Simulation of galvanostatic charge-discharge curves of carbon-based symmetrical electrochemical supercapacitor with organic electrolyte employing potential dependent capacitance and time domain analytical expressions

Electrochemical supercapacitors differ from conventional supercapacitors mainly because they have a very high storage of electrical energy per unit of mass and a capacitance dependent on electrical potential. When studying electrical circuits in the time domain that aim to simulate the curves generated in the charging and discharging processes of electrochemical supercapacitors, as is the case with galvanostatic curves, the capacitance dependent on the electrical potential becomes a factor that considerably increases the degree of difficulty in obtaining the equations for simulating such curves. In this paper, a straightforward electrical circuit was used and fed by a source of electric current I of constant intensity in time in order to simulate the galvanostatic curve properties of a symmetrical supercapacitor evaluated by a galvanostatic cycle technique. Simulation of galvanostatic curves of these carbon-based supercapacitors with organic electrolyte also considered the effects of capacitance dependent on electric potential and the analysis was carried out in the time domain using a 2R(C + kUC(t)) electric circuit powered by a direct current source I. Analytical equations are presented and comparisons between experimental and theoretical curves were made on a quantitative basis.