Representation of windings in the 3D finite element description of electromagnetic converters

The development of numerical methods has made it possible to apply the method of 3D magnetic field computation in the analysis of electromagnetic converter performance. The complete model of an electromagnetic converter (EC) should not only include the field equations but also the circuit equations that describe winding connections. The windings of EC can be divided into two categories: (a) windings composed of thin stranded conductors, (b) windings composed of bars. In this paper the windings that fall under category (a) have been considered. Two finite element approaches have been considered: (a) scalar potential formulation in nodal element space and (b) vector potential formulation in edge element space. In both formulations the sources of the magnetic field can be successfully defined by the edge value of current vector potential T, proposed by Le Menach et al. (see IEEE Trans. Magn., vol.34, p.2509-2512). In the case of vector potential formulation the sources can also be defined by the facet values of current density J, discussed by Le Menach et al. and Demenko (see IEEE Trans. Magn., vol.34, p.2485-2488, 1998). The paper develops the ideas advanced in the references mentioned above and deals with both methods. Matrices that transform winding currents into magnetic field sources are presented. Moreover, methods of calculating the flux linkage with the winding are discussed.