Constant Phase Element in the Time Domain: The Problem of Initialization
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MDPI
Materia
Constant phase element (CPE) Fractional calculus Time domain Initial conditions ZARC Supercapacitor and battery modeling
Date
2022-01-21Referencia bibliográfica
López-Villanueva, J.A.; Rodríguez Bolívar, S. Constant Phase Element in the Time Domain: The Problem of Initialization. Energies 2022, 15, 792. [https://doi.org/10.3390/en15030792]
Sponsorship
University of Granada TIC105Abstract
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.