This paper presents a new Mixed Integer Linear Programming model (MILP) to account for the Security-Constrained Unit Commitment Problem (SCUC). Transmission Constraints are introduced through bus balances, line power bound flows, and bus voltage angle differences. Line status is also considered. Binary variables regarding line status (active or inactive) are introduced for this purpose. These variables allow discrete decisions on the connectivity of buses, reducing the angle coupling between buses, with several advantages. Three examples are solved. The results indicate that this method can obtain feasible solutions with CPU times of 2.5 s (for a 6-bus system) and 500 s (for the IEEE 118-bus system), and they reached cost savings up to 4.9% of the total generating cost for one day of programming horizon, in comparison with classical models. Relations of the network are illustrated graphically, and an analysis of the results is presented through new evaluation indexes. (C) 2018 Elsevier Ltd. All rights reserved.