Modeling and nonlinear dynamic analysis of fractional permanent magnet synchronous generators

The effect of fractional-order on system dynamic behaviors is studied in this paper. First, a fractional-order mathematical modeling of permanent magnet synchronous generator (PMSG) is established in two-phase synchronous rotating coordinates and the chaos model is obtained by means of time scaling transformation and a linear affine transformation. Then, numerical simulations with different system order are given, which include integer order and fractional-order. Finally, the effect of fractional-order on the bifurcation and the chaos pattern are analyzed in detail. The study provides a valuable reference to the future research on fractional-order systems and the dynamic behaviors of PMSG.