Homogenization of Form-Wound Windings in Frequency and Time Domain Finite-Element Modeling of Electrical Machines

In this paper, the authors deal with the finite-element (FE) modeling of eddy-current effects in form-wound windings of electrical machines using a previously proposed general frequency- and time-domain homogenization method. By way of demonstration and validation, a real-life 1250-kW induction machine with double-layer stator winding is considered. The skin and proximity effects in one stator conductor (copper bar) are first quantified by means of a simple low-cost FE model, leading to complex and frequency-dependent coefficients for the homogenized winding (reluctivity for proximity effect and conductivity or resistance for skin effect). These complex coefficients are subsequently translated into real-valued and constant coefficients that allow for time-domain homogenization when introducing a limited number of additional degrees of freedom in the FE model. All results obtained with the homogenized model (considering one conductor or a complete slot) agree well with those produced by a brute-force approach (modeling and finely discretizing each conductor).