Sub/super-synchronous oscillations induced by the interaction between wind turbines and the grid pose increasing challenges to the dynamic analysis of power-electronics-dominated power systems. For microgrids comprising a large number of distributed direct-drive wind turbines (DDWTs), detailed electromagnetic transient modeling becomes computationally prohibitive, while conventional single-machine equivalent models often fail to capture critical oscillatory characteristics. To address these issues, this paper proposes an impedance-sensitivity-based clustering and equivalent modeling method for DDWT groups in a microgrid. First, a frequency domain impedance model of DDWTs is established, and the impedance sensitivities of key control parameters are analyzed under various steady-state operating conditions. By jointly considering the absolute magnitude of impedance sensitivity and its variation across operating points, a sensitivity-informed criterion is developed to select physically meaningful clustering indices capable of distinguishing wind turbines with different operating conditions. Based on the selected indices, a k-means clustering algorithm is employed to group distributed DDWTs, and a multi-machine equivalent model is constructed accordingly. Simulation studies under impedance disturbances validate the effectiveness of the proposed equivalent model in accurately reproducing the oscillation characteristics of a microgrid with multiple DDWTs.
Qi et al. (Sat,) studied this question.