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# Armature winding inductance

QuickField simulation example

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

Problem Type
Plane-parallel problem of DC magnetics.

Geometry

Given
Permanent magnet coercive force Hc = 820 kA/m, remanence Br = 1.1 T;
Slot current I = 200 A, number of turns w = 100, three-phase stator winding scheme: A-A, Z-Z, B-B, X-X, C-C, Y-Y
Core permeability μ is given by the B-H curve:

Calculate the phase coil inductance for the normal operating conditions.

Solution
The inductance is the ratio of a magnetic flux to the total current that produced this flux. In case of multi turn winding you should multiply the calculated result by the coil number of turns squared:
Inductance = ( Flux / I ) * w²

To be able to measure the flux created solely by the energized coil you can turn off magnetization of the rotor permanent magnets and turn off the current in all phase coils but one. But this would cause significant deviation in core saturation from the normal operating point. Which, in turn, would make the calculated inductance value inaccurate.

We solve the problem into two steps:

1. Simulate the motor in normal operating conditions with all coils energized and the permanent magnets in place. The solution provides the actual magnetic permeability of the core. File name is Magn5_base.pbm,
2. Create and simulate a coupled problem that imports magnetic permeability distribution from the first problem. In this coupled problem we do not energize coils and turn off magnetization in permanent magnets. Only one coil is energized with a small test current. Linearity of the problem guarantees that the magnetic flux is exactly proportional to the current that generates the flux. File name is Magn5_a.pbm

Results
Phase inductance is 6.18e-6 * 100 * 100 = 0.0618 H.
Relative magnetic permeability distribution in the steel parts