Abstract: The widespread application of renewable energy sources makes the operation of distribution networks more complex. To compensate for the limitations of traditional regulating equipment in responding to the dynamic variations in active and reactive power in distribution networks, soft open points, as flexible power electronic devices, are employed to regulate the power flow. However, the topology and installation location of soft open points can affect their power flow control capability, making the determination of the optimal topology and installation location of multi-terminal soft open points a critical issue. Firstly, a nonlinear programming model is established based on the constraints of the distribution network system, and the nonlinear model is transformed into a second-order cone programming model through relaxation techniques. Secondly, a modified particle swarm optimization algorithm incorporating a constriction factor is adopted to efficiently search for the optimal installation positions of multiterminal soft open points across various topology structures. Thirdly, the optimization results are validated, and the economic feasibility of the optimal installation scheme is evaluated. Subsequently, the relaxation errors associated with various optimal topology solutions for multi-terminal soft open points are analyzed. Finally, the impact of various topologies and positions of multi-terminal soft open points on the operational level of the distribution network is obtained through comparative analysis. The results indicate that in the same operating scenario, the performance of the multi-terminal soft open point improves with an increasing number of terminals; however, the improvement effect diminishes as the number of terminals grows. The effectiveness of this method has been validated on the IEEE 33-node system.