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Modeling, nonlinear dynamic analysis and control of fractional PMSG of wind turbine

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Abstract

This study aims to reveal the laws of the relationship between fractional-order system and integer-order system. Meanwhile, delayed feedback control is introduced to control the fractional-order PMSG (permanent magnet synchronous generator) model of a wind turbine. First, the fractional-order mathematical model of PMSG is established. Next, numerical simulations under different system orders are given and the system dynamic behaviors are analyzed in detail. Then, the delayed feedback control method is introduced to control the fractional-order PMSG and the control results when different parameters vary are analyzed. Complex dynamics are presented and some interesting phenomena are discovered. It is found that the system order influences the dynamics of the system in many aspects such as chaos pattern, bifurcation behavior, period window, shape and size of strange attractor. The delayed time, feedback gain, feedback limitation, system order can obviously influence the control result except the initial state of the system. Moreover, the feedback limitation has a minimum to successfully control the system to stable states and the system order also has a maximum to do so.

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Acknowledgements

Project supported by China Postdoctoral Science Foundation (Grant No: 2013M530426).

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Authors and Affiliations

  1. State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi Province, China

    Gangquan Si, Jianwei Zhu, Lijie Diao & Zhiqiang Ding

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  1. Gangquan Si
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Correspondence to Gangquan Si.

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Si, G., Zhu, J., Diao, L. et al. Modeling, nonlinear dynamic analysis and control of fractional PMSG of wind turbine. Nonlinear Dyn 88, 985–1000 (2017). https://doi.org/10.1007/s11071-016-3289-9

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