Orienting and assigning terminals to coil conductor regions in 3D periodical domains

Introduction

This chapter explains how to assign a coil conductor region (without losses,with losses and simplified geometrical description or with losses and detailed geometrical description) to volumes and discusses the procedure required to create its electric terminals and define the current sense when a periodicity exists in a Flux 3D project.

When the Flux 3D project contains a periodicity, the orientation procedure is influenced by the presence of a symmetry condition imposing a tangent magnetic field at the boundaries of the FEM domain (allowing the representation of only a part of the device) and thus deserves a special attention from the user.

In the following sections, the example of a three-phase rotating machine winding will be adopted to explain:

how to assign a coil conductor region to volumes when they are cut by the periodicity planes;
how to orient the current sense of the coil conductor regions by assigning their terminals coherently, depending on the existence of a tangent field symmetry and on the type of periodicity (even/cyclic or odd/anti-cyclic) in the project.

Example of a rotating machine

The example of a rotating machine with 3-phase windings is taken, where a periodicity with or without a symmetry plane with physical aspects Tangent magnetic fields is present in the project. There are three phases referred to as phase A, phase B and phase C and five regions per phase named:

PHASE_A_1	PHASE_B_1	PHASE_C_1
PHASE_A_2	PHASE_B_2	PHASE_C_2
PHASE_A_3	PHASE_B_3	PHASE_C_3
PHASE_A_4	PHASE_B_4	PHASE_C_4
PHASE_A_5	PHASE_B_5	PHASE_C_5

Such a region can be cut by the periodic planes or by a symmetry plane with physical aspects Tangent magnetic fields

3-phase windings of a rotating machine. There are three phases: phase A (orange), phase B (purple) and phase C (green) and five regions per phase
A quarter of the device is described due to a periodicity	Half a quarter of the device is described due to a periodicity and a Tangent magnetic fields symmetry

How to assign a coil conductor region to volumes when it is cut by the periodicity planes?

The volumes of a coil conductor region must correspond to a whole coil. When the periodicity planes cut such a region, its volumes are split into two separate groups of contiguous volumes. The two groups are linked by their periodic faces, as described in the following figures.

This section explains how to assign a coil conductor region to volumes when it is cut by the periodicity planes by one of the following commands:

Assign regions to volumes (completion mode)
Assign regions to volumes (modification mode)

	Region PHASE_A_1. It consists of one group of contiguous volumes	Region PHASE_A_4. It is split into two separate groups of contiguous volumes, because it is cut by periodicity planes.
With a symmetry plane
Without any symmetry plane

You must select all the volumes of a coil conductor region by the command Assign regions to volumes (completion mode) or Assign regions to volumes (modification mode), even if the region has two separate groups of contiguous volumes (see the following figure).

Selection of the volumes of region PHASE_A_4 cut by periodicity planes
Real coil displayed by clicking on the icon Display or not the full device	Volumes to select for coil conductor region cut by the periodicity planes.

How to define the electric terminals?

This section explains how to define the electric terminals of coil conductor regions when a periodicity exists in a Flux 3D project through one of the following commands:

Orient wires of coil conductor region (completion mode)
Orient wires of coil conductor region (modify mode)

The general procedure to orient a coil conductor region with these commands is described in the following documentation page: Current orientation of coil conductor regions in Flux 3D.

However, this general procedure becomes slightly different in projects:

with an even/cyclic periodicity,
with an odd/anti-cyclic periodicity,
with an even/cyclic periodicity and a Tangent magnetic fields symmetry,
with an odd/anti-cyclic periodicity and a Tangent magnetic fields symmetry.

These four cases are addressed in the following subsections.

Cyclic or anticyclic periodicity:

When there is a cyclic or anticyclic periodicity, at least one internal face (i.e. faces on the boundaries of the coil volumes are not allowed) representing a cross section of the coil is required. If no such face exists, you must create some by entering the Modeler Context, or by another way. These faces do not have to be in the same plane or orthogonal to the current density. The way of defining the terminals for a coil with the command Orient wires of coil conductor region (completion/modification mode) is described below. It depends whether the region is cut by the periodicity planes or not:

Select internal terminals,
Select the faces of the input / output terminal intersecting the coil,
Select the line indicating the side of the input terminal and the positive current direction.

The selected faces and lines for the terminals of regions of phases A, B and C must be so that the current is turning in the same direction in coils of phase A and B, and in the opposite direction in phase C to have a rotating magnetic flux density in the air gap of the machine, according to the theory of the rotating magnetic fields.

Selection of the faces and line of the input terminal of regions for cyclic periodicity
Configuration	Region PHASE_A_1
Cyclic periodicity PHASE_A_1 PHASE_A_2
Configuration	Region PHASE_A_4
Cyclic periodicity PHASE_A_3 PHASE_A_4 PHASE_A_5 PHASE_B_1 PHASE_B_2 PHASE_B_3 PHASE_B_4 PHASE_B_5
Configuration	Region PHASE_C_1
Cyclic periodicity PHASE_C_1 PHASE_C_2 PHASE_C_3 PHASE_C_4 PHASE_C_5

Selection of the faces and line of the input terminal of regions for anticyclic periodicity
Configuration	Region PHASE_A_1
Anticyclic periodicity PHASE_A_1 PHASE_A_2
Configuration	Region PHASE_A_4
Anticyclic periodicity PHASE_A_3 PHASE_A_4 PHASE_A_5 PHASE_B_1 PHASE_B_2 PHASE_B_3 PHASE_B_4 PHASE_B_5
Configuration	Region PHASE_C_1
Anticyclic periodicity PHASE_C_1 PHASE_C_2 PHASE_C_3 PHASE_C_4 PHASE_C_5

Cyclic periodicity and “Tangent magnetic fields” symmetry:

When there is a cyclic periodicity and a Tangent magnetic fields symmetry, the faces of the terminals to select are those located on the symmetry plane. The way of defining the terminals for a coil with the command Orient wires of coil conductor region (completion/modification mode) is described below. It depends whether the region is cut by the periodicity planes or not:

Select external terminals,
Select the faces of the input terminal. They are located on the symmetry plane,
Select the faces of the output terminal. They are located on the symmetry plane.

The selected faces for the terminals of coils of phases A, B and C must be so that the current is turning in the same direction in coils of phase A and B, and in the opposite direction in phase C to have a rotating magnetic flux density in the air gap of the machine, according to the theory of the rotating magnetic fields.

Selection of the faces of the terminal of regions (view from underneath)
Configuration	Region PHASE_A_1
PHASE_A_1 PHASE_A_2
Configuration	Region PHASE_A_4
PHASE_A_3 PHASE_A_4 PHASE_A_5 PHASE_B_1 PHASE_B_2 PHASE_B_3 PHASE_B_4 PHASE_B_5
Configuration	Region PHASE_C_1
PHASE_C_1 PHASE_C_2 PHASE_C_3 PHASE_C_4 PHASE_C_5

Anticyclic periodicity and “Tangent magnetic fields” symmetry:

When there is an anticyclic periodicity and a Tangent magnetic fields symmetry, the faces of the terminals to select are those located on the symmetry plane.

The procedure of defining the terminals for a coil with the command Assign regions to volumes (completion/modification mode) is described below. It depends whether the region is cut by the periodicity planes or not:

If the region is not cut by the periodicity planes, for regions PHASE_A_1 and PHASE_A_2:
- Select external terminals,
- Select the faces of the input terminal. They are located on the symmetry plane,
  - Select the faces of the output terminal. They are located on the symmetry plane.
If the region is cut by the periodicity planes and the positive current enters the region on the symmetry plane, for regions PHASE_A_3, PHASE_A_4, PHASE_A_5, PHASE_B_1, PHASE_B_2, PHASE_B_3, PHASE_B_4 and PHASE_B_5:
- Select external terminals,
- Select the faces of the input terminal. They are located on the symmetry plane,
- Select no face for the output terminal.
If the region is cut by the periodicity planes and the positive current comes out of the region on the symmetry plane, for regions PHASE_C_1, PHASE_C_2, PHASE_C_3, PHASE_C_4, PHASE_C_5:
- Select external terminals,
- Select no face for the input terminal,
- Select the faces of the output terminal. They are located on the symmetry plane.

Selection of the faces of the terminals of regions (view from underneath)
Configuration of regions	Region PHASE_A_1
PHASE_A_1 PHASE_A_2
PHASE_A_3 PHASE_A_4 PHASE_A_5 PHASE_B_1 PHASE_B_2 PHASE_B_3 PHASE_B_4 PHASE_B_5
PHASE_C_1 PHASE_C_2 PHASE_C_3 PHASE_C_4 PHASE_C_5

Alternative approach to define the electric terminals in projects without a physical symmetry

Under certain circumstances, coil conductor regions reuniting the following characteresitics may exist in a Flux project:

the coil conductor region is cut by the periodicity planes;
the coil conductor region does not have internal faces that could be assigned to an internal terminal;
the coil conductor region is not cut by a symmetry plane enforcing the physical condition Tangential magnetic fields, normal electric fields.

An example of such a coil conductor region is given by the ring-shaped conductor shown below (and by the coil conductor region PHASE_C_1 in the rotating machine example considered above as well). In such cases, it is easier to create the required electric terminal on the periodicity planes, and the procedure depends on the periodicity type. These two possibilities are covered in the next two paragraphs.

Cyclic periodicity

When the project has a cyclic periodicity, there are no symmetries exists and the region is cut by the periodicity planes, the faces the terminals to be selected are those located on the periodicity planes.

The procedure to define the terminals for a coil with the command Orient wires of coil conductor region (completion mode/modify mode) is described below:

select external terminals;
select the faces of the input terminal accordingly with orientation of the current in the coil conductor region. These faces are located on a periodicity plane;
select the faces of the output terminal. They are located on the other periodicity plane.

Selection of the faces representing the terminals of a coil conductor region with a cyclic periodicity.
Configuration	Selection of the faces
First approach with upper terminals
Second approach with lower terminals

Anticyclic periodicity

When the project has an anticyclic periodicity, there are no symmetries and the region is cut by the periodicity planes, the faces of the terminals to be selected are those located on the periodicity planes as well.