PDE battery model simplification for charging strategy evaluation

A safe, fast charging strategy is desired in the utilisation of rechargeable Lithium-ion batteries. Traditionally, experimental methods are used in exploring and evaluating new strategies, but these require extensive time and cost. This paper aims to establish a model-based system for quick and accurate evaluation of charging strategies. Starting from a nonlinear coupled partial differential equation (PDE) battery model that accurately captures system dynamics, simplification techniques are conducted based on the identification of separable time scales within the states. By pertinent use of a singular perturbation approach, a PDE model simplification framework containing families of simplified battery models is established. All assumptions are explicitly stated and shown to enable families of simplified models to be rigorously justified. An evaluation procedure synthesised from the simplified models and averaging theory is proposed. This procedure is implemented on several typical battery charging strategies. The benefits relative to simulation on other higher order models are assessed in terms of computational efficiency and accuracy and demonstrate significant computational savings are possible with the proposed approach.