Review of Physical Degradation Models for Lithium-Ion Batteries
Authors: Reniers Jorn Maurits , Mulder Grietus , Howey David Alastair 
Published: February 2020

The lifetime of a lithium-ion battery is a key element in the business case for grid-connected batteries. Battery degradation is the result of many different processes.
Various battery degradation models exist, of differing complexity, accuracy and data-requirements. The simplest model is a linear degradation model assuming a maximum energy throughput over the battery’s lifetime. A second class are the empirical degradation models, interpolating large data sets. Different empirical models include different operating conditions, depending on the dominant degradation mechanisms appearing in the data set. Thirdly, electrochemical degradation models try to capture the physics of the degradation processes. Various electrochemical degradation models exist, e.g. for the growth of the SEI layer [1], for particle fracking [2], lithium-plating [3], etc. Even for the same physical degradation mechanism, many different models are used. For example, for the growth of the SEI layer, some only consider the reaction itself (‘a rate-limited process’) [1], while others also model the diffusion through the SEI layer (‘diffusion limited process’) [4].
However, most studies only looked at one or two degradation models. This study aims to give a comprehensive overview of existing physical models. The single particle model is used to model the battery states to keep the calculation time short. The different degradation models are implemented as add-ons to this model leading to a flexible battery degradation model, which allows to assess the effects of individual degradation models, as well as how different degradation mechanisms interact. Finally, it is shown how variable operating conditions affect the degradation according to the different models and how a combination of degradation models can fit a large experimental data set.
Three basic degradation trends can be observed in actual battery degradation data. Some types of cells degrade faster at the start of their life and their degradation rate decreases over time. The degradation patterns of other cells is more linear, with the amount of capacity lost more or less constant. Other cells show an accelerating degradation, especially towards the end of their lifetime when the capacity suddenly decreases very strongly. Different degradation models will predict different degradation trends. Models limited by the kinetics of the reaction, such as certain models for SEI layer growth or lithium plating, produce a broadly constant degradation trend. Models which include a diffusion limitation predict the typical square root of time behavior, with a decreasing degradation trend. Various models for crack growth or loss of active material on the other hand predict an accelerating degradation trend.
Sometimes, two degradation models enhance each other. For instance, certain models for loss of active material increase the current density on the remaining electrode surface which will increase the overpotentials and thus lead to more growth of the SEI layer if a kinetic limited model is used. Other models produce negative feedback mechanisms, for instance when growth of the SEI layer removes cyclable lithium from the graphite, which increases the anode potential and therefore reduces the lithium plating.
The different degradation models respond very differently to the operating conditions of the battery. The attached figure shows the predictions of various models to 14 different cycling regimes with different temperatures, currents and voltage windows. Models which include chemical reactions typically show a larger decrease in capacity loss at higher temperature while models which include a physical stress model show the opposite behavior. The effects of the voltage windows and the magnitude of the current is less clear-cut and is often a compound effect which also includes the effect of the charge which can be accessed in one cycle on top of the real degradation per cycle.
When considering a small degradation set, it might seem as if all the models are the same and all can predict the observed degradation. But when variable cycling conditions are simulated, the difference between the various models becomes apparent. Fitting a large data set requires multiple degradation models to capture the different degradation trends observed for different operating conditions. This will be illustrated with a large data set for a commercially available lithium ion cell.
[1] G. Ning and B. N. Popov, J. Electrochem. Soc., vol. 151, no. 10, p. A1584, 2004.
[2] R. Deshpande, M. Verbrugge, Y.-T. Cheng, J. Wang, and P. Liu, J. Electrochem. Soc., vol. 159, no. 10, pp. A1730–A1738, 2012.
[3] X.-G. Yang, Y. Leng, G. Zhang, S. Ge, and C.-Y. Wang, J. Power Sources, vol. 360, pp. 28–40, Aug. 2017.
[4] M. B. Pinson and M. Z. Bazant, J. Electrochem. Soc., vol. 160, no. 2, pp. A243–A250, Dec. 2012.

Figure 1