As renewable energy integration increasingly displaces synchronous generation, ensuring grid security under uncertain operating conditions becomes increasingly important. This paper proposes a continuous multi-period Chance-Constrained Security-Constrained Optimal Power Flow (CC-SC-OPF) formulation in the Nonlinear Programming (NLP) domain. The method

combines a rectangular-coordinate AC network representation with differentiable rational surrogates for scenario-based chance constraints, avoiding binary violation indicators while retaining the full non-convex AC network model. On a modified IEEE 9-bus system with S = 5 scenarios, the NLP formulation reduces execution time from 475.30 to 0.85 s (99.82%) relative to

the Mixed-Integer Quadratic Programming (MIQP) benchmark, with a 0.03% objective-value difference. For S = 10, the MIQP exceeds the 3 600 s time limit, whereas the NLP converges in 1.34 s. Scalability tests on IEEE 9-, 30-, 118-, and 300-bus systems demonstrate convergence for problems with up to approximately 1.9 million decision variables. These results demonstrate the

improved computational tractability of the proposed continuous reformulation for risk-aware power-system operation.