  The impasse surface is an important concept in the differential-algebraic
equation (DAE) model of power systems, which is associated with short-term
voltage collapse. This paper establishes a necessary condition for a system
trajectory hitting the impasse surface. The condition is in terms of admittance
matrices regarding the power network, generators and loads, which specifies the
pattern of interaction between those system components that can induce voltage
collapse. It applies to generic DAE models featuring high-order synchronous
generators, static loads, induction motor loads and lossy power networks. We
also identify a class of static load parameters that prevent power systems from
hitting the impasse surface; this proves a conjecture made by Hiskens that has
been unsolved for decades. Moreover, the obtained results lead to an early
indicator of voltage collapse and a novel viewpoint that inductive compensation
to the power network has a positive effect on preventing short-term voltage
collapse, which are verified via numerical simulations.
