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In the paper, transient stability analysis of an N-machine power system is carried out using the decomposition-aggregation method. In the study, transfer conductances, mechanical damping, electromagnetic damping and speed governor action are taken into consideration. The system decomposition is performed so that every subsystem includes three machines, instead of only two machines as for the pair-wise decomposition. The system mathematical model is derived and decomposed into (N ¿¿ l)/2 sixth-order and one second-order interconnected subsystems. A vector Lyapunov function, whose elements are Lyapunov functions of the free (disconnected) subsystems, is constructed and used for the system aggregation. A seven-machine power system is used as an illustrative example, and an asymptotic stability domain estimate is determined for the system. It is found that the proposed decomposition scheme can lead to a considerable reduction in the conservativeness of the decomposition-aggregation method. It is found also that the pair-wise decomposition-aggregation approaches developed so far are not suitable for stability analysis of largescale power systems.