We consider frequency control in power systems made of several non-synchronous AC areas connected by a multi-terminal high-voltage direct current (HVDC) grid. We propose two HVDC control schemes to make the areas collectively react to power imbalances, so that individual areas can schedule smaller power reserves. The first scheme modifies the power injected by each area into the DC grid as a function of frequency deviations of neighboring AC areas. The second scheme changes the DC voltage of each converter as a function of its own area's frequency only, relying on the physical network to obtain a collective reaction. For both schemes, we prove convergence of the closed-loop system with heterogeneous AC areas.