Multi-terminal bipole HVDC systems are increasingly deployed to facilitate large scale renewable energy integration and enhance grid flexibility. For the bipole system, under balanced operating conditions, the currents in the positive and negative poles are symmetrical, resulting in zero current flowing through the dedicated metallic return (DMR). However, system asymmetry can happen when for instance one pole of the converter station is disconnected or unequally injecting the power. Under such operating condition, the currents in the positive pole and negative pole become unbalanced, resulting in a nonzero current flow through the DMR.

To mitigate the nonzero current flow through the DMR, the local supplementary pole balancing control can be employed. It is built based on the concept of the DC voltage droop control. The pole balancing control has been confirmed to effectively mitigate the neutral currents a in asymmetrical bipole system. However, while supplementary pole balancing control is carried out for improving operational performance, its impact on the stability of the system remains unexplored. Furthermore, when the number of the terminals is increased and multiple control strategies are adopted, maintaining system stability becomes a significant challenge. This paper presents a small signal stability analysis for multi-terminal bipole HVDC systems with integrated supplementary pole balancing control. The aim is to evaluates the impact of the supplementary pole balancing control on system stability, a linearized state-space model of the multi-terminal bipole HVDC system is developed to capture the dynamics of the converters, DC network, and outer control loops. Eigenvalues analysis is performed to identify critical system modes and assess their damping characteristic. Additionally, sensitivity analysis is employed to determine the influence of balancing control gains, providing insight into the interactions among different control strategies.

Simulation results demonstrate that, the supplementary pole balancing control can operate effectively alongside other control strategies, thereby contributing to the overall stability of the multi-terminal bipole HVDC system.