This paper proposes a new adaptive control strategy for a wind energy conversion system based on a permanent magnet synchronous generator and a pulse-width modulated current source converter. Most of the studies on wind farms are based on double fed induction technology. Nevertheless, the proposed conversion system is a good alternative due to its high efficiency and reliability. Electrolytic capacitors are not required in this type of converter and the voltage in the DC-link as well as the generated reactive power can be dynamically modified according to the wind velocity, being even negative if required. However, it is challenging from the control and stability standpoint. Capacitive filters placed on the AC side, which are required for safe commutation, can create resonances with the power grid. Reactive power is generated according to the capacity of the converter, the wind velocity and the load profile. The adaptive control strategy uses an adaptive PI which is self-tuned based on a linear approximation of the power system calculated at each sample time. A model reference is also proposed in order to reduce the post-fault voltages. Simulation results demonstrate the advantages of the proposed control.