Finite element calculation of harmonic losses in AC machine windings

The finite-element method (FEM) with circuit constraints is used to study the problem of harmonic losses in stranded conductors typically found in AC machines. A discussion of the method is given along with examples using actual motor windings. The results of the finite element calculations are compared to a closed-form solution which ignores the effects of eddy currents on the field (resistance limited case) and which is commonly used in machine design to find the eddy factor. The agreement is good at low frequency but begins to diverge after the first few harmonics