  The paper analyzes the mechanisms of the individual-machine and also its
advantages in TSA. Based on the critical-machine monitoring of the original
system trajectory, it is clarified that the individual-machine strictly follows
the machine paradigms. These strict followings of the paradigms bring the two
advantages of the individual-machine method in TSA: (i) the individual-machine
trajectory stability is characterized precisely, and (ii) the
individual-machine trajectory variance is depicted clearly at IMPP. The two
advantages are fully reflected in the precise definitions of individual-machine
based transient stability concepts. In particular, the critical machine swing
is clearly depicted through the IDSP or IDLP of the machine, the critical
stability of the system is strictly defined as the critical stability of the
most-severely disturbed machine, and the individual-machine potential energy
surface is also precisely modeled through the IMPE of the machine. Simulation
results show the effectiveness of the individual-machine in TSA.
