Identifying a vanishing eigenvalue in voltage collapse analysis with consideration of limits

Modal analysis has been widely employed in voltage stability studies. Literature shows that monitoring the least eigenvalue/singular value as a function of load increase may drive one to incorrect conclusions, since these values present a sharp variation at the bifurcation point. A ´well behaved´ eigenvalue may be identified, even when limits on the reactive power generation are considered. For this purpose, the centre manifold theorem is employed. Results provide an interesting insight into modal analysis, since some interesting theoretical points are addressed. Some original results are also discussed