Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

Okumu Otieno Kevin,Troon John Benedict,Samuel Muthiga Ngaga

doi:10.11648/j.ijsd.20210701.11

Okumu Otieno Kevin, Troon John Benedict + Show 1 more

Open Access

https://doi.org/10.11648/j.ijsd.20210701.11

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Abstract

Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.

Highlights

Distribution characteristics refer to the wind speed parameters like the mean, variance, standard deviation, and covariance
The 2-parameter distributions involve scale and shape parameter where the scale guides on how windy the region is and the shape parameter guides on how peaked the region is and the 3-parameter include the third parameter called threshold parameter which helps in understanding the minimum expected wind speed in the region [12]
To find the precise threshold parameter, we investigate different threshold values using Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) values

Summary

Introduction

Distribution characteristics refer to the wind speed parameters like the mean, variance, standard deviation, and covariance. These parameters vary from place to place depending on various factors like the length of data observed, the site of an experiment, and time of observing the wind speed data among others. There is a need to study the variations of these parameters for any specific site before installing the wind plant. This is only possible if there is an approved statistical distribution that has been examined and recommended for the site or region of interest. The 2-parameter distributions involve scale and shape parameter where the scale guides on how windy the region is (statistically meaning the distribution of the wind) and the shape parameter guides on how peaked the region is (statistically indicating the most frequently expected wind speed) and the 3-parameter include the third parameter called threshold parameter which helps in understanding the minimum expected wind speed in the region [12]

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