Hopf Bifurcation and Eigenvalue Sensitivity Analysis of Doubly Fed Induction Generator Wind Turbine System

This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. The oscillatory instability of the DFIG has been observed by simulation study. The detailed mathematical model of the DFIG closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian's eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. The eigenvalue sensitivitiy analysis with respect to machine and control parameters are performed to assess the impact of parameters upon system stability. Moreover, the Hopf bifurcation boundaries of the key parameters are also given that can facilitate the tuning of those parameters to ensure stable operation.