Abstract
The stability analysis and controller design problems for the fractional-order (FO) direct-drive permanent magnet synchronous generator (FOD-PMSG) wind turbine with parameter uncertainties and external disturbance are addressed. Takagi–Sugeno (T-S) model is used to approximate nonlinearities, and the parallel distributed compensation (PDC) technique is employed to construct the fuzzy state feedback controller. In order to suppress the external disturbance more effectively, the global Mittag-Leffler stability definition satisfying the H∞ performance index is proposed for the first time. Using the FO Lyapunov direct method, applying the Cauchy matrix inequality (CMI), and combining with the Schur complement lemma, the sufficient conditions of Mittag-Leffler stability meeting the H∞ performance index are given in the form of linear matrix inequalities (LMIs). Simulation results clearly show that the proposed control scheme can make the system get rid of the chaotic state quickly and have strong robustness under parameter uncertainties and external disturbance varying randomly.
Highlights
D-PMSG is of great interest for large offshore wind farms with rich wind energy resources, less land occupation, and low water consumption due to the outstanding advantages of small mechanical loss, low maintenance cost, high reliability, strong grid connection adaptability, and simple structure [1, 2]
Wind turbine systems (WTSs) have the characteristics of randomness of wind energy, strong coupling nonlinear complex characteristics, and bad working environment, which lead to the inevitable changes of system parameters and external disturbances in the process of the system operation and make WTSs show chaotic phenomenon under certain working conditions. is will seriously affect the stable operation of WTSs, have a greater impact on the grid, and make power quality worse. e nonlinear dynamic behaviour, chaos generation mechanism, and chaotic control of the D-PMSG have recently received wide attention and become an active research area
It is found for the first time that permanent magnet synchronous motor (PMSM)-based wind energy conversion systems (WECs) have chaotic operation state [5]
Summary
D-PMSG is of great interest for large offshore wind farms with rich wind energy resources, less land occupation, and low water consumption due to the outstanding advantages of small mechanical loss, low maintenance cost, high reliability, strong grid connection adaptability, and simple structure [1, 2]. Numerous research results have been obtained in the analysis and control of chaos characteristics of the permanent magnet synchronous motor (PMSM) [3, 4] It is found for the first time that PMSM-based wind energy conversion systems (WECs) have chaotic operation state [5]. In order to expand the system stability region and improve the stable performance of the WTSs, as an improvement, the present research aims to design the suitable controller scheme for the D-PMSG model with parameter uncertainties and external interference in the fractional domain instead of traditional controller schemes. Motivated by the aforementioned progress, we design a fuzzy state feedback H∞ robust controller that is determined through a quadratic Lyapunov function and solving a set of LMIs. In this paper, the main objective of this study is to address the chaos control problem of FOD-PMSG-based WTSs with uncertain parameters and external disturbances.
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