Civil Engineering Reference
In-Depth Information
of the induced voltage is given by Faraday's law of electromagnetic induc-
tion, namely:
=−
φ
d
dt
e
(6-2)
where
= the magnetic flux linking the rotor turn.
This voltage in turn sets up the circulating current in the rotor. The elec-
tromagnetic interaction of the rotor current and the stator flux produces the
torque. The amplitude of this torque is given by the following:
φ
TK
=⋅
Φ
⋅
I
⋅
cos
φ
(6-3)
2
2
where K = constant of proportionality
Φ
= amplitude of the stator flux wave
I
= amplitude of induced current in the rotor bars
2
φ
= phase angle by which the rotor current lags the rotor voltage.
2
The rotor will accelerate under this torque. If the rotor was on frictionless
bearings with no mechanical load attached, it is completely free to rotate
with zero resistance. Under this condition, the rotor will attain the same
speed as the stator field, namely, the synchronous speed. At this speed, the
current induced in the rotor speed is zero, no torque is produced and none
is required. The rotor finds equilibrium at this speed and will continue to
run at the synchronous speed.
If the rotor is now attached to a mechanical load such as a fan, it will slow
down. The stator flux, which always rotates at the constant, synchronous
speed, will have relative speed with respect to the rotor. As a result, the
electromagnetically induced voltage, current, and torque are produced in
the rotor. The torque produced must equal that needed to drive the load at
that speed. The machine works as the motor in this condition.
If we attach the rotor to a wind turbine and drive it faster than the syn-
chronous speed, the induced current and the torque in the rotor reverse the
direction. The machine now works as the generator, converting the mechan-
ical power of the turbine into electrical power delivered to the load connected
to the stator terminals. If the machine was connected to a grid, it would feed
power into the grid.
Thus, the induction machine can work as the electrical generator only at
speeds higher than the synchronous speed. The generator operation, for that
reason, is often called the super-synchronous speed operation of the induc-
tion machine.
As described above, the induction machine needs no electrical connection
between the stator and the rotor. Its operation is entirely based on the
electromagnetic induction, hence, the name. The absence of rubbing electrical
contacts and simplicity of its construction make the induction generator very
