Hybrid finite-element method for discretising cylindrically symmetric parts in electrotechnical models

In many technical devices such as transformers and electrical machines, large differences in geometric dimensions are observed. As a consequence, the generation of a 3D computational grid for the whole device leads to unacceptably large numbers of elements or can even fail. In addition to the commonly applied cartesian or cylindrical symmetries of the overall geometry, the model can be subdivided into parts featuring translational or cylindrical symmetries. Such parts are discretised separately, accounting for the local symmetry, and are then combined with the surrounding 3D model. Excitations and boundary conditions of the submodels are not necessarily symmetric but are expected to be smooth in the direction of the symmetry. Then, the field distribution at the interface is well approximated by a set of spectral elements along the dimension of symmetry. Coupling between the model parts is carried out by means of Lagrange multipliers. A single-phase transformer with thin insulation sheets is taken as an example to illustrate the proposed hybrid discretisation. The cross-section of the cylindrically symmetric part containing thin sheets, is represented by a fine 2D finite-element mesh so that all the geometrical details can be resolved, and the rest of the structure is discretised by a 3D mesh. Nevertheless, a fully 3D field distribution is calculated in all model parts. Only a small number of harmonic functions is needed to account for the azimuthal field variation at the cylindrical interface. Hence, the number of unknowns in the numerical model is reduced significantly, while a high level of accuracy is maintained