Fractional-order Modelling and Parameter Identification of Electrical Coils

The accurate modelling of an electrical coil over a wide range of frequency is the keystone for a precise modelling of an electrical machine. As a consequence of copper losses, eddy-current losses and hysteresis losses; electrical coils with conductive ferromagnetic core show different behaviour from that of an ideal coil. Throughout this paper, dynamic modelling and performance analysis of conventional as well as fractional-order models of an electrical coil with an interchangeable core are achieved. Measurement results are acquired through an integration between Matlab and the high-speed measurement system LTT24. In order to assess the accuracy of these models, simulation results are compared with experimental results whereas unknown parameters are identified through an optimization process that is based on the method of least squares. It is known that the parameters of fractional-order model (Lα, α, Cβ, β) can not be measured directly. Therefore, the paper proposes a possibility based on system analysis to derive these parameters (indirect measurement) from the parameters of the classical model. A frequency band beyond the self-resonant frequency of the electrical coil is explored, thus the parasitic capacitance between coils windings must be considered as an important part of the equivalent circuit. The dependency of model parameters on frequency due to skin-effect is also examined.