This paper presents a finite element investigation into the proximity losses in a high-speed permanent magnet (PM) machine for traction applications. A three-dimensional (3D) finite element analysis (FEA) is employed to evaluate and identify the endwinding contribution into the overall winding power loss generated. The study is focused on the end-winding effects that have not been widely reported in the literature. The calculated results confirm that the end-winding copper loss can significantly affect the eddycurrent loss within copper and it should be taken into account to provide reasonable prediction of total losses. Several structures of the end-winding are analyzed and compared in respect to the loss and AC resistance. The results clearly demonstrate that the size of the end-winding has a significant impact on the power loss. The calculated results are validated experimentally on the high-speed permanent magnet synchronous machine (PMSM) prototype for selected various winding arrangements.
The aim of this paper is to derive an analytical equations for the temperature dependent optimum winding size of inductors conducting high frequency ac sinusoidal currents. Derived analytical equations are useful designing tool for research and development engineers because windings made of foil, square-wire, and solid-round-wire windings are considered. Temperature dependent Dowell’s equation for the ac-to-dc winding resistance ratio is given and approximated. Thermally dependent analytical equations for the optimum foil thickness, as well as valley thickness and diameter of the square-wire and solid-round-wire windings are derived from approximated thermally dependent ac-to-dc winding resistance ratios. Minimum winding ac resistance of the foil winding and local minimum of the winding ac resistance of the solid-round-wire winding are verified with Maxwell 3D Finite Element Method simulations.