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Synchronous motor power-angle diagram

The main characteristic of a synchronous motor is the electromagnetic torque vs. load angle dependence. In sinchonouse motor the rotor turns with the same speed as the stator magnetic field rotates. The load angle is measured between the rotor position and stator magnetic field. Without mechanical loading the load angle is zero - the rotor is always aligned with the stator field. As the mechanical loading increases, the rotor begins to lag behind the stator field and load angle increases.

Problem type:
Plane-parallel problem of DC magnetics.

Geometry
Motor z-length is 65 mm.

permanent magnet synchronous motor cross section

Given:
Phase current density j = 3 А/mm2
Coercive force of NdFeB permanent magnets Hc = 730 kА/m

Task
Build the power-angle diagram of a permanent magnet synchronous motor.

Solution
We assume that the rotor rotates in synchronism with the stator field. Hence the electromagnetic torque does not change with time.
To measure the torque you should specify momentary values of winding currents j*cos(phase angle) and set the rotor in proper position. For this analysis it doesn't matter whether the rotor or stator is rotating. It is convenient to rotate the stator relative to the rotor. Otherwise, when the rotor is rotated, the permanent magnets coercive force direction should have to be adjusted for each relative position
To automate the solution of a series of problems, it is convenient to use the LabelMover utility, which will automatically change the model and measure the electromagnetic torque.

Result
Magnetic field distribution and torque calculation for the load angle of 30 electrical degrees.

Power angle diagmamm of a permanent magnet synchronous motor

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