A Comparison of Time-Domain Implementation Methods for Fractional-Order Battery Impedance Models

Abstract

This paper is a comparative study of the multiple RC, Oustaloup and Grünwald–Letnikov approaches for time domain implementations of fractional-order battery models. The comparisons are made in terms of accuracy, computational burden and suitability for the identification of impedance parameters from time-domain measurements. The study was performed in a simulation framework and focused on a set of ZARC elements, representing the middle frequency range of Li-ion batteries’ impedance. It was found that the multiple RC approach offers the best accuracy–complexity compromise, making it the most interesting approach for real-time battery simulation applications. As for applications requiring the identification of impedance parameters, the Oustaloup approach offers the best compromise between the goodness of the obtained frequency response and the accuracy–complexity requirements.

Equivalent Circuit Model to Reach Complicated Surface Photovoltage Transient Shapes in ZnO Thin Films

“…These pathways do not necessarily directly contribute to any exponential deconvolution of the transient curve. A popular notion is that the relaxation of carrier-confined large ensembles in inhomogeneous structures exhibits a multiexponential or stretchedexponential form [18]. With these assumptions, the decay can initially be related to direct carrier recombi-02023-5 nation and capture processes, until various distributions of trapping centers are filled.…”

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

“…1 The current excitation xðtÞ is set as a sinusoidal signal defined in (19), and its initial phase ϕ or (angular) frequency f is changed in simulation verification. The resulting TDR is then calculated in (26), where the discretization parameters of λ ¼ 1:01 and f max ¼ ω max =2π ¼ 10 9 Hz are applied to approximate the transfer function. Moreover, the PSpice simulation is also performed as a reference in Analog Behavioral Modeling (ABM), 16 and the comparative TDR simulation results in measurement time t ¼ ½0,0:2 ms are shown in Figures 4 and 5.…”

“…Recently, the impedance approximations of SPFOC by multiple RC circuits are applied to TDR analysis, 24,25 which offers the best compromise between accuracy and complexity compared to the integer-order transfer function approximations of s α . 26 Here, a TDR approximation method is proposed to directly analyze the transfer function of SPFOC, rather than the transfer function of s α , by the sum of multiple RC circuits in the Cole distribution function. The main contributions of our work are as follows: (1) a novel solution to discretization of SPFOC into the sum of first-order circuits is proposed based on the Cole distribution function, which could be applied to represent the impedance/admittance transfer function of SPFOC in integer-order expressions, and (2) the TDR analysis of SPFOC to a sinusoidal input signal is deduced in inverse Laplace transform, which can be easily extended to an arbitrary periodic signal based on the Fourier series theory.…”

“…Similarly, Tsirimokou 23 obtains rational approximations of the fractance elements ( and ) represented by in Foster and Cauer networks. Recently, the impedance approximations of SPFOC by multiple RC circuits are applied to TDR analysis, 24,25 which offers the best compromise between accuracy and complexity compared to the integer‐order transfer function approximations of 26 …”

Energy Management Systems for Optimal Operation of Electrical Micro/Nanogrids

“…In [6], Ospina Agudelo et al investigate battery impedance modelling issues. In particular, their article introduces three main approaches for the implementation of the time-domain response of battery fractional order models (FOM)s, i.e., multiple RC (mRC), Oustaloup (OU), and Grünwald-Letnikov.…”