Articles | Volume 7, issue 5
Wind Energ. Sci., 7, 2039–2058, 2022
Wind Energ. Sci., 7, 2039–2058, 2022
Research article
18 Oct 2022
Research article | 18 Oct 2022

Flight trajectory optimization of Fly-Gen airborne wind energy systems through a harmonic balance method

Filippo Trevisi et al.

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Cited articles

Argatov, I., Rautakorpi, P., and Silvennoinen, R.: Apparent wind load effects on the tether of a kite power generator, J. Wind Eng. Indust. Aerodynam., 99, 1079–1088,, 2011. a
awebox: Modelling and optimal control of single- and multiple-kite systems for airborne wind energy,, last access: 27 May 2022. a
Cobb, M. K., Barton, K., Fathy, H., and Vermillion, C.: Iterative Learning-Based Path Optimization for Repetitive Path Planning, With Application to 3-D Crosswind Flight of Airborne Wind Energy Systems, IEEE T. Control Syst. Technol., 28, 1447–1459,, 2020. a, b
De Schutter, J., Leuthold, R., Bronnenmeyer, T., Paelinck, R., and Diehl, M.: Optimal control of stacked multi-kite systems for utility-scale airborne wind energy, in: 2019 IEEE 58th Conference on Decision and Control (CDC), 11–13 December 2019, Nice, France, 4865–4870,, 2019. a
Dimitriadis, G.: Time Integration, in: Introduction to Nonlinear Aeroelasticity, in: chap. 3, John Wiley & Sons, Ltd, 63–111,, 2017. a, b
Short summary
The optimal control problem for the flight trajectories of Fly-Gen AWESs is expressed with a novel methodology in the frequency domain through a harmonic balance formulation. The solution gives the optimal trajectory and the optimal control inputs. Optimal trajectories have a circular shape squashed along the vertical direction, and the optimal control inputs can be modeled with only one or two harmonics. Analytical approximations for optimal trajectory characteristics are also given.