DC Stability Analysis of Bipolar Grid-Forming MMC Stations in Multi-Terminal HVDC Grids

This paper investigates the DC small-signal stability of bipolar multilevel modular converter (MMC) stations in highvoltage DC transmission (HVDC) grids when the DC voltage droop control (DVD) and the AC grid-forming (GFM) control are applied. It is found that this control structure, which is essential for the future HVDC grids, introduces strong poleto-pole coupling on the DC side that entails a DC admittance matrix (DAM) to capture the small-signal stability. Further, it is revealed that the eigenvalues of the DAM physically correspond to the common-mode and the differential-mode oscillations of the bipolar station in symmetrical operation, from which a clear relation between the eigenvalues and the monopolar DC admittances is formulated and mathematically proven, serving as the basis to guide the bipolar system stability design. Plus, it is found that the dedicated metallic returns (DMRs) and the grounding resistor only provide damping to the differential-mode oscillations, but not to the common-mode ones. All findings are verified by EMT simulations with detailed MMC models comprising 401 sub-modules per arm.