This paper presents how to determine the optimal operating points of Unified Power Flow controllers (UPFC) the line flow control of which can enhance system security level. In order to analyze the effect of these devices on the power system, the decoupled model has been employed as a mathematical model of UPFC for power flow analysis. The security index that indicates the level of congestion of transmission line has been proposed and minimized by iterative method. The sensitivity of objective function for control variables of and UPFC has been derived, and it represents the change in the security index for a given set of changes in real power outputs of UPFC. The proposed algorithm with sensitivity analysis gives the optimal set of operating points of multiple UPECs that reduces the index or increases the security margin and Marquart method has been adopted as an optimization method because of stable convergence. The algorithm is verified by the 10-unit 39-bus New England system that includes multiple FACTS devices. The simulation results show that the power flow congestion can be relieved in normal state and the security margin can be guaranteed even in a fault condition by the cooperative operation of multiple UPECs.