Optimal power dispatch in networks of high-dimensional models of synchronous machines

This paper investigates the problem of optimal frequency regulation of multi-machine power networks where each synchronous machine is described by a sixth order model. By analyzing the physical energy stored in the network and the generators, a port-Hamiltonian representation of the multi-machine system is obtained. Moreover, it is shown that the open-loop system is passive with respect to its steady states which implies that passive controllers can be used to control the multi-machine network. As a special case, a distributed consensus based controller is designed that regulates the frequency and minimizes a global quadratic generation cost in the presence of a constant unknown demand. In addition, the proposed controller allows freedom in choosing any desired connected undirected weighted communication graph.