The performance of the High voltage dc systems is dependent on the stiffness of the ac bus, it is connected to. With the traditional synchronous reference frame-phase locked loops (SRF-PLL), voltage source converters (VSC) systems with large PLL gains, connected to weak ac networks are shown to be prone to instabilities, when subject to disturbances. In this thesis a new Adaptive PLL is designed with a pre-filter topology which extracts the fundamental positive sequence component of the input voltage, to be fed into the SRF-PLL for tracking of its phase angle. Compared with other traditional PLL topologies, this Adaptive PLL shows superior immunity to voltage distortions, and also has a faster dynamic performance. The thesis presents a comparative analysis of the performance of the traditional SRF-PLL with the Adaptive PLL in a VSC control system, and its impact on stability for VSCs connected to weak ac systems (up to SCR=1.3).