The standard model of a lithium-ion battery, the Doyle-Fuller-Newman (DFN) model, is computationally expensive to solve. Typically, simpler models, such as the single particle model (SPM), are used to provide insight. Recently, there has been a move to extend the SPM to include electrolyte effects to increase the accuracy and range of applicability. However, these extended models are derived in an ad-hoc manner, which leaves open the possibility that important terms may have been neglected so that these models are not as accurate as possible. In this paper, we provide a systematic asymptotic derivation of both the SPM and a correction term that accounts for the electrolyte behavior. Firstly, this allows us to quantify the error in the reduced model in terms of ratios of key parameters, from which the range of applicable operating conditions can be determined. Secondly, by comparing our model with ad-hoc models from the literature, we show that existing models neglect a key set of terms. In particular, we make the crucial distinction between writing the terminal voltage in pointwise and electrode-averaged form, which allows us to gain additional accuracy over existing models whilst maintaining the same degree of computational complexity.

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, deriving in the process other common models, such as the Doyle–Fuller–Newman 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.

The paper numerically explores the electrochemical and thermal behaviour of a larger format 4680 cylindrical cell recently proposed by Tesla and explains the need to go “tabless.” An idealized spiral geometry is used for 2D simulations with the traditional tab-based current collection method and a new continuous current collection method compared. The new design is found to mitigate the ohmic losses experienced around the “jelly-roll” current collectors which are significant for the traditional tabbed case, thus leading to higher efficiency and capacity and reduced heat production.

This work presents a methodology for coupling two open-source modelling frameworks in a highly parallel fashion across multiple length scales to solve an electrical current and heat transport problem for commercial cylindrical lithium-ion batteries. The global current and heat transfer problems are formulated as resistor networks and solved using a finite difference method on a network extracted from an X-ray tomogram of an MJ1 18650 battery. The electrochemistry governing the heat generation is solved at the local level using a physically parameterized model. Electrochemical models are solved for different regions of a spirally wound cylindrical cell in parallel, coupled via charge conservation at the current collectors in a “battery of batteries” fashion, similar to the concept of modelling a pack. Thermal connections between layers in the spiral winding are established and heat transport is solved globally in a two-dimensional fashion, allowing for the subsequent extension to three dimensions. Great heterogeneity in local current density is predicted by the model which is also found to have some temperature dependence with ramifications for battery degradation.