Spectral Capacitance of Series and Parallel Combinations of Supercapacitors

The porous nature of the electrode material in supercapacitors and the apparent conductivity of their 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 few millihertz frequency. This is particularly crucial if the intended application requires a configuration using stacked supercapacitor banks, where errors in defining the metrics of the individual components accumulate. While manufacturers provide supercapacitor ratings at DC only, we show using a detailed impedance spectroscopy study of all possible series and parallel combinations of two different commercial 1 Farad carbon-carbon supercapacitors, that these nominal DC capacitances are not suitable to evaluate the equivalent capacitance. Instead, using a model consisting of a series resistance and a constant phase element, we employ a real effective capacitance (in proper Farad units) suitable for direct application. This effective capacitance can be used to define a frequency-dependent quality factor of a supercapacitor, and enables the easy calculation of series and parallel associations of identical or different devices.