A fast and scalable iterative methodology for solving the security-constrained optimal power flow (SCOPF) problem is proposed using problem decomposition and the inverse matrix modification lemma. The SCOPF formulation tackles system security operational planning by using short- and long-term post-contingency limits, probability of branch outages, and preventive and corrective actions, a probabilistic corrective-SCOPF problem formulation. Using two post-contingency states and contingency probabilities, the SCOPF could provide good system security at a lower cost than only preventive actions as the typical `N-1'-formulation does. Additional security is ensured using a post-contingency load-shedding limit constraint based on system operator policy. The proposed methodology is applied to a range of test systems containing up to 10,000 buses with a computational time of up to 3375 s for all 12,706 branch contingencies. Calculating contingency power flows takes 1.3% of the total solution time using the proposed methodology exploiting the inverse matrix modification lemma.
