Wind Energy Resource Assessment Methods

2 Wind Energy Resource Assessment Methods AYODELE TEMITOPE RAPHAEL1*

ABSTRACT

In this chapter, various methods for analyzing wind power potential and the expected wind energy of a candidate site are presented. The practical application of the methods are given and compared. The advantages and disadvantages of each method are pointed out. Also in this chapter, the motivations for wind energy resource exploitation for electricity generation are briefly discussed. The importance of wind speed measurement campaign and subsequent assessment of the data obtained from such exercise for the success of wind power project is highlighted. An overview of global wind resource in terms of total cumulative installed capacity, regional capacity and the emission saving due to increasing installed capacity are discussed. Key words: Assessment methods, Continuous distribution, Wind power density, Wind energy resource, Wind turbines, Wind speed. 1. INTRODUCTION

Wind is the prime mover of every wind turbine. Any small change in wind speed produces large changes in the output power of wind turbines. For example, a double increase in the wind speed increases the energy production of wind turbine eight times. Therefore, accurate knowledge of the wind resource of every local site is important at each and every stage of the development of a wind power project, i.e., from initial site selection through to operation. Once the wind speed on the site has been estimated, it is then necessary to make an accurate and reliable estimate of the resulting energy production from the potential site. This requires wind farm modelling and 1

Electrical and Electronic Engineering Department, Faculty of Technology, University of Ibadan, Nigeria *Corresponding author: E-mail: [email protected], [email protected]

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Energy Sci. & Tech. Vol. 8: Wind Energy

detailed investigation of the environmental and ownership constraints (Fact_sheet, 2011). The wind resource of a local site is usually expressed as a wind speed or energy density and typically, there is a cutoff value above which a wind farm development is feasible. The wind energy resource at a site has considerable impact on the amount of energy that is extractible by the wind turbines, which form the basis of any wind power project. Assessment of wind energy resource is the evaluation of the possibility of employing wind resource for power generation and subsequent estimation of the energy production of the site. The amount of wind resource is primarily quantified by the mean wind speed at the site, although the turbulence intensity, probability distribution of the wind speed and prevailing wind direction are also important factors (Lackner et al., 2007) 2. MOTIVATIONS EXPLOITATION

FOR

WIND

ENERGY

RESOURCE

The main motivations for wind energy resource exploitation for electricity generation are due to environmental issue, reliability of energy supply and the job opportunity.

2.1. Environmental Issue Energy has been the major driving force for technological development of mankind. As the world population grows, so also the demand for energy. The conventional generating systems make use of fossil fuel (coal, gas and oil) as input to the boiler through combustion. The by- products of the combustion (CO, NOx and SOx) are major causes of environmental pollution which is detrimental to both human and animal health. The carbon dioxide (CO2) emitted during combustion has been identified as the main cause of global warming which result in undesirable climate change. Wind energy provides an opportunity to mitigate these environmental consequences of energy use.

2.2. Security of Energy Supply Security of energy supply is another global concern. The energy crises that threatened the energy security in the early 1970s shifted research attention to renewable energy generation where energy from wind energy proved to be sustainable. Most of the oil reserves are located at the politically unstable regions, where incessant crises threatened the security of energy supply (Dincer, 2000) and therefore necessitates the need for diversification. Wind energy provides the solution because it is abundantly available in all regions of the world.

Wind Energy Resource Assessment Methods

31

2.3. Employment The development of wind energy in the past decade sprang up industries in the area of wind energy technologies such as generators, power electronics and turbines. These foster export market and creates a lot of job opportunities. The lending of land for wind farms has boosted economic activities in the rural areas. 3. IMPORTANCE OF WIND ENERGY RESOURCE ASSESSMENT

Knowledge of wind resources and wind characteristics of a potential site is important and relevant in the areas of wind turbine design, performance evaluation of wind turbines, determination of appropriate location for siting the wind turbines and the operational management of the turbines (Manwell et al., 2002)

3.1. Wind Turbine Design This involves having adequate knowledge of average wind conditions, as well as information on the turbulent nature of the wind. The knowledge of wind turbulence of a given site is necessary for cost optimization of modern large wind turbines (Hansen and Chr. Larsen, 2004) and crucial for the design of support structures for wind turbines (Jacquemin et al., 2007; Turk and Emeis, 2010). It helps in the design of appropriate control system that can mitigate the impact of structural loading on wind turbine due to turbulent wind.

3.2. Performance Evaluation of Wind Turbines This reflects how effectively the turbine could harness the energy available in a mass of moving air. How consistently the wind blows above the rated wind speed for a given turbine will determine how often the turbine will be operating at its maximum rated power generation capacity. Performance evaluation requires determining the expected energy productivity of a particular wind energy system based on the wind resource. It therefore serves as a vital index for evaluating the economic viability of a wind power project.

3.3. Determination of Appropriate Location This involves the ability to measure and predict the available wind resources at a particular site in determining whether the location is suitable and economically advantageous for siting wind turbines. Significant variations in seasonal average wind speeds are common and affect a local area’s available wind resources over the course of a year. To accurately predict

32


capacity factors and maintenance requirements for wind turbines, it is important to understand wind characteristics over a long and short time scales.

3.4. Operational Management of Wind Turbines The ability to accurately predict hourly wind speed variations is important for utilities to be able to properly plan their energy resource portfolio mix (wind energy with other sources of energy). Operational requirements include the need for wind resource information that can be used for load management, operational procedures (such as start-up and shutdown) and the prediction of maintenance or system life (Manwell et al., 2002). Experience over the years has shown that there are significant variations when considering wind characteristics from year to year, season to season, month to month, day to day, hour to hour and even second to second. In view of this, it is necessary to gain the full knowledge of the characteristics of a local wind regime at different time scales for a successful wind power project. 4. GLOBAL WIND RESOURCE AND WIND POWER POTENTIAL

The earth receives a total solar radiation of 1.58 billion TWh/yr which corresponds to an average of 350 W/m2 over the earth’s surface (Redlinger et al., 2002). Only a small part (3–5% of incoming radiation) is converted into the kinetic energy of the moving atmosphere through the generation of global, regional and local temperature differences, forming the basis for the world’s wind energy resource. Only a minute fraction of this kinetic energy in the moving air can be theoretically captured as useful wind energy. Nevertheless, the theoretical global potential for extracting energy from the wind farm exceeds the world’s total energy consumption. In comparison, global annual electricity consumption is on the order of 1.5 TW-yr/yr while the exploitable potential is in the order of 6 TW-yr/yr (Redlinger et al., 2002). This represents approximately four times the current global electricity consumption. Over the past few years, wind energy has shown remarkable rate of growth of any form of electricity generation with its development stimulated by concerns over climate change, energy diversity and energy security (Anaya-Lara et al., 2009). Fig. 1 depicts the annual and cumulative global wind power between 1996–2010 (GWEC, 2011). The figure reveals an exponential increase in global wind power installation with Europe leading other regions of the world with 84,074 MW installed capacity and Africa being the least region in terms of wind power installed capacity as shown in Fig. 2. According to IEA projection on wind power share of global electricity demand, wind power will continue to contribute to the total global energy


33

Fig. 1: Global annual and cumulative installed capacity (1996-2010) (MW)

Fig. 2: Global annual and cumulative installed wind capacity for different region (MW)

mix. According to the moderate scenario research reported in Global Wind Energy Outlook (GWEO) 2012, wind power contributed about 3.5% to the total global electricity generation mix in 2011 and the trend is expected to increase as shown in Fig. 3. This will curb emission growth and create a more sustainable energy future. Wind power has many environmental benefits, including the elimination of local air pollution and near zero water consumption. However, the greatest benefit is wind power contribution in reduction of CO2 emissions from the power sector, which is the single largest contributor to the global climate change problem (GWEO 2012). The research conducted on projected CO2 saving up to 2030 based on moderate scenario and reported in (GWEO 2012) implies cumulative savings of over 1.1 billion tonnes of CO2 by 2020 and more than 2.5 billion tonnes by 2030. Fig. 4

34


Fig. 3: Percentage wind power share of global electricity demand (IEA demand projection)

Fig. 4: GWEO projected annual and cumulative CO2 emission reduction

depicts both the projected annual and cumulative CO2 that is expected to be saved up to 2030 (GWEO 2012). 5. WIND SPEED MEASUREMENTS METHODS

Uncertainties in the prediction of a recoverable wind power from potential sites depend on the quality of the data for the wind resource and for the wind turbine’s power curve (Redlinger et al., 2002). There are two main methods identified for wind resource assessment: on-site measurement and micro-siting model which can estimate the spatial distribution of the wind resource over the entire area. Fig. 5 depicts the flow chart for data collection.


35

Fig. 5: Data collection method flow chart

5.1. On-site Measurement The best, most accurate, indication of the wind resource at a site is through on-site measurement using an anemometer. This is, however, a fairly costly and time consuming process. Instrument system for wind measurement can be viewed in three categories (Manwell et al., 2002): instruments used by national meteorological services, instruments designed specifically for measuring and characterizing the wind resource of a candidate site and instruments specially designed for determining gust, turbulence wind information for analyzing wind turbine response (this usually have high sampling rates compared to the other two). Most wind instruments basically consist of anemometers to measure wind velocity, wind vanes to measure wind direction, thermometers to measure the ambient air temperature and barometers to measure the air pressure. Fig. 6 shows a typical arrangement of instruments used for wind measurement. Once the data

36


Fig. 6: On-site measurement using mast

are obtained from the measuring instrument, the data can be analyzed in various ways. Some of the information that can be obtained from such analysis involves mean horizontal wind speeds over specified time intervals, variations in the horizontal wind speed over the sampling intervals (such as standard deviation, turbulence intensity, maximums and minimum horizontal wind speed), average horizontal wind direction, variations in the horizontal wind direction over the sampling intervals (standard deviation), speed and direction distributions, wind persistence, determination of gust parameters, statistical analysis including autocorrelation, power spectral density, spatial and time correlations with nearby measurements. Other important information that can be obtained from the measuring instruments includes diurnal, seasonal, annual power density and energy potential.

5.2. Micro-Siting Model Micro-siting model such as wind atlas modeling method is a comprehensive set of models for horizontal and vertical extrapolation of wind speeds, measured at a meteorological station (Redlinger et al., 2002) such as airport for estimation of wind resources at a nearby wind farm site. This model is based on physical principles of flows in the atmospheric boundary layer and they take into account terrain roughness, disturbance effects due to buildings and other obstacles and orography (terrain height variations such as hills). Terrain characteristics and their friction coefficients that are commonly adopted in micro-siting model are furnished in Table 1. Terrain roughness is often standardized and classified into roughness as depicted in Table 2.

5.3. Classification of Sites for Wind Power Generation The National Renewable Energy Laboratory (NREL) located in Colorado, United States, gave the standard classifications in which power density of a


37

Table 1: Friction coefficient Friction co-efficient ()

Terrain characteristics Smooth hard ground, calm weather Tall grass on level ground High cops, hedges, and shrubs Wooded countryside, many trees Small town with trees and shrubs Large city with tall buildings

0.10 0.15 0.20 0.25 0.30 0.40

Table 2: Roughness classes Roughness class 0 1 2 3 4

Description

Roughness length [z (m)]

Water surface Open areas with a few windbreaks Farm land with some windbreaks more than 1 km apart Urban districts and farm land with many windbreaks Dense urban or forest

0.0002 0.03 0.1 0.4 1.6

site can be compared for the purpose of wind power generation. The standards are given at 10 and 50 metres anemometer heights as depicted in Table 3 (NREL, 2011). From the table, wind power can be categorized into seven classes according to the wind speed (m/s) and wind power density (W/m2). Each wind power class corresponds to two power densities. For example, wind power class 3 represents the wind power density range between 150 and 200 W/m2. Table 3: Wind power class Wind power

At a height of 10 m (33 ft)

class

Wind speed (m/s)

1 1–2 2–3 3–4 4–5 5–6 6–7 7

0 4.4 5.1 5.6 6.0 6.4 7.0 9.4

Wind power density (W/m2) 0 100 150 200 250 300 400 1000

At a height of 50 m (164 ft) Wind speed (m/s) 0 5.6 6.4 7.0 7.5 8.0 8.8 11.9

Wind power density (W/m2) 0 200 300 400 500 600 800 2000

The most suitable sites for wind turbine siting are the turbulence-free locations. Wind turbulence is influenced by the surface of the earth and affects overall stability of the turbine which makes wind turbines less efficient (Khaligh and Onar, 2010). Wind can be more or less turbulent depending on the roughness of the terrain. There are roughness classes, which explain the relationship between wind speeds and landscape conditions.

38


Roughness class varies from 0 to 4, where class 0 represents water surfaces and open terrains with smooth surfaces and class 4 represents very large cities with tall buildings and skyscrapers. Two key parameters regarding the different geographical locations affect the wind turbine siting: the friction coefficient and the roughness classification (Khaligh and Onar, 2010). 6. WIND ENERGY ASSESSMENT METHODS

The first step in the assessment of wind power potential of a given site is the collection of wind speed data and its direction. Once this is done, there are four basic methods in estimating the wind energy potential of the site: direct data usage method, the bin method, velocity and power curve method, statistical method.

6.1. Direct Data Usage Method Given n wind speed i average over a short time interval t. The long-term average wind speed over the total period of data collection can be calculated by (1) and its variance can be determined as (2).

E( vi ) 

var( vi ) 

1 n   vi n  i 1 

1 n 2   vi  E( vi )    n  1  i 1 

(1)

(2)

The average wind power density, E(P/A) which is the average available wind power per unit area, can be estimated as (3)

E  P A 

1 1 n 3  .  vi 2 n i 1

(3)

Therefore, the average wind energy density per unit area E(Q/A), for a given period of time t, can be expressed as (4) where  is the air density.

E( Q A ) 

1 n 3   vi  E  P A  .( N t ) 2 i 1

(4)

6.2. Bin or Interval Method The bin or interval method can be used to summarize wind data and to determine expected turbine productivity (Manwell et al., 2002). In this case the data are separated into the wind speed intervals known as bins in which it occurs. For convenience, it is necessary to use the same size of bins. Consider wind speed data separated into qb bins of width ki, with mid-point


39

mi and frequency fi. This method involves plotting of histogram (bar graph) showing the number of occurrences and bin widths. The number of occurrence in each interval can be determined as (5). qb

N   fi i 1

(5)

The mean wind speed of this method can be determined as (6) and the variance as (7), respectively.

E( vi ) 

Var(vi ) 

1  qb   mi . f i  n  i 1 

2 1  qb 2  1 qb     mi fi  N   mi f i   N  1  i 1  N i 1   

(6)

(7)

The average power density can be expressed as (8) while the average energy density can be estimated as (9).

E  P A 

1 1 qb 3   mi fi 2 n i 1

qb qb  1 qb  E  Q A     E  Q A  .t       mi3 f i .t  i 1 i  1  2 i 1 

(8)

(9)

6.3. Velocity and Power Duration Curve Method The information about the nature of the wind regime at a potential site can be revealed by velocity duration curve. It is particularly useful when it is necessary to compare the wind power potential of different sites. The curve can be obtained by plotting the wind speed (y axis) against the number of hours in the year for which the speed equals or exceeds each particular value of wind speed (x axis) (Manwell et al., 2002). The flatter the curve, the more stable the wind speeds. The steeper the curve, the more irregular is the nature of the wind speed at the site. A power duration curve can be obtained from a velocity duration curve by cubing the wind speed (y axis), which is proportional to the available wind power for a given rotor swept area (Manwell et al., 2002). The areas under the power duration curves are proportional to the annual energy available from the wind at the site. The curve can help compare at a glance the wind power potential of local wind regimes. The power duration curve together with a specific wind turbine power curve can be combined to obtain another important curve known as wind turbine productivity curve. The productivity curve can give an approximate idea on the losses in energy production, i.e., the curve can

40


help reveal the difference between the available wind power of a given site and the actual wind power that can be captured by the wind turbine. Velocity duration curve of four different sites in the coastal region of South Africa is depicted in Fig. 7, while Fig. 8 presents the power duration curve of the sites. From the plot, it is easy to compare the energy potential of the sites. Therefore, it can be concluded from Fig. 8 that Napier presents the best site for wind power application of all the sites.

Fig. 7: Velocity duration curve for different sites in the coastal region of South Africa

Fig. 8: Power duration curve of four sites in the coastal region of South Africa

6.4. Statistical Methods Another important method that can be employed in estimating the wind power potential of a given site and in evaluating the wind energy extractible from the site is the statistical method. This technique is important especially for the locations where enough data are not readily available or only


41

summary data are obtained. The method can also be employed when projection of measured data from one location to another is required. It is also useful when data are not observed at the right height and needed to be extrapolated. Statistical methods rely on the use of probability density function f(i) of wind speeds (i). Once the empirical data are available, an empirical curve fitting approach could be used to determine the constant parameters of the best statistical distribution that best fit the wind speeds (Li, 2011). The challenge is to determine the most suitable continuous statistical distribution. The mean power density E(P/A) can be determined as (10) once the statistical distribution f(i) is known.

E  P A 

1  3   vi f (vi )dvi 2 0

(10)

It should be noted that f(i) could be Weibull, Rayleigh, Lognormal, Logistic, Generalised Extreme Value Distribution, etc. The average energy density can then be determined as (11).

 A .t  21   v

E Q A  E P

 0

3 i

f (vi )dvi .t

(11)

Weibull and Rayleigh distributions are the most adopted statistical distributions for the estimation of wind power density. This is because they are found to fit wind speeds in many regions of the world. However, it has been revealed that statistical distribution that fits wind speeds differs with regions and may not necessarily be Weibull or Rayleigh distributions (Ayodele and Ogunjuyigbe, 2013) as shown in Table 4. It is therefore imperative to Table 4: Examples of statistical distribution fit in different region of the world Sl no.

Region of the world

1

Sistan, South-East of Iran

2

6

llundain and Estella, Northern region of Spain Eastern Malaysia Darling city, South Africa Jeffrey Bay, Eastern Cape, South Africa Maltese Island

7

Silchar Assam, India

8

Mullinger, Belmullet, Coastal region of Ireland

3 4 5

Best fit statistical distribution Normal distribution (Haghifam and Omidvar, 2006). Lognormal distribution (Eskom, 2009) Burr distribution (Najid et al., 2009) Rayleigh distribution (Olaofe and Folly, 2012) Generalised Extreme value distribution (Ayodele, 2012) Logistic distribution (Scerri and Farrugia, 1996). Weibull distribution (Gupta and Biswas, 2010) Extreme value distribution (Jamdade and Jamdade, 2012)

42


determine which of the statistical distribution adequately describes the wind speed of a particular location as it serves as a prerequisite in estimating the expected power output for economic viability of a wind power project (Ayodele et al., 2012; Ayodele et al., 2013; Ayodele and Ogunjuyigbe, 2013).

6.5 Common Statistical Distribution for Fitting Wind Speeds Several continuous statistical distributions exist; the common ones that are found in literature to fit wind speed in different parts of the world are briefly highlighted in this section. 6.5.1. Weibull distribution The Weibull probability density function (pdf) for representing the Weibull distribution can be expressed by (12).

W ( v ) 

  v k  k  v k 1     exp   cc  c   

(12)

where fW() is the probability of observing wind speed, . Weibull shape and scale parameters are denoted by k and c, respectively. k is dimensionless and indicates the peak of the wind distribution of the site under consideration, c has the unit of wind speed (m/s) and indicates how windy the site is. The cumulative distribution function (cdf) is expressed as (13).

 v k   FW  v   1  exp       c   

(13)

There are various methods that can be used to evaluate the value of k and c. These include the graphical method, the Justus empirical method (Justus, 1978), the moment method, the maximum likelihood (Santhyajith, 2006) and Lysen empirical method (Lysen, 1983). 6.5.1.1. The graphical method The double logarithm of equation (13) yields equation (14). ln   ln  1  FW  v     k ln  v   k ln  c 

(14)

A plot of ln   ln 1  Fw  v    against ln  v  results in a straight line ( y  mx  b ). The gradient (m) of the line gives the value of k and the intercept


43

(b) on the axis will yield – k ln (c). Hence, k and c can be graphically determined as k = m and c  e



b k

.

6.5.1.2. Justus empirical method The Weibull parameters can be estimated once the average wind speeds,

E( vi ) and the variance of the wind speeds, var(vi) as expressed in equations (1) and (2) respectively are known. The Weibull parameter and the average wind speed are related by equations (15) and (16) (Lu et al., 2002; Gupta and Biswas, 2010).

 var(vi )  k    E(vi )    c where (17).



1.086

(1  k  10)

E(vi )  1 1



k

(15)



(16)

(.) is a gamma function and it has the properties of equation

  x     x 1 exp    d  ,  x   x x  0

(17)

Gamma function can be approximated as (18) (Jamil, 1994)



  

1

1

139



   ......  (x)  2 x x x 1 e  x 1   12 x 288 x 2 51840 x 3 

(18)

6.5.1.3. Maximum likelihood method The maximum likelihood method has been used to estimate the shape parameter (k) and the scale parameter (c) by solving equations (19) and (20) iteratively. Where n is the total number of wind speeds and vi is the ith value of measured wind speed.

-1 n  n  k   v ln  vi   ln  vi    i=1 i  k= - i=1  n n   k   vi   i=1 

(19)

44


1 1 n k k c =   vi   n i 1 

(20)

6.5.1.4. Lysen empirical method The Justus Empirical method makes use of gamma function to evaluate the scale parameter (c). This function was difficult to approximate before the advent of computer. Therefore, another method of evaluating the scale parameter was proposed (Lysen, 1983) as (21).

0.433   c  E(vi )  0.568   k  

1   k

(21)

Where k is the shape parameter determined by equation (15). 6.5.2. Rayleigh distribution The probability density function and the cumulative distribution function for the Rayleigh model are given by equations (22) and (23) respectively (Manwell et al., 2002).

R( v ) 

k    exp     v    4  Vm   2  V 2   m    



v

k   v    FR  v   1  exp    4  Vm    

(22)

(23)

Where k = 2 for the Rayleigh distribution. Rayleigh distribution is simple, compared to Weibull distribution in that only the knowledge of c is required unlike the Weibull distribution that requires both the knowledge of k and c. One major advantage of the Rayleigh distribution is that both the  R  v  and FR (v) can be obtained from the mean value of the wind speed. 6.5.3. Lognormal distribution Lognormal distribution finds application in many fields such as agriculture, entomology, economics, geology, quality control, etc. It has been found to


45

be a good competitor in live testing and probability studies (Zaharim et al., 2009). The probability density function and the cumulative distribution function are expressed as equations (24) and (25).

 LN ( v ) 

1 v 2

F v  

exp

(ln v   )2 2 2

1  ln v    erfc    2   2 

(24)

(25)

where v  0 is the wind speed (m/s),  > 0 is the lognormal shape parameter,  > 0 is the lognormal scale parameter and erfc (..…) is the complementary error function. Once the mean, E(vi) and the variance, var(vi) of the observed wind speed, vi are calculated using equations (1) and (2) respectively, then  and µ can be estimated as (26) and (27).



  ln  1   

1 2

 var( vi )  E[ vi2 ] 



  ln vm  ln  1   

(26)

 var( vi )  E( vi2 ) 

(27)

6.5.4. Logistic distribution Logistic distribution has the shape of normal distribution but with heavier tail, i.e., higher kurtosis. It has been found also that this distribution fits wind distribution in some part of the world (Scerri and Farrugia, 1996). The pdf and the cdf of this distribution can be expressed as (28) and (29) respectively.

 LGS( v ) 

 v   exp    s     ( v  )   s  1  exp    s    

FLGS  v  

1  v   1  exp    s  

2

(28)

(29)

46


where is the location parameter and s is the scale parameter of the distribution. Both parameters can be evaluated using equations (30) and (31) respectively.

  vm s

(30)

3 2

(31)

2

6.5.5. Generalized extreme value distribution The generalized extreme value is a family of continuous probability distributions developed within value theory to combine the Gumbel, Frechet and Weibull families. The probability density function for the generalized extreme value distribution with location parameter  , scale parameter  and shape parameter   0 is given by (32) (Kotz and Nadarajah, 2000). 1   TI       1   f ge (TI ,  0 )    exp    1          

For

1

1  1 (TI   )      1      

(32)

TI     0 

  0 is the type II case and it correspond to distribution whose tail decreases as a polynomial.   0 is the type III case and it correspond to distribution whose tail are finite. When   0 , then it is a type I case and its density function can be written as (33). It correspond to distribution whose tail decreases exponentially.

  T     (TI   )  1 f ge (TI ,  0 )    exp   exp  I           

(33)

Type I, II and III are sometimes referred to as Gumbel, Frechet and Weibull types respectively. The Cumulative distribution functions for   0 and   0 can be expressed as (34) and (35) respectively. 1   TI         Fge (TI ,  0 )  exp    1        

    

(34)


47

  T      Fge (TI ,  0 )  exp   exp  I       

(35)

6.5.6. Extreme value distribution Extreme value distribution is also referred to as the Gumbel distribution. It is found to fit wind speed in some regions of the world (Jamdade and Jamdade, 2012). The probability density function is given as (36).

f( EV ) 

1



 v    v    i   i     e   ee

(36)

The cumulative distribution function can be written as (37).

F( EV )  e

 v    i  e   

(37)

where  is the location parameter and  is the scale parameter. The two parameters can be estimated using method of moment methods as (38) and (39).



6 . var(vi )



  E(vi )  0.5772 

(38) (39)

7. APPLICATION OF WIND ENERGY RESOURCE ASSESSMENTS METHODS

The four resource assessment methods discussed earlier were applied to wind speed of Napier in order to determine the wind power and wind energy extractible from the site. The aim is to first determine both the wind power and energy density of the site using the four methods and then later compare the methods. These methods are direct data usage method, bin or interval method, power duration curve method and the statistical method. Napier is located on latitude 34° 36' 41.6'' S and longitude 19° 41' 30.3'' E in the coastal region of South Africa. The wind speed data are a ten-minute average data observed at the anemometer height of 60 m for a period of one year and are obtained from CSIR under the Wind Atlas of South Africa (WASA) project. Before the wind data were applied, it were first converted to hourly average by finding the average of six successive numbers of ten-minute average wind speeds. This was achieved by writing a program to execute this purpose in MALAB environment. It should be noted that the air density for this site is taken to be 1.225 kg/m3.

48


7.1. Direct Data Usage Method Using equations 1-4, the wind power density and the energy density of Napier was calculated. The result as depicted in Table 5 shows that the wind power density is 691.55 W/m2 and the energy density is 6.01 MWh/m2/ annum. n denotes number of one hour average wind speed for a period of one year. Table 5: Direct data usage method Quantity

Value

Mean wind speed

E( vi ) 

8.73 m/s

1 n   vi n i 1 

Wind power density

E  P A 

Variance of wind speed

var( vi ) 

Quantity

16.78 m/s

1  2   vi  E( vi )  n  1 i 1  n

691.55 W/m2

1 1 n 3  .  vi 2 n i 1

Wind energy density

E( Q A ) 

Value

1   vi3 t 2 i 1 n

6.01 MWh/ m2/annum

t  1hr

7.2. Bin or Interval Method The wind speed of Napier was separated into bins. Thereafter, the midpoint of each bin, the frequency of occurrence of each bin and the wind energy density for each bin were determined as shown in Table 6. From the Table 6, the wind energy density per annum is calculated as 5.9 MWh/m2/annum while the wind power density for the site is estimated as 674.2 W/m2 when equation (8) is applied. Fig. 9 depicts the histogram representation of the wind speed.

7.3. Statistical Method Using the statistical method, the appropriate wind distribution for the site must first be determined. In view of this, the continuous statistical distributions discussed in subsection 6.5 are tested. The result is depicted in Fig. 10. Three goodness of fits are used to determine the most suitable statistical distribution to be used for the estimation of wind power potential. These are: Coefficient of determination (R2), chi square test (  2 ) and Root Mean Square Error (RMSE). They are as given by equations 40, 41 and 42 respectively. The criteria are determined as follows: the closer the value of R2 to 1, the better the fit to the actual variables. Similarly, the lower the value of and RMSE, the better the goodness of fit.


49

Table 6: Wind power density using bin or interval method

i

Wind speed separated into

Mid-point mi (m/s)

Number of occurrence in

bin (m/s) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10 10–11 11–12 12–13 13–14 14–15 15–16 16–17 17–18 18–19 19–20 20–21 21–22 22–23 23–24 24–25

Wind energy density for each bin (kWh/m2)

each bin fi 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50 8.50 9.50 10.50 11.50 12.50 13.50 14.50 15.50 16.50 17.50 18.50 19.50 20.50 21.50 22.50 23.50 24.50

t  1hr

E  Q A each bin 

21 210 392 570 647 689 820 826 811 739 568 533 478 415 369 267 183 105 68 31 13 2 1 0 0

0.0016 0.4341 3.7516 14.9687 36.1117 70.2123 137.9304 213.4371 305.0589 388.0801 402.7377 496.5087 571.8262 625.3966 689.0274 608.9932 503.5111 344.6748 263.7122 140.7899 68.5979 12.1745 6.9768 0 0

 1 qb 3    mi fi .t  i 1  2 i 1  qb

The total energy density at the site  

1 2

Wind power density E  P A     .

   2 R    N  

5904.9 kWh/m2/annum

1 n 3  vi , where n = 8760. 674.2 W/m2 n i 1 

  ƒ     ƒ      n   ƒ  -   ƒ  

N  ƒ(vi ) ƒ(U ) _

  ƒ   -   ƒ 2 vi

1  mi3 fi t 2

2

vi

vi

(U )

2 ( U)

( U)

   2     

2

(40)

where f(vi) is the actual wind power distribution and f(U) is the statistical distribution of interest which could be any of Weibull, Rayleigh, lognormal, logistic, Generalised Extreme value and Extreme value distributions.

50


Fig. 9: Histogram representation of wind speed

Fig. 10: Plot showing the fitting of statistical distribution with the actual data N

2 

 y  x  i

i

(41)

i 1

N n

where xi is the ith actual wind speed, is the ith predicted wind speed from any of the distribution functions of interest. Also, N is the number of the wind speed dataset and is the number of constant wind speed data.

1 RMSE(%)   N

  ƒ( U)  N

i 1



ƒ(vi )

1 2  2

  

(42)

The results of the performance evaluation are furnished in Table 7. Table 7 reveals that Weibull distribution provides the best fit. Therefore, in determining the wind power density and the energy density, Weibull distribution is employed.


51

Table 7: Performance evaluation criteria for determining the best fit statistical distribution Distribution Weibull Rayleigh Lognormal Logistic Generalised extreme value Extreme value

R2

2

RMSE

0.98 0.92 0.84 0.89 0.96 0.78

0.0013 0.0032 0.0063 0.0041 0.0018 0.0081

0.0063 0.0093 0.026 0.011 0.0078 0.031

The Wind power density using statistical method can be calculated by substituting equation (12) into (10) as (43) and (44). 

E(P/ A)  21   vi3 W ( v )dv

(43)

 k  v k 1   v k    E(P/ A)  21   v 3    exp       dv cc 0   c    

(44)

0

When equation (44) is integrated and re-arranged, then equation (45) is obtained.

 

   

 3 3   1 k 1 E( P / A )    E  vi    3 2  1 1 k 

(45)

Equation (45) can be re-written as (46)



E( P / A )  1 c 3  1  3 k 2 where

c

E(vi )  1 1



k



(46)



k and c are the Weibull shape and scale parameter, respectively,  (…..) is the gamma function and has the properties of (17). The parameters can be determined by any of the graphical methods, Justus empirical method, maximum likelihood method and Lysen empirical method. The energy density can be estimated as (47)



E(Q/ A )  1 tc 3  1  3 k 2



(47)

In order to determine the wind power density and the energy density of the site, it is required to determine the Weibull parameters. Any of the four methods discussed in sub-section 6.5.1.1–6.5.1.4 can be used to

52


determine the parameters. The results obtained from the four methods are presented in Table 8. Fig. 11 depicts the linear plot used to determine the Weibull parameters when graphical method is used. Table 8: Determination of Weibull parameters Graphical Justus empirical Maximum likelihood Lysen empirical k c

2.22 9.51

2.24 9.85

2.23 9.86

2.24 9.86

The shape and scale parameters in Fig. 11 are estimated as (48) and (49) respectively.

km

y2  y1 0  4   2.22 x2  x1 2.3  0.5 ce



b k

 9.51

m/s

(48) (49)

It is generally believed that the maximum likelihood method is superior compared to other methods (Seguro and Lambert, 2000) for time series wind speed data. From the table however, it can be observed that Justus and Lysen empirical methods are as accurate as the maximum likelihood method in determining the Weibull parameters. The power density is therefore calculated as 694 W/m2 and the energy density as 6.23 MWh/m2/ annum (using equations 46 and 47, respectively).

7.4. Velocity and Power Duration Curve Velocity and power duration curves are good at comparing the best candidate site among various potential sites for wind power project. However, it seems it over estimate the energy yield from the site compared to other methods. Estimation of the power duration curve (i.e. area under the curve) depicted in Fig. 12 reveals that, the energy yield of Napier is approximately 9.8 MWh/m2/annum.

7.5. Comparison of the Wind Energy Assessment Methods Table 9 presents the summary results obtained when the four wind energy resource assessment methods are applied to the wind data of Napier. The aim is to allow comparison of the results using the methods at a glance. The table shows that the difference in the results presented by direct data usage method, bin or interval method and statistical method differ from one another by less than 3%. However, the power duration curve present an over estimated result compared to other methods.


53

Fig. 11: Graphical method of determining Weibull parameters Table 9: Comparison of wind energy assessment methods as applied to the wind data of Napier S/N Wind energy assessment methods 1 2 3 4

Direct data usage Bin or interval Statistical Velocity and power duration curve

Wind power density (W/m2) 691.6 674.2 694.0 –

Wind energy density (MWh/m2)/annum 6.01 5.91 6.23 Approximately 9.8

8. CONCLUSIONS

Accurate knowledge of the wind resource of every potential site is vital to the development of any wind power project. In view of this, the wind

Fig. 12: Power duration curve for Napier

54


assessment methods for determining the wind power potential and the energy density of a given site has been presented. The study shows that there is no significant difference (less than 3%) between direct data usage method, bin or interval method and statistical method. However, direct data usage method and bin or interval method is simpler to use but requires the full knowledge of the wind speed data of the site. The statistical method is mathematically rigorous but does not require the full knowledge of the wind speed of the site. This method is suitable where wind speed data are not readily available especially in the developing countries. All it requires is the wind speed distribution function that best describes the wind speed of the site and its parameters. The velocity and power duration curve method can help reveal the best candidate site among many potential sites but may not be suitable in estimating the expected wind energy yield as it tends to overestimate the energy potential of a site. REFERENCES Anaya-Lara, O., Jenkins, N., Ekanayake, J., Cartwright, P. and Hughes, M. 2009. Wind energy generation, modelling and control. John Wiley and Son Ltd, pp. 1–286. Ayodele, T.R. 2012. Analysis of wind energy resource and impact of its integration into power system. Tshwane University of Technology. Ayodele, T.R., Jimoh, A.A., Munda, J.L. and Agee, J.T., 2012. Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa. Energy Conversion and Management, 64: 614–625. Ayodele, T.R., Jimoh, A.A., Munda, J.L. and Agee, J.T., 2013. A statistical analysis of wind distribution and wind power potentials in the coastal region of South Africa. International Journal of Green Energy, 10(6): 1–21. Ayodele, T.R. & Ogunjuyigbe, A.S.O., 2013. Wind energy resource, wind energy conversion system modelling and integration: A survey. International Journal of Sustainable Energy, DOI: 10.1080/14786451.2013.855778, pp.1–15. Dincer, I., 2000. Renewable energy and sustainable development: A crucial review. Renewable and Sustainable Energy Reviews, 4: 157–175. Eskom, 2009. Annual report. Fact Sheet, 2011. Wind resource estimation. Wind Energy the Fact, 1: 38–58. G.W.E.C. 2011. Global wind statistic. Global Wind Energy Council, 1040 Brussel, Belgium, pp.1–4. G.W.E.O. 2012. Wind energy and climate change. Global Wind Energy Outlook, pp.1–52. Gupta, R. and Biswas, A. 2010. Wind data analysis of silchar (Assam, India) by Rayleigh,s and Weibull methods. Journal of Mechanical Engineering Research, 2 (1): 10–24. Haghifam, M.R. and Omidvar, M. 2010. Wind farm modeling in reliability assessment of power system International Conference on Probabilistic Methods Applied to Power Systems,( PMAPS), pp.1–5. Hansen, K.S. and Chr. Larsen, G. 2004. Analyses of wind turbine design loads. IEA Annex XVII, Database on Wind Characteristics, Risø National laboratories. Jacquemin, J., Traylor, H., Muir, N.F., Corle, A.D., Baldock, N.J. and Devaney, L. 2007. Effective turbulence calculation using iec 61400-1 edition 3: Reading consensus through dialogue. Riso National Laboratory, Denmark. Jamdade, S.H. and Jamdade, P. 2012. Extreme value distribution model for analysis of wind speed data for four locations in Ireland. International Journal of Advanced Renewable Energy Research, 1 (5): 254–259.


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