Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous generator-based wind energy conversion system

Abstract

In this paper, the method for the nonlinear control design of a permanent magnet synchronous generator based-wind energy conversion system (WECS) is proposed in order to obtain robustness against disturbances and harvest a maximum power from a typical stochastic wind environment. The technique overcomes both the problem of nonlinearity and the uncertainty of the parameter compared to such classical control designs based on traditional control techniques. The method is based on the differential geometric feedback linearization technique (DGT) and the Lyapunov theory. The results obtained show the effectiveness and performance of the proposed approach.

Keywords

permanent magnet synchronous generator / wind energy conversion system / stochastic / differential geometric / feedback linearization / maximum power point tracking / Lyapunov / robust control

References

[1] Harrabi N, Souissi M, Aitouche A, Chabaane M. Intelligent control of wind conversion system based on PMSG using T-S Fuzzy Scheme. International Journal of Renewable Energy Research, 2015, 5(4): 52–60

[2] Emna M E, Adel K, Mimouni M F. The wind energy conversion system using PMSG controlled by vector control and SMC strategies. International Journal of Renewable Energy Research, 2013, 3(1): 41–50

[3] Munteanu I, Bratcu A I, Cutululis N A, Ceang Ă E. Optimal Control of Wind Energy Systems: Toward a Global Approach. London: Springer, 2008

[4] Yadaiah N, Ramana N V. Linearization of multi-machine power system: modeling and control—a survey. International Journal of Electrical Power and Energy Systems, 2007, 29(4): 297–311

[5] Ghasemi S, Tabesh A, Askari-Marnani J. Application of fractional calculus theory to robust controller design for wind turbine generators. IEEE Transactions on Energy Conversion, 2014, 29(3): 780–787

[6] Tabesh A, Iravani R. On the application of the complex torque coefficients method to the analysis of torsional dynamics. IEEE Transactions on Energy Conversion, 2005, 20(2): 268–275

[7] Tabesh A, Iravani R. Frequency response analysis of torsional dynamics. IEEE Transactions on Power Systems, 2004, 19(3): 1430–1437

[8] Farmad M, Farhangi S, Gharehpetian G B, Afsharnia S. Nonlinear controller design for IPC using feedback linearization method. International Journal of Electrical Power & Energy Systems, 2013, 44(1): 778–785

[9] Boukhezzar B, Siguerdidjane H. Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization. Energy Conversion and Management, 2009, 50(4): 885–892

[10] Shi Z, Li X, Hu S. Direct feedback linearization based control in variable air volume air-conditioning system. Procedia Physics, 2012, 24(Part B): 1248–1254

[11] Bodson M, Chiasson J. Differential-geometric methods for control of electric motors. International Journal of Robust and Nonlinear Control, 1998, 8(11): 923–954

[12] Tailor M R, Bhathawala P H. Linearization of nonlinear differential equation by Taylor’s series expansion and use of Jacobian linearization process. International Journal of Theoretical and Applied Science, 2011, 4(1): 36–38

[13] Jouybari-Moghaddam H, Hosseinian S H, Vahidi B. Grid reconnection detection for synchronous distributed generators in stand-alone operation. International Transactions on Electrical Energy Systems, 2015, 25(1): 138–154

[14] Akhrif O, Okou F A, Dessaint L A, Champagne R. Application of a multivariable feedback linearization scheme for rotor angle stability and voltage regulation of power systems. IEEE Transactions on Power Systems, 1999, 14(2): 620–628

[15] Lu Q, Sun Y Z. Nonlinear stabilizing control of multi machine systems. IEEE Transactions on Power Systems, 1988, 4(1): 36–38

[16] Hunt L R. Su R, Meyer G. Design for multi-input nonlinear systems in differential geometric control theory. Progress in Mathematics, 1982, 27:268–298

[17] Isodori A. Nonlinear Control Systems. 3rd ed. Berlin: Springer-Verlag, 1995

[18] Beschi M, Berenguel M, Visioli A, Guzmán J L, Yebra L J. Implementation of feedback linearization GPC control for a solar furnace. Journal of Process Control, 2013, 23(10): 1545–1554

[19] Yuan X, Chen Z, Yuan Y, Huang Y, Li X, Li W. Sliding mode controller of hydraulic generator regulating system based on the input/output feedback linearization method. Mathematics and Computers in Simulation, 2016, 119(C): 18–34

[20] Mahboub M A, Drid S, Sid M A, Cheikh R. Robust direct power control based on the Lyapunov theory of a grid-connected brushless doubly fed induction generator. Frontiers in Energy, 2016, 10(3): 298–307

[21] Zarchi H A, Arab Markadeh Gh R, Soltani J. Direct torque and flux regulation of synchronous reluctance motor drives based on input–output feedback linearization. Energy Conversion and Management, 2010, 14(1): 71–80

[22] Bouzidi M, Benaissa A, Barkat S. Hybrid direct power/current control using feedback linearization of three-level four-leg voltage source shunt active power filter. International Journal of Electrical Power and Energy Systems, 2014, 61: 629–646

[23] Mehrasa M, Pouresmaeil E, Akorede M F, Jorgensen B N, Catalão J P S. Multilevel converter control approach of active power filter for harmonics elimination in electric grids. Energy, 2015, 84: 722–731

[24] Alizadeh M, Kojori S S. Augmenting effectiveness of control loops of a PMSG (permanent magnet synchronous generator) based wind energy conversion system by a virtually adaptive PI (proportional integral) controller. Energy, 2015, 91: 610–629

[25] Drid S, Tadjine M, Nait-Said M S. Robust backstepping vector control for the doubly fed induction motor. IET Control Theory & Applications, 2007, 1(4): 861–868

[26] Mehrasa M, Pouresmaeil E, Zabihi S, Rodrigues E M G, Catalão J P S. A control strategy for the stable operation of shunt active power filters in power grids. Energy, 2016, 96: 325–334

[27] Phan D C, Yamamoto S. Rotor speed control of doubly fed induction generator wind turbines using adaptive maximum power point tracking. Energy, 2016, 111: 377–388

[28] Cheikh R, Menacer A, Drid S. Robust control based on the Lyapunov theory of a grid-connected doubly fed induction generator. Frontiers in Energy, 2013, 7(2): 191–196

[29] Bianchi F D. Wind Turbine Control Systems: Principles, Modeling and Gain Scheduling Design. London: Springer-Verlag, 2007

[30] Nguyen H M, Naidu D S. Direct fuzzy adaptive control for standalone wind energy conversion systems. In: Proceedings of the World Congress on Engineering and Computer Science, 2012, San Francisco, USA

[31] Nichita C. Study and development of structures and digital control laws for the realization of 3 kW wind turbine simulator. Dissertation for the Doctoral Degree. France: Université du Havre, 1995 (in French)

[32] Welfonder E, Neifer R, Spanner M. Development and experimental identification of dynamic models for wind turbines. Control Engineering Practice, 1997, 5(1): 63–73

[33] Chapman J W, IIic M D, King C A, Eng L, Kaufman H. Stabilizing a multi machine power system via decentralized feedback linearizing excitation control. IEEE Transactions on Power Systems, 1993, 8(3): 830–839

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature