàn I L;kà1I L;kà2áááI L;kàn

h n;k?1à

X n

i?1

c i

!

U oc;k c1c2c3ááác2nt1

"#T

8

>><

>>:

e13TThen the online parameters’identi?cation matrix of the GECM model is built.

Considering the model complexity,when the number of the RC networks n is more than5,a big error will arise from the linear dis-crete method.However,if other non-linear parameters’identi?ca-tion method is used such as the Kalman?lters,there will cause a huge computing costs due to the complex model structure.So the evaluation tests are only conducted for the GECM models with n=1–5and the results are shown in Fig.12.

Fig.12shows that for the HPPC test,the DST test and the FUDS test,the maximum of the absolute voltage errors is within32mV

H.He et al./Energy Conversion and Management64(2012)113–121119

and the maximum of the RMSE is less than15mV.Fig.12a shows that for the HPPC test,the GECM model with one RC network has the biggest voltage error,while the GECM model with two RC net-work performs best,but the mean of voltage error is not signi?cant compared with the GECM model with three,four,?ve RC networks. Fig.12b shows that the statistics of the RMSE are less than1mV, and the GECM model with two RC networks is the best.Fig.12c shows that the GECM model with two RC networks has the small-est statistics values among the?ve models for the DST test; Fig.12d shows the GECM model with two RC networks has the smallest mean of the RMSE while its maximum of the RMSE is big-ger than the GECM model with?ve RC networks.However,the GECM model with two RC networks is simpler than that with?ve RC networks and is still the nest battery model after considering the practical applications.

Fig.12e and f shows that for the FUDS test,the maximum of the voltage error of the GECM model with?ve RC networks performs better than the GECM model with two RC networks,However the GECM model with two RC networks performs the best in the abso-lute minimum,the mean of the voltage errors and statistics values of the RMSE.It can be concluded that the GECM model with two RC networks still shows the best performance.

In summary,the GECM model with two RC networks,also called the DP model,is the best model for the lithium-ion battery simula-tion.Further,it does not mean that the more RC networks the mod-el has,the more accurate the model is.On the contrary,the performance of the GECM model with more than three RC net-works becomes worse in some aspects.

5.Conclusion

This paper carries out a systematic evaluation on the seven typ-ical battery models based on the HPPC test,DST test,FUDS test,and the GECM model with different RC networks is discussed further. Main conclusions are summarized as follows:

(1)The Seven commonly used battery models:Shepherd model,

Unnewehr Universal model,Nernst model,Combined model, Rint model,Thevenin model,and the DP model are summa-rized,the model equations are deduced and the model parameters’identi?cation method is designed based on the recursive least squares method with an optimal forgetting factor.

(2)The battery test bench is built and the experiment schedule

is designed,which includes a characteristic test and an aging cycle test followed.The online identi?cation process is con-ducted under the HPPC test,the DST test,the FUDS test for a LiFeO4lithium-ion battery.

(3)An evaluation method of the battery models is proposed and

the evaluation results show that the voltage relaxation effect of the lithium-ion battery cannot be ignored,the Thevenin

120H.He et al./Energy Conversion and Management64(2012)113–121

model and the DP model both have good dynamic perfor-mance,and the DP model performs much batter for its more re?ned simulation of the voltage relaxation.

(4)A further discussion on the GECM model with different RC

networks indicates that the GECM model with two RC net-works,also called the DP model,is the best model for the lithium-ion battery simulation.The performance of the GECM model with more than three RC networks will become worse in some aspects.

We can conclude that the DP model shows the best perfor-mance among the seven commonly used models through our com-prehensive comparison.The DP model performs the best in the DST test,which further proves that the DP model is suitable for the development of model-based BMS used in EVs. Acknowledgements

This work was supported by the National High Technology Research and Development Program of China(2011AA112304, 2011AA11A228,2011AA1290)in part,the International Coopera-tion Research Program of Chinese Ministry of Science and Technol-ogy(2010DFB70090,2011DFB70020)in part and also the research foundation of National Engineering Laboratory for Electric Vehicles in part.The author would also like to thank the reviewers for their corrections and helpful suggestions.

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