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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2017.2723436, IEEE Access

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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < computational burden in solving the highly coupled partial differential equations involved with first-principle models, empirical based models have been widely researched. For example, Al Hallaj et al. presented a one-dimensional model with lumped parameters to simulate the thermal behavior of Li-ion batteries. These model parameters were extracted by fitting the experimental data collected from a Sony (US18650) cell[22]. Li et al. established a two-dimensional computational fluid dynamics (CFD) model to emulate the thermal management issues of a battery pack cooled by air, where systematical tests were performed to validate the proposed CFD model[23]. Similarly, Cicconi et al. built a 3D model for analyzing the thermal behavior of a Li-ion battery, which was experimentally validated under a standard ECE-15 cycle. This cell model was then leveraged as the boundary condition in the CFD model of a battery pack to evaluate the cooling effect[24]. The empirical based models have developed from cell models to module and pack models that consider all aspects that have impacts on thermal characteristic of the whole system. However, the existing empirical based models either lack experimental validation under varied test conditions (e.g. temperature and/or charging/discharging rate) or need theoretical analysis on involved electrochemical reactions. In order to overcome the above-mentioned drawbacks, this paper presents a thermal model for a cylindrical Li-ion battery based on the finite element method. Firstly, a model with a simplification method as well as the thermal characteristic is analyzed. Then, the thermal property parameters and the boundary conditions are given based on theoretical analysis and experiments. Finally, the model accuracy under different ambient temperatures and discharge rates is validated through the experiments. The remainder of this paper is arranged as follows: The finite element model of Li-ion batteries is introduced in Section II. The proposed model is validated through experimental tests in Section III, followed by the key conclusions summarized in Section IV. II. FINITE ELEMENT MODELLING A cylindrical battery with a capacity of 2.7Ah is considered in this study, and the detailed structure is illustrated in Fig. 1. It consists of a wound jelly-roll with a metallic can, where the positive and negative current collectors are welded on both sides. The jelly-roll structurally comprises of sheets of electrodes, current collectors and separators. It is worth noted that the positive terminal is made of aluminum, and the positive and negative electrode collectors are made from aluminum and copper, respectively. The used materials and their parameters are shown in Table I. A. Heat transfer mechanism The thermal equilibrium of a Li-ion battery can be represented by QP  Qe  Qa (1) where QP is the generated heat, Qe is the exchanged heat between the battery and its ambient environment, and Qa is the accumulated heat, which can be deduced by temperature variation. The heat exchange between the battery and its ambient

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environment is achieved mainly through three heat transfer types, i.e., radiation, conduction and convection. Compared with the conduction, the heat transferred through radiation and convection is relatively minor, and thus can be reasonably ignored. Thereby, the heat balance equation can be further simplified as T k C p ,k    (k T )  q (2) t The left side stands for the increment of the thermodynamic energy of each element. The first term in the right side is the energy increment through conduction, and the second term is the battery heat generation rate. ρk, Cp,k and λk represent the density, specific heat and thermal conductivity of each battery element, respectively, and q is a cumulative value of different heat generation rates. In order to further simplify the calculation of the battery temperature field, several assumptions are made here: (1) The thermal conductivity of each material is the same in one direction. (2) The specific heat and thermal conductivity of each material are not affected by the temperature gradient. (3) During charging/discharging, the current density is uniform, and its heat generation rate is consistent. Based on these assumptions, a battery 3-D heat transfer equation under the Cartesian coordinate is derived as Eq. (3), which lays the foundation for calculating the battery temperature field. T  2T  2T  2T C p  kx 2  k y 2  kz 2  q (3) t x y z where T, ρ and Cp are the temperature, average density, specific heat of the battery. kx, ky and kz represent the thermal conductivity of the battery in coordinate X, Y and Z, and q is the heat generation rate. B. Li-ion battery finite element model TABLE I MATERIALS AND PARAMETERS OF THE BATTERY Density Specific heat Component Material (kg/m3) [J/(kg·°C)] Cathode LiFePO4 2300 1300 Positive collector Can (Positive terminal) Anode

Al

2710

903

Al

2710

903

Graphite

1347

1437

Negative collector

Cu

8930

386

Negative terminal

Steel

7900

460

Separator

PE

1400

1551

Electrolyte

Organic solution (EC+DEC+EMC+DMC)

1223

1375

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Parameter

ε δi λm / W / (m·k) λf / W / (m·k) λi / W / (m·k)

The positive electrode sheet 0.25 0.455 1.48 0.59 1.201

The negative electrode sheet 0.3 0.304 1.04 0.59 0.895

The separator 0.47 0.241 0.351 0.59 0.466

According to the above analysis and the known parameters, the calculated results of battery heat physical parameters are derived and listed in Table III. TABLE III CALCULATED RESULTS OF BATTERY HEAT PHYSICAL PARAMETERS Heat Specific Density transfer Component material heat 3 kg/m rate J/(kg·°C) W/(m·k) Mixture of the λx=λz=1.6 anode, the The cell core 2000 900 cathode and the λy =3 separator The aluminum can (the positive terminal) The negative terminal The insulation film

Al

2710

903

238

Steel

7900

460

20

PVC

920

1000

0.3344

2) Cell heat generation rate The generated heat in batteries can be assorted into two categories: the polarized heat and the chemical reaction heat. The amount of polarized heat mainly depends on the internal resistance, while the chemical reactions can be exothermic or endothermic. Compared with the polarized heat, the chemical reaction heat is limited, especially at high charge/discharge rates. (1) The heat generation rate of the cell core can be calculated based on the Bernardi heat generation model shown as dU 0 dU 0 I I q  [(U 0  U )  T ]  [I  R  T ] (9) Vb dT Vb dT where Vb is the cell volume, I is the charge/discharge current, T is the temperature, R is the battery internal impedance, and dU0/dT is the coefficient of open-circuit voltage varying with temperature. (2) The positive and negative terminals can be regarded as the resistance loads, and the heat generation rate can be calculated by I 2 Rm q (10) Vm where I is the working current flowing through the terminals, Rm is the resistance of the positive/negative terminal, which can be obtained by direct measurement, and Vm is the corresponding volume of the positive/negative terminal. The heat generation rates of each component are calculated under various temperatures and charge/discharge rates. The results are shown in Table IV. TABLE IV

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HEAT GENERATION RATES OF MAIN COMPONENTS AT VARIOUS TEMPERATURE AND DISCHARGE RATES (W/M3) Temperature 263K 298K 298K Discharge rate 3C 1C 3C Electricity core Positive terminal Negative terminal

93585

12825

45156

1136

126

1136

6616

735

6616

3) Initial conditions (1) The initial temperature T ( x, y, z, 0)  T0 (11) where T0 is the initial temperature used to define the starting temperature at the beginning of simulation. (2) Heat transfer coefficient The surface heat transfer coefficient is set as 5 W/(m2·K) under natural convection and 10 W/(m2·K) under forced convection[1]. The heat transfer boundary conditions are assumed under the forced convection in this study.

III. MODEL VALIDATION In order to verify the accuracy of the presented model, experimental tests were conducted in our laboratory. The datasets were attained for model characterization and comparison by a well-established battery test system. It comprises of a battery cycler, a thermal chamber, a host computer, the tested Li-ion batteries and an infrared imaging device. The battery cycler is used to charge or discharge the batteries in accordance with pre-defined loading profiles. It has the capability of recording various parameters, including terminal voltage, loading current and accumulated capacity. The accuracy of the voltage and current measurement is up to 1 mV and 1 mA, respectively. The infrared imaging device was used to measure the surface temperature of the battery. Several thermocouples were installed on the battery surface to measure the local temperature of the battery as shown in Fig.3. Their detailed specifications are listed in Table V. The sensor glues make the temperature sensors more tightly attached on the battery surface. These glues have no obvious impacts on the local temperature nearby as seen from the infrared imaging in Fig. 4(b).

Fig. 3. The positions of thermocouples on cylindrical cell TABLE V PARAMETERS OF INFRARED IMAGING DEVICE AND THERMOCOUPLE



Device

type

Temperature ranges(°C)

Accuracy (% of reading)

Measurement modes

Thermo Vision™ A20M

-20 to 250

±2%

Spot, Area, Difference

The thermo-c ouple

TSC Thermo-co uple

-200 to 350

±4%

spot

o

The infrared imaging device

Temperature/ C

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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < D. Analysis of the results The errors between simulated and measured values are around 10% at different ambient temperatures and discharge rates, with a maximum value of 11.56%. This means a good agreement between the simulation and experimental results. However, there is also an unavoidable discrepancy, which may be ascribed to the following reasons: (1) Measurement error: the employed infrared imaging device is more capable of measuring the relative temperature rather than the absolute temperature. Despite the thermocouples with high precision have been deployed to compensate for the measurement error, their measurement accuracy is still highly sensitive to the ambient temperature and the contact conditions between the battery surface and the thermocouples. (2) The surface heat transfer coefficient was assumed to be 10 W/(m2 K) under the forced convection in simulation. Taking the ventilation environment of the thermal tank into account, the surface heat transfer coefficient may differ at different parts of the battery. (3) The presented finite element model was built based on several assumptions, and some internal chemical reactions were ignored. The temperature variations are idealized and averaged, which results in symmetrical temperature gradient inside the battery. (4) Radiant heat loss was ignored in simulation so that the simulation results are always higher than that of the experiments. The data shows that the temperature in simulation is always 1~2°C higher than that in the experiments.

[2] [3] [4] [5]

[6]

[7] [8] [9] [10] [11] [12] [13]

[14] [15]

IV. CONCLUSIONS In order to predict the thermal behavior of a cylindrical Li-ion battery, an enabling thermal model has been proposed based on the finite element method in this paper. Several simplification assumptions are made in order to reduce the model complexity, and thus enhance the computation efficiency. The boundary conditions and the thermal parameters of the battery components are determined through theoretical analysis or experiments. Finally, the accuracy of the presented thermal model is validated through experimentation. The results show that the errors between simulated and measured values are around 10% at different ambient temperatures and discharge rates. The presented model can be embedded into battery management systems, and used to simulate the battery temperature distribution.

[16] [17] [18] [19] [20] [21] [22] [23]

ACKNOWLEDGEMENT The project was supported by the State Key Program of National Natural Science Foundation of China (No. U1564206).

[24] [25] [26]

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