Spectral Capacitance of Series and Parallel Combinations of Supercapacitors

Allagui A.
Elwakil A.S.
Maundy B.J.
Freeborn T.J.

The porous nature of the electrode material in supercapacitors and the apparent conductivity of the electrolyte cause their impedance to show a complex frequency-dependent behavior, which in turn makes it incorrect to treat them as ideal capacitors, even at a frequency of a few millihertz. This is particularly crucial if the intended application requires a configuration that uses stacked supercapacitor banks, in which errors in defining the metrics of the individual components accumulate. Although manufacturers provide supercapacitor ratings under DC only, by using a detailed impedance spectroscopy study of all possible series and parallel combinations of two different commercial 1 Farad carbon–carbon supercapacitors, we show that these nominal DC capacitances are not suitable to evaluate the equivalent capacitance. Instead, by using a model that consists of a series resistance and a constant-phase element, we employed a real, effective capacitance (in proper Farad units) suitable for direct application. This effective capacitance can be used to define the frequency-dependent quality factor of a supercapacitor and enables the easy calculation of series and parallel associations of identical or different devices. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim