PDE model for thermal dynamics of a large Li-ion battery pack

Technologies for storage of electric energy are central to a range of applications-from transportation systems, including electric and hybrid vehicles, to portable electronics. Lithium-ion batteries have emerged as the most promising technology for such applications, thanks to their high energy density, lack of hysteresis, and low self-discharge currents. One of the most important problems in battery technology is achieving safe and reliable operation at low cost. Large packs of batteries, required in high-power applications such as submarines, satellites, and electric automobiles, are prone to thermal runaways which can result in damage on a large scale. Safety is typically ensured by over-design, which amounts to packaging and passive cooling techniques designed for worst-case scenarios. Both the weight and the cost of the batteries can be considerably lowered by developing models of thermal dynamics in battery packs and model-based estimators and control laws. At present, only detailed numerically-oriented models (often referred to as CFD or FEM models) exist, which are used for computationally intensive off-line tests of operating scenarios, but are unsuitable for real-time implementation. In this paper, we develop a model of the thermal dynamics in large battery packs in the form of two-dimensional partial differential equations (2D PDEs). The model is a considerable simplification of the full CFD/FEM model and therefore offers the advantage of being tractable for model-based state estimation, parameter estimation, and control design. The simulations show that our model matches the CFD model reasonably well while taking much less time to compute, which shows the viability of our approach.