Passivity‐Based Robust Stability Analysis of the Converter–Grid Interaction and Passivity‐Shaping Controller Design

ABSTRACT With the increasing integration of high‐voltage direct current (HVDC) systems based on modular multilevel converter (MMC) technology in the power grid, the stability of the transmission system is increasingly affected. Guaranteeing robust stability for the AC‐side converter–grid interaction presents a challenge due to uncertain and time‐varying grid conditions. Passivity based stability criteria offer a powerful approach to assess converter‐driven stability. Passivity indices are utilized to evaluate and shape the converter input admittance. In this paper, existing passivity‐based stability theorems are examined and one less restricting and one less conservative stability criterion is derived. Additionally, a multi‐objective passivity‐shaping controller design is proposed that combines requirements for both robust stability and robust performance in a joint optimization.