Flight Stability of Rigid Wing Airborne Wind Energy Systems

Abstract

The flight mechanics of rigid wing Airborne Wind Energy Systems (AWESs) is fundamentally different from the one of conventional aircrafts. The presence of the tether largely impacts the system dynamics, making the flying craft to experience forces which can be an order of magnitude larger than those experienced by conventional aircrafts. Moreover, an AWES needs to deal with a sustained yet unpredictable wind, and the ensuing requirements for flight maneuvers in order to achieve prescribed control and power production goals. A way to maximize energy capture while facing disturbances without requiring an excessive contribution from active control is that of suitably designing the AWES craft to feature good flight dynamics characteristics. In this study, a baseline circular flight path is considered, and a steady state condition is defined by modeling all fluctuating dynamic terms over the flight loop as disturbances. In-flight stability is studied by linearizing the equations of motion on this baseline trajectory. In populating a linearized dynamic model, analytical derivatives of external forces are computed by applying well-known aerodynamic theories, allowing for a fast formulation of the linearized problem and for a quantitative understanding of how design parameters influence stability. A complete eigenanalysis of an example tethered system is carried out, showing that a stable-by-design AWES can be obtained and how. With the help of the example, it is shown how conventional aircraft eigenmodes are modified for an AWES and new eigenmodes, typical of AWESs, are introduced and explained. The modeling approach presented in the paper sets the basis for a holistic design of AWES that will follow this work.

Sensitivity analysis of a Ground-Gen Airborne Wind Energy System design

“…In this work, an ultra-light aircraft, Zefiro [2], is used as a baseline to introduce trends and perform a sensitivity analysis on some independent variables. In this section, a reduced optimization, where only operational design variables are considered, is run to find the optimal working set-points as function of wind speed.…”

“…The pitch angle θ (Angle which brings from the body coordinate system F B to the stability coo. system F S [2]) and the reel-out factor γ ro = Vro Vw as function of wind speed are considered as design variables. The optimizer, in this case, looks for the working set-points in order to maximize power production while satisfying constraints.…”

“…Positional eigenmode initially decreases its real part and, after rated power, it increases again. Finally, the imaginary part of the pendulum eigenmode, which for a straight crosswind motion can be approximated with [2] Im(λ pend ) ≈ ω pend ≈ T mL 0 t ,…”

“…The physical model in T-GliDe is based on LT-GliDe (Linearized Tethered Gliding system Dynamics) [2]. T-GliDe is not restricted to a generation type (i.e.…”

“…Bearing this in mind, the present work introduces a new design approach where the AWES is designed based on market metrics, while ensuring good dynamic characteristics, which may enhance controllability and reliability. Based on the theory developed in [2], a multidisciplinary design and optimization framework (T-GliDe: Tethered Gliding system Design) has been built with the aim of designing an AWES maximizing power production or minimizing cost-related objective functions, while satisfying constraints related to flight stability on top of conventional constraints. This approach differs from optimization approaches based on low-fidelity models [3,4] or on approaches which focus on the aero-structural design for specific design load cases [5,6], which typically do not include flight dynamics, and from approaches which find power output and loads by running time simulations, which include control [7].…”