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

Modal analysis has been widely employed in voltage stability studies. Liter ature shows that monitoring the least eigenvalue/singular value as a functi on of load increase may drive one to incorrect conclusions, since these val ues present a sharp variation at the bifurcation point. A 'well behaved' ei genvalue may be identified, even when limits oil the reactive power generat ion are considered. For this purpose, the centre manifold theorem is employ ed. Results provide an interesting insight into modal analysis, since some interesting theoretical points are addressed. Some original results are als o discussed.