Winds Engery

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Wind speed and power density analysis based on

Weibull and Rayleigh distribution functions

Year: 2012

Asif Jalal

2012-MS-MED-24

Supervisor

Prof. Dr. Nasir Hayat

Department of Mechanical Engineering

University of Engineering & Technology Lahore-Pakistan


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Wind speed and power density analysis based on Weibull

and Rayleigh distribution functions

This thesis is submitted to Department of Mechanical Engineering, University of Engineering &Technology, Lahore, for the partial fulfillment of the requirement for the award of degree in

Master of Science in

Mechanical Design Engineering

Approval on __________________


University of Engineering & Technology Lahore-Pakistan

External Examiner

Dean

Faculty of Mechanical Engineering

Internal Examiner

Professor Dr. Nasir Hayat

Chairman



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In the Name of ALLAH, the Most Gracious and the Most Merciful.


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This thesis is dedicated to my parents, my

brothers and especially, my sister.


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Acknowledgements

Firstly, I would like to express my gratitude, praise and acknowledgement to Almighty ALLAH,

who is the only Creator and Owner of the universe, I am nothing merely the kindness of ALLAH.

Through, His kindness of My Lord, I am able to achieve my all goals in my life.

Secondly, I would like to thanks my dedicated supervisor Professor Dr. Nasir Hayat. His

motivation, direction and guidance really helped me to achieve my ultimate task. I shall be very

thankful to him for this act of kindness.

And, I would not restrain myself to express acknowledgement and honest appreciation to Mr.

Nadeem Faisal Deputy Director PMD (CPDC Karachi) Pakistanfor providing me precious

and confidential department data and technical help in this research work.

Lastly, I would yield this opportunity to thank respected Chairman and Dean of the faculty along

with all Post Graduate Research Committee and faculty members for their insightful comments

and observations.


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Abstract

Large scale industrial growth and depleted hydro power sources in the country urges the

researchers to transcend the focus towards the renewable energy sources because they are clean,

abundant and environment friendly as compared to orthodox energy sources. Among the

renewable energy sources, the wind energy is most rapidly growing than others. The key objective

of this paper is to study and investigate the wind characteristics and wind potential at the site of

Turbat. For this purpose, the measured 3-hourly time series data was taken from the Pakistan

Meteorological department (CPDC, Karachi) for the period of 21 months (Jan 2012- Sep13). The

obtained data was statistically evaluated with the help of Weibull and Rayleigh functions. The

average wind speed is more than 4 m/s for every month. The average values of most probable wind

speed and wind speed carrying maximum energies are 3.83 m/s and 7.732 m/s respectively. The

overall variation in the values of standard deviation is from 1.699 to 3.306. The values of Weibull

shape parameter are in the range of 1.508 to 3.010. Similarly, the range of Scale parameter is from

4.674 m/s to 7.429 m/s. The monthly mean value of wind power and energy densities of the

selected site are 140.145 W/m2and 101.775 kWh/m2respectively. The mean power potential of

the site is then compared with the power calculated through Weibull and Rayleigh functions. It

was exposed that the Weibull distribution describe the actual data better than the Rayleigh

function. This statement was further enriched by the assessment of performance of these twodistribution with the RMSE, 2, R2tests.


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Table of ContentsAcknowledgements------------------------------------------------------------------------------------------------------------- 5

Abstract---------------------------------------------------------------------------------------------------------------------------- 6

Chapter # 1 ----------------------------------------------------------------------------------------------------------------------- 12

INTRODUCTION: ------------------------------------------------------------------------------------------------------------ 12

Chapter # 2 ----------------------------------------------------------------------------------------------------------------------- 16

LITERATURE REVIEW --------------------------------------------------------------------------------------------------- 16

Chapter # 3 ----------------------------------------------------------------------------------------------------------------------- 19

BASIC THEORY IN WIND ENERGY --------------------------------------------------------------------------------- 19

3.1 Introduction of Wind energy --------------------------------------------------------------------------------------- 19

3.2 Brief history of Wind energy --------------------------------------------------------------------------------------- 20

3.3 Wind Resource Assessment----------------------------------------------------------------------------------------- 20

3.4 Extrapolation of wind speed at different height------------------------------------------------------------- 22

3.5 Presentation of Data -------------------------------------------------------------------------------------------------- 22

3.5.1 Data collection---------------------------------------------------------------------------------------------------- 22

3.5.2 Organization of Data-------------------------------------------------------------------------------------------- 22

3.5.3 Tabulation of data ----------------------------------------------------------------------------------------------- 23

3.5.4 Graphical representation -------------------------------------------------------------------------------------- 23

3.6 Measure of central tendency of the data----------------------------------------------------------------------- 23

3.6.1 Mean ----------------------------------------------------------------------------------------------------------------- 23

3.6.2 Median-------------------------------------------------------------------------------------------------------------- 24

3.6.3 Mode ----------------------------------------------------------------------------------------------------------------- 24

3.7 Measure of Dispersion----------------------------------------------------------------------------------------------- 24

3.7.1 Range ---------------------------------------------------------------------------------------------------------------- 24

3.7.2 Mean deviation--------------------------------------------------------------------------------------------------- 24

3.7.3 Standard deviation---------------------------------------------------------------------------------------------- 25

3.8 Wind data parameter estimation--------------------------------------------------------------------------------- 25

Chapter # 4----------------------------------------------------------------------------------------------------------------------- 27

DATA COLLECTION AND ANALYSIS------------------------------------------------------------------------------ 27

4.1 Site description and data collection ------------------------------------------------------------------------------ 27

4.2 Statistical analysis of the data------------------------------------------------------------------------------------- 28

4.3 Frequency distribution Table -------------------------------------------------------------------------------------- 30

4.4 Statistical Distributions ---------------------------------------------------------------------------------------------- 30


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4.4.1 Weibull distribution --------------------------------------------------------------------------------------------- 32

4.4.2 Rayleigh distribution------------------------------------------------------------------------------------------- 34

4.5 Evaluation of Weibull and Rayleigh distributions---------------------------------------------------------- 35

4.6 Rated wind speed for wind turbine------------------------------------------------------------------------------ 36

4.7 Cut in velocity ----------------------------------------------------------------------------------------------------------- 36

4.8 Rated wind speed of Turbine generator ------------------------------------------------------------------------ 36

4.9 Full load------------------------------------------------------------------------------------------------------------------ 36

4.10 Cut out Velocity------------------------------------------------------------------------------------------------------ 37

4.11 Wind power density calculation --------------------------------------------------------------------------------- 37

4.11.1 Swept area of Blade -------------------------------------------------------------------------------------------- 37

4.11.2 Density of air ----------------------------------------------------------------------------------------------------- 38

4.11.3 Wind power density using weibull distribution------------------------------------------------------- 38

4.11.4 Wind power density using Rayleigh distribution ---------------------------------------------------- 39

4.11.5 Error in the calculation of power density--------------------------------------------------------------- 39

4.12 Wind energy density calculation-------------------------------------------------------------------------------- 39

4.13 Analysis type ----------------------------------------------------------------------------------------------------------- 39

Chapter # 5 ----------------------------------------------------------------------------------------------------------------------- 41

RESULTS & DISCUSSIONS ---------------------------------------------------------------------------------------------- 41

5.1 Measurement of average wind speed ---------------------------------------------------------------------------- 41

5.2 Measurement of standard deviation ----------------------------------------------------------------------------- 42

5.3 Monthly values of Vmpand Vmax.E--------------------------------------------------------------------------------- 43

5.4 Coefficient of Variation ---------------------------------------------------------------------------------------------- 44

5.5 Weibull parameters estimations---------------------------------------------------------------------------------- 44

5.6 Frequency distribution table --------------------------------------------------------------------------------------- 47

5.7 Comparison of Actual, Weibull and Rayleigh probabilities---------------------------------------------- 49

5.7.1 Monthly comparison -------------------------------------------------------------------------------------------- 49

5.7.2 Yearly comparison----------------------------------------------------------------------------------------------- 54

5.8 Performance estimation of Statistical models----------------------------------------------------------------- 56

5.8.1 Monthly R2value ------------------------------------------------------------------------------------------------- 57

5.8.2 RMSE and Chi-square test----------------------------------------------------------------------------------- 59

5.9 Calculation of Wind power density------------------------------------------------------------------------------ 59

5.10 Calculation of Wind energy density ---------------------------------------------------------------------------- 62

5.11 Error estimation during power density calculations ------------------------------------------------------ 64


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5.11.1 Weibull distribution ------------------------------------------------------------------------------------------- 64

5.11.2 Rayleigh distribution ------------------------------------------------------------------------------------------ 65

5.11.3 Comparison of error estimation using Weibull function and actual wind data------------ 66

CONCLUSIONS --------------------------------------------------------------------------------------------------------------- 67

REFERENCES ----------------------------------------------------------------------------------------------------------------- 69


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List of Figures

Figure 1.1: Total installed capacity of the world wind energy ever since 1997 to 2014 ....... 13

Figure 1.2: Wind map of Pakistan showing wind potential of all provinces [5] ................... 15

Figure 4.1: Location of Turbat in Balochistan, Pakistan........................................................ 28

Figure 4.2: Swept area of the blade of wind turbine............................................................... 38

Figure 5.1: Average wind speed per month for year 2012-13................................................. 41

Figure 5.2: Monthly values of standard deviation................................................................... 42

Figure 5.3: Monthly values of Coefficient of Variation for year 2012-13 .............................. 44

Figure 5.4: Monthly values of shape parameter for year 2012-13......................................... 46

Figure 5.5: Monthly variation in the values of scale parameter for year 2012-13 ................ 46

Figure 5.6: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Feb 2012.. 49

Figure 5.7: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Jun 2012.. 50

Figure 5.8: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Sep 2012.. 50

Figure 5.9: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Nov 2012. 51

Figure 5.10: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Jan 2013 51

Figure 5.11: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Jun 2013 52

Figure 5.12: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Aug 2013 53

Figure 5.13: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Sep 2013 53

Figure 5.14: Comparison of Actual, Weibull and Rayleigh PDF, CDF for year 2012......... 54

Figure 5.15: Comparison of Actual, Weibull and Rayleigh PDF, CDF for year 2013......... 55

Figure 5.16: Comparison of Actual, Weibull and Rayleigh PDF, CDF for year 2012-13 .... 56

Figure 5.17: Monthly values of R2 for Weibull and Rayleigh distribution, year 2012......... 57

Figure 5.18: Monthly values of R2 for Weibull and Rayleigh distribution, year 2013......... 58Figure 5.19: Average monthly wind power density of the Turbat site.................................. 61

Figure 5.20: Average monthly wind power density for Turbat site....................................... 61

Figure 5.21: Monthly wind energy density calculated with mean speed, Weibull and

Rayleigh functions for year 2012............................................................................................... 62

Figure 5.22: Monthly wind energy density calculated with mean speed, Weibull and

Rayleigh functions for year 2013............................................................................................... 63

Figure 5.23: Comparison of average error estimated for 2 years, evaluated by Weibull and

Rayleigh distributions w.r.t actual observed wind data.......................................................... 65


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List of Tables

Table 1.1: Wind resources assessment of Pakistan [4] ............................................................ 14

Table 5.1: Monthly values of Vmpand Vmax.E for the year 2012-13 ........................................ 43Table 5.2: Monthly values for Shape and Scale parameters of Weibull distribution........... 45

Table 5.3: Distribution of frequencies calculated from wind speed data for year 2012 ....... 47

Table 5.4: Distribution of frequencies calculated from wind speed data for year 2013 ....... 48

Table 5.5: Evaluation of Statistical models used ...................................................................... 59

Table 5.6: Monthly comparison of power densities calculated from actual wind data,

Weibull and Rayleigh models .................................................................................................... 60

Table 5.7: Yearly average values of wind power and energy density .................................... 63

Table 5.8: Classes of wind power density at 10 m and 50 m height [33] ............................... 64


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Chapter # 1

INTRODUCTION:

Pakistan is an emerging country having population of above 180 million but the average energy

per capita of the year is about 450 kWh; whereas, the Worlds average value of energy

consumption per year is 2730 kWh [1]. Almost, 37% population of remote areas are still awaiting

to be connected with the national grid [1].Billions of dollars are being spent on the import of oil

for thermal power houses; resultantly, worse economy, air pollution, acid rain emission and abrupt

climate change. Enormous industrialization is taking place, Hydro Power /water resource are

depleting and oil and gas resources are, if local than scarce in availability and else, wounding the

budget of whole economy. Hence, depletion, pollution and energy shortage is further scorching to

our deficit economy badly, which requires severe attention and ultimate solution. Therefore, to

meet the emergent electricity demand of the country and to save the environment as well as

economy, we need Renewable energy sources in addition with existing power resources as these

are free, environment friendly and enriched in Pakistan.

In renewable energy sources, wind is most speedily growing source in the world. Likewise, other

renewable energy source, it is clean, abundantly available, reliable and does not affect the

environment. Wind energy added more consideration and importance worldwide after the oil crisis

in 1973 and 1979 [2]. Currently, based upon the global wind energy statistics, the total wind energy

capability of the world at the end of 2014 is 371,559 MW with the added capacity of 52,654 MW

in 2014 only, having annual growth rate of 16.4% [3]. This wind energy capacity of the world, at

the end of 2013 and 2012, was 319,036 MW and 282,810 MW respectively [3]. In Fig. 1.1the

total mounted aptitude of the wind energy of the world has been shown since year 1997 to 2014

[3].


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Figure 1.1: Total installed capacity of the world wind energy ever since 1997 to 2014

In the Word, China is leading with total wind energy installed capacity of 114,763 MW by the

addition of 23,350 MW in the year 2014 only, having growth rate of 25.7% [3]. USA came 2ndin

the list having total installed capacity of the wind 66,754 MW at the end of year 2014. Germany,

Spain and India are at the number 3 rd, 4thand 5thspot having total installed capacity of 40,468

MW, 22,986.5 MW and 22,465 MW respectively by the end of year 2014 [3].

In Europe, total wind energy capacity has grown from 119 GW in 2013 to 132 GW in 2014 [3].

Germany is leading in Europe having total install capacity of 40,468 MW followed by Spain, UK,

France and Italy with installed capacity of 22,986 MW, 12,440 MW, 9,296 MW and 8,662 MW

respectively [3]. In Asia, china is at the top of wind installed capacity followed by India, Turkey

(most wind form is on its Asian part), Japan and South Korea having wind installed capacities of

22,465 MW, 3,763 MW, 2,788 MW and 609 MW respectively [3]. In Pakistan, work is in progress

on different projects regarding wind energy and currently has total wind installed capacity of 256

MW by the end of 2014, with the addition of 156 MW in the subsequent year [3]. Pakistan is at

the 43thnumber in the list of world wind installed capacity [3].

Wind energy has been recognized as a one of the significant and latent source of energy for

Pakistan. The country has a total estimated gross wind power capacity of around 346,000 MW [4].

Currently, the total installed power generation capacity (containing hydel, thermal and nuclear


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sources) of Pakistan is 22,800 MW while the actual power generation is around 9,000 MW due to

many aspects [4]. The demand varies between 16,500 MW (in summer) to 10,000 MW (in winter)

[4]. Hence this shortfall of electricity can easily be encountered by the installation of more wind

power projects.

Table 1.1, reveals that Pakistan has over 9% of total land which is appropriate for utmost utility-

scale wind turbine application [4]. The total wind generation capacity of this area is above 349,000

MW [4]. This is worthwhile to mention here that about 3.5% of the area has a wind potential of

class 4 or greater and has a potential of 132,990 MW, which is the prerequisite of price effective

wind power generation [4]. So, the demand of the country can easily be encountered by installing

more wind energy projects.

Table 1.1: Wind resources assessment of Pakistan [4]

Pakistan Meteorological department (PMD) with the collaboration of National Renewable energy

laboratory (NREL) and U.S Agency for international development (USAID) has developed a

mesoscale map of Pakistan as shown in Fig. 1.2.This map shows that there is an immense wind

potential available in areas of southern Sind, north Balochistan, central KPK, Gilgit-Baltistan and

different areas of Punjab and Azad Kashmir.

Furthermore, PMD conducted a survey (Phase-I) alongside the coastal belt of Sind province having

total area of 9300 sq. km and pointed out that this area has exploitable electric potential of about

11,000 MW [5]. The wind corridor of Gharo-katibandar, spreading 60 km along the coastal of

Sind, alone has a wind potential of 60,000 MW [6]. Now, in Phase-II, survey is being done on the

northern area of Pakistan.


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Figure 1.2: Wind map of Pakistan showing wind potential of all provinces [5]

Keeping in the view of highlighted most wind potential regions in Pakistan, this article is hereby

purposed to deep spot the site of Turbat, Balochistan as having good wind power potential and

energy density. Data was collected from Pakistan meteorological department (PMD), analyzed and

results were then statistically equated using Weibull and Rayleigh distribution functions,

accordingly. In order to get precise results, monthly and yearly analysis was done on the data.

Most probable wind speed and maximum carrying energy by wind are also calculated here, which

are required for the design of wind turbine blade profile for a particular site. Both, Weibull and

Rayleigh functions were then evaluated with the help of performance tests, to determine which

distribution function better described the actual data. After selecting the suitable distribution, the

Wind power density and energy density has been calculated. And based upon these results, it is

decided that in which class this site falls in wind power classification table. The error which

occurred during the calculation of wind power density has also been calculated here.


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Chapter # 2

LITERATURE REVIEW

Many researchers have calculated the wind power potential at different sites of the World. In

Pakistan alongside PMD, many scholars calculated the wind power potential at different locations

of the country. Wind power density has been calculated at the place of Hawksbay Karachi, Gharo,

Kati-Bandar, Jiwani, Quetta, Babaurband and Jhimpir (mostly beside the coastal belt of Pakistan).

In [1]the wind power potential is calculated at Hawksbay Karachi Sind, Pakistan. 2 years (2009-

10) data was taken and power densities were calculated using Weibull and Rayleigh distributions.

Mean wind speed and power density on yearly basis at the site was found to be 5.9 m/s and 197

W/m2 at the height of 80m. The site was found appropriate for wind energy projects. In [2]the

wind power density is calculated at the site, located in Gharo Sind, Pakistan. Five years data was

taken (2003-07), measured at 30 m height and investigated with the help of Weibull and Rayleigh

function. The average wind speed at the site was above 5 m/s. The wind power and energy density

of the site are 260 W/m2 and 2300 kWh/m2 respectively [2]. These power generations then

evaluated through the wind turbine of dissimilar manufacturers and found that this site has suitable

wind power potential and appropriate for wind generation projects [2]. In [4] the wind power

potential of three provinces of the country was analyzed and Jiwani (a site of Balochistan) was

taken as a case study and its specific power density was assessed. At the end, a practical scheme

is proposed for the integration of wind power output of the turbine to the national grid.

Kharo SF et al. [7]investigated the power density of wind for the site Babaurband Sind, Pakistan

at 4 different altitudes and then assessed the wind power likely to be generated over commercial

wind turbines. At 80m height, the yearly-mean wind speed was found to be 6.712 m/s while wind

power density was 310 W/m2. The values of power densities were higher from April to August.

To illustrate the feasibility of wind turbine installed, economic analysis was done and cost per

kWh was found to be 0.0263 US$/kWh. The site was found to be suitable for wind energy projects.

Calculation of wind power potential outside the Pakistan includes; S.H. Pishgar-Komleh et al. [8]

computed power potential of the wind using Weibull and Rayleigh functions at the site of

Firouzkooh region of Iran. 10 years (2001-10) data, based upon 3-h period, was taken and

analyzed. The average value of wind power was found to be 203 and 248 Wm-2 year-1based upon


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average and root-mean cube speed methodologies [8]. The site was found suitable for wind turbine

installation, because it falls in class 4 of wind power classification. Results shows that Weibull and

Rayleigh models close-fitting the actual data well with R2value of 0.97. E.K Akpinar et al. [9]

calculated power potential of wind at Keban-Elazig, a site in the Turkey. 5 years (1998-2002) data

was taken and analysed through the Weibull and Rayleigh distribution functions. Weibull

distribution better describe the observed wind data than the Rayleigh distribution at the nominated

site. The yearly value of average power density was found to be 15.603 W/m2, so this is not a

suitable site for grid connection usage. This power density of this rank can be utilized for non-grid

application like battery charging and water pumping [9]. L. Fyrippis et al. [10]inspected the wind

power prospective of Koronos village, a location present in the Naxos Island, Greece. Wind

characteristics were statistically analysed with the help of Weibull and Rayleigh distribution

functions. It was exposed that the Weibull distribution tailored the actual data finer than the

Rayleigh. The yearly values of mean wind speed and power density at the designated site was 7.4

m/s and 420 W/m2respectively,so this site comes underneath Class 7 of the wind classification

i.e. this is an excellent site for wind energy projects. B. Safari, J. Gasore [11] statistically

investigated the wind power potential with the help of Weibull and Rayleigh models in Rwanda at

five different stations. 20 years (1974-93) data was taken from the meteorological station of

Rwanda. At the selected site, Weibull probability density function was found to be more suited for

the empirical distribution of the data.

In South Africa, Ayodele TR et al. [12]examined physical characteristics and power potential of

the wind in the coastal region at ten different sites. 1 year data was taken based on the 10-min

average wind speed at 20m and 60m height. Performance tests like Correlation coefficient and

RMSE test were applied firstly to check that which distribution can better describe the data at the

site. The daily variation, wind speed characteristics, peak periods of electricity and the turbulence

intensity were found at the selected site. Besides these, Optimum and most probable wind speed

and shear exponential were also calculated here. Data was analyzed using Weibull distribution

because of its better fitting than the Rayleigh and lognormal distribution and results showed that

Napier site has excellent wind potential while Calvinia site has low wind potential having values

of 694 W/m2 and 216.29 W/m2respectively.


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Likewise, many scholars have also calculated the characteristics and power potential of the wind

at different places of many countries of the world similar to, determination of wind energy potential

in Bishkek, Kyrgyzstan presented in [13], statistical analysis was done using Weibull and Rayleigh

models to determine the wind power density at the site of Malaysia in [14], Wind speed

characteristics and power potential of wind was determined in Akure, South west Nigeria and

presented in [15], Characteristics and power potential of wind was examined in Osmaniye, Turkey

[16].


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Chapter # 3

BASIC THEORY IN WIND ENERGY

3.1 Introduction of Wind energy

The movement of atmospheric air, sensed as wind by us, touches every single corner of the earth

in this planet. There might be some places that never experienced any rain but nobody ever

envisioned a place where wind lost. The movement of air is just because of the solar heating of the

earth and winds carrying a portion of energy in solar radiation, which is firstly absorbed by earth

and then transferred in various forms back to the atmosphere. As, the surface of the earth is not

similar because of the presence of the land, seas, desert and forest; therefore, the portion of energy

that is fascinated varies both in space and time. This generates, difference in atmospheric

temperature, pressure and density, which in sequence produces forces that transport air from one

place to other. As water and land absorbs radiations in a different way just like valley and

mountains do, this difference causes the air to move.

Throughout the year, as compare to Polar Regions, tropical sections of the earth receive additional

solar energy to radiate the earth. Because, neither tropic regions always remain warm from year

to year nor do the poles get cold, there is an altercation of thermal energy through latitudes where

wind serve as the medium of convection. Likewise: uneven heating, earths rotation also plays an

important part in the movement of air. Rotation of earth generates Coriolis forces which move the

air particles toward the Northern and Southern hemisphere. So, localized wind systems get

established over the, mountains, valleys, deserts and seas.

However, unlike sunshine (i.e. comparatively uniform in a particular region over a specified period

of time) winds are inconsistent, changing in space and time, varying from one place to other,

gusting in fluctuating strengths over different period of time and commencing seconds to years.

Winds transmit the kinetic energy of the atmosphere, which is convertible into electricity with the

help of wind turbines and conveyed through wires in desired areas far-off from the point of

generation. Wind generation capacity can be harnessed on the large scale and after connecting it

with national grid, it can contribute to encounter the load and energy necessities of the country.


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3.2 Brief history of Wind energy

The usage of wind energy can be sketched back to ancient civilization, thousands of years ago. It

had been exposed from ancient human antiquities that wind energy was discovered and used at

different sites of the earth. Before the invention of steam engine, wind was the only source ofpower for ships at that time. These wind mills were introduced to the western world in 1100 AD.

By the start of 13th century these windmills extensively used in the Europe. Near the

commencement of 14thcentury, Dutch had become leading in the designing of windmills.

Wind energy had been in usage ever since the earlier civilization for the grinding of grains,

pumping water from well and to command the sail boats. Before the industrialization of Europe,

wind mill were used for different purposes like irrigation, pumping of drainage and processing of

other merchandises like Spices, paints and tobacco etc. There were many types of the wind mill

operational by the middle if the century in Holland. These wind mills had a rotating shaft

accommodated at the mainpost. Wind mills got severe competition and hurried to decline after the

invention and advancement in the steam engine and the growth of the electricity distribution

systems in the 19thcentury.

The motivation behind the development of wind energy was due to increased prices of oil and

apprehension over restricted fossil fuel resources during the oil embargo of 1973. The trend of

declining of fuel prices abruptly reversed and many countries started thinking to utilize the

renewable energy sources like wind, solar, biomass and wave, because these sources have very

low CO2 emission throughout their life cycle and have a potential to limit the abrupt climate

change.

3.3 Wind Resource Assessment

Equatorial regions of earth collect more solar heat than Polar Regions, which origins huge scale

convection current in the stratosphere and as a result wind generates. It has been estimated by

meteorologists that about 1% of the arriving solar energy at earth is rehabilitated into wind energy.

Solar energy which reaches earth in ten day has more energy contents than the worlds entire fossil

fuels assets (including Coal, oil and gas), hence wind resource is extremely larger than we expect.

1% of daily incoming energy is equal to the daily consumption of the present world. It is inspiring


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that the global wind reserve is very large and is widely distributed. As the development is made,

technically and frugally, wind energy can serve as a remedy to the world energy crisis.

Even though wind resource approximations have significance, more detailed calculations are

required to enumerate the resources in a specific area. Winds are sporadic source of energy but

they characterize a reliable energy source year by year. Now days, large number of studies

regarding grid systems incorporation reveals that the irregularity of wind energy is no more barrier

for its large scale use. Further, most of the wind turbines are being use for the generation of

electricity in the worldwide either parallel to grid systems or in remote locations. The purpose of

installing wind turbine is to diminish the fossil fuel consumption and to reduce the total electricity

generation price.

First step in the assessment of wind resource is to identify the preliminary area. In this way

relatively large region is separated for appropriate wind resource area grounded on the statistics

like airport data of wind, topography, highlighted trees and supplementary facts.

Second step is to evaluate the wind resource and this relates to wind assessment plans to illustrate

the wind potential in a distinct area where wind power improvement is being deliberated. The

utmost common objectives of this extent of measurement are to:

Enumerate, whether adequate wind resource occurs inside the area to rationalize extra site

precise inquiries;

Relate areas to discriminate comparative progress prospective. Wind resources are

characterized by wind power classes and each class symbolizes a range of yearly average

wind power densities and corresponding mean wind speed;

Achieve demonstrative data for approximating the performance and the financial

sustainability of particular wind turbine;

Display of potential wind turbine scheduling locations by matrix investigation of wind, site

and wind turbine.

Third stage is regarding micrositing at the minimum scale of wind resource evaluation. The chief

objective of these three stages is to compute the small size inconsistency of the wind resource

above the territory of curiosity. Eventually, micro siting is being used to position one or additional

wind turbines on a portion of land to exploit the total energy yield of the wind plant.


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3.4 Extrapolation of wind speed at different height

Wind speed changes with the change of height, so there is need of an equation which can predict

the wind speed at one height to other height; because, it is not necessary that wind speed data is

always measured from wind turbine hub height. To adjust the data with the required wind turbine

hub height, we use power law method as shown in equation [17];

=

(1)

Where V represents the wind speed at a required height; Z represents the wind speed at

reference height; Zr and is the surface roughness factor varies from 0.128 to 0.160 for a

homogenous surface [18]. The typical value of surface roughness factor is 0.14 which is widely

accepted for low roughness surfaces and well unprotected sites [12].

3.5 Presentation of Data

Statistical procedures and investigation are predominantly concerned with the collection,

organization and explanation of arithmetical data which form the sample or subset.

3.5.1 Data collection

There are two types of data available in statistics as hereunder:

1. Original data is called primary data; because, it has not gone through any kind of statistical

treatment;

2. The data which has gone through any kind of statistical treatment like tabularized,

categorized or presented in some other form at least once is called secondary data.

3.5.2 Organization of Data

There are three methods which are mostly used in the statistics to organize the data which are [35]:

1. Classification;

2. Tabulation;

3. Graphical representation.


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In order to transport the data in appropriate and easy form, primary data is summarized and

grouped together into classes, this process is called classification. Two ends of the class are called

the class interval. Class boundaries are achieved by the accumulation of the upper limit of one

class interval and the lower limit of next upper class and divided by two.

3.5.3 Tabulation of data

An organized arrangement of data for statistical information characterized in rows and columns is

called the tabular form of the data. These table are further classified into two types such as

(1) General purpose, constructed for reference

(2) Particular purpose used to analyze or support in investigating data

3.5.4 Graphical representation

This is a pictorial representation of data between different variables likewise the graph between

mean wind speed and variance of the observed data. There may be different kinds of graphs

dependent upon the nature of the data used and the purpose of the graph. Similarly, in frequency

distribution, a graphical demonstration of frequency gives brief and clear information.

3.6 Measure of central tendency of the data

Central tendency measure and predicts the central region of data. Central tendency of the data can

be enumerated with the following methods;

3.6.1 Mean

The mean or average value of the wind speed data can be calculated by adding all the values of

velocities and then dividing the total number of sample values

Vavg= +2+3++ (2)Vavg=

Vini= (3)

Here, n represents the total observing wind speed data available.


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3.6.2 Median

The median of the set of data values, is the value which inhabits the middle position when data has

been organized into ascending or descending order. If, in any case two middle values are accessible

then median will be the average of these two.

Med = [V(n+1) /2] when n is odd (4)

Med = [V n/2, V (n+2) / 2] whenn is even (5)

Here, n is againrepresents the total number of observing wind speed data.

3.6.3 Mode

The mode of the data is the value which occur the most number of time. Mode is not essentially a

single value and actually may not present some time. In case of frequency distribution, the valuewhich is maximum is called the mode of the distribution. If the frequency curve has one peak it

has one mode while, curve having two maxima, have two modes.

3.7 Measure of Dispersion

The measure of central tendency of any data just describe the central point of the data but in order

to calculate; how positions are spacious or scattered on both side of the centre; we use measure of

dispersion of the data. Following methods are used to measure the dispersion:

3.7.1 Range

The simplest method to measure the dispersion of the data is to calculate the range, which is a

difference between the lowermost and uppermost values in the distribution. Range is easy to

calculate and to measure the dispersion but it does not give the measurement of dispersion

comparative to centre value.

3.7.2 Mean deviation

The mean deviation basically calculate the ranges of the magnitude of the deviance from central

value like from mean, median and mode. The formula to calculate the mean deviation is as

Md = = (6)

Mean deviation is premeditated from arithmetic mean.


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3.7.3 Standard deviation

In order to get more information about the results of data set, the scattering or inconsistency of

the data can be examined with the help of Variance or standard deviation. The formula to

calculate the variance of the data set is;

2=

2= (7)The division with n-1 is referred to as the number of degrees of freedom. If, we just take the

positive square root of the variance we will get the standard deviation of the data, so the formula

to calculate the standard deviation of the data becomes

Standard deviation = = 2So equation (8) in case of standard deviation becomes

= 2= /2

(8)

Now, the coefficient of variation can also be defined as

Coefficient of variation = COV =

100So, COV can also be written as

COV = 100 (9)Coefficient of variation gives the amount of deviation present in the hourly time sequence data or

the amount of turbulence present in the wind data. It has no unit because standard deviation and

mean of data both have same dimensions of variable used.

3.8 Wind data parameter estimation

Besides, calculating the average wind speed and standard deviation of the data, the other two

parameters, which are also very important for the design of wind turbine are most probable wind

speed and wind speed carrying maximum energy. Here most probable wind speed Vmpcorrespond

to the peak of the probability density function, whereas the wind speed carrying maximum energy

(represented as Vmax.E ) is used to estimate the design of wind turbine or rated wind speed [2].

These wind speeds can be calculated as [17, 19];


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Vmp= c /

(10)

Vmax.E = c +2 /

(11)

For the design of wind turbine, it is proposed that rated wind speed must be very much near to thewind speed transporting maximum energy because wind speed has maximum efficiency at rated

wind speed [20].


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Chapter # 4

DATA COLLECTION AND ANALYSIS

4.1 Site description and data collection

Pakistan has immense wind power potential available in different regions of the country but most

of the sites which have studies yet lies along the coastal belt of the Sind and Balochistan. Besides

the coastal belt, very few areas have been studied to assess the wind potential of the site. Turbat is

one of those sites which despite having the wind energy capacity has not yet harnessed for wind

potential. So, keeping in view of the above, a site of Turbat is selected to determine the wind

potential of the site and to determine, either this site is feasible for wind energy projects or not.

Turbat is a city situated in southern Balochistan, which is a largest province (Area-wise) of

Pakistan. Turbat is positioned on the left bank of Kech River and has total population of around

about 90,000. The climate of Turbat is relatively cool and windy. Turbat metrology station is

located at 250 59 N latitude and 630 04 E longitude at a height of 155m (508feet) above sea level.

The site has high population and many limitations (like hilly areas) to supply energy, therefore

searching for other alternatives renewable energy sources like wind or solar is essential for the

survival of mankind. Now a days, due to the more concern of world towards the global warming

and green-house effect of the gases by the exhausts of power plants, alternate energy should be

clean, environmental friendly and renewable in nature.

The selected site is suitable for the installation of wind projects because:

Surface is not smooth due to the presence of the hilly areas so, water or thermal projects

are not suitable at the site while wind energy projects can be utilized for small scale

purposes i.e. for single house only.

Unavailability of infrastructure for water or thermal power houses.

Site is situated 155 m above the ground level and as height increases, capacity of power

generation also increases from wind turbine.

Site has good observed wind speed.


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Figure 4.1: Location of Turbat in Balochistan, Pakistan

The data was taken from Pakistan Meteorological department (PMD) Karachi centre (CPDC

Karachi), consisting of 21 months (Jan 2012 - Sep 13) and is based upon the 3-hourly time series

data measured using anemometer at a height of 8.8 m above the ground level. Figure. 4.1.Shows

the location of Turbat and nearby regions of the selected site in Baluchistan.

So as to estimate the wind potential of a specific site, it is very imperative to determine the

following characteristics such as mean wind speed, the availability of wind speed for particular

time period, persistency of wind gusting, the most probable wind speed, the wind carrying

maximum energy and wind power potential of the site [2]. The estimation of wind power density

describes the amount of energy available for each unit of time and swept area of the blade is

accessible at the nominated site for transformation of electricity with the help of a wind turbine.

4.2 Statistical analysis of the data

The most important and critical aspect in the assessment of wind resources is the dispersal of wind

speed. Wind speed data has wide ranges of wind and in order to determine the key parameters

from the data, we have to apply some statistical analysis on the data. In statistical analysis, we

apply statistical distributions functions.


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Wind speed is measure in the form of the integer and each value is observed many times during

the month or year. As in previous section, it has been explained in detail that average value of the

data set can be calculated with the help of equation (2)or (3). Besides measuring the mean value

of data, we are also fascinated in the unpredictability of the set of numbers and we want to find the

abnormality present in each number with respect to the mean value and then locate the average of

these abnormalities.

In order to develop the frequency curves, we use continuous mathematical functions; which are

convenient to use instead of using the discrete values. So, the probability values p (Vi) become a

density function which is f (V) and is called as Probability density function (PDF). If velocity V

of the wind is a continuous random variable having range (0,) then it must satisfyf (V) 0 , 0 < V < 1 (12)

An additional useful probability measure of the data is Cumulative density function (CDF). In case

of continuous function, let F (V) represents the cumulative density function for the variable V,

which is a continuous variable having range

0 < V < The CDF can be defined as:

F (V) = (13)Here, speed is considered as per continuous random variable and so F (V) has the properties of

CDF are:

F (0) = 0 (14)

F (= 1 (15)It is not necessarily that the value of F (0) will be zero in the case of discrete random variablebecause there are cool spells with generally zero wind speed measure and included in F (0).

However, in the case of continuous random variable F (0) is the integral with the sign of integration

limits.


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4.3 Frequency distribution Table

The number of occurrence of an event in each class is entitled the frequency of the class. If we

convert this frequency in tabular form, then this frequency is called the frequency table.

In order to describe and analyze the population and climatological data, the important and

compulsory step is to draw the frequency distribution of the data. This is done by approximating

the features of the population frequency distribution of the sample.

Frequency distribution are of two types:

1.

Discrete distribution

2. Continuous distribution

Discrete distribution has a function of discrete random variable i.e. one that varies in stage, for

probability distribution.

While Continuous distribution has a function of continuous random variable i.e. temperature,

pressure, wind speediness, for probability density.

Frequently, for our convenience, a discrete random variable might be treated as continuous random

variable while for some special purposes continuous random variable can be transformed to

discrete random variable. More consideration is now giving to better fit the frequency distributions

to climatological data.

4.4 Statistical Distributions

There are many distributions which can be utilize to describe and analyze the wind data such as:

Weibull distribution

Rayleigh distribution

Chi-square distribution

Normal distribution

Log-normal distribution

Gamma distribution

Among all these distributions, we will discuss here some continuous frequency distributions only,

which are associated to our work. The selected distributions are Weibull, Rayleigh, normal and


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Weibull distribution is most important, common and well acknowledged distribution for the

calculation of wind power and energy all over the world because of its adaptability. This is the

only distribution which cannot be derived from any further distribution like other continuous

distributions. By keeping the shape parameter (k) of Weibull distribution as k = 3.6, k = 2, k = 1,

Weibull distribution changes into normal, Rayleigh and exponential distribution respectively. So,

the Weibull distribution is only the essential and unique continuous distribution from others.

Various statistical models are being used to describe and analyze the wind data in which some are

normal, lognormal, Weibull and Rayleigh distributions functions [21, 22]. Among all these

distributions functions, Weibull and Rayleigh distributions functions are generally applied and

accepted worldwide because both these distributions provide finer approximations to observed

wind speed data [13].

4.4.1 Weibull distribution

The Weibull distribution (entitled afterward the Swedish physicist Weibull, who practical it while

reviewing material in stiffness and fatigue in the 1930s) provides a close estimate to the probability

laws of several natural occurrences. Previously, it has been used to characterize the wind speed

distribution for application in wind capacity studies. In existing years most attention has been

concentrated on this method for wind energy solicitation not only due to its greater tractability and

easiness but also because it can provide a good fitting to investigational data.

The two parameter Weibull distribution function is most suitable, widely recognized and

recommended by many researches for analyzing the wind speed data [23, 24, 25]. The variation in

wind speed is categorized by probability density function and Cumulative density function in

Weibull distribution [2]. Probability density function (PDF) describes the probability of wind at a

specified velocity of wind i.e. what is the probability of wind speed having magnitude 3 m/s, can

be describe by the Probability density function while the cumulative distribution function (CDF)

of wind velocity V gives the probability of wind velocity equal to, lower than or inside the specifiedrange of the wind speed i.e. what is probability of wind blowing between 1 m/s and 3 m/s, is

describe by cumulative density function. The Probability density function (PDF) in case of Weibull

distribution is described and calculated as [2];

f (V) =

exp [ ] (18)


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Here V represents the wind speed, K is shape parameter for weibull having no unit, C denotes the

Weibull scale parameter possessing similar unit as wind speed and f (V) indicates probability

density function of perceiving wind speed.

The corresponding cumulative density function (CDF) is described as [2];

F (V) = 1- exp [ ] (19)

Here F (V) represents the cumulative density function for wind speed (V) .

4.4.1.1 Estimation of Weibull shape and Scale parameter

There are numerous methods which are being used to compute the Weibull shape and scale

parameters like:

Maximum likelihood method;

Empirical method;

Modified maximum likelihood method;

Energy pattern factor method.

There is a lot of search going on to determine that which method can better describe the value of

Weibull shape and scale parameters. The value of shape and scale parameters mostly depend upon

the sites specification, duration of the data and the dispersion of the data. Here in this study theseparameters are calculated using Empirical method.

In empirical method, these parameters are calculated with the help of average wind speed and

variance or standard deviation. These parameters are calculated here using equations (3)& (7).

The formulas for the calculation of k and c are [2];

k = .86

(20)

c = +( ) (21)

Here ( ) is the Gamma function and describes as [26, 27];

( ) = dt (22)


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Similarly, scale parameter for weibull distribution can also be evaluated by using the equation

[28];

c =.7

.84 +.86 .7 23)Using the weibull shape parameter (k) and scale parameter (c), mean wind speed of the data can

be determine or verified as

Vm= c 1 (24)

Here Vmdenotes the mean wind speed and k is a shape while c is a scale parameter.

4.4.1.2 Behavior of calm wind speed

Weibull distribution better describe the data when wind speed is more than 1 knot or 0.5 m/s. It

has been experimentally proved that Weibull distribution does not give better fit for wind speed

having magnitude less than 0.5 m/s, so in order to apply Weibull distribution to data, wind speed

data must be greater than zero.

So, observation of calm cannot be involved in the computation of F (V) while applying Weibull

distribution to any observed data of wind speed. To include the consequence of zero wind speed,

values like Vavgand

Vavg3are to be multiplied with the factor of (1-f) where f characterizes that

portion of time when zero wind speed has been logged.

4.4.2 Rayleigh distribution

Besides having many advantages, Weibull distribution also has certain constraints too. The most

vital restrain in the application of weibull distribution is that it cannot describe the probability of

very small or zero wind speed [29]. For this purpose, additional distribution for example Rayleigh

is used and verified here, which is being extensively used by the researchers to determine power

potential of the wind at the particular site. In this research work, two specified distributions arebeing used and results of both are compared, so that we could find out which distribution is better

to predict the wind speed data.


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In Rayleigh distribution function, we assumed that the shape parameter (k) has fixed value such as

K = 2 [19, 30], so in this distribution, expressions to calculate the probability density function

(PDF) and cumulative density function (CDF) are [2];

f (V) = 2 exp 4 2 (25)

F (V) = 1 - exp 4 2 (26)

Here the shape parameter is taken to be 2 while scale parameter can be calculated by equations

(21)or (23).

4.4.2.1 Facts of Rayleigh distribution

It is very hard to make comprehensive generalization concerning the capability of Rayleigh

distribution function to fit the data, although curves display very good amplitude and extended

width for higher wind speeds. The effectiveness of this distribution is to predict the power output

of the site. Both distribution may yield acceptable results but the results of Weibull distribution

are more accurate while Rayleigh distribution is easier to use. When the mean wind speed is larger,

graphs of data give flatter shape while peak becomes sharp when average speed of wind is less

than 2.0 m/s.

4.5 Evaluation of Weibull and Rayleigh distributions

So as to compute the accuracy of the Weibull and Rayleigh models, the root mean square error

(RMSE) test, the Chi-square (2) test then the correlation coefficient or coefficient of

determination (R2) can be used [12].

These parameters can be premeditated as follow [12];

RMSE = 2= /2

27)

2 = 28)R2 =

29)


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4.10 Cut out Velocity

The speed of the wind at which wind turbine shuts dow to avaoid destruction due to high intensity

of wind is called cut out velocity. The range of this high velocity might be 20.0 m/s to 28.0 m/s.

This is also called as furling velocity.

4.11 Wind power density calculation

The power density of wind is an estimator that displays the ability of the site regarding resources

of wind. Wind has immense power that flows by speed Vthrough a swept area of wind turbine

Aincreases as a cube of its velocity and can be described as [31];

Power =2 2

Power = 2 (AV) 2So we have

P (V) =23 (31)

PD=P

=23 (32)

Here P (V) denotes power the wind in (W) and P (V) / A denotes the wind density for each swept

area A (Wm-2) and expressesdensity of the air in (kg/m3) at this particular site.

So, equation (31) reveals that in order to get a maximum power from wind, it requires:

Higher wind speed as power output from wind turbine is directly proportional to cubic

power of mean wind speed so, a small deviation in wind speed can consequence in a huge

alteration in the wind power output.

Longer length of blades in order to attain a large swept area of blades of the wind turbine

Higher value of air density

4.11.1 Swept area of Blade

Swept area of the as shown in Fig. 4.2.The swept area of the wind turbine blade can be calculated

by this equation:

A = 2 2= l (l+ 2r) (33)


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First of all, monthly analysis was done and all the values of parameters were calculated like

Average wind speed, Variance of the data, most feasible wind speed, wind speed bearing

maximum energy, Weibull shape and scale parameters. After calculating these parameters,

frequency distribution table was drawn. In frequency distribution table comparison between the

actual, Weibull and Rayleigh probabilities is made. Then after selecting the suitable distribution

to better fit the data, Wind power potential and wind energy density has been calculated.

Similarly, analysis was done on the 1 yearly basis and all these parameters again calculated and

then again analysis was done 2-years basis and all these parameters are again calculated.

At the end, comparison has been made between the values calculated monthly, 1 yearly and 2

yearly basis.


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Chapter # 5

RESULTS & DISCUSSIONS

In this research work, analysis and assessment of both; wind speed data and power potential of

wind is executed. Wind speed characteristics such as mean, availability of wind, wind duration

and standard deviations are determined to compute the power potential and energy density of the

wind at the selected site.

5.1 Measurement of average wind speed

InFig. 5.1.The monthly mean wind speeds (Vavg) have been calculated at the site of Turbat for

the year 2012 and 2013. It could be seen that the average value of wind speed is more than 4 m/s

in each month. The average wind speed remains high from the start of the year to the mid of the

year i.e. January to June and then its value decreases. The range of average wind speeds is between

4.065 ms-1and 6.422 ms-1. The maximum monthly mean wind speeds are 6.422 ms -1and 5.610

ms-1for the months of Feb 2012 and Mar 2012, respectively. Similarly, minimum speeds are 4.065

ms-1and 4.180 ms-1for the months of Oct 2012 and Sep 2013, respectively.

Figure 5.1: Average wind speed per month for year 2012-13

0

1

2

3

4

5

6

7

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

AverageWindspeed(m/s)

Months

Year 2012 Year 2013


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From Fig. 5.1.It could be seen that the average wind speed has higher values for the months of

June, July and August, which are among the warmer months. The energy demand in these months

also increases due to hot weather in Pakistan. In contrast, average wind speed has lowest values

for the months of October, November and December, which are among the coldest months.

5.2 Measurement of standard deviation

The monthly variation in the values of standard deviation has been shown in Fig. 5.2

Figure 5.2: Monthly values of standard deviation

The value of standard deviation for 2012 is maximum for the month of Feb 2012 having value of

3.306 while minimum value is 1.683 for the month of Aug 2012. Similarly, the maximum and

minimum values of standard deviation for the year 2013 are 3.152 and 2.146 for the months of

July 2013 and Feb 2013 respectively. The range of standard deviation is 1.607 having overall

minimum and maximum values as 1.699 and 3.306 for the months of January 2012 and February

2012 respectively.

For better results, analysis was done on month basis and then average value of all the months was

taken. Hence the overall average value of Mean velocity is Vavg = 4.83 ms-1and standard deviation

is = 2.54.

0

0.5

1

1.5

2

2.5

3

3.5


Stan.Deviation()

Months

Year 2012 Year 2013


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5.3 Monthly values of Vmpand Vmax.E

Beside average wind speed and standard deviation, the other two crucial considerations for the

evaluation of wind power potential are maximum feasible wind speed (Vmp) and wind speed

bearing maximum energy (Vmax.E), bothare correspondingly calculated here. Inside Table. 5.1.

Monthly values of both these velocities are shown. It can be seen that the maximum values of Vmp

for year 2012 are 5.244 m/s and 4.916 m/s for the months of February and July respectively

whereas the minimum value is 3.220 m/s for the month of Nov 2012. Similarly, for the year 2013,

the maximum values of Vmp are 4.002 m/s and 3.974 m/s for the months of June and March

respectively while the minimum value is 2.481 m/s for the month of Aug 2013.

The maximum values of Vmax.E for the year 2012 are 10.086 m/s and 9.009 m/s for the months of

February and March respectively; while, the minimum value is 5.842 m/s for the month of Aug

2012. Similarly, for the year 2013, the maximum values of Vmax.E are 8.928 m/s and 8.759 m/s for

the months of August and June respectively while the minimum value is 6.588 m/s for the month

of Feb 2013.

Table 5.1: Monthly values of Vmpand Vmax.E for the year 2012-13

Month 2012 2013

Vmp Vmax.E Vmp Vmax.E

January 4.588 6.214 2.876 7.702February 5.244 10.086 3.505 6.588

March 4.434 9.009 3.974 7.412

April 4.332 8.015 3.464 6.772

May 4.711 7.612 3.592 7.694

June 4.603 8.666 4.002 8.759

July 4.916 7.959 3.218 8.061

August 4.051 5.842 2.481 8.928

September 4.194 7.055 2.659 7.561

October 3.499 6.138 - -

November 3.220 7.682 - -

December 3.245 7.842 - -

Yearly 4.253 3.265 7.677 7.807


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The average value of all the months for Vmpand Vmax.E are 3.83 m/s and 7.732 m/s respectively.

5.4 Coefficient of Variation

Coefficient of determination is a measure of the dispersion of data in any probability distribution.

It describes the amount of variation or the turbulence present in the hourly time series data. In Fig.

5.3. The monthly values of coefficient of variation has been shown. COV is calculated with the

help of Equation (9). The graph of COV shows that starting six months of the year have lower

values of COV which shows that there is less amount of turbulence or dispersion is available, so

these months are most suitable than the last six months for the wind energy application. COV is

some time expressed as a percentage value.

Figure 5.3: Monthly values of Coefficient of Variation for year 2012-13

5.5 Weibull parameters estimations

Two parameters of Weibull distribution i.e. k and c are calculated here using equation (20)and

(21)respectively. Values of Weibull shape and scale parameters for each month are presented in

Table. 5.2., for the year 2012 and 2013. As it could be seen that Weibull shape parameter has

maximum value of 3.010 for the month of Jan 2012 and minimum value of 1.784 for the month of

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80


CoefficientofVariation(COV)

Months

Year 2012 Year 2013


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Dec 2012. Similarly for year 2013, the maximum value of k is 2.105 for the month of Mar 2013

while has minimum value of 1.508 for the month of Jul 2013.

Table 5.2: Monthly values for Shape and Scale parameters of Weibull distribution

Month Parameter 2012 2013January k

c3.0105.247

1.6954.865

February kc

2.0577.249

2.0934.782

March KC

1.9786.329

2.1055.397

April kc

2.1195.856

2.0324.834

May kc

2.3935.906

1.9125.291

June kc

2.0906.285

1.8875.972

July kc

2.3886.169

1.5085.102

August kc

2.7384.782

1.7515.218

September kc

2.3005.375

1.6504.674

October kc

2.2144.590

--

November kc

1.7965.064

--

December kc

1.7845.145

--

Yearly kc

2.4965.666

1.8195.137

The monthly deviation in the values of Shape parameter has been shown in Fig. 5.4.

The scale parameter for the year 2012 has topmost value of 7.249 m/s for the month of Feb 2012

and has minimum value of 4.590 m/s for the month of Oct 2012.


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Figure 5.4: Monthly values of shape parameter for year 2012-13

Similarly for the year 2013, the topmost value of scale parameter is 5.291 m/s and minimum value

is 4.674 m/s for the month of Sep 2013. The value of scale parameter varies from 4.674 m/s to

7.249 m/s and has a range of 2.575.

In Fig. 5.5monthly variation of scale parameter has been represented.

Figure 5.5: Monthly variation in the values of scale parameter for year 2012-13

0

0.5

1

1.5

2

2.5

3

3.5


Shapeparamete

r(k)

Months

Year 2012 Year 2013

0

1

2

3

4

5

6

7

8


S

caleparameter(c)

Months

Year 2012 Year 2013


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These parameters control the sketch of curve formed by Weibull and Rayleigh distributions.Shape

parameter defines the range and determine the shape of plot while Weibull scale parameter

determines the profile of the distribution just as a transformation of the Abscissa scale.

The value of shape factor c shows the probability of wind speed flowing, so greater value of cindicates the higher value for the possibility of wind speed. In contrast, the maximum value of k

displays the greater possibility for frequent and uniform wind blowing across the side.

5.6 Frequency distribution table

In order to derive best results using statistical analysis, it is better to arrange the actual time series

data in the form of frequency distribution. For year 2012, time series data has been organized in

the form of frequency distribution and given here in Table. 5.3.

Table 5.3: Distribution of frequencies calculated from wind speed data for year 2012

i Bins Vavg fi Actual Weibull Rayleigh

1 0-1 0.5 0 0.000 0.000 0.000

2 1-2 1.5 70 0.033 0.106 0.109

3 2-3 2.5 285 0.135 0.140 0.1404 3-4 3.5 369 0.175 0.154 0.151

5 4-5 4.5 256 0.122 0.147 0.143

6 5-6 5.5 425 0.204 0.126 0.122

7 6-7 6.5 213 0.101 0.098 0.0958 7-8 7.5 163 0.078 0.069 0.068

9 8-9 8.5 121 0.058 0.045 0.046

10 9-10 9.5 68 0.032 0.027 0.028

11 10-11 10.5 83 0.039 0.015 0.01612 11-12 11.5 13 0.006 0.007 0.008

13 12-13 12.5 13 0.006 0.004 0.004

14 13-14 13.5 6 0.003 0.002 0.002

15 14-15 14.5 4 0.002 0.001 0.001

16 15-16 15.5 8 0.004 0.000 0.000

17 16-17 16.5 0 0.000 0.000 0.000

18 17-18 17.5 0 0.000 0.000 0.00019 18-19 18.5 1 0.001 0.000 0.000

Wind speed frequency inside specific ranges (bins) has been indexed in column IV while the

column V represents the actual probability density distribution computed from actual data of wind

speed. Similarly, column VI and VII represents the probabilities calculated using Weibull and


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Rayleigh distributions respectively. The Weibull probability distribution function and cumulative

distribution functions are being calculated here by equations (18) and (19) respectively. In the

same way probability density function and cumulative density function for Rayleigh distribution

are calculated with the help of equations (25)and (26)respectively.

Likewise, for year 2013 frequency distribution table has been shown in Table 5.4.

Table 5.4: Distribution of frequencies calculated from wind speed data for year 2013

i Bins Vavg fi Actual Weibull Rayleigh

1 0-1 0.5 0 0.000 0.000 0.000

2 1-2 1.5 139 0.090 0.137 0.130

3 2-3 2.5 258 0.167 0.155 0.161

4 3-4 3.5 260 0.168 0.151 0.1655 4-5 4.5 235 0.152 0.131 0.147

6 5-6 5.5 228 0.148 0.105 0.116

7 6-7 6.5 119 0.077 0.078 0.083

8 7-8 7.5 85 0.055 0.055 0.054

9 8-9 8.5 73 0.047 0.036 0.032

10 9-10 9.5 58 0.038 0.013 0.009

11 10-11 10.5 58 0.038 0.013 0.009

12 11-12 11.5 12 0.008 0.007 0.004

13 12-13 12.5 10 0.006 0.004 0.00214 13-14 13.5 5 0.003 0.002 0.001

15 14-15 14.5 0 0.000 0.000 0.000

16 15-16 15.5 4 0.003 0.000 0.000

Similarly, comparison of Actual, Weibull and Rayleigh probabilities has been made in Table. 5.4.

For year 2013. It can be seen in the table that probabilities of wind calculated using Weibull

distribution are much closer to the probabilities computed from actual frequencies of the wind than

the Rayleigh distribution. So, Weibull distribution better describing the actual data than the

Rayleigh distribution.

As, Weibull distribution displays better fit upon measured data of wind speed at the particular site

therefore Weibull distribution should be applied to evaluate the power potential of wind at the

candidate site instead of using Rayleigh distribution.


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5.7 Comparison of Actual, Weibull and Rayleigh probabilities

The comparison between the Actual, Weibull and Rayleigh distribution has been made using the

frequency distribution given in Table 5.3 and Table 5.4. With the intention of check that which

distribution better fit the actual data. First of all, monthly analysis was done among these three

probabilities, then yearly comparison was also made to check the better distribution between

Weibull and Rayleigh.

5.7.1 Monthly comparison

First of all, monthly comparison between the Actual probability density function has been made

with Weibull and Rayleigh probability density function. Some months graphs have been shown

as a sample here. One month is selected from each Quarter of the month i.e. each one month in

three month (Quarter). So, total of the 8 graphs of monthly analysis have been shown.

Figure 5.6: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Feb 2012

In Fig. 5.6.actual, Weibull and Rayleigh probability density functions have been shown for the

month of Feb, 2012. Both distributions describing the actual data well but Weibull distribution

seems to describe the actual data better than Rayleigh distribution having R2value of 0.817 while

for Rayleigh is 0.813.

In Fig. 5.7.probabilities are compared for the month of June 2012. Both distributions describing

the actual data well having R2value of near about 90%.

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Probabilitydensityfunction

Wind speed (m/s)

Actual Probability

Weibull Dist.

Rayleigh Dist.

February, 2012


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Figure 5.9: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Nov 2012

In Fig. 5.10.the comparison of probabilities is done for the first month of 2013 i.e. January. Again

here Rayleigh distribution describe the data better than the Weibull having R2of very close to one

i.e. 96.6 %

Figure 5.10: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Jan 2013

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ProbabilityDensity

Function

Wind speed (m/s)

Actual Probability

Weibull Dist.

Rayleigh Dist.

November 2012

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

ProbabilityDensityFunctio

n

Wind speed (m/s)

Actual probability

Weibull dist.

Rayleigh Dist.

January, 2013


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Similarly, for the month of June, comparison has also made between the probabilities calculated

from Actual data, Weibull and Rayleigh models as presented in Fig. 5.11.Both distribution

describing the Actual data well.

Figure 5.11: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Jun 2013

For the month of August 2013, comparison of the probabilities calculated from actual wind speed

data, weibull and Rayleigh distribution functions has been made and been represented in the Fig.

5.12.

It could be seen from the figure that, for this particular month, although both distribution

representing the actual probability well but Rayleigh distribution seems to donate the actual

distribution better than the Weibull distribution.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Probab

ilityDensityFunction

Wind speed (m/s)

Actual probability

Weibull dist.

Rayleigh Dist.

June, 2013


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Figure 5.12: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Aug 2013

Likewise, for the month of September, 2013 Rayleigh distribution seems to donate the actual

data better than the distribution as shown in Fig. 5.13.

Figure 5.13: Comparison of Actual, Weibull and Rayleigh Pdf for the month of Sep 2013

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

ProbabilityDensityFunction

Wind speed (m/s)

Actual Probability

Weibull Dist.

Rayleigh Dist.

August 2013

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10 11 12 13

ProbabilityDensityFunction

Wind speed (m/s)

Actual Probability

Weibull Dist.

Rayleigh Dist.

September 2013


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5.7.2 Yearly comparison

As monthly comparison has been made between the probabilities calculated with the help of Actual

data, Weibull distribution and Rayleigh distribution, now comparison between these three

probabilities has been made on yearly basis. Along with the comparison of PDF, comparison has

also been made between the cumulative density function, calculated with the help of Weibull and

Rayleigh functions. These probabilities are calculated using the frequency distribution table as

shown in Table 5.3. & 5.4. For year 2012, comparison has been shown in Fig. 5.14.

Figure 5.14: Comparison of Actual, Weibull and Rayleigh PDF, CDF for year 2012

From Fig. 5.14.it is clear that for the year 2012, in case of probability density function, Weibull

is representing the data well with R2value of 91%. Similarly, cumulative density function is also

better describe by the Weibull distribution.

Comparison of PDF and CDF has also made for the year 2013 as shown in Fig. 5.15.

0

0.2

0.4

0.6

0.8

1

1.2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

CumulativeDensityFu

nction

ProbablityDensityFu

nction

Wind speed (m/s)

Actual Probability

Weibull Pdf

Rayleigh Pdf

Weibull Cdf

Rayleigh Cdf

Jan 2012 - Dec 12


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Figure 5.16: Comparison of Actual, Weibull and Rayleigh PDF, CDF for year 2012-13

So, at the site of Turbat both Weibull and Rayleigh distributions matched the perceived data quite

well. The deviation within the distributions depends upon the value of shape factor k. In

Rayleigh distribution k has fixed value i.e. 2, consequently in Weibull distribution the calculated

value of k is also approaches to 2 i.e. 2.059 therefore the results of both distributions are almost

similar. Whereas the difference between these two distributions is very minor but Weibull seems

to denote the actual data better than the Rayleigh. It is also clear from the above figures that there

are very less chances for the wind speed to exceed the limit of 20 m/s at the site.

5.8 Performance estimation of Statistical models

With the intention of estimating the proficiency of the two distributions taken into account here,

error analysis is also done on the data. Following tests are performed:

The coefficient of determination (R2) or Correlation test,

The root mean square error (RMSE) test,

the Chi-square (2) test

These tests are used to check the accuracy of the distributions in this study.

0

0.2

0.4

0.6

0.8

1

1.2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Cu

ulativedensity

Function

ProbabilityDensityFun

ction

Wind speed (m/s)

Actual Probability

Weibull PDF

Rayleigh PDF

Weibull Cdf

Rayleigh Cdf

Jan 2012 - Sep 13


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5.8.1 Monthly R2value

Monthly R2values have been evaluated for the Weibull and Rayleigh distribution, in order to check

that which distribution better describe the data. In Fig 5.17. Monthly values of R2 have been

representing for the year 2012. It is clear that although both distribution have almost similar values

but Weibull distribution has comparatively higher values of months than the Rayleigh.

Figure 5.17: Monthly values of R2 for Weibull and Rayleigh distribution, year 2012

Similarly, for the year, 2013, R2values are also calculated for each month as shown in Fig. 5.18.

Here again, Weibull has higher values of R2test than Rayleigh distribution. So, theses graphs show

that Weibull distribution is better describing the observed wind data at the site of Turbat.

0

0.2

0.4

0.6

0.8

1


R2

Months

Weibull Dist. Rayleigh Dist.


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Figure 5.18: Monthly values of R2

for Weibull and Rayleigh distribution, year 2013

Average value of R2for all month calculate for both distributions are

Monthly average R2value in case of Weibull distribution = 0.874

Monthly average R2value in case of Rayleigh distribution = 0.852

Similarly, yearly R2values for Weibull and Rayleigh distributions are

Year 2012:

Weibull distribution = 0.944Rayleigh distribution = 0.951

Year 2013:

Weibull distribution = 0.918

Rayleigh distribution = 0.905

Year 2012 & 2013:

Weibull distribution = 0.946

Rayleigh distribution = 0.942

So, after viewing the statistics given above, R2test give better result as the number of observation

increases as monthly R2values are mostly below the 90% while the yearly values are above the

90% showing good correspondence of both distributions with actual wind data. As Weibull

distribution has higher values of R2test, so Weibull distribution better describe the actual data.

0

0.2

0.4

0.6

0.8

1

1.2

Jan Feb Mar Apr May Jun Jul Aug Sep

R2

Months

Weibull Dist. Rayleigh Dist.


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5.8.2 RMSE and Chi-square test

Monthly values or RMSE and Chi-square are also calculated just like R2values. After calculating

the monthly values, average values of all months has been evaluated for both RMSE and Chi-

square tests.

Table 5.5: Evaluation of Statistical models used

Index Weibull Rayleigh

RMSE 0.0040 0.0043

2 2.019 10-6 2.347 10-6

From Table. 5.5.it is clear that Weibull has lower values for both RMSE and Chi-square tests.

Any distribution model having values of both tests i.e. RMSE and Chi-Square tests closer to zero

while the value of R2near to unity; is considered to be the better for the estimation of real wind

speed data, so Weibull distribution better describe the perceived data than the Rayleigh one

because it has higher value of R2and lower values for both RMSE and 2tests.

5.9 Calculation of Wind power density

The monthly values of power density for wind are shown in Table. 5.6.Average values of power

density are relatively high for the months from Feb to Jul than the months from Aug to Dec. The

power consumption of the country in these months (i.e. Feb-July) is also comparatively higher

than the other months (i.e. AugDec). The highest value of average wind power density is for the

month of Feb 2012 i.e. 306.090 W/m2 and the minimum value of average wind power density is

for the month of Oct 2012 i.e. 75.100 W/m2.

The power density at the sel

Winds Engery

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