Environmental Engineering Reference
In-Depth Information
Power curve V90-3.0 MW
3,500
3,250
3,000
2,750
2,500
2,250
2,000
1,750
1,500
1,250
1,000
750
500
250
0
0
5
10 15
Wind speed (m/s)
20
25
Figure 2.7
Power curve for the Vestas V90, 3.0 MW turbine. (Reproduced with permission of Vestas
Wind Systems A/S)
and the overall average output of the turbine or wind farm. Details of this procedure can be
found in Reference [7]. Average outputs lie typically in the range of 0.25-0.45 of the rated
output depending on the mean wind speed at the site in question. These so called
load factors
or
capacity factors
are much lower than would be expected for conventional generators and
are discussed in some detail in Chapter 3.
The aerodynamic manner in which the wind turbine rotor extracts energy from the wind
is described in a number of textbooks [8-10]. There is a well defi ned upper limit to the
aerodynamic effi ciency
C
p
of a rotor; this is known as the Betz limit and is approximately
0.59. It refl ects the fact that the air is not forced to fl ow through the rotor (e.g. as in a ducted
turbine) but can fl ow around it instead. Conventionally
C
p
, is plotted as a function of the tip-
speed ratio
λ
(defi ned by
λ
=
Ω
R
/
U
where
Ω
is the angular velocity of the rotor,
R
the radius
and
U
the incident wind speed). The ratio
is defi ned in this way to provide a generalized
representation of the wind turbine rotor performance that is applicable to all combinations of
incident wind speed and rotor rotational speed.
A typical
C
p
-
λ
characteristic is shown in Figure 2.8. It is apparent that to operate at peak
effi ciency (for large modern wind turbines
C
p
is normally in the range 0.4-0.5), the tip speed
ratio must be held constant for maximum output and this requires the rotor speed to be con-
trolled in proportion to the wind speed. This is one reason why most larger modern wind
turbines are designed to operate at variable speed (see Chapter 4 for a more complete discus-
sion). This is attractive from an integration perspective as the rotor has inertia available to
absorb or release energy when accelerating or decelerating respectively, thus smoothing short
term variations in wind speed. Consequently its electrical power output varies less and can
be more easily accommodated by the electrical system.
The
C
p
-
λ
of Figure 2.8 assumes a fi xed blade confi guration. If the blade orientation is
changed, then the effi ciency will change too. In fact if the blades are
pitched
or
feathered
,
i.e. rotated about their axis so as to reduce the angle between the blade chord and the resultant
incident wind, then the lift forces on the blade that produce the torque will reduce. This will
λ
