Extraction of the parameters of a fractional order equivalent circuit model based on time-domain relaxation measurements

Abstract

In this work we apply concepts from fractional calculus to achieve a time-domain description of parallel resistor-constant-phase-elements for the accurate fitting of time-domain current-step responses. To achieve an accurate description of the fractional equivalent circuit in the time domain we formulate an equation based on the Mittag-Leffler function from fractional mathematics. Advantages of this approach allow a direct evaluation of impedance parameters for the assumed equivalent circuit model function without any further transformation to the frequency domain. To this end we explore the ability of fractional order models to fit the time-domain response of a system and if the real impedance spectrum could be reproduced by comparisons to actually measured impedance spectra of 18650 cells.