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Assessment of turbulence intensity oflocal wind regimesT.R. Ayodelea & A.S.O. Ogunjuyigbea

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International Journal of Sustainable Energy, 2014http://dx.doi.org/10.1080/14786451.2014.885029

Assessment of turbulence intensity of local wind regimes

T.R. Ayodele∗ and A.S.O. Ogunjuyigbe

Department of Electrical and Electronic Engineering, Faculty of Technology, University of Ibadan, Nigeria

(Received 16 October 2013; final version received 3 December 2013)

This paper analyses the turbulence intensity of seven different sites in the coastal region of South Africa.The study is based on 12 months, 10-minute average wind speed measurement. The turbulence intensityis calculated using mean wind speed and the standard deviation method. Some of the key results showthat generalised extreme value distribution gives the best fit to the turbulence intensity in the entire sites.The annual shape parameter of the distribution ranges from 0.11 at site WM06 to 0.3 at site WM05. Thescale parameter varies from 3.55 at site WM04 to 6.06 at site WM02, while the location parameters spanbetween 7.07 at site WM04 and 10.65 at site WM01. The annual turbulence intensity varies from 9.6% atsite WM04 to 15.9% at site WM03. The result also reveals that sites with higher turbulence intensity havelower wind power potential and hence are less attractive for wind power application.

Keywords: wind regime; turbulence intensity; generalised extreme value distribution; South Africa

1. Introduction

Wind is one of the principal sources of structural loading for turbines and their support structures(Jacquemin et al. 2007). Material fatigue is governed by wind speed fluctuation, i.e. turbulence.The close relationship between fatigue on a wind turbine and the wind field turbulence intensitycharacteristic has recently made the assessment of turbulence intensity of a local wind regimea subject of research (Hansen and Larsen 2004a). Fatigue loading of wind turbine is commonlyassumed to be proportional to the standard deviation of wind speed even under full or partial wakeconditions; hence there is need for both the models and the measurements to evaluate turbulenceintensity of a given site. The knowledge of turbulence intensity is necessary for cost optimisationof modern large wind turbines (Hansen and Larsen 2004b) and is crucial for the design of supportstructure for wind turbines (Jacquemin et al. 2007; Turk and Emeis 2010).

The assessment of wind speed characteristics and its distribution around the world are wellreported in the literature (Ulgen and Hepbasli 2002; Weisser 2003; Gupta and Biswas 2010).Similarly, quite a number of studies have been conducted on the wind power potential of differ-ent sites where appropriate statistical distribution parameters were estimated and the availablewind energy at a given site was quantified (Ulgen and Hepbasli 2002; Mostafaeipour et al. 2011).However, there is a paucity of literature on the turbulence intensity of local wind regime. In Wills(1992), a vertical profile of turbulence intensity depending on different wind speed classes basedon data from the West Sole gas platform was presented (Wills 1992). The analysis of the 4 years,

∗Corresponding author. Email: tayodele2001@yahoo.com

© 2014 Taylor & Francis

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2 T.R. Ayodele and A.S.O. Ogunjuyigbe

10-minute average mean wind speed data from the offshore measuring platform (Forschung inNord-und ost see1) in German Bight was carried out (Turk and Emeis 2010) to obtain the depen-dence of turbulence intensity on the wind speed. It was concluded that turbulence intensity dependson roughness length and is therefore a function of wind speed. Furthermore, it is argued (Frandsen2007) that fatigue equivalent loading to which turbines are subjected to in wind turbine clusters

can be represented structurally by a change in turbulence intensity alone. A model was thereforeproposed to combine all loading situations by deriving an effective turbulence value for each windspeed bin (Frandsen 2007). Frandsen and Thogersen presented a study of an offshore applica-tion of a fatigue model for wind turbines operating partly in ambient turbulence and partly wake(2007). Cochran demonstrated the importance of determining the atmospheric turbulence at thetest site for small-scale wind turbines (2002). He believes that the knowledge gain from such testwill help to give insight into the influence of atmospheric turbulence on the expected performanceof the turbines. Modelling and measurements of power losses and turbulence intensity in windturbine wakes at Middelgrunden offshore wind farm were studied by Barthelmie et al. (2007).In their work, three methods of estimating turbulence intensity were presented: one is based onwind speed and standard deviation of wind speed from the nacelle anemometer and another frommean power output and its standard deviation. The third is turbulence intensity derived from windspeed and standard deviation from a meteorological mast at a site prior to wind farm construction.It was concluded that there is an agreement between turbulence intensity derived from powermeasurement and the meteorological mast than with those derived from data from the nacelleanemometer. Wind speed measurement and estimation of turbulence intensity of a complex ter-rain at Bosnia and Herzegovina in Mostar were performed by Bourgeois et al. and the result fromthe measurement were validated with the CFD model using WindSim. The aim of their work wasto analyse the suitability of the site in view of the planned wind farm and the determination of thetechnical requirements for the wind turbine (Bourgeois and Winkelmeier 2012). The result showsa good agreement of the normalised vertical profile between the measurement and the model. Toobtain a suitable distribution of the turbulence intensity, it is necessary to carry out short averagemeasurement (usually, 10-minute average) on the site for not less than one year (Hansen andLarsen 2004a; Baldocchi 2012).

This paper analyses and models the turbulence intensity of seven different local wind regimesin the coastal region of South Africa. We use 10-minute average mean and standard deviation ofwind speed from a cup anemometer at 60 m installed height and operated for a period of one year.

2. Site and data description

The measurement of average wind speed and average wind speed standard deviation were obtainedfrom the Wind Atlas of South Africa (WASA) under the WASA project (CSIR 2011). The mea-surements consisted of 10-minute average wind speed sampled at a frequency of 0.5 Hz. The winddata were recorded at different anemometer heights of 10, 20, 40 and 60 m for a period of oneyear. The cup anemometer (Model: P2546) used for the wind speed measurement is manufacturedby WindSensor, Denmark, and calibrated by Svend Ole Hansen ApS, Denmark. The wind speedsensor has a range of 1–96 m/s with an accuracy of 0.1 m/s. The wind speed data were loggedby CompactFlash Module (Model: CR1000/CFM100). The data logger was manufactured byCampbell Scientific, Inc., UK, and calibrated by Campbell Scientific Ltd, UK. During the periodunder consideration, the gross data recovery percentage (the actual percentage of expected datareceived) was 97.6% and the net data recovery percentage (the percentage of expected data whichpassed all quality assurance tests) was 94.8%. The two percentages are high which indicates thatboth the sensors and the data loggers performed well. It is therefore believed that the data aregood enough to draw reliable conclusions. The description of the sites is given in Table 1.

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International Journal of Sustainable Energy 3

Table 1. Description of sites’ locations.

S/n Site Town Location

1 WM01 Alexander Bay 28◦36′06.7′′S, 16◦39′51′′E2 WM02 Calvinia 31◦31′29.7′′S, 19◦21′38.7′′E3 WM03 Vredendal 31◦43′49.4′′S, 18◦25′10.11′′E4 WM05 Napier 34◦36′1.6′′S, 19◦41′30.3′′E5 WM07 Prince Albert 32◦58′0.2′′S, 22◦33′23.8′′E6 WM08 Humansdorp 34◦06′32′′S, 24◦30′49′′E7 WM10 Butterworth 32◦05′26.5′′S, 28◦08′09.0′′E

3. Atmospheric turbulence

Atmospheric turbulence is defined as a continuous, three-dimensional flow that is nonlinear andcontains whirls of different sizes (Carpman 2011). One of the main properties of atmosphericturbulence is the dissipation of wind’s kinetic energy into thermal energy via the creation anddestruction of progressively smaller eddies (or gusts) (Mirhosseini, Sharifi, and Sedaghat 2011).Turbulent wind over a long period (i.e. an hour or more) may have a relatively constant mean, butmay vary over shorter times (minutes or less).Atmospheric turbulence can otherwise be consideredas random wind speed fluctuations that are imposed on the mean wind speed (Mirhosseini, Sharifi,and Sedaghat 2011). These fluctuations occur in all three directions: longitudinal (in the directionof the wind), lateral (perpendicular to the average wind) and vertical. Atmospheric turbulence canbasically be measured by turbulence intensity and can be calculated as the standard deviation (overa short interval, i.e. 10 minutes) of wind speed divided by the mean wind speed (Rareshide et al.2009) as given by Equation (1). Turbulence intensity depends on terrain, atmospheric stabilityand wakes from neighbouring turbines. Lower turbulence results in less maintenance and betterperformance of wind turbine. Turbulence intensity is site-specific and differs from one site toanother. According to Carpman (2011), turbulence intensity ranges from 10% to 50% in NewEngland and the value may even be lower for offshore. In another study (Frandsen and Thogersen2007), typical values at turbine hub height range between 6–8% offshore and 10–12% over land.A similar result in the North-east of Saudi Arabia (Shafiqur et al. 2009) showed that turbulenceintensities are 17.3%, 14.6% and 13.7% at different heights of 20, 30 and 40 m:

Ti% =√

var(vi)

E(vi)∗ 100. (1)

In this study, the monthly turbulence intensity for the entire sites was calculated based onEquation (1) and the results are presented in Table 2. It is evident from the table that site WM04presents the least turbulence intensity, while site WM02 has the highest turbulence intensity. Themonthly turbulence intensity varies from 8.7% in April at site WM04 to 20.5% in May at siteWM02. The annual value ranges from 9.6% at site WM04 to 15.9% at site WM02.

The analyses of the turbulence intensity of the four distinct seasons in the country were per-formed. These seasons are defined as (Ayodele et al. 2011): Spring (Sprg) (September–October),Summer (Sumr) (November–March), Autumn (Autm) (April–May) and Winter (Wint) (June–August). The turbulence intensity for these seasons is estimated for the entire sites. The resultsare furnished in Table 3. From the table, it can be seen that turbulence intensity is lower duringwinter in all the sites compared with other seasons of the year. This shows that wind speed issmoother during winter, i.e. the degree of gustiness is lower.

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4 T.R. Ayodele and A.S.O. Ogunjuyigbe

Table 2. Monthly turbulence intensity Ti (%) for the entire sites.

Month WM01 WM02 WM03 WM04 WM05 WM06 WM07

Jan. 15.6 17.5 13.2 9.5 14.9 11.5 12.8Feb. 16.4 17.9 13.9 10.5 15.1 12.1 15.1Mar. 15.4 17.2 13.4 9.3 14.1 11.1 14.1Apr. 15.2 14.4 11.0 8.7 12.1 10.8 13.2May 14.1 20.5 11.7 10.3 12.0 11.0 12.5Jun. 18.7 12.5 10.4 9.4 10.9 11.2 11.2Jul. 14.9 11.1 10.2 10.0 11.0 11.0 12.6Aug. 14.2 12.5 10.6 8.8 11.0 11.3 11.4Sep. 15.2 14.5 11.8 9.8 13.1 11.6 12.8Oct. 14.2 16.3 12.4 9.7 13.8 11.7 12.6Nov. 14.7 17.3 13.0 10.6 14.4 10.8 12.5Dec. 14.9 16.4 13.2 9.15 14.8 11.9 13.0Annual 15.3 15.9 12.1 9.6 13.1 11.3 12.7

Table 3. Seasonal turbulence intensity for the entire sites Ti (%).

Season WM01 WM02 WM03 WM04 WM05 WM06 WM07

Autm 14.63 17.54 11.35 9.51 12.05 10.90 12.84Sprg 14.39 15.33 12.11 9.74 13.45 11.61 12.69Sumr 15.38 17.25 13.33 9.78 14.64 11.48 13.44Wint 14.04 12.02 10.39 9.23 11.13 11.14 11.70

4. Statistical distribution model of turbulence intensity for the sites

Efforts were made at modelling the turbulence intensity of each of the sites statistically. Severalstatistical distributions were considered; however, the five statistical distributions that best modelthe turbulence intensity of the sites are presented in this paper. These are t-location scale parameter,generalised extreme value distribution, Weibull distribution, Rayleigh distribution and lognormaldistribution.

4.1. t-Location scale distribution

The t-location scale distribution is helpful in modelling data distribution with heavier tails. Itapproaches the normal distribution as the shape parameter (ψ) approaches infinity and smallervalue of ψ yields heavier tails. Its distribution function ft(TI) can be defined as

ft(TI) = �((ψ + 1)/2)

�√

ψπ�(ψ/2)

[ψ + ((TI − γ )/�)

ψ

](ψ+1)/2

, (2)

where ψ > 0 is the shape parameter, � > 0 is the scale parameter and γ is the locationparameter.

4.2. Generalised extreme value distribution

The generalised extreme value is a family of continuous probability distributions developedwithin the value theory to combine the Gumbel, Frechet and Weibull families. The probabil-ity density function (pdf) for the generalised extreme value distribution with location parameterα, scale parameter ξ and shape parameter η �= 0 is given by the following equation (Kotz and

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International Journal of Sustainable Energy 5

Nadarajah 2000):

fge(TI , η �= 0) =(

1

ξ

)exp

(−

(1 + η

(TI − α)

ξ

)−1/η) (

1 + η(TI − α)

ξ

)−1−1/η

. (3)

For

1 + η(TI − α)

ξ> 0,

Where η > 0 is the type II case and it corresponds to the distribution whose tail decreases as apolynomial. η < 0 is the type III case and it corresponds to the distribution whose tail is finite.

When η = 0, then it is the type I case and its density function can be written as Equation (4).It corresponds to the distribution whose tail decreases exponentially:

fge(TI , η = 0) =(

1

ξ

)exp

(− exp

((TI − α)

ξ

)− (TI − α)

ξ

). (4)

Types I, II and III are sometimes referred to as Gumbel, Frechet and Weibull types, respectively.The cumulative distribution function for η �= 0 and η = 0 can be expressed as Equations (5)

and (6), respectively,

Fge(TI , η �= 0) = exp

(−

(1 + η

(TI − α)

ξ

)−1/η)

, (5)

Fge(TI , η = 0) = exp

(− exp

((TI − α)

ξ

)). (6)

4.3. Weibull distribution

The Weibull pdf and its cumulative distribution function can be expressed as Equations (7) and(8), respectively,

fW(TI) = k

c

(TI

c

)k−1

exp

[−

(TI

c

)k]

, (7)

FW(TI) = 1 − exp

[−

(TI

c

)k]

, (8)

where fW(TI) is the Weibull probability distribution of turbulence intensity TI . Weibull shape andscale parameters are denoted by k and c, respectively. Weibull k and c can be determined usingthe maximum likelihood method (Seguro and Lambert 2000) as given by Equations (9) and (10),respectively,

k =[∑n

i=1 T kI ln(TI)∑n

i=1 T kI

−∑n

i=1 ln(TI)

n

]−1

, (9)

c =[

1

n

n∑i=1

T kI

]1/k

. (10)

�(•) is a gamma function and is defined as follows:∫ ∞

0ξ x−1 exp(−ξ)dξ and �(1 + x) = x�(x). (11)

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6 T.R. Ayodele and A.S.O. Ogunjuyigbe

4.4. Rayleigh distribution

The pdf and the cumulative distribution function for the Rayleigh model are given byEquations (12) and (13), respectively (Manwell, Mcgowan, and Rogers 2002):

fR(TI) = π

2

(TI

(E(TI))2

)exp

[−π

4

(TI

E(TI)

)k]

, (12)

FR(TI) = 1 − exp

[−π

4

(TI

E(TI)

)k]

, (13)

where k = 2 for the Rayleigh distribution.

4.5. Lognormal distribution

Lognormal distribution pdf and the cumulative distribution function are given by Equations (14)and (15), respectively,

fLN(TI ) = 1

TIσ√

2πexp

−(ln TI − μ)2

2σ 2, (14)

FLN(TI) = 1

2erfc

[− ln TI − μ

σ√

2

], (15)

where TI ≥ 0 is turbulence intensity, σ > 0 is the lognormal shape parameter, μ > 0 is thelognormal scale parameter and erfc(•) is the complimentary error function.

Once the mean, E(TI), and the variance, var(TI), of the turbulence intensity, TI , are calculatedusing Equations (16) and (17), respectively,

E(TI) = 1

n

[n∑

i=1

TI

], (16)

var(TI) = 1

n

[n∑

i=1

(TI − E(TI))2

], (17)

then σand μ can be estimated by using Equations (18) and (19), respectively,

σ =√

ln

(1 + var(TI)

E[T 2I ]

), (18)

μ = ln E(TI) − 1

2ln

(1 + var(TI)

E(T 2I )

). (19)

4.6. Performance evaluation of the distribution functions

Three goodness-of-fit criteria namely: coefficient of determination (R2), chi-square test (χ2) androot mean square error (RMSE) were used to evaluate the distribution function that best fits theturbulence intensity of each of the site among the five most probable distributions earlier discussed.These are as given by Equations (20)–(22), respectively. R2 is simply the square of the correlationcoefficient. It is used to determine to what extent a prediction can be made from a model. The

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International Journal of Sustainable Energy 7

relationship between the variables is determined as 0 ≤ R2 ≤ 1 with 1 being the perfect fit. Thecloser the value of R2 to 1, the better the fit to the actual variables. Similarly, the lower the valueof χ2 and RMSE, the better the goodness of fit:

R2 =

⎡⎢⎢⎢⎣ N

∑f(TI )ft,LG,W,ge,R(TI ) − (∑

f(TI )

) (∑ft,LG,W,ge,R(TI )

)(√

N(∑

f 2(TI )

)− (∑

f(TI )

)2) (√

n(∑

f 2t,LG,W,ge,R(TI )

)− (∑

ft,LG,W,ge,R(TI )

)2)

⎤⎥⎥⎥⎦

2

,

(20)

χ2 =∑N

i=1 (yi − TI i)

N − n, (21)

Where TI i is the ith actual turbulence intensity, yi is the ith predicted turbulence intensity fromthe t-location scale, logistic and normal distribution functions. Also, N is the number of the windspeed dataset and n is the number of constant turbulence intensity data

RMSE(%) =[

1

N

N∑i=1

[(ft,LG,W,ge,R(TI ) − f(TI )

)2]]1/2

, (22)

where f(TI ) is the pdf of the actual turbulence intensity distribution and N is the number ofobservation.

The results of the performance evaluation are presented in Figures 1– 3. From the figures,it is obvious that the entire sites can best be modelled statistically using generalised extremevalue parameters with very close competition from lognormal and t-location scale distributions.However, the t-location scale distribution is not strictly positive, since turbulence intensity is pos-itive definite; hence, it cannot be used to fit turbulence intensity. We can therefore state that thegeneralised extreme value distribution can best be utilised for effective prediction of turbulenceintensity for wind power application at these sites. This is in accordance with the conclusion thatturbulence is non-Gaussian (Baldocchi 2012). It is skewed and Kurtotic. The statistical distribu-tions were compared with the actual turbulence intensity data in Figure 4. It can be concluded fromthe figures that the generalised extreme value distribution gives the best model for the turbulenceintensity in the entire sites.

0

0.2

0.4

0.6

0.8

1

1.2

t-locationGeneralised Ex-tremeWeiblognormRay

Coe

ffici

ent o

f det

erm

inat

ion

(R^2

)

WM01 WM02 WM03 WM04 WM05 WM06 WM07Sites

Figure 1. Performance evaluation of the distribution using the coefficient of determination (R2) criterion.

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8 T.R. Ayodele and A.S.O. Ogunjuyigbe

0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

t-locationGeneralised Ex-tremeWeiblognormRay

Chi

squ

are

WM01 WM02 WM03 WM04 WM05 WM06 WM07Sites

Figure 2. Performance evaluation of the distribution using the chi-square criterion.

WM01 WM02 WM03 WM04 WM05 WM06 WM070

0.01

0.01

0.02

0.02

0.03

0.03

t-locationGeneralised Ex-tremeWeiblognormRay

Sites

RM

SE

Figure 3. Performance evaluation of the distribution using the RMSE criterion.

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Turbulence intensity (%)WM07

Pro

babi

lity

Den

sity

Fun

ctio

n

Actual Data Generalized Extreme Value t-location Weib Ray Lognorm

0 10 20 30 40 500

0.02

0.04

0.06

0.08

Turbulence intensity (%)WM03

Pro

babi

lity

Den

sity

Fun

ctio

n

Figure 4. Probability distribution comparison of turbulence intensity with the actual data at an anemometer height of60 m at sites (a) WM03 and (b) WM07.

Based on the observation in Figure 4 and conclusion drawn from subsection 4.6, the parametersof the generalised extreme value distribution were determined, and the results are presented inTable 4. The parameters are site-specific and should be determined for each potential site, but themethodology can be severally applied.

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International Journal of Sustainable Energy 9

Table 4. The mean E(TI (%)), standard deviation σ(TI (%)) and the generalised extremevalue distribution parameters estimation of the turbulence intensity for the sites.

WM01 WM02 WM03 WM04 WM05 WM06 WM07

E(TI (%)) 15.28 15.66 12.05 9.57 13.13 11.32 12.72σ(TI (%)) 11.03 11.29 8.47 8.47 9.57 6.64 8.21ξ 5.50 6.06 4.53 3.55 5.30 3.96 4.30η 0.20 0.22 0.25 0.12 0.30 0.11 0.19α 10.65 10.56 8.08 7.07 8.17 8.53 9.21

The table shows that the scale parameter (ξ ) varies from 3.55 in site WM04 to 6.06 in siteWM02, the shape parameter (η) ranges from 0.11 in site WM06 to 0.3 in site WM05 and thelocation parameter (α) varies from 7.07 in site WM04 to 10.65 in site WM01.

5. Influence of turbulence intensity on wind power potential of the sites

An earlier study of the wind power potential of these sites (Ayodele et al. 2012, 2013) shows thatthe wind speed in the entire sites can best be modelled using the Weibull distribution (Ayodele et al.2012, 2013). The wind power density (Pd(v)) of a given site using the Weibull distribution fW(v)can be calculated using Equation (23) (Celik 2004) which can further be written as Equation (24):

Pd(v) = 1

2ρ

∫ ∞

0v3fW(v)dv, (23)

Pd(v) = 1

2ρv3

m

[�(1 + 3/k)

�3(1 + 1/k)

], (24)

Where ρ is the air density (kg/m3) which is taken as 1.225 kg/m3, �(•) is the gamma functionwhich can be defined as follows:

�(·) =∫ ∞

0tz−1e−tdt. (25)

Wind power density in each of the sites was computed from the annual average wind speed andplotted against the annual turbulence intensity as shown in Figure 5. It is observed from the figurethat the power density tends to be lower at a site with higher turbulence intensity. Based on thisempirical relationship, it can be said that sites with high turbulence intensity are less attractivefor wind power application.

9 10 11 12 13 14 15 16200

300

400

500

600

700

Turbulence Intensity (%)

Pow

er d

ensi

ty (

Wat

t/m2 ) WM01

WM02

WM03

WM04

WM05

WM06

WM07

Figure 5. The plot of power density against turbulence intensity for the entire sites at 60 m anemometer height.

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10 T.R. Ayodele and A.S.O. Ogunjuyigbe

20 40 6014.0

15.0

16.0

17.0

18.0

Height (m)WM01

Tu

rbu

len

ce in

ten

sity

(%

)

20 40 6015.0

16.0

17.0

18.0

19.0

Height (m)WM02

Tu

rbu

len

ce in

ten

sity

(%

)

20 40 6011.5

12.0

12.5

13.0

13.5

Height (m)WM03

Tu

rbu

len

ce in

ten

sity

(%

)

20 40 608.0

10.0

12.0

14.0

16.0

Height (m)WM04

Tu

rbu

len

ce in

ten

sity

(%

)

(b)(a)

(d)(c)

Figure 6. Turbulence intensity at different anemometer heights of 10, 20, 40 and 60 m at sites (a) WM01, (b) WM02,(c) WM03 and (d) WM04.

(a) (b)

(c) (d)

Figure 7. Plot of turbulence intensity versus wind speed at 60 m anemometer height at sites (a) WM01, (b) WM03, (c)WM04 and (d) WM06.

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Table 5. Coefficient of the cubic polynomial that models the relationship between theturbulence intensity and wind speed of the sites.

WM01 WM02 WM03 WM04 WM05 WM06 WM07

P1 −0.035 0.035 −0.035 −0.012 −0.018 −0.015 −0.017P2 1.100 1.100 1.000 0.460 0.700 0.550 0.600P3 −10.00 −10.00 −10.00 −5.400 −8.400 −6.000 −6.800P4 41.00 44.00 40.00 28.00 41.00 29.00 33.00

The influence of height on the turbulence intensity was also investigated. This was made possiblewith the data collected at the other anemometer heights of 10, 20, 40 and 60 m. The result is shownin Figure 6.

This figure clearly showed that the turbulence intensity decreases with height. This is expectedas the flow of mass of air tends to be smoother at higher height due to the less impact of landtopography on the flow of moving air. The gustiness of the wind at different wind speeds for fourof the sites is shown in Figure 7. This graph together with the wind distribution can be used todetermine the level of turbulence present under typical operation condition. The graph can alsobe used by the turbine manufacturer to predict maintenance scheduling.

The scattered plot was fitted using Matlab fitting toolbox, all the sites are best fitted to the cubicpolynomial as given by Equation (26). The coefficient of the polynomial is depicted in Table 5:

Ti = P1v3 − P2v2 + P3v − P4. (26)

6. Relationship between shear exponent and turbulence intensity at the site

Wind speed changes with height, this change in wind speed with height is called wind shear andis characterised by the exponent (m(i)) as given by the following power law equation (Di Piazzaet al. 2010):

v2(i) = v1(i)

(H2

H1

)m(i)

, (27)

Where v2(i) is the wind speed at the height H2 and v1(i) is the wind speed at the height H1. Theshear exponential (m(i)) is the factor that depends on surface roughness and atmospheric stabilityand it is site-specific (Nigim and Parker 2007). Shear exponent can be determined by taking thelogarithm of Equation (27) as given in Equation (28). The larger the shear, the more the windspeed increases at higher elevation:

m(i) = log(v2(i)/v1(i)

)log (H2/H1)

. (28)

The variation in shear exponent with anemometer height was determined using site WM02; theresults are depicted in Table 6. The result shows that shear exponent increases with height. Thisindicates that wind speeds are much greater at higher heights.

The relationship between shear exponent (determined from wind speed at 20 and 60 manemometer height) and turbulence intensity was explored. The results are presented in Figure 8.The correlation coefficient between the shear exponent and turbulence intensity was calculatedfor each of the sites and the result is displayed in Table 7. From the result shown in the figure, it isobserved that there is a negative correlation between the turbulence intensity and shear exponent.This is a further confirmation that turbulence intensity decreases while shear exponent increaseswith height.

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12 T.R. Ayodele and A.S.O. Ogunjuyigbe

Table 6. Mean shear exponent E(m(i)

)at dif-

ferent anemometer heights at site WM02.

Height 10–20 m 20–40 m 40–60 m

E(m(i)

)0.0759 0.1459 0.1821

Figure 8. The plots of turbulence intensity against shear exponent at sites (a) WM02, (b) WM03, (c) WM04 and (d)WM06.

Table 7. Correlation coefficient between turbulence intensity and the shear exponentin all the sites.

Site WM01 WM02 WM03 WM04 WM05 WM06 WM07

Corr. −0.36 −0.37 −0.43 −0.45 −0.48 −0.23 −0.20

7. Influence of height on the parameters of the generalised extreme value distribution

In order to have insight into the impact of height on the parameters of generalised extreme valuedistribution that best fit the turbulence intensity of the sites, the data of site WM01 at differentanemometer heights of 10, 20, 40 and 60 m were used for the analysis. The result is shown inFigure 9. The figures reveal that scale, shape and location parameters decrease with the height.This is in line with the fact that turbulence intensity decreases with height.

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International Journal of Sustainable Energy 13

(a) (b)

10 20 30 40 50 600.18

0.20

0.22

0.24

0.26

0.28

0.30

Height (m)

Sha

pe P

aram

eter

5.45

5.5

5.55

5.6

5.65

5.7

5.75

Sca

le p

aram

eter

10 20 30 40 50 6010.0

10.5

11.0

11.5

12.0

Height (m)

Loca

tion

para

met

er

Figure 9. Influence of height on generalised extreme value parameters at site WM01: (a) scale and shape parameter and(b) location parameter.

8. Conclusion

The assessment of the turbulence intensity of seven local wind regimes in the coastal region ofSouth Africa has been presented. The results show that the generalised extreme value distributiongives best statistical distribution fit to turbulence intensity. A site with higher turbulence intensityhas lower wind power potential and hence is less attractive for wind power application. It has alsobeen shown that the generalised extreme value distribution shape, scale and location parametersdecrease with height and hence turbulence intensity decreases with height. This indicates thatmore wind power can be captured at higher wind turbine hub height. Therefore, the knowledgeof turbulence intensity does not only give information on the support structure for wind turbinesbut also gives an idea on wind power potential of the site. It has also been revealed that negativecorrelation exists between turbulence intensity and shear exponent. Future research will look intothe generalised mathematical relationship between turbulence intensity and wind power density.

Acknowledgement

The authors want to thank the Department of Energy (DoE), South African Wind Energy Programme (SAWEP) and theRoyal Danish Embassy for their initiative on Wind Atlas for South African Project and making the data for this workavailable through CSIR.

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