Kybernetika 55 no. 6, 1034-1049, 2019

A novel LMI-based robust model predictive control for DFIG-based wind energy conversion systems

Amir Gholami, Alireza Sahab, Abdolreza Tavakoli and Behnam AlizadehDOI: 10.14736/kyb-2019-6-1034

Abstract:

The optimal and reliable performance of doubly fed induction generator is essential for the efficient and optimal operation of wind energy conversion systems. This paper considers the nonlinear dynamic of a DFIG linked to a power grid and presents a new robust model predictive control technique of active and reactive power by the use of the linear matrix inequality in DFIG-based WECS. The control law is obtained through the LMI-based model predictive control that allows considering both economic and tracking factors by optimization of an objective function, constraints on control signal and states of system and effects of nonlinearities, generator parameter uncertainties and external disturbances. Robust stability in the face of bounded disturbances and generator uncertainty is shown using Lyapunov technique. Numerical simulations show that the proposed control method is able to meet the desired specification in active and reactive power control in the presence of varieties of wind speed and pitch angle.

Keywords:

linear matrix inequality, optimization, robust model predictive control, doubly fed induction generator, active and reactive power

Classification:

93C10, 93D09, 93C40, 93C42, 37N35

paper.pdf

References:

  1. S. Boyd, L. Ghaui, E. Feron and V. Balakrishnan: Linear Matrix Inequalities in Control Theory. SIAM, Philadelphia 1994.   DOI:10.1137/1.9781611970777
  2. P. Campo and M. Morari: Robust model predictive control. In: Proc. American Control Conference, Minneapolis 1987.   CrossRef
  3. S. Chondrogiannis and M. Barnes: Stability of doubly-fed induction generator under stator voltage orientated vector control. IET Renew. Power Gener. 2 (2008), 170-180.   DOI:10.1049/iet-rpg:20070086
  4. M. Depenbrock: Direct self-control (DSC) of inverter-fed induction machine. IEEE Trans. Power Electron. 3 (1988), 420-429.   DOI:10.1109/63.17963
  5. J. Dong, S. Li, S. Wu, T. He, B. Yang, H. Shu and J. Yu: Nonlinear observer-based robust passive control of doubly-fed induction generators for power system stability enhancement via energy reshaping. Energies 10 (2017), 8, 1082.   DOI:10.3390/en10081082
  6. M. Duong, F. Grimaccia, S. Leva, M. Mussetta and E. Ogliari: Pitch angle control using hybrid controller for all operating regions of SCIG wind turbine system. Renew. Energy 70 (2014), 197-203.   DOI:10.1016/j.renene.2014.03.072
  7. M. Fei and B. Pal: Modal analysis of grid-connected doubly fed induction generators. IEEE Trans. Energy Convers 22 (2007), 728-736.   DOI:10.1109/tec.2006.881080
  8. V. Ghaffari, S. Vahid Naghavi, A. A. Safavi and M. Shafiee: An LMI framework to design robust MPC for a class of nonlinear uncertain systems. In: Control Conference (ASCC), Asian 2013.   DOI:10.1109/ascc.2013.6606169
  9. S. Hao, E. Abdi, F. Barati and R. McMahon: Stator-flux-oriented vector control for brushless doubly fed induction generator. IEEE Trans. Ind. Electron. 56 (2009), 4220-4228.   DOI:10.1109/tie.2009.2024660
  10. B. Hopfensperger, D. Atkinson and R. Lakin: Stator-flux-oriented control of a doubly-fed induction machine with and without position encoder. IEE Proc. Electr. Power Appl. 147 (2000), 241-250.   DOI:10.1049/ip-epa:20000442
  11. J. Hu, Y. He, L. Xu and B. Williams: Improved control of DFIG systems during network unbalance using PI-R current regulators. IEEE Trans. Ind. Electron. 56 (2009), 439-451.   DOI:10.1109/tie.2008.2006952
  12. J. Hu, J. Zhu and D. Dorrell: Model-predictive direct power control of doubly-fed induction generators under unbalanced grid voltage conditions in wind energy applications. IET Renew. Power Gener. 8 (2014), 687-695.   DOI:10.1049/iet-rpg.2013.0312
  13. M. Kothare, V. Balakrishnan and M. Morari: Robust constrained model predictive control using linear matrix inequalities. Automatica 32 (1996), 10, 1361-1379.   DOI:10.1016/0005-1098(96)00063-5
  14. M. Liserre, R. Cardenas, M. Molinas and J. Rodriguez: Overview of multi-MW wind turbines and wind parks. IEEE Trans. Ind. Electron. 58 (2011), 4, 1081-1095.   DOI:10.1109/tie.2010.2103910
  15. Y. Lu and Y. Arkun: Quasi-min-max MPC algorithms for LPV systems. Automatica 36 (2000), 4, 527-540.   DOI:10.1016/s0005-1098(99)00176-4
  16. R. Pena, J. Clare and G. Asher: Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proc. Electr. Power Appl. 143 (1996), 231-241.   DOI:10.1049/ip-epa:19960288
  17. N. Poursafar, H. Taghirad and M. Haeri: Model predictive control of nonlinear discrete time systems: a linear matrix inequality approach. IET Proc. Control Theory Appl. 4 (2010), 1922-1932.   DOI:10.1049/iet-cta.2009.0650
  18. W. Qiao: Dynamic modeling and control of doubly fed induction generators driven by wind turbines. In: Proc. IEEE/PES Power Systems Conference and Exposition, Seattle 2009.   DOI:10.1109/psce.2009.4840245
  19. X. Sun, B. Zhang, X. Tang, B. McLellan and M. Höök: Sustainable energy transitions in China: Renewable. Energies 9 (2016), 980.   DOI:10.3390/en9120980
  20. F. Tahir and I. M. Jaimoukha: Robust model predictive control through dynamic state-feedback: An LMI approach. IFAC Proc. Vol. 40 (2011), 1, 3672-3677.   DOI:10.3182/20110828-6-it-1002.03112
  21. I. Takahashi and T. Noguchi: A new quick-response and high-efficiency control strategy of an induction motor. IEEE Trans. Ind. Appl. (1986), 820-827.   DOI:10.1109/tia.1986.4504799
  22. B. Yang, L. Jiang, L. Wang, W. Yao and Q. Wu: Nonlinear maximum power point tracking control and modal analysis of DFIG based wind turbine. Int. J. Electr. Power Energy Syst. 74 (2016), 429-436.   DOI:10.1016/j.ijepes.2015.07.036
  23. B. Yang, X. Zhang, T. Yu, H. Shu and Z. Fang: Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine. Energy Convers. Manag. 133 (2017), 427-443.   DOI:10.1016/j.enconman.2016.10.062
  24. W. Yao, J. Lin, W. Jinyu, W. Qinghua and C. Shijie: Wide-area damping controller for power system inter-area oscillations: A networked predictive control approach. IEEE Trans. Control Syst. Technol. 23 (2015), 27-37.   DOI:10.1109/tcst.2014.2311852
  25. S.-Y. Yu, C. Bohm, H. Chen and F. Allgower: Robust model predictive control with disturbance invariant sets. In: Proc. Amer. Contr. Conf., Baltimore 2010.   DOI:10.1109/acc.2010.5531520
  26. D. Zhi and L. Xu: Direct power control of DFIG with constant switching frequency and improved transient performance. IEEE Trans. Energy Convers. 22 (2007), 110-118.   DOI:10.1109/tec.2006.889549
  27. D. Zhi, L. Xu and B. Williams: Model-based predictive direct power control of doubly fed induction generators. IEEE Trans. Power Electron. 25 (2010), 341-351.   DOI:10.1109/tpel.2009.2028139