Abstract
The Weibull distribution is frequently used for the assessment of wind energy potential and modeling of wind speed data. The parameters of Weibull distribution are determined by a number of methods; Maximum Likelihood Methods is one of them. The values of scale and shape parameters of Weibull distribution are found by the help of Maximum Likelihood function. Two different techniques are used to find the parameters. One is known as iterative method, in which a start value of ‘k’ is set and iterations are terminated when given criterion is reached. The second method is Newton Raphson method of finding roots. We report here a problem of non-convergence of iterative method. We suggest the Newton Raphson method as the best choice for finding the value of ‘k’ through Maximum Likelihood Method.
Highlights
We are living in machine era; people, at work place have been replaced by machines or robots
Iterative Method In iterative method a start value of ‘k’ is selected and wind speed data is used to calculate sums in eq (3), since sum of Logarithm of wind speeds is needed in the calculation, zero wind speeds are neglected in this method
It is found that the values of scale and shape parameters increase with increasing start value of ‘k’
Summary
We are living in machine era; people, at work place have been replaced by machines or robots. Fast depletion of fossil fuels has made people around the world to think for alternate source of energy. Wind energy is a good choice as an alternate source of energy. Most of the countries have been generating electrical energy through wind [3]. The modeling of wind power plays in important role in assessing wind potentials [8]; different statistical distributions and mathematical techniques have been employed to model wind data [9]. The simplest Weibull distribution has two parameters; its Probability Density Function (PDF) is given in eq (1). 2. ANALYSIS Various statistical and mathematical methods are employed to find parameters ‘k’ and ‘c’. The values of Weibull parameters by this method are given by equations (3) and (4); ‘k’ and ‘c’ are found by iterative method or by Newton Raphson Method. The new value of ‘k’ is generated through eq (3) and used in iteration, the process continues until a given criterion is reached
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