Optimal Control of a Rigid-Wing Rotary Kite System for Airborne Wind Energy

Schutter, Jochem De; Leuthold, Rachel; Diehl, Moritz

doi:10.23919/ecc.2018.8550383

Cited by 10 publications

(10 citation statements)

References 13 publications

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“…A periodic optimal control problem is formulated to maximize the average cycle power (P ) of a single AWES subject to equality and in-equality constraints described above (De Schutter et al, 2019;Leuthold et al, 2018). The trajectory optimization problem is discretized into 100 intervals using direct collocation.An initial guess is generated using a homotopy technique similar to (Gros et al, 2013) with an estimated circular trajectory based on a fixed number of loops (here n loop = 4) at a 30 • elevation angle and an estimated aircraft speed.…”

Section: Wind Boundary Conditionmentioning

confidence: 99%

Offshore and onshore ground-generation airborne wind energy power curve characterization

Sommerfeld

Dörenkämper

Schutter³

et al. 2020

Preprint

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Abstract. Airborne wind energy systems (AWESs) aim to operate at altitudes well above conventional wind turbines (WTs) and harvest energy from stronger winds aloft. While multiple AWES concepts compete for entry into the market, this study focuses on ground-generation AWES. Various companies and researchers proposed power curve characterizations for AWES, but no consensus for an industry-wide standard has been reached. An universal description of a ground-generation AWES power curve is difficult to define because of complex tether and drag losses as well as alternating flight paths over changing wind conditions with altitude, as compared to conventional WT with winds at fixed hub height and rotor area normalization. Therefore, this study determines AWES power and annual energy prediction (AEP) based on the awenox optimal control model for two AWES sizes, driven by representative 10-minute onshore and offshore mesoscale WRF wind data. The wind resource is analyzed with respect to atmospheric stability as well as annual and diurnal variation. The wind data is categorized using k-means clustering, to reduce the computational cost. The impact of changing wind conditions on AWES trajectory and power cycle is investigated. Optimal operating heights are below 400 m onshore and below 200 m offshore. Efforts are made to derive AWES power coefficients similar to conventional WT to enable a simple power and AEP estimation for a given site and system. This AWES power coefficient decreases up to rated power due to the increasing tether length with wind speed and the accompanying tether losses. A comparison between different AEP estimation methods shows that a low number of clusters with three representative wind profiles within the clusters yields the highest AEP, as other wind models average out high wind speeds which are responsible for a high percentage of the overall AEP.

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Section: Wind Boundary Conditionmentioning

confidence: 99%

Offshore and onshore ground-generation airborne wind energy power curve characterization

Sommerfeld

Dörenkämper

Schutter³

et al. 2020

Preprint

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“…Although there exist many other interesting AWE concepts, e.g. those 31 based on tethered rotorcrafts [2,3], we will limit the scope of this paper to rigid-wing lift-32 Disclaimer/Publisher's Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions, or products referred to in the content.…”

Section: Introduction 22mentioning

confidence: 99%

“…transferred to the ground station through the tethers. Each aircraft k ∈ K generates 232 an amount of electrical power P turb,k := η turb κ k u a,k3 , with η turb the on-board turbine 233 efficiency. Note that for the case of power consumption, i.e.…”

mentioning

confidence: 99%

AWEbox: an Optimal Control Framework for Single- and Multi-Aircraft Airborne Wind Energy Systems

Schutter¹,

Leuthold²,

Bronnenmeyer³

et al. 2022

Preprint

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In this paper we present AWEbox, a Python toolbox for modeling and optimal control of multi-aircraft systems for airborne wind energy (AWE). AWEbox provides an implementation of optimization-friendly multi-aircraft AWE dynamics for a wide range of system architectures and modeling options. It automatically formulates typical AWE optimal control problems based on these models, and finds a numerical solution in a reliable and efficient fashion. To obtain a high level of reliability and efficiency, the toolbox implements different homotopy methods for initial guess refinement. The first type of methods produces a feasible initial guess from an analytic initial guess based on user-provided parameters. The second type implements a warmstart procedure for parametric sweeps. We investigate the software performance in two different case studies. In the first case study we solve a single-aircraft reference problem for a large number of different initial guesses. The homotopy methods reduce the expected computation time by a factor of 1.7 and and the peak computation time by a factor of 8, compared to when no homotopy is applied. Overall, the CPU timings are competitive to timings reported in the literature. When the user initialization draws on expert a priori knowledge, homotopies do not increase expected performance, but the peak CPU time is still reduced by a factor of 5.5. In the second case study, a power curve for a dual-aircraft lift-mode AWE system is computed using the two different homotopy types for initial guess refinement. On average, the second homotopy type, which is tailored for parametric sweeps, outperforms the first type in terms of CPU time by a factor of 3. In conclusion, AWEbox provides an open-source implementation of efficient and reliable optimal control methods that both control experts and non-expert AWE developers can benefit from.

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“…However, they are the standard in most AWES power estimation studies (e.g. [84,86,30,10]). AWES need to dy-namically adapt their flight trajectory to changing winds in order to optimize power production.…”

Section: Introductionmentioning

confidence: 99%

Ground-generation airborne wind energy design space exploration

Sommerfeld

Dörenkämper

Schutter³

et al. 2020

Preprint

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Abstract. While some Airborne Wind Energy System (AWES) companies aim at small-scale, temporary or remote off-grid markets, others aim to integrate utility-scale, multi-megawatt AWES into the electricity grid. This study investigates the scaling effects of single-wing, ground-generation AWESs from small to large-scale systems, subject to realistic 10-minute, onshore and offshore wind conditions derived from the numerical mesoscale weather research and forecasting (WRF) model. To reduce computational cost, wind velocity profiles are grouped into k = 10 clusters using k-means clustering. Three representative profiles from each cluster are implemented into a nonlinear AWES optimal control model, to determine power-optimal trajectories, system dynamics, as well as instantaneous and cycle-average power. We compare the performance of three different aircraft masses and two sets of nonlinear aerodynamic coefficients for each aircraft size, with wing areas ranging from 10 m2 to 150 m2. We predict size and weight-dependent, optimal AWES power curves, annual energy production (AEP) and capacity factor (cf). Tether impacts, such as power losses associated with tether drag and the tether contribution to total system mass are quantified. Furthermore, we estimate a minimum average cycle-average lift to weight ratio, above which ground-generation AWES can operate, to explore the viable AWES mass budget.

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Optimal Control of a Rigid-Wing Rotary Kite System for Airborne Wind Energy

Cited by 10 publications

References 13 publications

Offshore and onshore ground-generation airborne wind energy power curve characterization

Offshore and onshore ground-generation airborne wind energy power curve characterization

AWEbox: an Optimal Control Framework for Single- and Multi-Aircraft Airborne Wind Energy Systems

Ground-generation airborne wind energy design space exploration

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