Constant Phase Element in the Time Domain: The Problem of Initialization

Juan Antonio López-Villanueva and Salvador Rodríguez Bolívar
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Juan Antonio López-Villanueva: Department of Electronics and Computer Technology, CITIC, University of Granada, 18071 Granada, Spain
Salvador Rodríguez Bolívar: Department of Electronics and Computer Technology, CITIC, University of Granada, 18071 Granada, Spain

Energies, 2022, vol. 15, issue 3, 1-14

Abstract: The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values.

Keywords: constant phase element (CPE); fractional calculus; time domain; initial conditions; ZARC; supercapacitor and battery modeling (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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