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ESTIMATION OF WEIBULL PARAMETERS AND WIND POWER DENSITY AND STUDY OF SYNERGY
BETWEEN WIND AND SOLAR ENERGIES AT ANABAR, NAURU
by
Amitesh Chandra
A supervised research project submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics
Copyright © 2018 by Amitesh Chandra
School of Computing, Information and Mathematical Sciences
Faculty of Science, Technology and Environment
The University of the South Pacific
July, 2018
ii
iii
Acknowledgements
I would like to sincerely thank my Principal Supervisor, Dr. MGM Khan, Associate
Professor of Statistics at the University of South Pacific, for his encouragement,
motivation, exemplary guidance and perceptive analysis from the initial to the final
stage of this research work. Without his tireless effort and patience, this piece of
work would not have taken shape.
My profound thanks and appreciation also goes to my Co-Supervisor, Dr. M.
Rafiuddin Ahmed, Professor of Mechanical Engineering at the University of South
Pacific, for providing me with the research data, for guiding me throughout the
project and for his valuable suggestions to make sense out of the data analysis.
Working under the supervision and guidance of Dr. Khan and Dr. Ahmed was an
exceedingly knowledgeable experience.
Very special thanks to Professor Siraj Ahmed of Department of Mechanical
Engineering of the MANIT Camus, Bhopal for his valuable assistance in providing
the software assistance in C programming.
My heart felt appreciation goes to the following family members for being there for
me in so many ways. They have been my strength and inspiration throughout the
writing process and they are my parents, Mr. Ishwar Chand and Mrs.Sneh Lata, my
only brother Mr.Vineet Chandra and my dearest wife. Preeti Chandra.
Finally to my two little angels Ruhi and Ajitesh, who endured patiently the long
periods of selfish devotion I spent on the production of this project, I am profoundly
grateful for their love and understanding.
To all my friends who have assisted, you will never know the difference you made.
iv
Abstract
The renewal energy, particularly from wind and solar, is emerging as world’s fastest
source of accepted substitute energy. Wind and solar energies are inexhaustible
sources of energy with increased consumption around the world at a faster pace
while the advancement of new wind projects continues to be hindered by absence of
reliable wind resource data particularly in the developing countries. This emergences
demand the need of evaluation of these resources. Wind and Solar resource
evaluation in Nauru has received limited attention to date. The research in this thesis
collected wind data from Anabar, which is located at the North-East of Nauru, and
looked into the possibility whether solar energy can complement the wind energy at
day time and if wind energy can compensate for lack of solar energy at night time.
The study also looked at the seasonal variation of wind including Weibull parameters
for this region, which is very close to the equator.
The Weibull parameters and wind power density at Anabar, Nauru, are estimated
form the measured wind speed data at 34 m above ground level (AGL) for the period
from September 2012 to June 2016. Ten numerical methods, namely Maximum
Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM),
Least Square Method (LSM), Method of Moments (MM), Median and Quartiles
Method (MQ), Energy Pattern Factor Method (EPFM), WAsP, Empirical Method of
Justus (EMJ), Empirical Method of Lysen (EML) and New Moments Method were
used to estimate the Weibull parameters. To analysis the efficiency of the methods,
goodness of fit tests were performed using the correlation coefficient (R2), root mean
square error (RMSE), mean absolute error (MAE) and mean absolute percentage
error (MAPE). The results revealed that the empirical method of Justus is the most
accurate model for predicting the correct wind power density for this site, followed
by energy pattern factor method. A wind power density of 87.7 W/m2 was obtained
for the location. The Weibull parameters were also estimated for the wet and dry
seasons separately; Nauru has only two seasons with summer round the year. It was
found that the wet season has higher wind speeds and wind power density compared
to the dry season. The diurnal variations of the wind shear coefficient and the
turbulence intensity were also obtained. The solar and wind resource synergy was
also studied for possible operation in tandem to offset lulls in each other. It was
observed that at night time wind energy can compensate for the lack of solar energy.
v
A hybrid system is a potential solution to the energy needs of the country. The
findings in this research could assist energy investors in designing solar/wind hybrid
system as an alternative energy source to ease dependency on fossil fuel for Pacific
Island Countries (PICs).
vi
Preface
This supervise research project entitled “Estimation of Weibull parameters and wind power density and analysis of synergy between wind and solar energies at Anabar, Nauru” is submitted to the University of the South Pacific, Suva, Fiji in fulfillment of the requirements to acquire a degree in Master of Science in Mathematics. Developed and developing nations alike encounter challengers due to the prolific use of limited fossil reserves as the energy demand increases proportionally with the world’s population. Thus, the renewal energy, particularly from wind, solar and hydro, is gaining momentum as a possible energy substitute. If explored, wind energy could be a substitute to ease high dependence on petroleum. However, reliable wind data is needed for the development of new projects to generate this energy needs in particular for the developing countries. In this project, the study looks at the wind and solar data for a tropical region Nauru. The findings in this research could assist energy investors in designing solar/wind hybrid system as an alternative energy source to ease dependency on fossil fuel for PICs. The research is divided into four chapters. Chapter 1 gives an overview of the Nauru energy profile, introduces about the global power sector and discusses on the general global air circulation. It provides the research aims and objectives, and also focuses on the literature review and studies on the similar work done in other parts of the world. Finally, the chapter provides some insight on the instruments and sensors that are used to record the data on the tower and their specifications. Chapter 2 discusses about the materials used for recording the data and the methods employed for analyzing the data. Chapter 3 analyses and interprets the results of the study. It looks at the performance analysis of different methods and provides estimation of parameters for the Weibull distribution Chapter 4 gives conclusion and provides key findings of this research with recommendations for further research.
vii
Abbreviations
a shape parameter of Weibull distribution, dimensionless
AGL above ground level
CV coefficient of variation
COE coefficient of efficiency
EPF energy pattern factor method
LS least square method
MAE mean absolute error
MAPE mean absolute percentage error
ML maximum likelihood method
MML modified maximum likelihood method
MO moments method
MQ median and quartile method
EMJ empirical method of Justus
EML empirical method of Lysen
NMO new moment method
RMSE root mean square error, m/s
n number of observations performed
R2 correlation coefficient
U wind speed (m/s)
U average wind speed (m/s)
scale parameter of Weibull distribution ( / )m s
Г gamma function
air density 3 ( / )kg m
standard deviation of wind speed, ( / )m s
α wind shear coefficient
viii
WAsP wind atlas analysis and application program
WPD wind power density, W/m2
ix
Table of Contents
Acknowledgments iii
Abstract iv
Preface vi
Abbreviations vii
List of Tables xii
List of Figures xiii
List of Appendices xv
CHAPTER 1: INTRODUCTION 1
1.1 Overview of Nauru Energy Profile 1
1.2 Global Power Sector 3
1.3 Research Aim 4
1.4 Research Objective 4
1.5 Review of Literature and Studies 5
1.6 Instrumentation and Data Collection 10
CHAPTER 2: Materials and Methods 15
2.1 Introduction 15
2.2 Probability Distribution Functions (PDF) for the Wind Data Analysis 15
2.2.1 Weibull Distribution 16
2.2.2 Rayleigh Distribution 17
2.2.3 Advantages of the Weibull Distribution over Rayleigh Distribution 18
2.3 Methods of Estimating Weibull Parameters 18
2.3.1 The Maximum Likelihood Method (ML) 18
2.3.2 The Modified Maximum Likelihood Method (MML) 19
2.3.3 The Least Square Method (LS) 19
2.3.4 Method of Moments (MO) 20
2.3.5 Median and Quartile Method (MQ) 20
x
2.3.6 Energy Pattern Factor Method 21
2.3.7 WAsP method 21
2.3.8 Empirical Method of Justus 22
2.3.9 Empirical Method of Lysen 22
2.4.0 New Moment Method 23
CHAPTER 3: Results and Discussions 24
3.1 Introduction 24
3.2 Wind Speed Analysis 24
3.3 Diurnal Variation of Wind Shear Coefficient 27
3.4 Turbulence Intensity 29
3.5 Synergy Assessment between Solar and Wind Resource 32
3.6 Correlation between Variables 36
3.7 Performance Analysis of Different Methods 37
3.7.1 Coefficient of Determination (R2) 37
3.7.2 Root Mean Square Error (RMSE) 38
3.7.3 Coefficient of Efficiency (COE) 38
3.7.4 Mean Absolute Error (MAE) 38
3.7.5 Mean Absolute Percentage Error (MAPE) 39
3.7.6 Wind Power Density (WPD) 39
3.8 Estimation of Parameters for Weibull Distribution 40
3.9 Performance of the Two-Parameter Weibull PDF Method 41
3.10 Summary 44
xi
CHAPTER4: Conclusion 45
Bibliography 47
Appendices 52
Appendix A 52
Appendix B 53
Appendix C 53
xii
List of Tables Table 1 Top five countries-Total installed capacities as end of 2015 4
Table 2 Specifications of the measurement sensors 12
Table 3 Mean wind speed at different seasons (2012-2016) at 34 m AGL 25
Table 4 Performance of the Weibull distribution models for the year overall
period (2012-2016) 40
Table 5 Performance of the Weibull distribution models for the Wet Season
(Overall) 41
Table 6 Performance of the Weibull distribution models for the Dry Season
(Overall) 41
xiii
List of Figures
Figure 1 Ideal terrestrial pressure and wind systems 2
Figure 2 Photograph of the NRG wind tower at Anabar, Nauru 12
Figure 3 Picture of NRG SymphoniePlus3 data logger 13
Figure 4 Picture of Anemometer NRG #40 sensor 13
Figure 5 Picture of NRG 200P wind vane sensor 13
Figure 6 Picture of NRG BP-20 barometric pressure sensor 13
Figure 7 Picture of NRG 110 temperature sensor 13
Figure 8 Map of Nauru. Anabar is located at the North-east of Nauru 14
Figure 9 Picture of Easterly trade wind flow around Nauru 14
Figure 10 Graph of Yearly Mean Wind Speed Variation between
(2012 to 2016) 24
Figure 11 Graph of Average monthly wind speeds at 34 m and 20 m AGL 25
Figure 12 Graph of Overall daily wind speed 26
Figure 13 Graph of Overall monthly average temperature and 26
barometric pressure
Figure 14 Graph of Average diurnal wind shear coefficient, 27
Figure 15 Graph of Overall diurnal variation of Temperature and
Mean solar insolation 28
Figure 16 Graph of Overall diurnal variation of wind speed and
temperature at 34 m AGL 29
Figure 17 Graph of Overall Diurnal variation between speed and
pressure at 34m AGL 29
Figure 18 Graph of Average diurnal variation of turbulence intensity
at 34m and 20m AGL 30
Figure 19 Graph of Average wind speeds at 34m and 20m AGL during
summer period (Wet season). 31
xiv
Figure 20 Graph of Average wind speeds at 34 m and 20 m AGL during
winter period (Dry season) 31
Figure 21 Graph of Overall Diurnal solar and wind resource 32
Figure 22 Graph of Overall daily mean solar insolation 33
Figure 23 Wind frequency distribution and Weibull distribution curve– 2012 34
Figure 24 Wind frequency distribution and Weibull distribution curve– 2013 34
Figure 25 Wind frequency distribution and Weibull distribution curve – 2014 34
Figure 26 Wind frequency distribution and Weibull distribution curve – 201535
Figure 27 Wind frequency distribution and Weibull distribution curve – 2016 35
Figure 28 Wind frequency distribution and Weibull distribution curve
for the overall period (2012-2016) 35
Figure 29 Wind frequency distribution and Weibull distribution curve for
Wet season Overall 36
Figure 30 Wind frequency distribution and Weibull distribution curve for
Dry season Overall 36
Figure 31 Overall spearman rank correlation between wind shear coefficient
and hourly average temperature 37
xv
List of Appendices
Appendix A Hourly mean data 52
Appendix B Monthly mean data 53
Appendix C Performance Ranking of the ten methods 53
1
Chapter 1
Introduction 1.1 Overview of Nauru Energy Profile
Nauru is a small Micronesian coral island nation situated in the South Pacific 3000
km to the North-East of Australia, located about 40 kilometers south of the equator at
0o 32’ 0” S, 166o 55’ 0” E. It has a population of approximately 10,000 people with a
land area of 21 square kilometres surrounded by fringing reef 120-400 m wide [1]. It
is the smallest state in the South Pacific and the second smallest state by population
in the world. It has a tropical climate and doesn’t experience cyclones. It has cyclic
rainfall and is faced with periodic droughts. According to a Nauru’s report submitted
to the UNFCCC in 2014, Nauru is heavily dependent on imported petroleum in
particular diesel [2]. It has an average fuel demand of 10 million litres per year [3].
The 2013-2014 Nauru’s national budget indicated an allocation of AUD$25 million
(26% of total expenditure budget) for the purchase of the imported petroleum. 70%
of the imported petroleum is used for the generation of power [2].
A solar PV system on Nauru College which began its operations in 2008 is currently
producing approximately 54,000 kWh per year. This helps in saving close to 1,300
litres of fuel per month. The success of this project shows that Nauru has the
prospective of renewable energy which needs to be explored in order to reduce the
high dependency on imported petroleum products.
If explored, wind energy could be an alternative renewable energy source. It is an
inexhaustible source of energy which is gaining importance around the globe. The
barrier to this development is the lack of reliable and accurate wind resource data
especially in the small Island developing countries [4] .Wind resources evaluation
has so far received only limited attention in Nauru and further studies on the wind
data analysis and accurate wind energy potential assessment is needed. Nauru being
very close to the equator is not expected to have very strong wind. It has
predominately easterly trade winds.
2
Fig.1. Ideal terrestrial pressure and wind systems [5]
Winds circulate around the globe due to the rotation of the earth and the incoming
energy from the sun. The direction of the wind at various levels in the atmosphere
determines the local climate and the weather systems. Wind circulates in each
hemisphere in three distinct cells which assists in transporting energy and heat from
the equator to the poles. The energy from the sun drives the wind at the surface as
warm air rises and colder air sinks [6].
The circulation cell close to the equator is known as the Hadley cell named after
eighteenth century scientist George Hadley. At the equator wind are generally lighter
due to the weak horizontal pressure gradients created by the warm surface condition.
The rise of the warmer air at the equator produces clouds and causes instability in the
atmosphere. This causes thunderstorms and release significant amount of latent heats
which provides energy to drive the Hadley cell. The rising air eventually encounters
the stable stratosphere, stops rising and spreads northward and southward along the
tropopause [7]. The latitude of the Hadley cell covers about 300 from the equator. At
this latitude some of the air that sinks to the surface returns to the equator to
complete the Hadley Cell. This movement of air produces the northeast trade wind in
the Northern Hemisphere and the south east trade wind in the Southern Hemisphere.
The direction of the wind flow is impacted by the Coriolis force. The Coriolis force
turns the wind to the right in the Northern Hemisphere and left in the Southern
Hemisphere.
The Inter tropical Convergence Zone (ITCZ) is an area of low pressure near to the
equator in the boundary between two Hadley cells. The clouds and rain is created by
the cooling and condensing of the rising air and as a result warm and wet climate is
experienced along the ITCZ. The changing seasons causes ITCZ to migrate slightly.
3
Land areas tend to hear faster in comparison to the oceans. Since Northern
Hemisphere has more land area, the heating effect of the land influences the ITCZ.
During summer in the Northern Hemisphere, it is approximately 5o north of the
equator, while in winter it shifts. This shift positions it approximately back at the
equator. This shift in ITCZ also causes the shift of the major wind belts slightly north
in summer and south in winter. These movement of wind belts causes wet and dry
seasons.
1.2 Global Power Sector
In 2015 there was a boost in the wind power across the region with an addition of 63
GW to make it a global total of 433 GW. According to [8] this was an increase of
22% over the 2014 market. Growth in some of the larger market was hindered due to
the future policy changes. China has added 30.8 GW of new capacity in 2015 which
is more than the entire EU. The top five countries in terms of new installations are
China, United States, Germany, Brazil and India. New markets are opening across
Africa, Asia, Latin America and the Middle East
The countries that installed their first large scale wind turbines includes Guatemala,
Jordan and Seriba while Samoa initiated its first project. Wind was the leading
source of new power generation in Europe and United states followed by China.
Towards the end of 2014 operational small-scale turbines amounted to more than
830,330.
Globally by the end of 2015 wind power capacity is estimated to meet at least 3.7%
of total electricity consumption. The top five countries total capacity or generation of
renewable energy by sectors as end of 2015 is shown in table 1 below.
4
Table 1: Top five countries-Total installed capacities as end of 2015 [9]
Rank Renewable Power capacity
Hydropower capacity
Solar PV Capacity
Wind Power Capacity
Biomass power capacity
Geothermal power capacity
1 China China China China USA USA 2 USA Brazil Germany USA China Philippin
es 3 Brazil USA Japan Germany German
y Indonesia
4 Germany Canada USA India Brazil Mexico 5 Canada Russian
Federate Italy Spain Japan New
Zealand
According to IEO [9] by the end of 2030 wind power will account for 20% of the global electricity amounting to 2,110 GW, and in return will create around 2.4 million new jobs. The industry is projected to grow by 60GW in 2016.
1.3 Research Aim
The aim of this research is to study the wind data for possible harvesting of wind energy in Nauru based on Anabar data.
1.4 Research Objective
The objective of this research is
1. Analyze the characteristics of wind speed at Anabar for a duration of 4 years 2. To determine the distribution of wind speed. 3. To determine the wind energy potential. 4. To study synergy between wind and solar energy resources. The specific tasks to achieve the objective are as follows;
a. To determine the distribution of speed (overall and yearly)
b. To determine daily average speed (31 days)
c. To determine the daily average speed and standard deviation
(Year/Month/Day)
d. To determine monthly average(Year/Monthly)
5
e. To determine monthly average (12 months)
f. To determine hourly average (24 hours) of wind speed, temperature, pressure,
and wind shear coefficient ( ) for overall and each year.
g. To determine the correlation between and temperature.
1.5 Review of Literature and Studies
Solar, wind, ocean, geothermal and hydropower energy are some of the well-known
energy sources. Wind energy is perhaps one of the oldest sources of energy used by
mankind [10] and the technology for solar/wind hybrid systems is gaining
importance. Although the solar and wind energy resources are available widely,
harvesting of these energy resources poses challengers of variability and
intermittency. Several researchers around the globe have concluded that solar and
wind resources can operate in tandem to offset lulls in each other. However there is
not much understanding on how much wind and solar resource complement each
other in different parts of the world. Synergy characteristics assessment of wind and
solar is essential for deciding future hybrid wind power generating system which will
reduce energy production costs and enhance more supply from renewables. It has
emerged from recent studies that in comparison with the stand alone systems, co-
located solar wind power system are more reliable. More planning and testing for
solar/hybrid system is needed [11]. Takle and Shaw [12] were one of the first to do
analyses on the complementary behavior of solar and wind energy in 1979. The
study revealed that wind and solar energy were observed to be highly complementary
on an annual basis but slightly complementary on the daily basis. Very little work
till date has concentrated on the pre-feasibility studies on the assessment of solar and
wind energy resources globally [13]. A study on the Northeastern part of the Arabian
Peninsula showed higher values of solar energy recorded in the months of summer
than winter months and higher values of wind power were found on winter days [14].
The correlation between solar and wind power potential was calculated to be -0.75
for the Northeastern part of the Arabian Peninsula. A recent study in the Australian
continent has revealed that there exists significant synergy of solar and wind
resources indicating that there is a great potential for future development of
solar/wind hybrid systems [13].
6
In Fiji, introduction of wind power technology dates back to 1952. Initially the wind
mills were installed at Waimari Rakiraki at a height of 7.2 metres. However wind
data analysis was not carried out. The absence of accurate wind energy data has
caused a major hindrance in the development of renewable energy for the Pacific
Islands Countries (PICs) [15].
In a study by [16], Kadavu Island and Suva Peninsula recorded overall wind speed of
about 3.5 – 6.35 m/s for the region. This falls in the low-medium wind speed regime.
The study noted South East as the prevailing wind direction for the region which
corresponds to the trade winds. This study further highlighted the possibility of
exploring wind resource as a substitute for Pacific Islands to ease its dependence on
diesel based power generation. In comparison with the developed nations, small - to -
medium sized turbines should be adequate to provide for the energy needs of PICs
due to its smallness in terms of its population. An assessment of wind quality and
wind power prospects on Fiji Islands revealed that the yearly wind speed of Fiji is
between 5 and 6 m/s with average power density of 160 W/m2 [17].
The establishment of wind power technology to generate energy is slowly emerging
in PICs such as New Caledonia, Tonga, Cook Islands, Samoa; however there has
been no work done in Papua New Guinea and barely anything has been done at
Tuvalu either. The University of the South Pacific has installed 34 meters Integrated
Renewable Energy Resource Assessment System (IRERAS) in Kiribati, Nauru,
Niue, Tuvalu, Tokelau, Tonga, Fiji, Vanuatu, Solomon and Cook Islands [15] to
collect data on wind and solar energies.
In 2006, New Caledonia did done some wind mapping exercise to measure data for
energy production. The study indicated that Nauru has a good wind system probably
towards the North east measuring a wind speed of approximately 6 m/s at a height of
50 m [18]. This would mean that it could provide probably around 25% of the
demand for domestic activities on the island. Nauru participates in the Pacific Islands
Greenhouse gas abatement through Energy projects (PIGGAREP) of the secretariat
of the Pacific Regional Environment Program (SPREP). As part of the (PIGGAREP)
support for Nauru, wind energy sources monitoring equipment were installed at
Anabar to test the potential of wind energy sources for generating power. Though the
Japanese did some technical trial in 1981 on the west coast, generating a net power
7
of 15 kW, no further development has taken place since then. This could have been
an engineering trial to gain experience with the technology [18].
There are several distributions which can be applied to calculate the wind speed
distributions. These include Beta distribution, Gamma distribution, lognormal
distribution, inverse Gaussian distribution, Rayleigh distribution and Weibull
distribution. In recent years Weibull distribution has been one of the most widely
accepted distribution and recommended tool to determine the potential of wind
energy [19]. It has been widely employed in various parts of the world in the
statistical analyses of the wind characteristics and the wind power density [20]. A
study was carried out on 5 different locations around the world to estimate energy
output for small-scale wind power generation for a total of 96 months. It was found
that Weibull representative data estimates the wind energy output accurately as the
overall error in estimation for the monthly energy output was recorded at 2.79% [21].
The Weibull shape parameter defines the data distribution width. Larger shape
parameter indicates that the distribution is narrower and the peak value is higher. The
abscissa scale of plot of data distribution is controlled by the Weibull scale parameter
[22].
In a comprehensive study by [23], a review of wind speed probability distributions
used in wind energy analysis was carried out for weather stations in the Canarian
Archpelago.It was concluded that the two parameter Weibull distributions has lot of
advantages over the other PDFs. The advantages include and not restricted to:
its flexibility
it is only dependent on two parameters
the parameter estimation is simple
it can be expressed in the closed form which simplifies its usage
the parameters has specific goodness of fit tests since its estimation is from
the sample.
The study further noted that though the Weibull distribution is widely accepted
distribution in the area of wind analysis it is not suited for all wind regimes
encountered in nature such as regimes with high percentage of null wind speeds and
bimodal distributions. Therefore its usage cannot be generalised. To minimize errors
8
a suitable probability density function must be carefully selected for different wind
regime.
Some of the widely used numerical methods to estimate Weibull parameters are
moment method, empirical method, graphical method, maximum likelihood method,
modified maximum likelihood method and energy pattern factor method [24, 25].
In a study on 11 cities in Iran with different climates, Sedghi et al. [26] revealed that
based on the RMSE, chi-square test and wind energy error test, Weibull distribution
was found to be the most applicable method. Moment and modified maximum
likelihood methods were the best method while graphical method demonstrated to be
the least performing method for estimating the energy production of wind turbines.
The average values of shape and scale parameters for the cities under studies were
1.65 and 5.01 respectively. A study in the northeast region of Brazil revealed that
equivalent energy method was the most efficient method while graphical method and
the energy pattern factor method were the least effective methods for determining
shape and scale parameters to fit the Weibull distributions [27].
Maximum likelihood method is recommended for estimation of Weibull parameters
when the data is in time series format. Modified maximum likelihood method is
recommended when the data is in the frequency distribution format. Graphical
method is found be less robust in terms of accuracy since it is affected by external
variables such as bin size. It was used in the age when computers were not readily
available and were less powerful since it can be executed manually with less
calculation [28]. Energy pattern factor method and moment method were ranked as
one of the most accurate methods for wind power evaluation in Garoua, Cameroon
based on the chi-square test, correlation coefficient, RMSE and Kolomgorov-
Smrinov goodness of fit test. The study highlighted that the wind conditions in
Garoua did not have the ability to generate electricity. Instead the study highlighted
that the wind meals could be installed for producing community water supply,
livestock watering and farm irrigation [4]. A study in the Adamaoua region of
Cameroon concluded that energy pattern factor method gives the most accurate
estimation of the Weibull parameters while modified maximum likelihood method
and Graphical method were the least effective method. The alternative suggested to
energy pattern factor method was maximum likelihood method [29].
9
In a study by Fadare [30] on the analysis of wind energy potential based on the
Weibull method in Ibadan, Nigeria, it was seen that Ibadan is a low wind energy
region. The annual mean wind speed was 2.75 m/s. The mean wind speed and the
power density predicted by the Weibull probability density function were 2.947 m/s
and 15.484 W/m2 respectively. In a study by Shu et al. [10], statistical analysis of the
wind energy potential in Hong Kong found that Weibull distribution function
indicated a good representation of the measured data. The study highlighted that
moment method, maximum likelihood method and the power density method showed
little difference for the estimation of Weibull Parameters. The scale parameter varied
from 2.85 m/s to 10.19 m/s while the shape parameter was between the ranges of
1.65-1.99. Variations in the Weibull parameters were recorded for different seasons
with autumn recording the highest scale parameter and summer recording the lowest
shape parameter. An average wind power density of 915.23 W/m2 was recorded.
Isaac and Joseph [31] in a study in Hong Kong found out that the shape parameter
varied from 1.63 to 2.03 and the scale parameter ranged from 2.76 to 8.92 at a height
of 89.6 m above mean sea level.
The work of Adaramola et al. [32] studied the annual and seasonal wind speed
characteristics and Weibull parameters at a height of 12 m along the coast of Ghana
using the two parameter Weibull probability density function. Ghana recorded an
annual wind speed in the range of 3.88 m/s to 5.30 m/s. The study concluded that
wind turbines with cut-in wind speeds of less than 3 m/s and rated wind speed of 9-
11 m/s will be appropriate for wind energy generation. Wind power potential was
statistically analysed for Mil-E Nader, Iran, at three different heights of 10 m, 30 m
and 40 m based on 10 minute measurements. The eighteen month average wind
speed was 6.84 m/s at a height of 30 m AGL [33]. The wind rose showed two
dominant wind directions at 30 and 60 indicating an ideal condition for wind
production. An average wind speed of 4.5 m/s was estimated at a height of 34 m
AGL on the main island Tongatapu of Tonga [34]. They also estimated the annual
energy production for the site with the Bonus 300 kW Mk III wind turbine. Weibull
parameter distribution function was used to carry out wind energy potential
assessment for the Iranian cities of Tabriz and Ardabil [35]. The measurement was
taken at a height of 10m above ground level. Tabriz recorded an yearly average wind
speed of 1.99 m/s and Ardabil recorded 4.16 m/s. The study of 10 years wind data
10
from Oran meteorological station for Oranie region at a height of 10 m above ground
level [36] revealed that Oran has an average wind potential with an annual mean
wind speed of 4.2 m/s with an annual mean power density of 129 W/m2. An
assessment of wind power potential along the coast of Tamaulipas state in
northeastern Mexico was carried out using Wind Atlas Analysis and Application
Program (WAsP). Mean wind intensity field and the corresponding mean power
density were modeled using WAsP [37]. The result indicated that wind energy
appeared to be a promising renewable source for generating electricity along the
coast of Tamaulipas. In a study by Sharma and Ahmed [16] for the two locations on
the island of Fiji at a height of 34 m and 20 m AGL, mean wind speeds of 6.38 m/s
for Suva location and 3.88 m/s for Kadavu Island were recorded. Annual energy
production for a number of sites was estimated using the wind resource grid which
was created around the sites. Annual energy production of 400-500 MWh and 650
MWh were estimated for the Suva and Kadavu locations. The research supported the
concept of wind resource as an alternative to the diesel based power generation for
the Pacific.
The present work involves estimation of Weibull parameters and wind power density
using ten numerical methods to determine which ones are the best in predicting the
parameters of the Weibull distribution for the available data and also analyse the
synergy between wind and solar resources.
1.6 Instrumentation and Data Collection
The data used for the purpose of this study were collected by an Integrated
Renewable Energy Resource Assessment System (IRERAS). The IRERAS tower is
a 34 m tall Renewable NRG system that is hinged onto the base plate and supported
and balanced by guy wires and a gin pole. The tower is used for wind measurements
around the globe because of its design features. It is tough in strength and is resistant
to corrosion since it is manufactured using galvanized steel tubes.
The seven sensors on the IRERAS measure wind speed, wind direction, barometric
pressure, solar insolation, temperature, rainfall and relative humidity. NRG
SymphoniePlus3 data logger logs the data from the seven sensors and stores in an SD
card. The data were transferred on the mobile network to a databank in the
11
University of the South pacifics ICT centre via a GSMipack combined with a SIM
card. The sensors are connected to a PV solar panel for additional power.
NRG #40 model cup anemometers were used to measure the wind speed at heights of
20m and 34m AGL. The wind direction was recorded with a wind vane. The
measured range of the anemometers is from 1 m/s to 96 m/s with an accuracy of 0.1
m/s in the range 5-25 m/s. Two anemometers were installed at 34 m height consisting
of rugged Lexan cups molded in one piece. This enhances the performance of the
anemometers and makes them durable. Low level AC sine wave voltage were
induced by four pole magnets in to a coil producing an output signal ranging from 0
Hz to 125 Hz .The correction factor of the factory-calibrated anemometers were
programmed into the data logger.
Wind vane model NRG#200P was mounted at a height of 30 m aligned to a north
direction to measure the wind direction. It is made up of stainless steel and
thermoplastics which ensures it is free from corrosion and is of high strength. It has
continuous rotation strength of 0 to 360o. This rotation produces an analog DC
voltage from the conductive plastic potentiometer that is directly proportional to the
wind direction.
The atmospheric pressure was measured by a barometric pressure sensor model:
NRG#BP20. Its design makes the sensor adapt to the remote areas to take
measurements. The sensor has a range of 15 kPa to 115 kPa. The output terminal
measures the voltage output proportional to the pressure. The tower is mounted with
a temperature sensor model: NRG#110S. This sensor is able to accurately measure
temperature due to it being enclosed in a circular six-plate radiation shield. The
sensor has a range of -40o C to 65oC with accuracy of ±1.1oC. The data logger has 15
channels capable of logging mean, standard deviation, maximum and minimum of
the data. These data are calculated every 10 minutes interval and is stored in the SD
card and is also transmitted to the data bank once a day as an email attachment. This
is made possible since SymphoniePlus3 data logger is configured to be used as an
internet-enabled data logging system.
12
Wind tower On-Site Installation
Fig.2. A photograph of the NRG wind tower at Anabar, Nauru. Figure 2 shows the layout map of the wind tower. The tower is installed on site with
the help of technicians. The tower is installed using specific method together with the
data logger and the sensors. A winch is used to raise the tower initially. The
calibrated anemometers, wind vane, and sensors are mounted on the boom. A copper
rod is also mounted to protect it from lightening. The gin pole aids the winch in
lifting the tower with the sensors. The wires are slackened and given tension to assist
in the lifting process. The guy wires help the winch to fully raise the tower. It is
adjusted continuously in the lifting process of raising the tower.
Table 2: Specifications of the measurement sensors [13].
Parameter Sensor type Range Accuracy
Wind speed
Wind direction
Pressure
Temperature
NRG #40 anemometer
NRG 200P direction vane
NRG BP-20 barometric
pressure sensor
NRG 110S
1.0-96.0 m/s
0-360o
15.0-115 kPa
-40 °C to 65 °C
0.1 m/s
N/A
±1.5 kPa
±1.1 °C
13
Fig.3: NRG SymphoniePlus3 data logger
Fig.4: Anemometer NRG #40
Fig.5: NRG 200P wind vane
Fig.6 NRG BP-20 barometric pressure sensor
Fig.7 NRG 110 temperature
14
Fig.8. Map of Nauru. Anabar is located at the North-east of Nauru
Fig. 9.Map showing the easterly trade wind flow around Nauru
15
Chapter 2
Materials and Methods
2.1 Introduction
The daily wind speed data used in this study are as part of a KOICA sponsored
project to the University of the South Pacific of Anabar, Nauru with coordinates (S
000o 30.658 and E 166° 57.064) for the period of 2012 to 2016 (5 years). The data
were recorded in time series format in RWD file which was then transferred into
Microsoft excel sheet. The wind speed data was measured continuously with a cup-
generator anemometer at hub heights of 34 m and 20 m respectively. The wind speed
characteristic and their distributional parameters were analysed using Weibull
approach for the ten methods (maximum likelihood method, modified maximum
likelihood method, least square method, method of moment, median and quartile
method, energy pattern factor method, WAsP method, empirical method of Justus,
empirical method of Lysen and new moment method using R software and C
programming. R is a language and an environment for statistical computing which
has built in mechanisms for organizing data, running calculation on the information
and creating graphical representations of the data. WAsP is a PC programme which
is able to extrapolate vertical and horizontal wind data. It is able to generalise a long
term wind data for a site under study and estimates the wind conditions for another
[36].
2.2 Probability Distribution functions (PDF) for the Wind Data Analysis
Scientific literature in renewable energy suggests variety of probability density
function that is used to describe wind speed frequency distributions. According to
Weisser [38] the two most commonly used probability distributions are Rayleigh
distributions and the Weibull distributions. The Weibull distribution is named after
Swedish physicist Weibull. He applied the concept in 1930s while studying material
in tension and fatigue [19].It provides approximation to the probability laws of many
natural phenomena.
The Rayleigh distribution which is a special case of Weibull uses the mean wind
speed as the only parameter in the wind analysis. Weibull uses two parameters which
16
make it better to represent a wide variety of wind regimes. Both of the distributions
are defined for values greater than zero and are often called ‘skewed distribution’
The two parameters; dimension less shape parameter ( a ) and scale parameter ( ) of
the Weibull distribution are generally the ones mentioned in the literature dealing
with renewable energy and has been seen working well with different estimation
methods.
2.2.1 Weibull Distribution
The Weibull two parametric functions for wind speed is expressed mathematically as
1
( ) ; 0, 0, 1aa Ua Uf U e U a
(1)
And the cumulative distribution function is
1 exp aUF U
(2)
Where, f U is the probability of observing the wind speed, , is the Weibull
shape parameter and is the Weibull scale parameter (m/s). The scale parameter , denotes how windy the site under study is, whereas the shape parameter indicates
the wind potential and what peak the distribution can reach [38].
The approximation that can be used to calculate the Weibull parameters and
once the meanU and the variance 2 of the wind data are found is given by [38]:
1.086
; (1 10)a aU
(3)
11
U
a
(4)
17
The average wind speed U is
1
1 n
ii
U Un
(5)
and the wind speed variance 2 is
22
1
1 1
n
ii
U Un
(6)
and the gamma function of ( )U can be obtained as:
( 1)
0
( ) t UU e t dt (7)
2.2.2 Rayleigh Distribution
This distribution is regarded as the simplest velocity probability distribution since it
takes into account of only one parameter which is the mean wind speed, U . The
Rayleigh probability density function is given by [39, 40]:
2
2( ) exp 2 4
UU
UUU
f
(8)
And the cumulative distribution function is
2
1 exp4
Uf UU
(9)
18
2.2.3 Advantages of the Weibull Distribution over Rayleigh Distribution
The advantages of Weibull distribution according to Justus et al. [41] are;
It is more general than Rayleigh distribution as it depends on the two parameter a
and . Rayleigh has shape parameter 2a which makes Weibull easier to work
with rather than general bi-variate normal distribution, which requires five
parameters.
Weibull distribution function is not only flexible and simple to use but it fits a
wide collection of recorded wind data.
The Weibull parameters a and when known at a particular height, the
parameters can be adjusted to another desired height.
2.3 Methods of Estimating Weibull Parameters
There are many methodologies available in the literature that are used to determine
the Weibull parameters using the long term meteorological observations, the
application of which is related to many factors including surface roughness, relief
conditions and urbanization locations [42]. In the present work, ten different methods
were used to obtain the Weibull parameters as described in the following sections.
2.3.1 The Maximum Likelihood Method (ML)
The method of maximum likelihood is the most popular technique for deriving estimators [43-46]. If 1,..., nU U are the wind speed values with the Weibull density function given in (1), the shape parameter ( a ) and scale parameter ( ) are the values that maximize the likelihood function 1 1, ,..., ,n
n i iL a U U f U a . Then,
solving ln 0L a and ln 0L the equation of ML estimate of the scale parameter is obtained as:
1
1 nai
iU
n (10)
Finally, using (10) the equation of estimating the shape parameter ( a ) is obtained as:
1
1
1
ln1 1 ln 0
nai in
ii n
aii
i
U UU
a n U, (11)
19
which may be solved to obtain the estimate of a using Newton-Raphson method or any other numerical procedure because (11) does not have a closed form solution. When a is obtained, the value of is found from (10). 2.3.2 The Modified Maximum Likelihood Method (MML)
This method is a variation of the maximum likelihood method which is applied when
wind speed data is in the frequency distribution format. The Weibull parameters are
estimated using the following equations [28]:
1
1 1
1
l n l n
0
n na
i i i i ii i
na
i ii
U U P U U P Ua
P UU P U (12)
1
1
1 0
n aa
i ii
U P UP U
(13)
Where iU is the wind speed central to bin i , n is the number of bins, ( ) is the
frequency with which the wind speed falls in bin , ( ≥ 0) is the probability that
the wind speed equals or exceeds zero. Equation (12) is solved iteratively, after
which to find a value; Equation (13) can be solved explicitly.
2.3.3 The Least Square Method (LS)
The following formulae are used to determine Weibull parameters [42]:
1 1 12
2
1 1
l n l n l n 1 l n l n l n 1
l n l n
n n n
i i i ii i i
n n
i ii i
n U F U U F Ua
n U U (14)
1 1l n l n l n 1
e x p
n n
i ii i
a U F U
n a (15)
20
2.3.4 Method of Moments (MO)
If the wind speed values 1,..., nU U follow Weibull distribution given in (1) then an
unbiased estimate of r th moment is given by 1 1r ar
r r a , where ( )s
is a Gamma function defined by 1
0
s us u e du .
Then, finding the first moment ( 1 ) and the second moment ( 2 ), the value of a and can easily be determined by the following equations [43, 47]:
22 11 1a a
(16)
2
211
11
aU
a
(17)
where, U and are the mean and standard deviation of wind speed. Finally, after
some calculation we can find the Weibull parameters as: 1.0983
0.9874aU
(18)
11
U
a
(19)
2.3.5 Median and Quartile Method (MQ)
Given that the median of wind speed is mU and quartiles 0.25U and 0.75U , and
0.25 0.75 0.25, 0.75p U U p U U , the shape parameter and scale parameter λ
can be computed by the relations [43]:
0 . 7 5 0 . 2 5 0 . 7 5 0 . 2 5
l n l n 0 . 2 5 / l n 0 . 7 5 1 . 5 7 3l n ( ) l n ( )
aU U U U
( (20)
1/ ln 2 amU (21)
21
2.3.6 Energy Pattern Factor Method
The energy pattern factor method (EPFM) is associated with the averaged data of
wind speed and is defined by the following equations [27];
3
3pfUEU
(22)
23.691
pf
aE
(23)
11Ua
(24)
where pfE is the energy pattern factor, 3U is the mean of wind speed cubes 3 3 ( / )m s and 3
U is the cube of mean wind speed.
2.3.7 WAsP method
The WAsP method, also known as the ‘equivalent energy method’ has a prerequisite
for fitting the Weibull distribution to measured wind speed data. The WAsP
algorithm does not attempt to directly fit the measured frequency histogram but
requires that:
a. The mean power density of the fitted Weibull distribution is equal to that of the
observed distribution.
b. The proportion of values above the mean observed wind speed is same for the
fitted Weibull
distribution as for the observed frequency [48].
Hence the above requirements lead to the following equations [49]:
3
13
31
n
ii
UU
n a (25)
22
F U , the cumulative distribution function gives the ratio of values less than U ;
therefore the proportion of values exceeding U is obtained from 1 F U . From
criterion (b) above symbol J is defined as the proportion of the observed wind
speeds which exceeds the observed mean wind speed, as
1 F U J (26)
3
13
ln
31
n
ii
U JU
na
(27)
Initially J is calculated using Equation (24) and the parameter a is obtained from
Equation (25), iteratively.
2.3.8 Empirical Method of Justus (EMJ)
Justus presented the empirical method in 1977 [41]. It is considered to be a special
case of the moment method [4] where average wind speed and standard deviation are
used to determine the Weibull parameters as follows [46]:
1 . 0 8 6
a U (28)
1/ 1Ua
(29)
2.3.9 Empirical Method of Lysen (EML)
Lysen introduced this empirical method where a is calculated similar to the method
of Justus but is defined as [41, 46].
1 0 . 5 6 8 0 . 4 3 3 aU a (30)
23
2.4.0 New Moment Method (NMO)
This New Moment Method is proposed in a study by [50] as a new estimation
approach for calculating Weibull estimation. Literature generally suggests that
moments are able to fully characterize a probability distribution. Mean and variance
are the first two statistical moments. These provide information on location and
variability. This is already used in moment’s method. The third moment has not
been used so far in the literature for estimation of moment procedure which defines
skewness of a distribution. It forms an integral component in estimation procedure as
wind power is an important factor for estimating the suitability of location in terms
of optimum usage of energy. In NMO, the author used the first three moments
corresponding to mean, variance and skewness. They concentrate on minimizing the
squared deviances between the first three population moments and the corresponding
sample moments and is expressed with the weighted sum of squared deviations as
follows [50]:
2 22 _ __2 2 3 3
1 2 31 2 3 1 1 1U U Ua a a
(31)
where __
1
knk i
i
UUn
is the kth sample moment and 1 2 , and 3 are the chosen
weights given that 1 2 3 1 (32)
Ideally the weights are chosen by a decision maker giving importance of each
objective function within the suitability of the problem. However, for the purpose of
this study all 3 objective functions will be given equal importance. This means the
weights are chosen as 1/3 within the estimation procedure. The NMO function given
in (31) is minimized with respect to the parameters of the Weibull distribution using
the Nelder- Mead method which is a simplex method in minimization using R. This
method does not require derivatives. The initial values for optimization process are
used from the moment’s method (MO) where 10-4 is taken as convergence tolerance.
24
Chapter 3
Results and Discussion
3.1 Introduction
In this research, as discussed in previous chapters, the wind speed characteristic and
their distributional parameters were analysed using Weibull approach for the ten
methods (maximum likelihood method, modified maximum likelihood method, least
square method, method of moment, median and quartile method, energy pattern
factor method WAsP method, empirical method of Justus, empirical method of
Lysen and new moment method using R software and C programming. In this
chapter, the results are presented and discussed.
3.2 Wind Speed Analysis
The daily wind speed data recorded at the site Anabar in Nauru for the period of 5 years from 2012 to 2016 are analyzed.
Fig.10. Yearly Mean Wind Speed Variation between 2012 to 2016
Figure 10 presents the yearly variation of the wind speed for the five years from
2012-16. The mean wind speed is approximately 4 m/s for the majority of the years
except 2013 and 2016 where the mean annual wind speed is close to 5 m/s.
0
1
2
3
4
5
6
2012 2013 2014 2015 2016
mea
n w
ind
spee
d, m
/s
Year
25
Fig.11. Average monthly wind speeds at 34 m and 20 m AGL
Figure 11 shows the monthly wind speed variation at 34 m and 20 m. The mean wind
speed is calculated to be 4.33 m/s and 3.60 m/s at the heights of 34 m and 20 m
respectively. The lowest mean wind speed was recorded in the month of October and
the highest wind speed was recorded in the month of March.
Table 3: Mean wind speed at different seasons (2012-2016) at 34 m AGL.
Year
Season Wet Season
(m/s) Dry Season
(m/s) 2012 4.30 3.52 2013 5.48 4.68 2014 4.45 3.50 2015 4.10 3.91 2016 4.96 4.10
2012-16(overall) 4.66 4.00
Table 3 shows the seasonal variation in the mean wind speed. The highest wind
speed was recorded for the year 2013.In comparison to the dry season; the wet
season generally recorded higher wind speeds.
0
1
2
3
4
5
6
Jan Feb Mar Apr May Jun Jul AugSep Oct NovDec
Mea
n w
ind
spee
d, m
/s
Months
speed34 AGL speed20mAGL
26
Fig.12. Overall daily wind speed
Figure 12 presents the graph for the overall daily wind speed recorded for the site at
34 m AGL. The variation in the average wind speed at the daily basis is not much.
This is anticipated as Nauru being the equatorial region the winds are generally
consistent at the equator due to minimal changes in the atmospheric temperature and
pressure [42]. The average mean wind speed is 4.34 m/s.
Fig.13.Overall monthly average temperature and barometric pressure
Figure 13 presents the variation of the monthly temperature and barometric pressure.
In comparison to the global average atmospheric pressure of 1013.25 mBar [42], the
0
1
2
3
4
5
6
7
8
1 21 41 61 81 101121141161181201221241261281301321341361
Mea
n w
ind
spee
d,m
/s
Days
1000
1001
1002
1003
1004
26
27
28
29
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Pres
sure
, mB
ar
Tem
pera
ture
, deg
C
Temperature Pressure
27
average atmospheric pressure at Anabar is lower. The variation between the pressure
and temperature is quite minimal due to the fact of Nauru being an equatorial region.
The variation in the monthly average temperature is almost insignificant in
comparison with the countries away from the equator. The monthly average
temperature was a little higher in May and November.
3.3 Diurnal Variation of Wind Shear Coefficient
.14Fig : Average diurnal wind shear coefficient, α
The mean wind speeds at 34 m and 24 m were calculated to determine the wind shear
coefficient, α. The power law was applied to estimate the wind shear coefficient [43]:
1
2 1
2
l nln
U Uh h
(33)
Wind shear has a lot of influence on the assessment of wind resources as well as the
design of the wind turbines. Higher wind speed variation is observed at night and
during the early hours of the day. The vertical wind speeds were a significantly lower
between 9 am - 4 pm. This is due to the temperature inversion effect which causes
variation in wind speeds at different height resulting in the increase in temperature
with height. At the ground level the cool dense air is trapped due to the movement of
warm air above it. The rising sun heats up the ground causing the cold air near to the
ground to also heat up resulting in the break-up of the inversion [7]. As the ground
heats up, warm air rises. This vertical movement of air causes an increase in the wind
speed immediately above the previously trapped air mass. This explains why the
wind speed at a height of 20 m increases more in day time than at 34 m height. For
0
0.1
0.2
0.3
0.4
0.5
0 4 8 12 16 20 24
Win
d sh
ear c
oeffi
cien
t, α
Hour of day
28
example at around 3pm the mean wind speed at 34 m is higher than at 20 m
producing the lower wind shear coefficient of 0.28 during this time. A similar trend
was noted in the works of Aukitino et al. [43] for Kiribati also an equatorial region.
The average wind shear coefficient is 0.35 for Anabar.
The analysis on the hourly data collected as per Appendix A is illustrated below. The
diurnal variation of the temperature and mean solar insolation is shown in Figure 15
as the temperature inversion effect has a strong impact on the wind shear. It is clearly
shown that the temperature reduces significantly as the night falls.
Fig.15.Overall diurnal variation of Temperature and Mean solar insolation
Figure 15 shows the diurnal variation of the temperature and the mean solar
insolation. This variation is due to the gain of energy from the sun and the energy
loss caused by emission of infrared radiation. Temperature rises when the gain in
energy is greater than the loss in energy and the temperature falls when the net
energy is negative. The ground becomes warmer after the sun rise due to the
absorption of solar energy. The rising sun adds more energy to the air than the air is
emitting [7]. At about midday the incoming solar energy gains momentum. After
noon though the gain in solar energy is reduced, the surface temperature continues to
rise as the gain in the energy is still far greater than the loss in energy. At around
2pm maximum daily temperature is reached. This is when the loss in energy starts to
outweigh the gain in energy causing the temperature to decrease all night long. The
temperature is at a minimum around sunrise and the cycle repeats.
0100200300400500600700800
2425262728293031
0 4 8 12 16 20 24 Mea
n so
lar i
nsol
atio
n, W
/m2
Tem
pera
tue,
deg
C
Hour of day
Temperature Mean solar insolation
29
Fig.16.Overall diurnal variation of wind speed and temperature at 34 m AGL
Fig.17 Overall Diurnal variation between speed and pressure at 34m AGL
3.4 Turbulence Intensity
The simplest measure of turbulence is the turbulence intensity. Turbulence is
basically defined as the measure of the difference in wind speed with respect to time.
It is defined as the dissipation of the Kinetic energy of the wind into thermal energy
by the creation and destruction of smaller eddies [39]. Turbulence intensity (TI) is
defined as the coefficient of variation of the wind speed, that is, the ratio of the
standard deviation of the wind speed to the average wind speed as per the equation
below [43],
2425262728293031
3.8
4
4.2
4.4
4.6
4.8
0 4 8 12 16 20 24
Tem
pera
ture
, deg
C
Mea
n w
ind
spee
d, m
/s
Hour of day
speed 34 m AGL Temperature
998
1000
1002
1004
1006
1008
3.8
4
4.2
4.4
4.6
4.8
0 4 8 12 16 20 24
Pres
sure
, mB
ar
Mea
n w
ind
spee
d, m
/s
Hour of day
speed 34 m AGL Pressure
30
UTIU
(34)
The most frequent range of turbulence intensity in atmospheric wind is between 0.1
and 0.4 [39]. Generally the highest turbulence intensities are recorded at lower wind
speeds as the flow in air tends to become smoother at greater heights.
Fig.18.Average diurnal variation of turbulence intensity at 34m and 20m AGL
Figure 18 shows the diurnal variation of turbulence intensity. The result indicates
high turbulence intensity at 20 m AGL in comparison with 34 m AGL. The highest
turbulence intensity of (21.8%) is recorded at 1700h. The lowest (14.0%) is recorded
at 0700 hrs. The overall average turbulence intensity is 15.3% at 34 m AGL and
20.8% at 20 m AGL. The allowable turbulence level is 18% for 15 m/s winds for
design standards of turbines according to the International Electro technical
Commission (IEC61400-1) [16]. Analysis of the data sample gives an indication that
the average turbulence level is slightly higher than the allowable limit. Higher value
of turbulence intensity was recorded between 10th-18th hours of the day. Higher
turbulence level has a lot of effects on the turbine loads, blade performance and
power output. The monthly mean data from Appendix B was used to compare the
average wind speeds at the heights of 34 m and 20 m for the two different seasons.
0
5
10
15
20
25
0 4 8 12 16 20 24
Turb
ulan
ce in
tens
ity,%
Hour of day
TI 34 m AGL TI 20 m AGL
31
Fig.19. Average wind speeds at 34m and 20m AGL during summer period (Wet season).
Figure 19 shows that during the wet season (summer period) the mean wind speed is
increasing between the months of November to March and begins to decrease in
April. The average wind speed is 4.66 m/s and 3.83 m/s at 34 m AGL and 20 m AGL
respectively. Similar trend was reported by Aukitino et al. [43].
Fig.20. Average wind speeds at 34 m and 20 m AGL during winter period (Dry season)
Figure 20 shows that during the dry season (winter period) the mean wind speed is
decreasing for the months of May and June and slightly increased for the month of
July and decrease gradually from August to October. The average wind speed is 4.00
m/s and 3.36 m/s at 34 m AGL and 20 m AGL respectively.
0
1
2
3
4
5
6
Nov Dec Jan Feb Mar Apr
Mea
n w
ind
spee
d m
/s
speed 34 m speed 20 m
0
1
2
3
4
5
May Jun Jul Aug Sep Oct
Mea
n w
ind
spee
d, m
/s
speed 34 m speed 20 m
32
3.5 Synergy Assessment between Solar and Wind Resource
Fig.21: Overall Diurnal solar and wind resource
Figure 21 shows the graph of the solar and wind resource synergy. The overall
analysis for the period under study shows the diurnal temperature cycle that is driven
by the daily changes in the energy budget near the ground [7]. The change in
temperature is driven by incoming solar radiation gains versus outgoing terrestrial
energy losses. After sun rise the ground warms after absorbing solar energy. All
morning along the air temperature increases due to the fact that the rising sun adds
more energy to the air than the air is emitting. The incoming solar energy peaks by
noon. The solar energy gains are reduced after noon. The loss in energy exceeds
gains therefore the temperature decreases all night along. The temperature reaches
minimum around sun rise and the cycle continues. The wind speed also gains
momentum during noon. The maximum mean solar insolation and wean speed is
750.33 W/m2 and 4.74 m/s respectively and is recorded at the 13th hour of the day.
The findings reveals that wind energy can fairly compensate for lack of solar energy
at night time while during the day time both sources of energy are recorded at
optimum level. This finding for a region close to the equator reveals similar findings
done in Australia by [13] which states that strong temporal synergy of solar and wind
resource exists in Australia.
3.8
4
4.2
4.4
4.6
4.8
0
100
200
300
400
500
600
700
800
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Mea
n w
ind
spee
d , m
/s
Mea
n so
lar i
nsol
atio
n, W
/m2
Hours
Mean solar insolation speed34mAGL
33
A complementary behavior to some extent was seen between solar and wind resource
for the equatorial region of Nauru. A further study is recommended to look in to the
viability of extracting the solar and wind resource for this equatorial region as the
resource extraction introduces challenges of variability and intermittency as majority
of the research in this area is concentrated over the Northern Hemisphere.
Fig.22. Overall daily mean solar insolation
Figure 22 displays the bar graph for the daily mean solar insolation. The average
mean solar insolation is 400 W/m2.
Figures 23-30 show how the calculated Weibull function, for each numerical method,
relates with the observed wind speed histogram. This generally gives an indication of
the method which best fits to the data of the collected wind speed and how the curve
matches the histogram of the measured data. The Weibull density function gets
relatively narrower and more peaked as a gets larger. The value of a ranges from
1.916 to 2.070, 1.949 to 2.160 and 1.892 to 2.269 whereas the values ranges from
4.773 to 4.900, 5.038 to 5.300 and 4.430 to 4.500 for the overall period under study,
wet season overall and dry season overall respectively.
0
100
200
300
400
500
600
700
1 21 41 61 81 101121141161181201221241261281301321341361
Mea
n so
lar i
nsol
atio
n, W
/m2
Days
34
Fig.23. Wind frequency distribution and Weibull distribution curve for the year – 2012
Fig.24. Wind frequency distribution and Weibull distribution curve for the year – 2013
Fig.25. Wind frequency distribution and Weibull distribution curve for the year - 2014
35
Fig.26. Wind frequency distribution and Weibull distribution curve for the year – 2015
Fig.27. Wind frequency distribution and Weibull distribution curve for the year - 2016
Fig.28. Wind frequency distribution and Weibull distribution curve for the overall period (2012-2016)
36
Fig.29. Wind frequency distribution and Weibull distribution curve for - Wet season Overall
Fig.30. Wind frequency distribution and Weibull distribution curve for - Dry season Overall
3.6 Correlation between Variables
Spearman rank correlation was used to measure the association between the hourly
average temperature and the wind shear coefficient. The result is shown in Fig.31. It
was found that there is highly significant negative correlation between the
temperature and the wind shear coefficient,
(r = -0.9678261, p-value < 0.001).
37
Fig.31. Overall spearman rank correlation between wind shear coefficient and hourly average
temperature
3.7 Performance Analysis of Different Methods
The efficiency and the performance of the ten different methods used for estimating
the Weibull parameters was determined through the means of goodness of fit such as
coefficient of determination R2 and the error estimates such as root mean square
error (RMSE),coefficient of efficiency (COE), mean absolute error (MAE), mean
absolute percentage error (MAPE).
3.7.1 Coefficient of Determination (R2)
Arithmetically, R2 is calculated using the following equation:
2
2 1
2
1
( )1
( )
N
i ii
N
ii
y UR
y z (35)
The highest value of R2 can reach up to 1. Higher R2 value indicates the better fit [4].
38
3.7.2 Root Mean Square Error (RMSE)
The root mean square error (RMSE) determines the deviation between the
experimental and predicted values. Smaller (RMSE) value normally indicates
accurate modeling. The calculated (RMSE) value approaches close to zero as the
deviation between the calculated and predicted values become smaller [19]. It is
expressed as:
RMSE
12
2
1
1 ( )n
i ii
y UN
(36)
3.7.3 Coefficient of Efficiency (COE)
The Coefficient of Efficiency (COE) is the measure of predicted values with respect
to actual values for the estimation of the wind speeds. It usually ranges from minus
infinity to 1. A higher value of COE indicates better agreement [30]. It is expressed
as:
2
1
2
1
( )
( )
n
i ii
N
ii
y UCOE
y z (37)
where n is the number of observations is, iy is the thi actual data iU is the predicted
data with the Weibull distribution, z is the mean of actual data.
3.7.4 Mean Absolute Error (MAE)
The mean absolute error is the measure of the absolute difference between two
continuous variables. The name simply suggests it is the average of the absolute
errors . Lower value of MAE indicates better accuracy. The MAE is mathematically
expressed as [37]:
1
1 ˆn
t ti
MAE Y Yn
(38)
39
3.7.5 Mean Absolute Percentage Error (MAPE)
The mean absolute percentage error MAPE is a measure of prediction accuracy of a
forecasting method. Though the value of MAPE is not restricted, a lower value
indicates better accuracy like MAE. It is mathematically expressed as [49]:
1
ˆ100 nt t
i t
Y YMAPEn Y
(39)
where, is the actual wind speed and is the predicted wind speed at t
( ).
3.7.6 Wind Power Density (WPD)
Wind power density 2 ( / )W m describes the ability of the conversion of kinetic energy
into power [51]. Higher wind power density indicates the greater potential of wind
power plant. This could be the initial guiding factor in determining the suitable
regions for the wind power projects. Wind power density can also be stated as the
kinetic energy of the air mass per unit area per second 1A ; 1t . Statistically the
mean wind speed follows Weibull distribution. Wind power density is calculated
mathematically as [51];
31 3 λ 1 2
WPDa
(40)
where, WPD is the wind power density ( / ), ρ is the air density at the site
(1.16 kg/m3).
The months were further grouped in to wet and dry seasons. Wet season usually
starts in November and continues to April of the next year, while drier conditions
occur from May to October. For both the seasons Weibull parameters were obtained
and a goodness of fit test and error analysis was also carried out. It is noted that
values of scale parameter are low during the dry season and high during the wet
season. The Weibull parameters were obtained for both the seasons and the goodness
of fit test and error analysis was also carried out. For the wet season as shown in
Table 5, energy pattern factor method and WAsP method gave the highest value of
tY t̂Y
1,2,...,t n
40
2 R , while median and quartile method gave the highest value of COE while WAsP
method gave the lowest values of RMSE, MAE and MAPE. This indicates that
software WAsP is the better method to estimate the WPD for the overall wet season.
As shown in Table 6 for overall dry season maximum likelihood method gave the
highest value of 2 R , median and quartile method gave the highest value of COE,
WAsP method gave the lowest value of RMSE and empirical method of Lysen gave
the lowest value of MAE and MAPE. This indicates that empirical method of Lysen
is more suitable followed by empirical method of Justus for estimating the WPD for
the overall dry season.
3.8 Estimation of Parameters for Weibull Distribution
Tables (4-6) illustrates the value of the Weibull parameters a and obtained using
the ten different methods and various performance measures using the goodness of
fit and the error estimates COE, RMSE, MAE and MAPE. The ranking in the
performance assessment of the ten proposed methods by using different statistical
indicators are presented in Appendix C. It can be seen from Table 4 that empirical
method of Justus gives the highest value of 2 R , the lowest values of RMSE, MAE
and MAPE and the fourth highest value of COE for the overall period under study.
This indicates that this method is the most suitable for estimating the wind power
density for Anabar.
Table 4. Performance of the Weibull distribution models for the year overall period (2012-2016)
Weibull method
Weibull
Parameters
Mean Wind
Speed
Statistical Test Mean Absolute
Error
Mean Absolute
Percentage Error
λ U WPD R2 RMSE COE MAE MAPE
MLM 2.0204 4.8873 4.3305 89.0542 0.99829 0.09182 0.98358 0.06111 2.85307 LSM 1.9163 4.7728 4.2341 87.8744 0.99317 0.18373 0.93091 0.15657 5.58252 MQ 2.2122 4.8388 4.2854 79.3584 0.98857 0.23762 1.18834 0.12420 3.86577 MM 2.0568 4.9017 4.3422 88.2354 0.99828 0.09214 1.00743 0.04982 2.70631 EPFM 2.0635 4.9007 4.3412 87.8953 0.99830 0.09172 1.01532 0.04665 2.66127 MMLM 1.9810 4.8295 4.2808 87.7378 0.99670 0.12761 0.96711 0.10346 4.10982 WAsP 2.0700 4.9000 4.3404 87.5868 0.99823 0.09344 1.02452 0.04466 2.69410 EMJ 2.0685 4.9008 4.3412 87.6911 0.99832 0.09113 1.02102 0.04379 2.58978 EML 2.0685 4.9033 4.3434 87.8271 0.99824 0.09336 1.02195 0.04576 2.70864 NMO 2.1710 5.5569 4.9212 112.1772 0.93600 0.56237 0.90378 0.52435 13.89253
41
3.9 Performance of the Two-Parameter Weibull PDF Method
The proposed ten Weibull methods are effective in evaluating the parameters of the
Weibull distribution for the available data. However there is a need to search for the
most suitable Weibull estimation method that shall provide an efficient and accurate
evaluation of the available wind energy potential. The proposed ten methods
efficiency were analyzed based on the correlation coefficient 2R and root mean
square error (RSME) in comparison with Coefficient of Efficiency (COE), Mean
Table 5. Performance of the Weibull distribution models for the Wet Season(Overall)
Weibull method
Weibull
Parameters
Mean Wind
Speed
Wind power
Density
Statistical Test Mean Absolute
Error
Mean Absolute
Percentage Error
λ U WPD R2 RMSE COE MAE MAPE
MLM 2.0466 5.2395 4.6418 108.3052 0.99763 0.11431 0.98040 0.09348 3.56292 LSM 1.9494 5.0375 4.4669 101.3374 0.98967 0.23888 0.97394 0.21157 6.49502 MQ 2.2158 5.3094 4.7023 104.6919 0.99633 0.14242 1.08765 0.06368 3.60514 MM 2.0900 5.2579 4.6570 107.2036 0.99760 0.11527 1.00064 0.08309 3.59807 EPFM 2.1083 5.2577 4.6566 106.3103 0.99777 0.11100 1.01701 0.06914 3.38820 MMLM 2.0084 5.1837 4.5936 106.9208 0.99568 0.15445 0.96227 0.13165 4.64786 WAsP 2.1600 5.3000 4.6937 106.4878 0.99777 0.11091 1.05349 0.03818 2.82232 EMJ 2.1016 5.2576 4.6566 106.6245 0.99768 0.11330 1.01155 0.07435 3.46127 EML 2.1016 5.2602 4.6589 106.7812 0.99773 0.11208 1.01121 0.07163 3.38676 NMO 2.1650 5.9209 5.2435 148.1597 0.94025 0.57444 0.89511 0.53052 13.31823
Table 6. Performance of the Weibull distribution models for the Dry Season(Overall)
Weibull method
Weibull
Parameters
Mean Wind
Speed
Wind power
Density
Statistical Test Mean Absolute
Error
Mean Absolute
Percentage Error
λ U WPD R2 RMSE COE MAE MAPE
MLM 2.0555 4.4861 3.9741 67.6830 0.99971 0.10744 0.99027 0.07033 3.16044 LSM 1.8918 4.4476 3.9472 72.1752 0.98973 0.20375 0.85825 0.16702 5.72063 MQ 2.2687 4.4663 3.9562 61.1096 0.98396 0.25459 1.20717 0.10327 3.64515 MM 2.0897 4.4967 3.9833 67.0913 0.99691 0.11180 1.01384 0.05943 2.95870 EPFM 2.0907 4.4970 3.9831 67.0549 0.99690 0.11200 1.01433 0.05931 2.95726 MMLM 2.0100 4.4302 3.9259 66.6919 0.99592 0.12842 0.97363 0.09104 4.00034 WAsP 2.0600 4.5000 3.9863 68.1655 0.99720 0.10646 0.98651 0.06966 3.04947 EMJ 2.1013 4.4972 3.9831 66.7376 0.99673 0.11502 1.02362 0.05589 2.91620 EML 2.1013 4.4994 3.9851 66.8357 0.99675 0.11462 1.02341 0.05584 2.91571 NMO 2.1635 5.0762 4.4955 93.4262 0.93716 0.50395 0.88140 0.45843 12.70901
42
Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Wind power
density and the mean wind speed U analysis in order to determine which of the
Weibull parameter calculation methods yields a better results.
The performance rankings for the ten Weibull distribution models were analyzed
based on the maximum R2 and minimum RSME in comparison with the mean wind
speed and the error analysis. Low RMSE value indicates successful forecasts
whereas high value indicates deviation. The best parameter estimation is disclosed by
the highest value of R2.
It is also observed from the statistical analysis that the values of RMSE and R2 have
magnitudes very close to each other for all the numerical methods considered in this
study.
However for the overall period under study, empirical method of Justus is the most
accurate model followed by energy pattern factor method and the WAsP method
with an average wind power density of approximately 87 W/m2. These three methods
calculated mean wind speed is very close to the overall mean wind speed of 4.34 m/s
at 34 m AGL. The least precise models are the least square method and new moment
method.
The overall seasonal analysis for the wet and dry season indicates WAsP and
empirical method of Lysen respectively is the most suitable method to fit the Weibull
distribution curves for the wind speed data.
Figures (23-30) shows the Weibull distribution described by its relative frequency
versus the mean wind speed for the period under study. It is possible to validate how
the curves representing the Weibull probability density function for the each of the
ten numerical methods considered in the analysis, match with the histograms,
indicating which method may be considered the best fit to the data of wind velocity
collected. When considering moments method as the most accurate Weibull method,
it’s observed that Weibull estimated a value for the overall period under study is
2.068 and the Weibull value is 4.900 m/s. Usual a value for most wind conditions
ranges from 1.500 to 3.000 [29]. The Weibull scale parameters generally determine
the wind speed for optimum performance of a wind energy conversion system and
the speed range over which it is expected to ideally operate.
43
In a study by Rocha et al. [27] for the northeast region of Brazil, equivalent energy
method was found to be an efficient method for determining the scale and shape
parameter using the similar statistical analysis. The study by Kidmo [4] for Garoua,
Cameroon using the similar statistical test revealed that energy pattern factor method
was ranked first followed by method of moment as one of the most accurate method
while modified maximum likelihood method proved to be the most inadequate
method for estimating the Weibull parameters. The winds gave the power densities
between 9.388 and 64.129 W/m2 at a height of 34 m. The study by Chang [22]
revealed that maximum likelihood method provides more accurate estimation of
Weibull parameters in both simulation test and observation data analysis. Energy
pattern factor method performed the best and graphical method performed the worst
according to the study by Werapun et al. [52] on Phangan Island, Thailand in
estimating the Weibull parameters using Kolmogorov-Sminorov test, R2 and RMSE.
The study by Shu et.al [10] revealed that there exists very little difference between
method of moment, the maximum likelihood method and the power density method
in estimating the Weibull parameters while analyzing wind characteristics and wind
potential in Hong Kong. The performance comparison of the proposed methods in a
study by kaoga et al. [29] showed that maximum likelihood method turned to be the
most reliable method in estimating the Weibull parameters for the district of Maroua.
The study at Kanyakumari in India concluded that energy pattern factor method is
the most efficient method for calculating Weibull parameters [19]. It was also
observed from the statistical analysis of the study that the values of R2 and RSME
have magnitudes close to each other. The study on Iran’s cities reveals that the
empirical, modified maximum likelihood and moments methods estimated the wind
speed with minimum error [26]. Method of moment and modified maximum
likelihood method were found to be the best methods for estimating the energy
production of wind turbines.
New moment method introduced in the work of [50] ranked it as a superior method
over other methods. This is based on estimation capability of power density with
exception to the power density error criterion which is based on the difference
between theoretical wind power density and reference mean wind power density. The
study used the initial values for the optimization process from the estimates of the
Graphical method using Matlab program. However in this current study the initial
44
value estimates are taken from moments method and is optimized using R. The
findings contradict with the findings of [50] as this method demonstrated to be one of
the least performing methods.
The study by Chaurasiya et al. [46] on Kayathar, Tamil Nadu India showed that
modified maximum likelihood method was the most efficient method to evaluate
Weibull parameters. The study by aukitino et al. [43] on Kiribati revealed that
moment method was the most appropriate method to determine wind power density
for the equatorial region with an average wind speed of 5.355 m/s and 5.4575 m/s for
the Tarawa and Abaiang site respectively. The studies highlighted above tend to
compliment the findings of the present study at Anabar. It is also noted that the
Weibull distribution models that is suited best to estimate Weibull distributions differ
based on the data set and the area under study. The suitability of the method to some
extend also depends on the statistical test that is used to rank the methods.
3.10 Summary
In this chapter, ten methods of estimating Weibull parameters are proposed. The
performance analysis was also performed on the methods using several goodness of
fit tests. Upon investigation it was found that the empirical method of Justus is the
most accurate method followed by energy pattern factor method and the WAsP
method. These three methods calculated mean wind speed is very close to the overall
mean wind speed. The least precise models are the least square method and new
moment method.
45
Chapter 4
Conclusion
In this project, Weibull parameters and wind power density for Anabar, Nauru are
estimated using ten different methods. The suitability of the different methods to
estimate Weibull parameters may vary with the characteristics of the sample data.
This includes and not limited to sample data size, sample data distribution, sample
data format, and goodness of fit tests. Based on the 5 years wind speed data
measured at 34 m above ground level from September 2012 to June 2016, the aim of
this study was to provide logical analysis to the engineers in determining the wind
power density calculations from any wind energy conversion system.
The following key conclusions can be drawn from the present study:
1. The performance of the ten proposed methods for the estimation of the
Weibull parameters as estimated based on the correlation coefficient 2 R and
root mean square error (RMSE) in comparison with the error analysis.
2. The empirical method of Justus followed by energy pattern factor method and
WAsP are found to be the most efficient method to determine the Weibull
shape and scale parameter at Anabar, Nauru.
3. It is also observed from the statistical analysis that the 2 R and RMSE values
show similar trends for all the methods except the new moment method hence
the other nine proposed method out of the ten are effective in evaluating the
parameters of the Weibull distribution for Anabar.
4. The actual mean wind speed for the overall period (2012-2016) is 4.34 m/s at
a height of 34 m AGL. This wind speed is considered to be reasonably good
due to the fact that Nauru is an equatorial region.
5. The overall turbulence intensities are of order 15% and 20% at 34 m and 20
m AGL respectively. The dominant wind direction in the region is the
easterly trade winds corresponding to the doldrums and the trade winds. The
Wind power density is approximately 87 W/m2.
6. The Weibull probability distribution scale parameters are higher in values
in comparison to the shape parameter a for the overall and the seasonal
distributions.
46
7. There exist some sort of synergy between wind and solar resources. Wind
energy is able to compensate for the lack of solar energy at night while both
are at optimum during day time. This shows that the equatorial region of
Anabar, Nauru shows good potential for future development of solar/wind
hybrid systems.
8. The present work promotes the idea of exploring more on the possibility of
having solar/wind hybrid synergy system for the pacific region to ease the
dependency on diesel based power generation system.
47
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Appendices
Appendix A: Hourly Mean Data
Summary statistics for maximum hourly mean at 34 m
speed34m speed20m speed34SD speed20SD Pressure TempC TempK Solar 1 4.231823 3.398784 0.601904 0.687128 1003.003 26.77327 299.9233 0 2 4.221936 3.387767 0.604606 0.68509 1002.344 26.64994 299.7999 0 3 4.220253 3.388099 0.604655 0.68563 1001.68 26.53908 299.6891 0 4 4.179501 3.361017 0.602223 0.681258 1001.232 26.44698 299.597 0 5 4.187816 3.371727 0.604434 0.680816 1001.097 26.39476 299.5448 0 6 4.240383 3.409776 0.605527 0.683579 1001.275 26.35943 299.5094 0 7 4.278801 3.432351 0.599103 0.682744 1001.691 26.34267 299.4927 2.5115451 8 4.276075 3.445898 0.616618 0.704446 1002.905 27.0505 300.2005 91.441132 9 4.276505 3.534033 0.674785 0.760956 1004.675 28.32638 301.4764 280.04719 10 4.41674 3.755711 0.729661 0.81636 1005.558 29.1043 302.2543 471.68726 11 4.557197 3.946315 0.760575 0.847679 1005.674 29.60189 302.7519 627.10661 12 4.701376 4.103144 0.783726 0.871616 1005.301 29.89444 303.0444 717.30655 13 4.73902 4.151105 0.790764 0.882007 1004.545 30.06415 303.2141 750.33132 14 4.690371 4.106411 0.791096 0.881688 1003.529 30.10481 303.2548 666.96051 15 4.583935 4.010084 0.775031 0.862921 1002.709 30.01129 303.1613 592.37294 16 4.484021 3.896758 0.761398 0.845136 1002.085 29.80053 302.9505 514.19466 17 4.389953 3.768607 0.741403 0.822476 1001.793 29.4723 302.6223 352.7073 18 4.306057 3.629564 0.704491 0.784104 1001.754 28.94448 302.0945 175.95827 19 4.178172 3.440866 0.648134 0.727615 1001.781 27.99808 301.1481 34.236266 20 4.169883 3.379567 0.616043 0.696943 1002.059 27.28401 300.434 0.0893128 21 4.175006 3.3646 0.603314 0.683223 1002.675 27.15684 300.3068 0 22 4.203045 3.394131 0.597958 0.681279 1003.207 27.08173 300.2317 0 23 4.224126 3.411531 0.593825 0.682208 1003.456 26.98506 300.1351 0 24 4.259611 3.431976 0.599303 0.688555 1003.384 26.88397 300.034 0
2012 Hr. 2013 Hr. 2014 Hr. 2015 Hr. 2016 Hr. Overall (2012-16)
Hr.
Speed (m/s)
4.38 13 5.44 12 4.33 13 4.56 14 5.02 13 4.74 13
Temp (oC)
29.99 15 30.29 14 30.39 14 29.84 14 29.76 14 30.11 14
Solar (N/m2)
786.96 13 842.22
13 751.92 13 673.96 13 686.39 13 750.33 13
Pressure (mbar)
1006.02 10 1005.68 11 1005.59 11 1005.52 11 1006.39 11 1005.67 11
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Appendix B: Monthly mean data Month speed34m speed34mSD Pressure TempC TempK Solar 1 January 4.627264 0.696341 1002.292 27.78532 300.9353 201.0703478 2 February 4.986185 0.725006 1001.966 27.77635 300.9264 206.1840585 3 March 5.140009 0.733154 1002.825 27.83696 300.987 207.8494736 4 April 4.547118 0.653461 1003.048 27.78025 300.9302 218.8589757 5 May 4.187293 0.640664 1003.59 28.1558 301.3058 228.7881496 6 June 4.049652 0.638452 1002.585 28.02268 301.1727 200.1574966 7 July 4.295139 0.670346 1003.192 28.06775 301.2178 212.9516629 8 August 4.069722 0.664619 1003.538 27.89372 301.0437 228.0256445 9 September 3.903946 0.630444 1003.446 28.00678 301.1568 244.8942551 10 October 3.503216 0.584747 1003.921 28.06626 301.2163 244.1207897 11 November 4.05535 0.657125 1002.607 28.24844 301.3984 229.5127198 12 December 4.585908 0.704297 1001.81 27.99666 301.1467 209.818846
Appendix C: Performance ranking of the ten methods
Table C-1. Performance ranking of the 10 selected method for the overall period (2012-2016) using different statistical Indicators. Statistical Test
Weibull Method R2 RMSE COE MAE MAPE Average
Ranking Overall Ranking
MLM 3 3 6 6 6 4.8 6 LSM 8 8 9 9 9 8.6 9 MQ 9 9 1 8 7 6.8 7 MM 4 4 6 5 4 4.6 5 EPFM 2 2 5 4 2 3 2 MMLM 7 7 8 7 8 7.4 8 WAsP 6 6 2 2 3 3.8 3 EMJ 1 1 4 1 1 1.6 1 EML 5 5 3 3 5 4.2 4 NMO 10 10 10 10 10 10 10
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Table C-2. Performance ranking of the 10 selected method for the wet season overall using different statistical Indicators.
Statistical Test
Weibull Method R2 RMSE COE MAE MAPE Average
Ranking Overall Ranking
MLM 5 5 7 7 5 5.8 6 LSM 9 9 8 9 9 8.8 9 MQ 7 7 1 2 7 4.8 5 MM 6 6 6 6 6 6 7 EPFM 1 2 3 3 3 2.4 2 MMLM 8 8 9 8 8 8.2 8 WAsP 1 1 2 1 1 1.2 1 EMJ 4 4 4 5 4 4.2 4 EML 3 3 5 4 2 3.4 3 NMO 10 10 10 10 10 10 10
Table C-3. Performance ranking of the 10 selected method for the dry season overall using different statistical Indicators. Statistical Test
Weibull Method R2 RMSE COE MAE MAPE Average
Ranking Overall Ranking
MLM 1 2 6 6 6 4.2 6 LSM 8 8 10 9 9 8.8 9 MQ 9 9 1 8 7 6.8 7 MM 3 3 5 4 4 3.8 4 EPFM 4 4 4 3 3 3.6 2 MMLM 7 7 8 7 8 7.4 8 WAsP 2 1 7 5 5 4 5 EMJ 6 6 2 2 2 3.6 2 EML 5 5 3 1 1 3 1 NMO 10 10 9 10 10 9.8 10