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Main > Application > Sample problems

Magn5: Armature Winding Inductance

This example demonstrates how to calculate the inductance of a single stator phase coil in a permanent magnet synchronous motor.

Analysis Type:

Plane problem of DC magnetics.

Geometry model:

Three-phase permanent magnet synchronous motor

The length of the motor in the axial direction is 200 mm.


The magnet coercive force Hc = 320 kA/m;
The magnet remanence Br = 0.4 T;
The rated current density in the stator coil j = 2 A/mm2;
The core permeability μ is given by the B-H curve.


We calculate the phase coil inductance for the normal operating point dividing the magnetic flux through the coil by the current density that generates the flux. With QuickField, you would normally turn off permanent magnets' magnetization and the current in all phase coils but one. In our case, however, this would cause significant deviation in core saturation from the normal operating point. Which, in turn, would make the calculated inductance value inexact.

To avoid that, we are splitting the problem into two parts:

  • The 1st part, Magn5_base.pbm, will define the magnetization of the magnets and the current densities in all phase coils according to the normal operating point requirements. Its solution will provide the magnetic permeability distribution across the magnetic core allowing us to fix the operating point on the saturation curve of the motor.
  • The 2nd part, Magn5_a.pbm, will import the core magnetic state from the 1st part Magn5_base.pbm keeping the real saturation level of the core and, at the same time, becoming linear. Linearity of the problem guarantees that the magnetic flux is exactly proportional to the current that generates the flux. So, calculating the phase coil inductance we can use the phase coil current that suits us best.

The 2nd part of the problem keeps all sources except the A-phase switched off. We calculate the inductance as the magnetic flux divided by the current with the help of Inductance Wizard.


Plot of relative permeability

Current, dI

31.2 A

Flux linkage,

36.9 uW

Inductance, dL

1.18 uH

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