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A method for deriving dynamic security regions of power systems is developed. A power system operating state is defined to be dynamically secure with respect to a given disturbance if the system, starting in that state maintains transient stability after experiencing the disturbance. Specifically, these are regions of prefault angles such that the post-fault system is asymptotically stable. The proposed approach is to construct affine approximations to the nonlinearities in the transient stability model and then derive quadratic bounds on the errors between the nonlinearities and their approximation. These are then used to derive sufficient conditions for a polytope of operating states to be dynamically secure.
Kaye et al. (Wed,) studied this question.