To insure stable operation and eliminate twice torque ripple, a topology for a six phase permanent magnet synchronous generator (SP-PMSG) with a neutral point connected together was analyzed in this paper. By adopting an extended transformation matrix, the mathematic model of the space vector control was established. The voltage and torque equations were deduced while considering the third harmonic flux and inductance. In addition, the suppression third harmonic method and the closed loop control strategy were proposed. A comparison analysis indicates that the cooper loss minimum method and the current magnitude minimum method can meet different application requirements. The voltage compensation amount for each of the methods was deduced which also takes into account the third harmonic effect. A simulation and experimental result comparison validates the consistency through theoretical derivation. It can be seen that all of the two control strategies can meet the requirements of post-fault.