Research Papers: Energy Systems Analysis

Application of the Maximum Entropy Method for Determining a Sensitive Distribution in the Renewable Energy Systems

[+] Author and Article Information
Gholamhossein Yari

School of Mathematics,
Iran University of Science and Technology,
Tehran 16846-13114, Iran
e-mail: Yari@iust.ac.ir

Zahra Amini Farsani

School of Mathematics,
Iran university of Science and Technology,
Tehran 16846-13114, Iran
e-mails: Z_aminifarsani@iust.ac.ir;

National Oceanic and Atmospheric Administration.

1Present address: Department of Statistics, Ludwig-Maximilians-University of Munich, Ludwigstr. 33, Munich 80539, Germany.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received August 18, 2014; final manuscript received March 26, 2015; published online May 8, 2015. Assoc. Editor: Reza H. Sheikhi.

J. Energy Resour. Technol 137(4), 042006 (Jul 01, 2015) (7 pages) Paper No: JERT-14-1259; doi: 10.1115/1.4030268 History: Received August 18, 2014; Revised March 26, 2015; Online May 08, 2015

In the field of the wind energy conversion, a precise determination of the probability distribution of wind speed guarantees an efficient use of the wind energy and enhances the position of wind energy against other forms of energy. The present study thus proposes utilizing an accurate numerical-probabilistic algorithm which is the combination of the Newton’s technique and the maximum entropy (ME) method to determine an important distribution in the renewable energy systems, namely the hyper Rayleigh distribution (HRD) which belongs to the family of Weibull distribution. The HRD is mainly used to model the wind speed and the variations of the solar irradiance level with a negligible error. The purpose of this research is to find the unique solution to an optimization problem which occurs when maximizing Shannon’s entropy. To confirm the accuracy and efficiency of our algorithm, we used the long-term data for the average daily wind speed in Toyokawa for 12 yr to examine the Rayleigh distribution (RD). This data set was obtained from the National Climatic Data Center (NCDC) in Japan. It seems that the RD is more closely fitted to the data. In addition, we presented different simulation studies to check the reliability of the proposed algorithm.

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Fig. 2

The simulated BGWD in comparison with its ME estimation (R2=0.8803)

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Fig. 1

The simulated HRD in comparison with the ME estimation of HRD (R2=0.9286)

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Fig. 3

ME estimation of the BRD in comparison with the joint BRD (R2=0.8565)

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Fig. 4

Wind-speed model via ME method (R2=0.774)




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