16-Mar-2014, Request for Comments, AWELabs-002 Density of Individual Airborne Wind Energy Systems in AWES Farms Leo Goldstein Airborne Wind Energy Labs Austin, TX, USA ABSTRACT The paper shows that individual airborne wind energy systems in an AWES farm can be placed much denser than at the tether distance from each other. A simple control algorithm for multiple individual AWES in the farm is described and analyzed. 2014 Leo Goldstein, Airborne Wind Energy Labs 1
1. Introduction 1 Recently, the airborne wind energy field has experienced significant progress in research, development and commercialization. The overview of the field can be found in [1] and [2]. Article [3] has analyzed scalability of an individual airborne wind energy system. A complementary way of scaling up an airborne wind energy plant is use of multiple individual AWES in an AWES farm. AWES farms can be put on the land or off-shore. AWES farms also allow obtaining continuous power output from intermittent AWES devices. However, how close can be individual systems placed in the farm, given that the wind can change direction? In [4], Makani Power suggested that individual systems could be placed in an array at one tether length from each other. This paper shows that individual AWES can be placed much denser than that. 2. AWES placement and control As shown in Fig. 1, multiple identical individual AWES are placed in a hexagonal pattern or lattice, as was suggested before. Fig. 1 In the absence of the wind change, the wings are designed to move in identical trajectories, such as circles or helixes. A line connecting the ground station and the center of that trajectory will be called a system axis. The control principle is that axes of all individual systems are kept parallel to each other and projecting downwind at all times, through all wind direction changes. The axes direction can be easily computed by a farm control system and communicated to each individual AWES many times per 1 Author s email: leo.goldstein@awelabs.com 2
second. Course corrections in response to the wind change are applied in the same way as corrections for the wing deviations from the intended path. Fig. 2 shows two adjacent AWES with ground stations GS1 and GS2 in a position that presents the largest risk of a collision when one of them is directly downwind from another. The wings move in helixes between planes A1-B1 and A2-B2. The axes are shown by black dash-dot lines. The circles show trajectory of the outer tips of the wings. AWES (the ground stations, wings and tethers) are drawn in the green. It is easy to show for efficient AWES (as defined in [3]) and nominal wind speed, that deviations of the tether from the straight line in the radial direction are not significant (less than half wing span). Consequently, each wing and its tether s projection to any radial plane (a plane containing the axis) are always within a cylinder, having an axis in the system axis and the trajectory path of the outer wing tip in the plane B as its base. These cylinders are shown in blue dashed lines. As long as two cylinders do not intersect, corresponding AWES cannot collide in mid-air. Wind A1 B1 2q+b B2 A2 GS1 X GS2 ψ B1 Fig. 2 Knowing wingspan b, radius of the wide helix base q (measured at the wing centers) and axis angle to the horizontal plane ψ, we can easily compute the minimum distance X between the ground stations GS1 and GS2. 3. Distance between adjacent AWES Fig. 3 shows the flight of individual AWES. V and W are velocities of the wind and the wing, respectively. Dashed circle shows the large circular base (measured by the wing center), having radius q with the center at altitude h. l D denotes distance between the ground station and the wing, h is altitude of the center of the helix base. It is assumed that l D and h do not change significantly within the system work cycle (or do not change at all), and q << l D. 3
W V, wind wing q l D h ground station ψ Fig. 3 Diameter of the circle, made by wing tips, is 2q+b. The tether is curved under its weight, inertial force and drag. In all but very weak wind, the tether s sag under its own weight is very small. The inertial force is radial, while the drag is tangential, so they are perpendicular to each other. As mentioned above, the tether curving under inertial force does not bring it out far enough to get outside of the imaginary cylinder. The tether can get outside of the cylinder in the tangential direction because of the drag, but it will stay within the imaginary cylinder in the projection onto each radial plane, including the plane shared with any adjacent system. Thus, the parallel cylinder axes can be as close as 2q+b from each other. This allows expressing the minimum distance between ground attachments GS1 and GS2 from geometric considerations as X = 2q+b sin ψ Based on [3] and assuming reasonable values q = 2.5b, l D/b = 36 and ψ= 30, we obtain X = 1 3 l D (2) l D is slightly larger than the tether length. The number of the ground stations per unit of surface is proportional to the square of the distance between them. In this case, the number of the ground stations is increased slightly less than 9 times compared with the spacing of the ground stations at approximately the tether length distance from each other. The minimum distance can be even decreased. For example, in many practical cases the wing and its tether stay within a brown cone. The cones can be brought closer to each other than the cylinders. Similar calculation can be done for other trajectories of the wing or a wing system (which can have multiple wings), including the wing system described in [5]. The difference is, of course, that the (1) 4
imaginary cylinder would be not circular, but based on the projection of the wing trajectory to a plane, perpendicular to the system axis. 4. Discussion The proposed solution for tight packing of airborne wind energy systems and its proof are subject to certain limitations. Formula (1) is derived assuming that the wind speed is close to the nominal wind speed. The sag of the tether under its own weight can be disregarded at high tension of the tether in a strong wind, but it becomes significant when the wind is very weak. Practically that means that the wings of the AWES in the described farm have to be retrieved at higher wind speed than the wings in individual AWES. In the same time, launching and retrieving wings in the farm is more difficult than in an individual AWES. Other practical difficulties are related to changes in the wind direction, wind shear, aerodynamic interference between the wings and the tethers in the farm and control errors. On the other hand, formula (1) is a proof that tight packing of AWES is possible, not a limit on packing density. Even tighter packing can be achieved by controlling the wings to move synchronously (in phase). In this case, trajectories of the wings and the tethers can cross each other without the wings and the tethers colliding. Of course, such synchronous control is much more difficult to achieve and maintain. Finally, the discussion above does not consider turbulence and wind energy loss in the wake of a wing, which would affect other wings downwind. As the robust control systems appear, then mature and allow denser and denser packing of AWES, these effects will limit maximum density of AWES in a farm. 5. Conclusion A simple control method for multiple AWES in AWES farm is proposed. Formula (1) for the minimum distance between ground stations for this control method is derived. For a specific example AWES, the proposed control method allows almost 9 times denser packing of individual AWES in the farm than placing ground stations at the tether length from each other. Formula (1) is not a physical or geometrical limit. Denser packing can be achieved with more sophisticated control methods. 6. Disclosure statement The author has pending patent applications related to the article content. 5
7. References [1] U. Ahrens, M. Diehl and R. Schmehl, Airborne Wind Energy, Berlin: Springer, 2013. [2] L. Fagiano and M. Milanese, Airborne Wind Energy: an overview, in 2012 American Control Conference, Montréal, Canada, 2012. [3] L. Goldstein, "Scalability of Airborne Wind Energy Systems," 16 February 2014. [Online]. Available: http://www.awelabs.com/wp-content/uploads/awes_scalability.pdf. [Accessed 10 March 2014]. [4] Makani Power, "Makani Power Specs," [Online]. Available: http://www.makanipower.com/technical-specifications/. [Accessed 9 February 2014]. [5] L. Goldstein, "Airborne Wind Energy Conversion Systems with Ultra High Speed Mechanical Power Transfer," in Airborne Wind Energy, Berlin, Springer, 2013. 6