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The evaluation of the stability of a power system during a transient requires that the dynamics of the subsystems be decomposed into relative and collective motions. This decomposition must establish a distinction between synchronous and frequency equilibria. Such a decomposition is made possible by specifying a system center of angle which is defined as the inertia weighted average of all rotor angles. The angular velocity of the center of angle accurately describes the frequency of the system. An angular coordinate of each rotating element in the system can be specified relative to the center of angle. In terms of these coordinates a simple expression is obtained for the exact transient kinetic energy of the system. A transformation relating center of angle referenced variables to the usual one machine reference allows the simultaneous use of both references each where best suited.
Tavora et al. (Mon,) studied this question.