Environmental Engineering Reference
In-Depth Information
TABLE 3.3
Estimated Wind Power Per Area, Perpendicular to the Wind
Wind Speed, m/s
Power, kW/m
2
0
0
5
0.06
10
0.50
15
1.68
20
4.00
25
7.81
30
13.50
From Equation 3.2 the power/area in the wind can be calculated for different wind speeds (Table 3.3).
However, not all the power in the wind can be extracted, as the maximum theoretical efficiency for
wind turbines is 59%.
Note that if the wind speed is doubled, the power is increased 8 times, and the power at 25 m/s is
125 times the power at 5 m/s. Because there is so much power and energy in the wind at high speeds,
there is usually some damage to structures and trees during severe storms and major damage due
to tornadoes and class 3 and above hurricanes. This is also the reason wind turbines do not extract
all the available energy at high wind speeds. All wind turbines have some means of control, or they
would be destroyed in high winds.
EXAMPLE 3.1
A wind turbine with a radius of 2 m, area 12.6 m
2
, would have approximately 100 kW of wind power
across that area due to a 25 m/s wind speed.
A first estimation of wind power potential (power/area) can be calculated using the annual mean
wind speed, which can be estimated from the mean hourly speeds or other measurements of wind
speed. However, use of average or mean wind speeds will underestimate the wind power because
of the cubic relationship. For example, Culebra, Puerto Rico; Tiana Beach, New York; and San
Gorgonio, California, each has an annual average wind speed of 6.3 m/s, but their annual average
power potential is 220, 285, and 365 W/m
2
, respectively [2]. For a better estimate of the wind power
potential for any extended time period, you would need to know the frequency distribution of the
wind speeds; the amount of time for each wind speed value, or a wind speed histogram; and the
number of observations within each wind speed range.
EXAMPLE 3.2
Suppose the wind blows at 5 m/s for 1 h and 15 m/s for another hour. During the 2 h period, the average wind
speed is (5 15)/2 10 m/s. Power/area calculated from the average wind speed is 500 watts/m
2
. However,
the power/area for the first hour is 62.5, and for the second hour the power/area is 1687.5, and the average for
the 2 h is 875 W/m
2
, which is 375 W/m
2
larger than the value calculated by using the average wind speed.
Wind power also depends on the air density:
Pr
VP
760
273
,
kg
m
3
R
1.2929
(3.3)
T
where Pr atmospheric pressure, mm of Hg; VP vapor pressure, mm of Hg; and T temperature,
Kelvin.
The vapor pressure term is a small correction, around 1%, and can be neglected. High temperatures and
low pressures reduce the density of air, which will reduce the power per area. A major factor for change in
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