Chaos and Coexisting Attractors of Kolmogorov-Type Permanent-Magnet Synchronous Generators

This paper investigates the dynamic behavior of a Kolmogorov-type permanent-magnet synchronous generator for wind power systems. Firstly, the chaotic model of the salient-pole permanent-magnet synchronous generator is derived and subsequently transformed into a Kolmogorov-type system. Secondly, by analyzing the derived Kolmogorov system, the system's stability is established, and the boundary ellipsoid of the chaotic attractor is determined via the Casimir energy function. Thirdly, the analysis focuses on the mechanisms leading to chaos, including period-doubling bifurcation and the onset of double Hopf bifurcation. Finally, the basins of attraction associated with the coexisting static attractors are determined to characterize their long-term dynamical behavior. The analytical results show good agreement with the numerical simulations.