equivalent-machine trajectory variance is depicted clearly at the equivalent-machine MPP (trajectory-depiction advantage). After that, the two advantages of the equivalent machine are reflected in the definitions of the transient stability concepts.In particular, the one-and-only equivalent-machine swing is clearly depicted through its EMPP (reflection of trajectorydepiction advantage); The critical stability of the equivalent system is decided through the critical stability of the one-andonly equivalent machine (reflection of the two advantages). In the end of the paper, it is clarified that the equivalent-system stability is completely identical to the original-system stability. However, the equivalent-system severity might be different from the original-system severity because the inner-groupmachine motion might be fierce under certain circumstances.The contributions of this paper are summarized as follows: (i) The transient characteristics of the equivalent machine are systematically explained through the individual-machine perspective. This explains the mechanism of the equivalentmachine from an individual machine manner.(ii) The equivalent-machine transient stability is established based on the machine paradigms. This provides a precise modeling and stability characterization for the equivalent machine. (iii) All the transient stability concepts can be defined strictly through equivalent machine. This further validates the reasonability of the machine paradigms.The reminder of the paper is organized as follows. In Section II, the mechanisms of the equivalent-machine are analyzed. In Section III, the characteristics of the equivalent machine are explained from the individual-machine perspective. In Section IV, the equivalent-machine based system stability is given through the strict followings of the machine paradigms. In Section V, the advantages of the individualmachine based transient stability concepts are analyzed. In Section VI, simulation cases show the effectiveness of the equivalent-machine in TSA. In Section VII, the relationship between the original-system and the equivalent-system is analyzed. In Section VIII, detailed analysis about the mirror system is given. Conclusions are given in Section IX.In this paper, because the individual-machine and the equivalent-machine are defined in the COI-SYS and COI-NCR, respectively, the transformation between the two motion references is solved by using the mirror system. In addition, stability evaluations in this paper are mainly depicted by EAC rather than the transient energy.
II. MECHANISMS OF THE EQUIVALENT-MACHINE A. EQUIVALENT MACHINE MONITORING
