Bivariate quadratic method in quantifying the differential capacitance and energy capacity of supercapacitors under high current operation

•A bivariate quadratic method for the electrical characteristics of supercapacitors.•The capacitance and energy capacity are derived directly from terminal measurements.•The capacitance–voltage characteristic is more complex than a linear function.•The capacitance exhibits variation between charging and discharging states.•Up to 79% of the total energy is available within the 50%–100% nominal voltage range.

Capacitance and resistance are the fundamental electrical parameters used to evaluate the electrical characteristics of a supercapacitor, namely the dynamic voltage response, energy capacity, state of charge and health condition. In the British Standards EN62391 and EN62576, the constant capacitance method can be further improved with a differential capacitance that more accurately describes the dynamic voltage response of supercapacitors. This paper presents a novel bivariate quadratic based method to model the dynamic voltage response of supercapacitors under high current charge–discharge cycling, and to enable the derivation of the differential capacitance and energy capacity directly from terminal measurements, i.e. voltage and current, rather than from multiple pulsed-current or excitation signal tests across different bias levels. The estimation results the author achieves are in close agreement with experimental measurements, within a relative error of 0.2%, at various high current levels (25–200 A), more accurate than the constant capacitance method (4–7%). The archival value of this paper is the introduction of an improved quantification method for the electrical characteristics of supercapacitors, and the disclosure of the distinct properties of supercapacitors: the nonlinear capacitance–voltage characteristic, capacitance variation between charging and discharging, and distribution of energy capacity across the operating voltage window.