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

Finite element methods for 3-D magnetic field calculations in electromagnetic converters, i.e. in transformers, electric machines and actuators, are discussed. An edge element method using a magnetic vector potential and the nodal element method using a scalar magnetic potential are considered. Systems with stranded conductors are analysed with particular attention being paid to the calculation of matrices that describe the winding distribution in both the edge element space and the facet element space. These matrices transform winding currents into magnetic field sources and are used in the calculation of flux linkages with the windings. In the proposed methods, multiturn windings are replaced by a set of plane single-turn loops, e.g. by triangular loops. The points of intersection of the element facets with these loops are determined in order to find the matrix that describes the winding in the facet element space. The matrix that describes the winding in the edge element space is calculated on the basis of the intersection points of element edges with loop surfaces. The methods have been successfully applied to the calculations of winding inductances and in the field-circuit analysis of a permanent magnet motor.