A review on applications of holomorphic embedding methods
The holomorphic embedding method (HEM) stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables. The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2023-12-01
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| Series: | iEnergy |
| Subjects: | |
| Online Access: | https://www.sciopen.com/article/10.23919/IEN.2023.0037 |
| _version_ | 1827381451703713792 |
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| author | Kaiyang Huang Kai Sun |
| author_facet | Kaiyang Huang Kai Sun |
| author_sort | Kaiyang Huang |
| collection | DOAJ |
| description | The holomorphic embedding method (HEM) stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables. The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion involving one or multiple embedded complex variables. This transformation empowers the utilization of complex analysis tools to tackle the original problem effectively. Since the 2010s, the HEM has been applied to steady-state and dynamic problems in power systems and has shown superior convergence and robustness compared to traditional numerical methods. This paper provides a comprehensive review on the diverse applications of the HEM and its variants reported by the literature in the past decade. The paper discusses both the strengths and limitations of these HEMs and provides guidelines for practical applications. It also outlines the challenges and potential directions for future research in this field. |
| first_indexed | 2024-03-08T13:56:25Z |
| format | Article |
| id | doaj.art-bd603a8a62d3408889a2eac68d039bb7 |
| institution | Directory Open Access Journal |
| issn | 2771-9197 |
| language | English |
| last_indexed | 2024-03-08T13:56:25Z |
| publishDate | 2023-12-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | iEnergy |
| spelling | doaj.art-bd603a8a62d3408889a2eac68d039bb72024-01-15T14:27:52ZengTsinghua University PressiEnergy2771-91972023-12-012426427410.23919/IEN.2023.0037A review on applications of holomorphic embedding methodsKaiyang Huang0Kai Sun1Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN 37996, USADepartment of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN 37996, USAThe holomorphic embedding method (HEM) stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables. The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion involving one or multiple embedded complex variables. This transformation empowers the utilization of complex analysis tools to tackle the original problem effectively. Since the 2010s, the HEM has been applied to steady-state and dynamic problems in power systems and has shown superior convergence and robustness compared to traditional numerical methods. This paper provides a comprehensive review on the diverse applications of the HEM and its variants reported by the literature in the past decade. The paper discusses both the strengths and limitations of these HEMs and provides guidelines for practical applications. It also outlines the challenges and potential directions for future research in this field.https://www.sciopen.com/article/10.23919/IEN.2023.0037holomorphic embedding methodpower flowpolynomial solutionsnonlinear algebraic equationsdifferential equations |
| spellingShingle | Kaiyang Huang Kai Sun A review on applications of holomorphic embedding methods iEnergy holomorphic embedding method power flow polynomial solutions nonlinear algebraic equations differential equations |
| title | A review on applications of holomorphic embedding methods |
| title_full | A review on applications of holomorphic embedding methods |
| title_fullStr | A review on applications of holomorphic embedding methods |
| title_full_unstemmed | A review on applications of holomorphic embedding methods |
| title_short | A review on applications of holomorphic embedding methods |
| title_sort | review on applications of holomorphic embedding methods |
| topic | holomorphic embedding method power flow polynomial solutions nonlinear algebraic equations differential equations |
| url | https://www.sciopen.com/article/10.23919/IEN.2023.0037 |
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