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A Comparison of LCM Results to Calorimetric Data in Predicting Heat Generation from Lithium-Ion Pouch Cells

^{1}Available literature on the heat generation of large format cells at high C-rates are scant and was the impetus for this study.

The lumped capacitance method (LCM) is a useful technique that can greatly simplify an otherwise complicated problem in transient heat transfer. However, the validity of LCM results hinges on how well certain assumptions and conditions hold. The criterion in this case is to have spatial temperature uniformity throughout the cell. This condition becomes tenuous as the cell is inherently anisotropic and is subjected to increasingly higher C-rates. Often times, computer simulation models summarily assume pouch cells have negligible temperature difference across their thicknesses regardless of size or C-rate.^{2} They have also considered thermal properties to be isotropic and independent of temperature.^{3}

The objective of this research is to determine how well the LCM predicts the rate of heat generation in a large format pouch cell at several different C-rates of full constant-current discharge. The rate of heat generation will be also measured by a battery calorimeter. The LCM data will be compared to the calorimetric data.

*Experimental Setup*

The initial step in this investigation was to determine the average convection coefficient of the cell geometry when oriented as a vertical plate in natural convection. This was accomplished by first having the 14Ah cell self-heat during a 5C discharge. An infrared video camera recorded the cell surface temperature as it naturally cooled to ambient room temperature. Using the lumped capacitance model (LCM), an average convection coefficient was found from curving the LCM model. The predicted cooling rate was found to have an extremely good correlation to the measured data. This was due in large part to the high area-to-volume ratio of the cell format. The derived value of the average convection coefficient was then used in an energy balance equation. It was then possible to model the rate of heat generation of the pouch cell under different rates of discharge by simply knowing the cell surface and ambient temperatures as well as some thermodynamic properties.

This same cell then underwent various rates of discharge while having its surface temperature recorded by the infrared video camera at ambient room temperature. From this data, the rate of heat loss through convection and stored within the bulk mass was calculated and summed to equate to the internal rate of heat generation. Precautions were taken to minimize heat loss through conduction.

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*Preliminary Results*

During a full discharge at a C/5 constant-current rate, the heat generation predicted by LCM did extremely well in matching the calorimetric data. However, during a 1C discharge, the rate of heat generation predicted by LCM tended to be in lower than that measured by the calorimeter for most of the time. The average rate of measured heat generation was 2.82W while LCM predicted 2.13W. This computes to LCM being 24% lower than the calorimetric data on average.

The major contributor to the discrepancy between the LCM calculations and calorimetric data is the rate of temperature change as a function of time. This value is used to calculate the rate of heat storage within the cell. Heat storage (and heat generation for that matter) are volumetric phenomena. It is very difficult to accurately calculate this rate of temperature change based on surface measurements. In addition, as the C-rates become increasingly higher, temperature gradients become more pronounced throughout the cell core. This has a detrimental effect on being able to apply LCM.

**References**

[1] Bandhauer, T.M., Garimella, S., and Fuller, T.F., “A critical review of thermal issues in lithium-ion batteries,” *Journal of Electrochemical Society*, pp. R1-R25 (2011).

[2] Kim Yeow, Ho Teng, Marina Thelliez, and Eugene Tan, “*3D Thermal Analysis of Li-ion Battery Cells with Various Geometries and Cooling Conditions Using Abaqus”,* SIMULIA Community Conference, Providence, RI, May 15, 2012

[3] S. Al Hallaj, H. Maleki, J. Hong, and J. Selman, *Journal of the Electrochemical Society*, 83, 98 (1998)