PART 2 INDUCTION MOTOR
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 :
Sketch of cage rotor:
Typical wound rotor for induction motors:
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:
Where f_{e} is the system frequency in hertz and P is the number of poles in the machine. This rotating magnetic field B_{s} passes over the rotor
bars and induces a voltage in them. The voltage induced in the rotor is given by:
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, B_{r}. Hence the interaction between both magnetic field would give torque:
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 perphase equivalent circuit, representing the operation of an induction motor is shown below:
As in any transformer, there is certain resistance and selfinductance in the primary (stator) windings, which must be represented in the equivalent circuit of
the machine. They are  R_{1}  stator resistance and X_{1}  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 E_{1}.
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 lockedrotor or blockedrotor 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 lockedrotor conditions is called E_{R0}, the magnitude of the induced voltage at any slip
will be given by: E_{R} = sE_{R0}. And the frequency of the induced voltage at any slip is: f_{r} = sf_{e}
This voltage is induced in a rotor containing both resistance and reactance. The rotor resistance R_{R} 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 L_{R}, the rotor reactance is:
The rotor current flow is:
Therefore, the overall rotor impedance talking into account rotor slip would be:
To produce the final perphase 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:
The rotor current:
And the rotor impedance:
If we make the following definitions:
The final perphase equivalent circuit is as shown below:

