Reach Us
+44-1522-440391

^{1}Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Iran

^{2}Department of Chemical Engineering, Shahid Bahonar University of Kerman, Iran

^{3}Department of Aerospace Engineering, Payame Noor University, Iran

^{4}Department of Computer Engineering, Payame Noor University, Iran

^{5}Department of Civil Engineering, Hakim Sabzevari University, Iran

- *Corresponding Author:
- Bahador Abolpour

Department of Chemical Engineering

Faculty of Engineering, ShahidBahonar University of Kerman

Post Code 76175, Kerman, Iran

**Tel:**98-711-8312254

**Fax:**98-711-8203239

**E-mail:**[email protected]

**Received Date**: December 08, 2016; **Accepted Date:** January 23, 2017; **Published Date**: January 25, 2017

**Citation: **Abolpour B, Abolpour B, Bakhshi H, Yaghobi M (2017) An Appropriate Extreme Value Distribution for the Annual Extreme Gust Winds Speed. J Fundam Renewable Energy Appl 7: 223. doi:10.4172/20904541.1000223

**Copyright:** © 2017 Abolpour B, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Visit for more related articles at** Journal of Fundamentals of Renewable Energy and Applications

In this study, an extreme value distribution of the gust wind speeds is obtained in a large selected area of Iran. The generalized Pareto distribution is used to find out the type of wind speed distribution. The three parameters of the generalized extreme value distribution function are reduced to either type I Gumbel, type II Frechet or type III reverse Weibull distribution function for the annual extreme gust wind speeds. It is obtained that, the annual extreme gust wind speeds at 102 stations have a reverse Weibull function distribution. It is also obtained that, type I Gumbel extreme value function is the best model for many of the studied stations.

Annual extreme gust wind; Extreme value distribution; Gumbel; Frechet; Reverse Weibull

Today, wind power is an important dynamically energy source. Using the wind as a source of energy has been increased [1]. A set of wind turbines in a same location products the electrical power. To maximize this generated power, these locations are built far from shores or in open fields far away from buildings and trees. The suitability of these locations must be obtained using a set of data that approves the wind speed and direction in these locations.

It is observed that, extreme wind speeds are physically bounded. Weibull and reverse Weibull distributions are used for annual the extreme winds [2-5]. It is indicated that, annual fastest-mile wind speeds have the reverse Weibull distribution. A two-parameter generalized Pareto distribution is usable for analyzing the extreme gust wind speeds instead of all Type I distributions. The solution range of the tail-length parameter c of the generalized Pareto distribution may indicates the extreme events for c value approaching zero the Type I Gumbel, for c>0 the Type II Frechet and for c<0 the Type III reverse Weibull are suitable extreme value functions. More details have been presented in a previous study in USA [6].

Wind load on a structure is a function of various parameters such as wind speed and direction, geometry of the structure and local topography [7,8]. First, design and wind pressures on the external surfaces of the structure are calculated. Then these pressures are converted to the load impact. The amount of wind pressures on the structures in Iran is calculated using the following equations [9]:

(1)

(2)

Where p and q are the design and wind pressures (dN/m^{2}), respectively. V is the basic wind speed (km/h) and Cq and Ce are the shape and speed variation coefficients, respectively. Analyzing the wind speed data indicates that, the maximum annual wind speed at particular locations follows Type I extreme value distribution. This type is the most frequently used model for wind speed [2,10]. The probability distribution of the wind load (as a function of V) is a valuable parameter for the structural design of buildings. Nevertheless, this parameter is not necessarily for Type I distribution, because the wind pressure is a function of V^{2} (instead of *V*). Since some of parameters are random in nature, it is difficult to determine the wind load distribution. Previous studies showed the uncertainty of the wind load and low values of c in the cumulative distribution function (CDF), consequently. Therefore, wind load can be represented by a Type I distribution [2,4,5,11] for close to zero values of *c*.

**Procedure**

Considering W (t) as a series of wind speed at a specific site and V as the extreme gusts associated with W (t), the generation of V distribution is not known. However, V can be estimated using its tail quantile probability of a suggestion contingent cumulative distribution function (CDF), F(v), (for and V=W (t) - u where u is a sufficiently large threshold of W (t)):

(3)

Where v is a contingent investigation of V and c and d are the shape and scale parameters, respectively. Equation 3 is the generalized pareto distribution (GPD) and will considered an extreme gust of wind as the basis for the review. Element on the right side of this Equation is known as the generalized Pareto. Many researchers used the GPD to estimate annual wind speed extreme [4,5,11,12].

**Wide distribution type I (Gumbel)**

There is strong evidence in scientific literature, which advocates the use of the Gumbel distributions to fit extremes events [13-18]. Wide distribution of values as its name implies is useful to describe the probabilistic nature [19]. CDF of this variable for is:

(4)

Where u and α are parameters of the distribution. The mean and standard deviation can be calculated using the following limits:

(5)

(6)

Therefore, if the mean and standard deviation are determined, equations5 and 6 can be changed and the corresponding values for the distribution parameters can be obtained from these equations.

**Wide distribution type II**

Sometimes the best estimate of the distribution of the maximum load on a structure can be provided by Type II [20,21]. CDF of this variable for is:

(7)

Where u and k are parameters of the distributionand for c>0. The mean and standard deviation can be calculated using the following limits:

(8)

(9)

Note that, the coefficient of variation, V_{x}, is a function of k and is calculated elsewhere [20].

**Wide distribution type III (Weibull)**

This distribution is defined by three parameters. There are different functions for the largest and smallest values [22]. For x ≤ w CDF can be defined as follow:

(10)

Where w, u and k are parameters of the distribution and for c<0. Mean and variance also are calculated using the following equations:

(11)

(12)

For x ≥ Æ CDF is defined as follow:

(13)

Where Æ, u and k are parameters of the distribution. Mean and variance for this range of values is defined as follows:

(14)

(15)

Gamma distribution is defined as follow:

(16)

If the GPD assumption were correct, the plot of the cumulative mean exceedance (CME) should follow a straight line. Therefore, c and d can be obtained from the characteristics of this line.

Wind speed data was obtained from the center of Iran weather databases. This database included 287 weather stations. 181 of these stations had data ranged from 5 to 54 years. It was felt that hurricanes and tornadoes were worthy of separate consideration. Thus, the stations had been affected by hurricanes and tornadoes were deleted. A minimum record length of 15 years was chosen to allow an adequate amount of wind data to be analyzed in this study. Because of climatic characteristics, a smaller sample may not adequately represent all possible wind patterns. Therefore, stations with less than 15 years of record were removed from the database. Finally, 109 meteorological stations were selected for analysis.

**Figures 1 and 2** show the mean, standard deviation and maximum values of the annual extreme gust wind speed at all 109 stations in Iran. The parameters c and d were quantified using the CME method. The annual series of median wind speed, V_{med}, provided satisfactory results [5]. It is assumed that the extreme events occur in succession.

As a result, pieces of nonlinear CME can be removed. Thus the parameter c will obtain with a more accurate. These findings, is identical with the results by other researchers [23,24]. The extreme gust wind v is plotted against the reduced variate W, by both Gumbel and reverse Weibull distributions in **Figures 3-5**.

(17)

As shown in **Figures 6 and 7**, Type III reverse Weibull distribution, are most suitable for delineating the annual extreme gust wind speeds at the 109 stations; So the inverse Weibull distribution for 109 stations, is the basic representative. The result is in agreement with the conclusion suggested by other studies for severe winds. However, analysis of data of V_{RN} (wind speed estimates using the reverse Weibull distribution) and V_{GN} (wind speed estimates using the Gumbel distribution) present in these figures show the opposite results. It is observed that V_{RN} and V_{GN}, for gust winds with great intervals in many of stations, Type I Gumbel distribution has a higher accuracy than Type III distribution. The results of about 102 stations for both Types I and III distributions are approved. Some examples in **Figures 3-5** are presented.

Preliminary annual extreme gust wind speed distribution in the selected 109 stations in Iran was investigated. Based on calculations using CME, it is obtained that the annual extreme gust wind speeds at 102 stations have a reverse Weibull function distribution. However, the results of data analysis and graphic curves showed that Type I Gumbel extreme value function is the best model for many of the studied stations. Wind speed predictions based on Gumble distribution may be unsuitable for the most of time intervals. However, taking into account the time intervals, for a maximum duration of 54 years in 109 selected stations, distributed type I in the modeling extreme gust wind speed, at 102 stations have represented better results.

- World Wind Energy Association (2009) World wind energy report 2008.
- Cheng EDH, Chiu ANL (1994) Short-record-based extreme wind simulation. J NatInstof StandTechnol99: 391-397.
- Cheng EDH, Chiu ANL(1995) Regional design wind speed estimation. Proceedings of the 9th International Conference on Wind Engineering.
- Gross J, Heckert A, Lechner J, Simiu E (1994) Extremevalue theory and applications. (Simiu Edition), Kluwer Academic Publishers, Dordrecht, Netherlands.
- Simiu E, Heckert N (1996) Extreme wind distribution tails: A peak over threshold approach. J StructEng 122: 539-547.
- Cheng E, Yeung C (2002) Generalized extreme gust wind speeds distributions. J Wind EngineerIndustAerodyn90: 1657-1669.
- American Society of Civil Engineers (2010) Minimum design loads for buildings and other structures. ASCE. pp: 424.
- Huang S, Li R, Li QS (2013) Numerical simulation on fluid-structure interaction of wind around super-tall building at high Reynolds number conditions. StructEngineerMechInt J 46: 2.
- Ministry of Housing and Urban Development (2009) National building regulations, Iran.
- Pinto JG, NeuhausCP, Kruger A, Kerschgens M (2009) Assessment of the wind gust estimate method in mesoscale modeling of storm events over West Germany. MeteorologischeZeitschrift 18: 495-506.
- Gross JL, Heckert NA, Lechner JA, Simiu E (1995) A study of optimal extreme wind estimation procedures. Proceedings of 9th International Conference on Wind Engineering, New Delhi, India, 69-80.
- Heckert N, Simiu E, Whalen T (1998) Estimates of hurricane wind speeds by “peak over threshold” method. JStruct Engineer 124: 445-449.
- Garciano LE, Koike T (2007) Aproposed typhoon resistant design of a wind turbine tower in the philippines. Doboku GakkaiRonbunshuu F63: 181-189.
- Jagger TH, ElsnerJB (2006) Climatology models for extreme hurricane winds near the United States. J Climate 19: 3220-3236.
- Sanabria LA, Cechet RP (2007) A statistical model of severe winds. GeosciAustr Record.
- Sorensen JD, Nielsen SRK (2007) Extreme wind turbine response during peration. J Phys Conf Ser75: 012074.
- Langreder W, Hojstrup J (2007) Going to extremes: A parametric study on peak-over-threshold and other methods. European Wind Energy Conference, Milan, Italy.
- Kunz M, Mohr S, Rauthe M, Lux R, KottmeierCh (2010)Assessment of extreme wind speeds from Regional Climate Models-Part 1: Estimation of return values and their evaluation. Nat Hazard Earth Sys Sci 10: 907-922.
- Hosking J, Wallis J (1987) Parameter and quantile estimation for the generalized pareto distribution. Technometrics 29: 339-349.
- Smith R (1990) Handbook of applicable mathematics. Wiley, New York.
- Van Den Brink HW, Konnen GP (2008) The statistical distribution of meteorological outliers. Geophys Res Lett 35: 1-5.
- Johnson NL, Kotz S, Balakrshnan N (1995) Continuous univariate distributions. (2nd Edn) Wiley, New York, USA.
- Holmes J, Moriarty W (1999) Application of the generalized pareto distribution to extreme value analysis in wind engineering. J Wind EngIndustAerodyn83: 1-10.
- Holmes J (2000) Private communication.

Select your language of interest to view the total content in your interested language

- Adsorption Process
- Advanced Photovoiltoic Cells
- Advanced Photovoiltoic Panels
- Advanced Photovoiltoic Systems
- Advanced Photovoiltoic Technologies
- Alternative Energy
- Biomass Energy
- CO2 Mitigation
- Clean Energy
- Coal Energy
- Composting
- Energy Management
- Environmental Policy
- Fossil Fuel
- Geothermal Energy
- Green Energy
- Greenhouse
- Harvesting
- Harvesting Field Greens
- Heavy Metals
- Humic Substance
- Hydro Electric Energy
- Hydro Energy
- Hydrogen Energy
- Hydrogen and Biodiesel
- Hydropower Energy
- Immobilization
- Incineration Research
- Industrial Waste
- Modern Biomass Biofuel
- Organic Matter
- Petrolium and Petrochemistry
- Photovoltoics
- Renewable Energy
- Renewable Energy and Research
- Renewable Geothermal Energy
- Resource Efficiency
- Solar Energy (Thermal and Electrical)
- Solar Radiation
- Waste Hierarchy
- Wind Energy

- Total views:
**1586** - [From(publication date):

January-2017 - Jul 19, 2019] - Breakdown by view type
- HTML page views :
**1436** - PDF downloads :
**150**

**Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals**

International Conferences 2019-20