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This paper proposes a new control strategy of shunt flexible ac transmission system (FACTS) devices to improve the first swing stability limit of a simple power system. It is shown that the speed based bang-bang control (BBC) is unable to use the entire decelerating area in maintaining stability. The proposed control strategy improves the stability limit first by maximizing the decelerating area and then fully utilizing it in counterbalancing the accelerating area. This requires to continue the operation of shunt FACTS devices at full capacitive rating until the machine speed reaches a reasonable negative value during the first return journey. Afterwards, the control can be switched to continuous type to improve system damping in subsequent swings. The proposed control strategy is then applied to both static var compensator and static synchronous compensators placed in a single machine infinite bus system. The same control strategy is also used for some faults in a multimachine system. In both the systems, it is found that the proposed control can provide significantly higher stability limit than that of the BBC. The mechanism of improving the stability limit is also described.