The permanent magnet synchronous generator (PMSG)-based wind farm with a modular multilevel converter (MMC) based HVDC system exhibits various oscillations and can experience dynamic instability due to the interactions between different controllers of the wind farm and MMC stations

which have not been properly examined in the existing literatures. This paper presents a dynamic modeling approach for small signal stability analysis of PMSG-based wind farms with a MMCHVDC system. The small signal model of the study system is validated by the comprehensive electromagnetic transient (EMT) simulations in PSCAD/EMTDC. Then the eigenvalue approach and participation factors analysis are utilized to comprehensively evaluate the impact of different controllers

system's parameters and the circulating current suppressing controller (CCSC) on the small signal stability of the entire system. From eigenvalue analysis

it is revealed that as the output active power of the wind farm increases within the rated range

the overall system will exhibit a sub-synchronous oscillation (SSO) instability mode

an extremely weak damping mode

and a low frequency oscillation instability mode. From participation factors analysis

it is observed that the SSO mode and weak damping mode are primarily related to the internal dynamics of the MMC

which can be suppressed or improved by CCSC. It is determined that the low frequency oscillation mode is primarily caused by the interactions between the phase locked loop (PLL) control of the wind farm and the voltage and frequency (V-F) control of the MMC station. The analysis also depicts that the larger proportional gain value of the V-F control of the MMC station and smaller PLL bandwidth of the wind farm can enhance the small signal stability of the entire system.