  This paper presents a decentralized controller for sharing primary AC
frequency control reserves through a multi-terminal HVDC grid. By using
Lyapunov arguments, the proposed controller is shown to stabilize the
equilibrium of the closed-loop system consisting of the interconnected AC and
HVDC grids, given any positive controller gains. The static control errors
resulting from the proportional controller are quantified and bounded by
analyzing the equilibrium of the closed-loop system. The proposed controller is
applied to a test grid consisting of three asynchronous AC areas interconnected
by an HVDC grid, and its effectiveness is validated through simulation.
