Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

TL;DR

This paper reviews fractional-order models for electrochemical capacitors and introduces new q-deformed models to better capture their anomalous impedance and relaxation behaviors, validated with experimental data.

Contribution

It proposes novel q-deformed models based on modified evolution equations to improve the description of dissipative electrochemical capacitors.

Findings

New q-deformed models accurately fit experimental impedance data.

Models effectively describe time-domain relaxation in supercapacitors.

Enhanced understanding of anomalous behaviors in electrochemical energy devices.

Abstract

Electrochemical capacitors are a class of energy devices in which complex mechanisms of accumulation and dissipation of electric energy take place when connected to a charging or discharging power system. Reliably modeling their frequency-domain and time-domain behaviors is crucial for their proper design and integration in engineering applications, knowing that electrochemical capacitors in general exhibit anomalous tendency that cannot be adequately captured with traditional integer-order-based models. In this study we first review some of the widely used fractional-oder models for the description of impedance and relaxation functions of dissipative resistive-capacitive system, namely the Cole-Cole, Davidson-Cole, and Havriliak-Negami models. We then propose and derive new q-deformed models based on modified evolution equations for the charge or voltage when the device is discharged into a parallel resistive load. We verify our results on anomalous spectral impedance response and time-domain relaxation data for voltage and charge obtained from a commercial supercapacitor.