  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.
