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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.

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International audienceThe modular multilevel converters (MMCs) have emerged as the most suitable converter technology for HVDC applications. Besides the recognized advantages over conventional voltage source converters, one of the remarkable features of the MMC is its ability to store energy in the distributed submodule capacitors. This important feature can be used to mitigate the fluctuations of the DC voltage, which is inherently volatile against power disturbances compared to the frequency of conventional AC systems. This paper proposes a novel control strategy, called virtual capacitor control, which enables the utilization of the energy storage capability of the MMC to attenuate voltage fluctuations of HVDC systems. With the proposed control, the MMC behaves as if there were a physical capacitor whose size is adjustable and can be even bigger than the physical capacitor embedded in the converter. This control allows the system operator to optionally adjust this virtual capacitor of each MMC station and, thus, it provides an additional degree of freedom to the HVDC system operation. The EMT simulations of a 401-level MMC-based HVDC link system show the effectiveness of the proposed control to improve dc voltage transient dynamics

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