Due to increasing penetration of wind power into traditional grid, co-working of synchronous generators with wind turbines is gaining attention in terms of system stability. This paper deals with the transient stability enhancement of such systems by generalized unified power flow controller (GUPFC) having grid frequency switching quasi multi-pulse converters. Besides independent real and reactive power flow control capability of the two series converters, one series converter is commissioned to damp synchronous/induction generator speed fluctuations by a self-tuning fuzzy damping scheme in which output scaling factor is adjusted on-line according to a second fuzzy rule-base defined on error and error-integral of the synchronous generator speed. Damping function is further enhanced via simplex optimized gains cascaded to fuzzy inference system. AC bus voltage and DC link voltage of GUPFC are effectively controlled by the shunt converter without disturbing other control loops.