Estimation of Wind Power Probability Density Distribution Functions Parameters By Using Meta-Heuristic Algorithms

Year 2024, Volume: 10 Issue: 2, 329 - 346, 31.08.2024

Tuğba Akman , Hasan Hüseyin Sayan , Yusuf Sönmez

Abstract

Wind energy is a very popular renewable energy resource and is used as an energy source global because of its benefits of being environmentally friendly, renewable and having great reserves. The probability density distribution of wind speed can be used to estimate wind power density. In this study, Weibull and Rayleigh density distributions were employed to analytically eliminate the presumption that the total wind power is described by a single random variant and to calculate the wind power probability density distribution. In the modeling of complex high-dimensional stochastic wind power, although it can be solved with various mathematical approaches, since there are generally large-scale power systems containing many generators, buses, planning periods and non-linear stochastic variables, it is quite leisurely in searching for the optimum point and most of the time the solutions are far from reality. Consequently, heuristic methods have now substituted classical mathematical methods in obtaining wind parameters. Therefore, the advantage of heuristic methods compared to classical methods is that they can produce efficient solutions in a shorter time and with greater precision. Therefore, in this study, the main metaheuristic algorithms Symbiosis Organisms Search (SOS) and Artificial Bee Colony (ABC) algorithms and the classical statistical methods Energy Pattern Factor and Maximum Likelihood Method were employed to investigate the accuracy of wind power parameter calculations. According to the results obtained, error analyzes were calculated and the accuracies of the methods were compared.

Keywords

Power Systems, Wind Energy, Optimization, Metaheuristic Search Algorithms

Ethical Statement

I confirm that the above submission has not been published before and is not under consideration for publication elsewhere. The authors declare that there is no conflict of interest regarding the publication of this paper.

Rüzgar Enerjisi Olasılık Yoğunluk Dağılımı Fonksiyonları Parametrelerinin Meta-Sezgisel Algoritmalar Kullanılarak Tahmini

Abstract

Rüzgar enerjisi oldukça popüler bir yenilenebilir enerji kaynağıdır ve çevre dostu olması, yenilenebilir olması ve büyük rezervlere sahip olması gibi faydaları nedeniyle dünya çapında bir enerji kaynağı olarak kullanılmaktadır. Rüzgar hızının olasılık yoğunluk dağılımı, rüzgar gücü yoğunluğunu tahmin etmek için kullanılabilmektedir. Bu çalışmada, toplam rüzgar gücünün tek bir rastgele değişkenle tanımlandığı varsayımını analitik olarak ortadan kaldırmak ve rüzgar gücü olasılık yoğunluk dağılımını hesaplamak için Weibull ve Rayleigh yoğunluk dağılımları kullanılmıştır. Karmaşık yüksek boyutlu stokastik rüzgar enerjisinin modellenmesinde, çeşitli matematiksel yaklaşımlarla çözülebilmesine rağmen genellikle çok sayıda jeneratör, bara, planlama periyodu ve doğrusal olmayan stokastik değişkenler içeren büyük ölçekli güç sistemleri bulunduğundan oldukça yavaştır. Optimum noktayı ararken çoğu zaman çözümler gerçeklikten uzak olmaktadır. Sonuç olarak, rüzgar parametrelerinin elde edilmesinde günümüzde klasik matematiksel yöntemlerin yerini sezgisel yöntemler almıştır. Dolayısıyla sezgisel yöntemlerin klasik yöntemlere göre avantajı, daha kısa sürede ve daha yüksek hassasiyetle etkin çözümler üretebilmesidir. Bu nedenle, bu çalışmada rüzgar gücü parametre hesaplamalarının doğruluğunu araştırmak için bilinen başarılı metasezgisel algoritmalardan Symbiosis Organisms Search (SOS) ve Yapay Arı Kolonisi (ABC) algoritmaları ile klasik istatistiksel yöntemlerden Enerji Eğilim Faktörü ve Maksimum Olabilirlik yöntemleri kullanılmıştır. Elde edilen sonuçlara göre hata analizleri hesaplanmış ve yöntemlerin doğrulukları karşılaştırılmıştır.

Keywords

Güç Sistemleri, Rüzgar enerjisi, Optimizasyon, Meta Sezgisel Algoritmalar

References

• [1] J. Wang, J. Hu and K. Ma, ‘’Wind speed probability distribution estimation and wind energy assessment,’’ Renew. Sustain. Energy Rev., vol. 60, pp. 881–899, 2016.
• [2] J. Zhang, Y. Wei, Z. Tan, K. Wang and W. A Tian, ‘’Hybrid method for short-term wind speed forecasting,’’ Sustainability, vol. 9, no.4, pp. 1-10, April 2017.
• [3] Z.R. Shu, Q.S. Li and P.W. Chan, ‘’Investigation of offshore wind energy potential in Hong Kong based on weibull distribution function,’’ Appl. Energy, vol.156, pp. 362–373, 2015.
• [4] M. Elshahed, M. M. Elmarsafawy and H. Z. Eldin, ‘’Stochastıc chance constraınt wıth dıscrete probabılıtıes of wınd sources ın economıc dıspatch,’’ International Conference on Renewable Power Generation, April 2016. doi:10.1049/cp.2015.0389
• [5] N. Masseran and A.M. Razali, ‘’Modeling the wind direction behaviors during the monsoon seasons in peninsular Malaysia,’’ Renew. Sustain. Energy Rev., vol. 56, pp. 1419–1430, 2016.
• [6] J.F. Manwell, J.G. Mccowan and A.L. Rogers, ‘’Wind Energy Explained: Theory, Design and Application,’’ Second Edition; JohnWiley & Sons, New York, NY, USA, 2010.
• [7] P.K. Goyal and T.K. Datta, ‘’Effect of wind directionality on the vulnerability of rural houses due to cyclonic wind.’’ Nat. Hazards Rev., vol. 14, pp. 258–267, 2013.
• [8] T. V. Ramachandra and B. V. Shruthi, “Wind energy potential mapping in Karnataka, India, using GIS,” Energy Convers. Manag., vol. 46, no. 9–10, pp. 1561–1578, 2005. doi: 10.1016/j.enconman.2004.07.009
• [9] E. Dokur and M. Kurban, “Wind Speed Potential Analysis Based on Weibull Distribution,” Balk. J. Electr. Comput. Eng., vol. 3, no. 4, pp. 231–235, 2015. doi:10.17694/bajece.72748
• [10] E. C. Morgan, M. Lackner, R. M. Vogel, and L. G. Baise, “Probability distributions for offshore wind speeds,” Energy Convers. Manag., vol. 52, no. 1, pp. 15–26, 2011. doi:10.1016/j.enconman.2010.06.015
• [11] P. Ramírez and J. A. Carta, “Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study,” Energy Convers. Manag., vol.46, no.15–16, pp.2419–2438, 2005. doi:10.1016/j.enconman.2004.11.004
• [12] S. Vela, “A review of wind speed probability distributions used in wind energy analysis case studies in the Canary Islands,” vol. 13, pp. 933–955, 2009. doi:10.1016/j.rser.2008.05.005
• [13] O. A. Jaramillo and M. A. Borja, “Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case,” vol.29, pp.1613–1630, 2004. doi:10.1016/j.renene.2004.02.001
• [14] A. Serban, L. S. Paraschiv and S. Paraschiv, “Assessment of wind energy potential based on Weibull and Rayleigh distribution models,” Energy Reports, vol. 6, pp. 250–267, April 2020. doi:10.1016/j.egyr.2020.08.048
• [15] P. Wais, “A review of Weibull functions in wind sector,” Renew. Sustain. Energy Rev., vol. 70, pp. 1099–1107, February 2017. doi:10.1016/j.rser.2016.12.014 [16] M. Ali, M. K. Mridul and A. Al Mahbub, “Comparative wind power assessment by weibull distribution function in Faridpur,” Proc. 2020 11th Int. Conf. Electr. Comput. Eng. ICECE 2020, pp. 13–16, 2020. doi:10.1109/ICECE51571.2020.9393088
• [17] I. Y. F. Lun and J. C. Lam, “A study of Weibull parameters using long-term wind observations,” Renew. Energy, vol. 20, no. 2, pp. 145–153, 2000. doi:10.1016/S0960- 1481(99)00103-2
• [18] A. S. S. Dorvlo, “Estimating wind speed distribution,” Energy Convers. Manag., vol. 43, no. 17, pp. 2311–2318, 2002. doi:10.1016/S0196-8904(01)00182-0
• [19] S. H. Pishgar-Komleh, A. Keyhani and P. Sefeedpari, “Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: Firouzkooh county of Iran),” Renew. Sustain. Energy Rev., vol. 42, pp. 313–322, 2015. doi:10.1016/j.rser.2014.10.028
• [20] A.H. Shahirinia, E.S. Soofi and D.C. Yu. “Probability distributions of outputs of stochastic economic dispatch,” Electrical Power and Energy Systems, vol.81, pp. 308–316, 2016.
• [21] G.J. Osorio, J.M. Lujano-Rojas, J.C.O. Matias, J.P.S. Catalao, “A probabilistic approach to solve the economic dispatch problem with intermittent renewable energy sources,’’ Energy vol. 82, pp. 949-959, 2015.
• [22] T.G. Hlalele, R.M Naıdoo, J. Zhang and R.C. Bansal, “Dynamic Economic Dispatch With Maximal Renewable Penetration Under Renewable Obligation,’’ IEEE Access, vol. 8, pp. 38794-38808, 2020.
• [23] S. N. Keshmiri and W. Gao, “Multi-Objective Stochastic Economic Dispatch,’’ IEEE, North American Power Symposium 2010, doi:10.1109/NAPS.2010.5619590
• [24] J. Hetzer, D. C. Yu and K. Bhattarai, “An Economic Dispatch Model Incorporating Wind Power,’’ Ieee Transactıons On Energy Conversıon, vol. 23, No. 2, pp. 603-611, June 2008.
• [25] A. Albani and M.Z. Ibrahim, “Statistical Analysis of Wind Power Density Based on the Weibull and Rayleigh Models of Selected Site in Malaysia,’’ Pakistan Journal of Statistics and Operation Research, Vol.9, No.4 pp. 393-406, 2014. doi:10.1234/pjsor.v9i4.580
• [26] C.Peng, H. Sun, J. Guo and G. Liu, “Dynamic economic dispatch for wind-thermal power system using a novel bi-population chaotic differential evolution algorithm,’’ Electrical Power and Energy System, vol.42, pp.119–126, 2012.
• [27] H.T. Jadhav, R. Roy, “Gbest guided artificial bee colony algorithm for environmental economic dispatch considering wind power,’’ Expert Systems with Applications, vol.40, pp.6385–6399, 2013.
• [28] S. Velamuri, S. Sreejith, P. Ponnambalam, “Static economic dispatch incorporating windfarm using Flower pollination algorithm,’’ Perspectives in Science, vol.8, pp. 260-262, 2016.
• [29] E. Arriagada, E. López, M. López and J. Vannier Claudio, “A Stochastic Economic Dispatch Model with Renewable Energies Considering Demand and Generation Uncertainties,’’ IEEE Grenoble Conference, DOI: 10.1109/PTC.2013.6652496, 2013.
• [30] Z. Zhang and Y. Sun, “A versatile probability distribution model for wind power forecast errors and ıts application in economic dispatch,’’ IEEE Transactıons on Power Systems, vol.28, no.3, pp.3114-3125 august 2013.
• [31] Z. Demirkol and M. Çunkaş, “The Renewable Energy Potential for Afyonkarahisar,’’ Selcuk University Journal of Engineering Science and Technology, May 2014. doi:10.15317/Scitech.201416130
• [32] M. Kurban, Y. Kantar and F.O. Hocaoglu, “Statıstical analysis of wind speed and power densities using weibull distribution,’’ Afyon Kocatepe University Journal of Scıence, vol.7, no.2, pp.205-218, 2007.
• [33] X. Liu, “Economic load dispatch constrained bywind power availability: a wait-and-see approach,’’ IEEE Transactıons On Smart Grıd, Vol.1, No.3, pp. 347-355, December 2010.
• [34] C. Peng, H. Sun, J. Guo and G. Liu, “Dynamic economic dispatch for wind-thermal power system using a novel bi-population chaotic differential evolution algorithm,’’ Electrical Power and Energy Systems, vol.42, pp. 119–126, 2012.
• [35] H.T. Jadhav, R. Roy, “Gbest guided artificial bee colony algorithm for environmental/economic dispatch considering wind power,’’ Expert Systems with Applications, vol.40, pp. 6385–6399, 2013.
• [36] Z. Zhang, Y.Z. Sun, D.W. Gao, J. Lin and L. Cheng, “A versatile probability distribution model for wind power forecast errors and ıts application in economic dispatch,’’ IEEE Transactions On Power Systems, vol.28, no.3, pp. 3115-3125, August 2013.
• [37] F. Zia and M. Nasir, “Optimization methods for constrained stochastic wind power economic dispatch,’’ 2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. pp.1-5, June 2013.
• [38] Q. Han, Z HaoHu, T. F. Chu, “Non-parametric models for joint probabilistic distributions of wind speed and direction data,’’ Renew. Energy 2018, vol.126, pp. 1032–1042, 2018.