In this paper, we study the model electrical circuit containing a supercapactor. For solve the electrical circuit operation used fractional definition: the Caputo definition, Conformable Fractional Derivative (CFD) definition and combination of both definition of non-integer order containing fractional time derivatives the Conformable Fractional Derivative in Caputo sense. The state equation for a given electrical circuit has been developed. An electrical circuit model was built and were performed in three measurement series each with a different external resistance. The results of the electrical circuit with calculations using differential equations and the classical method were analyzed.
The paper presents an analysis of the electrical circuit with the supercapacitor in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations developed for two types of definitions of fractional derivative: Caputo and the Conformable Fractional Derivative (CDF). The voltage characteristics of the charge supercapacitor were compared with the results of analytical tests. The voltage was measured on the supercapacitor. Next was determined with of solution are the best fit compared: classic case solution and solution using the fractional order definition. The tests were carried out for three different resistance values. Using the method of least-squares optimization the analytical results and measurements were compared with each other by the function of matching error.
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