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where 1 pv3 is the power density in the wind, 161 pv3 is the available power density from the wind, A is the swept area, and n is the efficiency of the wind turbine.

The mean power output from the wind turbine over a period from 0 to T is proportional to the cube of the mean cubic wind velocity, <v>:

Anemometers—instruments that measure or record wind velocity— can be used in wind surveys. Anemometric records have to be converted to eolergometric data—that is, data on wind power density. The mean cubic velocity, <v>, must be calculated from velocity measurements taken at frequent intervals.

The usual anemometric averages, v (the arithmetical averages of v), are not particularly suitable for siting wind turbines. Consider a wind that blows constantly at a speed of 10m/s (average speed, v = 10m/s). It carries an amount of energy proportional to v3 = 1000. A wind that blows at 50m/s 20% of the time and remains calm the rest of the time also has a v of 10m/s, yet the energy it carries is proportional to 0.2 x 503 = 25,000 or 25 times more than in the previous case. In the first case, <v> = 10 m/s, while in the second, <v> = 29.2 m/s.

The quantity, <v>, can be measured directly by dedicated instruments but is more conveniently derived from anemometers equipped with adequate electronics to process v into <v> and store the data for later use.

Eolergometric surveys are complicated by the variability of the wind energy density from point to point (as a function of local topography) and by the necessity of obtaining vertical wind energy profiles. It is important that surveys be conducted over a long period of time—one year at least—so as to collect information on the seasonal behavior.

Values of v are easier to obtain than those of <v> and, consequently, there is the temptation to guess the <v> from the v values. However, the ratio, <v>/v is a function of the temporal statistics of the wind velocity and is strongly site dependent. For perfectly steady winds, this ratio will, of course, be 1. For the extreme case of the example in one of the preceding paragraphs, it is 2.92. When, for lack of better information, one assumes that the wind speed distribution follows the Rayleigh rule, then the ratio is 1.24.

If one could predict the exact behavior of the wind, one would be able to design a wind turbine optimally matching the local conditions. Unfortunately, the wind is notoriously fickle, varying substantially throughout a day, from season to season and even from year to year. This means that even if one has precise data about the wind collected over a full year, there is no guarantee that the next year will be identical.^ Nevertheless, for planning wind farms, a year's worth of detailed data is useful. Failing this, it is possible to use statistical information to make a somewhat educated guess about wind behavior.

If all one knows about a site is its average wind velocity, v, one can make the assumption that the wind obeyed a Rayleigh distribution (see, for example, Figure 15.6), that is, that the probability, p(v), of the wind having a velocity, v, is where a is the mode of the distribution, that is, the value at which the probability density function (pdf) peaks. Although a is not the mean value (in this case, v), there is a relation between the average wind velocity and the mode of the Rayleigh pdf:

A turbine is to be installed at a site in which the average wind speed is 9.6 m/s. Plot the probable distribution of the wind speed throughout the year. What is the probability of having a 12-m/s wind?

Example

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^Portnyagin et al. (2006) point out that very strong year-to-year wind variations makes the estimation of long-term wind behavior a difficult task.

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## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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