Fundamentals of wind energy - Wind Power Generation and Wind Turbine Design - page 22

Thus, the power output of mechanical energy captured by wind turbine
blades is

2 2 3 2

P =

1

r Au ( u − u ) =

1

r Au 4 (1 a − a ) (21)

me,out 2 1 4 1

2 2

where a is the axial induction factor, defi ned as

uu

−

a =

1 2

(22)

1

Substitute eqn (21) into (16) (where - 1 = - ), yields

2

Ca = 4(1 − a ) (23)

p

This indicates that the power coeffi cient is only a function of the axial induction
factor a . It is easy to derive that the maximum power coeffi cient reaches its maxi-
mum value of 16/27 when a = 1/3 (see Fig. 9).

5.3.4 Power curve
As can be seen from eqn (18), the effective electrical power output from a wind
turbine P eff is directly proportional to the available wind power P w and the total
effective wind turbine effi ciency h t .
The power curve of a wind turbine displays the power output (either the real elec-
trical power output or the percentage of the rated power) of the turbine as a function
of the mean wind speed. Power curves are usually determined from the fi eld mea-
surements. As shown in Fig. 10, the wind turbine starts to produce usable power at a
low wind speed, defi ned as the cut-in speed. The power output increases continu-
ously with the increase of the wind speed until reaching a saturated point, to which

0.70

0.60

c p,max

0.50

0.40

c p

0.30

0.20

0.10

0.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Axial induction factor a

Figure 9: Power coeffi cient as a function of axial induction factor a .