With a squirrel-cage induction motor, you can feed energy into an active supply simply by driving the motor above the synchronous speed. The power flow will reverse at the stator terminals. You can not easily and reliably use an induction motor as a stand-alone generator.
You can find on the internet instructions for using capacitors with an induction motor to make a stand-alone generator system, but those types of systems are not entirely satisfactory. The capacitor value and the load both have an effect on the generated voltage. Every time you start the system, you need to perform a starting sequence such as: first charge the capacitors from some external source, then connect them to the motor with a switch, then connect the load. You may need to increase the driving speed after you establish operation. If you connect or disconnect load items, you may need to add or remove capacitors.
If the motor is energized through an inverter, it is possible to design a satisfactory stand-alone system, but you still need an external battery or other source to get it started. The electronic system will be fairly complex.
Additional information re real and reactive power
An induction generator needs magnetizing current to operate. The magnetizing current does not represent real power but current that is out of phase with the voltage and causes energy to circulate back and forth between the source and the motor. Capacitors can be used for that purpose, but they need to be "tuned" to the motor and load. If the induction generator is connected to an AC source, that source can supply the magnetizing current (reactive volt-amperes), while the generator supplies power (watts) to the load.
I don't know if I'm too tired to see what's wrong in my question, but I'm indeed asking for the generator. which is the same component as the motor, only put in motion by something external at a speed higher than the synchronous. The problem is that generators GENERATE power, all I'm asking is where this power is. on the stator winding? how can it be, if there's already the excitation there? – user3149593 2 hours ago
I think it should be safe to assume that we are talking about a squirrel-cage induction motor. Wound rotor motors are included in electric machinery texts and courses, but they are almost never used compared to the many millions of induction motors in use.
Power in AC circuits is all about the phase relationship between voltage and current. To make things simple, we can assume that the current coming from the AC source is 90 degrees out of phase with the voltage and thus no real power comes from the source. The current in the load can be assumed to be in phase with the voltage. The current in the induction machine is the sum of the two. That is the mechanism that causes the power to come totally from the induction machine even though it is receiving magnetizing current from the AC source. That assumes just the right generated voltage. With the right driving speed, you can assure that no real power is taken from the source.
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.
Best Answer
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.