This article presents a variable-speed converter system for wind energy conversion. The considered system consists of a wind turbine with a permanent magnet synchronous generator (PMSG), a machine-side converter, a grid-side converter and control circuits. Mathematical models of the components of the wind energy system are described. The control algorithms of the converter systems based on the vector methods of control are also described. The considered wind energy system were studied by digital simulation. The simulation results are presented and discussed.