  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.
