Untransposed transmission lines, unbalanced tap changer operations, and unbalanced loading in weak distribution lines can cause unbalanced-voltage conditions. The resulting unbalanced voltage at the point of interconnection affects proper gird integration and reduces the lifetime of wind turbines due to power oscillations, torque pulsations, mechanical stresses, energy losses, and uneven and overheating of the generator stator winding. This work investigates the dynamic impact of unbalanced voltage on the mechanical and electrical components of integrated Fatigue, Aerodynamics, Structures, and Turbulence (FAST) wind turbine generation systems (WTGs) of Type 1 (squirrel-cage induction generator) and Type 3 (doubly-fed induction generator). To alleviate this impact, a serially-connected compensator for a three-phase power line is proposed to balance the wind turbine-side voltage. Dynamic simulation studies are conducted in MATLAB/Simulink to compare the responses of these two types of wind turbine models under normal and unbalanced-voltage operation conditions and demonstrate the effectiveness of the proposed compensator.