Network models of three-dimensional electromagnetic fields

Inducted currents analysis in multiply connected conductors using reluctance‐resistance networks

“…A reluctance network (R µ N) may be constructed by applying an edge element formulation in terms of magnetic vector potential [5,6]. In the reluctance model of an element, the network branches connect the centres of the facets with the centres of the element.…”

“…It should be noted that, in contrast to the classical formulation of the reluctance network, in the network constructed using the edge element method (EEM) mutual reluctances will normally appear [5,6]. Next, having accounted for the structure of element connections and by introducing a full mesh (loop) matrix k e , the branch fluxes may be expressed in terms of mesh (loop) fluxes ϕ circulating around element edges…”

“…The loop mmfs form the vector on the right hand side of (4), which may be related to the vector of branch currents i e associated with the edges of elements, that is currents flowing through the loops of the reluctance network [6], (see also Fig. 4a)…”

“…2b). The branch currents i b associated with the facets of elements are linked to the facet values of the current density J [6], and their distribution may be described by…”

“…As in the case of the reluctance networks, the resistance networks will contain mutual resistances [6]. The sum of branch emfs, represented by the product e k T e , is equal to the vector of loop emfs e ο in the loops of the resistance network.…”