Charge-discharge energy efficiency analysis of ultracapacitor with fractional-order dynamics using hybrid optimization and its experimental validation

Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

“…The technique of multiple swarms of particles used in Hu et al optimizes the parameters of the SC modeled with twelve different approaches. The hybrid optimization based approach was introduced in other works …”

“…The hybrid optimization based approach was introduced in other works. [13][14][15] In this article, the behavior of an SC is modeled using a basic electrical circuit with an equivalent resistance in parallel (Rp), an equivalent resistance in series (Rs), and a capacitor (C). These three parameters are estimated for five different mathematical approaches by applying interior point optimization and using a set of experimental data.…”

Memorized relaxation with singular and non-singular memory kernels for basic relaxation of dielectric vis-à-vis Curie-von Schweidler & Kohlrausch relaxation laws

“…This empirical Curie-von Schewidler (1872) relaxation law is used to derive fractional differential equations describing constituent expression for capacitor i.e. i(t) ∝ 0 D α t v(t), or i(t) ∝ v (α) (t), 0 < α < 1 that is 'fractional capacitor', [15,11,31,32,16,18,17,48,10,8,46,30,14]. Where 0 D α t is symbolizing process of fractional-differentiation.…”

Determination of supercapacitor parameters based on fractional differential equations

“…This alternative formulation allows to model different physical processes with dissipation and long‐range interaction. () Electric double‐layer capacitors (EDCL), supercapacitors (SCs), or ultracapacitors (UCs) are electrical energy storage devices where the energy is stored in the double‐layer capacitor as charge separation in the double‐layer formed at the interface between the solid electrode material surface and the liquid electrolyte in the micropores of the electrodes . Supercapacitors are able to store a large amount of energy than that of traditional capacitors; they have the capacity to deliver more power than that of batteries and they have a large number of charge/discharge cycles .…”