Soft open point （SOP） can provide real-time power flow control, fast fault self-healing and feeder load balancing, and has been widely used in distribution networks. However, grid voltage dips （GVD） are typical large disturbance conditions, and the stable operation mechanism of distribution network SOP under these conditions cannot be analyzed through small signal methods. Therefore, the mixed potential theory （MPT） is used to study the stability of SOP under GVD conditions, and the parameter optimization strategies and virtual capacitor control strategies are proposed. Firstly, a nonlinear average model of SOP is established. On this basis, the large signal stability criterion （LSSC） for SOP under GVD conditions is derived using MPT. In addition, in order to enhance the stability of the SOP system, parameter optimization strategies and control strategies for constructing virtual capacitors are proposed based on LSSC. Finally, the effectiveness of the above method is verified through MATLAB/Simulink time-domain simulation, namely: 1） based on LSSC, the stability of SOP under GVD can be effectively analyzed; 2） the system prameter optimization strategy based on LSSC and the construction of virtual capacitor control strategy can effectively improve the stable operation ability of the system under large disturbance conditions.