Time-domain Response of Supercapacitors using their Impedance Parameters and Fourier Series Decomposition of the Excitation Signal

Abstract: Supercapacitors are mostly recognized for their high power density capabilities and fast response time when compared to secondary batteries. However, computing their power in response to a given excitation using the standard formul{\ae} of capacitors is misleading and erroneous because supercapacitors are actually non-ideal capacitive devices that cannot be characterized with a single constant capacitance. In this study we show how to estimate accurately the time-domain power and energy of supercapacitors in response to any excitation signal represented in terms of its Fourier series coefficients with the sole knowledge of the frequency-domain impedance parameters of device. The presented theory is first verified and validated with simulations conducted on an equivalent fifth-order RC circuit emulating the behavior of a fractional circuit consisting of a resistance (Rs) in series with a constant phase element (CPE) of fractional impedance ZCPE = 1/C{\alpha}s{\alpha}. Then we do the same for a commercial supercapacitor modeled as an Rs-CPE circuit, and subjected to both a periodic triangular voltage waveform and a random voltage excitation. The results are conclusive and very promising for adopting the proposed procedure to estimate the power and energy performance of supercapacitors in response to real-world charging and discharging signals.