Impasse Surface of Differential–Algebraic Power System Models: An Interpretation Based on Admittance Matrices

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 article 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.