Overview
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Evaluating the inductance along the d/q-axis is important to analyze the
teeth of a rotor in an IPM motor.
The d/q-axis inductance accounting for the current phase can be obtained
using the PM motor inductance tool, but this inductance cannot be obtained
from actual experimentation.
However, the d/q axis inductance at the current phase 0 degrees which can
be obtained from actual experimentation can be calculated by converting
the inductance of one-phase of coil into three phases for each axis.
This example presents the use of a magnetic field analysis to obtain the
d/q-axis inductance by converting the inductance of the phase coils to
three phases and two axes. |
Magnetic Flux Density Distribution / Flux Linkage
The magnetic flux density distribution at a current of 5 A is indicated
in Fig. 1, and the flux linkage of the excitation coil for two currents
is indicated in Fig. 2.
The flux linkage is at a maximum when the rotation angle is 0 degrees because
the direction of the magnetic flux produced by the excitation coil and
the magnetizing direction are the same, as indicated in Fig. 1. The flux
linkage produced by the magnet cancels out the positive values at a rotation
angle of 45 degrees, but the linkage flux still has positive values because
of the magnetic flux of the excitation coil. The linkage flux is at a minimum
at a rotation angle of 90 degrees because the axes oppose one another.
The size of the inductance is the percentage of variation of the linkage
flux for the current variations indicated Fig. 2. |
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Inductance of One-phase and d/q-axis Inductance
The inductance of one-phase is indicated in Fig. 3, and the d/q-axis inductance
is indicated in Fig. 4. The analysis results, excluding the current phase
at 0 degrees indicated in Fig. 4, is obtained using the PM motor inductance
tool.
To obtain the d/q-axis inductance, obtain the mid-range value of the inductance
(La) as well as the amplitude (Las), and then calculate the d/q-axis inductance using the formula below.
The appropriate inductance is calculated when compared with the d/q-axis
inductance obtained using the PM motor inductance tool, as indicated in
Fig. 4. The leakage inductance is ignored. |
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