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In the flexible DC grids, selections of slope coefficients in system level controls and designs of smoothing reactors have a crucial influence on the system stability. In order to obtain their optimal values, a comprehensive small-signal stability model with the DC voltage slope control and smoothing reactors is proposed in this paper. Firstly, the linear state-space model of the entire system based on the small-signal method is deduced according to the coupling equations between the inputs, the outputs, and state variables related to converter stations and the AC sides, controllers, and the DC grid with smoothing reactors. Meanwhile, the influences of the MMC bridge arm circulating current and the capacitor voltage fluctuation of the sub-module are considered in this model. Secondly, the impacts of control parameters, smoothing reactor parameters, and bridge arm inductances are analyzed on the system stability through the Lyapunov stability theory. Finally, the simulation of Zhangbei four-terminal DC grid project in China is established to testify the correctness of the presented small-signal model and the conclusions about the impact of parameters on the system stability. The proposed method will provide some theoretical guidance for the system design and the parameter selection in DC grid applications.

Small-Signal Stability Modeling for MMC-Based DC Grids With Voltage Slope Control and Influence Analysis of Parameters