A Newton–Raphson‐Based Optimizer for the Optimal Generation Allocation Problem Considering Operation and Maintenance Costs of Renewable Energy Sources.

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Title: A Newton–Raphson‐Based Optimizer for the Optimal Generation Allocation Problem Considering Operation and Maintenance Costs of Renewable Energy Sources.
Authors: Pham, Ly Huu1 (AUTHOR) phamhuuly@tdtu.edu.vn, Quynh, Nguyen Vu2 (AUTHOR), Minh, Nguyen Van3 (AUTHOR), Nguyen, Thang Trung1 (AUTHOR), Nguyen, Quoc Trung4 (AUTHOR), Saha, Akshay Kumar (AUTHOR) saha@ukzn.ac.za
Source: International Transactions on Electrical Energy Systems. 6/29/2026, Vol. 2026, p1-26. 26p.
Subject Terms: *Renewable energy sources, Newton-Raphson method, Maintenance costs, Load dispatching in electric power systems
Abstract: A large share of the world's electricity is produced from coal and similar energy sources. Although these sources are commonly used, they carry significant costs and environmental issues, including the emission of harmful gases that contribute to global warming. To foster a more sustainable future, it is crucial to focus on generating electricity cost‐effectively while prioritizing low‐emission strategies. These strategies are implemented in the combined economic emission load dispatch (EELD) problem and economic load dispatch (ELD) problem considering renewable energy sources (RESs) by allocating the optimal power output of thermal power and renewable energy plants. This study presents a new method, called the Newton–Raphson‐based optimizer (NRBO), which draws inspiration from the Newton–Raphson approach. The NRBO thoroughly explores the optimal solutions search process using two main components: the Newton–Raphson Search Rule and the trap avoidance operator. Furthermore, the method utilizes several groups of matrices to enhance the results when addressing such problem variants. In the study, the proposed NRBO method has demonstrated its effectiveness through application in three distinct test systems, considering transmission line losses, generator limits, and overall system constraints. The proposed NRBO method was compared with other techniques in the literature via various criteria. The comparison results show that NRBO effectively explores and exploits options to find the optimal global solution, outperforming other methods while respecting all constraints and limits. [ABSTRACT FROM AUTHOR]
Copyright of International Transactions on Electrical Energy Systems is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Newton–Raphson‐Based Optimizer for the Optimal Generation Allocation Problem Considering Operation and Maintenance Costs of Renewable Energy Sources.
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  Data: <searchLink fieldCode="AR" term="%22Pham%2C+Ly+Huu%22">Pham, Ly Huu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> phamhuuly@tdtu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Quynh%2C+Nguyen+Vu%22">Quynh, Nguyen Vu</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Minh%2C+Nguyen+Van%22">Minh, Nguyen Van</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Thang+Trung%22">Nguyen, Thang Trung</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Quoc+Trung%22">Nguyen, Quoc Trung</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Saha%2C+Akshay+Kumar%22">Saha, Akshay Kumar</searchLink> (AUTHOR)<i> saha@ukzn.ac.za</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Transactions+on+Electrical+Energy+Systems%22">International Transactions on Electrical Energy Systems</searchLink>. 6/29/2026, Vol. 2026, p1-26. 26p.
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  Data: *<searchLink fieldCode="DE" term="%22Renewable+energy+sources%22">Renewable energy sources</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Maintenance+costs%22">Maintenance costs</searchLink><br /><searchLink fieldCode="DE" term="%22Load+dispatching+in+electric+power+systems%22">Load dispatching in electric power systems</searchLink>
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  Label: Abstract
  Group: Ab
  Data: A large share of the world's electricity is produced from coal and similar energy sources. Although these sources are commonly used, they carry significant costs and environmental issues, including the emission of harmful gases that contribute to global warming. To foster a more sustainable future, it is crucial to focus on generating electricity cost‐effectively while prioritizing low‐emission strategies. These strategies are implemented in the combined economic emission load dispatch (EELD) problem and economic load dispatch (ELD) problem considering renewable energy sources (RESs) by allocating the optimal power output of thermal power and renewable energy plants. This study presents a new method, called the Newton–Raphson‐based optimizer (NRBO), which draws inspiration from the Newton–Raphson approach. The NRBO thoroughly explores the optimal solutions search process using two main components: the Newton–Raphson Search Rule and the trap avoidance operator. Furthermore, the method utilizes several groups of matrices to enhance the results when addressing such problem variants. In the study, the proposed NRBO method has demonstrated its effectiveness through application in three distinct test systems, considering transmission line losses, generator limits, and overall system constraints. The proposed NRBO method was compared with other techniques in the literature via various criteria. The comparison results show that NRBO effectively explores and exploits options to find the optimal global solution, outperforming other methods while respecting all constraints and limits. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Transactions on Electrical Energy Systems is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/etep/1698833
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        Text: English
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        PageCount: 26
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      – SubjectFull: Renewable energy sources
        Type: general
      – SubjectFull: Newton-Raphson method
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      – SubjectFull: Maintenance costs
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      – SubjectFull: Load dispatching in electric power systems
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      – TitleFull: A Newton–Raphson‐Based Optimizer for the Optimal Generation Allocation Problem Considering Operation and Maintenance Costs of Renewable Energy Sources.
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              Text: 6/29/2026
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