In this paper, an AC superconducting multi-phase symmetric-winding machine is designed for a wind power generator to improve its performance and reduce losses, where four handpicked topological designs were explored and compared. In particular, it is found that using high-phase order of unique phasors further improves the performance. The iron losses are reduced, and the rippling behavior is lowered due to the smoother airgap magnetic flux density. Furthermore, a higher least-common-multiple (LCM) is achieved due to a better slot-pole combination for fractional-slot concentrated windings without having space sub-harmonics. Nonetheless, it is shown that creating a smooth airgap magnetic flux density does not improve the AC hysteretic superconducting losses; thus, further research is needed using additional approaches. Moreover, it is found that the Meisner effect is present in the machine and is inversely proportional to the AC hysteretic superconducting losses. Finally, the work shows that a 13-phase AC-superconducting machine can achieve a theoretical limit approaching 101.70 Nm/kg for the torque-to-weight ratio, outperforming classic winding layouts.