# Taking into account symmetries and periodicities

## Problem raised

With repetitive patterns (periodicities) or symmetries, only a reduced part of the device is represented in the finite element domain.

The electrical circuit can be described completely or partially.

What rules should be observed?

## Field – circuit coupling: recall

The conductors concerned by the field – circuit coupling are the solid conductors and the stranded conductors.

For these conductors, the base relation linking current **I**, voltage **U** and
the flux **Φ** is given below.

## Automatic management of the symmetries / periodicities

Concerning the stranded conductors (meshed coils and non-meshed coils), the computation of flux and the time derivative of the flux is carried out for the part of the device represented in the finite element domain.

To take into account the symmetries/periodicities, a specific coefficient called coil coefficient is defined in Flux. This coefficient, automatically computed by Flux, takes into account the number and types of the symmetries and/or the periodicities.

The flux obtained by numerical integration in the finite elements domain is multiplied by the coil coefficient in order to obtain the real flux embraced by the assembly of the coil turns.

Except for special cases, the user must describe the whole electrical circuit in order to obtain a coherent result in Flux.

## Manual management of the symmetries / periodicities

If the user wants to manage the constraints of the coupling linked to periodicities/symmetries “manually”, he can set the value of the coil coefficient and partially describe the electrical circuit of its device.

## Warning (3D)

With regard to 3D applications, the coil coefficient is used for the automatic duplication of the non-meshed coils.