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The problem of modeling and control of multi-terminal high-voltagedirect-current transmission systems is addressed in this paper, which containsfive main contributions. First, to propose a unified, physically motivated,modeling framework - based on port-Hamiltonian representations - of the variousnetwork topologies used in this application. Second, to prove that the systemcan be globally asymptotically stabilized with a decentralized PI control, thatexploits its passivity properties. Close connections between the proposed PIand the popular Akagi's PQ instantaneous power method are also established.Third, to reveal the transient performance limitations of the proposedcontroller that, interestingly, is shown to be intrinsic to PI passivity-basedcontrol. Fourth, motivated by the latter, an outer-loop that overcomes theaforementioned limitations is proposed. The performance limitation of the PI,and its drastic improvement using outer-loop controls, are verified viasimulations on a three-terminals benchmark example. A final contribution is anovel formulation of the power flow equations for the centralized referencescalculation.

Modeling and Control of High-Voltage Direct-Current Transmission Systems: From Theory to Practice and Back