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A wide area measurement, nonlinear, model predictive control (MPC) approach is introduced to provide first swing stability protection of vulnerable power system transmission lines. The authors consider large disturbance events and focus on the avoidance of first swing angular separation using flexible AC transmission systems (FACTS) devices. The presented control strategy for FACTS devices is designed to be numerically efficient (due to the short MPC horizons) and robust (against complicated separation mechanisms). Simulation studies conducted on a three-machine system illustrate that the proposed MPC approach achieves first swing large disturbance performance that is near optimal and superior to existing transient stability controllers. Moreover, the proposed control approach is demonstrated to improve critical clearance times and to improve transfer capacity in simulation studies on the 39 bus New England system.