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Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states; the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition

A Quick Method for Judging the Feasibility of Security-Constrained Unit Commitment Problems within Lagrangian Relaxation Framework