Calculation of electromagnetic rotor losses in high-speed permanent magnet machines
High-speed permanent magnet machines are currently being developed for a number of applications including gas-turbine generator sets and machine tools. Due to the high peripheral speed of the rotor and the relatively high conductivity of the magnets used, rotor eddy current loss can be substantial. Quite low levels of loss may present a serious problem if rotor cooling is poor. The accurate calculation of these losses, and appreciation of their dependence on machine parameters, are therefore of great importance for reasons of both efficiency and temperature rise. In this, thesis, a method has been developed to evaluate the asynchronously rotating harmonics with respect to the rotor and to calculate rotor power loss caused by these harmonics. The harmonics are determined by double Fourier analysis of the normal flux density data over the rotor surface. The data is obtained from finite element magnetostatic analysis of the machine at different rotor positions, with all possible harmonic sources present, except rotor induced eddy currents whose effect on harmonics was found to be negligible. Rotor power loss is calculated for each harmonic using a 2D rectilinear current sheet model of the machine. The magnitude of the current sheet, which is placed on the inner surface of a toothless stator, is adjusted to produce the same magnetostatic normal flux density over the rotor surface as that of the corresponding harmonic. The 2D current sheet model does not allow for 3D end effects and magnet segmentation. The accuracy of the analytical rectilinear current sheet model was verified by comparison with a cylindrical FE current sheet model, and by solving a benchmark eddy current problem that can be also solved using FE steady-state AC analysis. The current sheet model was used to calculate rotor loss in a number of generic machines, with two basic types of rotor construction: 1) non-salient rotor with arc shaped surface magnets and 2) salient rotor with chord shaped surface magnets. The results show that rotor loss depends strongly on the ratio of slot opening to slot pitch (s/X.) and on the ratio of total airgap to slot pitch (g/X). For the same fundamental airgap flux density, rotor loss reduces dramatically by increasing airgap length and reducing slot opening. Increasing the number of slots also reduces the loss. The results also show that rotor loss in a generator increases as the power factor moves from lagging to leading due to the armature reaction effect. Using a conducting sleeve, instead of a non-conducting one, with conductivity in the range of practical values, increases rotor losses dramatically. Reducing magnet conductivity reduces rotor loss. Rotor power loss in machines with non-conducting sleeve is concentrated on the surface of the magnet and a small part on the surface of the hub. In machines with chord shaped magnets, the power loss density can be very high in the parts of the steel hub near the intersection of two poles where local total airgap is small. The harmonics caused by inverter switching in a motor or rectifier switching in an alternator can cause a very significant increase in rotor loss, compared to a machine with a sinusoidal mmf. The results also show that the loss depends strongly on the switching strategy, e.g., switching harmonics in 6 step mmf waveform produce 3 times more loss than a 12 step mmf waveform. Although the developed method for calculation of rotor power loss does not take the effect of magnet peripheral discontinuity or segmentation into account, it is clear that segmentation reduces power loss by interrupting the eddy current return path, specially for harmonics with long wavelengths. The effect of segmentation requires further study.