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

TL;DR

This paper presents a method to accurately estimate the time-domain power and energy of supercapacitors using impedance parameters and Fourier series decomposition, validated through simulations on equivalent circuits and real supercapacitors.

Contribution

The study introduces a novel approach to determine supercapacitor power and energy response to arbitrary signals based solely on impedance parameters and Fourier analysis.

Findings

Method accurately predicts supercapacitor power and energy for various signals.

Validation confirms effectiveness on both simulated and real supercapacitor data.

Proposed approach is promising for real-world charging and discharging analysis.

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.