Convergence Region of Newton Iterative Power Flow Method: Numerical Studies
Power flow study plays a fundamental role in the process of power system operation and planning. Of the several methods in commercial power flow package, the Newton-Raphson (NR) method is the most popular one. In this paper, we numerically study the convergence region of each power flow solution und...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/509496 |
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| author | Jiao-Jiao Deng Hsiao-Dong Chiang |
| author_facet | Jiao-Jiao Deng Hsiao-Dong Chiang |
| author_sort | Jiao-Jiao Deng |
| collection | DOAJ |
| description | Power flow study plays a fundamental role in the process of power system operation and planning. Of the several methods in commercial power flow package, the Newton-Raphson (NR) method is the most popular one. In this paper, we numerically study the convergence region of each power flow solution under the NR method. This study of convergence region provides insights of the complexity of the NR method in finding power flow solutions. Our numerical studies confirm that the convergence region of NR method has a fractal boundary and find that this fractal boundary of convergence regions persists under different loading conditions. In addition, the convergence regions of NR method for power flow equations with different nonlinear load models are also fractal. This fractal property highlights the importance of choosing initial guesses since a small variation of an initial guess near the convergence boundary leads to two different power flow solutions. One vital variation of Newton method popular in power industry is the fast decoupled power flow method whose convergence region is also numerically studied on an IEEE 14-bus test system which is of 22-dimensional in state space. |
| format | Article |
| id | doaj-art-98657e7f3519472a8b1b3034b455c998 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-98657e7f3519472a8b1b3034b455c9982025-02-03T01:25:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/509496509496Convergence Region of Newton Iterative Power Flow Method: Numerical StudiesJiao-Jiao Deng0Hsiao-Dong Chiang1School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, ChinaSchool of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, ChinaPower flow study plays a fundamental role in the process of power system operation and planning. Of the several methods in commercial power flow package, the Newton-Raphson (NR) method is the most popular one. In this paper, we numerically study the convergence region of each power flow solution under the NR method. This study of convergence region provides insights of the complexity of the NR method in finding power flow solutions. Our numerical studies confirm that the convergence region of NR method has a fractal boundary and find that this fractal boundary of convergence regions persists under different loading conditions. In addition, the convergence regions of NR method for power flow equations with different nonlinear load models are also fractal. This fractal property highlights the importance of choosing initial guesses since a small variation of an initial guess near the convergence boundary leads to two different power flow solutions. One vital variation of Newton method popular in power industry is the fast decoupled power flow method whose convergence region is also numerically studied on an IEEE 14-bus test system which is of 22-dimensional in state space.http://dx.doi.org/10.1155/2013/509496 |
| spellingShingle | Jiao-Jiao Deng Hsiao-Dong Chiang Convergence Region of Newton Iterative Power Flow Method: Numerical Studies Journal of Applied Mathematics |
| title | Convergence Region of Newton Iterative Power Flow Method: Numerical Studies |
| title_full | Convergence Region of Newton Iterative Power Flow Method: Numerical Studies |
| title_fullStr | Convergence Region of Newton Iterative Power Flow Method: Numerical Studies |
| title_full_unstemmed | Convergence Region of Newton Iterative Power Flow Method: Numerical Studies |
| title_short | Convergence Region of Newton Iterative Power Flow Method: Numerical Studies |
| title_sort | convergence region of newton iterative power flow method numerical studies |
| url | http://dx.doi.org/10.1155/2013/509496 |
| work_keys_str_mv | AT jiaojiaodeng convergenceregionofnewtoniterativepowerflowmethodnumericalstudies AT hsiaodongchiang convergenceregionofnewtoniterativepowerflowmethodnumericalstudies |