Kybernetika 59 no. 2, 294-313, 2023

A family of Lyapunov-based control schemes for maximum power point tracking in buck converters

Jorge Álvarez, Jorge Ruiz and Miguel BernalDOI: 10.14736/kyb-2023-2-0294

Abstract:

This paper presents a novel family of Lyapunov-based controllers for the maximum power point tracking problem in the buck converter case. The solar power generation system here considered is composed by a stand-alone photovoltaic panel connected to a DC/DC buck converter. Lyapunov function candidates depending on the output are considered to develop conditions which, in some cases, can be expressed as linear matrix inequalities; these conditions guarantee that the output goes asymptotically to zero, thus implying that the MPPT is achieved. Simulation and real-time results are presented, which validate the effectiveness of the proposals.

Keywords:

linear matrix inequalities, solar energy, photovoltaic panel, maximum power point tracking, Lyapunov method, convex model

Classification:

93D30, 47N70, 93C10

References:

  1. A. Y. Abdelaziz and Y. Almoataz: Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems. Springer, 2020.   CrossRef
  2. M. M Algazar, H. A. El-Halim, M. E. El Kotb Salem and et al.: Maximum power point tracking using fuzzy logic control. Int. J. Electr.Power Energy Systems 39 (2012), 1, 21-28.   DOI:10.1097/BPB.0b013e32834ee5f8
  3. Z. Artstein: Stabilization with relaxed controls. Nonlinear Analysis: Theory Methods Appl. 7 (1983), 11, 1163-1173.   DOI:10.1016/0362-546X(83)90049-4
  4. A. B. G. Bahgat, N. H. Helwa, G. E. Ahmad and E. T. El Shenawy: Maximum power point traking controller for pv systems using neural networks. Renewable Energy 30 (2008), 8, 1257-1268.   DOI:10.3724/SP.J.1005.2008.01257
  5. J. Benedek, T.-T. Sebestyén and B. Bartók: Evaluation of renewable energy sources in peripheral areas and renewable energy-based rural development. Renewable Sustainable Energy Rev. 90 (2018), 516-535.   DOI:10.1016/j.rser.2018.03.020
  6. M. Bernal, P. Hušek and V. Kučera: Non quadratic stabilization of continuous-time systems in the Takagi-Sugeno form. Kybernetika 42 (2006), 6, 665-672.   DOI10.1007/s11003-006-0131-4
  7. M. Bernal, A. Sala, Z. Lendek and T. M. Guerra: Analysis and Synthesis of Nonlinear Control Systems: A Convex Optimisation Approach. Springer, Cham 2022.   CrossRef
  8. K. R. Bharath and E. Suresh: Design and implementation of improved fractional open circuit voltage based maximum power point tracking algorithm for photovoltaic applications. Int. J. Renewable Energy Ress. (IJRER) 7 (2017), 3, 1108-1113.   CrossRef
  9. S. {Boyd}, L. {El Ghaoui}, E. {Féron} and V. {Balakrishnan}: Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics 15, Philadelphia 1994.   CrossRef
  10. Ch. S. Chiu: Ts fuzzy maximum power point tracking control of solar power generation systems. IEEE Trans. Energy Convers. 25 (2010). 4, 1123-1132.   DOI:10.1109/TEC.2010.2041551
  11. Ch. S. Chiu and Y. L. Ouyang: Robust maximum power tracking control of uncertain photovoltaic systems: A unified ts fuzzy model-based approach. IEEE Trans. Control Systems Technol. 19 (2011), 6, 1516-1526.   DOI:10.1109/tcst.2010.2093900
  12. Z. M, Dalala, Z. U. Zahid, W. Yu, Y. Cho and J.-S. Lai: Design and analysis of an mppt technique for small-scale wind energy conversion systems. IEEE Trans. Energy Convers. 28 (2013), 3, 756-767.   DOI:10.1109/TEC.2013.2259627
  13. M. A. Elgendy, B. Zahawi and D. J. Atkinson: Assessment of the incremental conductance maximum power point tracking algorithm. IEEE Trans. Sustainable Energy 4 (2012), 1, :108-117.   DOI:10.1109/TSTE.2012.2202698
  14. R. Faranda, S. Leva and V. Maugeri: MPPT techniques for PV systems: Energetic and cost comparison. In: 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,IEEE 2008, pp. 1-6.   CrossRef
  15. P. Gahinet, A. Nemirovsky, A. J. Laub and M. Chilali: LMI Control Toolbox. Math Works, Natick 1995.   CrossRef
  16. A. K. Gupta and R. Saxena: Review on widely-used MPPT techniques for PV applications. In: 2016 International Conference on Innovation and Challenges in Cyber Security (ICICCS-INBUSH), IEEE 2016, pp. 270-273.   DOI:10.1109/ICICCS.2016.7542321
  17. H. K. Khalil: Nonlinear Control. Pearson Higher Ed, 2014.   CrossRef
  18. D. Lalili, A. Mellit, N. Lourci, B. Medjahed and E. M. Berkouk: Input output feedback linearization control and variable step size mppt algorithm of a grid-connected photovoltaic inverter. Renewable Energy 36 (2011), 12, 3282-3291.   DOI:10.1016/j.renene.2011.04.027
  19. Y. Mahmoud, M. Abdelwahed and E. F. El-Saadany: An enhanced mppt method combining model-based and heuristic techniques. IEEE Trans. Sustainable Energy 7 (2015), 2, 76-585.   CrossRef
  20. M. Mao, L. Zhang, L. Yang, B. Chong, H. Huang and L. Zhou: MPPT using modified salp swarm algorithm for multiple bidirectional pv-ćuk converter system under partial shading and module mismatching. Solar Energy 209 (2020), 334-349.   DOI:10.1016/j.solener.2020.08.078
  21. Y. Mokhtari and D. Rekioua: High performance of maximum power point tracking using ant colony algorithm in wind turbine. Renewable Energy 126 (2018), 1055-1063.   DOI:10.1016/j.renene.2018.03.049
  22. P. A. Owusu and S. Asumadu-Sarkodie: A review of renewable energy sources, sustainability issues and climate change mitigation. Cogent Engrg. 3 (2016), 1, 1167990.   DOI:10.1080/23311916.2016.1167990
  23. A. Pandey, N. Dasgupta and A. K. Mukerjee: High-performance algorithms for drift avoidance and fast tracking in solar mppt system    CrossRef
  24. D. Pilakkat and S. Kanthalakshmi: An improved p\&o algorithm integrated with artificial bee colony for photovoltaic systems under partial shading conditions. Solar Energy 178 (2019), 37-47.   DOI:10.1016/j.solener.2018.12.008
  25. A. Qazi, F. Hussain, N. A. B. D. Rahim, G. Hardaker, D. Alghazzawi, K. Shaban and K. Haruna: Towards sustainable energy: a systematic review of renewable energy sources, technologies, and public opinions. IEEE Acess 7 (2019), 63837-63851.   DOI:10.1109/ACCESS.2019.2906402
  26. M. Salimi: Practical implementation of the lyapunov based nonlinear controller in dc-dc boost converter for mppt of the pv systems. Solar Energy 173 (2018), 246-255.   DOI:10.1016/j.solener.2018.07.078
  27. A. Sandali, T. Oukhoya and A. Cheriti: Modeling and design of pv grid connected system using a modified fractional short-circuit current mppt. In: 2014 International Renewable and Sustainable Energy Conference (IRSEC), IEEE 2014, pp. 224-229.   CrossRef
  28. D. Sera, L. Mathe, T. Kerekes, S. V. Spataru and R. Teodorescu: On the perturb-and-observe and incremental conductance mppt methods for pv systems. IEEE J. Photovoltaics 3 (2013), 3, :1070-1078.   DOI:10.1109/JPHOTOV.2013.2261118
  29. M. Sokolov and D. Shmilovitz: A modified mppt scheme for accelerated convergence. IEEE Trans. Energy Convers. 23 (2008), 4, 1105-1107.   DOI:10.1109/TEC.2008.2001464
  30. E. D. Sontag: A universal construction of artstein's theorem on nonlinear stabilization. Systems Control Lett. 13 (1989), 2, 117-123.   DOI:10.1016/0167-6911(89)90028-5
  31. T. Taniguchi, K. Tanaka and H. O. Wang: Model contruction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Systems 9 (2001), 4, 525-538.   DOI:10.1109/91.940966