Supercapacitor equivalent electrical circuit model based on charges redistribution by diffusion

A new method for the determination of parameters for an equivalent electrical circuit model of supercapacitors is proposed. The method is based on the evaluation of the time dependence of voltage measured on the supercapacitor terminals after its charging by a defined current pulse. The measured time dependence of the voltage is fitted by an exponential function, where the exponent is proportional to the square root of time. This term reflects the redistribution of charges by diffusion inside the supercapacitor structure. The equivalent electrical circuit of supercapacitors is described by five parameters - two capacitors and three resistors. One capacitor corresponds to the Helmholtz capacitance, which is charged immediately with the time constant in the order of hundreds milliseconds, while the second one represents the diffuse capacitance, which is charged with the time constant in the order of hundreds seconds. The two resistors in the equivalent circuit model represent the equivalent series resistance and the leakage resistance, respectively, while the third resistor describes the resistance for charge diffusion in the supercapacitor structure. This resistance is time dependent and a way for calculating its value is demonstrated.