Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa

Energy Conversion and Management 64 (2012) 614–625

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Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa T.R. Ayodele ⇑, A.A. Jimoh, J.L. Munda, J.T. Agee Department of Electrical Engineering, Tshwane University of Technology, Private Bag X680, Pretoria 0001, Staatsartillerie Road, Pretoria West, South Africa

a r t i c l e

i n f o

Article history: Available online 24 August 2012 Keywords: Wind distribution Weibull distribution Capacity factor Wind turbine South Africa

a b s t r a c t The operating curve parameters of a wind turbine should match the local wind regime optimally to ensure maximum exploitation of available energy in a mass of moving air. This paper provides estimates of the capacity factor of 20 commercially available wind turbines, based on the local wind characteristics of ten different sites located in the Western Cape region of South Africa. Ten-min average time series wind-speed data for a period of 1 year are used for the study. First, the wind distribution that best models the local wind regime of the sites is determined. This is based on root mean square error (RMSE) and coefficient of determination (R2) which are used to test goodness of fit. First, annual, seasonal, diurnal and peak period-capacity factor are estimated analytically. Then, the influence of turbine power curve parameters on the capacity factor is investigated. Some of the key results show that the wind distribution of the entire site can best be modelled statistically using the Weibull distribution. Site WM05 (Napier) presents the highest capacity factor for all the turbines. This indicates that this site has the highest wind power potential of all the available sites. Site WM02 (Calvinia) has the lowest capacity factor i.e. lowest wind power potential. This paper can assist in the planning and development of large-scale wind powergenerating sites in South Africa. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, efforts have been made around the world to generate electricity from renewable energy sources. This is due to the infinite availability of their prime movers and in an effort to reduced harmful emissions into the environment. One of the ways in which electricity can be generated from these sources is to use wind turbines that convert the kinetic energy in a mass of moving air into electricity. At present, the wind power growth rate stands at over 20% annually. At the end of 2010, global cumulative wind power capacity reached 194.4 GW [1] and it is predicted that 12% of the world electricity may come from wind power by 2020 [2]. In South Africa, the interest in wind as a resource for electricity generation is receiving considerable support from stake holders. This was evident at the last wind power summit (Wind Power Africa 2011) held in Cape Town in May 2011. Currently, the major indigenous energy resource for electricity generation in the country is coal, which constitutes 85% of the primary energy mix. This contributes significantly to environmental pollution and leads to high emission of green house gas (GHG) in the country. South Africa is the 14th highest emitter of GHG in the world [3].

⇑ Corresponding author. Tel.: +27 735605380. E-mail addresses: [email protected], [email protected] (T.R. Ayodele). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.06.007

However, as a signatory to the UN Framework Convention on Climate Change, the country has committed itself to the international community to reduce GHG emission. Part of the plan to honour this commitment is contained in the ‘‘Integrated Resource Plan (IRP)’’ which has 56% of wind power in the first phase of its renewable energy feed-in tariff programme. In view of this, it is essential to have a reliable knowledge of the wind distribution and the appropriate turbine selection based on the analysis of local wind regimes at different sites in the country. An understanding of the performance of a wind turbine, in response to different wind speeds at a proposed site, is a prerequisite for the successful planning and implementation of a wind power project. Both the wind speed and its distribution have an influence on the performance of a wind turbine. Therefore, the operating parameters of wind turbines which are characterised by four parameters, the cut-in (vin), rated (vr), the cut-out (vco) wind speed and the turbine nominal power should be a good match with the prevailing wind characteristics and distribution of the local wind regimes [4]. However, selecting wind turbines to match a specific site has traditionally been done by designing a new turbine based on the wind characteristics of a given site. However, this method is time consuming and uneconomical. A more practical approach could be to select the turbine that best matches the wind characteristics of a specific site from the commercially available ones [5,6]. The turbine power curve operating parameters can be combined with the statistical wind distribution parameters of a

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

615

Nomenclature RMSE R2 GHG v

vi vin vr vco Cf pdf k c

c

vb vo vb(i) vo(i) t cdf

root mean square error coefficient of determination green house gas wind speed (m/s) vector of observed wind speed (m/s) cut in wind speed (m/s) rated wind speed (m/s) cut-out wind speed (m/s) capacitor factor probability density function Weibull shape parameter Weibull scale parameter (m/s) lower incomplete gamma function wind speed at hub height (m/s) wind speed at observed height (m/s) ith wind speed at hub height (m/s) ith wind speed at observed height (m/s) time (hrs) cumulative distribution function

given site to estimate the average power output of the turbine which will be used to determine the turbine capacity factor (Cf). Cf is important in determining the optimal turbine site-matching [7–9]. It reflects how effectively the turbine could harness the energy available in the mass of moving air. It also serves as a vital index for evaluating the economic viability of a wind power project. Various methods have been proposed in the literature for calculating the Cf of a wind turbine. Jangamshetti and Guruprasada Rau [10] derived a model for Cf using the main turbine curve parameters and the two Weibull function parameters that are derived from the cubic mean wind speed. A function for Cf in which a cubic polynomial was used to derive an expression for the average power output of a turbine using Simpson’s three-eighths rule was proposed in [6]. A computer simulation program ‘‘Wasp turbine editor’’ was used in [5] to determine the capacity factor for wind turbines. Albadi and El-Saadany [7] proposed an improved model for Cf using the mean wind speed, rather than the cubic mean wind speed. In this paper, the statistical distribution that best fits the local wind regime of ten different sites in the coastal region of South Africa is determined. Thereafter, the Cf of 20 different commercially available wind turbines is estimated analytically depending on the local wind regimes of the sites. The statistical parameters of the best resulting distribution are evaluated at different turbine hub heights. The impact of turbine operating parameters on the Cf is investigated. The rest of the paper is organised as follows, Section 2 describes the site and the data used for the study, Section 3 features the determination of the appropriate statistical distribution model that best fits the wind distribution at each of the sites. The model for estimating the capacity factor of the wind turbines is presented in Section 4. Results are discussed in Section 5 while Section 6 provides the conclusions of the study.

erfc

r l A

q KE Cp

gm gg Pavg Pr fw(v) AEP Hb Ho mi E() var()

given in Table 1. Each of the masts erected at each of these locations has 4 cup anemometers installed at different heights of 10, 20, 40, 60 and 62 m, respectively. The anemometers (model P2546A) are manufactured by WindSensor, Denmark and calibrated by Svend Ole Hansen ApS, Denmark. The data used are 10-min average wind speed sampled at 0.5 Hz for a period of 1 year. During the periods under consideration, the gross data recovery percentage (the actual percentage of expected data received) was 100% and the net data recovery percentage (the percentage of expected data which passed all quality assurance tests) was 100%. The percentages indicate that both the sensors and the data loggers performed optimally. It is therefore believed that the data are good enough to draw reliable conclusions. The arrangement of the anemometers can be found in [12]. 3. Statistical distributions models The first step in the estimation of a wind turbine Cf is the determination of the statistical distribution that best fits the characteristics of the local wind regime. In this section, the comparative assessment of the three continuous probability distribution models (Weibull, Rayleigh and lognormal) commonly used in describing the characteristics of wind speeds of a location was carried out to determine the model that best describes the behaviour of wind speed at each of the sites. R2 and RMSE are used to test the goodness of fit of these distributions. 3.1. Weibull distribution The Weibull pdf representing the Weibull distribution can be expressed by [13,14]

fW ðv Þ ¼ 2. Description of site and wind speed measurements Wind data for ten different sites along the coast of South Africa are used for this study. The data were obtained from the Wind Atlas of South Africa (WASA) under the WASA project [11]. The project is an initiative of South Africa Department of Energy (DoE) and co-sponsored by UNDP-GEF via the South African Wind Energy Programme and Royal Danish Embassy. Geographical locations of the sites are shown in Fig. 1 and the descriptions of the sites are

complementary error function lognormal shape parameter lognormal scale parameter turbine swept-area (m2) air density (kg/m3) kinetic energy in mass of (J) coefficient of performance transmission efficiency generator efficiency average turbine output power rated turbine output power (watts) Weibull distribution function annual energy production turbine hub height observed height ith exponential shear expectation variance

  k  k v k1 v exp  c c c

ð1Þ

where fW(v) is the probability of observing wind speed, v. Wind speed is a stochastic process of which the descriptive parameters (mean, variance and standard deviation) can be obtained. The Weibull shape and scale parameters are denoted by k and c respectively. k is dimensionless and it indicates how peak the site under consideration is, c has a unit of wind speed (m/s) and it shows how windy the site is. The cdf is expressed as following equation

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T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

Fig. 1. The locations of the masts along the coast of South Africa: Adapted from [11].

Table 1 The description of the 10 sites in the coastal region of South Africa. S/n

Site

Nearest town

Location

Period of data

1 2 3 4 5 6 7 8 9 10

WM01 WM02 WM03 WM04 WM05 WM06 WM07 WM08 WM09 WM10

Alexander Bay Calvinia Vredendal Vredenburg Napier Sutherland Prince Albert Humansdorp Noupoort Butterworth

28°360 06.700 S, 16°390 5100 E 31°310 29.700 S, 19°210 38.700 E 31°430 49.400 S, 18°250 10.1100 E 32°500 41.200 S, 18°060 34.500 E 34°360 41.600 S, 19°410 30.300 E 32°330 24.400 S, 20°410 28.700 E 32°580 00.200 S, 22°330 23.800 E 34°060 3200 S, 24°300 4900 E 31°150 0 05.7600 S, 25°010 50.1900 E 32°050 26.500 S, 28°080 09.000 E

July 2010–June 2011 July 2010–June 2011 July 2010–June 2011 July 2010–June 2011 July 2010–June 2011 October 2010–September 2011 July 2010–June 2011 September 2010–August 2011 September 2010–August 2011 September 2010–August 2011

Table 2 R2 and RMSE performance evaluation of the distributions. S/n

Site

Evaluation

Weibull

Rayleigh

Lognormal

Best distribution

1

WM01

R2 RMSE

0.9727 0.0074

0.9088 0.0147

0.9530 0.0112

Weibull

2

WM02

R2 RMSE

0.9958 0.0031

0.9956 0.0034

0.9127 0.0147

Weibull

3

WM03

R2 RMSE

0.9851 0.0055

0.9847 0.0058

0.8739 0.0161

Weibull

4

WM04

R2 RMSE

0.9807 0.0064

0.9801 0.0073

0.8413 0.0184

Weibull

5

WM05

R2 RMSE

0.9875 0.0039

0.9865 0.0043

0.8591 0.0134

Weibull

6

WM06

R2 RMSE

0.9902 0.0050

0.9718 0.0088

0.9247 0.0128

Weibull

7

WM07

R2 RMSE

0.9790 0.0066

0.9489 0.0110

0.8424 0.0186

Weibull

8

WM08

R2 RMSE

0.9959 0.0026

0.9841 0.0055

0.8574 0.0157

Weibull

9

WM09

R2 RMSE

0.9916 0.0041

0.9541 0.0112

0.9444 0.0106

Weibull

10

WM10

R2 RMSE

0.9945 0.0032

0.9945 0.0032

0.9208 0.0128

Weibull and Rayleigh

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

617

Fig. 2. The probability distribution comparison for site (a) WM02, (b) WM05, (c) WM07 and (d) WM10.

bility studies [17]. Probability density function and the cumulative distribution function are given by following equations Fig. 3. Block diagram of wind conversion system electrical power output.

  k  v F W ðv Þ ¼ 1  exp  c

ð2Þ

There are various methods that can be used to determine the value of k and c [4]. The graphical method, the standard deviation method, the moment method, the maximum likelihood method and the energy pattern factor method. It is suggested that the maximum likelihood method is best suited to time series wind data [15]. 3.2. Rayleigh distribution The probability density function and the cumulative distribution function for the Rayleigh model are given by (3) and (4) respectively [16].

fR ðv Þ ¼

p 2

v ðEðv i ÞÞ2

!

" F R ðv Þ ¼ 1  exp 

" exp 

p



v

4 Eðv i Þ

p



4

k #

v Eðv i Þ

ð3Þ

fLNðv Þ ¼

1 ðln v  lÞ2 pffiffiffiffiffiffiffi exp 2r2 v r 2p

ð5Þ

Fðv Þ ¼

  1 ln v  l pffiffiffi erfc  2 r 2

ð6Þ

where v P 0 is the wind speed (m/s), r > 0 is the lognormal shape parameter, l > 0 is the lognormal scale parameter, 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 (7) and (8) respectively

" # n 1 X Eðv i Þ ¼ vi n i¼1 varðv i Þ ¼

" # n 1 X ðv i  Eðv i ÞÞ2 n i¼1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   varðv i Þ ln 1 þ E½v 2i 

ð4Þ

where k = 2 for Rayleigh distribution. One major advantage of the Rayleigh distribution is that both the fR(v) and FR(v) can be obtained from the mean value of the wind speed, unlike the Weibull distribution that requires knowledge of both k and c. 3.3. Lognormal distribution Lognormal distribution is applied in many fields, such as agriculture, entomology, economics, geology, and quality control. It has been found to be a good competitor in life testing and proba-

ð8Þ

then r and l can be estimated using (9) and (10) respectively

r¼

k #

ð7Þ

1 2



l ¼ ln v m  ln 1 þ

 varðv i Þ Eðv 2i Þ

ð9Þ

ð10Þ

3.4. Performance evaluation R2 and RMSE were used to evaluate the goodness of fit of the three probability density functions and are given by (11) and (12) respectively. R2 is simply the square of correlation coefficient. It can be used to determine to what extent a prediction can be made from a model. The relationship between the variables is determined as 0 6 R2 6 1 with 1 being the perfect fit. The closer the value of R2 to 1, the better the fit to the actual variables. Sim-

618

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

Fig. 4. Variation in shear exponential for site (a) WM05 and (b) WM07.

ilarly, the lower the value of RMSE, the better the goodness of fit. The results of the performance evaluation are presented in Table 2.

The energy that is contained in wind is mainly kinetic energy of a large mass of air over the earth surface and it is given as

32

2

P

P

P 7 6 fW;R;LNðv i Þ fðv iÞ n fðv iÞ fW;R;LNðv i Þ 7 6 ffi7 R2 ¼ 6rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     P

2 5 4 P 2 P P 2 n fðv i Þ  fðv i Þ n fW;R;LNðv i Þ  ð fW;R;LNðv i Þ Þ2

KE ¼

ð11Þ

#12 N 1X 2 RMSEð%Þ ¼ ½ðfðW;R;LNÞ fðv iÞ Þ  N i¼1

4. Wind turbine power output modelling

"

ð12Þ

ð13Þ

where A is the turbine-swept area (m2), q is the air density (kg/m3), v is the wind velocity and t is the time required for the wind to move through the plane of the turbine blade. The power available is simply the kinetic energy divided by the time as given by following equation

P¼ where f(vi) is the probability density function of the actual distribution and N is the number of observation. From the table it can be deduced that the wind speed in the entire sites are best described by the Weibull distribution with the Rayleigh distribution being a close competitor. The distribution fittings of four of the sites are shown in Fig. 2a–d.

1 qAv 3 t 2

KE 1 ¼ qAv 3 t 2

ð14Þ

The electrical power output as depicted in Fig. 3 can be written as [7,9,10]

Pe ¼

1 qAC p gm gg v 3 2

ð15Þ

Table 3 The mean exponential shear E(m(i)) for each site. SITE

WM01

WM02

WM03

WM04

WM05

WM06

WM07

WM08

WM09

WM10

E(m(i))

0.104

0.120

0.107

0.182

0.162

0.157

0.137

0.196

0.116

0.118

Table 4 Wind turbine specifications from different manufacturers. Turbine index

Turbine manufacturers

A B C D E F G H I J K L M N O P Q R S T

MICON NEPC-MICON ENERCON-E40 VESTAS-V47 FIKTIONAL VESTAS-V52 FUHRLAENDER, GMBH GE-1.5S VESTAS-V63 NEG-NICON VESTAS-V82 VESTAS-V82 VESTAS-V80 ZEPHYROS-Z72 GAMESA EOLICA-G80 BONUS NEG-MICON GE-2.3 GE-2.5 GE-2.7

Turbine operating speed range (m/s)

vci

vr

vco

4 4 2.5 5 3.1 4 2.22 4 5 3.5 3 3 4 3 4 4 4 3 3.5 3.5

14 15 13 15 16 17 15 14 16 16 13 14 16 16 16 18 14 14 15 16

25 25 25 25 25 25 26.9 25 25 25 20 20 25 25 25 25 25 25 25 25

Rotor diameter (m)

Rated power (kW)

Hub height (m)

30 31 44 35 39 52 62 70.5 63 60 82 82 76 71.2 70 76 72 94 88 84

200 400 600 660 700 850 1300 1500 1500 1650 1650 1650 1800 2000 2000 2000 2000 2300 2500 2700

30 30.5 46 45 43 55 50 64.7 60 70 70 70 60 65 67 60 68 100 85 70

619

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625 Table 5 Annual mean wind speed at the turbine hub height (Vm (m/s)), Weibull Shape parameter (k), Weibull scale parameter (c (m/s)), and turbine capacity factor (Cf (%)). Sites

Parameters

Different wind turbines from different manufacturers with different hub heights A

B

C

D

E

F

G

H

I

J

–

WM01

Vm k c Cf

5.18 1.69 5.83 13.5

5.19 1.69 5.84 11.8

5.44 1.68 6.11 20.7

5.42 1.68 6.09 11.4

5.39 1.68 6.06 12.9

5.56 1.67 6.24 10.9

5.49 1.68 6.17 16.6

5.67 1.67 6.36 16.9

5.62 1.67 6.30 11.1

5.73 1.66 6.42 14.2

– – – –

WM02

Vm k c Cf

5.44 2.21 6.15 12.8

5.45 2.21 6.17 11.1

5.76 2.17 6.51 21.4

5.74 2.17 6.49 10.8

5.71 2.18 6.46 12.8

5.91 2.14 6.68 10.9

5.83 2.16 6.59 17.0

6.05 2.12 6.84 17.5

5.98 2.13 6.76 10.8

6.12 2.10 6.92 14.7

– – – –

WM03

Vm k c Cf

6.21 2.28 7.01 18.1

6.22 2.28 7.03 15.7

6.52 2.27 7.37 27.6

6.50 2.27 7.35 15.4

6.47 2.27 7.31 17.0

6.67 2.25 7.53 14.7

6.59 2.26 7.45 21.8

6.80 2.23 7.69 22.30

6.74 2.24 7.61 14.9

6.87 2.22 7.76 19.02

– – – –

WM04

Vm k c Cf

5.68 2.13 6.41 14.7

5.69 2.13 6.43 12.8

6.13 2.17 6.92 24.4

6.10 2.17 6.89 13.0

6.05 2.17 6.84 14.8

6.34 2.18 7.16 13.0

6.22 2.18 7.03 19.5

6.54 2.18 7.38 21.0

6.44 2.18 7.28 13.3

6.64 2.18 7.50 17.6

– – – –

WM05

Vm k c Cf

7.72 2.19 8.73 30.6

7.74 2.19 8.75 27.2

8.27 2.21 9.34 42.4

8.24 2.21 9.31 28.7

8.18 2.21 9.24 28.7

8.51 2.22 9.62 26.3

8.38 2.21 9.47 35.0

8.74 2.22 9.88 38.8

8.64 2.22 9.76 28.3

8.86 2.23 10.0 32.8

– – – –

WM06

Vm k c Cf

6.29 2.05 7.12 19.7

6.31 2.05 7.14 17.3

6.72 2.07 7.60 29.8

6.69 2.07 7.57 17.6

6.65 2.07 7.52 18.9

6.91 2.08 7.82 16.7

6.81 2.07 7.70 23.9

7.09 2.08 8.02 25.9

7.01 2.08 7.93 17.5

7.19 2.08 8.13 21.6

– – – –

WM07

Vm k c Cf

6.23 2.41 7.03 17.9

6.24 2.41 7.05 15.4

6.63 2.42 7.48 28.1

6.61 2.42 7.45 15.4

6.56 2.42 7.40 17.2

6.81 2.41 7.68 14.9

6.71 2.42 7.57 22.2

6.98 2.40 7.88 23.9

6.90 2.41 7.79 15.3

7.07 2.40 7.98 19.8

– – – –

WM08

Vm k c Cf

6.48 1.95 7.31 21.5

6.49 1.95 7.33 18.9

6.95 2.03 7.85 31.7

6.93 2.03 7.82 19.4

6.87 2.02 7.76 20.4

7.17 2.06 8.09 18.2

7.05 2.05 7.96 25.7

7.38 2.09 8.33 28.0

7.28 2.08 8.22 19.2

7.49 2.11 8.45 23.5

– – – –

WM09

Vm k c Cf

6.99 2.35 7.90 24.2

7.00 2.35 7.92 21.2

7.35 2.35 8.31 34.7

7.33 2.35 8.29 21.1

7.29 2.35 8.24 22.2

7.51 2.35 8.49 19.4

7.42 2.35 8.39 27.6

7.66 2.35 8.65 29.8

7.59 2.35 8.58 20.3

7.73 2.35 8.74 24.5

– – – –

WM10

Vm k c Cf

6.11 1.94 6.90 18.7

6.12 1.94 6.91 16.4

6.38 1.98 7.21 27.2

6.37 1.98 7.20 15.8

6.34 1.97 7.16 17.3

6.51 1.99 7.36 14.7

6.44 1.98 7.28 21.7

6.63 2.00 7.49 22.5

6.57 2.00 7.43 15.0

6.69 2.00 7.56 18.6

– – – –

K

L

M

N

O

P

Q

R

S

T

WM01

Vm k c Cf

5.73 1.66 6.42 21.9

5.73 1.66 6.42 19.2

5.61 1.67 6.30 12.8

5.67 1.67 6.37 14.7

5.69 1.66 6.39 13.2

5.61 1.67 6.30 10.1

5.70 1.66 6.40 17.2

6.01 1.63 6.73 21.3

5.87 1.65 6.58 17.1

5.73 1.66 6.42 14.2

WM02

Vm k c Cf

6.12 2.10 6.92 23.5

6.12 2.10 6.92 20.4

5.98 2.13 6.76 12.9

6.05 2.12 6.84 15.1

6.08 2.11 6.87 13.5

5.98 2.13 6.76 10.0

6.10 2.11 6.89 17.9

6.47 2.03 7.30 23.3

6.31 2.07 7.12 18.2

6.12 2.10 6.92 14.7

WM03

Vm k c Cf

6.87 2.22 7.76 29.6

6.87 2.22 7.76 25.8

6.74 2.24 7.61 17.1

6.81 2.23 7.69 19.46

6.84 2.23 7.72 17.8

6.74 2.24 7.61 13.4

6.85 2.23 7.74 23.4

7.21 2.16 8.14 28.6

7.05 2.19 7.96 23.0

6.87 2.22 7.76 19.0

WM04

Vm k c Cf

6.64 2.18 7.50 27.7

6.64 2.18 7.50 24.1

6.44 2.18 7.28 15.4

6.55 2.18 7.39 17.9

6.59 2.18 7.43 16.3

6.44 2.18 7.28 12.0

6.61 2.18 7.45 21.5

7.15 2.16 8.06 28.1

6.91 2.17 7.79 22.0

6.64 2.18 7.50 17.6

WM05

Vm k c Cf

8.86 2.23 10.0 45.3

8.86 2.23 10.0 40.7

8.64 2.22 9.76 30.3

8.75 2.22 9.89 32.80

8.80 2.22 9.93 31.4

8.64 2.22 9.76 24.4

8.82 2.22 9.96 39.3

9.40 2.23 10.6 45.5

9.15 2.23 10.3 38.6

8.86 2.23 10.0 32.8

WM06

Vm k c Cf

7.19 2.08 8.13 32.5

7.19 2.08 8.13 28.6

7.01 2.08 7.93 19.5

7.10 2.08 8.03 21.9

7.14 2.08 8.07 20.4

7.01 2.08 7.93 15.4

7.15 2.08 8.09 26.4

7.64 2.08 8.63 32.3

7.42 2.08 8.39 26.2

7.19 2.08 8.13 21.6

(continued on next page)

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Table 5 (continued) K

L

M

N

O

P

Q

R

S

T

WM07

Vm k c Cf

7.07 2.40 7.98 31.0

7.07 2.40 7.98 26.9

6.90 2.41 7.79 17.6

6.99 2.40 7.88 20.1

7.02 2.40 7.92 18.4

6.90 2.41 7.79 14.4

7.04 2.40 7.94 24.3

7.49 2.34 8.45 30.5

7.29 2.37 8.23 24.3

7.07 2.40 7.98 19.8

WM08

Vm k c Cf

7.49 2.11 8.45 34.8

7.49 2.11 8.45 30.8

7.28 2.08 8.22 21.3

7.39 2.09 8.34 23.7

7.43 2.10 8.38 22.2

7.28 2.08 8.22 16.8

7.45 2.10 8.41 28.6

8.02 2.16 9.04 35.0

7.77 2.14 8.76 28.4

7.49 2.11 8.45 23.5

WM09

Vm k c Cf

7.73 2.35 8.74 37.0

7.73 2.35 8.74 32.5

7.59 2.35 8.58 22.5

7.66 2.35 8.66 24.9

7.69 2.35 8.69 23.3

7.59 2.35 8.57 17.7

7.71 2.35 8.71 30.2

8.09 2.34 9.13 35.5

7.92 2.35 8.95 29.2

7.73 2.35 8.74 24.5

WM10

Vm k c Cf

6.69 2.01 7.56 28.5

6.69 2.01 7.55 25.0

6.57 2.00 7.43 17.0

6.63 2.00 7.49 19.1

6.65 2.00 7.52 17.5

6.57 2.00 7.43 13.4

6.66 2.00 7.53 22.8

6.98 2.01 7.88 27.3

6.84 2.01 7.73 22.2

6.69 2.001 7.56 18.5

where Cp is the coefficient of performance of the turbine, it is a function of tip speed ratio and the pitch angle. Theoretically, Cp has a maximum value of 0.59 known as Betz limit. The variable wind speed turbine has the ability to track the maximum Cp by adjusting the turbine speed according to the wind speed. gm is the mechanical transmission efficiency and gg is the generator efficiency. For pitch-controlled turbines, the power curve can be approximated with a parabolic law as given in following equation [18]

where f(v) is the Weibull distribution function as given in (1). Eq. (21) can be solved using integration by substitution and by parts as [7]

8 v 2 v 2ci > > > Pr v 2r v 2ci <

c is the lower incomplete gamma function and has a property of fol-

ðv ci 6 v 6 v r Þ

Pðv Þ ¼ Pr ¼ qAC p gm gg v > > > : 0 1 2

3 r

lowing equation

ðv r 6 v 6 v co Þ

cðu; aÞ ¼

ðv 6 v ci andv P v co Þ

P av g Pr

ð17Þ

The average output power of a wind turbine (pavg) is a very important factor in a wind energy conversion system as it is a better indicator of economics than the rated power. pavg can be estimated as (18) [6] where the probability density function f(v) represents the fraction of duration of wind speed v. The Cf of various wind turbines is evaluated using the Weibull distribution function in line with the conclusion in Section 3.4.

Z v co v ci

Pðv Þ f ðv Þdv

ð18Þ

Substituting (16) in (18) using Weibull distribution function results in following equation

P av g ¼

Z vr v ci

P av g ¼ P r

v 2  v 2ci Pr 2 f ðv Þdv þ v r  v 2ci w

"Z vr v ci

Z v co

v 2  v 2ci f ðv Þdv þ v 2r  v 2ci w

vr

Pr fw ðv Þdv

Z v co vr

ð19Þ

# fw ðv Þdv

Z vr v ci

v 2  v 2ci f ðv Þdv þ v 2r  v 2ci w

Z v co vr

1 CðaÞ

Z

u

xa1 ex dx

ð23Þ

0

fw ðv Þdv

Z

1

nx1 expðnÞdn and Cð1 þ xÞ ¼ xCðxÞ

ð24Þ

0

The Weibull parameters k and c were determined using maximum likelihood method as given by (25) and (26) respectively.

"Pn k¼

c¼

i¼1

v k lnðv bðiÞ Þ  k i¼1 v bðiÞ

Pni

Pn

v

i¼1 lnð bðiÞ Þ

#1

n

" #1 k n 1X v kbðiÞ n i¼1

ð25Þ

ð26Þ

where vb(i) is the wind speed at the turbine hub height. Average energy production of a turbine can be calculated for a specific period once the Cf is known as

AEP ¼ Cf :Pr  t

ð27Þ

where t is the time frame under consideration in hours, i.e. for annual average energy production t = 8760 h. 4.2. Shear exponential and wind speed estimation at hub height

ð20Þ

therefore

Cf ¼



C() is the gamma function. It has the properties of following equation

The capacity factor of a wind turbine is the ratio of the average output power of the turbine over a period of time to its potential output if it had operated at rated capacity the entire time.

pav g ¼

ð22Þ

ð16Þ

4.1. Analytical model of capacity factor

Cf ¼

 k   2   k  vco k C k 2c2 vr 2 v ci 2   eð c Þ c ; c ;  2 2 k k c c v r  v ci k

 Cf ¼

ð21Þ

Wind speed changes with height. Most wind speeds are observed at a height that does not match the hub height of most commercially available wind turbines. It is therefore necessary to redefine the wind speed from the observed height to the hub height of the wind turbines. This can be achieved using the power law equation [19]

621

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625 Table 6 Seasonal capacity factor (Cf (%)) for the sites. Sites

Season

Cf (%) of different wind turbines from different manufacturers with different hub heights for all the sites A

B

C

D

E

F

G

H

I

J

WM01

Autm Sprg Sumr Wint

10.7 15.6 15.5 10.7

9.2 13.7 13.6 7.8

17.5 23.4 22.4 18.2

9.2 13.3 12.8 9.3

10.7 14.8 14.2 11.0

9.2 12.7 11.9 9.5

14.1 18.8 17.9 14.7

14.4 19.4 18.0 15.2

9.2 12.9 12.0 9.6

12.3 16.3 15.0 13.0

WM02

Autm Sprg Sumr Wint

10.8 11.9 13.0 14.4

9.4 10.3 11.3 12.5

18.8 20.4 21.2 24.2

9.3 9.6 10.8 12.4

11.2 12.0 12.8 14.5

9.6 9.9 10.8 12.5

15.0 16.1 16.8 19.2

15.5 16.1 17.2 20.4

9.6 9.5 10.7 12.6

13.2 13.5 14.4 17.1

WM03

Autm Sprg Sumr Wint

16.0 19.3 19.6 15.9

13.9 16.7 17.2 13.8

26.0 29.3 28.4 25.9

13.9 16.3 16.5 13.7

15.8 18.1 18.0 15.7

12.3 14.3 14.4 12.2

20.6 23.1 22.5 20.5

22.0 24.5 23.5 21.7

13.9 15.9 15.7 13.7

18.3 20.2 19.4 18.1

WM04

Autm Sprg Sumr Wint

11.3 15.9 19.6 10.3

9.9 13.8 17.1 9.0

17.5 22.8 26.2 16.5

9.9 14.2 17.3 9.4

12.0 16.0 18.7 11.2

10.4 14.1 16.5 10.0

16.2 21.0 24.0 15.4

17.2 22.9 26.0 16.5

10.5 14.5 17.1 10.1

14.6 19.1 21.5 14.2

WM05

Autm Sprg Sumr Wint

29.4 26.8 34.7 28.6

26.2 28.4 30.9 25.5

40.7 43.6 46.5 39.9

27.6 29.2 32.1 26.9

27.7 29.3 31.8 27.1

25.5 26.4 29.3 24.9

33.8 35.6 38.3 33.1

37.2 39.1 42.3 36.5

28.0 28.2 31.1 26.7

31.7 32.6 35.6 31.5

WM06

Autm Sprg Sumr Wint

19.7 21.1 16.0 23.8

17.3 18.6 13.9 21.0

29.4 30.5 25.9 34.8

17.8 18.9 13.6 22.1

18.9 19.8 15.6 22.8

16.8 17.7 13.4 20.7

23.8 24.7 20.4 28.4

25.7 26.4 21.5 31.4

17.6 18.5 13.4 22.0

21.6 22.3 17.8 26.5

WM07

Autm Sprg Sumr Wint

15.3 19.7 17.8 18.4

13.3 17.2 15.5 16.1

25.0 30.3 27.7 29.4

13.3 17.1 15.0 16.7

15.2 18.7 16.9 18.2

13.2 16.3 14.5 16.3

19.9 23.9 21.8 23.5

21.2 25.9 23.0 26.0

13.4 16.8 14.6 17.0

17.7 21.3 18.9 21.7

WM08

Autm Sprg Sumr Wint

21.8 23.2 21.2 20.3

19.3 20.5 18.6 18.0

32.3 33.8 31.1 30.7

20.1 21.1 18.4 19.1

21.1 22.0 19.7 20.0

19.0 19.7 17.1 18.4

26.4 27.4 24.8 25.3

29.1 30.1 26.5 28.2

20.1 20.8 17.7 19.6

24.5 25.2 21.9 24.1

WM09

Autm Sprg Sumr Wint

24.5 28.9 22.1 28.9

21.3 25.4 19.2 21.459

35.5 40.1 32.2 34.123

21.6 25.6 18.8 21.8

22.6 26.1 20.2 22.6

19.9 23.1 17.4 20.1

28.2 32.1 25.4 27.9

30.8 35.0 27.0 29.935

20.8 24.5 17.9 21.2

25.3 28.8 22.1 25.1

WM10

Autm Sprg Sumr Wint

16.2 23.0 16.3 20.1

14.2 20.8 14.2 17.7

24.5 32.7 24.3 28.8

13.8 19.9 13.0 17.6

15.3 21.0 15.0 18.7

13.1 18.0 12.3 16.4

19.6 26.0 19.0 23.3

20.3 27.2 19.1 24.8

13.3 18.6 12.1 17.0

17.0 22.3 15.7 20.7

K

L

M

N

O

P

Q

R

S

T

WM01

Autm Sprg Sumr Wint

19.0 24.8 22.8 20.2

16.6 21.7 20.0 17.7

10.7 14.7 13.7 11.3

12.6 16.7 15.5 13.3

11.3 15.2 14.0 11.9

8.5 11.6 10.8 8.8

14.7 19.7 18.1 15.6

19.1 24.1 21.5 20.7

15.0 19.5 17.6 16.2

12.3 16.3 15.0 13.0

WM02

Autm Sprg Sumr Wint

21.0 22.1 22.9 27.3

18.2 19.0 19.8 23.6

11.4 11.7 12.7 14.9

13.5 14.1 14.9 17.4

12.0 12.3 13.2 15.7

8.9 9.1 9.9 11.6

15.9 16.4 17.5 20.9

21.2 21.6 22.2 27.6

17.8 17.8 18.6 23.0

13.2 13.5 14.4 17.1

WM03

Autm Sprg Sumr Wint

28.8 31.6 29.6 28.6

25.0 27.5 26.0 24.8

16.2 18.2 17.7 15.9

18.6 20.6 19.9 18.4

16.9 18.9 18.3 16.7

12.6 14.2 14.0 12.4

22.4 24.9 23.8 22.2

28.5 30.5 28.2 28.2

22.5 24.5 23.1 22.2

18.3 20.2 19.4 18.0

WM04

Autm Sprg Sumr Wint

23.4 30.0 33.2 22.5

20.3 26.1 29.0 19.5

12.5 16.7 19.3 11.7

14.9 19.4 21.8 14.4

13.3 17.7 20.2 12.9

9.7 13.1 15.1 9.4

17.7 23.4 26.5 17.1

24.3 30.4 32.7 24.0

16.3 21.0 23.2 16.0

14.6 19. 21.5 14.2

WM05

Autm Sprg Sumr Wint

43.1 46.3 49.0 42.4

38.8 41.4 44.1 38.1

30.0 30.4 33.3 28.7

31.7 32.8 35.7 31.1

30.4 31.3 34.3 29.8

24.3 24.2 26.7 23.1

37.8 39.6 42.8 37.0

43.8 45.3 48.6 43.1

37.2 38.3 41.6 36.6

30.5 32.1 34.7 29.9

WM06

Autm Sprg Sumr

32.0 32.1 28.4

28.3 28.5 24.6

19.6 20.3 15.7

21.9 22.6 18.2

20.4 21.1 16.5

15.5 16.3 12.3

26.0 26.8 21.9

30.0 30.1 25.5

26.1 26.5 21.9

21.6 22.3 17.8

(continued on next page)

622

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

Table 6 (continued) K

L

M

N

O

P

Q

R

S

T

Wint

37.9

33.8

24.1

26.6

25.2

19.2

32.0

36.5

31.8

26.5

WM07

Autm Sprg Sumr Wint

27.8 33.2 30.0 33.2

24.2 28.9 26.0 29.1

15.6 19.2 16.9 19.3

18.0 21.7 19.4 21.9

16.4 20.0 17.6 20.3

12.2 15.0 13.2 15.1

21.6 26.4 23.4 26.6

27.7 32.5 28.9 33.5

21.9 26.1 23.0 26.9

17.7 21.3 18.9 21.7

WM08

Autm Sprg Sumr Wint

35.7 36.9 33.5 34.6

31.7 32.7 29.3 30.8

22.1 22.9 19.9 21.5

24.6 25.4 22.3 24.0

23.1 23.8 20.6 22.7

17.6 18.2 15.6 17.2

29.6 30.6 26.9 28.9

36.3 36.9 32.4 36.4

29.6 30.3 26.3 29.5

24.5 25.2 21.9 24.1

WM09

Autm Sprg Sumr Wint

38.3 42.6 34.3 36.0

38.3 42.6 34.3 36.0

20.8 24.5 17.9 21.2

25.6 29.1 22.6 25.4

34.0 27.5 20.9 24.0

18.2 21.1 15.8 18.5

31.2 35.5 27.4 30.3

36.9 40.9 32.6 35.4

30.3 34.1 26.5 29.6

25.3 28.8 22.1 25.1

WM10

Autm Sprg Sumr Wint

26.2 33.8 25.0 30.5

22.9 29.7 21.7 27.0

15.3 20.7 14.4 18.9

17.4 22.9 16.4 21.1

15.8 21.1 14.9 19.5

12.0 16.3 11.1 15.0

20.7 27.4 19.3 25.0

25.5 31.7 23.4 30.0

20.5 26.3 18.7 24.6

17.0 22.3 15.7 20.7

Table 7 Wind turbines annual capacity factor (Cf (%)) estimation for the day periods (DAY), night periods (NIGHT), morning peak periods (M-PK) and evening peak periods (E-PK). Sites

Periods

Different wind turbines from different manufacturers K

L

M

N

O

P

Q

S

T

WM01

DAY NIGHT M-PK E-PK

18.6 8.4 4.5 26.3

16.4 7.3 3.9 23.1

26.1 15.3 9.5 36.4

15.3 7.4 3.7 23.4

16.8 9.1 5.3 24.1

14.1 7.9 4.3 21.3

20.8 12.4 7.7 29.5

R 21.1 12.8 7.2 31.8

14.3 7.9 4.0 16.3

17.5 11.5 6.5 26.5

WM02

DAY NIGHT M-PK E-PK

14.2 11.3 10.7 16.3

12.3 9.9 9.3 14.1

22.5 20.3 18.3 27.2

11. 10.3 8.8 13.9

13.5 12.1 10.9 16.3

11.0 10.7 9.1 10.2

17.6 16.4 14.6 21.3

17.4 17.5 14.6 22.9

10.6 10.9 8.9 14.0

14.4 14.9 12.4 18.9

WM03

DAY NIGHT M-PK E-PK

20.7 15.4 9.9 32.8

18.0 13.4 8.6 28.4

29.2 25.9 17.2 45.6

16.8 13.9 8.3 28.8

18.4 15.7 10.2 29.0

15.3 14.0 8.6 25.6

22.9 20.7 13.7 35.7

23.4 22.6 13.8 39.9

15.5 14.4 8.4 27.3

19.1 18.9 11.7 32.1

WM04

DAY NIGHT M-PK E-PK

17.8 11.4 7.2 25.1

15.6 10.0 6.2 21.9

26.7 22.0 14.1 38.0

15.1 10.8 5.9 23.0

16.7 12.9 8.0 23.8

14.2 11.7 6.7 21.5

21.1 17.8 11.3 30.2

22.0 19.9 11.1 34.2

14.4 12.0 6.3 22.9

18.2 16.9 9.7 28.1

WM05

DAY NIGHT M-PK E-PK

34.6 26.7 28.6 32.0

30.8 23.6 25.4 28.4

45.7 39.2 39.8 44.6

31.7 25.6 26.6 30.3

31.5 25.9 26.9 30.1

28.6 24.1 24.5 27.8

37.7 32.3 32.8 36.8

41.1 36.4 36.1 41.1

30.5 25.3 26.2 30.0

34.7 30.8 30.5 34.7

WM06

DAY NIGHT M-PK E-PK

21.7 17.8 16.6 22.1

19.0 15.6 14.5 19.3

30.9 28.7 25.3 33.3

18.6 16.7 14.5 20.0

19.8 17.9 15.9 21.0

17.1 16.3 13.9 18.8

24.6 23.2 20.4 26.7

25.9 25.9 21.5 29.4

17.6 17.2 14.2 19.8

21.4 21.8 18.0 24.4

WM07

DAY NIGHT M-PK E-PK

16.5 16.9 12.1 22.0

14.4 14.6 10.5 19.2

23.8 26.9 19.4 31.4

12.8 13.9 9.1 18.3

14.7 16.2 11.5 19.8

11.9 13.7 9.1 16.8

18.6 21.0 15.1 24.7

18.1 21.8 14.3 25.8

11.6 13.5 8.5 17.1

14.9 18.0 11.9 21.1

WM08

DAY NIGHT M-PK E-PK

27.7 15.5 20.1 20.5

24.4 13.6 17.7 18.0

37.8 25.8 29.9 31.4

24.3 14.6 18.0 18.8

24.9 16.0 19.2 19.9

21.9 14.6 17.0 17.9

30.4 21.0 24.2 25.3

32.7 23.5 26.2 27.9

23.0 15.3 17.8 18.8

27.1 19.9 21.9 23.3

WM09

DAY NIGHT M-PK E-PK

27.5 20.7 22.1 25.8

24.2 18.0 19.3 22.6

37.2 31.9 31.7 37.5

23.7 18.4 18.9 23.1

24.4 19.8 20.2 24.0

21.2 17.6 17.4 21.3

29.8 25.4 25.2 29.9

31.6 27.8 26.6 32.9

22.1 18.3 18.0 22.5

26.0 23.0 21.9 27.1

WM10

DAY NIGHT M-PK E-PK

15.4 11.6 10.2 17.0

13.1 10.0 8.8 14.6

23.1 22.3 18.4 27.7

11.5 10.7 8.2 14.1

13.7 12.7 10.4 16.4

12.6 13.4 10.6 15.4

18.5 18.6 15.3 22.2

21.7 25.4 20.0 27.0

16.5 18.5 14.7 20.1

19.2 23.3 18.4 23.4

623

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625 Table 7 (continued) Sites

Periods

Different wind turbines from different manufacturers L

M

N

O

P

Q

R

S

T

WM01

DAY NIGHT M-PK E-PK

26.4 17.4 10.6 38.2

23.2 15.2 9.2 34.0

16.1 9.4 5.2 24.5

18.0 11.3 6.7 26.8

16.5 10.0 5.6 25.3

12.8 7.4 4.0 19.5

21.2 13.2 7.4 32.1

247 18.1 11.2 37.2

20.4 11.9 8.2 31.2

17.5 11.1 6.4 26.5

WM02

DAY NIGHT M-PK E-PK

23.5 23.4 19.9 30.5

20.2 20.4 17.2 26.3

12.8 12.8 10.7 16.6

15.1 15.2 12.8 19.3

13.2 13.7 11.3 17.5

10.0 10.0 8.4 12.9

17.6 18.0 14.9 23.4

22.0 24.2 19.7 30.2

17.4 18.8 15.3 23.5

14.4 14.9 12.4 18.9

WM03

DAY NIGHT M-PK E-PK

29.8 29.5 18.8 49.0

26.0 25.7 16.3 42.9

17.7 16.4 10.1 29.8

19.8 19.1 12.1 32.3

18.0 17.5 10.6 30.7

13.8 13.0 7.9 23.3

23.6 23.1 14.1 40.4

27.5 29.8 18.6 49.5

22.5 23.6 14.4 38.6

19.1 18.9 11.7 32.1

WM04

DAY NIGHT M-PK E-PK

28.2 27.0 16.0 42.7

24.7 23.3 13.8 37.4

16.5 14.2 8.0 25.4

18.7 17.0 10.1 28.1

17.1 15.4 8.6 26.6

13.0 11.1 6.2 19.8

20.3 20.1 11.5 34.8

27.0 29.1 16.9 42.0

21.9 22.1 12.4 34.4

18.2 16.9 9.7 28.1

WM05

DAY NIGHT M-PK E-PK

47.2 43.3 42.3 48.0

42.6 38.7 37.9 43.1

32.6 27.4 28.2 32.1

34.9 30.7 30.6 34.7

33.5 29.4 29.2 33.3

26.3 21.9 22.7 25.7

41.6 37.0 36.6 41.7

46.6 44.6 42.3 48.3

40.2 37.0 35.9 41.0

34.7 30.8 30.5 34.7

WM06

DAY NIGHT M-PK E-PK

32.2 32.9 27.4 36.7

28.3 28.9 24.1 32.3

19.7 19.3 16.2 22.0

21.9 21.9 18.4 24.6

20.3 20.4 16.8 23.0

15.6 15.2 12.7 17.3

26.2 26.5 21.9 29.9

30.6 33.9 27.0 36.3

25.3 27.1 21.8 29.6

21.4 21.8 18.0 24.4

WM07

DAY NIGHT M-PK E-PK

23.7 29.0 19.7 32.7

20.6 25.0 16.9 28.5

13.6 16.0 10.6 19.4

15.6 18.5 12.6 21.7

13.8 16.6 10.8 19.9

10.7 12.5 8.2 15.2

18.3 22.2 14.4 26.1

21.4 27.7 18.1 30.5

17.4 21.9 14.2 24.9

14.9 18.0 11.9 21.0

WM08

DAY NIGHT M-PK E-PK

39.5 30.2 32.6 35.0

35.1 26.5 28.6 30.8

25.2 17.4 19.8 21.0

27.5 20.0 22.2 23.5

25.9 18.5 20.7 22.0

20.0 13.7 15.7 16.5

33.1 24.1 26.6 28.5

37.9 32.0 32.6 35.3

31.8 25.1 26.5 28.5

27.1 19.9 21.9 23.3

WM09

DAY NIGHT M-PK E-PK

38.3 35.4 33.3 40.5

33.9 30.9 29.2 35.8

24.3 20.6 20.1 24.8

26.5 23.2 22.4 27.3

24.8 21.5 20.7 25.7

19.2 16.1 15.8 19.5

31.9 28.3 26.9 33.4

36.0 34.8 31.6 39.5

34.6 28.0 26.0 32.5

26.0 22.9 21.9 27.1

WM10

DAY NIGHT M-PK E-PK

28.0 32.9 26.3 35.4

24.8 29.4 23.4 31.1

15.6 17.6 13.9 19.1

18.6 21.7 17.3 22.7

17.5 21.0 16.5 21.4

12.2 13.8 10.9 14.9

22.7 27.1 21.4 28.3

29.7 36.3 29.5 38.2

24.8 31.4 24.7 31.2

19.6 23.3 18.4 23.4

v 2ðiÞ ¼ v 1ðiÞ



H2 H1

K

mðiÞ ð28Þ

where v2(i) is the wind speed at height H2 and v1(i) is the wind speed at height H1. The exponential shear m(i) is the factor that is influenced by surface roughness and atmospheric stability. It is site specific and it usually falls in the range of 0.05–0.5 [20]. m(i) can be determined by taking the logarithm of Eq. (28) as given by following equation

mðiÞ

  v log v 2ðiÞ  1ðiÞ ¼ log HH21

ð29Þ

Once m(i) is known for a specific site, then individual wind speeds at various turbine hub heights can be extrapolated as

v bðiÞ ¼ v oðiÞ



Hb Ho

mðiÞ ð30Þ

where vb(i) is the wind speed at the hub height Hb, and vo(i) is the wind speed at the observed height Ho. It should be noted that shear exponential is subject to variation in time and is site specific. The plots of m(i) for site WM05 and

WM07 are shown in Fig. 4. To obtain a more accurate wind speed at a different hub height, m(i) should be calculated over time. In this case, m(i) is calculated over every 10-min average data for each of the sites. This is implemented in Matlab™. In determining the Cf of the commercially available wind turbines while taking the various heights into account, the new mean wind speed vm, k and c are calculated at each of the hub height of each turbine based on the 10 min average exponential shear calculated over time. These values are then used to determine the capacity factor for each of the turbines. The average exponential shear, E(m(i)) for each of the sites using the wind speeds at 20 m and 60 m height are given in Table 3.

5. Wind turbine specifications Twenty wind turbines from different manufacturers are obtained from the literature [9], WASP [11] and manufacturers website [21–24]. The turbine speed operating range, the rotor diameter, rated power and the hub height for each are shown in Table 4. The wind turbines are arranged in order of rated power from 200 kW to 2700 kW.

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5.1. Results and discussion Table 5 presents the annual mean wind speed, the capacity factor, the Weibull shape and the scale parameter at the turbine hub height for each of the 20 commercially available wind turbines for all the ten sites.

autumn (Autm) (April–May); and winter (Wint) (June–August). The Cf for each season is estimated for each sites based on the Weibull shape and scale parameters calculated from the extrapolated local wind speed. The results are presented in Table 6.

5.3. Diurnal and peak-periods capacity factor estimation 5.2. Seasonal capacity factor estimates of the sites There are four distinct seasons in the country: Spring (Sprg) (September–October); summer (Sumr) (November–March);

The day and night data, as well as the morning (M-PK) and evening peak-periods (E-PK) data, were extracted from the raw excel data sheet using a program written for that purpose in Matlab™. The Cf for each of the 20 turbines is calculated using

Fig. 5. Probability density comparison at 60 m height for the day, night, morning peak period (M_PK), evening peak period (E-PK) and the annual distribution for (a) WM01 (b) WM02 (c) WM03 and (d) WM04.

Fig. 6. Impact of (a) cut-in wind speed on the turbine Cf, (b) rated wind speed on the turbine Cf, (c) cut-in-wind speed on the turbine Cf, and (d) Turbine hub height on Cf and AEP.

T.R. Ayodele et al. / Energy Conversion and Management 64 (2012) 614–625

the statistical parameter of wind distribution of the ten sites. The results are given in Table 7. For simplicity, day time is the period from 07:00 to 19:00 and night is the period from19:00 to 07:00. In South Africa, two peak periods for electricity demand are identified: from 07:00 to 10:00 in the morning and from 18:00 to 20:00 in the evening. This information is important in the preliminary planning for electricity generation dispatch. Fig. 5 compares the pdf for various periods i.e., day, night, morning peak periods and the evening peak periods for all the sites. From the figure, it can be deduced that the probability of observing higher wind speeds is highest during the evening peak periods (18:00–20:00).

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70 m and rated power of 1600 kW, seems the most appropriate choice in the coastal region of South Africa. Acknowledgements The authors acknowledge the financial support of the Tshwane University of Technology. We also thank the Department of Energy (DoE), UNDP-GEF via South African Wind Energy Programme (SAWEP) and the Royal Danish Embassy for their initiative on Wind Atlas for South African Project and making the wind speed data available through the CSIR. References

5.4. Impact of turbine operating curve parameters and hub height on the wind turbine capacity factor Fig. 6a–c shows that Cf is mostly affected by the turbine cut-in wind speed vco and the rated wind speed vr while the cut-out wind speed vco has negligible impact on the Cf. The influence of hub heights on the Cf and the annual energy production (AEP) of wind turbines was demonstrated using the Weibull distribution parameters of site WM07 and the operating parameters of turbine K (Vestas-V82). The Weibull parameters of this site were first calculated from the actual wind speed measured at anemometer heights of 10, 20, 40 and 60 m, respectively. Then, the annual Cf and the AEP of turbine K were determined using Eqs. (22) and (26), respectively. The results are depicted in Fig. 6d. It can be observed from the results that an increase in the hub height of wind turbine from 10 m to 20, 40 and 60 m can potentially increase both the Cf and AEP by 5%, 14.5% and 33.3% respectively. 6. Conclusion The Cf for each of the 20 commercially available wind turbines using the local wind regimes of ten different sites in the coastal region of South Africa has been estimated. The estimation is based on an analytical model using appropriate statistical distribution determined using RMSE and R2 as a test of goodness of fit. The results show that the wind distribution in the entire sites can best be modelled using the Weibull distribution with the Rayleigh distribution being a close competitor. It has also been shown that site WM05 has the highest Cf, which ranges from 26.34% with turbine F to 45.45% with turbine R. Site WM02 has the lowest Cf which ranges from 10.04% with turbine P, to 23.53% with turbine K. The results also indicate that the wind turbines have a higher Cf in spring (September–October) at all the sites except WM03 with a higher Cf in summer (November–March) and WM06 in winter (June–August). More wind power can be harnessed during the day compared to the night, with most of the wind turbines except at site WM07 which has a higher turbine Cf during the night. The evening electricity peak periods (18:00–20:00) have a higher Cf when compared to the morning peak periods (7:00–10:00) at all the sites. Of the turbines considered for the study based on Cf estimation, turbine K with a cut-in wind speed of 3 m/s, a rated wind speed of 13 m/s, a cut-out wind speed of 20 m/s, a hub height of

[1] GWEC. Global Wind Statistic; 2010. [accessed 07.09.11]. [2] El-Sayed MA. Integrating wind energy into weak power grid using fuzzy controlled TSC compensator. International conference on renewable energies and power quality (ICREPQ, 2010), Granada, Spain; 2010. [3] South.Africa.info. South Africa Energy supply; 2010. . [4] Santhyajith M. Wind energy fundamentals, resources analysis and economic. Springer Publisher; 2006. [5] Akdag SA, Guler O. Wind characteristics analysis and determination of appropriate wind turbine for Amasra-Black sea region, Turkey. Int J Green Energy 2010;7:422–33. [6] Hu S, Cheng J. Performance evaluation of pairing between sites and wind turbines. Renew Energy 2007;32:1934–47. [7] Albadi MH, El-Saadany EF. Wind turbine capacity factor modeling – a novel approach. IEEE Trans Power Syst 2009;24:1637–8. [8] Jangamshetti SH, Guruprasada Rau V. Optimum siting of wind turbine generator. IEEE Trans Energy Convers 2001;16:8–13. [9] Yeh T, Wang L. A study on generator capacity for wind turbines under various tower heights and rated wind speeds using Weibull distribution. IEEE Trans Energy Convers 2008;23:592–602. [10] Jangamshetti SH, Guruprasada Rau V. Site matching of wind turbine generatore: a case study. IEEE Trans Energy Convers 1999;14:1537–43. [11] WASA. Data files; 2011. . [12] Szewczuk S. Wind Atlas for South Africa: Wind measurements and micro-scale modelling. Industrial and commercial use of energy conference, Cape Town; 2010. [13] Bilgili M, Sahin B, Kahraman A. Wind energy potential in Antakya and Iskenderun region, Turkey. Renew Energy 2004;29:1733–45. [14] Ulgen K, Hepbasli A. Determination of Weibull parameters for wind energy analysis of Izmir, Turkey. Int J Energy Res 2002;26:495–506. [15] Seguro JV, Lambert TW. Modern estimation of the parameters of Weibull wind speed distribution for wind energy analysis. J Wind Eng Ind Aerodynam 2000;85:75–84. [16] Manwell JF, McGowan JG, Rogers AL. Wind energy explained, theory, design and application. England: John Wiley and Sons Ltd.; 2002. [17] Zaharim A, Razali AM, Abidin RZ, Sopian K. Fitting of statistical distributions to wind speed data in Malysia. Eur J Sci Res 2009;26:6–12. [18] Pallabazzer R. Parametric analysis of wind siting efficiency. J Wind Eng Ind Aerodynam 2003;91:1329–52. [19] Di Piazza A, Di Piazza MC, Ragusa, Vitale G. Statistical processing of wind speed data for energy forecast and planning. International conference on renewable energies and power quality (ICRPQ, 10), Granada (Spain); 2010. [20] Nigim KA, Parker P. Heuristic and probabilistic wind power availability estimation procedures: improved tools for technology and site selection. Renew Energy 2007;32:638–48. [21] ENERCON; 2011. [accessed July 19]. [22] GAMESA; 2011. [accessed July 19]. [23] GE; 2011. [accessed July 20]. [24] VESTAS; 2011. [accessed: July 19].