# 3-phase Transformer

Transformers with MagNetThe model presented here is the simulated results of the ohmic losses and flux density of a 3 phase transformer with a three limbed paramagnetic core ( μ_p≈8.0412×〖10〗^(-3) N⁄A^2 ). The symmetry in the z-axis has been used to minimize the problem size and accelerate solution time. The coils are made of three concentric layers of different thickness.

### METHODS and RESULTS

## MESH

The initial 3D mesh contained 325,207 tetrahedra and 58,831 nodes for the Time-Harmonic 3D solver with second order Newton polynomials. The mesh is slightly modified during the simulation, hence the creation of non-uniform tetrahedral. A comparison between the initial and the final 3D mesh can be seen.

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## MAGNETIC FIELD

To the left is a cut section of the B-field magnitude on the XZ plane at the middle of the coils, at 0° and 90°. The B field density stays below 0.26 Tesla.

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## CURRENT DENSITY on MAIN COILS

This animation shows that the current density J on the surface of the main coils reaches 2.045 A/m2, each coil having a phase shift of 60°.

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## JxB LORENTZ FORCE

The force resulting from the interaction of the magnetic field and the current density is shown here to reach a peak of 329.5 kN.

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## IMPEDANCE of EACH WINDING

The impedance of each winding can easily be calculated using the results from the 3D Time-Harmonic solver. Using the complex current and voltage of the windings provided by MagNet, either in separate magnitude and phase or in real and complex components.

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## TIME AVERAGE OHMIC LOSS

The picture to the left shows the time average ohmic loss along z-axis oriented red arrow. The main winding has the highest ohmic power loss around 51 kW, the middle winding has approximate 31 kW ohmic power loss and the external winding has a 11 kW time average ohmic power loss. This graph was made using the Field Line Graph functionality of MagNet. The values given are time-averaged.

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