Research Article
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Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application

Year 2025, Early View, 1 - 1

Bayram Köse İbrahim Işıklı Mehmet Sagbas

https://doi.org/10.35378/gujs.1311992

Abstract

In this study, the scale and shape parameters of the Weibull probability distribution function (W.pdf) used in determining the profitability of wind energy projects are estimated using optimization algorithms and the moment method. These parameters are then used to estimate the wind energy potential (WEP) in Foça region of İzmir in Turkey. The values of Weibull parameters obtained using Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), Social Group Optimization (SGO), and Bat Algorithm (BA) were compared with the estimation results of the Moment Method (MM) as reference. Root mean square error (RMSE) and chi-square (χ^2) tests were used to compare the parameter estimation methods. The wind speed measurement values of the observation station in Foça were used. As a result of Foça speed data analysis, the annual average wind speed was determined as 6.15 m/s, and the dominant wind direction was found as northeast. Wind speed frequency distributions were compared with the measurement results and calculated with the estimated parameters. When RMSE and χ^2 criteria are evaluated together; it can be concluded that each used method behaves similarly for the given parameter estimation problem, with minor variations. As a result, it has been found that the optimization parameters produce very good results in wind speed distribution and potential calculations.

Keywords

Weibull distribution parameters Particle swarm optimization algorithm Social group optimization algorithm Sine cosine optimization algorithm Bat algorithm

References

  • [1] “BP Energy Outlook 2018 Edition”, BP, (2018).
  • [2] “World Energy Investment 2018”, IEA, (2018).
  • [3] Guo, P., Huang, X., Wang, X., “A review of wind power forecasting models”, Energy Procedia, 12: 770–778, (2011).
  • [4] Grundmeyer, M., Gervert, M., Lerner, J., “The importance of wind forecasting”, Renewable Energy Focus, 10(2): 64–66, (2009).
  • [5] Şenel, M.C., Koç, E., “The state of wind Energy in the World and Turkey general evaluation”, Mühendis ve Makina, 56(663): 46–56, (2015).
  • [6] Carta, J.A., Ramirez, P., Velazquez, S. “A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands”, Renewable and Sustainable Energy Rev, 13(5): 933–955, (2009).
  • [8] Mert, I., Karakuş, C., “A statistical analysis of wind speed data using Burr, generalized gamma, and Weibull distributions in Antakya, Turkey”, Turkish Journal of Electrical Engineering & Computer Sciences, 23(6): 1571–1586, (2015).
  • [9] Pishgar-Komleh, S., Keyhani, A., Sefeedpari, P., “Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: Firouzkooh county of Iran)”, Renewable and Sustainable Energy Rev., 42: 313–322, (2015).
  • [10] Wadi, M., Elmasry, W., “Statistical analysis of wind energy potential using different estimation methods for weibull parameters: A case study,” Electr Engineering, 103: 2573-2594, (2021).
  • [11] Chang, T.P., “Estimation of wind energy potential using different probability density functions,” Appl. Energy, 88(5): 1848–1856, (2011).
  • [12] Garcia, A., Torres, J., Prieto, E., De Francisco A., “Fitting wind speed distributions: a case study,” Sol. Energy, 62 (2): 139–144, (1998).
  • [13] Dutta, S., Genton, M.G., “A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families,” J. Multivar. Anal., 132: 82–93, (2014).
  • [14] Mazzeo, D., Oliveti, G., Labonia, E., “Estimation of wind speed probability density function using a mixture of two truncated normal distributions,” Renewable Energy, 115: 1260-1280, (2018).
  • [15] Yuan, K., Zhang, K., Zheng, Y., Li D., Wang Y., Yang Z., “Irregular distribution of wind power prediction,” J. Mod. Power Syst. Clean Energy, 6(6): 1172–1180, (2018).
  • [16] Lee, D., Baldick, R., “Probabilistic wind power forecasting based on the laplace distribution and golden search,” IEEE/PES Transmission and Distribution Conference and Exposition (T&D), 1–5, (2016).
  • [17] Wallner, M., “A half-normal distribution scheme for generating functions,” Eur. J. Comb., 87: 103138, (2020).
  • [18] Alavi, O., Mohammadi, K., Mostafaeipour, A., “Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran,” Energy Convers. Manage., 119: 101–108, (2016).
  • [19] Nagatsuka, H., Balakrishnan, N., “A method for estimating parameters and quantiles of the three-parameter inverse Gaussian distribution based on statistics invariant to unknown location,” J. Stat. Comput. Simul., 84(11): 2361–2377, (2014).
  • [17] Ahsanullah, M., Alzaatreh, A., “Some Characterizations of the LogLogistic Distribution,” Stochastics and Quality Control, 33(1): 23–29, (2018).
  • [18] Scerri, E., Farrugia, R., “Wind data evaluation in the Maltese Islands,” Renewable Energy, 7(1): 109–114, (1996).
  • [19] Alayat, M.M., Kassem, Y., Çamur, H., “Assessment of wind energy potential as a power generation source: A case study of eight selected locations in Northern Cyprus,” Energies, 11(10):2697, (2018).
  • [20] Sarkar, A., Deep, S., Datta, D., Vijaywargiya, A., Roy, R., Phanikanth, V., “Weibull and Generalized Extreme Value Distributions for Wind Speed Data Analysis of Some Locations in India,” KSCE J. Civ. Eng., 23(8): 3476–3492, (2019).
  • [21] Arreyndip, A.N., Joseph, E., “Generalized extreme value distribution models for the assessment of seasonal wind energy potential of Debuncha, Cameroon,” J. Renewable Energy, 2016: Article ID 9357812, (2016).
  • [22] D’Amico, G., Petroni, F., Prattico, F., “Wind speed prediction for wind farm applications by extreme value theory and copulas,” J. Wind Eng. Ind. Aerodyn., 145: 229–236, (2015).
  • [23] Sohoni, V., Gupta, S., Nema, R., “A comparative analysis of wind speed probability distributions for wind power assessment of four sites,” Turkish Journal of Electrical Engineering & Computer Sciences, 24(6): 4724–4735, (2016).
  • [24] Gul, M., Tai, N., Huang, W., Nadeem, M. H., Yu, M., “Evaluation of Wind Energy Potential Using an Optimum Approach based on Maximum Distance Metric,” Sustainability, 12(5): 1999, (2020).
  • [25] Wadi, M., Kekezoglu, B., Baysal, M., Tur, M.R., Shobole, A., “Feasibility Study of Wind Energy Potential in Turkey: Case Study of Catalca District in Istanbul”, 2nd International Conference on Smart Grid and Renewable Energy (SGRE), 1–6, (2019).
  • [26] Köse, B., Aygün, H., Pak, S. “Parameter estimation of the wind speed distribution model by dragonfly algorithm,” Journal of the Faculty of Engineering and Architecture of Gazi University, 38(3): 1747-1756, (2023).
  • [27] Akpinar, E.K., Balpetek, N., “Statistical analysis of wind energy potential of Elazığ province according to Weibull and Rayleigh distributions”, Journal of the Faculty of Engineering and Architecture of Gazi University 34(1): 569-580, (2019).
  • [28] Chaurasiya, P.K., Ahmed, S., Warudkar, V., “Study of diferent parameters estimation methods of weibull distribution to determine wind power density using ground based doppler SODAR instrument,” Alex Eng J, 57(4): 2299–2311, (2018).
  • [29] Guedes, K.S., de Andrade, C.F., Rocha, P.A.C., dos Mangueira, R.S., de Moura E.P., “Performance analysis of metaheuristic optimization algorithms in estimating the parameters of several wind speed distributions,” Applied Energy. 268: 114952, (2020).
  • [30] Gungor, A., Gokcek, M., Uçar, H., Arabacı, E., Akyüz, A., “Analysis of wind energy potential and Weibull parameter estimation methods: a case study from Turkey,” Int. J. Environ. Sci. Technol, 17(2): 1011–20. (2020).
  • [31] Chadee, J. C., Sharma, C., “Wind speed distributions: a new catalogue of defined models,” Wind Engineering, 25(6): 319–337, (2001).
  • [32] Wais, P., “A review of Weibull functions in wind sector,” Renewable and Sustainable Energy Reviews, 70: 1099–1107, (2017).
  • [33] Wang, J., Huang, X., Li, Q., Ma, X., “Comparison of seven methods for determining the optimal statistical distribution parameters: A case study of wind energy assessment in the large-scale wind farms of China,” Energy, 164: 432–448, (2018).
  • [34] Tuller, S.E., Brett, A.C. “The characteristics of wind velocity that favor the fitting of a Weibull distribution in wind speed analysis,” Journal of Climate and Applied Meteorology, 23(1): 124–134, (1984).
  • [35] Manwell, J.F., McGowan, J.G., Rogers, A.L., “Wind energy explained: theory, design and application,” John Wiley & Sons, (2010).
  • [36] Köse B., Aygün H., Pak S. (2021). Comparison Of Statistical Methods And Optimization Algorithms For Estimating Weibull Probability Distribution Parameters Used In Wind Energy, 23rd Congress on Thermal Science and Technology with International Participation (ULIBTK 2021), 189–195, (2021).
  • [37] Karadeniz, A., Eker, M.K., “Estimation of Weibull Function Parameters Using Six Different Methods With Balikesir-Balya Weather Station Data,” Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 17(51): 163–175, (2015).
  • [38] Kennedy, J., Eberhart, R., “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE Int. Conf., (1995).
  • [39] Mirjalili, S., “SCA: A Sine Cosine Algorithm for solving optimization problems”, Knowledge-Based Systems, 96: 120–133, (2016).
  • [40] Satapathy, S., Naik A., “Social Group Optimization (SGO): A New Population Evolutionary OptimizationTechnique,” Complex & Intelligent Systems, 2: 173–203, (2016).
  • [41] Das, S., Saha, P., Satapathy, S. C., & Jena, J.J., “Social group optimization algorithm for civil engineering structural health monitoring,” Engineering Optimization, 53(10): 1651–1670, (2021).
  • [42] Yang, X.S., A New Metaheuristic Bat-Inspired Algorithm, Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), 284: 65–74, (2010).
  • [43] Ekinci, S., “Power system stabilizer design for multi-machine power system using bat search algorithm,” Sigma Mühendislik ve Fen Bilimleri Dergisi, 33(4): 627–637, (2015).
  • [44] Doğru, A.S., Temel, B., and Eren. T. “Comparison of particle swarm optimization and bat algorithm methods in localization of wireless sensor networks,” International Journal of Engineering Research and Development, 11(3): 793–801, (2019).

Year 2025, Early View, 1 - 1

Bayram Köse İbrahim Işıklı Mehmet Sagbas

https://doi.org/10.35378/gujs.1311992

Abstract

References

  • [1] “BP Energy Outlook 2018 Edition”, BP, (2018).
  • [2] “World Energy Investment 2018”, IEA, (2018).
  • [3] Guo, P., Huang, X., Wang, X., “A review of wind power forecasting models”, Energy Procedia, 12: 770–778, (2011).
  • [4] Grundmeyer, M., Gervert, M., Lerner, J., “The importance of wind forecasting”, Renewable Energy Focus, 10(2): 64–66, (2009).
  • [5] Şenel, M.C., Koç, E., “The state of wind Energy in the World and Turkey general evaluation”, Mühendis ve Makina, 56(663): 46–56, (2015).
  • [6] Carta, J.A., Ramirez, P., Velazquez, S. “A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands”, Renewable and Sustainable Energy Rev, 13(5): 933–955, (2009).
  • [8] Mert, I., Karakuş, C., “A statistical analysis of wind speed data using Burr, generalized gamma, and Weibull distributions in Antakya, Turkey”, Turkish Journal of Electrical Engineering & Computer Sciences, 23(6): 1571–1586, (2015).
  • [9] Pishgar-Komleh, S., Keyhani, A., Sefeedpari, P., “Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: Firouzkooh county of Iran)”, Renewable and Sustainable Energy Rev., 42: 313–322, (2015).
  • [10] Wadi, M., Elmasry, W., “Statistical analysis of wind energy potential using different estimation methods for weibull parameters: A case study,” Electr Engineering, 103: 2573-2594, (2021).
  • [11] Chang, T.P., “Estimation of wind energy potential using different probability density functions,” Appl. Energy, 88(5): 1848–1856, (2011).
  • [12] Garcia, A., Torres, J., Prieto, E., De Francisco A., “Fitting wind speed distributions: a case study,” Sol. Energy, 62 (2): 139–144, (1998).
  • [13] Dutta, S., Genton, M.G., “A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families,” J. Multivar. Anal., 132: 82–93, (2014).
  • [14] Mazzeo, D., Oliveti, G., Labonia, E., “Estimation of wind speed probability density function using a mixture of two truncated normal distributions,” Renewable Energy, 115: 1260-1280, (2018).
  • [15] Yuan, K., Zhang, K., Zheng, Y., Li D., Wang Y., Yang Z., “Irregular distribution of wind power prediction,” J. Mod. Power Syst. Clean Energy, 6(6): 1172–1180, (2018).
  • [16] Lee, D., Baldick, R., “Probabilistic wind power forecasting based on the laplace distribution and golden search,” IEEE/PES Transmission and Distribution Conference and Exposition (T&D), 1–5, (2016).
  • [17] Wallner, M., “A half-normal distribution scheme for generating functions,” Eur. J. Comb., 87: 103138, (2020).
  • [18] Alavi, O., Mohammadi, K., Mostafaeipour, A., “Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran,” Energy Convers. Manage., 119: 101–108, (2016).
  • [19] Nagatsuka, H., Balakrishnan, N., “A method for estimating parameters and quantiles of the three-parameter inverse Gaussian distribution based on statistics invariant to unknown location,” J. Stat. Comput. Simul., 84(11): 2361–2377, (2014).
  • [17] Ahsanullah, M., Alzaatreh, A., “Some Characterizations of the LogLogistic Distribution,” Stochastics and Quality Control, 33(1): 23–29, (2018).
  • [18] Scerri, E., Farrugia, R., “Wind data evaluation in the Maltese Islands,” Renewable Energy, 7(1): 109–114, (1996).
  • [19] Alayat, M.M., Kassem, Y., Çamur, H., “Assessment of wind energy potential as a power generation source: A case study of eight selected locations in Northern Cyprus,” Energies, 11(10):2697, (2018).
  • [20] Sarkar, A., Deep, S., Datta, D., Vijaywargiya, A., Roy, R., Phanikanth, V., “Weibull and Generalized Extreme Value Distributions for Wind Speed Data Analysis of Some Locations in India,” KSCE J. Civ. Eng., 23(8): 3476–3492, (2019).
  • [21] Arreyndip, A.N., Joseph, E., “Generalized extreme value distribution models for the assessment of seasonal wind energy potential of Debuncha, Cameroon,” J. Renewable Energy, 2016: Article ID 9357812, (2016).
  • [22] D’Amico, G., Petroni, F., Prattico, F., “Wind speed prediction for wind farm applications by extreme value theory and copulas,” J. Wind Eng. Ind. Aerodyn., 145: 229–236, (2015).
  • [23] Sohoni, V., Gupta, S., Nema, R., “A comparative analysis of wind speed probability distributions for wind power assessment of four sites,” Turkish Journal of Electrical Engineering & Computer Sciences, 24(6): 4724–4735, (2016).
  • [24] Gul, M., Tai, N., Huang, W., Nadeem, M. H., Yu, M., “Evaluation of Wind Energy Potential Using an Optimum Approach based on Maximum Distance Metric,” Sustainability, 12(5): 1999, (2020).
  • [25] Wadi, M., Kekezoglu, B., Baysal, M., Tur, M.R., Shobole, A., “Feasibility Study of Wind Energy Potential in Turkey: Case Study of Catalca District in Istanbul”, 2nd International Conference on Smart Grid and Renewable Energy (SGRE), 1–6, (2019).
  • [26] Köse, B., Aygün, H., Pak, S. “Parameter estimation of the wind speed distribution model by dragonfly algorithm,” Journal of the Faculty of Engineering and Architecture of Gazi University, 38(3): 1747-1756, (2023).
  • [27] Akpinar, E.K., Balpetek, N., “Statistical analysis of wind energy potential of Elazığ province according to Weibull and Rayleigh distributions”, Journal of the Faculty of Engineering and Architecture of Gazi University 34(1): 569-580, (2019).
  • [28] Chaurasiya, P.K., Ahmed, S., Warudkar, V., “Study of diferent parameters estimation methods of weibull distribution to determine wind power density using ground based doppler SODAR instrument,” Alex Eng J, 57(4): 2299–2311, (2018).
  • [29] Guedes, K.S., de Andrade, C.F., Rocha, P.A.C., dos Mangueira, R.S., de Moura E.P., “Performance analysis of metaheuristic optimization algorithms in estimating the parameters of several wind speed distributions,” Applied Energy. 268: 114952, (2020).
  • [30] Gungor, A., Gokcek, M., Uçar, H., Arabacı, E., Akyüz, A., “Analysis of wind energy potential and Weibull parameter estimation methods: a case study from Turkey,” Int. J. Environ. Sci. Technol, 17(2): 1011–20. (2020).
  • [31] Chadee, J. C., Sharma, C., “Wind speed distributions: a new catalogue of defined models,” Wind Engineering, 25(6): 319–337, (2001).
  • [32] Wais, P., “A review of Weibull functions in wind sector,” Renewable and Sustainable Energy Reviews, 70: 1099–1107, (2017).
  • [33] Wang, J., Huang, X., Li, Q., Ma, X., “Comparison of seven methods for determining the optimal statistical distribution parameters: A case study of wind energy assessment in the large-scale wind farms of China,” Energy, 164: 432–448, (2018).
  • [34] Tuller, S.E., Brett, A.C. “The characteristics of wind velocity that favor the fitting of a Weibull distribution in wind speed analysis,” Journal of Climate and Applied Meteorology, 23(1): 124–134, (1984).
  • [35] Manwell, J.F., McGowan, J.G., Rogers, A.L., “Wind energy explained: theory, design and application,” John Wiley & Sons, (2010).
  • [36] Köse B., Aygün H., Pak S. (2021). Comparison Of Statistical Methods And Optimization Algorithms For Estimating Weibull Probability Distribution Parameters Used In Wind Energy, 23rd Congress on Thermal Science and Technology with International Participation (ULIBTK 2021), 189–195, (2021).
  • [37] Karadeniz, A., Eker, M.K., “Estimation of Weibull Function Parameters Using Six Different Methods With Balikesir-Balya Weather Station Data,” Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 17(51): 163–175, (2015).
  • [38] Kennedy, J., Eberhart, R., “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE Int. Conf., (1995).
  • [39] Mirjalili, S., “SCA: A Sine Cosine Algorithm for solving optimization problems”, Knowledge-Based Systems, 96: 120–133, (2016).
  • [40] Satapathy, S., Naik A., “Social Group Optimization (SGO): A New Population Evolutionary OptimizationTechnique,” Complex & Intelligent Systems, 2: 173–203, (2016).
  • [41] Das, S., Saha, P., Satapathy, S. C., & Jena, J.J., “Social group optimization algorithm for civil engineering structural health monitoring,” Engineering Optimization, 53(10): 1651–1670, (2021).
  • [42] Yang, X.S., A New Metaheuristic Bat-Inspired Algorithm, Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), 284: 65–74, (2010).
  • [43] Ekinci, S., “Power system stabilizer design for multi-machine power system using bat search algorithm,” Sigma Mühendislik ve Fen Bilimleri Dergisi, 33(4): 627–637, (2015).
  • [44] Doğru, A.S., Temel, B., and Eren. T. “Comparison of particle swarm optimization and bat algorithm methods in localization of wireless sensor networks,” International Journal of Engineering Research and Development, 11(3): 793–801, (2019).
There are 46 citations in total.

Details

Primary Language English
Subjects Wind Energy Systems, Renewable Energy Resources
Journal Section Research Article
Authors

Bayram Köse 0000-0003-0256-5921

İbrahim Işıklı 0000-0002-0778-7163

Mehmet Sagbas 0000-0001-5776-3947

Early Pub Date April 5, 2024
Publication Date
Published in Issue Year 2025 Early View

Cite

APA Köse, B., Işıklı, İ., & Sagbas, M. (2024). Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application. Gazi University Journal of Science1-1. https://doi.org/10.35378/gujs.1311992
AMA Köse B, Işıklı İ, Sagbas M. Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application. Gazi University Journal of Science. Published online April 1, 2024:1-1. doi:10.35378/gujs.1311992
Chicago Köse, Bayram, İbrahim Işıklı, and Mehmet Sagbas. “Estimation of Weibull Probability Distribution Parameters With Optimization Algorithms and Foça Wind Data Application”. Gazi University Journal of Science, April (April 2024), 1-1. https://doi.org/10.35378/gujs.1311992.
EndNote Köse B, Işıklı İ, Sagbas M (April 1, 2024) Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application. Gazi University Journal of Science 1–1.
IEEE B. Köse, İ. Işıklı, and M. Sagbas, “Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application”, Gazi University Journal of Science, pp. 1–1, April 2024, doi: 10.35378/gujs.1311992.
ISNAD Köse, Bayram et al. “Estimation of Weibull Probability Distribution Parameters With Optimization Algorithms and Foça Wind Data Application”. Gazi University Journal of Science. April 2024. 1-1. https://doi.org/10.35378/gujs.1311992.
JAMA Köse B, Işıklı İ, Sagbas M. Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application. Gazi University Journal of Science. 2024;:1–1.
MLA Köse, Bayram et al. “Estimation of Weibull Probability Distribution Parameters With Optimization Algorithms and Foça Wind Data Application”. Gazi University Journal of Science, 2024, pp. 1-1, doi:10.35378/gujs.1311992.
Vancouver Köse B, Işıklı İ, Sagbas M. Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application. Gazi University Journal of Science. 2024:1-.