Fundamentals of wind energy - Wind Power Generation and Wind Turbine Design - page 9

4 Wind energy characteristics

Wind energy is a special form of kinetic energy in air as it fl ows. Wind energy can
be either converted into electrical energy by power converting machines or directly
used for pumping water, sailing ships, or grinding gain.

4.1 Wind power

Kinetic energy exists whenever an object of a given mass is in motion with a trans-
lational or rotational speed. When air is in motion, the kinetic energy in moving
air can be determined as

(1)
where m is the air mass and - is the mean wind speed over a suitable time period.
The wind power can be obtained by differentiating the kinetic energy in wind with
respect to time, i.e.:

k E

= u

2

1

d 1
d2

E

k 2

(2)

P = = mu

w

t

However, only a small portion of wind power can be converted into electrical
power. When wind passes through a wind turbine and drives blades to rotate, the
corresponding wind mass fl owrate is

m

= r u

(3)

where r is the air density and A is the swept area of blades, as shown in Fig. 3.
Substituting (3) into (2), the available power in wind P w can be expressed as

P = r Au

3

1

(4)

w 2

An examination of eqn (4) reveals that in order to obtain a higher wind power, it
requires a higher wind speed, a longer length of blades for gaining a larger swept
area, and a higher air density. Because the wind power output is proportional to the
cubic power of the mean wind speed, a small variation in wind speed can result in
a large change in wind power.

4.1.1 Blade swept area
As shown in Fig. 3, the blade swept area can be calculated from the formula:

⎡

( )

2

⎤

( )

Al =+−=+

⎣

p r r

2

p l l 2 r

(5)

⎦