Induction machine - the rotor voltage that produces the rotor current and the rotor magnetic field is induced in the rotor windings rather than being physically connected by wires. No dc field current is required to run the machine.
  There are basically 2 types of rotor construction:
    Squirrel Cage - no windings and no slip rings
    Wound rotor - It has 3 phase windings, usually Y connected, and the winding ends are connected via slip rings.
  Wound rotor are known to be more expensive due to its maintenance cost to upkeep the slip rings, carbon brushes and also rotor windings.
  Cutaway diagram of a typical large cage rotor induction motor :

electric machinery

  Sketch of cage rotor:

electric machinery

  Typical wound rotor for induction motors:

electric machinery

  When current flows in the stator, it will produce a magnetic field in stator as such that Bs (stator magnetic field) will rotate at a speed:

electric machinery

  Where fe is the system frequency in hertz and P is the number of poles in the machine. This rotating magnetic field Bs passes over the rotor bars and induces a voltage in them. The voltage induced in the rotor is given by:

voltage induced in the rotor

  Hence there will be rotor current flow which would be lagging due to the fact that the rotor has an inductive element. And this rotor current will produce a magnetic field at the rotor, Br. Hence the interaction between both magnetic field would give torque:

magnetic field

  An induction motor relies for its operation on the induction of voltages and currents in its rotor circuit from the stator circuit (transformer action). This induction is essentially a transformer operation, hence the equivalent circuit of an induction motor is similar to the equivalent circuit of a transformer.   A transformer per-phase equivalent circuit, representing the operation of an induction motor is shown below:

transformer equivalent circuit

  As in any transformer, there is certain resistance and self-inductance in the primary (stator) windings, which must be represented in the equivalent circuit of the machine. They are - R1 - stator resistance and X1 - stator leakage reactance.
  Also, like any transformer with an iron core, the flux in the machine is related to the integral of the applied voltage E1.
  When the voltage is applied to the stator windings, a voltage is induced in the rotor windings. In general, the greater the relative motion between the rotor and the stator magnetic fields, the greater the resulting rotor voltage and rotor frequency. The largest relative motion occurs when the rotor is stationary, called the locked-rotor or blocked-rotor condition, so the largest voltage and rotor frequency are induced in the rotor at that condition. The smallest voltage and frequency occur when the rotor moves at the same speed as the stator magnetic field, resulting in no relative motion.
  The magnitude and frequency of the voltage induced in the rotor at any speed between these extremes is directly proportional to the slip of the rotor. Therefore, if the magnitude of the induced rotor voltage at locked-rotor conditions is called ER0, the magnitude of the induced voltage at any slip will be given by: ER = sER0. And the frequency of the induced voltage at any slip is: fr = sfe
  This voltage is induced in a rotor containing both resistance and reactance. The rotor resistance RR is a constant, independent of slip, while the rotor reactance is affected in a more complicated way by slip.
  The reactance of an induction motor rotor depends on the inductance of the rotor and the frequency of the voltage and current in the rotor. With a rotor inductance of LR, the rotor reactance is:

rotor inductance

  The rotor current flow is:

rotor current flow

  Therefore, the overall rotor impedance talking into account rotor slip would be:

rotor current flow

  To produce the final per-phase equivalent circuit for an induction motor, it is necessary to refer the rotor part of the model over to the stator side. In an ordinary transformer, the voltages, currents and impedances on the secondary side can be referred to the primary by means of the turns ratio of the transformer.

  Exactly the same sort of transformation can be done for the induction motor's rotor circuit. If the effective turns ratio of an induction motor is aeff , then the transformed rotor voltage becomes:

transformed rotor voltage

  The rotor current:

The rotor current

  And the rotor impedance:

The rotor impedance

  If we make the following definitions:


  The final per-phase equivalent circuit is as shown below:

Equivalent circuit INDUCTION MOTOR