1. Department of Electrical Engineering LGEB Laboratory, Biskra University, Biskra 07000, Algeria; Laboratory of Innovative Technology (LTI), University of Picardie Jules Verne, IUT de l'Aisne 02880 Cuffies, France; Unité de Développement des Equipements Solaires, UDES, Centre de Développement des Energies Renouvelables, CDER 42415 Tipaza, Algeria 2. Department of Electrical Engineering LGEB Laboratory, Biskra University, Biskra 07000, Algeria 3. Laboratory of Innovative Technology (LTI), University of Picardie Jules Verne, IUT de l'Aisne, 02880 Cuffies, France 4. LSPIE Laboratory, Department of Electrical Engineering, University of Batna2, Rue Chahid Med El-Hadi Boukhlof 05000, Algeria
Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous generator-based wind energy conversion system
Ridha CHEIKH1(), Arezki MENACER2, L. CHRIFI-ALAOUI3, Said DRID4
1. Department of Electrical Engineering LGEB Laboratory, Biskra University, Biskra 07000, Algeria; Laboratory of Innovative Technology (LTI), University of Picardie Jules Verne, IUT de l'Aisne 02880 Cuffies, France; Unité de Développement des Equipements Solaires, UDES, Centre de Développement des Energies Renouvelables, CDER 42415 Tipaza, Algeria 2. Department of Electrical Engineering LGEB Laboratory, Biskra University, Biskra 07000, Algeria 3. Laboratory of Innovative Technology (LTI), University of Picardie Jules Verne, IUT de l'Aisne, 02880 Cuffies, France 4. LSPIE Laboratory, Department of Electrical Engineering, University of Batna2, Rue Chahid Med El-Hadi Boukhlof 05000, Algeria
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.
N Harrabi, M Souissi, A Aitouche, M Chabaane. 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
M E Emna, K Adel, M F Mimouni. 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
I Munteanu, A I Bratcu, N A Cutululis, E Ceang Ă. Optimal Control of Wind Energy Systems: Toward a Global Approach. London: Springer, 2008
4
N Yadaiah, N V Ramana. Linearization of multi-machine power system: modeling and control—a survey. International Journal of Electrical Power and Energy Systems, 2007, 29(4): 297–311 https://doi.org/10.1016/j.ijepes.2006.06.011
5
S Ghasemi, A Tabesh, J Askari-Marnani. Application of fractional calculus theory to robust controller design for wind turbine generators. IEEE Transactions on Energy Conversion, 2014, 29(3): 780–787 https://doi.org/10.1109/TEC.2014.2321792
6
A Tabesh, R Iravani. 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 https://doi.org/10.1109/TEC.2005.847970
7
A Tabesh, R Iravani. Frequency response analysis of torsional dynamics. IEEE Transactions on Power Systems, 2004, 19(3): 1430–1437 https://doi.org/10.1109/TPWRS.2004.831684
8
M Farmad, S Farhangi, G B Gharehpetian, S Afsharnia. Nonlinear controller design for IPC using feedback linearization method. International Journal of Electrical Power & Energy Systems, 2013, 44(1): 778–785 https://doi.org/10.1016/j.ijepes.2012.08.036
9
B Boukhezzar, H Siguerdidjane. 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 https://doi.org/10.1016/j.enconman.2009.01.011
10
Z Shi, X Li, S Hu. Direct feedback linearization based control in variable air volume air-conditioning system. Procedia Physics, 2012, 24(Part B): 1248–1254 https://doi.org/10.1016/j.phpro.2012.02.187
M R Tailor, P H Bhathawala. 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
H Jouybari-Moghaddam, S H Hosseinian, B Vahidi. Grid reconnection detection for synchronous distributed generators in stand-alone operation. International Transactions on Electrical Energy Systems, 2015, 25(1): 138–154 https://doi.org/10.1002/etep.1829
14
O Akhrif, F A Okou, L A Dessaint, R Champagne. 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 https://doi.org/10.1109/59.761889
15
Q Lu, Y Z Sun. Nonlinear stabilizing control of multi machine systems. IEEE Transactions on Power Systems, 1988, 4(1): 36–38 https://doi.org/10.1109/59.32483
16
L R Hunt. R Su, G Meyer. Design for multi-input nonlinear systems in differential geometric control theory. Progress in Mathematics, 1982, 27:268–298
17
A Isodori. Nonlinear Control Systems. 3rd ed. Berlin: Springer-Verlag, 1995
18
M Beschi, M Berenguel, A Visioli, J L Guzmán, L J Yebra. Implementation of feedback linearization GPC control for a solar furnace. Journal of Process Control, 2013, 23(10): 1545–1554 https://doi.org/10.1016/j.jprocont.2013.02.002
19
X Yuan, Z Chen, Y Yuan, Y Huang, X Li, W Li. 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 https://doi.org/10.1016/j.matcom.2015.08.020
20
M A Mahboub, S Drid, M A Sid, R Cheikh. 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 https://doi.org/10.1007/s11708-016-0411-0
21
H A Zarchi, R Arab Markadeh Gh, J Soltani. 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 https://doi.org/org/10.1016/j.enconman.2009.08.031
22
M Bouzidi, A Benaissa, S Barkat. 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 https://doi.org/10.1016/j.ijepes.2014.03.071
23
M Mehrasa, E Pouresmaeil, M F Akorede, B N Jorgensen, J P S Catalão. Multilevel converter control approach of active power filter for harmonics elimination in electric grids. Energy, 2015, 84: 722–731 https://doi.org/10.1016/j.energy.2015.03.038
24
M Alizadeh, S S Kojori. 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 https://doi.org/10.1016/j.energy.2015.08.047
25
S Drid, M Tadjine, M S Nait-Said. Robust backstepping vector control for the doubly fed induction motor. IET Control Theory & Applications, 2007, 1(4): 861–868 https://doi.org/10.1049/iet-cta:20060053
26
M Mehrasa, E Pouresmaeil, S Zabihi, E M G Rodrigues, J P S Catalão. A control strategy for the stable operation of shunt active power filters in power grids. Energy, 2016, 96: 325–334 https://doi.org/10.1016/j.energy.2015.12.075
27
D C Phan, S Yamamoto. Rotor speed control of doubly fed induction generator wind turbines using adaptive maximum power point tracking. Energy, 2016, 111: 377–388 https://doi.org/10.1016/j.energy.2016.05.077
28
R Cheikh, A Menacer, S Drid. Robust control based on the Lyapunov theory of a grid-connected doubly fed induction generator. Frontiers in Energy, 2013, 7(2): 191–196 https://doi.org/10.1007/s11708-013-0245-y
29
F D Bianchi. Wind Turbine Control Systems: Principles, Modeling and Gain Scheduling Design. London: Springer-Verlag, 2007
30
H M Nguyen, D S Naidu. 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
C Nichita. 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
E Welfonder, R Neifer, M Spanner. Development and experimental identification of dynamic models for wind turbines. Control Engineering Practice, 1997, 5(1): 63–73 https://doi.org/10.1016/S0967-0661(96)00208-0
33
J W Chapman, M D IIic, C A King, L Eng, H Kaufman. Stabilizing a multi machine power system via decentralized feedback linearizing excitation control. IEEE Transactions on Power Systems, 1993, 8(3): 830–839 https://doi.org/10.1109/59.260921