I. Introduction
Interconnection of off-shore wind farms into weak ac grids via high voltage direct current (HVDC) transmission systems has been a challenge in the recent years [1]. Voltage source converters (VSCs) are the most commonly used type of converters in HVDC applications. While VSCs provide noticeable advantages in HVDC systems, several studies have identified serious control problems when VSCs, equipped with the standard vector current control (VCC), are connected to a very weak ac grid. In [1]–[5], it was discovered that the converter fails to transfer 1 p.u. power when connected to very weak ac grids. This phenomenon has been studied using time-domain simulations and impedance models [6]–[9]. The main identified problem in previously discussed research is the low frequency resonance that can interact with the current controller, or the phase-locked loop (PLL) dynamics when the power converter is synchronized to weak ac grid [1], [10]–[12].