Extraction of the parameters of a fractional order equivalent circuit from time-domain data

Kurzfassung

The derivation of impedance spectra and impedance parameters from time-domain data has been an interesting topic of investigations for some years now. Currently applied techniques usually consist of transforming the time-domain data into the frequency-domain by means of Fourier or Laplace-transformations[1]. Different approaches fit the time-domain data with a series of exponential functions that translate into a series of parallel resistor-capacitor elements, to achieve an accurate description of the resulting impedance spectra[2]. 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. Preliminary results show that the time domain data fits have high accuracy. Comparing the resulting impedance spectra to actually measured impedance spectra show the dependence of applied current-step magnitude, relaxation time and sampling rate. A meaningful fitting result can easily be transformed to achieve a distribution of relaxation times by means of the method proposed by Boukamp[3]. Future endeavors will also explore the ability of fractional order models to accurately model arbitrary load response of electrochemical systems as is oftentimes applied in industrial applications. References [1] K.Takano, K. Nozaki, Y. Saito, K. Kato, A. Negishi, J. Electrochem. Soc. 147 (2000) 922-929. [2] J. P. Schmidt, E.Ivers-Tiffeé, J.Power Sources. 315 (2016) 316-323. [3] B. A. Boukamp, Electrochim. Acta. 154 (2015) 35-46.