Electrical – Frequency of stator current in induction motors

In an induction motor, the speed of the rotor structure is always less than the speed of the stator field. However the rotor field rotates faster than the rotor structure so that the rotor and stator fields are synchronized with each other.

In a synchronous motor, the rotor magnetic field is produced by permanent magnets or by DC current in the rotor winding. In either case, the rotation of the magnetic field of the rotor is mechanically fixed to the motion of the rotor. For uniform torque to be produced, the both the rotor structure and the rotor field must move synchronously with the rotor field.

In other words, both synchronous and induction motors have synchronously turning magnetic field with torque produced in proportion to the angular displacement between the stator and rotor magnetic fields. In the induction motor, the rotor structure must turn at a slower speed than the magnetic fields while in a synchronous motor, the rotor structure must move synchronously.

Re: Question Edit

In a synchronous generator, the stator magnetic field rotates behind the rotor magnetic field with respect to torque angle. It is the relative motion between the rotor magnetic field and the stator windings that allows the magnetic field of the rotor to produce current in the stator. The current produced produces a rotating magnetic field in the stator that is synchronous with the rotor magnetic field but has a torque angle displacement.

Since the motor converts electrical energy to mechanical energy, the electrical input power must be equal to the mechanical power transmitted to the load plus power lost in the motor. Since the input voltage is constant, that would have to be reflected in the input current and power factor since power = voltage X current x power factor.

The mechanism by which electrical power is converted to mechanical power is explained using the equivalent circuit of the motor. Just as in a DC motor, a back EMF is generated in an AC synchronous motor. So the motor equivalent circuit is an AC back EMF generator in series with the internal impedance of the motor. The back EMF opposes the source voltage so that the stator current is proportional to the source voltage minus the back EMF divided by the internal impedance of the machine. With an AC machine, the voltage, current and impedance values are all complex numbers. The phase angle difference between the terminal voltage and the back EMF is determined by torque angle, the angle between the rotating stator and rotor magnetic fields. As the name implies, the torque angle is proportional to torque.

This leads me to another question which might help: Does the rotor's magnetic field of an induction motor affect the stator's current value?

I don't think that is related to the synchronous motor question. The induction motor rotor current is ultimately supplied by the stator, but the magnetic fields in both the stator and rotor are pretty much constant as long as the applied voltage and frequency are constant and the ratio of voltage to frequency is constant.