Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems
The numerical solution of transient stability problems is a key element for electrical power system operation. The classical model for multi-machine systems is defined as a set of non-linear differential equations for the rotor speed and the generator angle for each electrical machine, this mathemat...
- Autores:
-
Flórez, Whady Felipe
Hill, Alan F.
López, Gabriel J.
López, Juan D.
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/13181
- Acceso en línea:
- http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808
http://hdl.handle.net/10784/13181
- Palabra clave:
- Power system transient stability
Richardson extrapolation
dynamic equations
Estabilidad transitoria de sistemas de potencia
Extrapolación de Richardson
Ecuaciones dinámicas
- Rights
- License
- Attribution 4.0 International (CC BY 4.0)
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dc.title.eng.fl_str_mv |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
dc.title.spa.fl_str_mv |
Métodos numéricos acoplados con la extrapolación de Richardson para el cálculo de sistemas de potencia transitorios |
title |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
spellingShingle |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems Power system transient stability Richardson extrapolation dynamic equations Estabilidad transitoria de sistemas de potencia Extrapolación de Richardson Ecuaciones dinámicas |
title_short |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
title_full |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
title_fullStr |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
title_full_unstemmed |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
title_sort |
Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
dc.creator.fl_str_mv |
Flórez, Whady Felipe Hill, Alan F. López, Gabriel J. López, Juan D. |
dc.contributor.author.none.fl_str_mv |
Flórez, Whady Felipe Hill, Alan F. López, Gabriel J. López, Juan D. |
dc.contributor.affiliation.spa.fl_str_mv |
Universidad Pontificia Bolivariana |
dc.subject.keyword.eng.fl_str_mv |
Power system transient stability Richardson extrapolation dynamic equations |
topic |
Power system transient stability Richardson extrapolation dynamic equations Estabilidad transitoria de sistemas de potencia Extrapolación de Richardson Ecuaciones dinámicas |
dc.subject.keyword.spa.fl_str_mv |
Estabilidad transitoria de sistemas de potencia Extrapolación de Richardson Ecuaciones dinámicas |
description |
The numerical solution of transient stability problems is a key element for electrical power system operation. The classical model for multi-machine systems is defined as a set of non-linear differential equations for the rotor speed and the generator angle for each electrical machine, this mathematical model is usually known as the swing equations. This paper presents how to use direct Richardson extrapolation of several orders for the numerical solution of the swing equations and compares it with other commonly used implicit and explicit solvers such as Runge-Kutta, trapezoidal, Shampine and Radau methods. A numerical study on a simple three machine system is used to illustrate the performance and implementation of algebraic Richardson extrapolation coupled to several solution methods. Normally, the order of accuracy of any numerical solution can be increased when Richardson Extrapolation is used. A numerical example is provided for an electrical grid consisting of three machines and nine buses undergoing a disturbance. It is shown that in this case Richardson extrapolation effectively increases the order of accuracy of the explicit methods making them competitive with the implicit methods. |
publishDate |
2017 |
dc.date.issued.none.fl_str_mv |
2017-11-14 |
dc.date.available.none.fl_str_mv |
2018-11-16T16:28:58Z |
dc.date.accessioned.none.fl_str_mv |
2018-11-16T16:28:58Z |
dc.date.none.fl_str_mv |
2017-11-14 |
dc.type.eng.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion article publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.local.spa.fl_str_mv |
Artículo |
status_str |
publishedVersion |
dc.identifier.issn.none.fl_str_mv |
2256-4314 1794-9165 |
dc.identifier.uri.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808 http://hdl.handle.net/10784/13181 |
dc.identifier.doi.none.fl_str_mv |
10.17230/ingciencia.13.26.3 |
identifier_str_mv |
2256-4314 1794-9165 10.17230/ingciencia.13.26.3 |
url |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808 http://hdl.handle.net/10784/13181 |
dc.language.iso.none.fl_str_mv |
eng |
language |
eng |
dc.relation.isversionof.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808 |
dc.rights.eng.fl_str_mv |
Attribution 4.0 International (CC BY 4.0) |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.uri.none.fl_str_mv |
http://creativecommons.org/licenses/by/4.0 |
dc.rights.local.spa.fl_str_mv |
Acceso abierto |
rights_invalid_str_mv |
Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0 Acceso abierto http://purl.org/coar/access_right/c_abf2 |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.spa.fl_str_mv |
Universidad EAFIT |
dc.source.none.fl_str_mv |
instname:Universidad EAFIT reponame:Repositorio Institucional Universidad EAFIT |
dc.source.eng.fl_str_mv |
Ingeniería y Ciencia; Vol 13 No 26 (2017); 65-89 |
dc.source.spa.fl_str_mv |
Ingeniería y Ciencia; Vol 13 No 26 (2017); 65-89 |
instname_str |
Universidad EAFIT |
institution |
Universidad EAFIT |
reponame_str |
Repositorio Institucional Universidad EAFIT |
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Repositorio Institucional Universidad EAFIT |
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2017-11-142018-11-16T16:28:58Z2017-11-142018-11-16T16:28:58Z2256-43141794-9165http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808http://hdl.handle.net/10784/1318110.17230/ingciencia.13.26.3The numerical solution of transient stability problems is a key element for electrical power system operation. The classical model for multi-machine systems is defined as a set of non-linear differential equations for the rotor speed and the generator angle for each electrical machine, this mathematical model is usually known as the swing equations. This paper presents how to use direct Richardson extrapolation of several orders for the numerical solution of the swing equations and compares it with other commonly used implicit and explicit solvers such as Runge-Kutta, trapezoidal, Shampine and Radau methods. A numerical study on a simple three machine system is used to illustrate the performance and implementation of algebraic Richardson extrapolation coupled to several solution methods. Normally, the order of accuracy of any numerical solution can be increased when Richardson Extrapolation is used. A numerical example is provided for an electrical grid consisting of three machines and nine buses undergoing a disturbance. It is shown that in this case Richardson extrapolation effectively increases the order of accuracy of the explicit methods making them competitive with the implicit methods.La solución numérica de problemas de estabilidad transitoria es un elemento clave para la operacion de sistemas eléctricos. El modelo clásico para sistemas multi-máquina se define como un conjunto de ecuaciones diferenciales no lineales para la velocidad del rotor y el ángulo del generador para cada máquina eléctrica, este modelo matemático se conoce generalmente como las ecuaciones de oscilación. Este artículo presenta la forma de utilizar la extrapolación directa de Richardson de varios órdenes para la solución numérica de las ecuaciones de oscilación y la compara con otros métodos implícitos y explícitos de uso común como los métodos Runge-Kutta, Trapezoidal, Shampine y Radau. Se presenta un estudio numérico sobre un sistema simple de tres máquinas para ilustrar el desempeño y la implementación algebráica de la extrapolación de Richardson. El orden de exactitud de cualquier solución numérica puede aumentarse cuando se utiliza la extrapolación de Richardson. Se proporciona un ejemplo numérico para una red eléctrica que consta de tres máquinas y nueve buses que sufren una perturbación. Se demuestra que en este caso la extrapolación de Richardson aumenta efectivamente el orden de exactitud de los métodos explícitos haciéndolos competitivos con los métodos implícitos.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4808Copyright (c) 2017 Whady Felipe Florez, Jorge W Gonzalez, Alan F Hill, Gabriel J Lopez, Juan D LopezAttribution 4.0 International (CC BY 4.0)http://creativecommons.org/licenses/by/4.0Acceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 13 No 26 (2017); 65-89Ingeniería y Ciencia; Vol 13 No 26 (2017); 65-89Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power SystemsMétodos numéricos acoplados con la extrapolación de Richardson para el cálculo de sistemas de potencia transitoriosinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionarticlepublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Power system transient stabilityRichardson extrapolationdynamic equationsEstabilidad transitoria de sistemas de potenciaExtrapolación de RichardsonEcuaciones dinámicasFlórez, Whady FelipeHill, Alan F.López, Gabriel J.López, Juan D.Universidad Pontificia BolivarianaIngeniería y Ciencia13266589ing.ciencORIGINAL3.pdf3.pdfTexto completo PDFapplication/pdf778043https://repository.eafit.edu.co/bitstreams/93e27644-89ce-44dc-8cb8-8cfc62157b5b/downloadb6a0802472b50951960c0d60166f31d1MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html374https://repository.eafit.edu.co/bitstreams/b4c8a809-93f3-4b54-8d5c-50b10dbd97fa/downloadb55019f6d180971972dc44c206d25f58MD53THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/fe1adcd7-b132-464a-b85f-008775186ee1/downloadda9b21a5c7e00c7f1127cef8e97035e0MD5110784/13181oai:repository.eafit.edu.co:10784/131812020-03-01 17:29:35.4http://creativecommons.org/licenses/by/4.0Copyright (c) 2017 Whady Felipe Florez, Jorge W Gonzalez, Alan F Hill, Gabriel J Lopez, Juan D Lopezopen.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |