Thermal simulation of high-power Li-ion battery withLiMn1/3Ni1/3Co1/3O2 cathode on cell andmodule levelsYasir Abdul-Quadir*,†, Tomi Laurila, Juha Karppinen and Mervi Paulasto-Kröckel

Department of Electronics, School of Electrical Engineering, Aalto University, Otakaari 7, 02150 Espoo, Finland

SUMMARY

Thermal modeling of temperature rise in high-power Li-ion battery cells and modules is presented here. Simulationresults are validated by experiments. Results indicate that entropy heat generation plays a significant role inheat generation of Li-ion battery cells and should be included in simulation as a function of state of charge(SOC). Simulation results utilizing measured overpotential resistance and entropy heat generation provide the bestfit when compared to experimental results. Resistance data provided by supplier shows significant difference comparedwith measured data and should be critically examined for any module design purposes. Copyright © 2013 John Wiley& Sons, Ltd.

KEY WORDS

Li-ion battery; CFD simulation; overpotential resistance; entropy change

Correspondence

*Yasir Abdul-Quadir, Department of Electronics, School of Electrical Engineering, Aalto University, Otakaari 7, 02150 Espoo, Finland.†E-mail: Yasir.abdul.quadir@aalto.fi

Received 9 November 2011; Revised 13 December 2012; Accepted 5 March 2013

1. INTRODUCTION

Management of heat effects associated with lithium-ionbatteries (LIBs) remains a challenge, as excessive localtemperature rise in Li-ion cells causes reduction of cyclelife and may lead to thermal runaway of individual cellsor of an entire battery pack. Especially in battery packswhere the cells are closely packed, in order to exploit theadvantage of Li-ion’s high energy and power density,thermal runaway of a cell can propagate and cause an entirebattery to fail drastically. There is a strong interdependencebetween temperature variation within the battery and electro-chemical performance. In general, a rise in temperatureduring the course of charging and discharging the battery isdetrimental to battery performance in that it may acceleratedegradation of the electrolyte, electrodes, and separator.Consequently, knowledge of temperature distribution andheat dissipation is an important factor in the developmentof thermal management strategies for LIBs. Thermal model-ing can play a key role in controlling the operating tempera-ture and temperature uniformity of LIBs within a suitablerange [1–3].

Many researchers have used commercial finite elementmodeling (FEM) or computational fluid dynamics (CFD)tools to study temperature rise and thermal managementof battery modules and packs. Wu et al. [1] used a transient2D heat transfer model to simulate the temperature

distribution in LIB modules. The experimental and simula-tion results showed that cooling by natural convection wasnot an effective means for removing heat from the batterysystem. On the other hand, it was found that forcedconvection cooling can mitigate temperature rise in thebattery. Ghosh et al. [3] performed CFD analysis usingFLUENT (commercially available CFD software) to ana-lyze the thermal performance of a battery cell containerfor the Ford Fusion hybrid electric vehicle (HEV). Theobjective of the design was to maintain the cells at theirdesired operating temperature range with a near-uniformtemperature among the battery cells in the container whileminimizing energy losses associated with the pressuredrop. By changing the design to allow for better airflow,they managed to minimize the temperature gradient to1.8 �C within the assembly. Riza Kizilel et al. [4] usedphase change material (PCM) and compared its effective-ness against air cooling. They also used FEMLAB 3.1(commercially available FEM software) to simulate thetemperatures in the module. They concluded that PCMtechnology appears to be an elegant and effective alterna-tive to forced air cooling of compact packs and allows amuch simplified cooling design for plug-in HEVs. ChrisMi et al. [5] performed thermal modeling on a lithiumbattery pack suitable for HEV applications. They alsoused a 2D finite element analysis model to simulate thetemperature rise in the cells. Uniform heat distribution

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Copyright © 2013 John Wiley & Sons, Ltd.

was assumed for each cell in the model. Matsushita et al. [6]used a 3D FEM model to thermally characterize a large-capacity lithium-ion secondary battery as a backup powersupply for next-generation communications. They usedequivalent material properties for all the constituents of thecell. The heat generation applied to the cell was based onI2R. The resistance value was calculated from the voltagechange during discharge. They concluded that the flat-typebattery model is thermally better than the cylindrical typeand that cooling of the battery cell can be improved if theempty space in the cell is filled with liquid electrolyte. Kimand Pesaran [7] in 2006 used CFD to compare air and liquidcooling on a battery module. The CFD model simulationimplied that capturing the internal heat flow paths andthermal resistances inside a cell using a sophisticated three-dimensional cell model were critical for the improved predic-tion of cell/battery thermal behavior.

The main challenge in battery thermal modeling is thecorrect estimation of heat dissipation in the battery cellduring charge/discharge. Being an electrochemical system,the estimation of heat dissipation becomes tricky as the bat-tery undergoes following processes during charge/discharge:

1. Interfacial reactions2. Changes in the heat capacity of the system3. Phase changes4. Mixing5. Electrical work6. Heat transfer with the surroundings

Bandhauer et al. [8] critically reviewed the availableliterature on major thermal issues for LIBs. They con-cluded that majority of the experimental work that measureheat produced by the LIB has been carried out on coin cellsand at low to moderate charge/discharge rates (<1C). Theyalso commented that entropic heat is nearly the same orderof magnitude as the irreversible heat for the 1C dischargerate, thus having a nonnegligible impact on the heatgeneration and performance of a cell. Furthermore, in thethermal simulation section of the review, they concludedthat, typically, the entropic heat tends to be neglected whilesimulating heat generation in battery cells. They arguedthat because the entropic heat is significant, even at moder-ately high charge and discharge rates, the entropic heatingas a function of state of charge (SOC) should be includedin all thermal simulations.

The present work looks at the thermal simulation meth-odology for battery cells and modules. We have used CFDsoftware as well as experimental data [9] to simulate thetemperature rise of the cell and the module and comparedthe outcomes with the measured results. In Reference [9],we have determined the overpotential heat by measuringthe overpotential resistance as well as the entropy heatby measuring the entropy heat coefficient. These are usedas input values in the present simulations. Further, wewill compare the simulation result obtained by using internalresistance data provided by the supplier with those obtainedby the measured values. With this work, we would like to

ascertain whether the measured resistance values as well asmeasured entropy heat can be used for simulating tempera-ture rise at the cell and module levels. This work would alsoconcludewhether the data provided by the supplier is enoughto predict the temperature rise in batteries (which seeminglydoes not include any change in entropy effect).

2. EXPERIMENTAL DETAILS

2.1. Cell Level

The battery used in the experiments is a high-power com-mercially available (Kokam SLPB100216216H) [10] LIBwith a rated capacity of 40Ah, as shown in Figure 1 (thelocation of the thermocouples used in measuring thesurface temperature of the battery cell is also shown). Thespecifications of the cell are listed in Table I. The numberof anode and cathode layers as well as their dimensionswas measured by disassembling a fully discharged cell.

An equation proposed by Bernardi et al. [11] is cited fre-quently in the literature in its simplified form [Equation (1)]for heat generation in a battery cell.

q ¼ I Eoc � Vð Þ � I T@Eoc

@T

� �(1)

The first term on the right-hand side of Equation (1) rep-resents the overpotential heat. This results from ohmic lossesin the cell, activation overpotential at the interfaces, and masstransfer limitations. The second term represents the entropicheat. The derivative of the potential with respect to tempera-ture in Equation (1) is often referred to as the entropic heatcoefficient.

Figure 1. Battery cell used in the current work (including the ther-mocouple locations used for measuring cell surface temperature).

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Based on the above equation, the following measure-ments were carried out on the battery cell to calculate theheat generation in a cell.

2.1.1. Uniformity of heat generation in a batterycell and temperature rise on the surface of the cell

Equation (1) is based on the assumption that there is auniform heat generation in a battery cell. To prove thisassumption in the present case, the temperatures duringdischarge were measured on seven different points on thesurface of the cell at 1C and 2C discharge rates (Figure 1).

The measurements were carried out at ambient tempera-ture. The results were needed to validate the simulation results.

2.1.2. Qp: Overpotential heat calculated bymeasuring overpotential resistances with fourdifferent methods

The overpotential resistance with four different methods[resistance by V–I characteristics, resistance by open circuitvoltage (OCV) and cell voltage, resistance by intermittentdischarge, and resistance by AC impedance method] wasmeasured for the cell. Details about the experiment and theresults can be found in Reference [9]. Table II provides ashort description of the measured resistance, including theother measurements that were necessary to validate the heatgeneration in a battery cell. Figure 2 shows the differentoverpotential resistance values measured in the current work.The graph clearly shows that the overpotential resistancemeasured by AC impedance method is less than half of theresistances measured by the other three methods. Similar re-sults were obtained by Onda et al. [12]. It is most likely thatthis is because the impedance measurements are carried outat a very low current (0.5A in the current study, which isequivalent to 0.0125C) while the resistances measured bythe other three methods use much higher current ratings(12–80A). The general trend shown in all four resistancesis similar, with the resistance increasing with decreasingSOC. This is expected, as during discharge, Li ions are

transferred from anode to cathode, and associated concentra-tion gradients increase in magnitude. At the end of the dis-charge cycle, the Li ions are depleted from the anode, andmore energy is needed to transfer the remaining Li ions tothe cathode.

2.1.3. Qs: Entropy heat generation is calculated bymeasuring the change in OCV at different SOCs andtemperatures (dEoc/dT).

The following method was used to measure the entropychange of the battery cell for 1C discharge.

1. Cell was kept at OCV for about 21–23 h at roomtemperature.

2. Temperature was changed by 10 �C after every 2.5 h.3. Eoc was measured at temperatures 25, 35, 45 and 55 �C.

The steps were repeated for different SOCs. The batterywas discharged to a desired SOC level at 1C.

Details of the entropy change measurement are presentedin Reference [9]. The results indicate that while the value ofthe entropy change (dEoc/dT) is relatively small, it cannot beneglected. Results also indicate that entropy heat (Qs) isexothermic between 1.0 and 0.8 SOC during discharge andis endothermic between 0.6 and 0.4 SOC, becoming exother-mic again at 0.2 SOC and below. The phenomena behind thisbehavior are discussed in detail in Reference [9] and can beclearly seen in Figure 3 (temperature on the cell surfacewas measured at seven different points; the graph plots theminimum, maximum, and the average temperatures fromthese seven points). A more detailed description on thechanges brought about by the change in entropy on theelectrode structure can be found elsewhere [13].

2.2. Module Level

Figure 4 shows the module made of seven battery cells.Figure 5 shows the schematic of the module with cells 4and 7 highlighted. The temperatures of these cells weremonitored, as they were the hottest and coolest of all thecells in the module. As can be seen in the figure, a fan islocated at the top of the module. The cells are separatedfrom each other by a foam material. The battery manage-ment system’s (BMS) printed circuit board (PCB) islocated just under the fan. Because this PCB also includesthe cell balancing circuit, its components can get quite hot.The fan is mostly used to cool this PCB. The currentdesign of the model ensures that the battery cells are notexposed to poor quality environment (dust, particles,etc.), as the main use of these battery cells is in workmachines used in the mining industry.

3. SIMULATION

The temperature distribution in each layer of the cell isgoverned by

Table I. Battery cell details [10].

Size 220mm� 215mm� 10.7mmAnode material GraphiteCathode material Lithium cobalt manganese

nickel oxide (LiMnNiCoO2)Electrolyte Solution of lithium

hexafluorophosphate (LiPF6)Nominal voltage 3.7 VCut-off voltage 2.7 VOperating temperature Charge: 0 to +40 �C

Discharge: –20 �C to +60 �CCapacity 40AhMaximum charge current 80 A (2C)Maximum discharge current 400 A (10C)Anode thickness 125 mmCathode thickness 107 mmSeparator thickness 21 mmNo. of layers of cathode

and anode34

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Figure 2. Measured overpotential resistances by four different methods [9].

Table II. Description of measurements carried out in Reference [9].

Parameter obtained Explanation How they were measured

1 Uniformity of heat distributionin a battery cell

Measured the battery surfacetemperature at 1C discharge

Using seven thermocouples attached at thesurface of battery cell

2 Overpotential resistanceR(V–I)

Obtained the resistance value byV–I characteristics at different C-rate

Charging and discharging tests were carriedout for variousC-rates (0.3C–2C). The obtainedcell voltage and charge–discharge current V–Icharacteristic as function of SOC. The slopeof the curves provided the overpotentialresistance.

3 Overpotential resistanceR(OCV–V)

Obtained the resistance value bymeasuring the OCV at different SOCs

Battery cell was charged or discharged to thedesired SOC level with 1C current. Once thedesired SOC level was achieved, the batterywas left to stabilize. The cell voltage afterthe chosen stabilization period was taken asOCV (Vo). Overpotential resistance can bemeasured by dividing the differencebetween cell voltage V and Vo by the chargingor discharging current

4 Overpotential resistanceR(60sec)

Measured the resistance value byintermittent discharge (with holdingtime of 10min)

Battery cell is discharged (with a known C-rate)to a known SOC and then kept at that SOCfor 10 min. The drop in voltage in 60 s, afterthe commencement of discharge, is thendivided by the current to calculate theoverpotential resistance corresponding tothe particular SOC.

5 Resistance by AC impedancemethod

Obtained the resistance by measuringohmic and charge transfer resistanceat various SOC

First EISmeasurementswere carried out for fullycharged cell. The cell was then incrementallydischarged by 10% SOC until the voltagereached 2.7 V (0% SOC). Discharge currentwas 20 A, and AC impedance was measuredat each of 10% SOC increments.

6 Entropy coefficient (dVo/dT) Obtained the value by measuring theOCV at different temperatures

(a) Battery cell was kept at OCV (Vo) for about21–23 h at room temperature.

(b) Temperature was changed by 10 �C afterevery 2.5 h.

(c) Vo was measured at temperatures 25, 35,45, and 55 �C.

The steps were repeated for different SOCs.

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@2T

@x2@2T

@y2þ @2T

@z2þ q:

k¼ 1

a@T

@t(2)

where, x, y, and z are spatial directions, k is thermal con-ductivity, a is thermal diffusivity, and

q: ¼ f SOC; ið Þ; (3)

which has been determined experimentally [9] (i is thedischarge/charge current).

Thermal modeling of batteries at the module level isvery similar to electronics system modeling (uniform heatsource). However, at the cell level, the modeling becomescomplicated due to the system’s electrochemical nature.While in electronic modules, the internal resistance of theheat source (mainly die or chips) is relatively constant

Figure 4. Battery module: the right picture shows an open battery module with thermocouples attached.

Figure 5. Battery module schematic.

Figure 3. (a) Temperature rise in battery cell with 1C discharge. Figure shows the uniformity of heat generation and Entropy effect.(b) Measured entropy coefficient [9].

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(some changes in Gallium arsenide material is found, butonly at high temperatures), internal resistance in a batterycell is very dynamic in nature. Further, in electronicmodules, the resistance changes generally only withtemperature, while in battery cells, the resistance changeis dependent on the SOC and charge–discharge rates inaddition to temperature.

To solve Equation (3), commercial CFD softwareFlotherm v.9.1 [14] is used. Its main advantage is thepossibility to predict fluid flows, both laminar and turbu-lent. The battery cell is modeled as a solid block ofanisotropic thermal conductivity. The specific heat of thebattery was measured, and the details are presented inReference [9]. The heat generation in the battery cellwas modeled as a uniform heat source. A convectiveheat transfer coefficient of 8 W/m2K (which depictsnatural convection) was used for all the sides in celllevel modeling.

Defining an appropriate grid is one of the main challengesof the employed method. Whereas a rough grid leads to fastcomputations, a fine grid is necessary to model areas withhigh temperature, pressure, and velocity gradients. Gener-ally, a finer grid leads to better accuracy. The grid does nothave to be uniform, and several tools exist to simplify griddefinition. For instance, the grid can be refined just locallyin areas that are assumed to contain high gradients or thatare of special importance.

Several sources of error in modeling a given geometryexist. Because a Cartesian grid is used, only rectangulargeometries can be modeled precisely. Oblique, bent, andcurved surfaces have to be approximated by many cubesor prisms, for instance. Although material properties canbe accurately specified, they are often not exactly known.Initial assumptions can often be rough, which is anothertypical reason for an imprecise solution.

Following are the rest of the simulation model details:

• Modeling state: Transient• Modeling type: Automatic Algebraic Turbulent model(does not require any user-defined velocity or length scale)

• Ambient temperature: 20 �C or depending on measure-ment data

• Fan speed: 10 000 rpm• Discharge rate: 1C (40A) and 2C (80A)

For 1C discharge at the cell and module levels, the sim-ulation time was 1 h, and for 2C discharge, it was 30min.For 1C discharge at the cell level, there were 120 substeps.An increasing power of 1.5 was used for the time steps.The smallest time step used was 2.5 s. For the module level,an additional 80 substeps were used, with an increasingpower of 1.5, and the smallest time step was 5 s. The numberof outer iterations was 20, and temperature was monitoredat the battery cell surface (corresponding to the measure-ment points).

The fan is modeled as a linear fan with 12 facets and aswirl speed of 10 000 rpm. A very fine grid was needed to

capture the airflow from the fan to the module. Figure 6shows the 3D isometric view of the model in Flothermwith the grid.

Table III provides the details of the material propertiesof the different parts used in the simulation.

The thermal conductivity of the battery cell is calculatedby equivalent thermal conductivity using the equation

kin ¼

XNi¼1

kiti

XNi¼1

ti

for in-plane thermal conductivity and

kthrough ¼

XNi¼1

ti

XNi¼1

ti=ki

for through-plane conductivity, where t

is the thickness of given layer and k is the thermal conduc-tivity of that layer.

Using the above equations with the values providedin Table 3, we obtain a through-plane thermal conductiv-ity of 0.4W/mK and in-plane thermal conductivity of38W/mK.

Figure 6. 3D isometric view of the battery module in Flotherm.

Table III. Material properties of different parts used insimulation model.

Material

Thermalconductivity

(W/mK)Specific

heat (J/KgK)Density(Kg/m3)

Battery cell In-plane: 38 670Through-plane: 0.4

Enclosure (Al) 150 900 2700Foam 0.033 1300 1000Cathode 0.5 [6]Anode 0.5 [6]Separator 0.1 [6]

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4. RESULTS AND DISCUSSION

4.1. Uniformity of heat generation in the cell

Figure 3a shows the result of the temperature measuredon the battery during 1C discharge. The figure clearlyshows that the temperature on the surface of the cell isrelatively uniform, with the hottest point being in themiddle of the cell (position 7 in Figure 1). The resultimplies that, for thermal simulation, a uniform heatsource approximation could be applied to the batterymodel. Figure 3b shows the entropy coefficient mea-sured in Reference [9]. The figure shows that entropy heat(Qs) is exothermic between 1.0 and 0.8 SOC duringdischarge and is endothermic between 0.6 and 0.4 SOC,becoming exothermic again at 0.2 SOC and below. Thiscorresponds to the area in Figure 3a where the battery tem-perature is almost constant.

5. RESISTANCE OF A CELL

Full details of the results obtained from the measurementof the overpotential resistance of the cell are presented inReference [9]. As mentioned above, our results indicatethat any of the three overpotential resistances that aremeasured at higher current is suitable for calculating heatgeneration in a cell. For simplicity’s sake, we have usedresistance measured by R(60sec) method in this work.

Figure 7 compares the supplier’s resistance value withthe one obtained in Reference [9]. While the shapes ofthe curves are very similar, with a dip in the resistancevalue obtained at around 0.7 SOC in both cases, the valuesprovided by the supplier are much smaller compared to ourmeasured data. At the end of the curve, a steep increase inthe resistance is seen (in both cases) as the battery isdepleted. The reasons behind the anomaly seen in theresistance behavior based on the supplier’s data are notknown at the moment, due to the lack of any experimentalinformation about the measurement procedure.

5.1. Temperature rise of a cell duringdischarge

Figure 8 compares the simulation results obtained by (i)measured overpotential and entropy heat and (ii) supplier’sdata with the measured data for 1C and 2C discharge forone cell.

The results indicate that the CFD simulation results arein good agreement with the measured results. The resultsobtained from supplier’s data fit relatively well for 1Cdischarge, until 0.8 SOC, while for 2C, the difference isquite significant. The main reason is that the supplier’sresistance values are much smaller compared to our mea-sured data. The effect of entropy change is shown effec-tively by the CFD simulation result. This implies that forthe accurate prediction of temperature rise at the rated level(1C) or lower, entropy change has to be taken into account.It is to be noted that results based on the supplier’s datagenerally lead to lower temperature values as comparedto measured and other simulated data.

5.2. Module level

The battery module with seven cells was discharged at 1Cand 2C. Temperature rise on the cell was measured with ak-type thermocouple at the surfaces of cell 4 and cell 7 (asshown in Figure 1). Figure 9 shows an infrared camerapicture of an open module after the discharge.

Figure 10 compares the CFD simulation result and theresults with supplier’s data with measured data.

The results again show an excellent fit for the CFDsimulation data compared with the measurements. Thesupplier’s data significantly differs from the measured datafor both 1C and 2C discharge.

While at the cell level the difference in supplier’s dataand the measurements was only marginal (for 1C dis-charge), this difference becomes significant at the modulelevel. This is because the difference is magnified, as thereare now seven cells in the module. A careful look atFigure 5 indicates that the heat tends to get stuck insidethe module due to the presence of (i) high thermal

Figure 7. Comparison of supplier’s internal resistance value with measured R(60sec) overpotential resistance.

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resistance material (battery cell and foam) and (ii) interfacesbetween the cells and the foam material. Moreover, there are

no channels available for the airflow from the fan to gothrough in the module. This effectively rules out the role ofconvection as a feasible heat transfer mechanism inside themodule. Thus, practically all heat transfer inside the moduletakes place with conduction. The effectiveness of heatconduction as a cooling mechanism is crucially dependenton the availability of a low thermal resistance heat path awayfrom the heat source to the surrounding environment. Thus,all features of the structure that contribute to an increase inthermal resistance along the conduction path will havedetrimental effects on cooling. Hence, owing to the effectof many interfaces between cells and the foam materialsuperimposed on the internal interfaces inside the cells, it isnot unexpected that the predictions based on a lumped resis-tance value will provide less accurate results here than in thecase of individual cells. The accumulated heat effect isshown effectively by the R(60sec) simulated results. Again,it is emphasized that results based only on the supplier’s dataleads to lower temperature than the measured one. This could

Figure 9. Infrared camera picture of the open battery module atthe end of 1C discharge.

Figure 10. Comparison of cell 4 temperature of the battery module for 1C and 2C discharge.

Figure 8. Comparison of temperature rise of cell surface at 1C and 2C discharge.

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lead to serious safety issues especially if the batteries aredriven to their limit.

This indicates that data provided by the supplier (inter-nal resistance) is not enough and that a thorough measure-ment of heat generation factor is necessary not only inaccurately predicting the temperature rise but also to helpin better thermal management of the module. A moduledesign based only on supplier’s data could lead to safetyissues especially if the temperature of the battery cellsreaches critical limit.

6. CONCLUSIONS

The current work looked at the accurate prediction of tem-perature rise in high-power LIB at the cell and modulelevels. The measured data for discharge is compared withCFD simulation and results obtained by using supplier’sdata. The results indicated that supplier’s data show a sig-nificant difference compared with measured data for boththe cell and module levels. Hence, supplier’s data shouldbe critically examined for any module design purposes.

The results also indicate that entropy heat generationbecomes significant at the rated level (1C) or below com-pared to overpotential heat and cannot be neglected. Takingelectrochemical reactions (entropy change effects) intoaccount would lead to a proper and better thermal design ofthe battery module and, subsequently, the battery packs.

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