A Novel Multiobjective Formulation for Optimal Wind Speed Modeling via a Mixture Probability Density Function

Ibrahim Mohamed Diaaeldin (), Mahmoud A. Attia, Amr K. Khamees, Othman A. M. Omar and Ahmed O. Badr ()
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Ibrahim Mohamed Diaaeldin: Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Abbassia, Cairo 11517, Egypt
Mahmoud A. Attia: Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Abbassia, Cairo 11517, Egypt
Amr K. Khamees: Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Abbassia, Cairo 11517, Egypt
Othman A. M. Omar: Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Abbassia, Cairo 11517, Egypt
Ahmed O. Badr: Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Abbassia, Cairo 11517, Egypt

Mathematics, 2023, vol. 11, issue 6, 1-19

Abstract: Over the past decades, the mathematical formulation of wind turbines (WTs) has been handled using different methodologies to model the probabilistic nature via different distribution functions. Many recently published articles have applied either the wind speed or the obtained active power from the WT on various probabilistic curves, such as Weibull, log-normal, and Gamma. In this work, the wind speed was modeled at five different locations in Egypt via a novel mixture probability distribution function (MPDF) that included four well-known distribution functions used to imitate the probabilistic nature of wind speed. Moreover, a decision-making multiple objective formulation was developed to optimally fit the MPDF with a minimum root mean square error (RMSE) and ensure reliable fitting by two other effective indices. Two methodologies, namely, equal and variable class widths, were investigated to model the density of wind speed and obtain a more realistic model for the tested wind speed profiles. The results showed the effectiveness of the proposed MPDF model as the RMSE was effectively minimized using multiobjective particle swarm optimization (MOPSO), showing nearly 10% improvement compared to the nondominated sorting genetic algorithm (NSGA-II).

Keywords: probabilistic distribution functions; mixture probability distribution functions; wind turbines; multiobjective optimization; decision-making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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