Page 90 - Fluid Power Engineering

68 Chapter Five

0.6
0.5
0.4
C p 0.3
0.2
0.1
0
0.05 0.067 0.84 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1/λ

FIGURE 5-4 Plot of power coefficient versus reciprocal of tip speed ratio
(1/λ =v 0 /ωR).

For small values of λ, which is high value of wind speed, the
value of β is large and value of a is low (Eq. 5-15). This leads to stall
conditions.
For larger values of λ, which is low wind speed, the value of β is
low, which leads to high drag. Note the value of a is high.
In summary, for small and large values of λ, the value of a is
nonoptimum and the value of C p is low (see Fig. 5-4). It is often con-
venient to conceptualize the relationship between C p and 1/λ, be-
cause 1/λ is proportional to wind speed. This relationship is seen in
Fig. 5-4.
For a given blade design, the theoretical relationships between
power and wind speed, power coefficient and tip speed ratio, and oth-
ers are calibrated with measurements. An empirical correction factor
is applied to compensate for the assumptions made in the theoretical
computations.

Constant-Speed Turbines, Stall-versus Pitch-Regulated
The nature of operation of a wind turbine with respect to rotor speed
is determined by the type of electric generator attached to the turbine.
Constant rotor speed operation is typical when a configuration is used
in which a generator is directly connected to the grid. The speed of
rotation of the generator is derived from the frequency of the grid. On a
50-Hz grid, the rotor speed will be 50 60/(number of poles/2). Number
∗
of poles is an even number that represents the number of north and
south magnetic poles in the generator. Most common configuration
of asynchronous generator is two or four poles. Thus, the generator
operates at 3,000 or 1,500 rpm. Similarly, a 60-Hz generator operates at
3,600 or 1,800 rpm. A grid-connected asynchronous generator is the
simplest and cheapest type of generator because the output energy