Abstract: As more and more new energy power generation is transmitted across regions through DC transmission, the multi-DC feed-to-receive system faces severe voltage stability risks. Relying on the grid strength represented by the generalized short-circuit ratio and its relationship with the voltage stability margin of the multi-infeed system, this paper proposes an iterative search algorithm for the nearest saddle-node bifurcation point in the multi-DC injection power space, which can be used to quickly calculate Euclidean distance from the current operation to the stable boundary. Firstly, according to the critical generalized short-circuit ratio of the DC multi-infeed system, the power space algebraic equations representing the saddle-node bifurcation of the system are constructed by using the singularity of the extended admittance matrix. Secondly, the right eigenvector corresponding to the generalized short-circuit ratio is proved to construct the normal vector of the stable boundary in the power parameter space, and the power space established by the generalized short-circuit ratio is convex. Finally, using the above results, an iterative search algorithm for the nearest saddle-node bifurcation point in the multi-DC power injection space is proposed. The calculation results of the example show that the proposed method meets the engineering requirements and provides a convenient tool for the stability risk identification of the multi-feed system.