Approximating the loadability surface in the presence of SNB–SLL corner points

Approximating the parameter-space stability boundary considering post-contingency corrective controls

“…However, (40) does no longer apply when the intersection is tangential, as is the case when s IP reaches a tangential intersection point (TIP) [15] of post , since then the projection of one normal onto the tangent space of the other surface is zero. In this case we have to follow the procedure described in [15] to find the normal vector and the Weingarten map for the dividing surface.…”

“…In this case we have to follow the procedure described in [15] to find the normal vector and the Weingarten map for the dividing surface.…”

“…In [15] it was proposed that a dividing surface DS jk should be defined for intersections of SNB and SLL surfaces. We can extend this notion to include all types of intersecting surfaces.…”

“…A systematic way of finding appropriate points to compute the approximations in was also suggested. A special situation relating to long-term voltage stability was described in [14] and further investigated in [15].…”

Approximating a post-contingency stable operation region in parameter space through time-domain simulation

“…In [16] a third order approximation is derived and a method for handling the intersections of saddle-node bifurcations and switching loadability limits is proposed.…”