The use of fractional order operators in modelling of RC electrical systems

The present study concerns the analysis of using the integro-differential fractional operators in the process of modelling of electrical systems. As the object of study, the RC circuit with the ultracapacitor was used. A mathematical model of the super capacitor has been introduced, based on the integro-differential fractional order operator. Throughout the modelling it was assumed that the ultracapacitor was ideal. The main goal of the work was to carry out the experimental tests. Static and dynamic characteristics of the RC circuit with the ultracapacitor were determined with a prepared laboratory test rig. The obtained experimental results were compared with simulation tests of the ultracapacitor dynamics. The analysis, modelling and the obtained results allowed for the assessment of applicability of the fractional order operators in modelling of electrical systems. The proposed fractional order model yielded more precise description of dynamic properties of the system.