Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems
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| Format: | Artículo científico |
| Language: | en |
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Universidad EAFIT
2017
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| author | Whady F. Florez |
| author_facet | Whady F. Florez |
| contents | Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems Whady F. Florez Jorge W. Gonzales Alan F. Hill Gabriel J. Lopez Juan D. Lopez Ingeniería dynamic equations Richardson extrapolation Power system transient stability 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 sys- tem 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. 2017 artículo científico 1794-9165 https://www.redalyc.org/articulo.oa?id=83554561003 https://www.redalyc.org/journal/835/83554561003/ https://www.redalyc.org/journal/835/83554561003/html/ https://www.redalyc.org/journal/835/83554561003/83554561003.epub https://www.redalyc.org/journal/835/83554561003/movil 10.17230/ingciencia.13.26.3 en http://www.redalyc.org/revista.oa?id=835 Ingeniería y Ciencia application/pdf Universidad EAFIT Ingeniería y Ciencia (Colombia) Num.26 Vol.13 |
| format | Artículo científico |
| id | redalyc_83554561003 |
| institution | Redalyc |
| language | en |
| publishDate | 2017 |
| publisher | Universidad EAFIT |
| spellingShingle | Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems Whady F. Florez Ingeniería dynamic equations Richardson extrapolation Power system transient stability Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems Whady F. Florez Jorge W. Gonzales Alan F. Hill Gabriel J. Lopez Juan D. Lopez Ingeniería dynamic equations Richardson extrapolation Power system transient stability 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 sys- tem 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. 2017 artículo científico 1794-9165 https://www.redalyc.org/articulo.oa?id=83554561003 https://www.redalyc.org/journal/835/83554561003/ https://www.redalyc.org/journal/835/83554561003/html/ https://www.redalyc.org/journal/835/83554561003/83554561003.epub https://www.redalyc.org/journal/835/83554561003/movil 10.17230/ingciencia.13.26.3 en http://www.redalyc.org/revista.oa?id=835 Ingeniería y Ciencia application/pdf Universidad EAFIT Ingeniería y Ciencia (Colombia) Num.26 Vol.13 |
| title | Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems |
| topic | Ingeniería dynamic equations Richardson extrapolation Power system transient stability |
| url | https://www.redalyc.org/articulo.oa?id=83554561003 https://www.redalyc.org/journal/835/83554561003/ https://www.redalyc.org/journal/835/83554561003/html/ https://www.redalyc.org/journal/835/83554561003/83554561003.epub https://www.redalyc.org/journal/835/83554561003/movil |