The modelling of carbon-based supercapacitors: Distributions of time constants and Pascal Equivalent Circuits

Stephen Fletcher, Iain Kirkpatrick, Roderick Dring, Robert Puttock, Rob Thring, Simon Howroyd

Research output: Contribution to journalArticlepeer-review


Supercapacitors are an emerging technology with applications in pulse power, motive power, and energy storage. However, their carbon electrodes show a variety of non-ideal behaviours that have so far eluded explanation. These include Voltage Decay after charging, Voltage Rebound after discharging, and Dispersed Kinetics at long times. In the present work, we establish that a vertical ladder network of RC components can reproduce all these puzzling phenomena. Both software and hardware realizations of the network are described.
In general, porous carbon electrodes contain random distributions of resistance R and capacitance C, with a wider spread of log R values than log C values. To understand what this implies, a simplified model is developed in which log R is treated as a Gaussian random variable while log C is treated as a constant. From this model, a new family of equivalent circuits is developed in which the continuous distribution of log R values is replaced by a discrete set of log R values drawn from a geometric series. We call these Pascal Equivalent Circuits. Their behaviour is shown to resemble closely that of real supercapacitors. The results confirm that distributions of RC time constants dominate the behaviour of real supercapacitors.
Original languageEnglish
Pages (from-to)247-253
Number of pages7
JournalJournal of Power Sources
Early online date11 Feb 2017
Publication statusPublished - 31 Mar 2017

Cite this