Asymptotic reduction and homogenization of a thermo-electrochemical model for a lithium-ion battery

• Published in: Applied Mathematical Modelling 2020-04, Vol.80, p.724-754
• Main Authors: Hennessy, Matthew G., Moyles, Iain R.
• Format: Article
• Language: English
• Subjects: Asymptotic methods; Asymptotic series; Biot number; Computer simulation; Electric cells; Electrochemistry; Electrodes; Heat generation; Homogenization; Lithium; Lithium-ion batteries; Lithium-ion battery; Management systems; Mathematical models; Model reduction; Onboard equipment; Porous electrode theory; Rechargeable batteries; Thermal analysis; Thermal management; Thermal runaway; Two dimensional models
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.11.018

•Two thermo-electrochemical models of a lithium-ion battery are proposed.•Asymptotics used to construct reduced models for common modes of battery operation.•Heat generation in thermal model dependent on the number of cells in a battery•Homogenization used to obtain a model of a battery composed of many cells.•Thermal runaway not induced by chemistry alone despite Arrhenius kinetics. In this study, matched asymptotic expansions are used to systematically reduce a thermo-electrochemical model of a lithium-ion battery based on volume averaging the electrode microstructure. In the cases with a constant or oscillating applied current, explicit asymptotic solutions of the full model can be obtained. In the case with a constant cell potential, the reduced model comprises a low-order differential-algebraic system. The asymptotic and numerical solutions of the volume-averaged model are compared with the numerical solutions of a thermal pseudo-two-dimensional (P2D) model, which treats the electrode as a collection of spherical particles. Excellent agreement is found between the models at (dis)charge rates up to 2C, and reasonable agreement is found at 4C. Homogenization is then used to derive a thermal model of a battery comprising several connected lithium-ion cells. We derive a closed-form solution to the homogenized model when the effective Biot number is small, which corresponds to a spatially uniform battery temperature. By comparing simulation times, we show that the asymptotically reduced and homogenized models provide substantial computational savings compared with the full numerical simulations, thereby making them ideal for use in onboard thermal management systems. We also show that thermal runaway does not occur in the model, despite accounting for the Arrhenius dependence of the reaction coefficients.