In the last years, the electrical grid has seen a deep change in the power production share between conventional generators, such as coal and gas turbines, to renewable ones, like wind and photovoltaic power plants. These resources are characterized by a power electronics-based interface to the grid. However, these resources do not offer any rotational inertia to the grid, that, in case of large disturbances, can suffer of large frequency deviation. Several strategies have been proposed in literature for damping the frequency deviation, mostly involving HVDC systems. The HVDC can request active power to the DC-connected AC areas in order to provide the needed energy to damp the frequency variation. However, all these strategies do not investigate the impact of the power variation on the frequency in the other DC-connected AC areas, that may result large if these system's inertia is low. This paper proposes a control strategy for minimizing the impact of the power request in these DC-connected AC areas varying the power consumption of near voltage-sensitive loads by means of a controlled voltage variation. As demonstrated in this work, the controlled voltage variation is able to reduce the frequency swing in these AC areas, matching the power variation request for frequency support with the power variation achieved from the voltage-sensitive loads.