Review of fractional-order electrical characterization of supercapacitors

The tests and calculation of the key performance metrics of supercapacitors including capacitance, power and energy stored are commonly reported by the academia and the industry based on formulæ valid only for ideal capacitors. This is inconsistent with the fact that supercapacitors exhibit electrical behaviors that are different from those of ideal capacitors whether they are looked at in the time domain or in the frequency domain. This results inevitably in errors in their characterization, design and system integration. Based on recent literature, this review article is an attempt to present and discuss the main differences between ideal capacitors and supercapacitors, and especially how the performance metrics of the latter depend on the operating frequency, the charging/discharging waveform type as well as their deviation from ideality. We present a set of calculation methods for supercapacitor metrics using fractional-order calculus when such devices are operated under the commonly used (i) sinusoidal excitation, (ii) step current input and (iii) linear voltage input. We hope to bring such analysis, which is proven to be much more reliable and effective than the standard integer-order-based analysis of ideal capacitors, to the attention of researchers, manufacturers, and end-users of these devices particularly as their range of application is surging.