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Turbine FV is a stability enhancing method used to protect power systems against the loss of synchronism after extreme contingency events. To avoid unnecessary FV action, smart control schemes can be used based on real-time instability prediction. In the last decade, several WAMS-based instability prediction methods have been developed. However, relatively long cumulative latencies in WAMS structures significantly reduce the efficiency of preventive control and can lead to system instability. To speed up FV action initiated by smart control scheme, this paper proposes a fast stability prediction method which is completely different from other methods described in literature. It uses only local measurements and requires performing simple mathematical operations. The basis of this method is the prediction of the magnitude of the power-angle characteristic. Just after the fault clearance, the method allows to predict transient instability and initiate MFV action. Based on the magnitude of the power-angle characteristic, the steady-state stability margin can be also computed. When this margin is too small, SFV action can be initiated as well. The validity of the proposed method has been verified by simulations performed for a large-scale real power system and detailed models of power system elements.