Can you clarify 'self-excited'?
According to Wikipedia "An induction machine requires externally supplied armature current; it cannot start on its own as a generator. Because the rotor field always lags behind the stator field, the induction machine always "consumes" reactive power, regardless of whether it is operating as a generator or a motor. A source of excitation current for magnetizing flux (reactive power) for the stator is still required, to induce rotor current. This can be supplied from the electrical grid or, once it starts producing power, from the generator itself."