Agriculture Reference
In-Depth Information
Substituting the mass of the air, Eq. (13.6) yields
1
2 ρ
AV 3
E k =
(13.7)
The density of air varies with temperature and pressure (and hence on altitude), and
can be estimated from the relation:
3.48 P / T (kg/m 3 )
ρ =
where P is the pressure in kPa and T is the temperature in Kelvin. At 25 Ctem-
perature and 1 atm (or 101 kPa) pressure, the value of air density is close to
1.2 kg/m 3 .
The swept area is the area that the blades cover when they rotate, and is the total
area in which the kinetic energy of the wind is captured by the turbine. The swept
area of rotor, A
r 2 , where r is the rotor radius or the distance from the hub to
= π
blade tip.
Thus, the theoretical model for power of wind turbine ( P w ) becomes
1
2 ρ
r 2 V 3
P w =
n
π
(13.8)
where n is the number of blades.
Introducing the efficiency term for turbine and generator, the energy model
becomes
1
2 ρ
r 2 V 3 E T E G
P w =
n
π
(13.9)
where
E T =
efficiency of turbine (or windmill) (40-50%)
E G =
efficiency of generator (80-85%)
Because of the cubed factor governing the wind speed, a small increase in wind
speed leads to a much greater increase in power. Thus using the average wind speed
does not reflect the actual power over time. Let us consider the wind speed of 5,
10, and 15 m/s. The average velocity here is 10 m/s. Due to increase in wind speed
to double and triple, the resultant energy will be increased by 8 and 27 times. The
average power is about 150% compared to that of average velocity.
Considering the above facts, for practical estimation, a general rule of thumb is
to double the power found using average wind speed.
13.5.13 Intermittency Problem with Wind Energy
One particular problem with wind energy is the intermittent nature of the resource.
The wind does not always blow. This is perhaps the leading criticism of wind power
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