Dexin Xie

3-D nonlinear transient eddy current calculation of online power transformer under DC bias

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.

Three-dimensional optimal shape design of magnetic pole in permanent magnet assembly for MRI taking account of eddy currents due to gradient coil field

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.

Utilizing design sensitivity analysis for 3D optimization of transformer tank shields considering eddy currents

A novel 3D shape optimization algorithm is presented for electromagnetic devices carrying eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity for the surface nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of transformer and the effectiveness is proved.

A Complex-Valued Rotating Magnetic Property Model and Its Application to Iron Core Loss Calculation

This paper presents a complex-valued model when considering rotational magnetic properties of an electrical steel sheet from the viewpoint of improving the computation efficiency. The effective magnetic reluctivity and magnetic hysteresis coefficients in this model were interpolated from measured data based on a 2-D rotational magnetic property measurement system, in which the effect of higher harmonic terms of magnetic field intensity after saturation was considered. To reduce the computation error to some extent resulted from complex approximation of magnetic field quantities, the effective magnetic coefficients were expressed as the function of magnitude and direction of magnetic flux density. Considering transformer and three-phase induction motor core models as examples, the magnetic field distribution and core loss were calculated and the effectiveness of the proposed model was verified with the experimental results.

A novel mesh regeneration using structural deformation analysis for 3-D shape optimization of electromagnetic devices

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.

Measurement and Modeling of Anisotropic Magnetostriction Characteristic of Grain-Oriented Silicon Steel Sheet Under DC Bias

Magnetostriction in grain-oriented (GO) electrical silicon steel arises vibration and noise of the transformer core, especially when operating under direct current (dc) bias. In this paper, the anisotropy of magnetostriction of GO silicon steel sheets along the rolling direction (RD) and other directions deviated from RD was measured based on a standard single-sheet measurement system. The effect of applied stress on magnetostriction was also measured and analyzed. The magnetostriction under alternating magnetic field plus dc biased field was measured and a constitutive equation considering single-valued curves of magnetostriction under dc bias when incorporated with magnetic finite-element analysis was investigated. Considering a simple model as an example, the effectiveness of the proposed modeling method was verified by the comparison of simulation data and measured ones.

Robust 3-D shape optimization of electromagnetic devices by combining sensitivity analysis and adaptive geometric parameterization

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.

Research on Preconditioned Conjugate Gradient Method Based on EBE-FEM and the Application in Electromagnetic Field Analysis

Gauss-Seidel preconditioned conjugate gradient (GS-PCG) method based on element-by-element (EBE) is derived and the calculation process of finite element method (FEM) is presented in this paper. The corresponding FEM program are developed and implemented on the magnetic field calculations which produced by straight conductor carrying current and 3-phases induction motor respectively. The validity and accuracy of the method have been verified by comparing the result with the analytical solution. Compared with Jacobi preconditioned conjugate gradient (J-PCG) method based on EBE-FEM, less computational time and cost are needed for the proposed method with same accuracy. The proposed method can be applied to electromagnetic field analysis of transformer and motor, which may refer large scale numerical computation.

Research on preconditioned conjugate gradient method based on EBE-FEM and the application in electromagnetic field analysis

The Gauss–Seidel preconditioned conjugate gradient method applying to element-by-element finite-element method (EBE-FEM) is derived and the calculation process is presented in this paper. The EBE-FEM is a parallel numerical algorithm, in which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level without assembling the global system matrix. The validity and accuracy of the proposed method have been verified through the applications to magnetic field analysis of a long straight current-carrying wire and a three-phase electric motor. Compared with the Jacobi preconditioned CG method applying to EBE-FEM, less computational time and cost are needed for the proposed method with the same accuracy. The proposed method can be applied to electromagnetic field analysis of power transformer and electric motor, which may be related to large-scale numerical computation.

Magnetostriction of Silicon Steel Sheets Under Different Magnetization Conditions

The magnetostriction of electrical steel is one of the main sources causing deformation and vibration in rotational machine and transformer cores. The presence of dc bias or higher harmonics of magnetic field in the electrical apparatus cores makes the vibration and noise of cores more serious. Therefore, it is necessary to identify how different magnetization patterns contribute to the magnetostriction noise. This paper performs the measurement of magnetostrictive strain in non-oriented and grain-oriented electrical steel sheets under sinusoidal excitation, one with a dc bias and the other with a third harmonic component, respectively. An investigation of the effect of dc biased magnetic field on the magnetostrictive property is carried out. The influences of a third harmonic of magnetic field with a variety of amplitudes and phase delay on magnetostriction are studied and the acoustic noise level is calculated due to the presence of the second (100 Hz) and fourth (200 Hz) harmonics of magnetostrictive strain. The research results are important for evaluating the noise of electrical machine and transformer core effectively.