Rapid growth of renewable energy sources (RES) in the generation capacity mix poses substantial challenges on the operation of power systems in various time scales. Particularly in the intra-hour time scale, the interplay among variability and uncertainty of RES, unexpected transmission/generation outages, and short dispatch lead time cause difficulties in generationload balancing. This paper proposes a method to quantify the intra-hour flexibility region. A robust security-constrained multiperiod optimal power flow (RSC-OPF) model is first constructed to quantify the frequency, magnitude, and intensity of insufficient flexibility. The randomness of RES is captured by uncertainty sets in this model. The N-k contingency, spinning reserve, and corrective control limit constraints are included. This model is then cast into a two-stage robust optimization (RO) model and solved by the column-and-constraint generation (C&CG) method. The emergency measures with a least number of affected buses are derived and subsequently assessed by the post-optimization sensitivity analysis. Finally, the operational flexibility region is determined by continuous perturbation on the RES penetration level and the forecast error. The IEEE 14-bus system and a realistic Chinese 157-bus system are used to demonstrate the proposed method.