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Subsynchronous oscillations (SSOs) induced by the interaction between wind farms based on direct-drive permanent magnet synchronous generators (D-PMSGs) and weak grids have attracted extensive attention. To better understand this SSO phenomenon, this paper derives multi-input multi-output (MIMO) transfer functions between the references of the current controller and the current of a grid-connected converter in the d-q frame, where the dynamic of PLL is considered. The dynamic of PLL lead to positive feedback in the MIMO transfer function, which impairs the stability of the overall system and induces the SSO phenomenon. Using the classical root locus method, the influence of correlated control parameters and different operation conditions on the system stability is substantially analysed. It is found that heavy load, low short circuit ratio (SCR) will intensify the SSO instability of system. Nonlinear electromagnetic transient simulations of a D-PMSG-based weak-grid-connected wind-farm system using PSCAD/EMTDC software effectively verify the correctness of the model proposed in the SSO analysis.

Subsynchronous Oscillation Analysis of Grid-Connected Converter Based on MIMO Transfer Functions