Accompanying the rapid development of AC/DC distribution systems, along with the random disturbances introduced by a significant number of distributed generations and loads, the difficulty of system stability analysis has increased. The phenomenon of DC bus voltage instability has become severe, affecting the safe and stable operation of power systems. This paper focuses on the research of multi-terminal AC/DC distribution systems. A reduced-order method for multi-terminal distribution systems is proposed. Through parameter equivalent transformation, the system model is simplified while maintaining its dynamic characteristics. Parameter sensitivity analysis is utilized to identify key parameters influencing the system’s dynamic behavior, achieving an analytical expression of the system’s dynamic characteristics. And stability domain analysis is applied to delineate the variations in system dynamic behavior and responses to random disturbances under different parameter settings. Then a multi-parameter optimization method is designed to enhance system stability while achieving fast system response. Finally, theoretical analysis is validated through software simulation and hardware-in-the-loop experiments.