  In this paper, we study efficient and robust computational methods for
solving the security-constrained alternating current optimal power flow
(SC-ACOPF) problem, a two-stage nonlinear optimization problem with disjunctive
constraints, that is central to the operation of electric power grids. The
first-stage problem in SC-ACOPF determines the operation of the power grid in
normal condition, while the second-stage problem responds to various
contingencies of losing generators, transmission lines, and transformers. The
two stages are coupled through disjunctive constraints, which model generators'
active and reactive power output changes responding to system-wide active power
imbalance and voltage deviations after contingencies. Real-world SC-ACOPF
problems may involve power grids with more than 30k buses and 22k contingencies
and need to be solved within 10-45 minutes to get a base case solution with
high feasibility and reasonably good generation cost. We develop a
comprehensive algorithmic framework to solve SC-ACOPF that meets the challenge
of speed, solution quality, and computation robustness. In particular, we
develop a smoothing technique to approximate disjunctive constraints into a
smooth structure which can be handled by interior-point solvers; we design a
distributed optimization algorithm to efficiently generate first-stage
solutions; we propose a screening procedure to prioritize contingencies; and
finally, we develop a reliable and parallel architecture that integrates all
algorithmic components. Extensive tests on industry-scale systems demonstrate
the superior performance of the proposed algorithms.
