Multi-parameter bifurcation analysis of subsynchronous interactions in DFIG-based wind farms

•A multi-parameter bifurcation analysis of SSI in DFIG-wind farms is performed.•The effect of compensation level, wind speed, rated power and control gain is studied.•The stability region in the full parameter space is determined.•The Hopf bifurcation acts as a precursor for sustained subsynchronous oscillations.•The dynamics is organized around smooth and non-smooth bifurcations of limit cycles.

This work analyzes the dynamics involved in subsynchronous interactions between wind farms and series-compensated transmission lines. This adverse phenomenon may arise when doubly-fed induction generators are radially connected to an ac transmission line with series capacitive compensation. The resulting subsynchronous oscillations can produce the system instability and cause a severe damage to the wind turbines. The study is carried out combining tools from bifurcation theory, eigenvalue analysis and nonlinear time-domain simulations. The impact on the subsynchronous mode due to the variation of a set of key parameters is considered. These parameters include the series compensation of the transmission line, the wind speed (generated power), the wind energy penetration level, and a gain of the internal control loop of the wind turbine. The bifurcation study determines that the underlying mechanism associated with the appearance of subsynchronous oscillations can be explained by means of Hopf bifurcations of the equilibrium point and their corresponding limit cycles. In addition, the saturation of the wind turbine converters plays an important role in the dynamics, introducing non-smooth bifurcations that are also analyzed.