  Analyzing system trajectory from the perspective of individual machines
provides a distinctive angle to analyze the transient stability of power
systems. This two-paper series propose a direct-time-domain method that is
based on the individual-machine equal area criterion. In the first paper, by
examining the mapping between the trajectory and power-vs-angle curve of an
individual machine, the stability property to characterize a critical machine
is clarified. The mapping between the system trajectory and individual-machine
equal area criterion is established. Furthermore, a unity principle between the
individual-machine stability and system stability is proposed. It is proved
that the instability of the system can be confirmed by finding any one unstable
critical machine, thence, the transient stability of a multimachine system can
be monitored in an individual-machine way in transient stability assessment.
