Estimating wind speed distribution

doi:10.1016/S0196-8904(01)00182-0

Energy Conversion and Management

Volume 43, Issue 17, November 2002, Pages 2311-2318

https://doi.org/10.1016/S0196-8904(01)00182-0 Get rights and content

Abstract

The Weibull distribution is used to model wind speeds at four locations in Oman. The scale and shape parameters were estimated using three methods, the Chi-square method, method of moments and regression method. It was observed that the estimates using the Chi-squared method gave the best overall fit to the distribution of the wind data. Both the scale and shape parameters varied widely over the months.

Introduction

Wind energy has been used for centuries for navigation and agriculture. Recently, wind energy has been receiving a lot of attention because of the focus on renewable energies [2], [9], [10], [18]. The effective utilization of wind energy entails having a detailed knowledge of the wind characteristics at the particular location. The distribution of wind speeds is important for the design of wind farms, power generators and agricultural applications like irrigation [10], [12].

In this article, we model the wind speeds at four stations in Oman. The stations are Marmul, Masirah, Sur and Thumrait. These stations have the highest long term average wind speeds in Oman. In addition to the regression and moment methods for estimating the parameters, a Chi-square method is introduced.

Several mathematical models have been used to study wind data. The Weibull distribution and its special case, the Rayleigh distribution, have been used to study wind data [3], [4], [5], [6], [7], [8], [17]. Corotis et al. [1] found the Rayleigh distribution to be better than the Weibull distribution. However, Hennessey [5] found that the energy output calculated using wind speeds derived from the Rayleigh distribution was within 10% of those derived from the Weibull distribution. Rehman and Halawani [16] used the Weibull distribution to study wind data from 10 locations in Saudi Arabia and concluded that the Weibull distribution is adequate.

Section snippets

Methods for estimating the parameters of the Weibull distribution

The three parameter Weibull probability density function is given by $f(v)= k c v−μ c^{k−1} exp − v−μ c^{k} .$

The corresponding cumulative distribution function is $F(v)=1− exp − v−μ c^{k},$ where v is the wind speed, k is a shape parameter, μ is a location parameter and c is a scale parameter.

In this article, we assume the two parameter Weibull distribution by setting the location parameter, μ, equal to zero. Stevens and Smulders [17], Hennessey [5] and Justus et al. [6] discussed several methods for estimating the

Data and computations

The data for this study is obtained from the published monthly summaries of weather data by the Oman Ministry of Communications (1986–1998) [14]. The data were captured using a cup anemometer at 10 m height. The data for the four stations, Marmul, Masirah, Sur and Thumrait were chosen for this study because they had the largest long term average wind speeds among the 25 weather stations in Oman. Until other locations have been studied, they are the most viable places for wind power

Results and discussion

Table 2 shows the estimated scale and shape parameters for the four stations using the mean and standard deviation for the method of moments and the empirical distribution in Table 1 for the regression and Chi-square methods. The plots of the empirical distributions and the estimated Weibull distributions are in Fig. 1a–d.

For each station, the estimated parameters are different for the three methods. The moment method gave, generally, the lower values for both the scale and shape parameters.

Conclusion

Wind data from four stations in Oman were modeled using the two parameter Weibull distribution. The parameters were estimated using the method of moments and the regression methods. A Chi-square method was introduced for estimating the parameters. The Chi-square method gave better estimates for the parameters as, indicated by the Kolmogorov–Smirnov statistic.

References (18)

R.B. Corotis et al.
Probability models of wind velocity magnitude and persistence
Solar Energy
(1978)
A.S.K. Darwish et al.
Wind energy potential in Iraq
Solar Wind Technol
(1988)
A. Garcia et al.
Fitting wind speed distributions: a case study
Solar Energy
(1998)
B.K. Gupta
Weibull parameters for annual and monthly wind speed distributions for five locations in India
Solar Energy
(1986)
G. Lewis
Wind power availability in Zimbabwe
Solar Wind Technol
(1986)
I.Y.F. Lun et al.
A study of Weibull parameters using long-term wind observations
Renew Energy
(2000)
J.O. Ojosu et al.
A survey of wind energy potential in Nigeria
Solar Wind Energy
(1990)
S. Rehman et al.
Statistical characteristics of wind in Saudi Arabia
Rene Energy
(1994)
J. Hennessey
Some aspects of wind power statistics
J Appl Meteorol
(1977)

There are more references available in the full text version of this article.

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Estimating wind speed distribution

Abstract

Introduction

Section snippets

Methods for estimating the parameters of the Weibull distribution

Data and computations

Results and discussion

Conclusion

Solar Energy

Solar Wind Technol

Solar Energy

Solar Energy

Solar Wind Technol

Renew Energy

Solar Wind Energy

Rene Energy

Some aspects of wind power statistics

J Appl Meteorol