The use of wind energy can significantly reduce the combustion of fossil fuel and the consequent emission of carbon dioxide. Producing energy with clean and renewable sources of energy has become imperative due to the present days' energy crisis and growing environmental consciousness. In wind engineering is very important to know the statistical properties of the wind for predicting the energy output of a wind energy conversion system or speed and behavior of a ships that is ran on wind. Because of the high variability in space and time of wind energy, it is important to verify that the analyzing method used for the measuring wind data will yield the estimated energy collected that is close to the actual energy collected.
The wind speed distribution, one of the wind characteristics, is of great importance for not only for structural and environmental design and analysis, but also for the assessment of the wind energy potential and the performance of wind energy conversion system as well. Over the last two decades many researches have been devoted to develop an adequate statistical model to describe wind speed frequency distribution. The earth's atmosphere can be present as a gigantic heat engine. It extracts energy from the sun and work is done on the gases in atmosphere and upon the earth-atmosphere boundary. There are regions where the air pressure is temporarily higher or lower than average. This difference in air pressure causes atmospheric gases to flow from the region of higher pressure to that of lower pressure. That is the wind. These regions are typically hundreds of kilometers in diameter.
Solar radiation, evaporation of water, cloud cover, and surface roughness all play important roles in determining the conditions of the atmosphere. The study of the interactions between these effects is a complex subject called meteorology, which is covered by many excellent textbooks.
1.Wind Speed Statistics.
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The speed of the wind is continuously changing, making it desirable to describe the wind by statistical methods. To analyze the wind speed we have to use statistical theory and methods. If we have a set of numbers vi
, such as a set of measured wind speeds, the mean of the set is defined as:
The sample size or the number of measured values is n.
In addition to the mean, we are interested in the variability of the set of numbers. We want to find the discrepancy or deviation of each number from the mean and then find some sort of average of these deviations. The mean of the deviations vi -v
is zero, which does not tell us much. We therefore square each deviation to get all positive quantities. The variance
of the data is then defined as:
The standard deviation is then defined as the square root of the variance:
Both the mean and the standard deviation will vary from one period to another or from one location to another. It may be of interest to some people to arrange these values in rank order from smallest to largest.We shall now define the probability p of the discrete wind speed vi being observed as:
With this definition, the sum of all probabilities will be unity:
where mi is the numbers of observation of a specific wind speed vi and w is the number of different values of wind speed observed.
We shall also define a cumulative distribution function F(vi) as the probability that a measured wind speed will be less than or equal to vi:
The cumulative distribution function has the properties:
F(−∞) = 0, F(∞) = 1
It is convenient for a number of theoretical reasons to model the wind speed frequency curve by a continuous mathematical function rather than a table of discrete values. When we do this, the probability values p(vi) become a density function f(v). The density function f(v) represents the probability that the wind speed is in a 1 m/s interval centered on v. The discrete probabilities p(vi) have the same meaning if they were computed from data collected at 1 m/s intervals. The area under the density function is unity, which is shown by the integral:
The cumulative distribution function F(v) is given by: