Dynamic modelling and interaction analysis of multi-terminal VSC-HVDC grids through an impedance-based approach

This paper presents an impedance-based interaction and stability analysis of multi-terminal HVDC systems. First, an analytical derivation procedure is presented to obtain the feedback impedance models of a voltage source converter (VSC) as a subsystem, with particular interest on the DC side impedance. Subsequently, in addition to the impedance models of other subsystems, an impedance aggregation method is applied to derive the dynamic closed-loop impedance matrix of the system considering the interconnected structure of the grid. Given the closed-loop impedance matrix, multi-input multi-output (MIMO) relative gain array (RGA) formulation is proposed to analyse nodal interactions between converters and the network. Furthermore, the impedance ratio matrix is proposed for HVDC stability analysis based on impedance models. Remarkably, these formulations are derived compactly without any knowledge of the internal states of any converter and therefore allows the ease of interoperability analysis. Finally, the impact of control architecture and strategy on the dynamic responses, interaction, and stability analysis from an impedance perspective is conducted as a case study. The analysis is done in the frequency domain and validated with the physical model of a three-terminal DC test grid built in Simscape (TM) MATLAB/Simulink (R).