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In this paper we propose distributed dynamic controllers for sharing bothfrequency containment and restoration reserves of asynchronous AC systemsconnected through a multi-terminal HVDC (MTDC) grid. The communicationstructure of the controller is distributed in the sense that only local andneighboring state information is needed, rather than the complete state. Wederive sufficient stability conditions, which guarantee that the AC frequenciesconverge to the nominal frequency. Simultaneously, a global quadratic powergeneration cost function is minimized. The proposed controller also regulatesthe voltages of the MTDC grid, asymptotically minimizing a quadratic costfunction of the deviations from the nominal DC voltages. The results are validfor distributed cable models of the HVDC grid (e.g. $\pi$-links), as well as ACsystems of arbitrary number of synchronous machines, each modeled by the swingequation. We also propose a decentralized, communication-free version of thecontroller. The proposed controllers are tested on a high-order dynamic modelof a power system consisting of asynchronous AC grids, modelled as IEEE 14 busnetworks, connected through a six-terminal HVDC grid. The performance of thecontroller is successfully evaluated through simulation.

Distributed Frequency Control through MTDC Transmission Systems