Hard limitations of polynomial approximations for reduced-order models of lithium-ion cells

Electrochemical models are a widespread framework to simulate lithium-ion (Li-ion) batteries and to design their battery management algorithms. To obtain numerically efficient models, the polynomial approximation (PA) is one of many order reduction techniques applied to the solid-state lithium-ion (...

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Bibliographic Details
Published in:Journal of applied electrochemistry 2020-03, Vol.50 (3), p.343-354
Main Authors: Ortiz-Ricardez, Fernando A., Romero-Becerril, Aldo, Alvarez-Icaza, Luis
Format: Article
Language:English
Subjects:
Algorithms
Batteries
Chemistry
Chemistry and Materials Science
Computer simulation
Dynamic models
Electric cells
Electrochemistry
Industrial Chemistry/Chemical Engineering
Lithium
Lithium-ion batteries
Mathematical analysis
Model reduction
Physical Chemistry
Polynomials
Rechargeable batteries
Reduced order models
Research Article
State of charge
System theory
Systems theory
Two dimensional models
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Summary:Electrochemical models are a widespread framework to simulate lithium-ion (Li-ion) batteries and to design their battery management algorithms. To obtain numerically efficient models, the polynomial approximation (PA) is one of many order reduction techniques applied to the solid-state lithium-ion (SSLi + ) diffusion equation, the core of the so-called pseudo-two-dimensional electrochemical model (P2DM). Although the validity of PA is constrained to slow-varying current scenarios, many algorithms reported in the literature to estimate the state-of-charge of Li-ion cells rely on low-order PA-based dynamic models (PADMs) derived from the P2DM. Moreover, assuming that most properties of their low-order counterparts are inherited, some authors suggest that PADMs of arbitrary high order can be used to provide very accurate approximations of the state-of-charge, even under complex operating conditions. Nevertheless, to authors knowledge, in the open literature there is not a proper analysis to support such assertion. In this paper, by introducing a systematic method to derive PADMs of arbitrary order, the ability of high-order PADMs to reproduce the average and surface concentrations described by the SSLi + diffusion equation is investigated in time and frequency domains, with the aid of classic control systems theory techniques. The main result shows that PADMs of order greater than 2 are structurally fragile as non-minimum-phase zeros as well as spurious unstable modes are induced by the PA technique, implying that high-order PADMs are not suitable for simulation or estimation purposes because of their weak internal structure. Graphic abstract
ISSN:0021-891X
1572-8838
DOI:10.1007/s10800-019-01395-y