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.

As the UK battery modelling community grows, there is a clear need for software that uses modern software engineering techniques to facilitate cross-institutional collaboration and democratise research progress. The Python package PyBaMM aims to provide a flexible platform for implementation and comparison of new models and numerical methods. This is achieved by implementing models as expression trees and processing them in a modular fashion through a pipeline. Comprehensive testing provides robustness to changes and hence eases the implementation of model extensions. PyBaMM is open source and available on GitHub. For more information visit www.pybamm.org.

Lithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. Here, we review prior work on “knees” in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of “internal state trajectories” (termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee “pathways”, including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation, some of which have internal state trajectories with signals that are electrochemically undetectable. We also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime.

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Differential voltage analysis (DVA) is a conventional approach for estimating capacity degradation in batteries. During charging, a graphite electrode goes through several phase transitions observed as plateaus in the voltage response. The transitions between these plateaus emerge as observable peaks in the differential voltage. The DVA method utilizes these peaks for estimating cell degradation. Unfortunately, at higher C-rates (above C/2) the peaks flatten and become unobservable. In this work, we show that, unlike the differential voltage, the peaks in the 2nd derivative of the expansion with respect to capacity remain observable up to 1C and thus make possible diagnostic algorithms at these charging rates. To understand why that is the case, we have developed an electrochemical and expansion model suitable for model-based estimation. In particular, we demonstrate that the single particle modeling methodology is not able to capture the peak smoothing effect, therefore a multi-particle approach for the graphite electrode is needed. Additionally, model parameters are identified using experimental data from a graphite/NMC pouch cell. The proposed model produces an excellent fit for the observed electric and mechanical swelling response of the cells and could enable physics-based data-driven degradation studies at practical charging rates.

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.

Predicting lithium-ion battery degradation is worth billions to the global automotive, aviation and energy storage industries, to improve performance and safety and reduce warranty liabilities. However, very few published models...