Closed electric loop: electric connectivity problem (3D)

Introduction

This paragraph deals with the description of “closed electric loops” in 3D problems with the scalar model (automatic formulations).

Reminder about computation principle

To solve the equations in a Transient Magnetic Application, two models are available:

• the vector model which uses the vector potential
• the scalar model which uses scalar potentials

In the scalar model (automatic formulations) there is no one equation that is solved by the finite elements method. Each region of the problem can have a specific formulation and, consequently, a specific equation. Thus, an interface exists between regions and, consequently, a coupling of formulations.

Connectivity problem

The coupling between the different potentials is sometimes forbidden in the sense that the hypotheses allowing the coupling between these potentials are no longer valid. This represents a connectivity problem .

Electric connectivity problem

The electric connectivity problem appears in the case of modeling conductor pieces with holes: a ring shaped solid conductor, a holed conducting plate…

More precisely, it appears in the conditions presented in the figure below.

Solution: the cut concept

To overcome this problem, it is necessary that a cut be created in the electric conductor. This is a “mathematic cut” which means a jump in the scalar potential.

Practically, a cut is modeled by using the entity:

Cut of electric loop entity.

Symmetry and periodicity

It is not necessary to add a cut when the electric conductor is cut by a periodicity or symmetry plane

Examples

Various situations are presented in the following figures.

Electric conductor with a hole

• examples without a connectivity problem …

Electric conductor without a hole

Electric conductor with a hole but the electric loop is not closed (air-gap)

Particular case

It's not necessary to add an electric loop cut in the particular case of a closed solid conductor supplied by an external circuit.

A “closed” solid conductor has its electrical terminals “superimposed” from geometric point of view.

The same geometrical face corresponds to the two terminals of the solid conductor and play the role of the cut.