  The problem of modeling and control of multi-terminal high-voltage
direct-current transmission systems is addressed in this paper, which contains
five main contributions. First, to propose a unified, physically motivated,
modeling framework - based on port-Hamiltonian representations - of the various
network topologies used in this application. Second, to prove that the system
can be globally asymptotically stabilized with a decentralized PI control, that
exploits its passivity properties. Close connections between the proposed PI
and the popular Akagi's PQ instantaneous power method are also established.
Third, to reveal the transient performance limitations of the proposed
controller that, interestingly, is shown to be intrinsic to PI passivity-based
control. Fourth, motivated by the latter, an outer-loop that overcomes the
aforementioned limitations is proposed. The performance limitation of the PI,
and its drastic improvement using outer-loop controls, are verified via
simulations on a three-terminals benchmark example. A final contribution is a
novel formulation of the power flow equations for the centralized references
calculation.
