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The coherency of generators in a multi-machine power system is identified by determining the instantaneous phase difference between their rotor angles using a complex wavelet transform. A new phase difference matrix is proposed that represents the relative phase difference between the dominant frequency components of each pair of oscillating rotor angles and maps it into a higher dimensional space where data points corresponding to coherent generators lie in proximity. Next, density-based spatial clustering of applications with noise (DBSCAN) algorithm is used for automated grouping of coherent generators. A new objective function is proposed for the determination of control parameters of the clustering algorithm. The proposed approach is tested on the New England (NE) 39-bus test system and IEEE 145-bus test system.