The reinforcement of the transmission systems by means of HVDC systems, appears to be one of the most suitable solutions to face the challenges related to the evolution of power systems. In this context, this paper aims to investigate the impact of the overlaid HVDC systems on stability of the surrounding AC grid. More in particular, the rotor-angle transient stability problem is addressed. Firstly, using a benchmark power system, it is shown that HVDC links controlled to track constant power references, do not intrinsically increase transient stability margins as an AC line naturally does. Such comparison highlights the need of supplementary control layers aiming the stability enhancement of the surrounding AC grid. A proposed control strategy to improve the angle stability of the surrounding AC system is presented. The control is based on three identified actions HVDC systems allows: Injection of damping power, injection of synchronising power and fast compensation of power disturbances. These actions are then extrapolated to MTDC grids and implemented using a novel control structure. This structure allows to keep the zero power balance in every moment (DC voltage disturbances are minimal) while dealing with active power limits of the converters. The proposed controllers are tested on the EMT-RV software using EMT models of all the devices in the grid. Simulation results allow to show the effectiveness of the proposed controllers for enhancing the rotor angle stability of the surrounding AC grid.