Coherent groups of generators, i.e., machines with perfectly correlated rotor angles, play an important role in power system stability analysis. This paper introduces a real-time methodology based on hierarchical clustering techniques for discovering the degree of coherency among generators using the synchronization coefficient and the correlation coefficient of the generators rotor angle as the coherency index. Furthermore, the Power Transient Stability Indices (PTSI) were employed to examine the versatile response of the power system. The method uses power systems transients Stability indices, i.e., power Connectivity Factor (CF) index which presents coherently strong generators within the groups, the power Separation Factor (SF) index which unveils to the extent that the generators in different groups tend to swing against the other groups in the event of a disturbance, and the overall system separation index which demonstrates the overall system separation status (CF/SF). The approach is assessed on an IEEE-39 test system with a fully dynamic model. The simulation results presented in this paper demonstrate the efficiency of the proposed approach.
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