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A reduced order model for subsynchronous oscillation analysis of direct drive wind farm was studied, and a balanced truncation method based on alternating direction implicit (ADI) was proposed. Firstly, the mathematical model of wind farm was built according to the mathematical representation of direct-driven permanent magnet synchronous wind turbine. The ADI method was used to solve the Lyapunov equation iteratively, and the controllable and observable Gramm matrixs were obtained. Then, the balanced truncation method was used to obtain the reduced order model. The time domain simulation waveform, Bode diagram, calculation time and subsynchronous oscillation mode of the full order model and the reduced order model were compared to verify the effectiveness of the proposed method. The simulation results show that the reduced order model has good consistency with the full order model, and the calculation speed is improved and the number of reduced order is greatly reduced.

The grid interconnections for direct-drive wind farms have triggered multiple new sub-synchronous oscillation events, which can prevent the power system from operating safely and stably. However, the excessively high order of the detailed model for large-scale wind farms with multiple direct-drive permanent magnet synchronous generators (PMSGs) connected to power systems poses a challenge when investigating small disturbance stability and instability mechanisms. This study establishes a model of the grid-connected PMSG system based on the voltage/power excitation–response relationship to describe the dynamic characteristics of the port of the PMSG, and the analysis of active and reactive response characteristics of PMSG lays the foundation for model simplification. Based on the unit model, a direct-drive wind farm aggregation equivalence method based on the excitation–response relationship is proposed. The equivalent model obtained by this method is suitable for the small disturbance stability analysis of direct-drive wind farms grid connected system, with good accuracy. The simulation verified the effectiveness of the aggregation model. [ABSTRACT FROM AUTHOR]

A stabiliser is designed based on the phase compensation method to suppress the instability of wind‐turbine type‐4 in the low frequency mode [direct current voltage loop mode and phase‐locked loop mode]. Referring to the second‐order equation of synchronous generator rotor motion, the authors simplify and reconstruct the full‐order linearised model of wind‐turbine type‐4 and establish a current source damping torque model suitable for analysing the stability of the direct current voltage loop and phase‐locked loop. By analysing the damping phase of the direct current voltage loop and phase‐locked loop, introducing a phase compensation loop, and adjusting the phase and amplitude of the damping transfer loop, the authors could effectively enhance the damping of the direct current voltage loop and the phase‐locked loop and suppress the low frequency oscillation of wind‐turbine type‐4. The stabiliser is introduced into the linear model and the time domain simulation model. The effectiveness of the stabilisers is verified by the eigenvalue analysis and time domain simulation results. [ABSTRACT FROM AUTHOR]