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...

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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
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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
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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
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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
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spelling 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