In the paper, a double output induction generator (DOIG) driven by a wind turbine is studied. The reference frame model of the system including a fully controlled rectifier on the rotor side is derived. Based on this model, the steady-state equations are obtained in terms of the stator and rotor currents, rotor voltage and the slip. These equations are solved both with a model of a wind turbine and that of a DHC motor driving the DOIG. The results are compared with experimental ones. Finally, an optimisation problem is formulated to investigate the conditions of transferring maximum power from the wind turbine to the grid system, and it is shown that using a DOIG in either subsynchronous or supersynchronous modes, it is possible to transfer maximum power to the network in a wide range of wind speeds without exceeding the ratings of the induction generator.