A Circuit Model Accounting for the Frequency-Dependent Behavior of Electrical Machine Windings

This paper presents a method to take into account, in a circuit model, the frequency-dependent behavior of electrical machine windings. First, the frequency-dependent inductances (both self and mutual) and resistances are determined thanks to time harmonic finite element (FE) computations in the frequency range of interest. The frequency-dependent behavior of the capacitances is investigated and the choice of using an electrostatic model is justified. Then, the different frequency-dependent parameters are included in a circuit model using behavioral voltage sources placed in series, which allows to forego using delicate fitting techniques within large scale lumped parameter models. Time-domain node voltages are then computed by reducing the circuit to the nodes of interest through the extraction of a reduced, frequency-dependent, nodal admittance matrix. An inverse fast Fourier transform can be readily applied to obtain the time evolution of inter-turn winding voltages. Alternatively, using vector fitting on the reduced equivalent circuit can further improve results by ensuring passivity and filtering unphysical high-frequency modes, with reasonable computational overhead. This enables the usage of the proposed method as a diagnostic tool before or during the phase of electrical winding design. A test winding with 69 turns is used for validation. An excellent agreement between experimental and simulation results is observed both in the frequency- and in the time-domain.