On the validity of the harmonic superposition principle for computing rotor eddy current losses in permanent magnet machines

One of the issues in the design of surface permanent magnet machines is the prediction of rotor eddy current losses due to space harmonics in the armature reaction field. In performing this calculation, it is a common practice to apply the superposition principle, i.e. the power loss due to each single armature reaction field harmonic is computed and then the single loss contributions are summed to find the total losses. Such method would be correct if all stator harmonics produced rotor eddy currents with different frequency, but this is not generally the case. This paper investigates if and under what conditions the harmonic superposition principle can be applied without causing calculation errors. The investigation is extended to different kind of permanent-magnet machines, including surface-mounted, Halback and interior permanent magnet rotor topologies.