Abstract: With the increasing penetration of photovoltaic in distribution networks,the source-grid-load correlation effect continues to increase,which increases the difficulty in analyzing the voltage stability of distribution networks.In this regard,this paper establishes a single-port coupling equivalent circuit based on the bus-voltage equation,which mainly includes three parts,i.e.,power （main grid power supply,distributed generator）,load,and the coupling relationship between them.Considering the coupling effect of multiple buses and lines on the voltage stability in distribution networks,the coupled voltage stability index （CVSI） is proposed based on the power flow solvability of the single-port coupling equivalent circuit,and the static voltage stability of distribution networks is quantitatively analyzed.In view of the fact that the traditional static voltage stability index is often highly nonlinear and difficult to apply to the optimization of distribution network operation,this paper simplifies the CVSI based on the second-order conical optimal power flow model and combines it with the EPSILON constraint method to transform the optimization model of distribution network operation into a multi-objective mixed-integer optimization model,and puts forward an optimal solution method of the Pareto frontier based on the principle of the comprehensive optimization of the multi-objective function.Finally,a real distribution network model in Taizhou City,Zhejiang Province,China,is analyzed as a case to verify the validity of the indexes and the model.