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

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.

[1]  I. Kovacic,et al.  Potential benefits of a non-linear stiffness in an energy harvesting device , 2010 .

[2]  Giuseppe Grassi,et al.  Observer-based projective synchronization of fractional systems via a scalar signal: application to hyperchaotic Rössler systems , 2012 .

[3]  V. Joshi,et al.  Design of fractional-order PI controllers and comparative analysis of these controllers with linearized, nonlinear integer-order and nonlinear fractional-order representations of PMSM , 2016, International Journal of Dynamics and Control.

[4]  Dirk Söffker,et al.  Data-driven stabilization of unknown nonlinear dynamical systems using a cognition-based framework , 2016, Nonlinear Dynamics.

[5]  Junmi Li,et al.  Stability analysis of fractional order systems based on T–S fuzzy model with the fractional order $$\alpha : 0<\alpha <1$$α:0 , 2014 .

[6]  J. A. Tenreiro Machado,et al.  Describing Function Analysis of Systems with Impacts and Backlash , 2002 .

[7]  Eduard Muljadi,et al.  Releasable Kinetic Energy-Based Inertial Control of a DFIG Wind Power Plant , 2016, IEEE Transactions on Sustainable Energy.

[8]  Luis E. Suarez,et al.  A Comparison of Numerical Methods Applied to a Fractional Model of Damping Materials , 1999 .

[9]  Runfan Zhang,et al.  Control of a class of fractional-order chaotic systems via sliding mode , 2012 .

[10]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[11]  Roberto Cárdenas,et al.  Overview of control systems for the operation of DFIGs in wind energy applications , 2013, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society.

[12]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[13]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[14]  A. M. Abou-Rayan,et al.  Nonlinear response of a parametrically excited buckled beam , 1993 .

[15]  Ding Lei,et al.  Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control , 2017, J. Optim. Theory Appl..

[16]  Malek Ghanes,et al.  Backstepping control of a wind turbine for low wind speeds , 2016 .

[17]  Samir A. Emam,et al.  Subharmonic parametric resonance of simply supported buckled beams , 2015 .

[18]  Lin Li,et al.  Fractional generalized Hamiltonian mechanics and Poisson conservation law in terms of combined Riesz derivatives , 2013 .

[19]  Xiao-Shu Luo,et al.  Fractional-order permanent magnet synchronous motor and its adaptive chaotic control , 2012 .

[20]  Harry G. Kwatny,et al.  Bifurcation of equilibria and chaos in permanent-magnet machines , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[21]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[22]  Alessandro Spadoni,et al.  Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications , 2015 .

[23]  Yang Guo-Liang,et al.  Sliding mode variable-structure control of chaos in direct-driven permanent magnet synchronous generators for wind turbines , 2009 .

[25]  YangQuan Chen,et al.  Fractional-order modeling of permanent magnet synchronous motor speed servo system , 2016 .

[26]  R. Bagley,et al.  Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .

[27]  S. Iniyan,et al.  A review of wind energy technologies , 2007 .

[28]  Nuno M. M. Maia,et al.  On a General Model for Damping , 1998 .

[29]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[30]  Bin Wang,et al.  Robust finite-time control of fractional-order nonlinear systems via frequency distributed model , 2016 .

[31]  贾立新,et al.  Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems , 2010 .

[32]  R. Moritz.  Population dynamics of the Cape bee phenomenon: The impact of parasitic laying worker clones in apiaries and natural populations , 2002 .

[33]  B. Huberman,et al.  Dynamics of adaptive systems , 1990 .

[34]  A. E. Matouk,et al.  Dynamical analysis, stabilization and discretization of a chaotic fractional-order GLV model , 2016 .

[35]  Guanrong Chen,et al.  Complex dynamics in a permanent-magnet synchronous motor model , 2004 .

[36]  G. R. Slemon,et al.  Electrical machines for variable-frequency drives , 1994, Proc. IEEE.

[37]  Sheng Li,et al.  Bifurcation and chaos analysis of multistage planetary gear train , 2014 .

[38]  Anita Alaria,et al.  Applications of Fractional Calculus , 2018 .

[39]  Abdelkrim Boukabou,et al.  Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems , 2016 .

[40]  P. Balasubramaniam,et al.  Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system , 2015 .

[41]  E. Lüscher,et al.  Resonant stimulation and control of nonlinear oscillators , 1989, Naturwissenschaften.

[42]  Guanrong Chen,et al.  Bifurcations and chaos in a permanent-magnet synchronous motor , 2002 .

[43]  Li Zhang,et al.  Control of finite-time anti-synchronization for variable-order fractional chaotic systems with unknown parameters , 2016 .

[44]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[45]  D. Baleanu,et al.  LMI-based stabilization of a class of fractional-order chaotic systems , 2013 .

[46]  Joao P. S. Catalao,et al.  Fractional-order control and simulation of wind energy systems with PMSG/full-power converter topology , 2010 .