Hiskens's impasse-surface avoidance conjecture for static-load power systems

Suppose Assumption 1 and Assumption 2 hold. Consider a differential-algebraic equation system with all loads purely static. Let $al V_t$ denote the generator buses and $al V_L$ the load buses. Hiskens's conjecture. The system trajectories never encounter the impasse surface if all of the following conditions are satisfied: the generator stator circuit has $G_{gi}=0$ and $B_{gi}<0$ for every $i\temporal\in\mathcal V_t$; the power network has $G_{ij}=0$, $B_{ij}>0$, and $B_{ii}=-\sum_{j=1,j\ne i}^n B_{ij}$ for every $i,j\in\mathcal V_L$; the active-power loads have $P_{si}^0\geq 0$ and $lpha_i=2$ for every $i\in\mathcal V_L$; and the reactive-power loads have $Q_{si}^0\geq 0$ and $\eta_i\geq 1$ for every $i\in\mathcal V_L$. The paper presents results that prove this conjecture, although the supplied parser status is unknown.