Conference Agenda

This short paper discusses novel numerical solutions for inner and outer current layer densities compensating the exterior magnetostatic field of a ferromagnetic shell with arbitrary shape. Test models are used for investigation of compensation error depending on the grid size and approximation of surface magnetization.

Air gap breakdown voltage is a decisive factor for insulation design of various electrical equipment, which is closely related to the electrostatic field distribution. This paper proposes a feature set including 66 physical and mathematical quantities extracted from the electric field calculation results to characterize rod-plane air gaps, which are defined in a conical region and on an interelectrode path. These features are input to an insulation prediction model established by least squares support vector machine (LS-SVM). A case study was carried out to predict the breakdown voltages of rod-plane air gaps with different rod sizes and gap distances. The prediction results have a high accuracy compared with experimental values and the mean absolute percentage errors (MAPEs) are within 1.4%.

In an electrostatic analysis using a numerical human body model constructed with voxels, the electric field strength is overestimated near staircase boundaries of different materials (called staircasing errors). To reduce these staircasing errors, mesh smoothing based on marching cubes is developed and applied to a part of the numerical human body model. In addition, to reduce the increase in computational time for electrostatic analysis due to this mesh smoothing using unstructured lattices, the geometric multi-grid method dealing with unstructured lattices is applied. As a result, this mesh smoothing method reduces the stair casing errors and this geometric multi-grid method takes up to 1/4 of the computation time of a general linear algebra solver. Furthermore, the most important finding is that the accurate electrostatic analysis by mesh smoothing leads to a reduction in the iteration count of the geometric multigrid method.

Developing simulation models for electromagnetic problems often deal with approximations of the full set of Maxwell’s equations, in order to obtain performant methods. This is also the case for the so-called Darwin model, which has the capability of including resistive, inductive and capacitive effects without the need of solving full wave Maxwell’s equations. However, an issue is the difficulty of prescribing realistic excitations of the model, e.g. via a terminal voltage. In this paper, the straight forward prescription of the scalar potential on electric ports is investigated via Poynting’s theorem, with the outcome that it can be considered a voltage excitation under certain conditions regarding the frequency.

We propose a Helicoidal Transformation for 2D Finite Element Method (FEM) calculation of AC losses in twisted conductors. The method is based on a helicoidal change of variables to transform the originally 3D problem into an equivalent 2D problem. For obtaining the critical state in superconductors we use the h-phi-formulation and E-J power law. The method is well suited for geometries with a helicoidal symmetry and we present the magnetic response and Joule losses of multifilamentary twisted wire in conducting matrix and CORC cable with a non-conducting core.

In this digest, a classical 3D finite element method is employed for evaluating the force of a flux-switching permanent magnet machine for linear bearingless applications with six degrees of freedom. Although the force is evaluated by integrating the Maxwell stress tensor near the wounded mover, the final manuscript will compare different methods of force computation.

This paper describes an unbounded approach for solving the Poisson equation by the Finite Element Method (FEM). With domain mapping, it is unnecessary to truncate the domain at an arbitrary distance, where the potential is assumed negligible. The formulation herein has applications for static fields, has a simple implementation, and can handle infinite heterogeneous domains, which is a limitation of several FEM software. Such an approach raises the simulation precision and can save computational resources.

An electrical capacitance tomography (ECT) system is analyzed by a 2D FEM. Special focus is given to the sensitivity matrix evaluation in order to avoid the inherent numerical errors originated by the capacitance computation and by using the difference approximations for the Jacobian matrix. The FEM is applied to obtain the electric field. A new approach for the sensitivity matrix is developed by calculating capacitances and the Jacobian matrix using the own FEM formulation. Comparisons with published works were done.

A new thin shell (TS) model based on the magnetic field formulation is presented and applied to approximate a shielded induction heater. All the thin regions (shield, inductors and plate) are modeled as reduced-dimension geometries in the computational domain. The physics of these regions are taken into account by a virtual discretization across their actual thickness. Results show that the proposed TS model with a suitable virtual discretization leads to a very accurate solution near edges and corners of the thin regions, at a fraction of the computation time required by a fully discretized model.

The calculation of the eddy current density in an electrical machine is difficult to analyze so that numerous applicable methods have been introduced to solve it. The development of the numerical method for the div and curl operator is governed by the magnetostatic approximation and achieved by using the stencil. Furthermore, the effect of the secondary magnetic field induced by the eddy current density with a high-frequency excitation should be evaluated to gain an accurate result. In order to establish the high-frequency effect, the discrete Laplacian operator in a two-dimensional system is applied using the finite-difference stencil. Various sizes of the finite difference stencil are considered to derive the needed equations for high accurate solutions. The curl, div, and discrete Laplace operator should be calculated simultaneously for the eddy current density where both the primary magnetic flux density and secondary magnetic flux density are taken into account. Calculated results are verified with a Finite Element Method (FEM) commercial tool.

We study a novel construction of sparse inverse mass matrices for degrees of freedom attached to dual edges and dual faces of the

barycentric dual grid. The construction is based on standard two-step process based on a consistent and a stabilization part. The

consistent part is fixed, while the stabilization part depends on some user-dependent parameters. In this work, we investigate to what

extent the convergence behavior of the sparse inverse mass matrices is influenced by the stabilization part used in their definition.

Similarly to mass matrices, several choices are available for the stabilization part. The geometric approach is found to be the best

one for the considered test cases. In this case, a remarkable fact is that the whole construction is entirely geometric: both consistent

and stabilization part coefficients can be determined purely by linear algebraic operations starting from geometric elements of the

pair of staggered grids.

Consideration of moving parts in the simulation of electrical machines is a necessity to characterize the machine behaviour at various operating points. For this purpose, the Sliding Interface Technique, based on Lagrange multipliers can be utilized. To reduce the computational effort of these simulations, it is interesting to employ model order reduction techniques such as the Proper Generalized Decomposition. In this contribution, the Sliding Interface Technique, which imposes no restrictions to finite element discretization on the interface between stator and rotor, is combined with the Proper Generalized Decomposition to abolish the restriction to conformally meshed domains, while keeping the symmetry and positive definiteness of the system.

A new formulation for a high-order frequency sensitivity analysis is obtained in a voltage source problem of a linear eddy-current system. This formulation is established through a variational formulation instead of as a discretized state equation. An analytic frequency-sensitivity formulation of order n is derived by directly differentiating the variational eddy-current system n times. The sensitivity analysis is performed in finite element analysis without modifying a stiffness matrix, which must be needed in a sensitivity analysis based on discretized state equation. Two numerical examples are conducted to demonstrate theoretical validity and numerical application of the high-order frequency sensitivity analysis.

The proper general decomposition method is applied to nonlinear periodic eddy current problems, and it is shown that the time-space separation allows very efficient computation and smaller memory requirements than traditional methods. The problem is split into a stationary partial differential equation, which is solved with the finite element method and an ordinary differential equation, which is solved with the harmonic balance method or a discrete Fourier transformation.

This paper proposes a Boundary Element Method (BEM) formulation coupled with a high-order surface impedance boundary condition (SIBC) for the computation of the impedance of axisymmetric ferromagnetic-core inductors. The formulation takes both the skin and the proximity effects into consideration. Additionally, it improves accuracy compared to the use of only a standard low order impedance boundary condition. A test case is solved for validation.

The tracking of the magnetic field lines can be expensive in terms of computing resources when the field sources are numerous and have complex geometries since, especially when accuracy is a priority, the calculation of the field is required in many of points. In some important applications the computational cost can be significantly reduced by using an approximation of the field in the integration regions. Chebyshev polynomials are particularly effective in this class of problems.

The challenge of paralleled foil windings modeling and validation with measurements is addressed in the view of two methods. First, a circuit-coupled FEM-based model is developed to calculate the current sharing between paralleled foil windings. Second, the impedance matrix of the foil winding is employed where the impedances are derived using FEM. Finally, an MFT prototype with parallel foil windings is manufactured. The accuracy and the suitability of both methods are evaluated by comparing the models results with measurements. The simulations and experimental results show the significance of additional losses in the paralleled windings due to circulating currents.