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Summary form only given. The paper first shows that the transient stability status of a power system following a large disturbance such as a fault can be early predicted based on the measured post-fault values of the generator voltages, speeds, or rotor angles. Synchronously sampled values provided by phasor measurement units(PMUs) of the generator voltages, frequencies, or rotor angles collected immediately after clearing a fault are used as inputs to a support vector machines (SVM) classifier which predicts the transient stability status. Studies with the New England 39-bus test system and the Venezuelan power network indicated that faster and more accurate predictions can be made by using the post-fault recovery voltage magnitude measurements as inputs. The accuracy and robustness of the transient stability prediction algorithm with the voltage magnitude measurements was extensively tested under both balanced and unbalanced fault conditions, as well as under different operating conditions, presence of measurement errors, voltage sensitive loads, and changes in the network topology. During the various tests carried out using the New England 39-bus test system, the proposed algorithm could always predict when the power system is approaching a transient instability with over 95% success rate.