Constant Phase Element in the Time Domain: The Problem of Initialization López Villanueva, Juan Antonio Rodríguez Bolívar, Salvador Constant phase element (CPE) Fractional calculus Time domain Initial conditions ZARC Supercapacitor and battery modeling This research was partially funded by the TIC105 research group of the University of Granada. 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. 2022-03-28T06:41:49Z 2022-03-28T06:41:49Z 2022-01-21 journal article 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] http://hdl.handle.net/10481/73797 10.3390/en15030792 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI