Dynamic Equivalence of Direct-Drive Wind Farms for Sub-synchronous Oscillation Characterization

[Objective] A high-precision and high-efficiency dynamic equivalent modeling method for wind farms is proposed to address the heavy computational burden caused by the curse of dimensionality in detailed electromagnetic transient modeling of large-scale direct-drive wind farms and to overcome the limitations of traditional single-machine equivalent models in accurately reflecting sub-synchronous oscillation characteristics. The method enables effective analysis of sub-synchronous oscillations in grid-connected wind power systems and reveals the inherent relationship between the oscillation behavior of the entire wind farm and that of key vibration source groups. [Methods] Based on an eigenvalue analysis of wind power grid-connected systems， the dominant eigenvalue participation factors were calculated to identify the key factors affecting the sub-synchronous oscillation characteristics. Based on the <i>K</i>-Means clustering algorithm， a dynamic equivalent modeling method for wind farm clustering is proposed， which uses the operating conditions， collection lines， and steady-state initial values of the system-state variables as clustering indicators. The corresponding clustering equivalent parameter calculation method was derived and presented. [Results] An electromagnetic transient simulation example was built for a networked system of 30 direct-drive wind turbines. The effectiveness of the clustering and aggregation equivalent model used for the sub-synchronous oscillation （SSO） analysis was verified from multiple perspectives by comparing the characteristic values and time-domain simulation results. [Conclusions] The proposed multimachine clustering equivalent modeling method for wind farms based on dominant eigenvalue participation factor guidance， fusion of operating conditions， collection lines， and initial values of state variables can significantly improve the accuracy and efficiency of SSO analysis， overcome the limitations of single-machine equivalence， and accurately capture and separate the contributions of different clusters （particularly vibration source clusters） within the wind farm to sub synchronous oscillations. This can provide a reliable modeling tool for the study of sub-synchronous oscillation mechanisms， stability evaluation， and suppression strategy formulation for large-scale direct-drive wind farm grid-connected systems.