Recently, sub-synchronous oscillation (SSO) issues were observed in direct-drive permanent magnet synchronous generator (D-PMSG) based wind power generation systems (WPGS) comprising multiple wind farms. Impedance model (IM) analysis has become an important method to study such problems. In this paper, an IM of a D-PMSG grid-connected system (GCS) is established considering the relationship between wind speed and wind turbine output power and the effect of voltage outer loop control. An impedance network model (INM) for a multi-wind-farm grid-connected system (MWFGS) is constructed with IMs of each wind turbine/farm and transmission lines according to the interconnection topology of them. Then, based on the IM of the D-PMSG-GCS, the influence of wind speed on the SSO characteristics is quantitatively analyzed, and the accuracy of the model is verified by comparing with the eigenvalue analysis results. Finally, the influencing factors such as distributed wind speed and network topology of MWFGS on SSO characteristics are quantitatively analyzed based on the INM, and the time-domain simulation verifications are performed in PSCAD/EMTDC. The results prove the effectiveness of INM in analyzing SSO problems of a large-scale WPGS. This is of great significance for the planning of large-scale D-PMSG-based WPGSs and the suppression of SSO.
