Battery Modeling Based on the Co

Shaohua Lin and Scott StantonANSYS Inc., Canonsburg, PA 1531

eric.lin@ansys.com, scott.stanton@ansy

Unive

Abstract—A new battery model by couplingand computational fluid dynamics (CFD) provides the insight of electrical performantemperature distribution of a battery pacpotentially suitable for hybrid electric vehiclvehicle (EV) battery modeling because of thehigh temperature nature of these applications

Hybrid vehicle (HEV) and electric vehifuture trend for automotive industry. Tintensive research in the related areas and has been one of the hottest topics. Models usually divided in two types: 1) physics thermal management simulation 2) electricfor system level simulation. Each type has cons. Computational fluid dynamics (CFDbeen well known for battery pack thermal [2]. The advantage of CFD is that it can athe temperature distribution based on the hboundary conditions, geometry, material prodrawback is that it does not have a goodmechanism. Therefore usually over-simplifare used to carry out CFD analysis. On the omodels are suitable for system level simulaof the most significant advantages of the that they are very fast in terms of simulatiosimply because they are lumped parameter parameters are curve fitted from lab medrawback is that it lacks of temperature dimakes it impossible for thermal managemtherefore propose a new battery model that cmodel types, circuit model based on CFDone hand the circuit model provides as a heother hand, realistic battery pack geometry temperature distribution as a function of dmaterial, flow rate, etc. The proposed battersimulated between the circuit model and Within each time step of the co-simugenerated by the circuit model is sent to source. CFD model then uses the heat fromcalculate the temperature distribution, a

oupling of Electrical Circuit and Computation

n 17 ys.com

Wenyu LGeneral Motors Company

Wenyu.lian@

Thomas X.Wu ersity of Central Florida, Orlando, FL 32816

thomas.wu@ucf.edu

g electrical circuit is proposed. It

nce as well as the k. The model is le (HEV)/ electric e high power and s.

icle (EV) are the There has been battery modeling of battery can be based model for cal circuit model its own pros and

D) simulation has management [1],

accurately predict heat or loss input, operties, etc. The

d heat generating fied heat sources other hand, circuit ation [3]-[5]. One circuit models is on speed. This is models and their

easurements. The istribution, which ment design. We combines the two

D calculation. On eat source. On the y is built to study discharging time, ry model is a co-the CFD model.

ulation, the heat CFD as the heat

m circuit model to and the average

temperature of a battery cell is sent as input to the temperature depencircuit model. The circuit model is system level simulator Simplorer implemented in ANSYS CFD simuland timing are handled by a dll modsize of time step used in the co-simurole. We will study the size of timfollowing section.

I. BATTERY M

Let’s first look at a single cell Fig.1.

Figure 1. A single cell battery model. The bthat represents the electrical characteristicsmodel components are temperature dependbattery model in Fluent CFD simulation. Thcell, and the blue object shows the air flow. cell calculated in Fluent CFD simulation wdependent components of the circuit model.

nal Fluid Dynamics

Lian y, Warren, MI 48090

@gm.com

back to the circuit model ndent components of the

implemented in ANSYS and the CFD model is

lator Fluent. Data transfer del written in C code. The ulation plays an important me step in details in the

MODEL battery model shown in

bottom is the circuit schematic s of a battery, and the circuit dent. The top is physics based he green cylinder is the battery The temperature of the battery

will be input to the temperature

978-1-4577-0541-0/11/$26.00 ©2011 IEEE 2622

In Fig.1, the bottom is the circuit represents the electrical characteristics of model is based on Chen’s model [3]. The mtwo parts, one to keep track of the capacity oor SOC and the other to simulate the transthe battery potential as a function of SOC. Iisothermal condition is assumed. In our mmodel components are temperature depeapproach proposed by Gao [4]. The top is tbattery model in CFD simulation. The CFDflow inlet on the left and one pressure outlebattery cell is in the middle of the domain. transfer takes the heat generated by the bSo, this is a standard conjugate heat tranCFD. For such a system, the power dissipaof time to the battery cell is used as the inpuaverage temperature of the battery cell as ais used as the output. Before we run the simto estimate the thermal constant of the systconstant is a function of the geometry, macondition, etc. A constant power load is applcell, then simulate it until the battery’ avereaches its steady state value. The batterysteady state at 1000 second, which is shown

Figure 2. The step response of the single cell modesource is applied to the cell, after about 1000 seconds tsteady state temperature at around 348K. Thereforconstant is about 1000 seconds.

We run the co-simulation using the timsecond, and exchange the average temperatucell and heat dissipated at the beginning obetween the circuit model and the CFD modalso run the co-simulation using time step sand 100 seconds, and exchange the battery htemperature between the circuit and CFD mresults of 25, 50, 70 and 100 seconds aagainst the 1 second results. Fig.3 showaveform of the battery terminal as the bover a resistive load. The voltage starts toreaches 4.25V, then it starts to decreasdischarges to 3.7V in 7000 sec. Let’s obstemperature of the cell, which rises to 332drop. At the end of the discharge, the temperapidly. Going back to Fig. 3, we can find this used as the time step, the difference is wisimulation takes 4 minutes. The time step case takes 2 hour and 30 minutes. Within 1

schematic that a battery. The

model consists of of the battery cell sient behavior of In Chen’s model,

model, the circuit endent using the the physics based D model has one et on the right. A Convection heat attery cell away. nsfer problem in ated as a function ut and the volume a function of time mulation, we need tem. The thermal aterial, boundary lied to the battery rage temperature

y cell reaches its in Fig. 2.

el. An arbitrary heat the battery reaches its re the thermal time

me step size of 1 ure of the battery

of each time step del. Similarly, we ize of 25, 50, 70,

heat and averaged models. Then the are benchmarked ows the voltage attery discharges

o increase until it se. It eventually serve the average 2 K and starts to erature rises very hat if 100 second ithin 1%, and the size of 1 second

1% accuracy, the

speed is about 37.5 times faster usseconds than 1 second. If we use thethe speed of is 9.4 times faster than tof 1 second, for the accuracy within

Figure 3. The voltage discharging curve ofThe battery is discharging through a resistiVolts in 7000 seconds. We run the simulat1,25,50,70, and 100 seconds. The results results of the 1 second time step size, whichstudy. Less than 1% difference is observedsecond, where the voltage changes more rathe process. This is because the larger time sdynamics at the two particular time instancewith respect to 1 second time step result.

Figure 4. The average temperature of the sisecond discharging process. The temperatuthen it starts to decrease. Towards the end temperature increases fairly rapidly. Again25, 50, 70 and 100 second to those of 1 secotemperature is well within 1%. Note that thesecond and 6090 second marked on the avtemperature contour of the battery cell asurrounding air flow will be showed in Fig.5

Similar phenomenon can be obscurve in Fig.4. Note that 25 secontime constant of the single cell constant resistive load discharge stthermal time constant should beaccuracy. For a quick study todischarging phenomenon, 1/10 of tstill provides very good results, wit36 times faster simulation speed in t

sing the time step of 100 e time step of 25 seconds, the speed of the time step 0.5%.

f the single cell battery model. ive load from 4.02 Volts to3.7 ion using the time step size of are benchmarked against the

h is the smallest time step in the d at both 600 second and 6800 apidly comparing to the rest of steps cannot fully catch the fast

es, but the error is less than 1%,

ngle battery cell over the 7000

ure increases till 1000 second, of the discharging process, the n we benchmark the results of ond time step. The difference in ere are two time instances 1890 verage temperature curve. The and the velocity field of the 5 and Fig.6 in the following.

erved for the temperature nd is 1/40 of the thermal

system. Therefore, for tudy, at least 1/40 of the e chosen for excellent get the trend of the

the thermal time constant th the benefits of getting this particular model.

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Figure 5. The temperature distribution of the battery field at 1890 second. The average temperature at this the velocity is about 20 m/s.

Figure 6. The temperature distribution at 6090 stemperature is 326K. Notice that the velocity field is1090 second. This is because we have assumed the fthis case.

An immediate question comes in mind, wsize of 1/40 of the thermal time constant stload is not simply a resistor, and ratherchanging load? In particular, will the 25 ssize that we used in constant resistivsufficiently small to capture the dynamicanother different load condition, which current of 60% duty cycle. The voltagetemperature results are shown in Figs. 7 and

Figure 7. The discharging voltage waveform of 60current. Two locations where the waveform changes rthe plot, the 25 second time step result is well within 1second time step result.

cell and the velocity moment is 332K and

econd. The average s the same as that of flow field is static in

will the time step till be valid if the r it is a rapidly second time step

ve load still be cs? Let’ observe is a pulse train

e waveform and 8, respectively.

0% duty cycle load rapidly are circled on 1% compared to the 1

The results of the time step obenchmarked against those of the 1still well within 1% difference. NoFig. 7, where the load suddenly dynamics cannot be fully captured therefore results in a tiny delay in phenomenon can also be observed of the constant resistive load dobserve the average temperature of The difference is within 1%.

Figure 8: The temperature corresponding toprocess shown in Fig.7. Note that the differethe 25 second curve is within 1%. There iscurve mainly because the larger time step cfully.

In terms of computational simulation takes 4 hours and 30 mithe 25 second time step takes 18 mfaster than that of 1 second time stFigs. 5 and 6 show the temperature system at time instances 1890 seconthat the velocity fields are identicawe have assumed the flow field is sthe flow and turbulence are solved field, and then the flow field is usefor the temperature calculation.

II. SACALIBILITY OF THE PROP

Next we model one 6 cell proposed model. The model is showare connected in series to provide 24

Figure 9. 6 cell battery pack model. It is sshown in Fig.1. The left is the circuit momodel. Note that the two arrows in betweenbetween the two models.

of 25 seconds are again 1 second. The results are otice the circled areas in

rises or falls, the fast by the 25 sec time step, the waveform. Similarly in the beginning and end

discharge process. Let’s the battery cell in Fig. 8.

o the pulse current discharging ence between the 1 second and s a tiny delay in the 25 second annot capture the rapid change

cost, the 1 second’s inutes. On the other hand

minutes, which is 15 times ep within 1% difference. and velocity fields of the

nd and 6090 second. Note l in both figures because

static. In CFD simulation, first to establish the flow ed as an initial condition

POSED BATTERY MODEL battery pack using the

wn in Fig.9, where 6 cells 4 V output.

imilar to the single cell model

odel and the right is the CFD n clearly indicates the coupling

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The temperature distribution of the battery pack at 8 various time instants during the discharge process are calculated and displayed. The battery pack discharges through a constant resistive load and the temperature profile is very similar to that of Fig. 4, therefore it is omitted. The temperature distributions of the battery pack on the cross section are shown from Fig. 10 to Fig. 17.

Figure 10. The temperature contour on the cross section of the 6 cell battery model at 50 second. The discharging process starts here.

Figure 11. The temperature contour on the cross section of the 6 cell battery model at 150 second. The temperature starts to increase.

Figure 12. The temperature contour on the cross section of the 6 cell battery model at 750 second. The temperature starts to increase rapidly to its first peak value.

Figure 13. The temperature contour on the cross section of the 6 cell battery model at 2000 second. The temperature starts to decrease.

Figure 14. The temperature contour on the cross section of the 6 cell battery model at 3500 second. The temperature continues to decrease at the constant slope.

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Figure 15. The temperature contour on the cross section of the 6 cell battery model at 4500 second. The temperature continues to decrease slowly.

Figure 16. The temperature contour on the cross section of the 6 cell battery model at 5300 second. The temperature starts to increase again.

Figure 17. The temperature contour on the cross section of the 6 cell battery model at 5700 second. The temperature starts to increase rapidly to its highest temperature, which is very close to the end of the discharging process.

In the beginning of the discharging process, the battery cell quick heats up to its first temperature peak as shown in Fig. 11. Then for a long period of time, the temperature

decreases slowly in Fig. 13 to Fig. 15. Note that the non-uniform temperature distribution of the battery pack is observed even when the temperature is changing slowly. Towards the end of the discharge process, a sudden temperature ramp up happens, as shown in Fig. 16 and Fig.17. Each cell heats up in different speed because they are located at different places of the battery pack. With the proposed model, valuable temperature distribution insights are made possible. Essentially, engineers can use the model to study the electrical and thermal characteristic of a battery under different load conditions. After the discussion of the 1 cell and 6 cell models, a 16 cell battery model is shown to demonstrate the scalability of the proposed model. Fig.18 and Fig.19 shows the flow field and temperature distribution of the model at an arbitrary time instance and note that the model in Fig.18 has a smaller cell diameter than that of the model in Fig.19.

Figure 18. The temperature distribution of the 16 cell model with smaller cell diameter size. The cell closer to inlet in general has lower temperature. However, it is interesting to find that the first and the last cell do not follow exactly the same trend. These seemingly strange results have a very legitimate explanation. The first and the last cell experience smaller heat transfer coefficient because the velocity there is smaller. The smaller velocity is due to fewer blockages in the neighborhood of the first and last cells. Without CFD analysis, this type of insight could otherwise have been ignored.

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Figure 19. The temperature distribution of a 16 cell model with larger cell diameter. The gaps between cells are smaller comparing to that of the model shown in Fig.20, which results in higher velocity therefore higher heat transfer coefficient. The temperature of this battery model is cooler than that of the model with smaller diameter.

We found that the battery model with larger cell diameter has more uniform temperature distribution and lower temperature values over all. This is because the smaller gaps between cells in the model with larger cell diameter result in higher velocity therefore higher heat transfer coefficient than the smaller cell diameter model.

III. CONLCUSION A new battery model that couples circuit model and CFD

model has been presented. In particular, two discharge conditions have been studied. One is constant resistive load discharge and the other one is a 60% duty cycle pulse current discharge. We have benchmarked the results of 25 second time step size against the 1 second time step size under both

discharge conditions. In the resistive load case, within 1% difference, the speed is 9.3 times faster using 25 second time step than the speed of 1 second time step. In the 60% duty cycle pulse current load case, within 1% difference, the speed is 15 times faster using 25 second time step than the speed of 1 second time step. Therefore, we conclude that 1/40 of the thermal constant is recommended to be the size of the time step in using the proposed battery model from both accuracy and minimizing computational cost perspectives. We also have studied the temperature distribution of a 6 cell battery pack at 8 time instances of the discharge process. To further demonstrate the scalability of the model, a 16 cell battery model has been model and studied. We varied the cell diameter to demonstrate the geometry impact to the values and uniformity of the temperature field.

ACKNOWLEDGEMENT The authors would like to thank Dr. Xiao Hu from ANSYS Corporation for valuable discussions.

REFERENCES [1] D. Ghosh, Maguire, and D.X. Zhu, “Design and CFD Simulation of a

Battery Module for a Hybrid Electric Vehicle Battery Pack,” SAE paper 2009-01-1386.

[2] M. Zolot, K. Kelly, M. Keyser, M. Mihalic, A. Pesaran, and A. Hieronymus, “Thermal Evaluation of the Honda Insight Battery Pack,” 36th Intersociety Energy Conversion Engineering Conference, 2001.

[3] M. Chen and G. A. Rincon-Mora, “Accurate electrical battery nodel capable of predicting runtime and I–V performance,” IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 504–511, Jun. 2006.

[4] Lijun Gao, Shengyi Liu, and Roger A. Dougal, “Dynamic Lithium-Ion Battery Model for System simulation”, IEEE Trans. Comp. Package. Technology, vol. 25, No 3, pp.495-505, Sep. 2002.

[5] S.X. Chen , K.J. Tseng, and S.S. Choi, “Modeling of Lithium-Ion Battery for Energy Storage System Simulation”, 2009 Asia-Pacific Power and Energy Engineering Conference (APPEEC), March 2009.

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