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

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 un-derstanding 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 dif-ferential capacitance in the PSpice & REG; program, and the theoretical and experimental comparison of the charge-voltage curves obtained during the transient discharge of the different EDLCs.