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Optimal Control Algorithms with Adaptive Time-Mesh Refinement for Kite Power Systems

Author

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  • Luís Tiago Paiva

    (SYSTEC–ISR, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal
    Instituto Superior de Engenharia do Porto, Politécnico do Porto, 4249-015 Porto, Portugal
    Current address: Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal.)

  • Fernando A. C. C. Fontes

    (SYSTEC–ISR, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal
    Current address: Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal.)

Abstract

This article addresses the problem of optimizing electrical power generation using kite power systems (KPSs). KPSs are airborne wind energy systems that aim to harvest the power of strong and steady high-altitude winds. With the aim of maximizing the total energy produced in a given time interval, we numerically solve an optimal control problem and thereby obtain trajectories and controls for kites. Efficiently solving these optimal control problems is crucial when the results are used in real-time control schemes, such as model predictive control. For this highly nonlinear problem, we derive continuous-time models—in 2D and 3D—and implement an adaptive time-mesh refinement algorithm. By solving the optimal control problem with such an adaptive refinement strategy, we generate a block-structured adapted mesh which gives results as accurate as those computed using fine mesh, yet with much less computing effort and high savings in memory and computing time.

Suggested Citation

  • Luís Tiago Paiva & Fernando A. C. C. Fontes, 2018. "Optimal Control Algorithms with Adaptive Time-Mesh Refinement for Kite Power Systems," Energies, MDPI, vol. 11(3), pages 1-17, February.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:3:p:475-:d:133132
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    References listed on IDEAS

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    1. Fernando A. C. C. Fontes & Hélène Frankowska, 2015. "Normality and Nondegeneracy for Optimal Control Problems with State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 115-136, July.
    2. Cherubini, Antonello & Papini, Andrea & Vertechy, Rocco & Fontana, Marco, 2015. "Airborne Wind Energy Systems: A review of the technologies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 1461-1476.
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    Cited by:

    1. Ali Arshad Uppal & Manuel C. R. M. Fernandes & Sérgio Vinha & Fernando A. C. C. Fontes, 2021. "Cascade Control of the Ground Station Module of an Airborne Wind Energy System," Energies, MDPI, vol. 14(24), pages 1-25, December.
    2. Manuel C. R. M. Fernandes & Sérgio Vinha & Luís Tiago Paiva & Fernando A. C. C. Fontes, 2022. "L 0 and L 1 Guidance and Path-Following Control for Airborne Wind Energy Systems," Energies, MDPI, vol. 15(4), pages 1-16, February.

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