  Physics-based electrochemical battery models derived from porous electrode
theory are a very powerful tool for understanding lithium-ion batteries, as
well as for improving their design and management. Different model fidelity,
and thus model complexity, is needed for different applications. For example,
in battery design we can afford longer computational times and the use of
powerful computers, while for real-time battery control (e.g. in electric
vehicles) we need to perform very fast calculations using simple devices. For
this reason, simplified models that retain most of the features at a lower
computational cost are widely used. Even though in the literature we often find
these simplified models posed independently, leading to inconsistencies between
models, they can actually be derived from more complicated models using a
unified and systematic framework. In this review, we showcase this reductive
framework, starting from a high-fidelity microscale model and reducing it all
the way down to the Single Particle Model (SPM), deriving in the process other
common models, such as the Doyle-Fuller-Newman (DFN) model. We also provide a
critical discussion on the advantages and shortcomings of each of the models,
which can aid model selection for a particular application. Finally, we provide
an overview of possible extensions to the models, with a special focus on
thermal models. Any of these extensions could be incorporated into the
microscale model and the reductive framework re-applied to lead to a new
generation of simplified, multi-physics models.
