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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 91367, 11 pages
http://dx.doi.org/10.1155/MPE/2006/91367

Voltage collapse in power systems: Dynamical studies from a static formulation

1Instituto de Ciências Exatas, Universidade Federal de Itajubá, Itajubá, MG 37500-903, Brazil
2Instituto de Sistemas Elétricos e Energia, Universidade Federal de Itajubá, Itajubá, MG 37500-903, Brazil
3Instituto de Engenharia de Sistemas e Tecnologia da Informação, Universidade Federal de Itajubá, Itajubá, MG 37500-903, Brazil

Received 10 August 2004; Revised 18 May 2005; Accepted 7 August 2005

Copyright © 2006 Luis Fernando Mello et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper addresses the problem of voltage collapse in power systems. More precisely, we exhibit a voltage collapse in a power system with two buses. This study is carried out with the help of two approaches. The first is a dynamical approach where a saddle-node bifurcation is analyzed and the second is an algebraic approach. Both approaches deal with the static behavior of the power system, but some dynamic aspects may be observed. An equivalence between the algebraic and dynamical approaches is obtained. The need to use both models comes from the fact that they are usually exploited in the literature, but a deep theoretical justification is still pending. Such a justification is meant in this work.