Wind power technology - Wind Power Integration: Connection and System Operational Aspects - page 58

This is known as the Betz limit, which states that a turbine can never extract more
than 59% of the power from an air stream (see the note at the end of the chapter for
a more detailed explanation of the Betz Limit).
It is also conventional to define a tip speed ratio ( l )

w R
V

l ¼ ð 3 : 5 Þ

where w¼ rotational speed of rotor; R ¼ radius to tip of rotor; V ¼ free wind speed.
l and C P are dimensionless and so can be used to describe the performance of
any size of wind turbine. Figure 3.2 shows that the maximum power coefficient is
only achieved at a single tip speed ratio, and for a fixed rotational speed of the wind
turbine this only occurs at a single wind speed. Hence one argument for operating a
wind turbine at variable rotational speed is that it is possible to operate at maximum
C P over a range of wind speeds.
The overall performance of the wind turbine is described by its power curve
(Figure 3.3).

0.59

C p

l = wR / V

Figure 3.2 Illustration of power coefficient/tip speed ratio curve (C p / l )

Cut-out speed

Rated power

600

Power curve

Cut-in speed

0

25

Wind speed (m/s)

Figure 3.3 Power curve of a wind turbine