  This work considers the task of finding an AC-feasible operating point of a
severely damaged transmission network while ensuring that a maximal amount of
active power loads can be delivered. This AC Maximal Load Delivery (AC-MLD)
task is a nonconvex nonlinear optimization problem that is incredibly
challenging to solve on large-scale transmission system datasets. This work
demonstrates that convex relaxations of the AC-MLD problem provide a reliable
and scalable method for finding high-quality bounds on the amount of active
power that can be delivered in the AC-MLD problem. To demonstrate their
effectiveness, the solution methods proposed in this work are rigorously
evaluated on 1000 N-k scenarios on seven power networks ranging in size from 70
to 6000 buses. The most effective relaxation of the AC-MLD problem converges in
less than 20 seconds on commodity computing hardware for all 7000 of the
scenarios considered.
