With the increasing maturity of new energy technologies, distributed power systems have been widely used in the field of new energy power generation. The grid-connected rectifier is an important device in the distributed power system. When the grid-connected rectifier operates in a weak power grid environment, its operating performance deviates from the design value, endangering the operation safety of the power system. In this paper, the small-signal impedance model of the three-phase LCL grid-connected rectifier in the DQ coordinate system is established. This model considers the influence of the phase-locked loop on the rectifier impedance characteristics and improves the accuracy of the model, and on this basis, the theoretical stability of the system is analyzed. The stability judgment of the system has important engineering guidance significance. The traditional generalized Nyquist stability criterion requires a lot of calculations and is difficult to use. Therefore, a system stability criterion based on the Gerschgorin circle theorem is proposed, which reduces the amount of calculation and provides a higher size for the system design. The simulation results are consistent with the theoretical analysis, which verifies the correctness of the method proposed in this paper.