As extreme weather events have become more frequent in recent years

improving the resilience and reliability of power systems has become an important area of concern. In this paper

a robust preventive-corrective security-constrained optimal power flow (RO-PCSCOPF) model is proposed to improve power system reliability under <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-k$ outages. Both the short-term emergency limit (STL) and the long-term operating limit (LTL) of the post-contingency power flow on the branch are considered. Compared with the existing robust corrective SCOPF model that only considers STL or LTL

the proposed RO-PCSCOPF model can achieve a more reliable generation dispatch solution. In addition

this paper also summarizes and compares the solution methods for solving the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-k$ SCOPF problem. The computational efficiency of the classical Benders decomposition (BD) method

robust optimization (RO) method

and line outage distribution factor (LODF) method are investigated on the IEEE 24-bus Reliability Test System and 118-bus system. Simulation results show that the BD method has the worst computation performance. The RO method and the LODF method have comparable performance. However

the LODF method can only be used for the preventive SCOPF and not for the corrective SCOPF. The RO method can be used for both.