For a DC distributed power system, system stability can be predicted by dividing it into source and load subsystems, and then applying the Nyquist criterion to the impedance interaction between the source and load model. However, the generalized Nyquist criterion is extremely complicated and cannot directly reveal effective control strategies to reduce interaction problems of cascade threephase AC systems. Specifically, as a current force rectifier, this characteristic makes it difficult to judge the stability of a cascade three-phase Vienna AC system. To deal with the aforementioned problems, a simplified small signal stability criterion is presented for an AC distributed power system. Based on the criterion, the small signal model and impedance based on the reduced order model in the dq domain are studied theoretically. For the instability issue, an impedance regulator design method is presented. The correctness of the simplified stability criterion and the effectiveness of the proposed impedance regulator method are validated by extensive simulation and experiment.