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It is difficult to determine if a feasible solution to unit commitment (UC) problem can be obtained by adjusting generation levels for the fixed commitment states. In this paper, a necessary and sufficient condition is developed to determine the feasibility of commitment states if the generation regions of the units with ramping constraints at each time period are known recursively before solving continuous economic dispatch problems. The condition is proved rigorously by applying the Benders decomposition feasibility theorem [Benders, JF 1962 and Geoffion AM 1972]. Based on this condition, an efficient method for solving UC problems with ramping constraints can be developed. Numerical test shows that the feasibility of commitment states can be determined very efficiently and effectively.