A Homogenized Thermal Model For Lithium Ion Batteries

Abstract

In this work homogenization theory is applied to existing thermal models for lithium ion batteries. We study a battery with prismatic cell geometry. The inner region of the battery has a thermal conductivity that is periodic in a local variable. In this work we describe the inner region by a homogenized partial differential equation. The obtained homogenized thermal conductivity tensor is equivalent with the tensor obtained by applying a thermal equivalent-resistance approach. Thermal equivalent-resistance approaches are reported in the literature on thermal modeling of lithium ion batteries. Furthermore, the homogenized thermal conductivity in different directions varies by a factor 10. The outer region of the battery consist of a casing that is wrapped around the inner region. The outer region is described by a nonhomogenized partial differential equation. Both regions is described by the two coupled partial differential equations in dimensionless form. The coupled model is applied to a conventional lithium ion pouch-cell battery with 17.5 Ah capacity. Input data to the model are obtained from experiments. The model is solved in 2 dimensions by means of the finite element method in the FEniCS software. As input parameters, an ambient temperature and an initial condition of 298 (K) are applied. Moreover is the external heat transfer coe cient estimated to be 18 (W/m2 K). Simulations of a 1C discharge from 100 to 10% state of charge is performed. The modeled battery consists in 2 dimensions of a rectangle with long and short sides. It was found that the temperature parallel with the long side varied significant compared with the temperature parallel with the short side. A maximum temperature is achieved in the center of the battery. This occurs at the time just before the battery is at end of discharge. The maximum temperature is 2.4 (K) above the ambient air temperature. A validation of the results are necessary.