For high-voltage direct-current (HVDC) transmission, the strength of the ac system is important for normal operation. An ac system can be considered as weak either because its impedance is high or its inertia is low. A typical high-impedance systemis when an HVDC link is terminated at a weak point of a large ac system where the short-circuit capacity of the ac system is low. Low-inertia systems are considered to have limited number of rotating machines, or no machines at all. Examples of such applications can be found when an HVDC link is powering an isand system, or if it is connected to a wind farm. One of the advantages of applying a voltage-source converter (VSC) based HVDC systemis its potential to be connected to very weak ac systems where the conventional linecommutated converter (LCC) based HVDC system has difficulties. In this thesis, the modeling and control issues for VSC-HVDC links connected to weak ac systems are investigated. In order to fully utilize the potential of the VSC-HVDC system for weak-ac-system connections, a novel control method, i.e., powersynchronization control, is proposed. By using power-synchronization control, the VSC resembles the dynamic behavior of a synchronous machine. Several additional functions, such as high-pass current control, current limitation, etc. are proposed to deal with  issues during operation. For modeling of ac/dc systems, the Jacobian transfer matrix is proposed as a unified modeling approach. With the ac Jacobian transfer matrix concept, a synchronous ac system is viewed upon as one multivariable feedback system. In the thesis, it is shown that the transmission zeros and poles of the Jacobian transfer matrix are closely related to several power-system stability phenomena. The similar modeling concept is extended to model a dc system with multiple VSCs. It is mathematically proven that the dc system is an inherently unstable process, which requires feedback controllers to be stabilized. For VSC-HVDC links using power-synchronization control, the short-circuit ratio (SCR) of the ac system is no longer a limiting factor, but rather the load angles. The righthalf plane (RHP) transmission zero of the ac Jacobian transfer matrix moves closer to the origin with larger load angles, which imposes a fundamental limitation on the achievable bandwidth of the VSC. As an example, it is shown that a VSC-HVDC link using powersynchronization control enables a power transmission of 0.86 p.u. from a system with an SCR of 1.2 to a system with an SCR of 1.0. For low-inertia systemconnections, simulation studies show that power-synchronization control is flexible for various operation modes related to island operation and handles the mode shifts seamlessly. / QC20100607