A Shifted Frequency Impedance Model of Doubly Fed Induction Generator (DFIG)-Based Wind Farms and Its Applications on S$^2$SI Analysis

The emerging sub-/super-synchronous interactions (S2SI) related stability issues caused by the interactions of doubly fed induction generator (DFIG)-based wind farms and the large-scale ac grids have aroused great concerns. For this particular issue, this article is aimed to fill the gap and propose new time-domain and phasor-domain sub-/super-synchronous impedance models (S2SIM), primarily to disclaim the electro-magnetic stability of the S2SI phenomena. First, the unified dq frame impedance model of the DFIGs have been proposed, including the individual and interactive impact of every control sections, such as the induction machine, the grid-side converter, the rotor-side converter, and the outer dc voltage controller, etc. Then, the more general time-domain S2SIM and phasor-domain shifted frequency S2SIM (SF-S2SIM) have been derived to reveal the electro-magnetic stability mechanism, especially aroused by S2SI. Next, the relationships between S2SIM/SF-S2SIM and the dq/sequence impedance models have been developed based on matrix transformation and the frequency shifting techniques. Finally, the electro-magnetic stability of the practical DFIG-based wind farms, associated with large-scale ac grids in China, have been well evaluated by the proposed S2SIM/SF-S2SIM based electro-magnetic stability method.