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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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Published in:	Ingeniería y ciencia (Medellín, Colombia) Colombia), 2017-12, Vol.13 (26), p.65-89
Main Authors:	Florez, Whady F, Gonzales, Jorge W, Hill, Alan F, Lopez, Gabriel J, Lopez, Juan D
Format:	Article
Language:	English
Subjects:	Accuracy Differential equations dynamic equations Electric power Electric power systems engineering ENGINEERING, MULTIDISCIPLINARY Extrapolation Implicit methods Mathematical models mathematics Nonlinear equations Numerical analysis Numerical methods Power system transient stability Richardson extrapolation Rotor speed Runge-Kutta method Simulation Solvers Transient stability
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creator	Florez, Whady F Gonzales, Jorge W Hill, Alan F Lopez, Gabriel J Lopez, Juan D
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.
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This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>This work is licensed under a Creative Commons Attribution 4.0 International License.</rights><rights>LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI \| INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. 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subjects	Accuracy Differential equations dynamic equations Electric power Electric power systems engineering ENGINEERING, MULTIDISCIPLINARY Extrapolation Implicit methods Mathematical models mathematics Nonlinear equations Numerical analysis Numerical methods Power system transient stability Richardson extrapolation Rotor speed Runge-Kutta method Simulation Solvers Transient stability
title	Numerical Methods Coupled with Richardson Extrapolation for Computation of Transient Power Systems
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