Security Constrained Optimal Power Flow is an important problem for power systems operators. The structure of the problem resembles stochastic programming problems in that one aims to find a cost optimal operation schedule that is feasible for all possible equipment outage scenarios (contingencies). Due to the presence of AC power flow constraints, the resulting problem is a large scale nonlinear programming problem. However it is known that only a small subset of the contingencies is active at the solution. We present an Interior Point based scheme that starts with the (small scale) base problem, generates likely active contingencies on-the-fly and integrates them into the algorithm using IPM warmstarting techniques. The final problem solved by this scheme is significantly smaller than the full contingency constrained problem, resulting in substantial speed gains. Numerical and theoretical results of our algorithm will be presented.