The Influence of Tether Sag on Airborne Wind Energy Generation

Trevisi, Filippo; Gaunaa, Mac; McWilliam, Michael

doi:10.1088/1742-6596/1618/3/032006

Cited by 12 publications

(21 citation statements)

References 8 publications

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“…The expressions of the non dimensional aerodynamic force X (which should not be confused with the non-dimensional state variables X) and Z correspond to the classical results for AWES modeled as a point mass flying in a straight crosswind motion. This is in accord with the findings on the flight path introduced in [16] and used here. Conversely, Ỹ appears just because of dihedral and sweep and the difference in relative wind speed between the inner and outer wing.…”

Section: Trim Conditionsupporting

confidence: 93%

“…In addition to the elastic force, the tether introduces also a drag component, which can be modelled as a concentrated force at the tether attachment [16], yielding…”

Section: Tether Reaction Forcementioning

confidence: 99%

“…To achieve stability, the flight path should be properly chosen: a circular path makes the problem nearly axial-symmetric, and there exists one turning radius which ensures maximum tether force and potentially maximum power production [16]. As this turning radius maximizes the tether force, a stable-by-design AWES, if perturbed from this path, would tent to return to the operational point which maximizes tether force.…”

Section: Introductionmentioning

confidence: 99%

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Flight Stability of Rigid Wing Airborne Wind Energy Systems

2021

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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.

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Section: Trim Conditionsupporting

confidence: 93%

“…In addition to the elastic force, the tether introduces also a drag component, which can be modelled as a concentrated force at the tether attachment [16], yielding…”

Section: Tether Reaction Forcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flight Stability of Rigid Wing Airborne Wind Energy Systems

2021

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“…where ρ is the air density, A is the wing area, and the lift and drag coefficients C L and C D are considered constant. The drag coefficient C D includes the contribution from the tether drag (Trevisi et al, 2020a). The gravitational force F g and the tether force T are…”

Section: Flight Dynamic Modelmentioning

confidence: 99%

“…The first analytical power equation of crosswind AWESs was derived by Loyd (1980), and additional refinements, such as the one proposed by Trevisi et al (2020a), made an effort to modify analytic equations to include gravitational and centrifugal effects. This kind of analytical models can be used to study how power and other relevant trends approximately scale with design parameters.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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Abstract. The optimal control problem for flight trajectories of Fly-Gen airborne wind energy systems (AWESs) 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 the potential reduction of the problem size by solving only for the main harmonics and allows the implicit imposition of periodicity of the solution. The trajectory is described by the Fourier coefficients of the dynamics (elevation and azimuth angles) and of the control inputs (onboard wind turbine 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, onboard 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 onboard 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 modeled with one harmonic for the onboard wind turbine 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 AWESs.

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Given a wingspan, which windplane design maximizes power?

Trevisi,

Croce

2024

J. Phys.: Conf. Ser.

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Windplanes (i.e. Fly-Gen airborne wind energy systems) harvest wind power via the turbines placed on the tethered wing, which flies crosswind trajectories. In this paper, the optimal design of windplanes is investigated with simplified models, enabling an intuitive understanding of their physical characteristics. The windplane is then idealized as a point mass flying circular fully crosswind trajectories. If the gravity is neglected, the dynamic problem is axial symmetric and the solution is steady. The generated power can be expressed in non-dimensional form by normalizing it with the wind power passing by a disk with radius the wingspan. Since the reference area is taken to be a function of just the wingspan, looking for the design which maximizes this power coefficient addresses the question ”Given a wingspan, which design maximizes power?”. This is different from the literature, where the design problem is formulated per wing area and not per wingspan. The optimal designs have a finite aspect ratio and operate at the maximum lift-to-drag ratio of the airfoil. Airfoils maximizing the lift-to-drag ratio are then optimal for windplanes. If gravity is included in the model, gravitational potential energy is being exchanged over one revolution. Since this exchange comes with an associated efficiency, the plane mass and the related trajectory radius are designed to reduce the potential energy fluctuating over the loop. However, for decreasing turning radii, the available wind power decreases because the windplane sweeps a lower area. For these two conflicting reasons, the optimal mass is finite.

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The Influence of Tether Sag on Airborne Wind Energy Generation

Cited by 12 publications

References 8 publications

Flight Stability of Rigid Wing Airborne Wind Energy Systems

Flight Stability of Rigid Wing Airborne Wind Energy Systems

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

Given a wingspan, which windplane design maximizes power?

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