The invention is a fast simultaneous feasibility test for security constrained unit commitment with network changes over time and contingencies. Given a proposed solution to a security constrained unit commitment problem, a simultaneous feasibility test evaluates a set of security constraints, determines whether the solution violates any of these constraints, and returns sensitivity coefficients for violated constraints with respect to the solution variables. The security constraints to be evaluated cover the initial network topology as well as changes to the topology over different time intervals in the model and over contingencies. These changes typically comprise the opening or closing of just a few lines in the network. This invention includes numerical algorithms that perform this simultaneous feasibility test quickly. The structure of the network changes over time intervals and contingencies and the small number of lines being changed are used in a novel way to speed up the computation. The speed of this computation enables this simultaneous feasibility test to be hosted on a single computer workstation and to be integrated into the security constrained unit commitment solver, leading to a speedup of the total time required to solve the security constrained unit commitment problem. This invention specifically applies a general mathematical technique used in a previous invention by the same inventors for network changes under contingencies to the network changes over time intervals. The elaboration and specification of this technique for network changes over time is the content of this invention.