Dynamics and Stability of Meshed Multiterminal HVDC Networks

This paper investigates the existence of an equilibrium point in multiterminal HVdc grids, assesses its uniqueness, and defines conditions to ensure its stability. An offshore multiterminal HVdc system including two wind farms is selected as an application test case. At first, a generalized dynamic model of the network is proposed, using multigraph theory. Such model captures the frequency dependence of transmission lines and cables; it is nonlinear due to the constant power behavior of the converter terminals using droop regulation, and presents a suitable degree of simplifications of the modular multilevel converters, under given conditions, to allow system level studies over potentially large networks. Based on this model, the existence and uniqueness of the equilibrium point are demonstrated by returning the analysis to a load-flow problem and using the Banach fixed point theorem. Additionally, the stability of the equilibrium is analyzed by obtaining a Lyapunov function by the Krasovskii's theorem. Computational results obtained for the selected four-terminal HVdc grid corroborate the requirement for the existence and stability of the equilibrium point.