Reasonable selection of control parameters is a precondition for stable operation in a flexible DC power grid, and their tunings will depend on the stability model of the flexible DC power grid. First, a small-signal model of such a grid based on DC voltage slope control is proposed, and the internal dynamic characteristics of the modular multilevel converter and the function of the circulating current suppressor are considered. Secondly, the root locus method is used to analyze the influence of the PI parameters and the slope parameter of the DC voltage slope controller, and of the PI parameters of the circulating current suppressor on the stability of the system. The participation factor method is adopted to identify the mode corresponding to the double frequency circulating current, and then the suppression effect of PI parameters on double frequency circulation is analyzed. Finally, a simulation of the Zhangbei flexible DC grid demonstration project is built on the PSCAD/EMTDC platform to verify the correctness of the proposed modeling methods and conclusions. This paper provides a theoretical basis for control parameter tuning in practical projects. This work is supported by the Beijing Natural Science Foundation (No. 3172015) and the Science and Technology General Project of Beijing Education Commission (No. KM201911232016).