Ferromagnetic coil frequency response and dynamics modeling with fractional elements

The modeling of coils with ferromagnetic cores is considered. An attempt is made at the application of fractional derivatives because of the success in the modeling of real phenomena in various other fields. Three coils with ferromagnetic cores have been selected for the analysis. In order to obtain a basis for the study, measurements have been taken on a specially designed setup including an arbitrary function generator and a data acquisition device. The measurement process has been controlled by an original algorithm written in C#. The studied model has been considered in several varieties (various numbers of fractional coil and capacitor branches) in a ladder-like structure. The estimation process has been performed in an original program written in C#, applying the COBYLA method for constrained optimization. The modeling and simulation results have been compared through their frequency characteristics. A more critical approach has also been applied, where the measurements and simulations are compared for both a non-sinusoidal waveform and a step function on the source output.