Towards a theory of voltage collapse in electric power systems

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

“…The system state tracks the system equilibrium sufficiently closely as the parameters change. This assumption is known as the quasistatic assumption [17]. Deviation of the state from the stable equilibrium can occur when the parameter rate of change becomes large enough or when discrete changes to the equations occur.…”

“…In a fold bifurcation, two equilibria coalesce and disappear. If one of the equilibria is stable, then the dynamic consequences of the fold bifurcation are well approximated by movement, slow then fast, along a particular dynamic trajectory called the unstable part of the center manifold of x * [17].…”

“…In particular, v quantitatively predicts the relative amounts of voltage decline at buses as the bifurcation is approached and as the initial part of the dynamic collapse occurs [17,18].…”

Control of Power Systems With Facts Devices Considering Different Load Characteristics

“…Although quite simple, it shows an interesting behaviour and can be used to present the main ideas and concepts. The results presented in this paper are calculated using the same parameter set as in (Dobson et al, 1989).…”

“…Nonlinear phenomena in power systems like voltage collapse or interarea oscillations have been investigated by many researchers (Ajjarapu et al, 1992;Budd et al, 2002;Chiang et al, 1990;Chiang et al, 1993;Dobson et al, 1989;Seydel, 2001). Understanding these phenomena is crucial because they can cause critical situations up to blackouts.…”