The widely used Doyler-Fuller-Newman (DFN) model for lithium-ion batteries is too computationally expensive for certain applications, which has motivated the appearance of a plethora of simpler models. These models are usually posed in an ad hoc manner, leading to inconsistencies with the DFN model and to multiple formulations of the same model, with the Single Particle Model (SPM) being a very good example of the latter. In this work, we discuss the concept of SPM-type models showing that, despite the multiple formulations found in the literature, these models always follow the same structure, and we extend this discussion to models accounting for thermal effects. Then, we present a Thermal Single Particle Model with electrolyte (TSPMe) derived in a systematic manner using asymptotic techniques. The validation of the TSPMe against a thermal DFN model shows very high accuracy with a computational cost over forty times smaller. The comparison against experimental data shows that the model does a reasonable job predicting the behaviour of a real battery, but a very good parameter set is required to obtain accurate predictions.

Accepted version to Electrochimca Acta, 27 pages, 13 pages of appendix, 12 figures