Supercritical Pitchfork Bifurcation of a Fractional‐Order Doubly‐Fed Induction Generator

To address the problem of the chaos phenomenon caused by the parameter drift of a doubly‐fed induction generator (DFIG) due to a changing operating environment, a fractional‐order stator voltage/flux‐oriented control model is developed, and bifurcation theory and numerical simulations reveal that the chaos mechanism originates from supercritical pitchfork bifurcation. First, the fractional‐order DFIG model is constructed by introducing Caputo fractional‐order derivatives and combining linear affine transformation and time‐scale transformation. Second, we analyze the bifurcation characteristics of the system's equilibrium point under diverse axial rotor voltages. Third, we apply the central manifold theorem to reduce the system dimensions to derive an equivalent downscaling model and describe the bifurcation behavior near the equilibrium point. Finally, the dynamics of the DFIG system at different fractional orders are explored by employing different numerical simulation methods for the changes in the rotor d ‐axis voltage component and the wind turbine output torque. The analytical results indicate that the DFIG system plunges into chaos via supercritical pitchfork bifurcation. As the fractional order diminishes, the system transitions from chaotic conditions to stable conditions. Transient chaos can occur in the DFIG system under particular combinations of fractional orders and parameters.