## Frequency-coupled impedance model-based sub-synchronous interaction analysis for direct-drive wind turbines connected to a weak AC grid

Recently, emerging sub-synchronous oscillation (SSO) issues caused by the interaction between power electronic converters and weak AC grids have provoked serious stability concerns. Impedance-based modelling approaches have been widely employed for stability analysis of such interactions. In this study, a sequence-domain frequency-coupled impedance model (FCIM) and the corresponding stability criterion are proposed. First, a fast identification method of the FCIM is proposed, in which the impedance-frequency curves of the FCIMs at multiple frequencies are measured, followed by identification of their transfer function models. Next, the proposed method is applied to model a practical system, where a SSO event once occurred due to the interactions between direct-drive wind turbines and a weak AC grid. The individual FCIMs of wind turbine generators, steam turbine generators and static var generator in this system are derived. After that, an aggregated FCIM is formed by combining the FCIMs without extra coordinate transformation. Then, the aggregated FCIM-based stability analysis is carried out to investigate the interaction between the wind farms and weak AC grids. In the end, the results of FCIM-based stability analysis are verified by time-domain simulations.