  We develop a new approach for construction of convex analytically simple
regions where the AC power flow equations are guaranteed to have a feasible
solutions. Construction of these regions is based on efficient semidefinite
programming techniques accelerated via sparsity exploiting algorithms.
Resulting regions have a simple geometric shape in the space of power
injections (polytope or ellipsoid) and can be efficiently used for assessment
of system security in the presence of uncertainty. Efficiency and tightness of
the approach is validated on a number of test networks.
