Nonlinear charge-voltage relationships in electric double layer capacitors performing under constant load resistance

Abstract

Nonlinear charge-voltage relationships in electrochemical double layer capacitors (EDLCs) performing under constant load resistance, are analyzed. Three commercial EDLCs with nominal capacitances in the range from 0.1 to 1 F and maximum voltage 5 V, are selected. The time evolution of the electric current obtained during the discharge through a resistor of an EDLC, which is initially charged at a constant potential, is gathered and the electric charge is determined from the area of the current-time curve. Evolution with the electric potential of the stationary charge stored in the EDLCs is interpreted by means of a fitting which leads to a polynomial model for the capacitance. The study of the nonlinear dependence with voltage of the charge allows us to deepen in understanding the differences between integral and differential capacitances of an EDLC, as well as consider the role played by the capacitance at the zero-voltage limit. The model is validated by means of the simulation of the equivalent circuit constituted by the series combination of the equivalent series resistance (ESR) and the differential capacitance in the PSpice® program, and the theoretical and experimental comparison of the charge-voltage curves obtained during the transient discharge of the different EDLCs.