To meet the increasingly high requirement of smart grid operations, considering AC power flow constraints in the NCUC (network-constrained unit commitment) is of great significance in terms of both security and economy. This paper proposes a decomposition method to solve NCUC with AC power flow constraints. With conic approximations of the AC power flow equations, the master problem is formulated as a MISOCP (mixed integer second-order cone programming) model. The key advantage of this model is that the active power and reactive power are co-optimised, and the transmission losses are considered. With the AC optimal power flow model, the AC feasibility of the UC result of the master problem is checked in subproblems. If infeasibility is detected, feedback constraints are generated based on the sensitivity of bus voltages to a change in the unit reactive power generation. They are then introduced into the master problem in the next iteration until all AC violations are eliminated. A 6-bus system, a modified IEEE 30-bus system and the IEEE 118-bus system are used to validate the performance of the proposed method, which provides a satisfactory solution with approximately 44-fold greater computational efficiency. (C) 2015 Elsevier Ltd. All rights reserved.