Hopf bifurcation analytical expression and control strategy in direct‐drive permanent magnet synchronous generator

• Published in: International journal of circuit theory and applications Vol. 52; no. 9; pp. 4513 - 4534
• Main Authors: Li, Qiangqiang, Chen, Wei, Wei, Zhanhong, Wang, Kun, Wang, Bo
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01-09-2024
• Subjects: center manifold theorem; Control stability; Control systems; Dimensional analysis; DPMSG; Dynamic models; Dynamical systems; Feedback control; H-infinity control; harmonic balance approximation; Hopf bifurcation; H∞ output control; Impact analysis; Nonlinear dynamics; Output feedback; Parameters; Permanent magnets; Robust control; Signal generation; Stability analysis; Stability criteria; Synchronous machines; Time domain analysis; Wind power
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.3928

Summary
The unstable operation of a direct‐drive permanent magnet synchronous generator (DPMSG) is exacerbated by periodic oscillation, having a significant impact on the safe and stable functioning of wind energy generation systems. This paper proposes an approximate solution method for analyzing the periodic oscillation of the Hopf bifurcation and a method for suppressing its bifurcation through H∞ robust control. Firstly, a three‐dimensional nonlinear dynamic model of the DPMSG is constructed. Secondly, the Hopf bifurcation of the system with changes in internal parameters is solved using the time domain and frequency domain methods, and the harmonic balancing method is used to approximate the periodic solution at the point of Hopf bifurcation. The order of the Hopf bifurcation neighborhood is then decreased using the central manifold theorem. Finally, this study suggests a H∞ output feedback control employing bifurcation parameters. The Nyquist criteria are used for evaluating small signal stability and convergence speed of the response system in DPMSG before and after dimensionality reduction. The simulation results suggest that the proposed strategy helps to tackle the periodic solution expression and instability difficulties caused by Hopf bifurcation. This paper provides theoretical suggestions for the future reliable operation of new energy generation systems.
The paper solves and suppresses the theoretical formulation of periodic oscillation generated by Hopf bifurcation. The harmonic balancing approximation method is used to solve the theoretical expression of the periodic solution; simultaneously, a H∞ control strategy to suppress the periodic oscillation generated by Hopf bifurcation is proposed.