**D. Jayakumar, Prashanthi Devi. M, S. Suriyanarayanan,S. Balasubramanian **

Dept of Environmental Sciences, Bharathiar University,

Coimbatore-641046. Tamil Nadu. India

**C. R. Ranganathan**

Dept of Mathematics, Tamil Nadu Agricultural University

Coimbatore -641003 Tamil Nadu. India

E-mail: [email protected]

Phone No: 91 0422 425459, Fax No. 091-422-422387

Wind energy is one of the important free renewable clean and non-polluting sources, which vigorously pursued in many countries. Of the several alternative energy sources wind is perhaps the most suitable and cost effective.

Compared with solar energy sources wind is more sensitive to variations with topography and weather patterns. These properties make wind resources assessment – the characterization of wind as an energy resource – a very important part of wind energy applications (Pacific North West Laboratory, 1979). Thus unlike other renewable resources, the wind resource varies with time of day and season of year and even some extent from year to year. Wind energy has inherent variances and hence it has been expressed by distribution methods like Weibull, Bivariate Normal and Gamma distributions (Christofferson and Gillette (1987), Ranganathan et al., 1991). With this in view, the present study has been initiated to attempt to estimate the available wind power potential using Gamma distribution in different parts of Tamil Nadu and mapped using GIS.

**Study Area and Data**

The study area Tamil Nadu lies within the latitude 8° 5′ – 13° 35’N and longitude 76° 15′- 80° 20′ E. Tamil Nadu is situated in the southern end of Indian peninsula, which is bounded by Karnataka & Andhra Pradesh in the north, Bay of Bengal in the east and Indian ocean in the south and Kerala in the West. The total area of this state is 1,30,058 Km2.

The basic data for this study consists of mean monthly wind speed data of 18 meteorological stations randomly distributed in Tamil Nadu for 11 years (1970-1980). The readings were taken at a height of 10meters above the ground level. The locations of the stations, the altitude and the descriptive statistics of monthly wind speed were analysed.

**Wind power estimation and Methodology**

The observed mean monthly wind speed has inherent variability and can be best described by a probability distribution method. Gamma distribution is one of the most useful continuous distributions often used to model natural events like precipitation and other climatological data of series (WMO, 1996) In this paper, we have used Gamma distribution to estimate the mean wind power of 18 stations in Tamil Nadu. The mathematical analysis of wind power calculations and fitting procedure of Gamma distribution to observe data are as follows:

The probability density function of the two-parameter Gamma distribution is defined by

————————————–(1.0)

where G(b) is the Gamma function defined by

———————————————-(2.0)

The Gamma distribution has a single peak at x = (b – 1)/a, (b < 1) and it takes a variety of shapes, depending on the values of b, ranging from reverse J shaped for b 1. The constant b is called shape parameter and a is called scale parameter. The cumulative Gamma distribution function is defined by

———————————-(3.0)

The value of the above function can’t be given in a closed form and it can be evaluated numerically using tables of incomplete Gamma function, which is available in several handbooks (eg. Pearson, 1957). The mean wind speed, says wbar, in any locality is given by the mean of the Gamma distribution and can be shown as

————————–(4.0)

The wind power at any location is given by where r is the air density. So the available mean wind power at any location is given by

—————————————-(5.0)

To estimate this value, we have to find the value of E (w3). This is done as follows. If G (v) is the cumulative distribution function of w3, then

G (v) = P {w3 £ v} = P {w £ v1/3} = ——————–(6.0)

Hence if g (u) is the density function of u, then,

The above equation gives an expression for available wind power at any location. As an example, for Kodaikanal station, the estimates of values of a and b are22.8 and 7.27 respectively. Hence the average wind speed is given by E (w) = 22.8/7.27 = 3.14 and the mean power, assuming the value of air density to be 1.25 is

In a similar manner, the mean wind speed and wind power were estimated for the remaining stations. The results of the two-parameter Gamma distribution were compared with two-parameter Weibull distribution estimates of both Method I & Method II (Ranganathan et al., 1991). These values were found to be on par with each other.

**Mapping and GIS**

GIS mapping method was used to map the wind power of the 18 different locations randomly distributed in Tamil Nadu. GIS package MapInfo was used to digitize the necessary layers of Tamil Nadu and to geocode the 18 wind power stations for this study. Using the predictors obtained from Gamma distribution, thematic maps were prepared for seasonality on monsoon scale and wind speed/power.

All the 18 stations in Tamil Nadu were selected to prepare wind power maps for different monsoon seasons. The data were classified into four ranges namely High, Moderate, Low and Very low for each season and mapped using GIS package MAPINFO.

An overall map of Gamma distribution for wind power was first prepared. Three stations namely Coimbatore, Kanyakumari and Tuticorin were found to have high wind power with values ranging from 51 to 82.4 (W/m2 ). In the moderate ranges four stations namely Pamban, Karaikal, Nagapattinum & Pondicherry were found at a range of 29.0 to 50.99 W/m2. The low range consisted of six stations (Palayamkottai, Kodaikanal, Madurai, Tiruchirapalli, Cuddalore, Meenampakkam) at a range 12.0 to 28.99 W/m2. The very low wind power was observed at Nungampakkam, Vellore, Mettur and Ooty (stations), which come in the range 2.0 to 11.99 W/m2 (Map 1).

In the Pre-monsoon map of wind power, the values were classified into four ranges. In the high range from 39 to 64 W/m2, three stations namely Tuticorin, Kanyakumari and Pondicherry were seen. In the moderate range of 19to 38 W/m2 four stations were observed. In the low range six stations ranging from 9 to 18 W/m2 were observed. The very low range of 0.8 to 8.0 W/m2 of the Pre-monsoon wind power consisted of five stations (Map 2).

In the monsoon season, three stations (Kanyakumari, Coimbatore, Tuticorin) recorded the high wind power whereas five stations recorded low wind power, which are Ooty, Mettur, Vellore, Nungampakkam and Cuddalore (Map3).

On comparison of the Pre-monsoon wind power map with the monsoon wind power map, it was observed that Tiruchirapalli of Pre-monsoon low range had shifted to monsoon high range and Pondicherry had shifted from the high range to the low range.

In the post monsoon season 4 stations namely Pamban, Tuticorin, Kanyakumari and Pondicherry recorded the highest wind power and five stations namely Ooty, Mettur, Vellore, Meenampakkam and Adirampattinam recorded the lowest wind power (Map 4).

On comparison of the percentage of the Gamma with the three monsoons, it was observed that the monsoon season recorded a high of 10.14% and the lowest recorded as 2.90% at post monsoon season. The highest wind power was recorded as 192.56% at Coimbatore stations in the monsoon season. Tuticorin and Kanyakumari remained in the high range throughout the year. On similar comparison with the other ranges, it was observed that there was a constant shift among the moderately low stations. In the very low range, Ooty, Vellore and Mettur remained constant throughout the year. Constant shift was observed in the other 12 stations during the change of season. **References**

- ESRI, 1998, ARC, Version 7.2.1, Manual User Reference.
- Inter-graph, 2002, https://www.intergraph.com/gis/
- Kim Y. and S. Openshaw, 2002, Comparison of alternative location-allocation algorithms in GIS School of Geography, University of Leeds LS2 9JT
- Klinkenberg B, 1997. Location-Alocation on networks,
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Map1

Map2

Map3

Map4

Map5

**Figure 5. Map 1 – 5** show the results of running different models for a rural area called Pivejan in Khorasan province of Iran (North East of the country). More details are discussed in the text.