  In this paper we propose a distributed dynamic controller for sharing
frequency control reserves of asynchronous AC systems connected through a
multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions,
which guarantee that the frequencies of the AC systems converge to the nominal
frequency. Simultaneously, the global quadratic cost of power generation is
minimized, resulting in an optimal distribution of generation control reserves.
The proposed controller also regulates the voltages of the MTDC grid,
asymptotically minimizing a quadratic cost function of the deviations from the
nominal voltages. The proposed controller is tested on a high-order dynamic
model of a power system consisting of asynchronous AC grids, modelled as IEEE
14 bus networks, connected through a six-terminal HVDC grid. The performance of
the controller is successfully evaluated through simulation.
