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Determination of supercapacitor parameters based on fractional differential equations
Author(s) -
HidalgoReyes J.I.,
GómezAguilar J.F.,
EscobarJimenez R.F.,
AlvaradoMartinez V.M.,
LopezLopez M.G.
Publication year - 2019
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2640
Subject(s) - fractional calculus , laplace transform , conformable matrix , mathematics , particle swarm optimization , convolution (computer science) , derivative (finance) , supercapacitor , mathematical analysis , mathematical optimization , computer science , capacitance , physics , artificial neural network , electrode , quantum mechanics , machine learning , financial economics , economics
Summary In this paper, we estimate the parameter values of a fractional‐order model of supercapacitors involving fractional derivatives of Liouville‐Caputo, Caputo‐Fabrizio, and Atangana‐Baleanu and fractional conformable derivative in the Liouville‐Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions.