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

Author

Listed:
  • Muhammad Shoaib

    (Department of Physics, Federal Urdu University of Arts, Sciences and Technology, Block 9, Gulshan-e-Iqbal, Karachi 75300, Pakistan)

  • Imran Siddiqui

    (Department of Physics, University of Karachi, Main University Road, Karachi 75270, Pakistan)

  • Shafiqur Rehman

    (Center for Engineering Research, The Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Saif Ur Rehman

    (Department of Physics, Federal Urdu University of Arts, Sciences and Technology, Block 9, Gulshan-e-Iqbal, Karachi 75300, Pakistan)

  • Shamim Khan

    (Islamia College Peshawar, University Campus, Peshawar Jamrod Road, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan)

  • Aref Lashin

    (College of Engineering, Petroleum and Natural Gas Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia
    Faculty of Science, Geology Department, Benha University, Benha 56521, Egypt)

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 ( P A ) is found to be 309.25 W/m 2 while the Weibull based wind power density ( P W ) is 297.25 W/m 2 . The MEP-based density for orders 5, 7, 8 and 9 ( P E ) is 309.21 W/m 2 , whereas for order 6 it is 309.43 W/m 2 . 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 ( Q 95 = 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. R 2 test is also performed giving analogous behavior of the fitted MEP-based pdf to the actual wind speed data ( R 2 ~ 0.9). The annual energy extracted using the chosen wind turbine based on Weibull function is P W = 2.54 GWh and that obtained using MEP-based function is P E = 2.57–2.67 GWh depending on the order of moments.

Suggested Citation

  • Muhammad Shoaib & Imran Siddiqui & Shafiqur Rehman & Saif Ur Rehman & Shamim Khan & Aref Lashin, 2016. "Comparison of Wind Energy Generation Using the Maximum Entropy Principle and the Weibull Distribution Function," Energies, MDPI, vol. 9(10), pages 1-18, October.
    • Handle: RePEc:gam:jeners:v:9:y:2016:i:10:p:842-:d:80909
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    References listed on IDEAS

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    1. Li, Meishen & Li, Xianguo, 2005. "MEP-type distribution function: a better alternative to Weibull function for wind speed distributions," Renewable Energy, Elsevier, vol. 30(8), pages 1221-1240.
    2. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    3. Zhang, Hua & Yu, Yong-Jing & Liu, Zhi-Yuan, 2014. "Study on the Maximum Entropy Principle applied to the annual wind speed probability distribution: A case study for observations of intertidal zone anemometer towers of Rudong in East China Sea," Applied Energy, Elsevier, vol. 114(C), pages 931-938.
    4. Islam, M.R. & Saidur, R. & Rahim, N.A., 2011. "Assessment of wind energy potentiality at Kudat and Labuan, Malaysia using Weibull distribution function," Energy, Elsevier, vol. 36(2), pages 985-992.
    5. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    6. Sulaiman, M.Yusof & Akaak, Ahmed Mohammed & Wahab, Mahdi Abd & Zakaria, Azmi & Sulaiman, Z.Abidin & Suradi, Jamil, 2002. "Wind characteristics of Oman," Energy, Elsevier, vol. 27(1), pages 35-46.
    7. Saleh, H. & Abou El-Azm Aly, A. & Abdel-Hady, S., 2012. "Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gulf, Egypt," Energy, Elsevier, vol. 44(1), pages 710-719.
    8. Liu, Feng Jiao & Chang, Tian Pau, 2011. "Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment," Energy, Elsevier, vol. 36(3), pages 1820-1826.
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    Cited by:

    1. Shafiqur Rehman & Md. Mahbub Alam & Luai M. Alhems & M. Mujahid Rafique, 2018. "Horizontal Axis Wind Turbine Blade Design Methodologies for Efficiency Enhancement—A Review," Energies, MDPI, vol. 11(3), pages 1-34, February.
    2. Markus Gross & Vanesa Magar & Alfredo Peña, 2020. "The Effect of Averaging, Sampling, and Time Series Length on Wind Power Density Estimations," Sustainability, MDPI, vol. 12(8), pages 1-13, April.
    3. M. Mujahid Rafique & Shafiqur Rehman & Md. Mahbub Alam & Luai M. Alhems, 2018. "Feasibility of a 100 MW Installed Capacity Wind Farm for Different Climatic Conditions," Energies, MDPI, vol. 11(8), pages 1-18, August.

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