The stochastic stability and H∞‐fuzzy control of stochastic bifurcation of a doubly‐fed induction generator

• Published in: Energy science & engineering Vol. 12; no. 3; pp. 617 - 636
• Main Authors: Chen, Wei, Li, Qiangqiang, Wei, Zhanhong, Wang, Kun
• Format: Journal Article
• Language: English
• Published: London John Wiley & Sons, Inc 01-03-2024; Wiley
• Subjects: Background noise; Bifurcations; Closed loop systems; Controllers; Density; DFIG; Dynamic stability; Eigenvalues; Equilibrium; Feedback control; Fuzzy control; Fuzzy sets; H-infinity control; H∞‐fuzzy control; Induction generators; Influence; Mathematical models; Methods; Monte Carlo simulation; Noise intensity; Ordinary differential equations; Output feedback; Probability theory; Stability analysis; stochastic bifurcation; Stochastic models; stochastic stability; T‐S fuzzy reconstruction; White noise; Wind farms; Wind power
• ISSN: 2050-0505; 2050-0505
• DOI: 10.1002/ese3.1634

Considering the dynamic behavior of doubly‐fed induction generators (DFIGs) under the influence of random factors, this paper not only analyzes the phenomenon of stochastic instability and bifurcation of a DFIG dynamic variable in its random space when they are affected by environmental noise, but also proposes a method based on the Tkagi–Sugneo (T–S) fuzzy control strategy to control its stochastic bifurcation. First, a four‐dimensional stochastic dynamic DFIG model is established by using multiplicative white noise to simulate the influence of environmental noise on electrical variables, and stochastic central manifold theory is used to reduce the dimensionality of a planar model in the bifurcation neighborhood. Then, the stochastic stability of the model is investigated based on singular boundary theory, while the steady‐state probability density of the stochastic DFIG is determined using the Fokker–Plank–Kolmogorov equation to obtain the location and probability density of its stochastic P‐bifurcation. Finally, the influence of stochastic bifurcation behavior is eliminated by H∞‐fuzzy output feedback control. The numerical simulation results indicate that the location and probability of stochastic bifurcation in a DFIG will vary with the change in noise intensity, and the bifurcation parameter values and stochastic stability domain are obtained. The harm caused by random factors can be solved based on H∞‐fuzzy output feedback, which provides a theoretical basis for the stable operation of the DFIG system.
The position and probability density of occurrence of its stochastic Hopf bifurcation is shown, demonstrating that noise intensity can generate a stochastic bifurcation in the doubly‐fed induction generator to destabilize it.