Identifying a vanishing eigenvalue in voltage collapse analysis with limits consideration

Modal analysis has been widely employed in voltage stability studies. The literature shows that monitoring the least eigenvalue/singular value as a function of load increase may drive one to draw the wrong conclusions, since these indices present a sharp variation at the bifurcation point. This letter shows that a "well-behaved" eigenvalue may be identified, even when reactive power limits are considered. For this purpose, the center manifold theorem is employed.