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

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