07 Jun 2022
07 Jun 2022
Status: this preprint is currently under review for the journal WES.

Flight Trajectory Optimization of Fly-Gen AWE Systems through a Harmonic Balance Method

Filippo Trevisi1, Iván Castro-Fernández2, Gregorio Pasquinelli1, Carlo Emanuele Dionigi Riboldi1, and Alessandro Croce1 Filippo Trevisi et al.
  • 1Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
  • 2Departamento de Bioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid, Leganés, 28911 Madrid, Spain

Abstract. The optimal control problem for flight trajectories for Fly-Gen Airborne Wind Energy Systems (AWES) is a crucial research topic for the field, as suboptimal paths can lead to a drastic reduction in power production. One of the novelties of the present work is the expression of the optimal control problem in the frequency domain through a Harmonic Balance formulation. This allows to reduce the problem size by solving only for the main harmonics and to implicitly impose periodicity of the solution. The trajectory is described by the Fourier coefficients of the dynamics (elevation and azimuth angles) and of the control inputs (on-board wind turbines thrust and AWES roll angle). To isolate the effects of each physical phenomenon, optimal trajectories are presented with an increasing level of physical representation from the most idealized case: i) If the mean thrust power (mechanical power linked to the dynamics) is considered as the objective function, optimal trajectories are characterized by a constant AWES velocity over the loop and a circular shape. This is done by converting all the gravitational potential energy into electrical energy. At low wind speed, on-board wind turbines are then used as propellers in the ascendant part of the loop; ii) If the mean shaft power (mechanical power after momentum losses) is the objective function, a part of the potential energy is converted into kinetic and the rest into electrical energy. Therefore, the AWES velocity fluctuates over the loop; iii) If the mean electrical power is considered as the objective function, the on-board wind turbines are never used as propellers because of the power conversion efficiency. Optimal trajectories for case ii) and iii) have a circular shape squashed along the vertical direction. The optimal control inputs can be generally modelled with one harmonic for the on-board wind turbines thrust and two for AWES roll angle without a significant loss of power, demonstrating that the absence of high-frequency control is not detrimental to the power generated by Fly-Gen AWES.

Filippo Trevisi et al.

Status: open (until 26 Jul 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Filippo Trevisi et al.

Filippo Trevisi et al.


Total article views: 212 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
152 54 6 212 2 1
  • HTML: 152
  • PDF: 54
  • XML: 6
  • Total: 212
  • BibTeX: 2
  • EndNote: 1
Views and downloads (calculated since 07 Jun 2022)
Cumulative views and downloads (calculated since 07 Jun 2022)

Viewed (geographical distribution)

Total article views: 177 (including HTML, PDF, and XML) Thereof 177 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 01 Jul 2022
Short summary
The optimal control problem for the flight trajectories of Fly-Gen AWE Systems is expressed with a novel methodology in the frequency domain through a Harmonic Balance formulation to find optimal flight trajectories and optimal control inputs. Optimal trajectories have a circular shape squashed along the vertical direction and optimal control inputs can be modelled with just one or two harmonics. Analytical approximations for optimal trajectories characteristics are given.