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Irene Woyna, Erion Gjonaj and Thomas Weiland
– The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions.
The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions.
The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE).
The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach.
Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.
Hai Van Jorks, Erion Gjonaj and Thomas Weiland
The purpose of this paper is to propose a transmission line model for induction machines, which serves to compute the common mode input impedance in the frequency range…
The purpose of this paper is to propose a transmission line model for induction machines, which serves to compute the common mode input impedance in the frequency range 10 Hz-1 MHz.
Special diligence is attributed to the modelling of eddy currents inside the core lamination. In order to determine the transmission line parameters accurately, two modelling approaches are compared. The first is a two-dimensional simulation approach where iron core lamination effects are included by means of an equivalent material approximation. The second approach consists in fully three-dimensional analysis taking into account explicitly the eddy currents induced in the laminations.
It is shown that homogenised equivalent material models may lead to large errors in the calculation of machine inductances, especially at high frequencies. However, the common mode input impedance, which is the final parameter of interest, seems to be less affected by the lamination modelling.
The paper compares different analytical and numerical approaches in the frequency range 10 Hz-1 MHz and tries to give benchmarks for errors which occur due to a number of commonly used model simplifications.