Non-Linear Analytical Model for the Study of Double-Layer Supercapacitors in Different Industrial Uses

Abstract

It is generally considered that the representation of a double layer supercapacitor (DLSC) cannot be performed with the usual capacitance and resistance series connected, as it induces a relatively high level of inaccuracy in the results. In multiple previous studies, more advanced models have been developed with very different approaches: models with distributed parameter circuits, based on artificial neural networks (ANNs), fractional order, etc. A non-linear model, less complex than the previous ones and whose behavior adequately represents the DLSCs, is the one formed by a variable capacitance, dependent on its internal voltage. This paper presents a mathematical study to obtain analytical expressions of all the electrical variables of DLSCs, voltage, current, dissipated power and so on, by means of a previous model. This study is carried out considering that the DLSC is charged and discharged through a voltage source and also discharged through a resistor. In later sections, the operational conditions of the DLSC in numerous industrial applications are presented. Finally, a comparative analysis is made between the results produced by the conventional model, with constant capacitance, and the developed model. This analysis is finally followed by the conclusions.