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An improved magnetic reluctivity model is developed to describe two-dimensional magnetic properties of anisotropic material. In this model, the behavior of magnetic field intensity is explained in terms of magnitude and direction of magnetic flux density, and reluctivity tensor always has zero off-diagonals. The proposed reluctivity model is incorporated into nonlinear finite element formulation using Newton-Raphson method, and applied to magnetic field analysis of a single-phase transformer core model. By comparing the analyzed B-waveforms with experimental ones, the effectiveness of the proposed reluctivity model and FE formulation is investigated. Index Terms--Anisotropic, electrical steel sheet, grain-oriented, magnetic reluctivity, two-dimensional magnetic property.

The Latin hypercube sampling (LHS) strategy is applied to the optimization of a magnet pole shape of large scale BLDC motor to minimize the cogging torque with an adaptive response surface method. In the strategy, the qualities of sampling points are evaluated in the viewpoint of uniform space-filling by using Min-distance and Max-distance metrics, and optimum sampling points are obtained in Pareto-optimal sense. An adaptive sampling point insertion is also achieved utilizing design sensitivities computed by using finite element method to get a reasonable response surface with a relatively small number of sampling points. The LHS strategy is incorporated with (1 d [lambda]) evolution strategy, and applied to the permanent magnet pole shape optimization of 6 MW BLDC motor, and the results are compared with those of other algorithms. Index Terms--BLDC motor, cogging torque, Latin hypercube sampling, optimization, Pareto-optimization, response surface method.

This paper presents an improved vector magnetic property model of anisotropic electrical steel sheet taking account of both the modeling accuracy and the computational cost when combined with finite element (FE) formulation. The reluctivity and hysteresis coefficients in the model are calculated using Fourier series expansion of measured B- and H-waveforms, which are obtained by using a self-developed double-excitation type 2-D measuring apparatus. The time-stepping FE formulation considering the improved vector magnetic property model is derived and applied to magnetic field analysis of a single phase transformer core model made of Grain-oriented silicon steel sheet. The convergence characteristic of non-linear FE analysis is discussed, and the effectiveness of the proposed magnetic property model in comparison with the experimental results is investigated. Index Terms--Finite element formulation, Fourier series expansion, grain-oriented silicon steel sheet, 2-D measuring apparatus.

An adaptive response surface method with Latin hypercube sampling strategy is employed to optimize a magnet pole shape of largescale brushless direct current (BLDC) motor to minimize the cogging torque. The proposed algorithm consists of the multi-objective Pareto optimization and (1 + [lambda]) evolution strategy to find the global optimal points with relatively fewer sampling data. In the adaptive response surface method (RSM), an adaptive sampling point insertion method is developed utilizing the design sensitivities computed by using finite-element method to get a reasonable response surface with a relatively small number of sampling points. The developed algorithm is applied to the shape optimization of PM poles for 6 MW BLDC motor, and the cogging torque is reduced to 19% of the initial one. Index Terms--Brushless direct current (BLDC) motor, cogging torque, Latin hypercube sampling, optimization, response surface method.

This paper presents an improved magnetic reluctivity model for vector magnetic properties of anisotropic electrical steel sheet based on Chua-type model using Fourier series expansion of measured B and H waveforms in the viewpoint of engineering application. In the modeling, B-spline surface interpolation is adopted to obtain smooth approximation of measured data. The accuracy of the proposed magnetic reluctivity model is verified by comparing its modeling results with experimentally measured B- and H-waveforms with 30PG110 grain-oriented silicon steel sheet. The nonlinear finite element (FE) formulation is also derived to incorporate the proposed reluctivity model, and applied to magnetic field analysis of a single phase transformer core model. By comparing the numerical results with experimental ones, the effectiveness of the reluctivity model and FE formulation is investigated. Index Terms--Finite element analysis, Fourier series expansion, grain-oriented silicon steel sheet, magnetic reluctivity model.

The cogging force of a permanent-magnet linear motor (PMLM) is a major component of the detent force, but unfortunately makes a ripple in the thrust force and induces undesired vibration and acoustic noise. It also deteriorates the control characteristics, particularly in regard to precise speed and position control. In this paper, we propose a new PMLM having a 9-pole 10-slot structure in order to reduce the cogging force. Our PMLM is properly wound for three-phase driving. Through a theoretical and finite-element analysis, we show that the 9-pole 10-slot PMLM removes almost all of the cogging force while giving 10% and 23% larger back-electromotive force and thrust force, respectively, than a conventional 8-pole 12-slot PMLM under the same conditions of exciting current, total number of windings, and total PM volume. Index Terms--Cogging force, detent force, permanent-magnet linear motor, thrust force.

A novel monohedral permanent magnet (PM) configuration is suggested and geometrically optimized to have higher magnetic efficiency as well as higher degree of access to imaging region of a magnetic resonance imaging (MRI) system. The configuration has a pair of main PMs magnetized in the opposite directions, respectively. The geometry of the main PMs is optimized by using genetic algorithm combined with a novel flexible magnetic field analysis method which combines finite-element method and new-type equivalent source method. Through an optimal design, the suggested PM configuration is proven to provide a sufficiently homogeneous and strong magnetic field for MRI application. Index Terms--Finite element method (FEM), magnetic resonance imaging (MRI), monohedral permanent magnet (PM), new-type equivalent source method (NESM).

In magnetic resonance imaging (MRI) magnets, field shimming technique is, in general, necessary to increase the field homogeneity in imaging region to an acceptable level after manufacturing. This paper presents a novel passive shimming method using permanently magnetized shimming pieces. In the method, the shimming design is modeled as an integer programming problem, and the distribution of shimming pieces is optimized. Through an application to a 0.3-T permanent magnet MRI system, the optimally designed shimming pieces are proven to improve the field homogeneity from 1456 to 784 ppm after just one iteration of shimming courses is carried out. Index Terms--Integer programming, magnetic resonance imaging (MRI), optimization, permanent magnet (PM).

Switched-reluctance motors produce acoustic noise and vibration caused by torque ripple. Applications of these motors where silent operation is desirable, such as in home appliances, has, thus, been limited. This paper describes a proposal for a new stator pole face having a nonuniform air-gap and a pole shoe attached to the lateral face of the rotor pole. These additions minimize the undesired torque ripple. The effects of each design parameter were investigated using a time-stepping finite-element method. The parameters were optimized by utilizing response surface method (RSM) combined with (1 + 1) evolution strategy. It has been shown, through numerical tests, that the optimized shape gives higher average torque and drastically reduced torque ripple. Index Terms--Air-gap profile, inductance, optimization, response surface method, switched-reluctance motor (SRM), torque ripple.

This paper proposes a new algorithm for the shape optimization of a large-scale brushless dc (BLDC) motor to reduce the cogging torque. In the algorithm, an adaptive response surface method (RSM) using the multiquadric radial basis function is employed to interpolate the objective function in design parameter space, and incorporated with (1 + 1) evolution strategy to find an optimal point. In the adaptive RSM, an adaptive sampling point insertion method is developed utilizing the design sensitivities computed by using the finite-element method to get a reasonable response surface with a relatively small number of sampling points. The developed algorithm is applied to the shape optimization of a 5-MW BLDC motor, and the cogging torque was reduced to 17% of the initial one. Index Terms--Brushless dc motor, cogging torque, design sensitivity, optimization, permanent magnet (PM), response surface method (RSM).

A new surrogate objective function is suggested for the global optimization of electromagnetic devices. The surrogate objective function is constructed using a [C.sup.1] piecewise response surface incorporated with the design sensitivities computed by using the finite-element method. The sampling data points used for constructing the response surface are adaptively inserted during the optimization process. After the surrogate objective function is constructed, the global optimum point is obtained by using a genetic algorithm. Applications to benchmark problems and the optimum design of a permanent magnet system show the effectiveness of the proposed algorithm. Index Terms--Design sensitivity, finite-element analysis, global optimization, response surface patches.

The pole piece of a permanent magnet magnetic resonance imaging (MRI) is optimally designed in three-dimensional (3-D) space, taking into account the nonlinearity of materials to get high homogeneous magnetic fields in the working region. The pole face is parameterized using a B-spline surface and optimized using 3-D nonlinear design sensitivity analysis based on the 3-D finite-element method. An optimal design result shows how the nonlinear magnetic property of the yoke and column, as well as the pole piece, affect the magnetic-field homogeneity in the working region, although the MRI system has a large air gap. Index Terms--Design sensitivity analysis, permanent magnet, geometric parameterization, magnetic resonance imaging (MRI), nonlinear.

This paper presents new methods for determining a proper relaxation factor of the Newton--Raphson method to accelerate the convergence characteristics of a nonlinear finite-element analysis. In the methods, the squared residual of the Galerkin's approximation is successively approximated to a quadratic function using the gradients or Brent's method, and a relaxation factor is determined by minimizing the quadratic function until a quasioptimum relaxation factor is obtained. The presented methods are applied to the TEAM Workshop problem 13, and the results are compared with a conventional method. Index Terms--Brent's method, Newton--Raphson method, nonlinear magnetic field analysis, relaxation factor, residual.

This paper presents a new method to analyze the three-dimensional (3-D) nonlinear transient eddy currents and losses of an online transformer in a power system under direct current bias. In the method, power system simulation is incorporated with 3-D field computation to obtain the magnetic parameters and the equivalent exciting source of the online transformer. Index Terms--DC biased, eddy current, power transformer, system simulation.

A three-dimensional (3-D) shape optimization algorithm is developed by combining the geometric parameterization of the design surface using spline technique and design sensitivity analysis. The design surface is parameterized using Bezier spline or B-spline, and the control points of the spline are taken as the design variables. Considering nonlinearity of the material, the design sensitivities for the nodal points on the design surface and the adjoint variable are computed based on 3-D nonlinear finite-element method. The parameterized design sensitivities for the control points of the spline are computed from those for the nodal points. Through a numerical implementation, the developed algorithm is proved to guarantee a smooth design surface. Index Terms--Design sensitivity analysis, geometric parameterization, nonlinear, shape optimization.

A completely open magnet geometry satisfies the requirement of a MRI system for the surgical procedure. This paper presents a new flexible design method to facilitate the construction of a completely open MRI magnet by combining the magnetic dipole pair model and optimization algorithm. A numerical implementation shows that the method provides a main magnetic field with sufficient homogeneity and strength at the imaging region, which is defined outside of the magnet structure, and minimizes the cost of the MRI equipment. Index Terms--Completely open MRI magnet, magnetic dipole, optimization, permanent magnet.

A new robust three-dimensional (3-D) shape optimization algorithm is suggested for electromagnetic devices, which combines design sensitivity analysis and adaptive geometric parameterization of the design surface. During the optimization process some extra control points are automatically inserted to describe the shape variations properly, and the control points are maintained so as not to be superfluous but to keep the design surface from oscillating. The newly inserted control points are located around the nodal points which have large fitting sensitivity. Through a numerical application, it is shown that the algorithm ensures a design with good performance as well as a smooth design surface. Index Terms--Adaptive geometric parameterization, Bezier surface, design sensitivity, fitting sensitivity, shape optimization.

The ferromagnetic pole pieces of permanent magnet assembly for magnetic resonance imaging is optimally designed taking account of the pulse excited gradient coil field. In the design, the transient design sensitivity analysis is combined with the three-dimensional finite element method to give a search direction The effects of the eddy currents, induced on the ferromagnetic pole pieces, on the main magnetic-field strength and homogeneity in diameter of interested region are also investigated. Index Terms--Bezier spline, magnetic resonance imaging (MRI), permanent magnet, shape optimization, transient design sensitivity.

A new finite-element mesh regeneration method is presented for three-dimensional shape optimization of electromagnetic devices. The method has its theoretical basis in the structural deformation of an elastic body under stress. When the design surface changes in the optimization process, the method maps the surface displacement onto the nodal points of the finite-element mesh without a change in mesh topology. Numerical examples with design sensitivity analysis show the method guarantees a smooth shape with proper mesh quality and keeps the initial mesh topology. Index Terms--Design sensitivity analysis, mesh deformation, structural deformation analysis, three-dimensional shape optimization.

We present a new design method for reducing cogging torque in brushless permanent-magnet (PM) motors. In our method, the auxiliary slots are put on the pole face of the magnetizing yoke, which results in a not fully magnetized zone (NFMZ) at the PM. Through Fourier expansion of the field and armature functions, the position and shape of the NFMZ that eliminate the cogging torque are found. In an example, we discuss the effectiveness and applicability of the new method. Index Terms--Auxiliary slots, brushless permanent-magnet (PM) motors, cogging torque, magnetizing yoke, not fully magnetized zone (NFMZ).

A procedure is proposed for calculating hysteresis loss of high temperature superconducting (HTS) bulk material in a time-varying magnetic field is described and discussed.

An accurate estimation for the magnetostrictive effect in highly grain-oriented electrical steel sheet (HGO-ESS) is helpful for determining the deformation and vibration originating from magnetostriction during the design stages of electrical equipment such as the motor and power transformer. In this article, a Preisach-based magnetostriction model for HGO-ESS is proposed to simulate the normal and shear magnetostriction properties under alternating and rotating magnetic fields. In the model, the Everett function databases are constructed and identified by using a set of measured symmetric magnetostriction butterfly loops under different rotating magnetic field conditions. The measurement butterfly loops are measured by a round-type two-dimensional single strain tester (R-2-D-SST). Finally, the simulation data and measurement data under different rotational magnetization conditions are compared to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]