# Asymptotic reduction, solution, and homogenisation of a thermo-electrochemical model for a lithium-ion battery

## TL;DR

This paper develops and compares asymptotic and homogenised models for lithium-ion batteries, demonstrating their accuracy and potential for thermal management without thermal runaway risk.

## Contribution

It introduces asymptotic and homogenisation techniques to simplify and analyze complex thermo-electrochemical battery models, enabling analytical solutions and improved thermal management.

## Key findings

- Asymptotic solutions agree with numerical models up to 2C charge rate.
- Homogenised models can be solved analytically for practical use.
- Thermal runaway does not occur in the model, only potential shifts.

## Abstract

We study two thermo-electrochemical models for lithium-ion batteries. The first is based on volume averaging the electrode microstructure whereas the second is based on the pseudo-two-dimensional (P2D) approach which treats the electrode as a collection of spherical particles. A scaling analysis is used to reduce the volume-averaged model and show that the electrochemical reactions are the dominant source of heat. Matched asymptotic expansions are used to compute solutions of the volume-averaged model for the cases of constant applied current, oscillating applied current, and constant cell potential. The asymptotic and numerical solutions of the volume-averaged model are in remarkable agreement with numerical solutions of the thermal P2D model for (dis)charge rates up to 2C, and reasonable agreement is found at 4C. Homogenisation is then used to derive a thermal model for a battery consisting of several connected lithium-ion cells. Despite accounting for the Arrhenius dependence of the reaction coefficients, we show that thermal runaway does not occur in the model. Instead, the cell potential is simply pushed closer to the open-circuit potential. We also show that in many cases, the homogenised battery model can be solved analytically, making it ideal for use in on-board thermal management systems.