Magnetic losses simulation in PM SM drive by FE: Harmonic superposition by method of locked rotor

The PWM-supplied permanent magnet synchronous machines are exposed to magnets' heating due to harmonic fields which rotate in relation to rotor. The corresponding losses can be calculated by FE simulation for each frequency, with superposition of all components of the losses. In certain conditions three dimensional modelling is required to get enough precision. However, time-stepping 3D finite element methods coupled with motion equations can lead to excessive computational time. Then a locked rotor approach with current sheet rotating may be interesting. In this case however, the superposition doesn't really work unless special procedure is applied. Magnetic loss dissipation cannot be correctly calculated with simple superposition of individual fields, e.g. the 5
^th
and 7
^th
harmonic rotating in opposite direction. This is because the resulting field has an alternative component with dissipative effects depending on its position. They will be more important if the component oscillates in the middle of magnets and less important in the middle of gap between them.