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Energies 2016, 9(10), 842; doi:10.3390/en9100842

Comparison of Wind Energy Generation Using the Maximum Entropy Principle and the Weibull Distribution Function

1
Department of Physics, Federal Urdu University of Arts, Sciences and Technology, Block 9, Gulshan-e-Iqbal, Karachi 75300, Pakistan
2
Department of Physics, University of Karachi, Main University Road, Karachi 75270, Pakistan
3
Center for Engineering Research, The Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4
Islamia College Peshawar, University Campus, Peshawar Jamrod Road, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan
5
College of Engineering, Petroleum and Natural Gas Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia
6
Faculty of Science, Geology Department, Benha University, Benha 56521, Egypt
*
Author to whom correspondence should be addressed.
Academic Editor: Simon J. Watson
Received: 12 July 2016 / Revised: 13 September 2016 / Accepted: 11 October 2016 / Published: 19 October 2016
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Abstract

Proper knowledge of the wind characteristics of a site is of fundamental importance in estimating wind energy output from a selected wind turbine. The present paper focuses on assessing the suitability and accuracy of the fitted distribution function to the measured wind speed data for Baburband site in Sindh Pakistan. Comparison is made between the wind power densities obtained using the fitted functions based on Maximum Entropy Principle (MEP) and Weibull distribution. In case of MEP-based function a system of (N+1) non-linear equations containing (N+1) Lagrange multipliers is defined as probability density function. The maximum entropy probability density functions is calculated for 3–9 low order moments obtained from measured wind speed data. The annual actual wind power density (PA) is found to be 309.25 W/m2 while the Weibull based wind power density (PW) is 297.25 W/m2. The MEP-based density for orders 5, 7, 8 and 9 (PE) is 309.21 W/m2, whereas for order 6 it is 309.43 W/m2. To validate the MEP-based function, the results are compared with the Weibull function and the measured data. Kolmogorov–Smirnov test is performed between the cdf of the measured wind data and the fitted distribution function (Q95 = 0.01457 > Q = 10−4). The test confirms the suitability of MEP-based function for modeling measured wind speed data and for the estimation of wind energy output from a wind turbine. R2 test is also performed giving analogous behavior of the fitted MEP-based pdf to the actual wind speed data (R2 ~ 0.9). The annual energy extracted using the chosen wind turbine based on Weibull function is PW = 2.54 GWh and that obtained using MEP-based function is PE = 2.57–2.67 GWh depending on the order of moments. View Full-Text
Keywords: Weibull distribution; maximum entropy; modified maximum likelihood method; Baburband; Pakistan Weibull distribution; maximum entropy; modified maximum likelihood method; Baburband; Pakistan
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Shoaib, M.; Siddiqui, I.; Rehman, S.; Rehman, S.U.; Khan, S.; Lashin, A. Comparison of Wind Energy Generation Using the Maximum Entropy Principle and the Weibull Distribution Function. Energies 2016, 9, 842.

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