In a previous post (Understanding Capacity Factor of Wind Farms), we discussed real productivity versus theoretical productivity of wind turbines. Here we will discuss factors that affect wind theoretical power output. Wind power is calculated mathematically, so what these equations tell you ideal values. Without going into equations, I can tell you that wind power depends on these factors:
- Area of rotor
- Wind velocity
- Air density
Rotor Area
Wind power output is directly proportional to rotor area. If rotor area is doubled, turbine output also doubles. Rotor area is the area swept by the blades of the wind turbine. So, the larger the turbine blades, the greater is the power output. This is clear by the data shown here.
|
Rotor Size and Maximum Power Output |
|
|
Rotor Diameter (meters) |
Power Output (kW) |
|
10 |
25 |
|
17 |
100 |
|
27 |
225 |
|
33 |
300 |
|
40 |
500 |
|
44 |
600 |
|
48 |
750 |
|
54 |
1000 |
| 64 |
1500 |
|
72 |
2000 |
| 80 |
2500 |
|
Sources: Danish Wind Industry Association, American Wind Energy Association |
|
Courtesy: www.science.howstuffworks.com
Wind Speed
Wind power is exponentially proportional to wind speed. If wind speed doubles, power generation becomes eight times greater. So, wind speed study of any proposed site is done extensively to ensure good returns on investment. Typically wind speeds are measured for a year at the site before any decision is taken.
Height of Tower
Wind speed depends on height of the turbine from the ground. At ground level, there are many obstructions in the form of buildings, houses, trees, etc. They obstruct smooth flow of wind and hence decrease its speed. Doubling the height of tower almost doubles wind power output. (Please compare to the actual productivity as affected by height).
Air Density
Wind power is directly proportional to air density. Air density is maximum at sea level. That is the reason why we have so many wind farms near or in seas or oceans (read more about on-shore and off-shore wind farms). At higher altitude, air density decreases significantly, so wind farms cannot be made in the mountains. Also, making the turbine taller and taller will not give more power.
Betz Limit
It would be good to mention Betz limit here. German physicist Albert Betz calculated in 1919 that the maximum power that a wind turbine can extract from wind is 59%. He derived his calculation from the conservation of momentum principle because wind is nothing but air that has momentum (i.e. motion). His calculations were independent of turbine design. Practically, wind turbines achieve 70-80% of the Betz Limit.
Much care has to be taken while setting up wind farms, so that we achieve maximum utilization of wind power.
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