The operation of high-power wind generators with weakened ac grids has historically been difficult because of stability and power quality issues. This paper presents an analytical stability study of a variable-speed directly-driven permanently-excited 2-MW wind generator connected to ac grids of widely varying strength and very weak grids. The generator includes two back-to-back full-scale vector controlled 3-level neutral-point-clamped (NPC) voltage-source-converters (VSC). A 47th order small-signal analytical wind generator model is developed within MatLab, and a summary of the model structure and controls is given. Model verification is demonstrated for fast and slow system variables employing detailed simulation software PSCAD/EMTDC. An eigenvalue stability study for weak ac networks is presented, and qualitative conclusions about inherent system dynamics and stability characteristics are given. These insights are employed to study the design of an ac voltage controller for weak ac networks. Two alternative controller designs are studied for their potential to enhance system robustness to changes in ac grid strength. Testing on the detailed simulator PSCAD/EMTDC is employed throughout to confirm conclusions from analytical studies.