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Weibull distribution for determination of wind analysis and energy production

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Engineering

World Journal of Engineering 12(3) (2015 ) 215-220

Engineering

1. Introduction

In recent years, due to the increasing energy consumption and environmental pollution, all over the world tends to clean and renewable sources of energy. Wind energy is one of the clean and renewable energy sources and is the kinetic energy that airflow to the wind. A portion of this energy can be converted to useful mechanical or electrical energy. Today, generation of electric energy from wind by using modern wind tribunes is very widespread in all around the world. As end of 2014, the wind energy installed power capacity in the world was 369.553 GW (GWEC, 2015).

Weibull distribution for determination of wind analysis and energy production

Faruk Oral

1,*

, I

smail Ekmekçi

2

and Nevzat Onat

3

1Bitlis Eren University, Faculty of Engineering Architecture, Department of Mechanical Eng., Bitlis, 13000, Turkey

2Istanbul Commerce University, Engineering and Design Faculty, Istanbul, 34840, Turkey

3Marmara University, Vocational School of Technical Studies, Istanbul, 34722, Turkey

*E-mail: foral@beu.edu.tr

(Received 3 February 2015; Accepted 18 May 2015) Abstract

In recent years, decreasing reserves and environmental problems related with fossil fuels have increased the demand for clean and renewable energy sources, as with all over the world and also in Turkey. Wind energy is the one of the most rapidly growing among the renewable energy sources in terms of technological and utilization. Turkey is one of the rich countries in Europe in respect to wind energy potential. Productive and effective use of this potential is very important for Turkey that is depended on foreign countries especially in respect to fossil energy sources.

Wind speed values are the most important data in calculation of electrical energy from wind turbines. In this study, latest developments and energy-power equations related to wind turbines are investigated. Using of the data obtained from the wind measurement station installed in Sakarya-Esentepe region, annual electrical energy production of an example wind plant is predicted.

Key words: Weibull distribution, Wind energy, Electrical energy production, Prediction.

Engineering

Wind energy potential in Turkey is good. But, Turkey is largely dependent on outside in terms of fossil fuels especially oil and natural gas and is in critical point with regard to installed power required to meet the energy demand. This situation made the country indirectly foreign-dependent for electric energy production and an importer country. For this reason, it is important to use wind energy potential of country. In recent years the production of electrical energy from wind can be seen an increase. At the end of 2014, installed wind energy capacity in Turkey reached to 3762 MW (TWEA, 2015).

ISSN:1708-5284

(2)

Basically, projecting and economical analysis a wind farm is done according to the amount of energy that can be produced in the selected plant area. In these analyses, wind speed, direction and frequency data are the most important parameters are used. Therefore, it is important to establish a wind measurement station and take the values above mentioned at least one year. In this study, by using the wind data obtained from wind measures made for energy generation purpose, determination of electric energy generation potential from wind tribune was researched. In the study, the power and energy equations of wind turbines were examined.

By using the wind data obtained from the wind measurement power station installed in Sakarya- Esentepe region, the annual electric energy generation of a model wind electric power station was estimated.

2. Wind turbines

Wind turbines have become today’s modern wind turbines by passing various variations throughout history. Wind turbines are classified according to the rotating axes, power and blade number. Modern turbines are generally categorized as two main groups by rotation axes: vertical and horizontal-axes wind turbines.

Vertical-axes wind turbines (VAWTs) are a type of wind turbine where the main rotor shaft is set vertically, perpendicular to the wind direction and the main components are located at the base of the turbine. Today, VATWs are generally used in experimental studies and low power stand-alone applications through their low efficiency and reliability disadvantages. In horizontal-axes wind turbines (HAWTs), rotation axe is parallel and blades are perpendicular to the wind direction. In HAWTs, rotor speed increase for lower rotor blades.

Therefore, HAWTs can be classified as high-speed (blades number from 1 to 4) and low-speed (blades number are more than 4) turbines according to the number of blades. Generally, low-speed turbines are used in stand-alone applications such as water pumping. Turbines used in wind farms for commercial production of electric power are usually three-bladed, high-speed and pointed into the wind by computer-controlled motors. Today, commercial wind turbines that have 120 m rotor diameter, 160m hub height and 5 MW rated power are now available.

3. Mathematical method

3.1. Weibull probability density function

In many studies made to determine the wind energy potential, it was determined that the wind speed data showed Weibull distribution feature (Akpinar and Akpinar, 2004; Kose et al., 2004;

Seguro and Lambert, 2000; Celik, 2003; Ulgen and Hepbasli, 2002; Bayülken and Bekdemir, 2007;

Weisser, 2003; Karsli and Geçit, 2003; Bilgili et al., 2004; Ozerdem and Turkeli, 2003; Ozerdem and Turkeli, 2005; Sahin et al., 2005; Bassyouni et al., 2015; Jiang et al., 2015). Therefore, Weibull distribution method is used to determine the wind speed distribution and statistical analysis in this study. Figure and scale parameters must be known to obtain the Weibull probability density function.

The general expression of the two-parameter Weibull probability density function for wind speed can be shown with the following equity (Karsli and Geçit, 2003; Incecik and Erdogmus, 1995).

(1)

Whereas f (v), v, k and c express the Weibull density function in the wind speed, the non- dimensional figure parameter and the scale parameter respectively. Cumulative Weibull distribution function can be expressed as follow (Ulgen and Hepbasli, 2002; Persaud et al., 1999).

(2)

There are several methods to determine the Weibull distribution parameters. Graphical method that is a highest possibility method is the most widely-used approaches. In this study, graphical method was used. Verity of this method is minimizing of the vertical differences between the observed and representing by segment wind speed data. The average wind speed of Weibull distribution can be expressed in the following equation (Celik, 2003).

(3)

In this equation, Γ() represents the gamma function and can be calculated with equation (4).

v c

m= Γ(1+k1)

F v v

c

( )

= − − k



 

 1 exp

f v k c

v c

v c

k k

( )

=   − 





−1

exp

(3)

(4)

3.2. Electrical power production from wind energy Wind is a moving airflow and has kinetic energy.

The power to be obtained from wind per unit area can be expressed with the following equation.

(5)

Whereas, A and ρ express the sweep area of turbine and air density respectively. The average wind power density (P) for Weibull distribution can be expressed with the following equation (Celik, 2003; Bayülken and Bekdemir, 2007; Arslan, 2010).

(6)

Basically, initial wind power (p(v)) is turns to mechanical power (Pmec) after via the turbine.

Mechanical power decreases to transmission power (Pt) because of bearing losses. Finally, transmission power is transformed into the electrical power (Pe).

In this wind turbine; if Cp, ηmec, ηeand p(v) are the turbine power coefficient, the mechanic system yield, electric system efficiency and the initial wind power respectively, the electrical power to be obtained from ideal wind turbine can be expressed as follows (Johnson, 2001).

pe = Cpηmecηep (v) (7) Cp value that is power factor of a turbine is expressed as the rate of mechanical power to theoretical power of wind. Maximum value of Cpis 59% and called as Betz Limit. A wind tribune starts power generation with its initial speed of V1(cut-in speed) and continues until it reaches to nominal power generation (PR) in speed of VR. After the tribune reaches its nominal power generation, it begins to slow down in a controlled manner. The tribune turns off itself in wind speeds above cut-off speeds (V0) and makes no energy generation. The energy generation amount to be obtained from an ideal wind tribune (ETW) can be expressed with the following equation (Arslan, 2010; Johnson, 2001; Jowder, 2009).

P p v f v dv c

= =  +k





( ) ( ) 0

1 3

2 1 3

ρ Γ p v

( )

= 12ρAv3

Γ( )y =

ex yx 1dx

0

(8)

Here, T expresses the time. Power carried by wind is never entirely converted to electrical energy because of turbine and transmission losses. The real value of electrical power (PTe) obtained from wind via wind tribune and generator can be calculated by means of the tribune performance curve (Arslan, 2010; Johnson, 2001; Jowder, 2009; Gökçek and Genç, 2009).

(9)

The real energy amount (ETA) that may be obtained from a wind tribune can be expressed with the following equation.

(10)

Efficiency of a wind tribune (ηT) is equal to the proportion of the real energy generation amount obtained from tribune to the ideal energy generation amount (Arslan, 2010).

(11)

The capacity factor (CF) of a wind tribune expresses the energy generation performance of a tribune and is the proportion of real energy generation amount to the energy generation amount in nominal power (Jowder, 2009; Gökçek and Genç, 2009).

(12)

C E

F TPTA R

= ηT TA

TW

E

=E 100

E T P v f v dv TP

a v a v a v a

TA Te R

V V

= =

+ + +

(

( ) ( )

1 0

1 3

2 2

3 4

))

+





f v dv f v dv

V V

V V

R R

( ) ( )

0

1

P v

v V

a v a v a v a

P V v V

P

Te R R

R

( ) ,

= ,

<

+ + +

( )

≤ <

0 1

1 3 2 2

3 4

1

,, ,

V v V

v V

R ≤ <





0

0 0

ETW T P f v dve P f v dvR

V V

V V

R R

=  +





( ) 0 ( )

1

(4)

4. Analysis and application

Wind speed and direction data are the most important parameters to predict the produced electrical energy amount from a wind energy conversion plant. In this study, 12-month wind data obtained from the wind measurement power station installed in Sakarya-Esentepe region including 2006 and 2007 years were used. In this station, measurements of wind speed for 10 m and 30 m height, wind direction of 30 m and ambient temperature for 3 m height are realized periodically.

The analysis study consists of two phases. In the first phase, statistical analysis of wind data is made.

In the analysis, in determination of wind speed distribution, two-parameter Weibull distribution is used. In the second phase, the wind power plant (WPP) analysis is made to determine the tribune locations of wind farm planned to install for purpose of energy generation in the region, to select wind tribune types and determine the energy amount to be generated. Digital height map of Sakarya-Esentepe region is formed for this purpose. By means of this map that covers approximately 150 km2 area, the

wind data measured at a point grew to the general region and the potential wind energy fields are surveyed. In next stage, electrical energy amount can be produced is estimated for an appropriate turbine model. In determination of wind turbine model, some parameters are used such as annual average wind speed, power density, capacity factor and transportation status of the region. Besides, in analysis of wind data, establishment of graphics and WPP analysis, the WindPRO and WAsP software were used (WindPRO Software, Ver. 2.5).

By making statistical analysis of wind data, the wind speed frequency distribution was obtained (Figure 1). The annual average wind speed and frequency are given in Figure 2. Figure 2 shows that the maximum wind speed frequency is in the north and annual frequency is greater than 22% in this direction. Also in the North-Eastern and North- Western, it was seen that aspects of the notably- sized wind frequency. Annual mean wind speed values are higher than 4 m/s in North, North- Eastern, North-Western, West and South. In Table 1, the monthly and annual average wind speed,

00 4 2 6 8 12 14 16

10

10 15

5 20

Wind speed (m/s)

Frequency (%)

Weibull (30.0 m), c = 5.1 m/s, k = 1.81, Vm = 4.5 m/s Actual data height: 30.0 m

Fig. 1. Frequency distribution of annual wind speed.

4m/s2m/s

( ) ( )

Fig. 2. Directional changing of frequency and wind speed.

Table 1.

Monthly and Annual Averages of Wind Speed, Weibull Parameters and Power Density

Weibull distribution Actual data

Months

Vm (m/s) k c (m/s)2 Pm (W/m2) Vm (m/s) Pm (W/m2)

January 6.22 2.11 7.02 258.00 6.16 261.19

February 5.37 1.99 6.06 177.06 5.23 178.54

March 5.28 1.91 5.95 178.77 5.27 181.05

April 4.24 2.03 4.79 86.53 4.16 87.90

May 3.99 1.94 4.50 76.60 3.91 77.74

June 3.92 1.90 4.41 72.95 3.85 74.43

July 4.33 1.83 4.87 99.89 4.22 101.48

August 4.24 1.88 4.78 92.35 4.20 94.18

September 4.29 1.98 4.84 91.55 4.21 93.15

October 3.62 1.92 4.08 57.88 3.56 58.79

November 4.56 1.89 5.13 114.50 4.47 116.10

December 4.25 1.55 4.73 120.43 4.24 121.12

Annual 4.55 1.81 5.12 121.01 4.49 122.26

(5)

Weibull parameters and average power density values are given. Besides, the change of monthly mean wind speed and power density values are given in Fig. 3 and the change of monthly mean power density according to the actual and Weibull distribution are given in Fig. 4. According to the Table 1, the highest and the lowest average wind speed values for 30 m hub height occur in January and October respectively. Annual average wind speed and power density values are determined as 4.55 m/s and 121.01 W/m2according to the Weibull distribution. In Table 1, it is showed that Weibull and real values of average wind speed and power density are too close to the each other (Figure 4).

As a result of the WPP analysis, Tahtallk and Sardivan Hill surroundings were selected as the wind farm installation area that is planned for purpose of model application (Figure 5). Besides, for the model wind farm, 3 pieces RE power MM92 type wind tribunes of which nominal power is 2 MW, hub height 120 m, rotor diameter 92.5 m were deemed appropriate. In Figure 5 and Table 2, placement and coordinates of the wind tribune are given.

The results of analysis made by using the wind data for the model wind farm are given in Table 3.

When the table is examined, it is seen that the annual total energy generation amount of the 6 MW wind farm is 10603.4 MWh, capacity factor value is 20.2% and park yield is 98.8%.

Wind speed Power density 7

6 5 4 3 2

Jan Feb Mar Apr May JulJun Aug OctSep Nov Dec

Months

50 0 100 150 250 300

Mean wind speed (m/s)

200

Mean power density (W/m2)

Fig. 3. Changing of monthly average wind speed and power density.

1

New WTG Site data Scale 1:20,000

Fig. 5. Locations of wind turbines.

Jan Feb Mar Apr May Jun Jul Aug Sep NovOct Dec

Months 0

50 100 150 200 250 300

Mean power density (W/m2 )

Weibull distribution Actual data

Fig. 4. Monthly average power densities.

Table 2.

Coordinates and locations of wind turbines

Horizontal distance to

Turbine Altitude Nearest nearest turbine Distanceas

number Coordinates (m) turbine (m) rotor diameter

T1 273.353 - 4.516.489 360 T2 907 9.8

T2 274.187 - 4.516.132 335 T3 522 5.6

T3 274.657 - 4.516.358 335 T2 522 5.6

Table 3.

Analysis results

WTG Manufacturer REpower

WTG type MM 92

Hub height (m) 120

Rotor diamater (m) 92.5

Installed power (MW) 6

WTG number 3

Rated power (MW) 2

Total energy production (MWh) 10603.4

Capacity factor (%) 20.2

Park efficiency (%) 98.8

(6)

5. Conclusion

In this study, by using the wind data obtained from wind measurements made for purpose of energy generation in a region, the amount of energy generation was estimated. Analysis of wind data and energy and power connections of wind tribunes were examined.

For this purpose, the wind data obtained from measures made at the wind measurement power station installed in Sakarya- Esentepe Region were used.

According to the wind speed measurements made at 30 m height, the annual actual mean wind speed is 4.49 m/s, the highest monthly mean wind speed occurs in January month and the lowest wind speed occurs in October. According to the analysis made pursuant to the Weibull distribution; the annual mean wind speed at 30 m height is 4.55 m/s, the highest and the lowest mean wind speed values occur in January and October respectively. The annual Weibull parameters k and c values are calculated as 1.81 and 5.12 m/s. The monthly Weibull parameters k and c values change between 1.55-2.11 and 4.08 m/s-7.02 m/s respectively. The value of annual mean actual power density is found as 122.26 W/m2 and its Weibull value is found as 121.01 W/m2. The highest value of the monthly mean power density is seen in January. The dominant wind blowing direction in the region is determined as the north. It is determined that the actual and Weibull results of the annual, monthly and seasonal mean wind speed and power density values are very close to each other.

As a result of the WPS analysis made for purpose of calculation of electric energy to be generated from wind in the region, a model wind farm was planned. For this wind farm, an appropriate wind tribune types and installation places of tribunes were determined. As a result of the analysis made for this purpose, the annual total energy generation amount, capacity factor and park yield values of the model wind farm were determined.

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Arslan O., 2010. Technoeconomic analysis of electricity generation from wind energy in Kutahya, Turkey. Energy 35, (1) 120–131.

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