Prof. Chris de Marco presented a broad expository lecture of the role of Hamiltonian structure in Power System Dynamics: a topic of major focus for M2ACS

Title: Optimization Problems Motivated by Hamiltonian Structure in Power System Dynamics

There exists a long literature on construction of Lyapunov functions to estimate basins of attractions associated with stable operating points of a synchronous electric power grid.Â We will illustrate an interpretation of these Lyapunov functions as solving an associated optimal control/variational problem, which describes the worst case, smallest “size of disturbance” that can drive the system unstable.Â In simplified models that possess what is often termed a “nearly” Hamiltonian structure, the associated optimal control problem admits a closed form solution for the cost of control, as a function of state variables.Â This solution is closely related to physical stored energy in the network, and equals the traditionally derived Lyapunov function.Â When the model admits such a closed form Lyapunov function, one useful class of optimization problem is that of computing a set of lowest energy saddle exit points, which characterize the “easiest” paths by which the system may lose stability.Â A more challenging class of problems, to date largely unaddressed in the literature, lies in relaxing the constraints on model structure that enable the closed form solution.Â Here one seeks computational tractable means of characterizing cost of control in the optimal control problem for a more detailed dynamical model of the grid.

Event Date:Â Monday, November 19, 2012 – 4:00 p.m. – 5:00 p.m.