This article summarizes the fundamental dynamics and control attributes and challenges faced by stationary and crosswind airborne wind energy (AWE) systems. AWE systems have undergone rapid and steady technological development over the past decade, with several organizations demonstrating basic economic and technical viability of their concepts. The theoretical and numerical analyses performed so far indicate that crosswind systems have the potential to achieve a power curve similar in shape to that of current commercial wind turbines, with rated power of 2–5 MW. The ongoing development activities are increasing the viability of the concept; yet, several technical issues remain and need to be addressed, to definitively show that this technology can be scaled up to industrial size. The expert analysis suggests that AWE technologies are at the dawn of their development, and there is significant untapped potential for the use of innovative solutions in multiple fields such as materials, power electronics, and aerodynamics, to tackle problems. These challenges present a wealth of opportunities for future, multidisciplinary research and development activities.

## Article

Currently, fossil fuels supply 80% of the Earth's total primary energy demand (TPED) 1,2 but are produced by a restricted number of countries. Furthermore, the fast development of countries like China and India is quickly increasing the global demand and production of primary energy, so that the TPED is likely to increase by 50% in the next 25 years. In the face of this uneven distribution of energy sources, projected demand increases, and climatological effects of fossil fuels, many governments have adopted plans and regulations that aim to reach “energy security” (i.e. the reliable availability of energy sources at low cost), to improve the sustainability of energy sources, and to limit emissions of greenhouse gases. These objectives have led to a shift toward renewable energy sources. For example, the European Union aims at supplying 20% of the total European primary energy consumption with renewable energies by the year 2020, and California has a plan for 33% renewables by 2020. Of all renewable sources, wind power is among the world's fastest growing, with a seven-fold expansion of output power in 2000-2008 and a global investment for new installations of more than \$67 billion in 2009, corresponding to about 60% of the 2009 global investment in renewables and to an increase of 14% over 2008, despite the financial crisis 1.

Many ground-based sites do not have access to sufficiently strong winds to make wind cost competitive with non-renewable resources, particularly when one takes into consideration the installation cost associated with towered wind turbines. These disadvantages, over the past several years, have prevented wind from representing a competitive alternative to fossil fuels in many locations, without the use of political incentives, and have motivated the study of tethered systems, known as airborne wind energy (AWE) systems. Because winds at 500-1000 m altitude carry upwards of 4 times the power density of ground level wind 3, and because installation costs can be reduced through the elimination of a tower, AWE systems have the potential to dramatically reduce the cost of wind energy.

Although present airborne concepts differ greatly in their engineering approaches, they all provide access to higher-altitude winds through towerless structures. Fundamental ideas that are now being developed in the context of AWE were already present in patents and publications in the ’70s (e.g. references 46) when the world was facing an energy crisis. These ideas remained dormant until more recent years, when several research groups and companies started to carry out theoretical, numerical and experimental analyses (e.g. references 718), due in part to advances in diverse fields like materials, aerodynamics, sensors, computation and control.

Because AWE systems replace rigid towers with tethers, they introduce additional degrees of freedom in flight. Furthermore, because AWE systems incorporate shapes that differ substantially from traditional aircraft and aerostats, the dynamics and control of these systems demand unique attention. While the replacement of a tower with tethers makes flight dynamics and control more challenging, it also introduces opportunities for performance optimization. AWE systems can adjust their flight altitude to hunt for optimal winds and can exploit crosswind motions in order to maximize the system's energy production. Therefore, control is not just necessary for obtaining adequate flight characteristics but is a key driver in optimizing the energy that is delivered by the systems. This article summarizes some of the fundamental dynamics and control attributes and challenges faced by stationary and crosswind AWE systems.

## Stationary airborne wind energy systems

Stationary systems can employ periodic adjustment of altitude in order to optimize power capture subject to loading constraints but are designed to otherwise remain in a fixed position with respect to the ground. Though different in their approaches, each stationary design features two key elements:

1. Airborne power generation, with one or more conductive cables running to the ground;

2. Uninterrupted operation in limited and non-existent winds, often without wasted power.

While uninterrupted operation is a clear benefit, the incorporation of heavy and expensive power generation equipment aloft introduces important pointing and system robustness requirements. Consequently, the flight dynamics and control of these systems demand attention.

## An overview of stationary wind energy concepts

A number of organizations have developed stationary AWE platforms adapted either from auto-gyro or aerostat platforms. Some of the innovators in this area include (see Fig. 1):

FIGURE 1 A sampling of stationary AWE systems, including Sky Windpower, Magenn, and Altaeros.

Sky Windpower19 Sky Windpower uses a flying electric generator (FEG) system wherein four rotors simultaneously extract power from the wind and provide the lift necessary to keep the structure aloft. Attitude is controlled by varying the relative speeds of the four rotors, thereby generating a net moment about the airborne structure's center of mass. Because power can be transferred in either direction along the conductive cable, the FEG can remain airborne in light and non-existent winds for a small price in terms of energy consumption.

Magenn Power14 Magenn pioneered a lighter-than-air wind energy system known as the Magenn Air Rotor System (MARS), wherein an aerostat doubles as a rotor by rotating about its transverse axis high in the air. The system benefits from continuous buoyant lift, which keeps the system operable with no power requirement at low wind speeds, and aerodynamic lift through the Magnus effect (wherein backspin induces a pressure difference between the upper and lower surfaces of the aerostat), which prevents the system from being blown far downwind in high wind speeds. Because the design is symmetric about its transverse axis, there is no meaningful notion of pitch angle, and in fact the MARS does not incorporate any significant active control. Passive flight dynamics are, however, important, particularly as they relate to the large gyroscopic coupling effects that arise due the large rotating airborne mass.

Altaeros Energies15 Altaeros Energies, a more recent lighter-than-air wind energy organization, has pioneered a system that is referred to as the Buoyant Airborne Turbine (BAT), which features a lighter-than-air duct, referred to as a “shroud,” that elevates a horizontal axis wind turbine to high altitudes. The shroud serves several important purposes: 1. Powerless operability at low and non-existent wind speeds; 2. Acceleration of the wind, providing the rotor with a greater kinetic energy flux than that which is available in the freestream; and 3. Aerodynamic lift, preventing the shroud from being blown downwind in high wind speeds. The need to align the system with the wind demands careful plant design for lateral stability and tight roll control in order to attenuate undesirable lateral perturbations. Furthermore, unlike the MARS, the aerodynamic lift on the Altaeros shroud is highly sensitive to the angle of attack, so pitch angle must be tightly controlled to ensure sufficient aerodynamic lift in strong winds and gusts. Because of the authors’ familiarity with the Altaeros BAT, this system will be used as the main example for the more detailed analysis to follow.

## Flight dynamics considerations for stationary systems

The dynamic model is a key driver of both plant and control designs. A general axis framework is given in Fig. 2, with key variables given in Table 1. Detailed dynamic equations are summarized in reference 20.

FIGURE 2 Axis systems for dynamic modeling of stationary systems, illustrated on the Altaeros Buoyant Airborne Turbine (BAT).

Table 1

Key model variables

VARIABLEDESCRIPTION

xg, yg, zgPosition of the airborne center of mass in the ground-fixed frame
u, v, wVelocity of the airborne center of mass in the body-fixed frame
uw,vw, wwWind velocity in the body-fixed frame
Φ, θ, ψRoll, pitch, yaw Euler Angles (respectively)
p, q, rAngular rates in the body-fixed frame
αAngle of attack
βSideslip angle
htTurbine angular momentum
VARIABLEDESCRIPTION

xg, yg, zgPosition of the airborne center of mass in the ground-fixed frame
u, v, wVelocity of the airborne center of mass in the body-fixed frame
uw,vw, wwWind velocity in the body-fixed frame
Φ, θ, ψRoll, pitch, yaw Euler Angles (respectively)
p, q, rAngular rates in the body-fixed frame
αAngle of attack
βSideslip angle
htTurbine angular momentum
The general equation of motion for the airborne system is then given by:
$M6x6v˙=CM6x6,v+Faeroα,β,v,vw,ht+Ftethersx+Fbuoyant,$
(1)
where:
$x=xg yg zg φ θ ψT,$
(2a)
$v=u v w p q rT,$
(2b)
$vw=uw vw wwT.$
(2c)

M6x6 is a 6x6 inertia matrix, which contains not only the solid airborne mass and inertia matrix but also the added mass coefficients, which represent fluid mass that accelerate and decelerate with the airborne system. C, Faero, Ftethers, and Fbuoyant represent Coriolis/centripetal, aerodynamic, tether-driven, and buoyancy-driven terms, respectively.

## Lateral/directional dynamic considerations

The lateral dynamics of the system can be characterized by its performance under wind direction changes. The most important observation in analyzing the lateral dynamics is that the tethers cannot exert a force perpendicular to their axis and cannot exert a moment about their axis. Defining γ as the angle between an axis through the center of mass and aligned with the tethers (referred to as the “tether axis”) and z axis, as shown in Fig. 3, it follows from the dynamic equations:

• $υ˙$ is driven entirely by Fyaero;

• $p˙ sinγ'+r˙ cosγ'$ is driven entirely by Mt , where $Mt=Mzaero cosγ + Mxaero sinγ$.

FIGURE 3 Diagram of the critical axes for lateral flight performance, illustrated on the Altaeros BAT.

where $γ'=arctanIxxtanγIzz .$

Thus, the tethers have no immediate ability to react to an acceleration disturbance along y or an angular acceleration about the zt’ axis. The ability to stabilize the lateral dynamics is then left to three possible mechanisms: 1. Stabilizing aerodynamic forces and moments about these key axes; 2. Stabilizing reaction forces and moments when the system is laterally perturbed from the direct downwind condition; and 3. Stabilizing feedback control. It is well-understood that a roll p input induced by the tethers can induce sideslip and easily stabilize translational motion. The more challenging problem of rotational motion about the zt’ axis can be addressed through the incorporation of several design characteristics, including: 1. Incorporation of a vertical stabilizer (tail) and horizontal stabilizers with negative dihedral (anhedral); 2. Spatially distributed tether release points on the base station; 3. Movement of the centers of mass and buoyancy forward on the shroud; and 4. Careful design of the shroud sidewall camber line such that the resultant aerodynamic center lies aft of the center of mass.

## Longitudinal dynamic considerations

Longitudinal dynamics are driven by the system response under wind speed changes and vertical wind perturbations, where the wind heading remains constant and the shroud is initially in a direct-downwind position. For lighter-than-air systems, which comprise the bulk of stationary AWE systems, it is essential that the airborne system immediately exhibits lift upon a wind speed increase that takes the system from a buoyancy-dominated regime to an aerodynamically-dominated regime. Most LTA systems, including the BAT, must attain a particular angle of attack in order to guarantee aerodynamic lift. Specifically, since each tether can only assume nonnegative tension, there always exists a range of pitch angles, from θmin to θmax , outside of which the BAT's shroud cannot maintain static equilibrium. At low wind speeds, where buoyant force dominates and tether tensions are low, this range is particularly small and is given by:
$θmax=arctanbFb−mg−ΔxFbcFb+ΔzFb,$
(3a)
$θmin=arctan-aFb−mg−ΔxFbcFb+ΔzFb,$
(3b)

where the design parameters of (3) are as follows: a represents the x distance from the cm to the forward tether attachment; b represents the x distance from the cm to the aft tether attachment; c represents the z distance from the cm to all tether attachments; Δx represents the x distance between the cm and center of buoyancy (positive signifies a cm forward of the cb); Fb represents the total buoyant force.

## Control strategies for stationary systems

Broadly speaking, the control of stationary wind energy systems consists of the selection (ideally optimization) of an altitude setpoint and a flight control system that tracks this altitude setpoint, along with suitable pitch angle and tether tension setpoints. While the overall strategy varies from one organization to another, a basic strategy is given in Fig. 4.

FIGURE 4 Basic block diagram of a typical control strategy for stationary AWE systems, including a high level (supervisory) altitude command optimization and lower level (local) flight control.

## Flight control energy optimization strategies

The supervisory control system is responsible for high-level decisions that affect the amount of power produced by the system, as well as its robustness under heavy weather scenarios. Unlike traditional towermounted wind systems and many of their airborne wind competitors, stationary AWEs can dynamically adjust their tether lengths to search for winds that are at or nearest to the rated wind speed for the turbine. Altitude setpoints can be determined on the basis of current and near-term forecast weather information, using a communications and control framework illustrated in Fig. 5. For the design of this supervisory-level optimization, tools from extremum seeking and model predictive control (MPC) both can be used to optimize a power performance objective (with MPC boasting the additional advantage that it can enforce operational constraints and take into account future weather predictions). In addition to optimizing the altitude of the system and landing the system during adverse weather, the supervisory control system can also make key operational decisions (e.g., autonomous landing, shutting off the turbine, commanding local control operation in open-loop mode) in the event of system faults.

FIGURE 5 Candidate hardware architecture for combined supervisory altitude optimization and lower level flight control.

The primary flight control system, depicted in Fig. 6, consists of several components that are aimed at regulating altitude, pitch, roll, and tether tensions. The specifics of the control algorithm will vary from system to system, but for the BAT, a two-step flight control algorithm is used, wherein an upper-level controller maps desired altitude and pitch angle (zdes and θdes) to setpoints (zsp and θsp) within a suitable flying envelope, and a lower-level controller adjusts tether release speeds in order to track these setpoints while ensuring that tethers remain in tension.

FIGURE 6 Low-level flight control strategy for stationary systems.

Thus, the final control input for each tether is the minimum of two values, namely: 1. The tether release speed command for altitude/attitude control; and 2. The tether release command for tension control. Because the prescribed tether tension setpoint is very small, tether tension control is only active when tethers are slack or nearly slack and would not be effective in regulating altitude and attitude. The mechanism for computing tether release speeds can vary from LQ-based linear state feedback 20, to more complex strategies like MPC21, which provides the added advantage of constraint enforcement at some computational cost.

## Crosswind airborne wind energy systems

Crosswind systems rely on high-speed periodic motions of a tethered wing to obtain a much greater apparent wind speed than the absolute wind relative to the ground. Such apparent wind generates a high lift force on the wing, which can be exploited to produce power. Note that this mechanism, depicted in Fig. 7, is the same as that of a traditional wind turbine if one considers the outermost part of the rotor blades only15. In fact, in a wind turbine the outermost 30% of the blade surface approximately contributes 80% of the generated power. Replacing the expensive structure of wind turbines with tethers yields a cost reduction and allows high-altitude winds to be reached, but demands careful control design.

FIGURE 7 Concept of crosswind airborne wind energy (AWE).

Crosswind systems can be divided into two categories, depending on how the aerodynamic forces generated by the wing are converted into electricity: 1. Onboard generation (OBG); and 2. Ground-level generation (GLG). Schematics of both types of system are given in Fig. 8.

FIGURE 8a Sketch of an AWE system with onboard generators. 8b Sketch of an AWE system with ground-based generators.

In OBG systems16, the wing is equipped with rotors and generators and the line is used both to sustain traction forces and to transmit the generated power to the ground (see Fig. 8a). Thus, the power generation of OBGs is a direct result of the apparent wind presented to the rotors. Because rotors are incorporated onto the wing, all OBG systems incorporate rigid wings, and because these systems are capable of presenting the rotors with apparent wind speeds several times greater than the true wind, the rotors can be sized substantially smaller than conventional turbines.

IIn GLGs (see Fig. 8b), since the electric generators are kept on the ground, the flying structure is much lighter than an OBG, and it can be either rigid (e.g., 12) or flexible (e.g., 11, 13, 22, 23). Solutions with one (11, 12), two (13, 22, 24) or three (23) lines exist. These lines are not required to also transfer electricity, in contrast to OBGs. On the ground, the lines are wound around one or more winches, linked to electric generators. The system composed by the electric generators and the winches is denoted as the ground station (see Fig. 9). Energy is obtained by continuously performing a two-phase cycle (see Fig. 10): in the traction phase, the wing is controlled to follow figure-eight paths and the lines are unrolled under high traction forces, maximizing the power generated by the electric generators that are driven by the rotation of the winches. Figure-eight patterns are slightly less efficient than loops (see 24), but they prevent line twisting. When a desired maximum line length is reached, the passive phase begins, and the electric generators act as motors, spending a fraction of the previously generated energy, to recover the wing and to drive it in a position which is suitable to start another traction phase. Table 2 summarizes some of the research institutions and companies currently developing crosswind AWE systems, highlighting the employed type of generator (GLG or OBG) and wing (flexible or rigid). It is interesting to note that OBGs and GLGs share the same potential for energy production, as indicated by the results of the seminal paper (Loyd, 1980), which will be recalled in the next section.

FIGURE 9 Photograph of a small-scale GLG system operating near Torino, Italy.

FIGURE 10 Sketch of the operating cycle of an AWE system ground-level generators; traction phase (solid) and passive phase (dashed).

Table 2

Features of selected crosswind AWE technologies.

INSTITUTIONGENERATOR POSITIONWING TYPENUMBER OF LINES

T.U. DelftGLGFlexible1
Politecnico di TorinoGLGFlexible2
K.U. LeuvenGLGRigid1
Swiss Kite PowerGLGSemi-Rigid2
Ampyx PowerGLGRigid1
KitenergyGLGFlexible2
Makani PowerOBGFlexible1
Skysails PowerGLGFlexible1
WindliftGLGFlexible3
EnerkiteGLGFlexible3
NTSGLGFlexible3
INSTITUTIONGENERATOR POSITIONWING TYPENUMBER OF LINES

T.U. DelftGLGFlexible1
Politecnico di TorinoGLGFlexible2
K.U. LeuvenGLGRigid1
Swiss Kite PowerGLGSemi-Rigid2
Ampyx PowerGLGRigid1
KitenergyGLGFlexible2
Makani PowerOBGFlexible1
Skysails PowerGLGFlexible1
WindliftGLGFlexible3
EnerkiteGLGFlexible3
NTSGLGFlexible3

## Simplified analysis of crosswind systems

Consider a wing with planform area A, moving in a 2-dimensional steady wind flow of given absolute wind speed $W→0$ (Fig. 11a). The velocity of the wing can be split in a component parallel to the absolute wind, $v→$, and in a crosswind component, $u→$. In a 2-dimensional cartesian coordinate system, whose axes are parallel to $v→$ and $u→$, respectively, the apparent wind speed is given by (see Fig 11b):
$Wa=W→0−v→−u→.$
(4)

FIGURE 11 Simple scheme of an airfoil in crosswind flight. (a) indicates the airfoil velocity components, (b) indicates the superimposed apparent wind velocity vector, and (c) indicates the resulting force vectors on the airfoil.

Now, consider two designs: 1. A direct downwind design, with the airfoil velocity relative to the ground being parallel to the absolute wind speed (i.e. $v→$), for example as in reference 14; 2. A crosswind design, i.e. with the airfoil velocity relative to the ground substantially perpendicular to the absolute wind speed (i.e. $u→≫v→$). Both GLG and OBG systems fall into this class. For the direct downwind design and for GLG systems, assume that a usable amount P of power can be generated by exploiting the motion of the wing in the same direction as the wind:
$P=FW→v→,$
(5)
where FW is the component, along the direction of $v→$ , of the total force acting on the wing. For OBG systems, the usable power is a function of the drag imparted to the onboard rotor(s) and the apparent velocity of the wing, i.e.:
$P=F→DturbW→a,$
(6)

where $F→Dturb$ is the drag force imparted by the apparent wind on the rotor plane.

It is conceptually apparent from Fig. 11 that a high lift-to-drag ratio (or aerodynamic efficiency), denoted as $E≜CLCD$, yields substantial advantages for crosswind designs. For GLG systems, high lift implies directly a high force in the direction of spooling (i.e., high power output), and for OBG systems high lift-to-drag ratio means a high ratio of apparent wind speed to true wind speed, hence allowing larger turbine drag $F→Dturb$. In fact, by analyzing the equilibrium of forces in the direction of $u→$ and maximizing the resulting power, it turns out that the maximum achievable power augmentation from crosswind flight is a function of E, it is identical for GLG and OBG systems, and is given by:
$P∗P∗=12E21+1E23/2,$
(7)

where P*crsw is the maximum attainable power in crosswind designs and P*downwind is the maximum power achievable with the direct downwind design. The detailed derivations of (7) are given in references 6 and 9.

Some quick calculations for a reasonably efficient wing (E = 8) show that crosswind motion can present a system with 35 times the power that is available through direct downwind operation. The simplified analysis recalled above assumes crosswind motion without considering several aspects, most notably the dynamic behavior of the system and the related control aspects. More details on these topics are given in the next section.

## Dynamics and control of crosswind systems

Measurement and control aspects are of paramount importance for the safe, reliable and optimal operation of crosswind AWE. The dynamics of tethered wings are nonlinear and the optimal flight paths, in terms of power generation, are typically unstable in open-loop, especially with relatively high aerodynamic efficiency. Hence, the controller has to stabilize the system and, at the same time, maximize the generated power, while keeping a high safety level, by maintaining a minimal distance from the ground.

As far as GLGs are concerned, there are several studies in the literature, concerned with the design of a control algorithm able to satisfy the above-mentioned requirements. The proposed approaches include nonlinear model predictive control (NMPC)7,8,10, adaptive control 20, evolutionary robotics techniques 27, direct inverse control 28 , and hierarchical control strategies. The latter have been tested experimentally with both large 29 and small scale 30,31 systems.

There is substantially less documented literature for OBGs, even though automatic control algorithms are known to be working for small-scale prototypes 16. The use of control surfaces, rather than tethers, in OBG systems allows designers to revert to proven flight control techniques. Automatic take-off/landing and transitions between the taking-off phase and the power-generation phase have been also tested 16. This section focuses on the dynamics and control of GLG systems during the traction phase, i.e. when the wing has to be controlled in order to continuously fly crosswind figure-eight paths. To this end, the turning dynamics of tethered wings, recalled next, play a crucial role.

## Turning dynamics of tethered wings in crosswind motion

Dynamical models for the steering behavior of tethered wings have been successfully employed for control design by different research groups and companies 29, 31, 32. See reference 33 for a short movie concerned with the tests described in reference 31. These models are quite accurate in crosswind conditions and have the advantage of being single-input, single-output. Consider an inertial frame $G≜X,Y,Z$, centered at the ground station, with the X axis parallel to the wind, the Z axis perpendicular to the ground and pointing upwards and the Y axis to complete a right-handed system (see Fig. 13). Considering the length r of the lines, the wing's trajectory is confined on a quarter sphere, given by the intersection of a sphere of radius r centered at the ground station with the planes $x,y,z∈ℝ3:x≥0 and z≥0$. Such a quarter sphere is commonly termed a “wind window” (see the dashed lines in Fig. 12).

FIGURE 12 Reference system, with wind window (dashed lines) and coordinate definitions.

FIGURE 13 Experimental results on a small-scale prototype.

The wing's position can be expressed by using the spherical coordinates θ,Φ (see Fig. 12). A non-inertial coordinate system $L≜LN,LE,LD$ can be also defined, centered at the wing's position (see Fig. 12). The LN axis, or local north, is tangent to the wind window and points towards its zenith. The LD axis, called local down, points to the ground station, hence it is perpendicular to the tangent plane to the wind window at the wing's location. The LE axis, named local east, forms a right hand system and spans the tangent plane together with LN.

Consider now the wing's velocity vector relative to the ground, $v→t=ddtp→t$. Then, the velocity angle γ(t) of the wing is defined as:
$γt≜arctanv→t∙e→LEtvt∙eLNt,$
(8)

where $e→LNt$ and $e→LEt$ denote the unit vectors of the LN and LE axes, respectively. The angle γ(t) is thus the angle between the local north $e→LNt$ and the wing's velocity vector $v→t$. This variable is particularly suited for feedback control, since it describes the flight conditions of the wing with just one scalar. Moreover, the time derivative $γ˙$ gives an indication on how fast the wing is being steered while flying in the wind window, i.e. its turning rate.

Under the assumptions of crosswind flight and small wing roll, the following dynamical model links γ to the steering input δ:
$γ˙t=K¯tδt+T¯t,$
(9)
where:
$K¯t=ρCLtA2m1+1Eeq22v→t,$
(10a)
$T¯t=gcosθtsinγtv→t+sinθtϕ˙t$
(10b)

In (9)–(10), m is the wing's mass (including the added mass given by the tethers) and g is the gravity acceleration. Finally, $Eeqt≜CLtCD,eqt$ the wing's equivalent efficiency, which accounts for the drag of both the wing and the lines.

The actual mechanism with which the steering angle, δ, is manipulated depends on the system's design. In references 26 and 29, where a single-line system is considered, the steering deviation is given by an actuator placed in a control pod, hung just below the wing. In references 31 and 32, where a three-line system is considered, the steering deviation is obtained by means of an actuator installed on the ground station, able to change the difference of length of the so-called wing's steering lines. A derivation of model (9)–(10), related to the latter system, is provided in reference 31, together with extensive remarks. It is worth recalling some of such considerations here. According to equation 9, there is basically an integrator between the control input δ(t) and the velocity angle γ(t), with a time-varying gain. In the first term of equation 10a, it can be noted that such a gain increases as the wing's speed does; thus, a larger speed provides higher control authority but it can also bring forth stability issues, if the control system is not properly designed. Equation 10b also implies that a larger area-to-mass ratio gives in general a higher gain, $K¯$, and that the steering behaviors of wings with similar design (i.e. similar aerodynamic coefficients) but different sizes are expected to be similar, provided that the area-to-mass ratio, $Am$, does not change much when the size is scaled up.

Equations 9–10 are confirmed by experimental data, as evidenced in Fig. 13a for a 9-m2 wing, with CL = 0.8, Eeq = 5.6, m = 2.45 kg, where the gray dots represent experimental data collected in the whole range of θ, Φ spanned by the wing during operation, while the black dots represent values collected when Φ ≤ 5̊, i.e. in cross-wind conditions. The linear relationship computed by using the lumped parameters, as given by model 10, matches quite well with the measurements, even with larger values of Φ, in the range ±35̊. Finally, Fig. 13b shows an example of the matching between the trajectory of $γ˙$ during figure-eight paths with a 6-m2 wing, with CL = 0.6, Eeq = 5.1, m = 1.7 kg, and the estimate given by models 9–10. The dynamical model 9–10 can be employed to design a control algorithm for the wing, as described in the next section.

## Automatic control of tethered wings in crosswind flight

The approach described here 29, 31, aims to simplify the control problem by using a hierarchical structure, where the nonlinear part of the controller is kept at the outermost level, while the inner controllers are linear and can be designed following standard techniques. A scheme of the overall control system is reported in Fig. 14.

FIGURE 14 Overview of a control system for crosswind flight of a tethered wing.

The aim of the innermost control loop is to achieve a desired steering deviation δ, by manipulating the electrical input to the actuation system. The middle control loop, designed on the basis of the wing's steering dynamics described above, employs the wing's velocity angle (or heading) as feedback variable, and provides the actuation controller at the lower level with a reference steering deviation, in order to track a desired velocity angle 31. The latter is issued by the controller at the outermost level, which computes the desired velocity angle on the basis of the wing's position relative the ground station and/or the wind direction, in order to achieve crosswind flying paths. Some of the considered feedback variables (most notably the wing's velocity angle and/or heading) are typically not directly measured; hence a suitable measurement and estimation system (see Fig. 14), comprising sensor fusion and filtering algorithms, must be implemented 32.

## Conclusions and future opportunities

Airborne wind energy systems have undergone rapid and steady technological development over the past decade, with several organizations demonstrating basic economic and technical viability of their concepts. This article summarizes several proof-of-concept prototype systems and dozens of aerodynamic, dynamic, and control analyses that have taken place amongst these organizations. The theoretical and numerical analyses performed so far indicate that crosswind systems have the potential to achieve a power curve similar in shape to that of current commercial wind turbines, with rated power of 2 to 5 MW. When combined with lower construction costs and with the stronger winds available up to 1000 m above the ground, such generators would be competitive with fossil fuels and usable in a wide range of locations around the world 24, 34. Several experiments with smaller prototypes, in the range of tens of kW, show encouraging results.

Ongoing development activities are increasingly the viability of the concept, yet several technical issues remain and need to be addressed, in order to definitively show that this technology can be scaled up to industrial size (i.e. 2-MW rated AWE generators). Aspects like grid connection, line wear, and maintenance for large scale generators still need to be addressed. Automatic control systems have only been tested for a limited amount of time. The operation and control of AWE farms, required to obtain utility-scale power production, will pose additional technical challenges related to the coordination of the different generators.

AWE technologies are at the dawn of their development, and there is significant untapped potential for the use of innovative solutions in multiple fields like materials, power electronics and aerodynamics, to tackle the above-mentioned problems. These challenges present a wealth of opportunities for future, multidisciplinary research and development activities.

## Acknowledgments

This research has received funding from the California Energy Commission under the EISG grant n. 56983A/10-15 “Autonomous flexible wings for high-altitude wind energy generation,” and from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n. PIOF-GA-2009-252284 - Marie Curie project “Innovative Control, Identification and Estimation Methodologies for Sustainable Energy Technologies.”

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