The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method

The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and op...
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Gespeichert in:

Autor*in:	Amr Khaled Khamees [verfasserIn] Almoataz Y. Abdelaziz [verfasserIn] Makram R. Eskaros [verfasserIn] Mahmoud A. Attia [verfasserIn] Ahmed O. Badr [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	probability distribution functions mixture probability distribution functions metaheuristic optimization methods Mayfly algorithm statistical error

Übergeordnetes Werk:	In: Processes - MDPI AG, 2013, 10(2022), 2446, p 2446
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:2446, p 2446

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/pr10112446

Katalog-ID:	DOAJ02575291X

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callnumber-first	T - Technology
author	Amr Khaled Khamees
spellingShingle	Amr Khaled Khamees misc TP1-1185 misc QD1-999 misc probability distribution functions misc mixture probability distribution functions misc metaheuristic optimization methods misc Mayfly algorithm misc statistical error misc Chemical technology misc Chemistry The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method
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topic_title	TP1-1185 QD1-999 The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method probability distribution functions mixture probability distribution functions metaheuristic optimization methods Mayfly algorithm statistical error
topic	misc TP1-1185 misc QD1-999 misc probability distribution functions misc mixture probability distribution functions misc metaheuristic optimization methods misc Mayfly algorithm misc statistical error misc Chemical technology misc Chemistry
topic_unstemmed	misc TP1-1185 misc QD1-999 misc probability distribution functions misc mixture probability distribution functions misc metaheuristic optimization methods misc Mayfly algorithm misc statistical error misc Chemical technology misc Chemistry
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title	The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method
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title_sort	mixture of probability distribution functions for wind and photovoltaic power systems using a metaheuristic method
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title_auth	The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method
abstract	The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and operation, it is necessary to tackle the stochastic nature of these sources. Operators require adequate techniques and procedures to mitigate the negative consequences of the stochastic behavior of renewable energy generators. Thus, this paper presents a modification of the original probability distribution functions (PDFs) where the original PDFs are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using a mixture of probability distributions, which can improve the fitting of data and reduce this error. The main aim of this paper is to model wind speed and solar irradiance behaviors using a two-component and a three-component mixture of PDFs generated from the integration of the original Weibull, Lognormal, Gamma, and Inverse-Gaussian PDFs. Three statistical errors are used to test the efficiency of the proposed original and mixture PDFs, which are the root mean square error (RMSE), the coefficient of correlation (<i<R</i<<sup<2</sup<), and the Chi-square error (<i<X</i<<sup<2</sup<). The results show that the mixture of PDFs gives better fitting criteria for wind speed and solar irradiance frequency distributions than the original PDFs. The parameters of the original and the mixture of PDFs are calculated using the innovative metaheuristic Mayfly algorithm (MA). The three-component mixture of PDFs lowered the RMSE by about 73% and was 17% more than the best original and the two-component mixture distributions.
abstractGer	The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and operation, it is necessary to tackle the stochastic nature of these sources. Operators require adequate techniques and procedures to mitigate the negative consequences of the stochastic behavior of renewable energy generators. Thus, this paper presents a modification of the original probability distribution functions (PDFs) where the original PDFs are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using a mixture of probability distributions, which can improve the fitting of data and reduce this error. The main aim of this paper is to model wind speed and solar irradiance behaviors using a two-component and a three-component mixture of PDFs generated from the integration of the original Weibull, Lognormal, Gamma, and Inverse-Gaussian PDFs. Three statistical errors are used to test the efficiency of the proposed original and mixture PDFs, which are the root mean square error (RMSE), the coefficient of correlation (<i<R</i<<sup<2</sup<), and the Chi-square error (<i<X</i<<sup<2</sup<). The results show that the mixture of PDFs gives better fitting criteria for wind speed and solar irradiance frequency distributions than the original PDFs. The parameters of the original and the mixture of PDFs are calculated using the innovative metaheuristic Mayfly algorithm (MA). The three-component mixture of PDFs lowered the RMSE by about 73% and was 17% more than the best original and the two-component mixture distributions.
abstract_unstemmed	The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and operation, it is necessary to tackle the stochastic nature of these sources. Operators require adequate techniques and procedures to mitigate the negative consequences of the stochastic behavior of renewable energy generators. Thus, this paper presents a modification of the original probability distribution functions (PDFs) where the original PDFs are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using a mixture of probability distributions, which can improve the fitting of data and reduce this error. The main aim of this paper is to model wind speed and solar irradiance behaviors using a two-component and a three-component mixture of PDFs generated from the integration of the original Weibull, Lognormal, Gamma, and Inverse-Gaussian PDFs. Three statistical errors are used to test the efficiency of the proposed original and mixture PDFs, which are the root mean square error (RMSE), the coefficient of correlation (<i<R</i<<sup<2</sup<), and the Chi-square error (<i<X</i<<sup<2</sup<). The results show that the mixture of PDFs gives better fitting criteria for wind speed and solar irradiance frequency distributions than the original PDFs. The parameters of the original and the mixture of PDFs are calculated using the innovative metaheuristic Mayfly algorithm (MA). The three-component mixture of PDFs lowered the RMSE by about 73% and was 17% more than the best original and the two-component mixture distributions.
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title_short	The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method
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author2	Almoataz Y. Abdelaziz Makram R. Eskaros Mahmoud A. Attia Ahmed O. Badr
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