(2014)
Rotor eddy current power losses in high speed permanent magnet synchronous generators.
*University of Southampton, Faculty of Engineering and the Environment, Doctoral Thesis*, 265pp.

## Abstract

Rotor electromagnetic losses can be problematic in high speed permanent magnet synchronous machines, especially when the speed or the electrical loading are high and the slotting and winding configuration results in high magnitude asynchronous harmonics. Accurate estimation of these travelling flux harmonics in the initial design stage is essential, as small errors can result in significant errors in the estimated rotor losses, which could lead to misinformed design decisions.

This Thesis makes a number of contributions to the subject of rotor losses in PM machines. It firstly investigates the accuracy of the commonly used current sheet method for estimating losses for each harmonic. In this method, the losses are calculated using a multi-layer model of the machine in which each asynchronous harmonic in the rotor frame is represented by current sheet on the surface of the bore of a slotless stator. The harmonics are calculated using double Fourier transform of flux density data on the surface of the magnet obtained from a number of magnetostatic finite element (FE) solutions at different rotor position. The losses are also calculated using 2D transient FEA with rotor motion, with appropriate mesh refinement and time step determined based on a mesh and time step dependence study. The results show that the current sheet method accurately calculates the losses in ring magnets if the amplitudes of the harmonics are estimated accurately.

Secondly, the Thesis extends 3 analytical methods that have been reported in the literature by Zhu and Howe (1993), Gieras (2004) and et al (2006) to estimate the amplitude of the no-load asynchronous travelling flux density harmonics, the magnet flux tooth ripple harmonics, in the rotor frame. The accuracy of these methods is evaluated by comparison to those calculated using non-linear finite element analysis for variants of a particular machine. The results show that ( et al, 2006) complex permeance method provides the closest estimate, when the level of saturation in the machine is negligible. However, if the saturation, of the tooth tip in particular is significant, then all methods underestimate the amplitudes of the harmonics. And accordingly, the estimated rotor losses are grossly underestimated by a factor of 1:3 in a machine with heavy tooth tip saturation.

Thirdly, the Thesis tackles the problem of losses in a loaded generator with sinusoidal currents. It is shown that the total losses in the machine are dependent on the power factor and the phase angle between the emf and current. The total loss cannot be simply calculated by adding the no-load loss due to magnet flux tooth ripple harmonics and the loss due to stator mmf asynchronous harmonics. This is due to the interaction between the stator mmf harmonics and the magnet flux tooth ripple harmonics, which need to be added vectorially. This is verified

by comparing the results calculated analytically (using the most accurate ’s meth d f calculating no-load harmonics), with those obtained from transient FEA in a machine with no significant saturation.

Fourthly, the Thesis investigates rotor losses in a generator with two slots per pole per phase connected to an uncontrolled diode rectifier, considering the two cases of constant current and constant voltage dc link. Two winding and rectifier configurations are considered: a 3-phase winding with a 3-phase, 6 pulse bridge rectifier and a double 3-phase winding with a 3-phase rectifier each, connected in series i.e., a 12 pulse rectifier. Both magnet flux tooth ripple and armature reaction stator mmf harmonics are considered in the calculation of rotor loss; the harmonics were added vectorially. It is shown that the machine with double 3-phase windings and 12 pulse rectifier has considerably lower rotor losses that the machine with one single 3-phase winding due to cancellation of high order harmonics.

Finally, limited studies are performed in the Thesis for the calculation of rotor losses in PMSGs with different slot opening, number of slots per pole and airgap (with magnet thickness adjusted to keep the airgap flux density and emf constant). It is shown that increasing the airgap and reducing slot opening reduced the losses The results plotted in a normalised form of loss per unit rotor surface area are versus the ratios of gap/slot pitch and slot opening divided by pole pitch. These curves are shown to give reasonable quick estimates of rotor losses in machines with different sizes. Also, rotor losses are calculated in three PMSGs with different numbers of slots per pole and winding / rectifier configurations. The results show that the popular 1.5 slots per pole concentrated winding configuration have considerably higher rotor losses due to the strong second harmonic than the other machines with lap windings.

The work in the Thesis was based on two-dimensional calculations, assuming ring magnets. Further work is needed to evaluate the 3D effect and magnet segmentation.

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