General Formulation of the Magnetostatic Field and Temperature Distribution in Electrical Machines Using Spectral Element Analysis

Abstract

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Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers

“…where β is the basis functions and Ω ξ,η is the computational domain of the element with local coordinate axes ξ and η [10]. The basis functions applied in the SEM are based on the Legendre polynomials, which are given by:…”

“…The derivative matrix replaces the derivative operators in (3). Finally, the system of linear equations for each element is obtained and assembled in a global matrix [10,16]. For the modeling of eddy current losses in conductive materials in the frequency domain, the partial differential equation shown in (1) takes the form of:…”

“…In order to minimize the mesh size, elongated mesh elements are preferred, which compromise the accuracy of the FEM. Alternatively, for this type of problem, higher order methods can be applied, such as the Spectral Element Method (SEM), in which elongated elements do not compromise the accuracy of the results [5,10].…”

“…In [5], a single spectral element was used to model the eddy current losses in a high-speed rotating cylinder. In [10], the formulation of the SEM for the magnetic field and temperature distribution in electric machines was discussed, and in [13], the application of the method to a linear synchronous machine was presented. In [14], a coupled FEM and SEM simulation was introduced, where the non-linear SEM was used for modeling of the rotor and the FEM was applied for the rest of the model.…”

High-Order Methods Applied to Nonlinear Magnetostatic Problems

“…Recently, two high-order methods have gained attention namely, the Spectral Element Method (SEM) and Isogeometric Analysis (IGA) [10,11]. They are applied to modeling of magnetic devices such as actuators and electrical machines in [12][13][14][15].…”