The temperature of batteries plays a critical role in their safe operation, performance and lifetime. To design and operate a thermal management system that keeps batteries in the optimal temperature range precise thermal models are necessary which compute the temperature of the cells. To facilitate the thermal modeling of pouch cells and pouch cell modules, a 3D thermal model based on the Thermal Quadrupole approach [1] is developed. The advantage of this approach is that it reduces the computation of a thermal series connection of multiple cell layers or cells to a simple matrix multiplication.
Figure 1 depicts an equivalent circuit representation of the thermal quadrupole. The parameters of the elements Z_(i=1,2,3) and J can be derived from the matrix representation according to the formalism of Pailhès et al. [2].
In our contribution we demonstrate how this theory can be applied to problems in the battery domain. The application can occur at various system levels, ranging from individual cell layers up to whole battery packs. To illustrate the theory, we model the thermal behavior of a pouch cell using the thermal quadrupole approach, simplifying the representation of the individual layers.
References
[1] D. Maillet, S. André, J. C. Batsale, A. Degiovanni, and C. Moyne, Thermal quadrupoles: Solving the Heat Equation through Integral Transforms. Chichester: Wiley, 2000.
[2] J. Pailhes et al., “Thermal quadrupole method with internal heat sources,” International Journal of Thermal Sciences, vol. 53, pp. 49–55, 2012, doi: 10.1016/j.ijthermalsci.2011.10.005.