Analysis of voltage collapse in structure preserving models of power systems

Unlike systems described by ordinary differential equations, the structure preserving model of the power system is described by a mixed set of differential and algebraic equations. The concept of bifurcation and its implication for voltage collapse is investigated. The authors clarify the problem of voltage collapse from the viewpoint of the structure preserving model of power systems. Bifurcation points of the algebraic equation and their relationship with voltage stability problems are explored. The dynamics of voltage collapse near the bifurcation surfaces of the algebraic equations is explicitly described using singular perturbation theory. The results are illustrated by a simple power system example