Mathematical Modeling of Electrochemical Capacitors

Analytic solutions to the mathematical model of an electrochemical capacitor (EC) are used to study cell performance under two types of operating conditions: (i) constant current and (ii) electrochemical impedance spectroscopy. The analytic solution under constant-current operation is used to investigate the relative importance of ionic resistance in the separator, and ionic and electronic resistances in the porous electrode in the design and operation of an EC. Model results are presented that show the trade-off between energy and power density, as the physical properties of the cell components are varied (e.g., electrode thickness). The analytic solution is also used to study the effect of cell design and operation on the heat generation during constant-current cycling. The impedance model is presented as an alternative to equivalent-circuit models for data analysis. The analytic solution can be used to gain a physical understanding of the various processes that occur in an EC.