Abstract

Lithium-ion batteries have become ubiquitous in consumer electronics, and more recently electric vehicles, due to their high energy density, long lifespan, and a low self-discharge rate. Their increasing demand necessitates design improvements in performance and reliability, which in turn requires accurate models of how they work. In mathematical models, the highly heterogeneous porous electrodes are usually approximated as comprising spherical particles of one size, leading to the so-called “single-particle model”. In this talk, we first extend this model to account for a distribution of particle sizes. We discuss its effects and the methods of reduction to an effective single particle, e.g. via averaging or asymptotic methods. Then, this model is further extended to include the electrolyte dynamics via a multiscale “pseudo-3D” approach, which we show can capture some basic behaviours of a battery seen in experiments (such as its rest period immediately after a (dis)charge) that were previously unexplained. The numerical models have been incorporated into the open source battery modelling software package PyBaMM, to enhance their usability and reproducibility.