Fractional-order models of the supercapacitors in the form of RC ladder networks

In the paper, mathematical models of the supercapacitors are investigated. The models are based on electrical circuits in the form of RC ladder networks. The elementary cell of the network may consist of resistances and capacitances that are connected in series or parallel. The dynamic behavior of the circuit is described using fractional-order differential equations and its properties are analyzed. The identification procedure with quadratic performance index is performed in time domain to identify the parameters of the supercapacitor models. The results of numerical simulations are compared with the results measured experimentally in the physical system. In addition, an example from the automotive industry is used for an experimental evaluation of the theoretical analysis and to present a perspective on the applicability of the approach for other industrial projects.