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Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell

1
Laboratory of Diffusion Processes, Ulyanovsk State University, Ulyanovsk 432017, Russia
2
Scientific Manufacturing Complex “Technological Centre”, Moscow 124498, Russia
3
Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences (INME RAS), Moscow 119991, Russia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Electronics 2019, 8(6), 650; https://doi.org/10.3390/electronics8060650
Received: 7 May 2019 / Revised: 5 June 2019 / Accepted: 7 June 2019 / Published: 9 June 2019
(This article belongs to the Section Power Electronics)
The effect of anomalous diffusion of lithium on the discharge curves and impedance spectra of lithium-ion batteries (LIB) is studied within the fractional differential generalization of the single-particle model. The distribution of lithium ions in electrolyte and electrode particles is expressed through the Mittag–Leffler function and the Lévy stable density. Using the new model, we generalize the equivalent circuit of LIB. The slope of the low-frequency rectilinear part of the Nyquist diagram does not always unambiguously determine the subdiffusion index and can be either larger or smaller than the slope corresponding to normal diffusion. The new aspect of capacity degradation related to a change in the type of ion diffusion in LIB components is discussed. View Full-Text
Keywords: lithium-ion battery; single-particle model; fractional derivative; anomalous diffusion; impedance; degradation; equivalent circuit; impedance lithium-ion battery; single-particle model; fractional derivative; anomalous diffusion; impedance; degradation; equivalent circuit; impedance
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Sibatov, R.T.; Svetukhin, V.V.; Kitsyuk, E.P.; Pavlov, A.A. Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell. Electronics 2019, 8, 650.

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