Kybernetika 59 no. 5, 655-669, 2023

Modeling of permanent magnet linear generator and state estimation based on sliding mode observer: A wave energy system application

Amal Nasri, Iskander Boulaabi, Mansour Hajji, Anis Sellami and Fayçal Ben HmidaDOI: 10.14736/kyb-2023-5-0655

Abstract:

This paper synopsis a new solution for Permanent Magnets Linear Generator (PMLG) state estimation subject to bounded uncertainty. Therefore, a PMLG modeling method is presented based on an equivalent circuit, wherein a mathematical model of the generator adapted to wave energy conversion is established. Then, using the Linear Matrix Inequality (LMI) optimization and a Lyapunov function, this system's Sliding Mode Observer (SMO) design method is developed. Consequently, the proposed observer can give a robust state estimation. At last, numerical examples with and without uncertainty are included to exemplify the effectiveness and applicability of the suggested approaches.

Keywords:

linear matrix inequality (LMI), modeling, state estimation, wave energy, permanent magnet linear generator (PMLG), sliding mode observer (SMO)

Classification:

93B07, 49M30

paper.pdf

References:

  1. T. Ackermann: Wind Power in Power Systems. John Wiley and Sons, 2012.   CrossRef
  2. J. Brooke: Wave Energy Conversion. Elsevier, 2003.   CrossRef
  3. D. Calabrese, G. Tricarico, E. Brescia, G. L. Cascella, V. G. Monopoli and F. Cupertino: Variable structure control of a small ducted wind turbine in the whole wind speed range using a Luenberger observer. MDPI, Energies 13 (2020), 4647.   DOI:10.3390/en13184647
  4. W. Chen and M. Saif: Unknown input observer design for a class of nonlinear systems: an LMI approach. Amer. Control Confer. (2006), 5.   DOI:10.1109/ACC.2006.1655461
  5. A. Clément, P. McCullen, A. Falcão, A. Fiorentino, F. Gardner, K. Hammarlund, G. Lemonis, T. Lewis, K. Nielsen, S. Petroncini and others: Wave energy in Europe: current status and perspectives. Renewable Sustainable Energy Rev. 6 (2002), 405-431.   DOI:10.1016/S1364-0321(02)00009-6
  6. A. F. de Falcao: Wave energy utilization: A review of the technologies. Elsevier 14 (2010), 899-918.   DOI:10.1016/j.rser.2009.11.003
  7. O. Farrok, Md R. Islam, Md R. I. Sheikh, Y. Guo, J. Zhu, Jianguo and G. Lei: Oceanic wave energy conversion by a novel permanent magnet linear generator capable of preventing demagnetization. IEEE Trans. Industry Appl. 54 (2018), 6005-6014.   DOI:10.1109/tia.2018.2863661
  8. S. Foteinis: Wave energy converters in low energy seas: Current state and opportunities. Elsevier 162 (2022), 112448.   DOI:10.1016/j.rser.2022.112448
  9. P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali: LMI Control Toolbox, the MathWorks Inc, Natick. MA 1995.   CrossRef
  10. Z. Gao and X. Liu: An overview on fault diagnosis, prognosis and resilient control for wind turbine systems. MDPI J., Processes 9 (2021), 300.   DOI:10.3390/pr9020300
  11. N. S. Jayalakshmi, D. N. Gaonkar and K. S. K. Kumar: Dynamic modeling and performance analysis of grid connected PMSG based variable speed wind turbines with simple power conditioning system. IEEE Int. Confer. Power Electron. Drives Energy Systems (PEDES) (2012), 1-5.   DOI:10.1109/PEDES.2012.6484474
  12. D. Luenberger: An introduction to observers. IEEE Trans. Automat. Control 16 (1971), 596-602.   DOI:10.1109/TAC.1971.1099826
  13. E. Mouni, S. Tnani and G. Champenois: Synchronous generator modelling and parameters estimation using least squares method. Simul- Modell. Practice Theory 16 (2008), 678-689.   DOI:10.1016/j.simpat.2008.04.005
  14. P. F. Odgaard and J. Stoustrup: Unknown input observer based detection of sensor faults in a wind turbine. IEEE Int. Confer. Control Appl. (2010), 310-315.   DOI:10.1109/CCA.2010.5611266
  15. H. Polinder, M. A. Mueller, M. Scuotto and M. G. de Sousa Prado: Linear generator systems for wave energy conversion. In: Proc. 7th European Wave and Tidal Energy Conference, Porto 2007, pp. 11-14.   CrossRef
  16. D. Remon, A. M. Cantarellas and P. Rodriguez: Equivalent model of large-scale synchronous photovoltaic power plants. IEEE Trans. Industry Appl. 52 (2016), 5029-5040.   DOI:10.1109/tia.2016.2598718
  17. O. Sename: New trends in design of observers for time-delay systems. Kybernetika 37 (2001), 427-458.   CrossRef
  18. M. G. Simões and F. A. Farret: Modeling and Analysis with Induction Generators. CRC Press 2014.   CrossRef
  19. B. Tagliafierro, I. Martínez-Estévez, J. Domínguez, A. J. C. Crespo, M. Göteman, J. Engström and M. Gómez-Gesteira: A numerical study of a taut-moored point-absorber wave energy converter with a linear power take-off system under extreme wave conditions. Appl. Energy, Elsevier 311 (2022), 118629.   DOI:10.1016/j.apenergy.2022.118629
  20. M. Trapanese, V. Boscaino, G. Cipriani, D. Curto, V. Di Dio and V. Franzitta: A permanent magnet linear generator for the enhancement of the reliability of a wave energy conversion system. IEEE Trans. Industrial Electron. 66 (2018), 4934-4944.   DOI:10.1109/TIE.2018.2838076
  21. Z. Wang, Y. Shen, X. Zhang and Q. Wang: Observer design for discrete-time descriptor systems: An LMI approach. Systems Control Lett. 61 (2012), 683-687.   DOI:10.1016/j.sysconle.2012.03.006
  22. J. Wang, F. Wang, X. Wang and L. Yu: Disturbance observer based integral terminal sliding mode control for permanent magnet synchronous motor system. Kybernetika 55 (2019), 586-603.   DOI:10.14736/kyb-2019-3-0586
  23. J. Wang, F. Wang, X. Wang and L. Yu: Disturbance observer based integral terminal sliding mode control for permanent magnet synchronous motor system. Kybernetika 55 (2019), 586-603.   DOI:10.14736/kyb-2019-3-0586
  24. Y. Zhang and G. Li: Non-causal linear optimal control of wave energy converters with enhanced robustness by sliding mode control. IEEE Trans. Sustainable Energy 11 (2019), 2201-2209.   DOI:10.1109/TSTE.2019.2952200
  25. Y. Zhang, G. Li and T. Zeng: Wave excitation force estimation for wave energy converters using adaptive sliding mode observer. IEEE Amer. Control Confer. (ACC) (2019), 4803-4808.   DOI:10.23919/acc.2019.8815196
  26. Y. Zhang, P. Stansby and G. Li: Non-causal linear optimal control with adaptive sliding mode observer for multi-body wave energy converters. IEEE Trans. Sustainable Energy 12 (2020), 568-577.   DOI:10.1109/TSTE.2020.3012412