Detection of the stability boundary associated to subsynchronous oscillations in DFIG based wind farms

In this paper, the detection and continuation of the Hopf bifurcation defining the stability boundary associated to subsynchronous oscillations (SSO) in DFIG-based wind farms is considered. In order to overcome the main limitation of standard numerical continuation packages for studying SSO in large scale power systems, a simplified test function, based only on the subsynchronous and supersynchronous modes, is proposed. These modes are computed with an adapted version of the Selective Modal Analysis (SMA) iterative method, which avoids the computation of all the eigenvalues of the system. The iterative procedure used for the detection of the Hopf bifurcation and the standard prediction-correction routines used for its continuation are tailored to accommodate both the proposed test function and the SMA based computation of the required eigenvalues. The methodology is illustrated on a relatively large scale system with 11 WF represented by 22 aggregated models and involving 690 state variables.