Under the Lagrangian Relaxation Framework

the procedure for solving units combination with security constraint(UCWSC) can be divided into two steps.The one step is to obtain a near feasible and suboptimal units combination at a horizontal time by solving the dual problem of UCWSC

and then a units combination is obtained by using some heuristic methods or by solving a series of integer programming problems

to regulate the situation of some units

therefrom

a feasible and near optimal configuration of units combination is obtained;the other step is solving the generating power of units being in operation at various dispatching time section

to make the generation cost to be the minimum.Therefore

judging a units combination being feasible or not in one time section is becoming moreimportant.For this

by using Bender's theorem for feasibility decomposition

the necessary and sufficient condition for determining the feasibility of a UCWSC and the numerical calculation method have been given

and being proven.Combined with the calculation example in test of one power system

the effective of the related theory and algorithm has been verified.