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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 the traditional <inline-formula> <tex-math notation="LaTeX">${RC}$ </tex-math></inline-formula>-based models. In this study, we first review some of the widely used fractional-order models for the description of impedance and relaxation functions of dissipative resistive&#x2013;capacitive system, namely, the Cole&#x2013;Cole, Davidson&#x2013;Cole, and Havriliak&#x2013;Negami models. We then propose and derive new <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math></inline-formula>-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.

Extended RC Impedance and Relaxation Models for Dissipative Electrochemical Capacitors