A Tensile Rotary Airborne Wind Energy System—Modelling, Analysis and Improved Design
Abstract
:1. Introduction
1.1. A Brief History of Daisy-Kite AWE Rotary Kite Turbine
1.2. Motivation and Main Work Organisation
2. Modelling Framework
2.1. Overall System Configuration
2.2. Power Extraction
2.2.1. Rotor Aerodynamics
2.2.2. Wing Characteristics
2.2.3. Lift-Kite Aerodynamics
2.2.4. Wind Models
- (1)
- The first is the uniform and constant wind speed used to analyse steady-state performance.
- (2)
- The second wind model assumes that the wind speed varies with time but is uniform in the plane perpendicular to the wind’s direction. This model is used for the simulation of dynamic system responses.
- (3)
- The third wind shear model accounts for the variations in wind speed in both time and altitude. The variation in wind speed with altitude is calculated following the power law [25]. This wind shear model is used for the entire system to integrate all modules into the same modelling scheme.
2.3. Ground Station—Power Take Off
3. Power Transmission—TRPT Representations and Tether Drag Models
3.1. Steady State TRPT Model
- Wind reference frame. It is defined as (), in which is parallel to the wind velocity vector, , which is parallel to the ground; is perpendicular to the wind vector and also parallel to the ground; and is perpendicular to the plane.
- Rotating reference frame for the lower ring. It is defined as (), with the origin at . lies on the system’s axis of rotation, and are in the plane of the lower ring, and is towards point A.
- Rotating reference frame for the upper ring. It is denoted by (), the origin is at , lies on the axis of rotation, and are in the plane of the upper ring, and is towards point B.
3.2. TRPT Dynamic Model 1: Spring—Disc Representation
3.3. TRPT Dynamic Model 2: Multi-Spring Representation
3.4. Tether Drag Models-Calculation of Torque Loss in TRPT
3.4.1. Simple Tether-Drag Model for Steady-State TRPT Representation
3.4.2. Improved Tether Drag Model for Dynamic TRPT Representations
4. Model Validation and Modifications
4.1. Steady State Model
4.2. Spring-Disc Representation Compared to Field-Testing Data
4.2.1. Steady-State Response Testing
4.2.2. Dynamic Response Testing
4.3. Multi-Spring Representation Compared to Field-Testing Data
4.3.1. Improving Computational Efficiency with Assumption of Rigid Wings
4.3.2. Multi-Spring Model Compared to Experimental Data
4.4. Comparison of Spring-Disc and Multi-Spring TRPT Models
4.4.1. Response to Short-Term Step Changes in Torque and Tension
4.4.2. Impact of TRPT Length
4.4.3. A Few Remarks
5. System Analysis and Improved/Optimised Design
5.1. TRPT Design Analysis
5.2. Rotor Design Analysis
5.2.1. System Elevation Angle
5.2.2. Blade Pitch Angle
5.2.3. Blade Length
5.3. Tether-Drag Analysis
5.3.1. Analysis with Simple Tether-Drag Model
5.3.2. Analysis with Improved Tether-Drag Model
5.4. Optimised/Improved Design
5.4.1. Optimised Rotor Design
5.4.2. Optimised TRPT Design
5.4.3. Optimised Elevation Angle and Tether Length
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AWE(S) | Airborne wind energy (system) | BEM | Blade element momentum |
DoF | Degree of freedom | EOM | Equation of motion |
RMSE | Root mean square error | TRPT | Tensile rotary power Transmission |
Appendix A. Pseudo Codes of Model Development
Appendix A.1. Spring–Disc TRPT Modelling
Inputs | Wind speed , TRPT geometry R and , elevation angle , initial conditions and , and generator torque |
Line 1 | Find and |
Line 2 | Find , and |
Line 3 | Find , and |
Line 4 | Find and |
Line 5 | |
Line 6 | |
Line 7 | , |
Line 8 | For each time step, i |
Line 9 | Find , and |
Line 10 | Find , and update |
Line 11 | Find and |
Line 12 | |
Line 13 | |
Line 14 | , |
Line 15 | End For |
Outputs | , , , , , , , |
Appendix A.2. Multi-Spring TRPT Modelling
Inputs | Wind speed , TRPT geometry R and , elevation angle , initial conditions and , generator torque , and number of tethers . |
Line 1 | Find and |
Line 2 | Find , and |
Line 3 | Find , and |
Line 4 | Find |
Line 5 | |
Line 6 | |
Line 7 | , |
Line 8 | For each time step, i |
Line 9 | Find , and |
Line 10 | Find , and |
Line 11 | Find |
Line 12 | |
Line 13 | |
Line 14 | , |
Line 15 | End For |
Outputs | , , , , , , , , |
Appendix B. Four TRPT Configurations
Appendix C. Comparison of Multi-Spring Model and Experimental Data
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Case | Test Date | Wing | TRPT | Wind Speed (m/s) | Power Output (w) | 1st Natural Frequency (Hz) |
---|---|---|---|---|---|---|
1 | 8 September 2019 | Rigid | 4 | 5.3 | 35 | 0.74 |
2 | 20 September 2018 | Rigid | 3 | 6.1 | 50 | 1.43 |
3 | 27 August 2018 | Rigid | 3 | 2.7 | 10 | 0.73 |
4 | 6 May 2018 | Soft | 2 | 5.8 | 10 | 1.47 |
5 | 18 June 2017 | Soft | 1 | 5.5 | 15 | 1.52 |
Wind Speed (m/s) | Change in Torque RMSE | Change in Tension RMSE |
---|---|---|
6 | 0.056 | 0.332 |
8 | 0.038 | 0.271 |
10 | 0.019 | 0.186 |
12 | 0.019 | 0.119 |
Models | Torque Loss (Nm) | TRPT–4 Efficiency (%) |
---|---|---|
Simple tether-drag model | 7.6 | 83.2 |
Improved tether-drag model ( neglected) | 4.9 | 89.2 |
Improved tether-drag model | 5.1 | 88.6 |
Rotor Radius | Blade Length | TRPT Radius | TRPT Section Length | Elevation Angle | TRPT Total Length | Tip Speed Ratio |
---|---|---|---|---|---|---|
2.22 m | 1.4 m | 0.5 m | 1.25 m | 18.5 | 190 m | 3.5 |
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Tulloch, O.; Yue, H.; Kazemi Amiri, A.M.; Read, R. A Tensile Rotary Airborne Wind Energy System—Modelling, Analysis and Improved Design. Energies 2023, 16, 2610. https://doi.org/10.3390/en16062610
Tulloch O, Yue H, Kazemi Amiri AM, Read R. A Tensile Rotary Airborne Wind Energy System—Modelling, Analysis and Improved Design. Energies. 2023; 16(6):2610. https://doi.org/10.3390/en16062610
Chicago/Turabian StyleTulloch, Oliver, Hong Yue, Abbas Mehrad Kazemi Amiri, and Roderick Read. 2023. "A Tensile Rotary Airborne Wind Energy System—Modelling, Analysis and Improved Design" Energies 16, no. 6: 2610. https://doi.org/10.3390/en16062610