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The Halbach magnet array has become more and more attractive in many electromagnetic engineering domains such as electrical motors for its potential features such as self-shielding and providing sinusoidal field distribution. This paper develops analytical models formulated in polar coordinates for predicting the field distribution of a segmented Halbach magnet cylinder with or without back iron. Based on the analytical models, the relationships between the air-gap flux density and four design parameters including pole-pair number, segment number per pole, permanent-magnet radial dimension, and air-gap length are analyzed. Further, the Taguchi method is employed to identify the settings of design parameters and determine the parameters which have a significant effect on the field distribution. The analytical models are verified by taking advantage of the finite-element method (FEM), which shows that all the results can be of considerable use in the design of permanent-magnet machines.Index Terms-Halbach array, Halbach cylinder, magnetic field, permanent magnet, Taguchi method.

In this article, a novel self-regulating and self-evolving particle swarm optimizer (SSPSO) is proposed. Learning from the idea of direction reversal, self-regulating behaviour is a modified position update rule for particles, according to which the algorithm improves the best position to accelerate convergence in situations where the traditional update rule does not work. Borrowing the idea of mutation from evolutionary computation, self-evolving behaviour acts on the current best particle in the swarm to prevent the algorithm from prematurely converging. The performance of SSPSO and four other improved particle swarm optimizers is numerically evaluated by unimodal, multimodal and rotated multimodal benchmark functions. The effectiveness of SSPSO in solving real-world problems is shown by the magnetic optimization of a Halbach-based permanent magnet machine. The results show that SSPSO has good convergence performance and high reliability, and is well matched to actual problems.

The variable-speed generator motor (VSGM) for pumped storage has a cylindrical rotor with three-phase lap or wave windings distributed in slots evenly and fed by a converter. For a large-scale VSGM, the electromagnetic force (EMF) on rotor end windings is an important contributor to distortion, vibration, and even damage of rotor end windings. A 3D finite element model of rotor end region of a 300 MW VSGM is set up. The distribution map of EMF density on involute and nose parts of rotor end windings, under rated load and three-phase short circuit at supersynchronous and subsynchronous speed, is drawn. Furthermore, the amplitude of EMF is calculated, and the radial, tangential, and axial components of EMF are analyzed. The results in this paper will lay a foundation for design of rotor end windings and their support structure.