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In this paper, voltage-source converter (VSC) based high-voltage dc (HVDC) transmission is investigated for interconnection of two very weak ac systems. By using the recently proposed power-synchronization control, the short-circuit capacities of the ac systems are no longer the limiting factors, but rather the load angles. For the analysis of the stability, the Jacobian transfer matrix concept has been introduced. The right-half plane (RHP) transmission zero of the ac Jacobian transfer matrix moves closer to the origin with larger load angles. The paper shows that, due to the bandwidth limitation imposed by the RHP zero on the direct-voltage control of the VSC, high dc-capacitance values are needed for such applications. In addition, the paper proposes a control structure particularly designed for weak-ac-system interconnections. As an example, it is shown that the proposed control structure enables a power transmission of 0.86 p.u. from a system with the short-circuit ratio (SCR) of 1.2 to a system with an SCR of 1.0. This should be compared to previous results for VSC based HVDC using vector current control. In this case, only 0.4 p.u. power transmission can be achieved for dc link where only one of the ac systems has an SCR of 1.0.