Weibull parameters for wind speed distribution in Salem city

¹Dept. of Mechanical Engg., SCSVMV, (Deemed Univ.) Enathur - 631 561, India

²Department of Mechanical Engg., Annamalai University - 608 002, India

³Department of Civil Engg., Annamalai University - 608 002, India

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Abstract

Emission dispersion occurs in the direction of the wind. The wind has a diluting effect on the flue gas concentrations behind a stack, which is approximately proportional to its horizontal velocity. The exponential increase of the wind velocity with altitude favours the dispersions of the flue gases from high stacks. As an energy source, the natural wind is extremely variable. To model wind features of Salem: The Weibull distribution has been chosen. Also available wind energy is estimated.

Keywords

Weibull distribution - Wind power- Pollution dispersion

Introduction

Wind speed frequency distribution is an important parameter for predicting the energy output of a wind energy conversion system. The Weibull function is a two parameter function, namely shape parameter k and scale parameter c. There are several methods available in the literature for the calculation of these two parameters as stated by Stevens and Smulders (1979). In this study, the shape parameter k and scale parameter c are calculated by (1) Frequency method (2) Maximum likely hood method. In this paper, alternate date of 6 time average wind data for the period April 2001-March 2002 are used.

Study area

The Salem city is situated in the central part of the state lies about 330 kms southwest of Chennai. The city skirted on all meteorological sides that is north, south, east and west buyinter connecting hills of the Eastern Ghats to Western Ghats. The city lies on the latitude of 12°,15’ and longitude of 78° 10’. The city experiences maximum temperature of 42°C and a mimimum of 25°C during summer and experiences a maximum of 30°C and minimum of 20°C during winter. Ambient air quality has been monitored at Salem Sowdeswari College in Salem city by Tamil Nadu Pollution Control Board under National Air Quality Monitory Programme (NAMP) since July 1996. This monitory station comes under the category of industrial mixed zone. Wind speed data studies in this paper is based on a series of measurements taken (4 hour basis) on every Mondays, Wednesdays and Fridays through all months of the year 2001- 2002.

Weibull distribution function

The Weibull distribution function which is a two-parameter function is expressed mathematically as follows :

Where k is the scale parameter, c is the shape parameter, and v is the wind speed. The cumulative distribution function is obtained by integrating equation (1) and takes form :

The mean of the Weibull distribution that is the mean wind speed , is expressed in terms of the gamma function and is given by:

Where v is expressed mean wind speed and Γ is the gamma function. 

Wind

An empirical formula relating wind a speed to height in the friction layer, that zone of air beneath 700 to 1000 m, is -

Where v= wind speed at height z m/s

Vo = wind speed at anemometer level zo, m/s

N = co efficient, approximately 1/7. The choice of the exponent n in the power law equation is a function of atmospheric stability, wind speed, the roughness length of the upwind terrain and the site elevation.

Fig.1 Monthly variation of wind power density

Fig.2 Monthly variation of the Weibull k value

Fig.3 Monthly variation of the Weibull c value

Table -1 Weibull Parameter

Table -2 Weibull Parameter

Table -3 Wind Power Potential (Maximum Likelihood Method)

Conclusion

Wind data covered in this paper is pertains for the year 2001-2002 of Salem city. For wind resource estimation the Weibull parameters c and k are derived for the city. The most generous months supplying wind power in Salem city is April, May and June. Smaller wind energy conversion systems are only suitable for the wind condition.

In air pollution concentration prediction models speed (uniform wind) at the height of release of pollutant is an important input to the model, The commonly used power law describes the wind speed profile with height. The exponent of the power law ‘n’ is now derived for industrial mixed zone of Salem city based on the above wind data and hence ground level concentration (GLC) of air pollutant can be estimated realistically.

References

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