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This paper presents a new approach to predict the time evolution of rotor angles of synchronous machines based on a modification of the Taylor series expansion in order to assess the transient stability of power systems in real time. To demonstrate the benefits of the proposed approach, a comparative analysis is made with other approaches which have been used for predicting the rotor angles, namely regression and interpolation algorithms and an approach based on original Taylor series expansion. The different prediction approaches are applied to the New England benchmark power system to predict the time evolution of the rotor angles in terms of stability and instability of first and second swing. The obtained results highlight the prediction accuracy of the proposed approach and the fulfilment of computational time requirements concerning real time applications.