To deal with the multi-scale nature of the quench propagation problem in superconducting magnets, this work presents a quasi-three-dimensional (Q3D) approach combining a two-dimensional finite-element method (FEM) in the transversal cross-section of the magnet for resolving the geometrical details, with a one-dimensional spectral-element method based on orthogonal polynomials in longitudinal direction for accurately and efficiently representing the quench phenomena. The Q3D formulation is elaborated and the idea is illustrated on a thermal benchmark problem. Finally, the method is validated against a conventional 3D simulation carried out by a commercial software. In terms of computational efficiency, it is shown that the proposed Q3D approach is superior to the conventional 3D FEM.
Surge arresters of station class are equipped with field grading elements that break the rotational symmetry of the arrester body. To avoid a computationally expensive full three‐dimensional (3D) simulation, a quasi‐3D simulation procedure is presented to study graded arresters. The method employs a hybrid discretization combining a two‐dimensional (2D) axisymmetric finite element (FE) method in axial and radial direction with a spectral element method in terms of trigonometric functions in azimuthal direction. Furthermore, the asymmetric boundary conditions associated with the support rods are taken into account by collocation in a saddle‐point system of equations. The method is validated and compared with a standard 3D FE simulation of a test problem. It is, subsequently, applied to study the electric field distribution of a graded station class surge arrester.
This work presents a quasi-three-dimensional (Q3D) approach for the magnetic field simulation in superconducting devices. First-order two-dimensional finite-element edge functions in the model's cross-section are combined with one-dimensional orthogonal polynomials along the longitudinal direction. The interfilament coupling currents arising in superconducting multi-filament materials are modelled by taking the associated magnetization into account. For this formulation, the Q3D ansatz is elaborated, verificated and applied to a superconducting cable model. In the end, the approach is compared to a conventional three-dimensional finite-element method against which the proposed Q3D method demonstrates a superior computational efficiency.
This work focuses on the robust optimization of a permanent magnet (PM) synchronous machine while considering a driving cycle. The robustification is obtained by considering uncertainties of different origins. Firstly, there are geometrical uncertainties caused by manufacturing inaccuracies. Secondly, there are uncertainties linked to different driving styles. The final set of uncertainties is linked to ambient parameters such as traffic and weather conditions. The optimization goal is to minimize the PM's volume while maintaining a desired machine performance measured by the energy efficiency over the driving cycle and the machine's maximal torque. The magnetic behavior of the machine is described by a partial differential equation (PDE) and is simulated by the finite-element method employing an affine decomposition to avoid reassembling of the system of equations due to the changing PM geometry. The Sequential Quadratic Programming algorithm is used for the optimization. Stochastic collocation is applied to compute moments of stochastic quantities. The robustness of the optimized configurations is validated by a Monte Carlo sampling. It is found that the uncertainties in driving style and road conditions have significant influence on the optimal PM configuration.
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