WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–2
y
✻
A
✲ u
z
✠
x
✲
Figure 1: Packet of air moving with speed u
An expression for air density is given in Chapter 2 and is repeated here for convenience:
ρ =3.485 p T
kg/m 3 (3)
In this equation, p is the pressure in kPa and T is the temperature in kelvin. The power in
the wind is then
P w = 1 2 ρAu3 = 1.742pAu3 W (4)
T
where A is area in square meters and u is wind speed in meters per second. For air at standard
conditions, 101.3 kPa and 273 K, this reduces to
P w =0.647Au 3 W (5)
The more general Eq. 4 should be used whenever the wind turbine elevation is more than
a few hundred meters above sea level or the temperature is significantly above 0 o C.
At standard conditions, the power in 1 m 2 of wind with a speed of 5 m/s is 0.647(5) 3
= 81 W. The power in the same 1 m 2 of area when the wind speed is 10 m/s is 647 W.
This illustrates two basic features of wind power. One is that wind power is rather diffuse.
It requires a substantial area of wind turbine to capture a significant amount of power. The
other feature is that wind power varies rapidly with wind speed. Overspeed protection devices
are therefore required to protect both the turbine and the load at high wind speeds.
The physical presence of a wind turbine in a large moving air mass modifies the local air
speed and pressure as shown in Fig. 2. The picture is drawn for a conventional horizontal axis
propeller type turbine.
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001