Extended <i>RC</i> Impedance and Relaxation Models for Dissipative Electrochemical Capacitors

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