Analysis on chaotic mechanism of direct-drive permanent magnet synchronous generators based on Lyapunov stability theory

The direct-drive permanent magnet synchronous generator (D-PMSG) is a highly nonlinear dynamic system. This paper aims to explore the complex chaotic motions or prominent chaotic features (e.g. the limit cycle) of the D-PMSG under certain parameter conditions and external inputs. Specifically, the mathematical model of the PMSG in d-q reference frame was converted into a dimensionless Loren chaotic equation through affine transform and timescale transform. Then, the Lyapunov stability theory was introduced to explore the eigenvalues of the Jacobian matrix corresponding to each equilibrium point under different inputs. On this basis, the author discussed how the D-PMSG shifts from equilibrium state to chaotic motions, and derived the conditions for the generation of the limit cycle. Finally, the chaotic features of the system were simulated with the aid of three-phase diagram, bifurcation map and the Lyapunov exponent (LE) spectrum. The simulation results show that the chaotic attractor will appear in the system, when system parameters change or the wind speed varies, posing a serious threat to the stable operation of the D-PMSG. © 2019 The Japan Society of Vacuum and Surface Science. All rights reserved.