Impedance-Based Small-Signal Stability Assessment of Bipolar MMC-HVDC System

In monopole Modular Multilevel Converter-based High Voltage Direct Current (MMC-HVDC) systems, the DC impedance is typically described by a single equivalent value. In contrast, a typical bipolar MMC-HVDC system includes two MMCs per terminal—one for the positive pole and one for the negative pole—which leads to more complex dynamic behavior on the DC side. In such cases, a single impedance value is insufficient to capture the full system dynamics. This paper proposes an impedance-based method for small-signal stability assessment of bipolar MMC-HVDC systems. First, the DC impedance model of a converter station, consisting of both the positive- and negative-pole MMCs, is derived. Due to the dynamic interaction between the two poles, the resulting DC impedance is formulated as a 2×2 matrix, rather than a single value as in the monopole case. Based on the DC impedance matrix and the Generalized Nyquist Criterion (GNC), the coupling between positive pole and negative pole on small-signal stability of the bipolar system is investigated. In addition, a case study is conducted to evaluate the influence of different phase-locked loop (PLL) bandwidths on system stability, demonstrating the effectiveness of the proposed approach.