Page 246 - Fluid Power Engineering

Basics of Electricity and Generators 213

relative speed. The rotor continues to accelerate until the external
torque has been fully resisted.
Slip is defined as:

ω 0 − ω 1
s = (10-38)
ω 0
For most generators, the slip is in the range of 1.5 to 4%. The rotor
speed is, therefore, very close to the synchronous speed.
A circuit of an induction generator with a variable resistor in the
rotor is in Fig. 10-11. The current in the rotor is given by: 5,7

s
(10-39)
i r = K i 2 2 2
R + s X r
rx
where K i is a constant, R rx and X r are total resistance (R r + R x ) and
reactance of the rotor. R x is the variable resistance in the rotor; this will
2
be described later in this section. Torque is proportional to i R rx /s:
r
sR rx
τ = K τ 2 2 2 (10-40)
R + s X r
rx
Power is, therefore:

sR rx ω
P = τω = K τ 2 2 2 (10-41)
R + s X r
rx
where ω is the speed of the rotor.
The relationship between the torque and the slip is given by the
curve in Fig. 10-12. When resistors (R x ) are added to the rotor, then
the curve shifts to the right. At higher level of wind energy, this allows
the generators to work at larger value of absolute slip, that is, it allows
generators to work at higher revolutions per minute while keeping a
steady torque.
Table 10-1 below compares the properties of a synchronous and
asynchronous generator.
Several improvements to the basic asynchronous generator are
described next.

During startup, there is a high demand for current from the

grid, which is expensive and, over time, damaging to the
equipment. A soft starter that controls the flow of current is,
therefore, part of an induction generator. This is illustrated in
Fig. 10-13.