Examinando por Autor "Allagui, Anis"

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Limit capacitance of the constant phase element
(Elsevier, 2024-06-15) Balaguera, Enrique H.; Allagui, Anis
The constant-phase element (CPE) is a universal electrical model widely used to describe the intricate nature of a multitude of materials and processes under real-world conditions. The physical interpretation of the corresponding anomalous phenomenology is a challenging task, which traditionally relies on calculating an effective capacitance in the sense of a classical charge accumulation. However, a picture of this electrical element is not yet complete for cases of practical interest, and many questions remain open in relation to the intrinsic characteristics that makes it “unphysical” at long time scales. In this work, we derive mathematical formulas for estimating the limit capacitance of the CPE associated with surface and normal time-constant distributions. For this purpose, we obtain the transient responses, in term of multi-exponential relaxation patterns, attributable to the charge processes of micro-capacitances that constitute the “macroscopic CPE” with a dynamical behavior described in terms of the Mittag-Leffler function. As both transient dynamics can be considered negligible in practice from a certain time instant, we subsequently find the limit capacitance from a direct comparison of both steady-state times in the style of CPE reference works. Simulations are used to show that the obtained limit capacitance yields reasonable values for cases of multidisciplinary interest. Our study contributes to the advanced understanding of the pervasive presence of the CPE in natural and engineering contexts, shedding light on the problem of infinite charge and energy in complex systems
Time delay in the charge/discharge of fractional-order capacitive energy storage devices
(Elsevier, 2024-11) Balaguera, Enrique H.; Allagui, Anis
Electrical energy storage devices exhibit dispersive properties that control their charge and discharge processes. To get a deeper understanding of these anomalous phenomena, it is essential to go beyond static viewpoints of circuit theory in order to accurately characterize the complex interplay of internal mechanisms. Specifically, the (dis)charging time of resistive-capacitive networks is commonly estimated as four times the product of the Thévenin resistance and the capacitance itself by assuming ideal exponential relaxations in spite of the intrinsic fractional dynamics of the real energy storage materials, leading to inaccurate and erroneous characterization protocols. The purpose of this work is to provide recommended practices to find the steady-state operation of such type of devices from time-domain data with a decelerated behavior of the Mittag-Leffler function at long time scales, introducing the concept of “incremental capacitance” in the transition from ideal to fractional-order capacitor and thus, an estimation of the charge/discharge time delay. Our theoretical analysis is validated by providing a representative example of experimental application, based on an electrochemical power source, such as supercapacitors under switching-type operation. We hope to bring such study to the attention of multidisciplinary readers, both from academia and industry, focused on energy storage device research