Scheduling for generation units in modern power markets is one of the most important tasks of independent system operators (ISO). To ensure secure and economical operation of power systems, ISOs solve the security constrained unit commitment (SCUC) problem. SCUC is a very complex and large-scale optimization problem. In addition, uncertainties imposed by wind generators and variable loads add to this complexity. Stochastic SCUC, one of the most important problems for scheduling generation units, considers different power system uncertainties. A considerable amount of previous works demonstrates the efficacy of decomposition techniques, such as benders' decomposition for Stochastic SCUC. Solving this problem, even with decomposition techniques, for large-scale systems with multiple uncertainties is very time-consuming. A major part of Stochastic SCUC constraints belongs to network security. This paper presents a method in which cumulants are used to detect and eliminate inactive network constraints during the solving process. As a result, the method reduces the number of network security constraints and decreases the simulation time considerably. Implementing the proposed method on a six -bus test system and a modified IEEE 118-bus system demonstrates its efficiency and accuracy.