Dynamic Control of MultiMachine Power Systems Based on Two-Step Optimization Over Admissible Trajectories

An optimal additive power control for an n-generator power system is developed that forces the system to move over optimal trajectories from appropriate initial states to a stable target state over finite time intervals [O, T]. This dynamic optimal control maintains system stability even if some of these initial states lie outside of the subspace of states leading to stable trajectories for the free-running system. Those initial states for which this technique generates admissible (or practical) controls constitutes a region of controllability. The technique presented in this paper first defines a set of admissible trajectories all originating in the designated initial state at time t = 0 and terminating in the stable target state at a fixed, arbitrary time t = T. A cost functional-defined on this set of trajectories is minimized through variational methods to yield an optimal fixed-time trajectory for the interval [0, T]. The fixed-time control required for this optimal trajectory is determined explicitly by means of the state equations. A second cost functional defined on the set of optimal fixed-time trajectories corresponding to all T ¿(0, ¿) is then minimized to generate an optimal free-time trajectory, control, and time interval [0, T*]. This minimization leads to admissible controls only for initial states in an appropriate region of controllability. Two-and four-machine examples are included for illustrating the technique.