Wind Speed Analysis by using Logistic

Distribution Model for four Locations in Ireland

By

Parikshit G. Jamdade

and

Shrinivas G. Jamdade

Why Wind Energy ?

• Most viable & largest renewable energy resource

• Plentiful power source

• Widely distributed & clean

• Can get started with as small as 100-200 W

• Produces no green house gas emissions

• Low gestation period

• No raw materials & fuels required

• No pollution

• No hassles of disposal of waste

• Quick returns

• Good alternative for conventional power plants

The main objectives of this study is

1] Wind Power Potential Assessment of a site for Wind Farm / Mill Projects.

2] Assessment of Wind Pattern Variations over a years with the help of Statistical Parameters

& Models .

3] Calculations of Wind Power Density - Available & Extractable at the Site.

4] Comparative Analysis of the Sites

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b

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Description of Ireland

• Developing country with increasing energy demand

• Member of the European Union (EU), the Organisation for Economic Co-operation and

Development (OECD) and the World Trade Organisation (WTO)

• In terms of GDP per capita, Ireland is one of the wealthiest countries in the OECD and EU

Ireland is a part of the United Kingdom which is having ample amount of sea shores for

wind farm developments

• Ireland is rich with urban habitats while farmlands in its rural parts

In urban areas there is a considerable presence of public parks, church yards, cemeteries,

golf courses and vacant areas exist. Some of these locations are ideal to use for

development of wind farms.

In rural parts considerable presence of farmlands exists. These farmlands are the main

source of vegetable crops for Ireland while other parts of rural areas are mostly developed

or semi developed grass lands supporting dairy, beef and sheep production. These grass

lands are ideal locations for harnessing wind energy because they are having lower surface

roughness.

• Ireland has rarely had extreme weather events with lower variations in temperatures

• The country is one of the largest exporters of related goods and services in the world

• Geographic characteristic of Ireland has helped to generate daily wind with reasonable

duration and magnitude

Transmission Network - Ireland

2232 MW Energy from Wind Power Plants

Power Generation Plants Numbers In Percentage

Thermal 20 54.05 %

Hydro 06 16.22 %

Wind 10 27.03 %

Pumped Storage 01 02.70 %

Total Power Generation Plants in Ireland

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In this study, data set of 2007 to 2011 years are obtained containing mean wind speed of

each month in a year with observation height of 10 m above ground level from “The Irish

Meteorological Service online data” site.

Data is an open source data and any one can access this data.

(http://www.met.ie/climate/monthly-weather-bulletin.asp )

The chosen stations from Ireland are

Name Latitude N° Longitude W°

Malin Head Co. Donegal 55°23'N 07°23'W

Dublin Airport Co. Dublin 53°21'N 06°15'W

Belmullet Co. Mayo 54°14'N 09°58'W

Mullingar Co. Westmeath 53°31'N 07°21'W

Annual and Seasonal Variations

• It’s likely that wind-speed at any particular location may be subject to slow long-termvariations

– Linked to changes in temperature, climate changes, global warming

– Other changes related to sun-spot activity, volcanic eruption (particulates),

– Adds significantly to uncertainty in predicting energy output from a wind farm

• Wind-speed during the year can be characterized in terms of a probability distribution

Power in the Wind -

Wind is a movement of air having kinetic energy. This kinetic energy is converted in to electrical energy

with the help of wind turbine. The amount of theoretical power available in the wind is determined by the

equation

WA = (1/2) x ρ x A x V3

where w is power,

ρ is air density, It is taken as 1.225 kg/m3 , A is the rotor swept area,

Swept Rotor Area = A = π x r2 where r is the rotor radius ]

and V is the wind speed.

If turbine rotor area is constant then theoretical Wind Power Density

Available (WPDA) is WA/A & written as

WPDA = (1/2) x ρ x V3

It is also called as Theoretical Maximum Available Power Density.

It is not possible to extract all the energy available in the wind as it has to move away from the blades of

the turbine & be replaced by the incoming mass of air. Therefore

Theoretical Extractable power is given as

WE = (1/2) x ρ x A x Cp x V3

Cp = Coefficient of Performance taken as 16/27 as per Betz Law. Cp is the ratio of power extracted by a

wind turbine to power available in the wind at the location.

Then theoretical Extractable power density is given as WE/A

WPDE = 0.5 x ρ x Cp x V3

It is also called as Theoretical Maximum Extractable Power Density.

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Probability Density Function

The probability density function (PDF) is the probability that the variate has the value x

For distributions, the empirical (sample) PDF is displayed as vertical lines representing

the probability mass at each integer x. In the fitting results window, the theoretical (fitted)

PDF is displayed as a polygonal line for better perception, though it is defined for integer

x values only

For continuous distributions, the PDF is expressed in terms of an integral between two

points

Cumulative Distribution Function

The cumulative distribution function (CDF) is the probability that the variate takes on a

value less than or equal to x. It is an integral of the PDF. It can be drawn by accumulating

the probability of the data as it increases from low to high.

For distributions, this is expressed as

In this case, the empirical CDF is displayed as vertical lines at each integer x, and the

theoretical PDF is displayed as a polygonal line:

For continuous distributions, the CDF is expressed as

so the theoretical CDF is displayed as a continuous curve.

Logistic Distribution

The CDF ( Cumulative Density Function) is

The PDF ( Probability Density Function) is

Where

There are various methods used for calculations

of empirical estimate F(Xi)

1] Simple Rank Method

i / N

2] Mean Rank Method

i / ( N + 1 )

which is recommended by IEEE Standards

3] Symmetrical CDF Method

( i - 0.5 ) / N

4] Median Rank Method

( i - 0.3 ) / ( N + 0.4 )

Fig. 1 Annual Variation in S parameter

Fig. 2 Annual Variation in μ parameter

Fig. 3 Variations in CDF of Wind Speed for Malin Head location

Fig. 4 Yearly ln [(1/ F(Vi)) -1] for Malin Head Location

Fig. 5 Variations in CDF of Wind Speed for Dublin Airport location

Fig. 6 Yearly ln [(1/ F(Vi)) -1] for Dublin Airport Location

Fig. 7 Variations in CDF of Wind Speed for Belmullet location

Fig. 8 Yearly ln [(1/ F(Vi)) -1] for Belmullet Location

Fig. 9 Variations in CDF of Wind Speed for Mullingar location

Fig. 10 Yearly ln [(1/ F(Vi)) -1] for Mullingar Location

Results

• In case of Malin Head, Dublin Airport and Mullingar in the year 2011 wind speed fluctuations are

larger while for Belmullet locations wind speed fluctuation is large in the year 2007.

• In case of Dublin Airport, Belmullet and Mullingar wind speed fluctuations were lesser in year

2010 while for Malin Head location in the year 2009 wind speed fluctuation was less.

• Fig. 2 is showing the annual variations in μ parameter of the Logistic Distribution for Malin Head

, Dublin Airport, Belmullet and Mullingar.

• Higher value of μ parameters indicates that the wind speed is having higher value thus available

power potential is large at that location.

• From Fig. 2 we can conclude that Malin Head is the best location for establishing wind farms as

compare to other locations while Belmullet is the second best location. Least good location is the

Mullingar for development of wind farms.

• In case of Malin Head, Dublin Airport, Belmullet and Mullingar in year 2008, 2008, 2009 and 2007

wind speeds are larger in magnitude while lower in the year 2010, 2009, 2010 and 2010 respectively

• In case of Malin Head, μ parameter is large in the year 2008 while S parameter is large in the year

2009 which shows that wind power production is large in the year 2008 but wind speed fluctuation is

large in the year 2009. μ parameter is lower in the year 2011 while S parameter is lower in 2009

indicating that wind power production is low in the year 2011 but wind speed fluctuation is low in

the year 2009.

• In case of Dublin Airport, μ parameter is large in the year 2011 while S parameter is large in year

2011 which shows that wind power production is large in the year 2011 but wind speed fluctuation is

large in year 2011. μ parameter is lower in the year 2010 while S parameter is lower in 2010

indicating that wind power production is low in year 2010 but wind speed fluctuation is low in the

year 2010.

• In case of Belmullet, μ parameter is large in the year 2011 while S parameter is large in the year 2007

which shows that wind power production is large in the year 2011 but wind speed fluctuation is large

in the year 2007. μ parameter is lower in the year 2010 while S parameter is lower in 2010 indicating

that wind power production is low in the year 2010 but wind speed fluctuation is low in the year

2010.

• In case of Mullingar, μ parameter is large in the year 2007 while S parameter is large in the year 2011

which shows that wind power production is large in the year 2007 but wind speed fluctuation is large

in the year 2011. μ parameter is lower in the year 2010 while S parameter is lower in 2010 indicating

that wind power production is low in the year 2010 but wind speed fluctuation is low in the year

2010.

• In the year 2010, wind power production in all locations is lower; having less fluctuation

in wind speed is in the year 2010 also.

• Summarizing from Fig. 1 and Fig 2, lower S parameter with lower μ parameter results in

lower wind power production. It indicates that the north and the west costal sites of

Ireland are having variable and gusty wind flow pattern as compared to east coastal sites

as they are having high value of μ and S parameters.

• Locations in middle land regions of Ireland are having a low speed magnitude of wind

with smooth wind flow patterns throughout the study period as they are having low value

of μ and S parameters.

• In case of Malin Head site CDF is having the large magnitude in the year 2008 as compared

to other years and their CDF plots are located to the left side of CDF of year 2008. This

indicates that the magnitude of wind speed is large in that year.

• For Dublin Airport site, for the year 2010, CDF plot lies on the extreme left side of other

years CDFs. This means that lower values of wind speed occurs in that year as compared to

other years which reduces the wind power production in the year 2010.

• For Belmullet site, CDF plots of all years are located in the range of wind speed from

20 m/s to 35 m/s except the year 2010. So wind power production is almost constant

throughout the years.

• For Mullingar site, CDF plots are plotted from wind speed 6.5 m/s to 17.5 m/s and they are

always low as compared to other sites. So wind power production is lower as compared to

other sites. Owing to this Mullingar site is the least suitable for setting wind power plant as

compared to other sites.

• In case of Malin Head location during the study period, 20% probability of getting the

wind speed varies from 29 m/s to 36 m/s, 50% probability of getting wind speed varies

from 25 m/s to 31 m/s while 70% probability of getting wind speed varies from 22 m/s to

29 m/s.

• In case of Dublin Airport location during study period, 20% probability of getting wind

speed varies from 20 m/s to 29 m/s, 50% probability of getting wind speed varies from

18 m/s to 23 m/s and 70% probability of getting wind speed varies from 17 m/s to 21 m/s

• In case of Belmullet location during study period, 20% probability of getting wind speed

varies from 22 m/s to 28 m/s, 50% probability of getting wind speed varies from 19 m/s

to 24 m/s while 70% probability of getting wind speed varies from 18 m/s to 22 m/s.

• In case of Mullingar location during study period, 20% probability of getting wind speed

varies from 11 m/s to 14.5 m/s, 50% probability of getting wind speed varies from 10 m/s

to 13 m/s and 70% probability of getting wind speed varies from 9.5 m/s to 11.5 m/s.

• This study shows that Malin Head is the best location for establishing wind farms as compare

to other locations while Belmullet is the second most suitable site. Least good location is the

Mullingar for development of wind farms.

• In case of Malin Head location on an average, 20% probability of getting wind speed is 32 m/s

, 50% probability of getting wind speed is 29 m/s and 70% probability of getting wind speed is

25 m/s.

• In case of Dublin Airport location on an average, 20% probability of getting wind speed is

24 m/s, 50% probability of getting wind speed is 21 m/s and 70% probability of getting wind

speed is 19 m/s.

• In case of Belmullet location on an average, 20% probability of getting wind speed is 26 m/s,

50% probability of getting wind speed is 22 m/s and 70% probability of getting wind speed is

21m/s.

• In case of Mullingar location on an average, 20% probability of getting wind speed is 13 m/s,

50% probability of getting wind speed is 12 m/s and 70% probability of getting wind speed is

10 m/s.

• With increasing wind speed trend over the years boosts the confidence of wind farm developers

for developing wind power plant. This wind power potential of Ireland if exploited would help

the cottage industries and villages for electrification and water pumping.

a

b

c

Conclusions

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conversion system, Energy Conversion Management, 43(16), pp. 2175 - 2187.

• Celick, A. N. (2004) A statistical analysis of wind density based on the Weibull and Rayleigh

models at the southern region of Turkey, Energy Conversion Management, 29(4), pp. 593 - 604.

• Carta, J. A. and Ramiez, P. (2005) Influence of the data sampling interval in the estimation of the

parameters of the weibull wind speed probability density distribution: a case study, Energy

Conversion Management, 46(15), pp. 2419 - 2438.

• Bansal, R. C. Zobaa, A.F. and Saket, R.K. (2005) Some issues related to power generation using

wind energy conversion systems: An overview, International Journal Emerging Electrical Power

System, 3(2), pp. 1 - 19.

• Chang, T. J. and Tu, Y.L. (2007) Evaluation of monthly capacity factor of WECS using

chronological and probabilistic wind speed data: A case study of Taiwan, Renewable

Energy, 32(2), pp. 1999 - 2010.

• Tingem, M., Rivington, M., Ali, S. A. and Colls, J. (2007) Assessment of the ClimGen stochastic

weather generator at Cameroon sites, African Journal of Environmental Science and

Technology, 1(4), pp. 86 - 92.

• Huang, S. J. and Wan, H.H. (2009) Enhancement of matching turbine generators with wind regime

using capacity factor curves stratergies, IEEE Transaction Energy Conversion, 24(2), pp. 551 -

553.

References

• Prasad, R. D., Bansal, R.C. and Sauturaga, M. (2009) Wind energy analysis for Vadravadra site in

Fiji islands: A case study, IEEE Transaction Energy Conversion, 24(3), pp. 1537 - 1543.

• Pryor, S. C. and Barthelmie, R. J. (2010) Climate change impacts on wind energy: a

review, Renewable and Sustainable Energy Reviews, 14, pp. 430 - 437.

• Jamdade, S. G. and Jamdade, P. G. (2012) Extreme Value Distribution Model for Analysis of Wind

Speed Data for Four Locations in Ireland, International Journal of Advanced Renewable Energy

Research, 1(5), pp. 254 - 259.

• Jamdade, S. G. and Jamdade, P. G. (2012) Analysis of Wind Speed Data for Four Locations in

Ireland based on Weibull Distribution’s Linear Regression Model, International Journal of

Renewable Energy Research, 2(3), pp. 451 - 455.

END

Distribution of Wind Speeds

• As the energy in the wind varies as the cube of the wind speed, an understanding

of wind characteristics is essential for:

1] Identification of suitable sites 2] Predictions of economic viability of wind farm projects

3] Wind turbine design and selection 4] Effects of electricity distribution networks and consumers

• Temporal and spatial variation in the wind resource is substantial

1] Latitude / Climate 2] Proportion of land and sea

3] Size and topography of land mass 4] Vegetation (absorption/reflection of light, surface temp, humidity)

• The amount of wind available at a site may vary from one year to the next, with even larger scale variations over periods of decades or more

• Synoptic Variations

– Time scale shorter than a year – seasonal variations

– Associated with passage of weather systems

• Diurnal Variations

– Predicable (ish) based on time of the day (depending on location)

– Important for integrating large amounts of wind-power into the grid

• Turbulence

– Short-time-scale predictability (minutes or less)

– Significant effect on design and performance of turbines

– Effects quality of power delivered to the grid

– Turbulence intensity is given by I = σ / V, where σ is the standard deviation on the wind speed