[Objective] AC microgrid back-to-back DC interconnect converters have significant power stability differences between the AC and DC sides in bidirectional power transmission, which may lead to a decrease in system stability and easily cause system instability. [Methods] The impedance characteristics of each port were analyzed through small signal modeling, and the bidirectional power stability of the AC and DC sides of the system was compared and analyzed by combining impedance expressions and Nyquist stability criteria. Aiming at the problems of negative impedance and bidirectional power stability differences under the traditional control, a port impedance coordinated optimization control strategy was proposed to simultaneously optimize the impedance of the three ports in the system. A voltage-power cooperative adjustment mechanism was introduced for the negative impedance on the AC side to achieve adaptive correction of the equivalent impedance characteristics through multivariate dynamic coupling. [Results] A Matlab/Simulink simulation model and a low-power prototype experimental platform were constructed, the simulation and experimental results showed that the proposed optimization control not only optimized the negative impedance of both the AC and DC sides of the system to the positive impedance, but also reduced the phase difference between the impedances on the DC side to zero, which greatly improved the stability margin of the system and enhanced the system bidirectional power stability. [Conclusion] The proposed port impedance coordinated optimization control strategy can effectively solve the problem of bidirectional power stability differences in back-to-back converter systems.