Applicability of the Lumped Capacitance Model to Predict Heat Generation in a Lithium-Ion Pouch Cell Under Various Rates of Discharge
Authors: Bazinski Stephen , Wang Xia 
Published: February 2020

The proper design for a battery thermal management system (BTMS) in an electric or hybrid electric vehicle requires that all of the factors which affect heat generation within the battery cell to be fully understood. As lithium-ion has become the de facto cell chemistry for use in traction battery packs, much research has been done that establishes the relationship between the rate of heat generation of a cell to its temperature, state-of-charge (SOC), and rate of charge or discharge. However, experimental studies of the thermal behavior of these cells have focused mainly on the small coin and cylindrical cell formats and at low C-rates. Available literature on the heat generation of large format cells at high C-rates are scant and was the impetus for this study.
Often times, the scarcity and expense of calorimeters specifically designed to accommodate large pouch cells have led researchers to instead turn to a classic approach in trying to quantify the amount of heat generated within a cycling cell. The lumped capacitance method (LCM) is a useful technique that can greatly simplify an otherwise complicated problem in transient heat transfer. However, as with many models, 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. They have also considered thermal properties to be isotropic and independent of temperature.
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. In addition, the source of error responsible for LCM data disagreeing with calorimetric data will be identified.

Experimental Setup

The initial step in this investigation was to uncover 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 an iterative process that best fitted the predicted cooling rate to the measured data. 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 lost 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.

Source of Discrepancy

The major contributor to the increasingly growing discrepancy between the LCM calculations and calorimetric data was 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.