WIND SYSTEM's POWER CALCULATION
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Wind generators are generally designed to yield maximum output at high air speeds. Likewise, the manufacturers rate their systems by the amount of power they can produce at a specific high speed, typically 24 mph (10.5 m/s) to 36 mph (16 m/s). In reality, you will rarely get these speeds. Note that the available energy of the moving air molecules is proportional to the cube of their speed, so even small decrease in the speed results in large decrease in the energy. A turbine rated for example at 5000 watts at 30 mph will produce only 625 watts or less at 15 mph.
Besides rated wattage, wind generator manufactures also normally provide a so-called Power Curve (also known as a Performance Graph or Power Output Graph), that plots the output in watts or kilowatts as a function of instantaneous wind speed.
These curves have S-shape that starts with zero at a certain "cut-in" speed, and leveling off to a rated power at a rated speed. Above the rated speed the curve usually goes slightly down and then abruptly goes back to zero at a certain cut-out speed, where turbines shuts down to protect itself from a damage. Although the power curves are more useful than rated power values, they only tells you how much electricity you may generate at specific instantaneous air speeds. Since the air speed varies all the time, you need to know the net amount of electricity you can expect to generate over certain period of time, say in a year. There are various climate maps that provide data on average air speed for various geographical regions. However, you can't simply apply an average air speed to the turbine's power graphs to determine the annual output. The case is, it all depends on how that average speed came about, i.e. if winds in your site vary a lot, or if they blow at a relatively constant speed. In a hypothetical case, if the wind is always either below a turbine's cut-in speed, or above cut-out speed, you will not produce any electricity at all, even though the average air speed may look good.
To assert the average amount of energy a wind system can generate annually, Battelle Laboratories estimated an actual average annual wind output in various US regions, rather than simply mean air speed. They introduced a numerical rating that corresponds to one of the seven wind power classes. Each class represents a range of wind power density based on the computer analysis of historical data. A similar mapping for Europe was done by Riso Laboratory.
| Wind Power Classes |
10 m (33 ft) | 50 m (164 ft) | ||
| Wind Power Density (W/m2) | Average Wind Speed m/s (mph) | Wind Power Density (W/m2) | Average Wind Speed m/s (mph) | |
| 1 | 0-100 | 0-4.4 (0-9.8) | 0-200 | 0-5.6 (0-12.5) |
| 2 | 100-150 | 4.4-5.1 (9.8-11.5) | 200-300 | 5.6-6.4 (12.5-14.3) |
| 3 | 150-200 | 5.1-5.6 (11.5-12.5) | 300-400 | 6.4-7.0 (14.3-15.7) |
| 4 | 200-250 | 5.6-6.0 (12.5-13.4) | 400-500 | 7.0-7.5 (15.7-16.8) |
| 5 | 250-300 | 6.0-6.4 (13.4-14.3) | 500-600 | 7.5-8.0 (6.8-17.9) |
| 6 | 300-400 | 6.4-7.0 (14.3-15.7) | 600-800 | 8.0-8.8 (17.9-19.7) |
| 7 | 400-1,000 | 7.0-9.4 (15.7-21.1) | 800-2,000 | 8.8-11.9 (19.7-26.6) |
These data provide annual average wind power density in watts per 1 square meter of a turbine sweep area. Average speeds in the table are based on the so-called Rayleigh speed distribution of equivalent mean wind power density and are given for the sea level. To get the same density above sea level, the air speed has to increase by 3% per 1000 metre (1% per 1000 ft) elevation.
The table provides data only for 10m and 50m heights. To estimate the air speed and output for the actual height of your tower you can use an empirical 1/7 power law. If you know the air speed V1 at a certain height h1, then the air speed V2 at a different height h2 can be estimated as: V2=V1×(h2/h1)1/7.
Similarly, since wind power density is proportional to cube of the speed, the power density at a different tower's height h2 will be: P2=P1×(h2/h1)3/7, where P1 is the power density at h1.
To estimate the average output of your system you first need to determine the wind class of your site from the wind map, and find from the above table the wind density in W/sq.m corresponding to your class and to the height of your tower. Then multiply this number by the efficiency of your system (which is typically 0.2 for residential size systems) and by turbine swept area in sq.m. For horizontal turbines the sweep area is A=π(D/2)2, where D is the diameter of the blades, π=3.14 (see Calculation of the energy in the wind).
Note that the values in the above table were obtained for those sites that are free of obstructions. If you have any obstruction such as a tree or a building within 300 feet (100 meters), it is generally recommended to place the turbine at least 10 feet (3 meters) plus the blade length above the top of the highest obstruction.
REFERENCES AND ADDITIONAL INFORMATION
Wind
Energy Resource Atlas of the United States
Renewable Energy for Home, Farm, and Business - a detailed book on making a wind-based system
Renewable Energy for Home, Farm, and Business - a detailed book on making a wind-based system
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