Three-dimensional Field Problems Research Articles

An Analytical Method for Calculating the Cogging Torque of a Consequent Pole Hybrid Excitation Synchronous Machine Based on Spatial 3D Field Simplification

Consequent pole hybrid excitation synchronous (CPHES) machines have the advantage of symmetrical bidirectional magnetomotive force increments. Compared with a traditional hybrid excitation motor (HEM), a CPHES machine improves the disadvantage of asymmetry in the adjustment range when magnetization and demagnetization occur. The calculation and analysis of the cogging torque of the CPHES machine are complex due to the complicated structure. This paper proposes an analytical method for calculating the cogging torque of a CPHES machine. This analytical method converts the complex three-dimensional magnetic field problem into a two-dimensional magnetic circuit problem and, through the accumulation method, can quickly and accurately calculate the cogging torque of the CPHES machine. In contrast with the finite element method, the calculation results basically follow each other, but the analytical method is more efficient and omits complicated meshing. This is of great significance to the preliminary electromagnetic design and performance optimization of a CPHES machine.

Parallel optimization of three-dimensional wedge-shaped underwater acoustic propagation based on MPI+OpenMP hybrid programming model

The three-dimensional wedge-shaped underwater acoustic propagation model exists analytical solution, which provides verification for models like FOR3D propagation model under certain situation. However, the solving process of a three-dimensional complex underwater sound field problem is hindered by intensive computing and long calculation times. In this paper, we exploit a hybrid parallel programing model, such as MPI and OpenMP, to accelerate the computation, design various optimization methods to improve the overall performance, and then carry out the performance and optimization analysis on the Tianhe-2 platform. Experiments show that the optimized implementation of the three-dimensional wedge-shaped underwater acoustic propagation model achieves a 46.5 speedup compared to the original serial program, thereby illustrating a substantial performance improvement. We also carried out scalability tests and parallel optimization experiments for large-scale practical examples.

Simulation of the electric field and the GPR resulting from vertical-driven rods earthing system in a multi-layers earth structure

A three-dimensional model for calculating the ground potential rise and the electric field distributed at the ground surface of an earthing system using driven vertical rods is presented. The electric field distribution is obtained by using Laplace's equation which is solved by finite element method. The presented model for simulating electrical field is a three-dimensional field problem with different types of earth models; one and two- layers earth models, in two different cases. The first case is represented by one driven rod while the second one is represented by three driven rods. The strength of the finite element method in this application is in its ability to allow a detailed representation of the types of the soil and different cases of the rod simulation. The new simulation model has been assessed through comparing the vertical field strength over the vertical driven rod surface, with that estimated one in other experimental and computational work. A primarily simulation for investigating the thermal effect is achieved and more investigation about this point will be presented in the future papers.

Proper Generalized Decomposition Method Applied to Solve 3-D Magnetoquasi-Static Field Problems Coupling With External Electric Circuits

In the domain of numerical computation, proper generalized decomposition (PGD), which consist in approximating the solution by a truncated sum of separable functions, is applied more and more in mechanics, and has shown its efficiency in terms of computation time and memory requirements. We propose to evaluate the PGD method to solve three-dimensional (3-D) quasi-static field problems coupling with an external electric circuit. The numerical model, obtained from the PGD formulation, is used to study the 3-D examples. The results are compared with those obtained when solving the full original problem. It is shown in this paper that the computation time rate versus the number of time steps is very small compared with the one in a classical time-stepping method, and can be very efficient to solve problems when small time steps are required.

A boundary conformal discontinuous Galerkin approach for electro-quasistatic field problems on Cartesian grids

A boundary conformal approach for solving three-dimensional electro-quasistatic field problems with a high order discontinuous Galerkin method on Cartesian grids is proposed. The method is based on a novel cut-cell discretisation which is applied only on elements intersected by curved material boundaries. A particular numerical quadrature is introduced which allows for an accurate integration of the high order finite element operators taking into account the exact geometry of the cut-cells. Furthermore, a general hybridisation of the cut-cell approach with the conventional finite element method in the homogeneous parts of the computational domain is proposed. Numerical examples are presented which demonstrate the accuracy of this discretisation method for practical problems with curved geometries.

Onset voltage of a particle-initiated negative corona in a co-axial cylindrical configuration

This paper presents a theoretical and experimental study of the effect of conducting particles on the onset voltage of a negative corona in air-insulated co-axial cylindrical configurations. The conducting particles are spheres or wires of varying dimensions. The particle is fixed either on the inner or the outer cylinder. The calculated onset voltage of the negative corona is based on the criterion developed for the formation of repetitive negative coronas, Trichel pulses. This calls first for an accurate calculation of the electric field in the vicinity of the particle where avalanches grow. The investigated gap in the presence of a particle is a three-dimensional field problem due to the asymmetrical position of the particle inside the gap. The three-dimensional electric field is calculated using the charge simulation technique with a new charge distribution. An experimental set-up is built up to measure the onset voltage of a negative corona initiated by particles in an air-insulated co-axial configuration to check the accuracy of the present calculation. The effect of varying field nonuniformity, particle shape, size and position on the onset voltage of the negative corona is investigated. The calculated onset voltage values agree well with those measured experimentally.

Optimal design of groundwater remediation systems using a multi-objective fast harmony search algorithm

A new multi-objective optimization methodology is developed, whereby a multi-objective fast harmony search (MOFHS) is coupled with a groundwater flow and transport model to search for optimal design of groundwater remediation systems under general hydrogeological conditions. The MOFHS incorporates the niche technique into the previously improved fast harmony search and is enhanced by adding the Pareto solution set filter and an elite individual preservation strategy to guarantee uniformity and integrity of the Pareto front of multi-objective optimization problems. Also, the operation library of individual fitness is introduced to improve calculation speed. Moreover, the MOFHS is coupled with the commonly used flow and transport codes MODFLOW and MT3DMS, to search for optimal design of pump-and-treat systems, aiming at minimization of the remediation cost and minimization of the mass remaining in aquifers. Compared with three existing multi-objective optimization methods, including the improved niched Pareto genetic algorithm (INPGA), the non-dominated sorting genetic algorithm II (NSGAII), and the multi-objective harmony search (MOHS), the proposed methodology then demonstrated its applicability and efficiency through a two-dimensional hypothetical test problem and a three-dimensional field problem in Indiana (USA).

Onset voltage of negative corona on stranded conductors

Theoretical investigation of the onset voltage of negative corona on stranded conductors is described in this paper. The method of calculation is based on the criterion developed for the formation of repetitive negative corona Trichel pulses. This calls first for an accurate calculation of the electric field in the vicinity of stranded conductors. The investigated gap is a three-dimensional field problem. To solve this problem, a new modification of the charge simulation technique is presented, where the simulation charges are helical of infinite length. Laboratory measurements of the onset voltage on stranded conductors are carried out to check the accuracy of the present calculations. The effects of varying the field nonuniformity on the onset voltage values are investigated. The calculated onset voltage values for stranded conductors agree satisfactorily with those measured experimentally.

An error evaluation scheme based on rotation of magnetic field in adaptive finite element analysis

The finite-element analysis is widely used in design stage of electromagnetic apparatuses. The analysis accuracy depends on the characteristics of the finite-element mesh, e.g., number of nodes, number of elements and shape of elements. Recently, the adaptive finite-element analysis is one of the most promising numerical analysis techniques. In process of the adaptive finite-element method, the error evaluation is one of the important schemes. In this paper, a new error evaluation scheme, which is suitable for electromagnetic problems, is proposed. The proposed error evaluation method is then applied to two-dimensional and three-dimensional magnetostatic field problems for its verification

Cold-cavity thresholds of microdisks with uniform and nonuniform gain: quasi-3-D modeling with accurate 2-D analysis

An electromagnetic analysis of thin-disk semiconductor resonators with uniform and nonuniform gain regions is presented. A "cold-cavity-with-gain" Maxwellian formulation, including accurate boundary and radiation conditions, is considered as an eigenvalue problem, for the real-valued parameters of frequency and threshold material gain. Although the well-known approximate effective-index method is used to reduce a three-dimensional (3-D) field problem to a two-dimensional (2-D) one, a rigorous formulation of the latter is retained. A quasi-3-D feature is provided through full account of the multiple-wave nature and dispersion of the effective index. Results obtained quantify the ultralow thresholds of the whispering-gallery modes and show the advantage of a ring-shaped gain region.

Efficient integral equation method for the solution of 3-D magnetostatic problems

Nonlinear three-dimensional (3-D) magnetostatic field problems are solved using integral equation methods (IEM). Only the nonlinear material itself has to be discretized. This results in a system of nonlinear equations with a relative small number of unknowns. To keep computational costs low the fully dense system matrix is compressed with the fast multipole method. The accuracy of the applied indirect IEM formulation is improved significantly by the use of a difference field concept and a special treatment of singularities at edges. An improved fixed point solver is used to ensure convergence of the nonlinear problem.

Three-dimensional analytic model for permanent magnet electric machines with finite core length

An analytically extended PM model with fictitious PM arrays is presented in the paper for solving the field problem of PM electric machines in three dimensions. To consider the effect of finite core length, each PM array is assumed to face a fictitious core array together with the actual armature core. By using the analytic approach and the PM model presented, the three-dimensional field problem for PM machines with different magnet aspect ratios and different axial magnet extensions may be accurately and efficiently solved. Two computed examples using the analytic approach have been verified by test results. Design curves given in the paper would be useful in PM machine design practice.

BEM treatment of three-dimensional anisotropic field problems by direct domain mapping

In this paper, the method of characteristics which has been employed to reduce two-dimensional steady-state anisotropic field problems to ones governed by the simple Laplace equation in a mapped domain, is extended to numerically treat similar three-dimensional problems by the boundary element method (BEM). The proposed process does not involve any rotation of coordinate axes as is normally done in the literature. The advantage of this approach is that the three-dimensional anisotropic field problem can then be easily solved with any readily available BEM programs for three-dimensional ‘isotropic’ potential theory. The validity of the proposed scheme is demonstrated by three numerical examples where the results are compared with those obtained using the finite element method with the commercial code ANSYS.

Analyses of three-dimensional eddy current field and thermal problems in an isolated phase bus

In this paper, a three-dimensional eddy current field model to calculate the eddy current losses in an isolated phase bus (IPB) is proposed. The rise in temperature of the conductors and enclosures in the IPB are evaluated using the proposed set of thermal equations. Computation results of a 20-kV/12.5-kA IPB scheme are reported to validate the algorithm. The withstand voltage ability and short-circuit stress of the IPB are also verified. The agreement between the computation and test results confirm that the design scheme being studied is successful and practical.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Algebraic multigrid methods for magnetostatic field problems

The finite-element (FE) method, which will be used for the discretization of three-dimensional magnetostatic field problems, usually yields a large and sparse matrix equation. For different FE-discretizations (i.e., Lagrange and Nedelec FE-functions) we will present appropriate algebraic multigrid solvers (preconditioners) for the efficient solution of the arising system of equations. Numerical results will demonstrate the applicability of the developed algebraic multigrid methods.

Method of overlapping patches for electromagnetic computation near imperfectly conducting cusps and edges

An asymptotic solution method for three-dimensional electromagnetic field problem inside and outside an imperfectly conducting cusp is proposed. Implementation of the method leads to a boundary value problem with singular boundary conditions. This problem can be solved numerically using the partition of unity method. Wave propagation in an L-shaped waveguide is modeled as an example.

A Lattice Gas Automaton Capable of Modeling Three-Dimensional Electromagnetic Fields

A lattice gas automaton (LGA) capable of modeling Maxwell's equations in three dimensions is described. The automaton is a three-dimensional interconnection of two-dimensional LGA cells, with appropriate operations at the junctions between cells to include the properties of polarization. A homogeneous mathematical description of the heterogeneous three-dimensional automaton is provided in terms of the underlying binary variables. The dynamics of the automaton conserve the scalar components of the electric and magnetic fields. The implementation of the automaton on the CAM-8 cellular automata machine is described. The LGA has been validated through calculation of resonant frequencies within various cavities. The numerical results indicate the success of the automaton in analyzing three-dimensional EM field problems. We have not proven analytically that this model reproduces Maxwell's equations in the macroscopic limit, as this is a topic of future study.

Three-dimensional analytic model of permanent magnet axial flux machine

A three-dimensional (3-D) magnetic field problem in an axial flux machine with a toroidal winding is considered. The precise solutions generated by the integral transform and Fourier methods in elementary subregions are joined using the iterative Schwartz algorithm. The comparison between two dimensional and 3-D models is performed and a correction factor taking into account the radial variation of the magnetic flux is given.

Rotational magnetization and rotational losses of grain oriented silicon steel sheets-fundamental aspects and theory

Rotational magnetization of grain oriented SiFe sheets involves three mechanisms: anisotropy, hysteresis and eddy currents. Apart from describing the respective physical background, the paper is focused on a separation of mechanisms. It discusses dependencies between field quantities which in the dynamic case are complicated by the fact that a three-dimensional field problem arises here. It is demonstrated that within a plane inner surface of a sheet, the magnetic behavior is independent of frequency in approximation. On the other hand, eddy currents yield phase shifts between individual surfaces. Respective rotational losses and their portions are discussed on the basis of Poynting's theorem. >