Investigation of Wind Characteristics and Estimation of Wind Power Potential of Narok County Using Weibull Distribution
Steven Okoth *
Department of Mathematics and Physical Sciences, Faculty of Pure, Applied and Health Sciences, Maasai Mara University, Kenya.
Otieno Fredrick
Department of Mathematics and Physical Sciences, Faculty of Pure, Applied and Health Sciences, Maasai Mara University, Kenya.
Isaac Motochi
Department of Mathematics and Physical Sciences, Faculty of Pure, Applied and Health Sciences, Maasai Mara University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Aim: To investigate wind characteristics and estimate wind power density of Narok weather station in Narok county using Weibull distribution.
Research Design: Historical hourly wind direction and speed data recorded by the Kenya Meteorological Department in Narok weather station was analyzed.
Place and duration: The study utilized data samples collected at Narok weather station over a period spanning from 2011 to 2021.
Methods: To assess the temporal characteristics, a statistical average technique was employed. The spatial aspect, specifically wind speed variation with height, was evaluated through wind speed extrapolation using the power law. The dominant wind direction was determined by plotting a polar chart based on a frequency distribution table prepared using both wind direction and wind speed data. The turbulence intensity of the wind was calculated using the turbulence intensity equation. The Weibull parameters were estimated using the maximum likelihood estimation method. The Weibull probability distribution was used to analyze wind speed distribution and power density. The extrapolated Weibull parameters were utilized to calculate wind power density at various heights. The accuracy of the wind regime distribution in Narok was assessed by employing the R2 technique.
Results: The wind regime in Narok exhibited an average annual wind speed of 4.3 m/s and a mean wind power density of 126 W/m2. Analysis of diurnal wind speed variation revealed peak wind speeds around noon, with wind speeds exceeding the cut-in wind threshold (3 m/s) between 0430hrs and 2100hrs. March and October were identified as the windiest months, exhibiting the highest wind power densities, while June and December demonstrated the lowest values. Wind speed and, consequently, wind power density increased exponentially with height. The prevailing wind directions in Narok were primarily from the East, followed by the North and North West. The wind regime in Narok exhibited turbulence, as indicated by average turbulence intensities exceeding 0.25. The wind regime in Narok was accurately described by the Weibull distribution, with an approximation accuracy of 0.94 based on the R2 error.
Conclusion: The wind regime in Narok is generally suitable for extracting wind power at heights above 15 m, regardless of the scale of the wind power extraction.
Keywords: Narok, wind speed, wind power density, wind turbine, Weibull probability distribution function
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