When three-phase current flows into the three-phase symmetrical windings of the stator of a permanent magnet synchronous motor, the magnetomotive force generated by the current combines to form a rotating magnetomotive force with a constant amplitude. Because its amplitude remains constant, the trajectory of this rotating magnetomotive force forms a circle, called a circular rotating magnetomotive force. Its magnitude is exactly 1.5 times the maximum amplitude of the single-phase magnetomotive force.
Where, F is the circular rotating magnetomotive force (T·m); Fφl is the maximum amplitude of the single-phase magnetomotive force (T·m); k is the fundamental winding coefficient; p is the number of pole pairs of the motor; N is the number of turns in series in each coil; and I is the effective value of the current flowing through the coil. Since the rotational speed of the permanent magnet synchronous motor is always the synchronous speed, the rotor main magnetic field and the rotating magnetic field generated by the stator circular rotating magnetomotive force remain relatively stationary. Two magnetic fields interact to form a composite magnetic field in the air gap between the stator and rotor. This composite magnetic field interacts with the rotor's main magnetic field, generating an electromagnetic torque Te that either drives or impedes the motor's rotation.
Where Te is the electromagnetic torque (N·m); BR is the rotor's main magnetic field (T); and Bnet is the composite magnetic field in the air gap (T). Due to the different positional relationships between the composite magnetic field in the air gap and the rotor's main magnetic field, the permanent magnet synchronous motor (PMSM) can operate in both motor and generator modes. The three operating states of the PMSM are shown in Figure 3. When the composite magnetic field in the air gap lags behind the rotor's main magnetic field, the generated electromagnetic torque is opposite to the rotor's rotation direction; in this state, the motor is generating electricity. Conversely, when the composite magnetic field in the air gap leads the rotor's main magnetic field, the generated electromagnetic torque is in the same direction as the rotor's rotation; in this state, the motor is operating as a generator. The angle between the rotor's main magnetic field and the composite magnetic field in the air gap is called the power angle.
The PMSM consists of two key components: a multi-polarized permanent magnet rotor and a stator with appropriately designed windings. During operation, the rotating multipolar permanent magnet rotor generates a time-varying magnetic flux in the air gap between the rotor and stator. This flux generates an alternating voltage at the stator winding terminals, thus forming the basis for power generation. The permanent magnet synchronous motor discussed here uses a ring-shaped permanent magnet mounted on a ferromagnetic core. Internal permanent magnet synchronous motors are not considered here. Because embedding a magnet into an electroplated ferromagnetic core is very difficult, by using magnets of appropriate thickness (500 μm) and high-performance magnetic materials in the rotor and stator cores, the air gap can be made very large (300~500 μm) without significant performance loss. This allows the stator windings to occupy a certain space in the air gap, thus greatly simplifying the manufacturing of permanent magnet synchronous motors.