1. Wind Speed Analysis by using Logistic
Distribution Model for four Locations in Ireland
By
Parikshit G. Jamdade
and
Shrinivas G. Jamdade

2. 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

3. 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
a
b
c

4. 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

9. Transmission Network - Ireland

10. 2232 MW Energy from Wind Power Plants

11. Total Power Generation Plants in Ireland
Power Generation Plants
Thermal
Hydro
Wind
Pumped Storage
Numbers
20
06
10
01
In Percentage
54.05 %
16.22 %
27.03 %
02.70 %
a
b
c

13. 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
Malin Head Co. Donegal
Dublin Airport Co. Dublin
Belmullet Co. Mayo
Mullingar Co. Westmeath
Latitude N°
55°23'N
53°21'N
54°14'N
53°31'N
Longitude W°
07°23'W
06°15'W
09°58'W
07°21'W

16. Annual and Seasonal Variations
•
•
It’s likely that wind-speed at any particular location may be subject to slow long-term
variations
– 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

17. 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.

18. Month
Month
2007
2011
December
December
November
October
September
2007
2011
November
October
September
Mullingar
2006
2010
August
July
June
May
April
Dublin
2006
2010
August
July
June
2005
2009
May
March
February
January
Wind Speed (m/s)
2005
2009
April
20
18
16
14
12
10
8
6
4
2
0
March
2008
35
30
25
20
15
10
5
0
February
Wind Speed (m/s)
December
2008
January
December
2007
2011
November
October
September
August
July
June
May
April
March
February
January
Wind Speed (m/s)
2007
2011
November
October
September
Belmullet
2006
2010
August
July
June
May
2005
2009
April
March
40
35
30
25
20
15
10
5
0
February
January
Wind Speed (m/s)
50
45
40
35
30
25
20
15
10
5
0
Malin Head
2005
2006
2009
2010
2008
Month
Month
2008

19. Month
2009
15000
10000
5000
0
Month
December
November
October
September
August
July
Month
June
May
April
March
February
January
Maximum Available Power Density
(w/m2)
December
Max. Available Power Density Dublin
2007
2008
20000
2010
2011
November
October
September
August
July
June
May
April
March
February
January
Maximum Available Power Density
(w/m2)
December
November
October
September
August
July
June
May
April
March
February
January
Maximum Available Power Density
(w/m2)
December
November
October
September
August
July
June
May
April
March
February
January
Maximum Available Power Density
(w/m2)
Max. Available Power Density Malin Head
2007
2008
2009
50000
2010
2011
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
Max. Available Power Density Belmullet
2007
2008
2009
25000
2010
2011
20000
15000
10000
5000
0
Month
Max. Available Power Density Mullingar
2007
2008
2009
4000
2010
2011
3500
3000
2500
2000
1500
1000
500
0

20. Month
8000
6000
4000
2000
0
Month
December
November
October
September
August
July
June
Month
May
2009
April
0
March
5000
February
10000
January
15000
December
November
October
September
August
July
June
May
April
March
February
January
Maximum Exractable Power Density
(w/m2)
December
November
October
September
August
July
June
May
April
March
February
January
Maximum Exractable Power Density
(w/m2)
20000
Maximum Exractable Power Density
(w/m2)
December
Max. Exractable Power Density Dublin
2007
2008
12000
2010
2011
10000
November
October
September
August
July
June
May
April
March
February
January
Maximum Exractable Power Density
(w/m2)
Max. Exractable Power Density Malin Head
2007
2008
2009
30000
2010
2011
25000
Max. Exractable Power Density Belmullet
2007
2008
2009
14000
2010
2011
12000
10000
8000
6000
4000
2000
0
Month
Max. Exractable Power Density Mullingar
2007
2008
2009
2010
2011
2000
1500
1000
500
0

21. 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

22. 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.

23. Logistic Distribution
The CDF ( Cumulative Density Function) is
The PDF ( Probability Density Function) is
Where

24. 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 )

25. Fig. 1 Annual Variation in S parameter
Fig. 2 Annual Variation in μ parameter

26. Fig. 3 Variations in CDF of Wind Speed for Malin Head location
Fig. 4 Yearly ln [(1/ F(Vi)) -1] for Malin Head Location

27. Fig. 5 Variations in CDF of Wind Speed for Dublin Airport location
Fig. 6 Yearly ln [(1/ F(Vi)) -1] for Dublin Airport Location

28. Fig. 7 Variations in CDF of Wind Speed for Belmullet location
Fig. 8 Yearly ln [(1/ F(Vi)) -1] for Belmullet Location

29. Fig. 9 Variations in CDF of Wind Speed for Mullingar location
Fig. 10 Yearly ln [(1/ F(Vi)) -1] for Mullingar Location

30. 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

31. •
•
•
•
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.

32. • 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.

33. • 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.

34. • 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.

35. Conclusions
• 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 a
the cottage industries and villages for electrification and water pumping.
b
c

36. References
•
•
•
•
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•
•
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37. •
•
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38. END

41. 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