Work

Fractional Energy: A Theoretical Characterization of the State of Charge of the Ultracapacitor Modeled as a Constant Phase Element

Year: 2026

Type: article

Abstract: Based on the Infinite State Representation (ISR) of the Riemann–Liouville integral, the energy stored in a fractional-order integrator is revisited, together with the energy dissipated through Joule losses. Using an idealized ultracapacitor model based on the Constant Phase Element (CPE), i.e., a fractional-order capacitor, theoretical expressions for the stored and dissipated energies during current charging of the CPE are derived. Numerical simulation of the fractional integrator over a frequency interval {ωmin, ωmax} validates a realistic CPE model, in which low-frequency modes correspond to energy storage, while high-frequency modes account for self-discharge and the origin of dissipated energy. This theoretical study leads to the definition of a new ultracapacitor model composed of an internal resistor and the previous realistic CPE, whose frequency-distributed representation enables prediction of the internal state variables and, consequently, the State of Charge.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10060411

Authors: Jean-Claude Trigeassou, Nezha Maamri

Institutions: Université de Bordeaux, Université de Poitiers, Laboratoire d'Informatique et d'Automatique pour les Systèmes

Language: English

Topic: Advanced Battery Technologies Research

Subfield: Automotive Engineering

Field: Engineering

Domain: Physical Sciences

SDG: Affordable and clean energy

Open Access status: gold

Estimated APC paid: $3,258