Extended RC Impedance and Relaxation Models for Dissipative Electrochemical Capacitors

• Published in: IEEE transactions on electron devices Vol. 69; no. 10; pp. 5792 - 5799
• Main Authors: Allagui, Anis, Benaoum, Hachemi, Elwakil, Ahmed S., Alshabi, Mohammad
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Capacitors; Discharge; Dissipation; Electric potential; Fractional-order calculus; Frequency-domain analysis; H-function; Impedance; impedance spectroscopy; Integrated circuit modeling; Mathematical models; q-exponential; relaxation response; Resistance; supercapacitors; Time domain analysis; Voltage
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2022.3197384

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-capacitive system, namely, the Cole-Cole, Davidson-Cole, and Havriliak-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.