In this paper, the stability limitations are analyzed for a voltage-source converter (VSC) based high-voltage direct-current (HVDC) link using power-synchronization control for two feasible operation modes: alternating-voltage control and reactive-power control. As a comparison, the analysis has been done by the phasor approach and the space-vector approach. While the phasor approach is straightforward to apply and gives intuitive analytical results, the space-vector approach reflects more dynamic insights of the system. This is achieved by using a unified dynamic modeling of both the ac system and the VSC by means of a new introduced modeling approach Jacobian transfer matrices. This approach shows that non-minimum-phase phenomena due to competing effects between alternating voltages and currents following phase-angle changes impose a fundamental limitation on the achievable bandwidth of the VSC-HVDC link. At moderate voltage levels, a VSC-HVDC link operating in alternating-voltage control mode is able to achieve higher bandwidth than in reactive-power control mode since the right-half plane (RHP) zero is located further from the origin in the former mode.