Terms Of Magnetic Vector Potential Research Articles

Subdomain Analytical Modeling of a Double-Stator Spoke-Type Permanent Magnet Vernier Machine

This paper proposes an analytical model of the double-stator spoke-type permanent magnet vernier machine (DSSTVM) using the subdomain method (SDM), which can be used to calculate the magnetic field distribution and corresponding electromagnetic parameters of the DSSTVM. The whole field domain is divided into several subdomains according to the magnetic characteristics of each region, within which Laplace’s and Poisson’s equations are solved accordingly in terms of magnetic vector potential (MVP). Then, the corresponding magnetic flux density distribution, back electromotive force (EMF), and electromagnetic torque of the DSSTVM can be obtained. Ultimately, finite element analysis (FEA) is adopted to validate the proposed analytical model’s effectiveness for quickly predicting the no-load and on-load performances of the DSSTVM.

A 3-D Hybrid Cell Boundary Element Method for Time-Harmonic Eddy Current Problems on Multiply Connected Domains

A novel 3-D hybrid formulation for time-harmonic eddy current problems in multiply connected domains is presented. The interior problem (in conductive regions) is discretized by the cell method (CM) in terms of magnetic vector potentials a, whereas the exterior problem (in the unbounded air domain) is discretized by the boundary element method (BEM) in terms of reduced scalar potentials ${\varphi }_{r}$ . Novel topological constraints are derived from magnetostatic energy conservation by using a decomposition of the magnetic field which minimizes the support and the number of cohomology generators. A fast algebraic procedure to pre-compute source fields to handle efficiently current-driven coils is also proposed. The final matrix system can be solved in a limited number of iterations by transpose-free quasi-minimal residual method with symmetric successive over-relaxation preconditioning. Convergence tests show that numerical results are in a very good agreement with third-order finite element method (FEM) on a 2-D axisymmetric model. The CM-BEM with piecewise uniform approximation shows also to be very effective when analyzing fully 3-D test cases, since second-order FEM accuracy is attained even with coarse mesh refinements, by using, however, a much lower number of degrees of freedom compared to FEM.

A finite element model for simulating second generation high temperature superconducting coils/stacks with large number of turns

An efficient two dimensional T-A formulation based approach is proposed to calculate the electromagnetic characteristics of tape stacks and coils made of second generation high temperature superconductors. In the approach, a thin strip approximation of the superconductor is used in which the superconducting layer is modeled as a 1-dimensional domain. The formulation is mainly based on the calculation of the current vector potential T in the superconductor layer and the calculation of the magnetic vector potential A in the whole space, which are coupled together in the model. Compared with previous T-based models, the proposed model is innovative in terms of magnetic vector potential A solving, which is achieved by using the differential method, instead of the integral method. To validate the T-A formulation model, it is used to simulate racetrack coils made of second generation high temperature superconducting (2G HTS) tape, and the results are compared with the experimentally obtained data on the AC loss. The results show that the T-A formulation is accurate and efficient in calculating 2G HTS coils, including magnetic field distribution, current density distribution, and AC loss. Finally, the proposed model is used for simulating a 2000 turn coil to demonstrate its effectiveness and efficiency in simulating large-scale 2G HTS coils.

Analytical Investigation on the Power Factor of a Flux-Modulated Permanent-Magnet Synchronous Machine

In recent years, flux modulation is increasingly receiving attention since it is capable of adjusting the pole-pair number and rotational speed of the magnetic field. This principle has already been applied to magnetic gear (MG) to realize the low-speed high-torque operation [1]. Flux-modulated permanent magnet synchronous machine (FM-PMSM) is an integration of a coaxial MG with a conventional outer rotor PM machine. Compared with the coaxial MG, a stator with armature windings is employed in the FM-PMSM to replace the inner rotor of the coaxial MG [2-3], as shown in Fig. 1 (a). A modulation ring with a number of ferromagnetic pole-pieces is sandwiched between the outer rotor and stator, and two air-gaps are thereby formed to separate the above three components from each other. The modulation ring could act as a mediator to match the pole-pairs differential between the two magnetic fields generated by the PMs and armature windings, respectively. The advantage of the FM-PMSM is that it could provide high torque at low speed directly without employing mechanical gearbox, mechanical issues, such as friction loss and mechanical fatigue, are thus avoided and high reliability could be achieved. However, it is found that the power factor of the FM-PMSM is relatively low [4], and few details in the published literatures are provided to explain the intrinsic causes of this problem. Therefore, this paper will develop an analytical model to predict the power factor of the FM-PMSM and investigate the essence of the low power factor. Because of the existence of the flux modulation, many high frequency harmonics are introduced into the magnetic field of the FM-PMSM. It is important to have a good knowledge of the magnetic field distribution in the FM-PMSM in order to accurately predict its power factor. This paper gives an alternative to the commercial finite element method (FEM) to quickly obtain the electromagnetic solution. This approach could provide many physical insights into the electromagnetic solution. In this paper, partial differential equations are used to describe the magnet field behavior in terms of magnetic vector potentials. The whole calculation domain is partitioned into six regions, viz. the stator slot and slot opening (Region I_i and Region II_i), the inner and outer air-gaps (Region III and Region V), the slots between modulation pole-pieces (Region IV_j), and the PMs (Region VI), as shown in Fig. 1 (b). In Region II_i, III, IV_j and V, the magnetic vector potentials are governed by Laplace's equations. And in Region I and Region VI, magnetic vector potentials are of Poisson's equations due to the existence of current and PMs, respectively. By applying the constraints on the interfaces between these regions, the solution of the magnetic field could be derived. Fig. 2 (a) compares the analytically and numerically calculated distribution of the radial flux density in the inner air-gap due to the PMs on the outer rotor. As can be seen, the analytical results have a good agreement with the FEM calculation, which indicates the developed analytical model could be employed as a powerful tool for predicting and analyzing the power factor of the FM-PMSM. With the knowledge of the solution of the magnetic field, the flux linkage of each phase winding could be obtained through the surface integral of the magnetic vector potential in Region I_i. Then, the self and mutual inductances of each winding could be deducted, which are 4.06 mH and 2.02 mH, respectively. Similarly, the analytically and numerically calculated inductances have a good agreement. Substituting the inductances, currents and resistances into the voltage equation, the voltage of each phase winding could be obtained as well. Fig. 2 (b) presents the waveforms of the voltage and current of phase-A winding versus the time at the rated power. Finally, the active and reactive power could be calculated by expressing the flux linkage in terms of impedances, and the predicted power factor of the studied FM-PMSM is 0.6, which is quite low compared with conventional PM machines. And the low power factor will inevitably lead to the increase of the capacity, volume and loss of the inverter.

Role of interlaminar interface on bulk conductivity and electrical anisotropy of CFRP laminates measured by eddy current method

The purpose of this paper is to deal with the characterization of bulk electrical conductivity in multilayer carbon fiber reinforced polymer (CFRP) laminate by using eddy current method. The correlation between probe signals and conductivities in different directions of unidirectional CFRP is obtained with the aid of numerical code, which is based on finite element method in terms of magnetic vector potential. The effect of interlaminar interface on the bulk conductivity of CFRP laminate is investigated by visualizing the lift-off curves of probe signal in complex plane. It is found out that the cross-ply laminate has much better electrical conductance than unidirectional plate, and the bulk conductivity of CFRP laminate depends mainly on the number of current paths produced by the overlapped fibers at the interfaces between two angled layers. In addition the polar diagrams of T–R probe signals at multiple angular positions are depicted to characterize the anisotropy of CFRP laminate.

Isogeometric FEM Implementation of High-Order Surface Impedance Boundary Conditions

High-order surface impedance boundary conditions are introduced in a 2-D variational formulation in terms of magnetic vector potential. The formulation is then discretized using the isogeometric analysis method, based on nonuniform rational B-splines, allowing an efficient computation of the curvature of the conductor surface. The formulation is validated through some test cases, already solved via the boundary element method.

Comparative leakage field analysis of electromagnetic devices using finite element and fuzzy methods

To get a better design of electromagnetic devices, it is important to understand the relationship between core configurations and leakage flux distributions. The possibility of increasing weight and dimensions of electrical machines requires more and more care in the evaluation of magnetic field distribution. This paper presents a method for calculating the steady-state leakage flux distributions for electromagnetic devices. Finite element method (FEM) has been used to carry out the field behavior of permanent-magnet (PM) generator in terms of magnetic vector potential (MVP) A, as A is the preferred potential to obtain the field variables like magnetic field density (B) and magnetic field intensity (H). Then, fuzzy model of the generator is developed using adaptive neuro-fuzzy inference system (ANFIS), for carrying out its leakage field analysis. Performance is evaluated by comparing finite element model with fuzzy model, and good correlation is achieved between them.

Magnetic field analysis of induction motor for optimal cooling duct design

Abstract It is important to understand the leakage flux distributions to get a better design of induction motors. Computer simulation using the finite element method (FEM) is an important tool for achieving this objective. This paper presents a method for calculating the steady-state leakage flux distributions in induction motors. FEM is used here to study the field behavior of an induction motor in terms of magnetic vector potential (MVP), which allows the easy determination of flux and flux density. Because of complexity of the domain, triangular elements, due to their flexibility to fit in any irregular geometry are used. With the help of MVP distribution obtained use of these elements have been made to study the effect of shape of the cooling duct on the rotor laminations of an induction motor. An optimum modified shape of ventilating hole is thus obtained without having any adverse effect on MVP and flux density.

Magnetic Eddy-Current and Thermal Coupled Models for the Finite-Element Behavior Analysis of Underground Power Cables

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We have modeled underground isolated power cables by using magnetic eddy-current (EC) and thermal coupled formulations solved by the finite-element method (FEM). The magnetic field equation expressed in terms of magnetic vector potential (MVP) is strongly coupled with the total current density equation, which includes the source and the EC densities for taking into account skin and proximity effects. The model uses the computed EC density of losses with electric conductivity temperature dependence introduced as a heat source in the free transient thermal equation completed by the convection heat transfer. We studied single and multicircuit three-phase arrangements at various cable spaces in order to analyze the magnetic flux density and the time-space temperature evolution. </para>

Effects of 3D Eddy Current Finite Element Formulations on ECT Signals

To obtain the simulated eddy current testing (ECT) signals of steam generator (SG) in nuclear power plant (NPP), nodal-based finite element (FE) analysis with magnetic vector potential (MVP) is usually used. To perform the numerical analysis, we derive the governing equation in terms of MVP and electric scalar potential (ESP) from Maxwell’s equations. To insure the uniqueness of solution, gauge condition has to be considered. In eddy current problems, Coulomb gauge condition (CGC) is usually used. In 2-D or 3-D axis-symmetric analysis, CGC is included during formulation and ESP is eliminated using some special assumption. Because CGC is not used during the formulation in 3-D analysis, we have to include artificially. And because of the heavy computation cost for 3-D analysis modified magnetic vector potential (MMVP) is used by elimination ESP. In this paper, effects of artificial treatment of CGC and elimination of ESP on ECT signal are investigated in order to help for obtaining accurate numerical simulation results.

Rate-dependent losses modeling for magnetostrictive actuators

Abstract The present paper tackles the magnetic field diffusion analysis in thin cylindrical rods of materials showing hysteresis effects and employed in commercial actuators. The problem is formulated in terms of magnetic vector potential. By this formulation the used magnetic constitutive relationship assumes magnetic induction as input. Since almost all of the hysteresis models that can be employed (like the Preisach model) to describe the B–H characteristic assume H as input field, the inversion of the hysteresis operator at each step is required. The alternative approach is to assume B as input field, by using an approximate version of the Preisach hysteresis operator as constitutive relation in a finite element eddy current model. This approach is quite new and sensibly reduces the computational effort, since it avoids the inversion of the hysteresis operator at each time step. The numerical results are provided and compared to experimental data on a commercial Terfenol-D actuator.

Vectorized Jiles–Atherton hysteresis model

This paper deals with vector hysteresis modeling. A vector model consisting of individual Jiles–Atherton components placed along principal axes is proposed. The cross-axis coupling ensures general vector model properties. Minor loops are obtained using scaling method. The model is intended for efficient finite element method computations defined in terms of magnetic vector potential. Numerical efficiency is ensured by differential susceptibility approach.

Vector potential formulation for magnetostatics and modelling of permanent magnets

A very general magnetostatic problem, involving inhomogeneous anisotropic materials filling irregular regions and with mixed boundary conditions is formulated in terms of magnetic vector potential. Some restrictions inherent to the introduction of a vector potential become apparent and additional conditions for the uniqueness of the vector potential naturally arise. The modeling of permanent magnets is introduced in both the vector potential and the field formulations by weakening the regularity requirements on the source term. The vector potential formulation is also shown to be equivalent to a penalized formulation widely used in numerical applications. TEL:: +39.0382.505655 KEYWORDS:: Magnetostatics,vector potential,existence and uniqueness,inhomogeneous and anisotropic materials,permanent magnets EMAIL:: perugia@dimat.unipv.it

A surface impedance method for 3D time transient problems

A new technique for modelling time transient thin skin depth eddy currents is presented. The nonconducting regions are modelled using conventional volume finite elements in terms of the magnetic scalar potential /spl psi/. The magnetic fields in the thin skin are determined approximately using 1D finite elements in terms of magnetic vector potentials, Most problems would result in one large volume matrix and many small 1D matrices. A staggered time transient solution to the two sets of equations in /spl psi/ and A is then carried out. A finite element implementation and some test examples are described.

Analysis of isotropic materials with vector hysteresis

This paper presents the implementation of an isotropic vector hysteresis model within a two dimensional time periodic finite element procedure, formulated in terms of magnetic vector potential. The standard vector Preisach Model is employed and an identification procedure based on the scalar Preisach distribution function is used. Nonlinearity is handled by means of the fixed point technique following the H-convergence scheme. The convergence of the procedure is assessed and the results obtained are discussed.

Finite element analysis for power electronics EMC applications

A CAD system for the analysis of power electronic circuits for EMC applications is being developed. The system is based on 3-dimensional finite-element electromagnetic field computations, with the source currents or voltages extracted either from measurements or from standard circuit analysis. The finite-element solver for this application is configured in terms of magnetic vector potential (A_) and modified electric scalar potential (V'), incorporating, unusually, the Coulomb gauge /spl nabla/.A_=0. Comparisons of computed electromagnetic fields with measurements of fields emitted from a 600 V, 300 A IGBT switching circuit are reported. Agreement in magnetic field strength is fair (within 8 dB/spl mu/A/m) at the low frequencies (10 kHz-20 kHz) considered.

Super convergence theory and its application to precision force calculation

In this paper, a superconvergence method based on an elemental and nodal averaging scheme is first introduced to treat the FEM solutions of the magnetic field problem in terms of magnetic vector potential. The precision of the flux density calculation can be greatly enhanced by using this method. This method is then applied to aid the design and, associated with the Maxwell tensor, the force profile calculation of a linear motor for the free-piston cooler drive. The effects of eddy currents, resulting from the moving magnet, on the linear motor force in various cases are also investigated.

A strong coupled model for analysing dynamic behaviours of non-linear electromechanical systems

A strong coupled model solving simultaneously electric circuit, magnetic field and mechanical motion equations is presented. The magnetic field is solved by a formulation in terms of magnetic vector potential. The working variable in the mechanical equation can be either the displacement or the velocity. The magnetic force is calculated by the virtual work method associated with the edge element. The non-linear system is solved by the Newton-Raphson method. The final matrix equation is symmetrized. A numerical example shows that, compared with a conventional sequential coupling model, the convergence of the present method is less dependent on time step values. >

Traitement semi-analytique du champ d'une source linéique de courant à proximité d'une bande conductrice mince

The authors study the electromagnetic interaction, in steady state conditions, between a straight conductor carrying sinusoidal current, and a finite thickness metallic plate. First, they develop a solution in terms of magnetic vector potential. Then, they give a special attention to the numerical évaluation of the field components in their integral form. A high stability appropriate quadrature method is proposed. The effect of some parameters on field diffusion within the metallic plate is also examined.

Flux penetration and losses in solid nonlinear ferromagnetics using state space techniques applied to electrical machines

A state space model is developed in terms of magnetic vector potential (M.V.P.), <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{A}</tex> , for the calculation of instantaneous values of eddy currents, flux penetration, and losses in nonlinear solid ferromagnetics. Finite differences in space and sampled data techniques in time are used to obtain the solutions. This formulation is very effective in simplifying the computer programming implementation to electrical machinery problems, which contain a mixture of regions of air-gaps and conductors. An application of this technique to a solid steel damper bar in a salient-pole synchronous machine of the type used in hydroelectric pumped-storage stations is presented. Resulting damper bar losses, due to sinusoidal excitation are given and found to be in good agreement with experimental test data. Also, instantaneous flux density and current density wave forms are given for various depths into the bar with vivid display of the effects of nonlinearity. Equivalent bar resistances and reactances determined by the present method are compared with corresponding results obtained by earlier techniques. Favorable comparison is achieved.