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• The study proves HVDC protection performance depends on embedded AC grid strength. • Analytical relations are presented to discuss embedded AC grid characteristics. • Effective action time of the DC protection system has been discussed. • The study can be used in the effective design of DC protection for the HVDC grids. To build up a secure AC/DC power grid, a reliable DC protection system is vital for multi-terminal HVDC systems. However, efficient and reliable DC protection has always been a major challenge. On the other side, the characteristics of the embedded AC grid have a mutual impact on transient interactions with HVDC system dynamics and protection. The whole AC/DC grid including the HVDC system and the embedded AC grid must remain stable after a severe disturbance i.e., DC fault. Thus, the DC protection should be designed in a way that not only is reliable but also fast enough to prevent system instability, especially in the case of a weak embedded AC grid. However, there has been a lack of research on how fast DC protection should be regarding the transient stability of the embedded AC grid. This study presents a novel survey into DC protection criteria of the multi-terminal HVDC systems regarding the transient stability of the embedded AC grid. The study analytically investigates the effects of different grid parameters including HVDC power, converter transformer reactance and arm reactor on system security. Then, the discussion has been extended to discuss DC protection criteria, e.g., required speed, for the multi-terminal HVDC systems. A variety of simulations have been tested in the PSCAD platform using a multi-terminal HVDC case study. The outcomes can be used for the protection study of the multi-terminal HVDC systems and the selection of appropriate CBs. [ABSTRACT FROM AUTHOR]