Estimating wind speed distribution
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
The corresponding cumulative distribution function iswhere 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)
- et al.
Probability models of wind velocity magnitude and persistence
Solar Energy
(1978) - et al.
Wind energy potential in Iraq
Solar Wind Technol
(1988) - et al.
Fitting wind speed distributions: a case study
Solar Energy
(1998) Weibull parameters for annual and monthly wind speed distributions for five locations in India
Solar Energy
(1986)Wind power availability in Zimbabwe
Solar Wind Technol
(1986)- et al.
A study of Weibull parameters using long-term wind observations
Renew Energy
(2000) - et al.
A survey of wind energy potential in Nigeria
Solar Wind Energy
(1990) - et al.
Statistical characteristics of wind in Saudi Arabia
Rene Energy
(1994) Some aspects of wind power statistics
J Appl Meteorol
(1977)
Cited by (189)
Diurnal variations in wind power density analysis for optimal wind energy integration in different Indian sites
2024, Sustainable Energy Technologies and AssessmentsElaboration of a Generalized Mixed Model for the wind speed distribution and an assessment of wind energy in Algerian Coastal regions and at the Capes
2024, Energy Conversion and ManagementNonparametric copula modeling of wind speed-wind shear for the assessment of height-dependent wind energy in China
2022, Renewable and Sustainable Energy ReviewsFlow control based 5 MW wind turbine enhanced energy production for hydrogen generation cost reduction
2022, International Journal of Hydrogen Energy