**SQUIRREL-CAGE INDUCTION MACHINE**

**Motor and generator principle of operations**

**
The rotating magnetizing field
represented by the space vector
B _{m }(or,
equivalently by the magnetizing current
I_{m}) moves at the synchronous speed
ω_{s }with respect to a stator (or
stationary) observer and at the slip speed
ω_{sl }=
ω_{s }-
ω_{m }with respect to a rotor
observer. In the motor mode of operation where
ω_{m}<
ω_{s}, the rotor effectively
moves backwards (clockwise) with respect to the field, inducing in each bar a
voltage having the polarity indicated and a magnitude proportional to slip
velocity u and to the field strength acting on the bar (in accordance with the
flux-cutting rule v = Blu). Since the magnetic field is sinusoidally distributed in
space, so will the induced voltages in the rotor bars. Ignoring the effects of
rotor leakage ( i.e. assuming that the rotor is purely resistive), the resulting
rotor currents are in phase with the induced voltages and are thus sinusoidally
distributed in space varying sinusoidally in time at slip frequency; they may
then be represented by the space vector
I_{r} which rotate at the slip speed
ω_{sl} with respect to the rotor and at synchronous speed
ω_{s }with respect to the stator. Because
B_{m }cannot
change with a fixed stator input voltage (in accordance with Faraday's law), a stator space vector
I_{R} is created in order to
compensate for the rotor effects so that the resultant stator current becomes
I_{s} = I_{R} +
I_{m}. The
electromagnetic force exerted on a rotor bar can be derived from the
f = Bli rule and it is acting
in the positive or anticlockwise direction (same as rotor speed) in the present
case of a motor. The resultant torque developed on the rotor also acts in the
same direction. Follow the path taken by one rotor bar as it travels around,
observing the polarity and magnitude (described by the size) of the bar current.**

I**n
the case of a generator
where ω _{m }> ω_{s}, all polarities and
directions are reversed as can be observed in the right figure (except for the
magnetizing component).**

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