IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v9y2016i10p842-d80909.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/9/10/842/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/9/10/842/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammadi, Kasra & Mostafaeipour, Ali & Sabzpooshani, Majid, 2014. "Assessment of solar and wind energy potentials for three free economic and industrial zones of Iran," Energy, Elsevier, vol. 67(C), pages 117-128.
    2. Chang, Tian-Pau & Liu, Feng-Jiao & Ko, Hong-Hsi & Cheng, Shih-Ping & Sun, Li-Chung & Kuo, Shye-Chorng, 2014. "Comparative analysis on power curve models of wind turbine generator in estimating capacity factor," Energy, Elsevier, vol. 73(C), pages 88-95.
    3. Jiang, Haiyan & Wang, Jianzhou & Wu, Jie & Geng, Wei, 2017. "Comparison of numerical methods and metaheuristic optimization algorithms for estimating parameters for wind energy potential assessment in low wind regions," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 1199-1217.
    4. Hu, Qinghua & Wang, Yun & Xie, Zongxia & Zhu, Pengfei & Yu, Daren, 2016. "On estimating uncertainty of wind energy with mixture of distributions," Energy, Elsevier, vol. 112(C), pages 935-962.
    5. Theodore Panagiotidis & Georgios Papapanagiotou, 2024. "A note on the determinants of NFTs returns," Working Paper series 24-07, Rimini Centre for Economic Analysis.
    6. Wu, Ximing & Perloff, Jeffrey M., 2007. "Information-Theoretic Deconvolution Approximation of Treatment Effect Distribution," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9vd036zx, Department of Agricultural & Resource Economics, UC Berkeley.
    7. Domenico Di Gangi & Fabrizio Lillo & Davide Pirino, 2015. "Assessing systemic risk due to fire sales spillover through maximum entropy network reconstruction," Papers 1509.00607, arXiv.org, revised Jul 2018.
    8. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.
    9. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    10. Liu, Feng-Jiao & Chen, Pai-Hsun & Kuo, Shyi-Shiun & Su, De-Chuan & Chang, Tian-Pau & Yu, Yu-Hua & Lin, Tsung-Chi, 2011. "Wind characterization analysis incorporating genetic algorithm: A case study in Taiwan Strait," Energy, Elsevier, vol. 36(5), pages 2611-2619.
    11. 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.
    12. Suwarno Suwarno & M. Fitra Zambak, 2021. "The Probability Density Function for Wind Speed Using Modified Weibull Distribution," International Journal of Energy Economics and Policy, Econjournals, vol. 11(6), pages 544-550.
    13. Stephen Satchell & Susan Thorp & Oliver Williams, 2012. "Estimating Consumption Plans for Recursive Utility by Maximum Entropy Methods," Research Paper Series 300, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Wu, Ximing & Perloff, Jeffrey M., 2007. "Information-Theoretic Deconvolution Approximation of Treatment Effect Distribution," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9vd036zx, Department of Agricultural & Resource Economics, UC Berkeley.
    15. Thanasis Stengos & Ximing Wu, 2010. "Information-Theoretic Distribution Test with Application to Normality," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 307-329.
    16. Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
    17. Ba Chu & Stephen Satchell, 2016. "Recovering the Most Entropic Copulas from Preliminary Knowledge of Dependence," Econometrics, MDPI, vol. 4(2), pages 1-21, March.
    18. Kwami Senam A. Sedzro & Adekunlé Akim Salami & Pierre Akuété Agbessi & Mawugno Koffi Kodjo, 2022. "Comparative Study of Wind Energy Potential Estimation Methods for Wind Sites in Togo and Benin (West Sub-Saharan Africa)," Energies, MDPI, vol. 15(22), pages 1-28, November.
    19. Millie Yi Mao & Aman Ullah, 2019. "Information Theoretic Estimation of Econometric Functions," Working Papers 201923, University of California at Riverside, Department of Economics.
    20. Tack, Jesse, 2013. "A Nested Test for Common Yield Distributions with Applications to U.S. Corn," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(1), pages 1-14, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:9:y:2016:i:10:p:842-:d:80909. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.