Wind energy systems can be classified into constant speed and variable speed ones. In constant speed schemes, the generator is directly connected to the electric grid. On the other hand, variable speed operation can be accomplished interposing a static converter in the energy flow between the generator and the grid, permitting a high control flexibility. The main control objectives are the maximization of the conversion efficiency and the elimination of torque oscillations propagated through the drive train. It is assumed in this paper that the most flexible part of the system lies on the turbine, constraining the control solutions to generator speed feedback. The control task is addressed from a passivity-based control viewpoint. The drive train dynamics is modelled as a port-controlled Hamiltonian system with dissipation. Then, stabilization of the desired operating point is achieved through energy shaping and damping injection. Depending on the damping matrix assignment, different control solutions are recovered. Finally, a dynamic feedback controller which preserves the system structure is proposed to improve the system performance without measuring the wind velocity.