This paper presents a novel fast security analysis method to perform simultaneous feasibility test (SFT) for security constrained unit commitment (SCUC). The method uses the Sherman-Morrison-Woodbury formula to calculate DC power flow with the incremental topology changes across time intervals and with the contingencies for each interval. The extremely fast SFT allows the SCUC Mixed Integer Programming (MIP) solver to check network security constraints in a callback, leading to a significant performance improvement over the traditional MIP-SFT iteration method.