  Modern power networks face increasing challenges in controlling their
transient frequency behavior at acceptable levels due to low inertia and
highly-dynamic units. This paper presents a distributed control strategy
regulated on a subset of buses in a power network to maintain their transient
frequencies in safe regions while preserving asymptotic stability of the
overall system. Building on Lyapunov stability and set invariance theory, we
formulate the transient frequency requirement and the asymptotic stability
requirement as two separate constraints for the control input. Hereby, for each
bus of interest, we synthesize a controller satisfying both constraints
simultaneously. The controller is distributed and Lipschitz, guaranteeing the
existence and uniqueness of the trajectories of the closed-loop system.
Simulations on the IEEE 39-bus power network illustrate the results.
