# On The Inverse Relaxation Approach To Supercapacitors Characterization

## TL;DR

This paper introduces a new inverse relaxation method for supercapacitor characterization that simplifies testing, avoids fixed current sources, and can replace traditional impedance measurements, with potential for automation.

## Contribution

A novel inverse relaxation technique for supercapacitors is developed, modeled, and experimentally validated, offering a simplified, automated alternative to existing characterization methods.

## Key findings

- The method measures capacitance at different time scales without fixed current sources.
- It distinguishes between 'easy' and 'hard' to access capacitance.
- The technique can replace traditional impedance and IEC 62391 tests.

## Abstract

A novel inverse relaxation technique for supercapacitor characterization is developed, modeled numerically, and experimentally tested on a number of commercial supercapacitors. It consists in shorting a supercapacitor for a short time $\tau$, then switching to the open circuit regime and measuring an initial rebound and long-time relaxation. The results obtained are: the ratio of "easy" and "hard" to access capacitance and the dependence $C(\tau)$, that determines what the capacitance the system responds at time-scale $\tau$; it can be viewed as an alternative to used by some manufacturers approach to characterize a supercapacitor by fixed capacitance and time-scale dependent internal resistance. Among the advantages of proposed technique is that it does not require a source of fixed current, what simplifies the setup and allows a high discharge current regime. The approach can be used as a replacement of low-frequency impedance measurements and the ones of IEC 62391 type, it can be effectively applied to characterization of supercapacitors and other relaxation type systems with porous internal structure. The technique can be completely automated by a microcontroller to measure, analyze, and output the results.