A Trajectory Controller for Kite Power Systems

with Wind Gust Handling Capabilities

Manuel C. R. M. Fernandes, Gonc¸alo B. Silva, Lu

ıs Tiago Paiva and Fernando A. C. C. Fontes

SYSTEC–ISR, Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, Porto, Portugal

Keywords:

Renewable Energy, Airborne Wind Energy, Kite Power Systems, Nonlinear Systems, Path-following Control,

Safe Mode Control.

Abstract:

In this paper, we address the generation of electrical power using Airborne Wind Energy Systems, comprising

a kite connected through a tether to a generator on the ground. We design a controller to steer the kite to

follow a pre-deﬁned periodic path, which includes a production mode, a tether retrieval mode, and a safe

mode capable of handling wind gusts.

1 INTRODUCTION

Electrical energy is crucial to satisfy modern human

needs, while the amount of energy available is directly

associated with development. Currently, the majority

of electrical energy generated worldwide comes from

fossil and nuclear fuels, which are now facing increas-

ing societal concerns of environmental sustainability.

To address these problems, countries are enact-

ing energy policies to encourage the use of renew-

able energies. In this context, in the last decades

there has been a fast growth and development of re-

newable energy systems. Very recently, Portugal’s to-

tal renewable energy production in March 2018 ex-

ceeded the country’s electricity consumption for the

month. Among the renewable energy sources, wind

is an important large scale alternative. Wind energy

is nowadays mainly extracted on-shore at low heights

by wind turbines mounted on towers with a few dozen

meters (50-200 m) and, despite the signiﬁcant num-

ber, still growing, of wind farms, most of the existing

wind energy remains unexploited since it is available

at high altitudes and off-shore.

One of the promising technologies to exploit the

stronger and more consistent high altitude and off-

shore winds is Airborne Wind Energy (AWE), namely

Kite Power Systems (Ahrens et al., 2013; Schmehl,

2018). These systems use a kite, with ﬂexible or rigid

wing, that is connected to a generator through a ca-

ble (tether). Most of such systems are based on ex-

ploiting crosswind kite power described by Loyd in

1980 (Loyd, 1980). The huge power that can poten-

tial be harvested from AWE systems is supported by

the facts that wind speeds grow fast with height and

that the aerodynamic lift is proportional to the square

of the apparent wind velocity

lift

/2c

(α)Av

. (1)

Thus, the maximum power extraction is obtained

when the kite ﬂies at high speeds in direction perpen-

dicular to the direction of the wind, which requires

this trajectory to be periodic.

In a kite power system with a ﬁxed generator on

the ground, which is our case, electrical power is gen-

erated as the kite rises by the wind, which causes the

cable to be unrolled and subsequently the generator

to produce electricity (see Figure 1). Since the cable

length is ﬁnite, when we reach that limit the cable is

retrieved with a minimum energy expenditure and the

process is repeated.

To automate this process and guarantee a positive

net power output it is necessary to design a controller

taking into account variations in wind direction and

intensity, among other factors.

Using a 3D simulation model of the kite dynam-

ics, considering all the forces acting on it, we design

a controller to follow a desired path. Then we ad-

dress the problem of handling wind gusts. When wind

reaches a certain speed threshold, where tether force

might be excessive, we activate gust mode in order to

prevent damage to the kite or other components. We

do this by stopping the kite reel-out (or reel-in, in case

the gust occurs in recovery mode), and directing it up-

wards to an equilibrium inclination. We set the angle

Fernandes, M., Silva, G., Paiva, L. and Fontes, F.

A Trajectory Controller for Kite Power Systems with Wind Gust Handling Capabilities.

DOI: 10.5220/0006914205330540

In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 1, pages 533-540

ISBN: 978-989-758-321-6

533

Table 1: Nomenclature.

A wing reference area of kite





rotation matrix from G to L

tether reel–out acceleration



−2



rotation matrix from L to G

aerodynamic drag coefﬁcient r tether length [m]

aerodynamic lift coefﬁcient ρ air density



kgm

−3



E energy produced [Ws] T tether tension [N]

aer

aerodynamic force [N] v

apparent wind velocity



−1



drag

drag force [N] v

wind velocity



−1



cent

centrifugal force [N] v

tether reel–out velocity



−1



cor

Coriolis force [N] u control vector

lift

aerodynamic lift force [N] x state vector

inert

inertial forces [N] α angle of attack [rad]

tether force [N] φ azimuthal angle [rad]

g gravitational acceleration



−2



β elevation angle [rad]

m mass [kg] ψ roll angle [rad]

P power produced [W] γ reference tracking angle [rad]

p kite position [m] τ local tangent plane

Figure 1: Example of a kite power system in the reel-out

phase (Argatov et al., 2009).

of attack to a high value, in order to have a low lift

force and consequently a low tether tension force.

This technology is still not completely developed

at a commercial stage. Therefore, there is a win-

dow of opportunity for new challenges, namely in

the development of new controllers and continuous

improvements to existing methodologies. A similar

principle can be applied when the kite moves in an-

other ﬂuid, such as water. An example is explored in

(Paiva and Fontes, 2017).

In the approach proposed here, the trajectory con-

troller acts on the roll angle to change the kite heading

direction in order to follow a moving reference point

belonging a desired path (see (Prodan et al., 2015),

(Caldeira and Fontes, 2010) for other approaches on

path-following control). Also, a innovative wind gust

mode is developed and tested. The numerical results

report that such strategy allows us to handle strong

wind velocities, preventing the system to crash, with-

out having to completely retract the kite.

This paper is organized as follows. In section 2,

we describe a model for the kite power system. In

section 3, we describe the design of a controller that

allows the kite to follow a desired path. In section 4,

we address the wind gust problem and how we handle

it. In section 5, we provide results obtained from our

simulations. In section 6, we summarize the conclu-

sions.

2 KITE POWER SYSTEM MODEL

2.1 Coordinate System

The dynamics of the kite are modelled in a spherical

coordinate system positioned at the center of mass of

the kite, see (Paiva and Fontes, 2018; Canale et al.,

2010). We consider three coordinate systems:

Global G: An inertial Cartesian coordinate system

(x,y,z) where the origin is on the ground at the

point of attachment of the tether and x is aligned

according to the wind direction v

= (v

,0,0).

The basis of this coordinate system is (

Local L: A non-inertial spherical coordinate system

(r, φ, β). The basis of this coordinate system is

(

) (Fig. 2).

Body B: A non-inertial Cartesian coordinate system

attached to the kite body. The basis of this co-

ordinate system is (

), with

coinciding

with the kite longitudinal axis pointing forward,

in the kite transversal axis pointing to the left

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

534

Figure 2: Global and Local coordinate systems (Paiva and

Fontes, 2018) .

Figure 3: Body coordinate system (Paiva and Fontes, 2018).

wing tip, and

in the kite vertical axis pointing

upwards (Fig. 3).

We consider the position

p =













r cos(β) cos(φ)

r cos(β) sin(φ)

r sin(β)





the rotation matrix from L coordinate system to G









cos(β)cos(φ) −sin(φ) −sin(β)cos(φ)

cos(β)sin(φ) cos(φ) −sin(β)sin(φ)

sin(β) 0 cos(β)





and the rotation matrix from G coordinate system to

= R

−1

= R

The apparent wind velocity is v

= v

−

p. We

assume that its radial component v

a,r

is strictly pos-

itive and that the kite body longitudinal axis aligns

naturally with the apparent wind velocity, that is

−v

/kv

k. Consider the local tangent plane τ, which

tangent to a sphere centred at the origin and contains

the axis

and

Let ψ be the roll angle measuring rotation around

the longitudinal axis (

). We consider that initially,

for ψ = 0,

is in the plane τ. Deﬁne ˜e

to be the

“unrotated” axis, with ˜e

when ψ = 0. We have

that ˜e

⊥

, and ˜e

⊥

. Thus, we can then deﬁne

˙p

lift

drag

grav

Figure 4: Forces acting on the kite (Paiva and Fontes, 2018).

˜e

. Finally, we consider the kite body has

an anti-clockwise rotation of ψ around the

axis: the

roll angle.

We assume here that the roll angle ψ can be con-

trolled directly. For example, in a two line kite where

d is the distance between attachment points and ∆r

is the relative difference between the lengths of each

line, we have sinψ = ∆r/d (cf. (Diehl, 2001)). Using

Rodrigues’ formula to rotate ˜e

by ψ around

, we

obtain

= ˜e

cosψ + (

× ˜e

)sinψ +

(

· ˜e

)(1 − cos ψ)

and ﬁnally, we deﬁne

to be

2.2 Acting Forces

The total force acting on the kite can be decomposed

into the tether, gravity, and aerodynamical compo-

nents (see Fig. 4)

p =

grav

aer

(α) (2)

where

= −T





−T





grav

= −mg





−mg









−mg sin β

−mg cos β





aer

(α) =

/2ρAkv

(α)

− c

(α)

In the local coordinate system

p =





¨r

φcos(β)









−r

− r

cos

(β)

2˙r

φcos(β) − 2r

βsin(β)

2˙r

β + r

cos(β)sin(β)





| {z }

−

inert

(3)

A Trajectory Controller for Kite Power Systems with Wind Gust Handling Capabilities

535

where the second term is −

inert

with

inert

repre-

senting the inertial forces (centrifugal and Coriolis) in

the local coordinate system.

Denoting the total resulting force by F, we have

F = m





¨r

φcos(β)





grav

aer

(α) +

inert

(4)

We assume that the tether acceleration ¨r can be con-

trolled directly by a

. Denoting by T the tension on

the tether at the base, we have T = F

− ma

. We also

assume that the angle of attack α and the roll an-

gle ψ can be controlled directly, possibly by varying

the differential lengths of the cable in the kite bridle.

Deﬁning the state x =



r, φ, β, ˙r,

φ,



and the control

u = (a

,α,ψ), the dynamic equation is

x(t) = f (x(t),u(t))







˙r













˙r

mr cos(β)







. (5)

2.3 Equilibrium Inclination

In strong winds or when the tether is being recoiled

sufﬁciently fast, it is possible to maintain the kite at

an equilibrium point with β = β

, φ = 0, and with the

angular velocities and angular accelerations equal to

zero.

Consider the case of high values of the appar-

ent wind speed, when the aerodynamical lift force is

much higher than gravity. In such case

T =

lift

drag

and when ˙r = 0, the drag is aligned with the wind,

horizontal, and the lift is vertical. Therefore

= arctan

lift

drag

= arctan





When the angle of attack varies between 0

and

degrees, the equilibrium inclination varies be-

tween 87

and 85

. For higher angles of attack, we

obtain lower lift to drag ratios and lower equilibrium

inclinations. At 13.3

we have a β

∗

= 76

3 TRAJECTORY CONTROLLER

The total cycle consists of a production phase when

the tether is reeled-out (˙r > 0) until a maximum value

of tether length r

max

is attained. Then, follows a re-

traction phase when the tether is reeled-in (˙r < 0) until

a minimum value of tether length r

min

is attained.

In order to have a predictable behaviour and op-

timize the energy produced by the system, the kite

should track a pre-deﬁned path. In the production

phase, we deﬁne the path of Figure 5 in the spherical

rectangle β ∈ [30, 50], φ ∈ [−40,+40] degrees, where

the kite should move almost cross wind. In the retrac-

tion phase, the kite goes to the vertical plane φ = 0,

raises the elevation angle to the equilibrium inclina-

tion, and pulls back the tether.

We deﬁne the desired production path on a (φ,β)

coordinate system, making it independent of the

tether length. We use a reference target approach to

control the heading direction of the kite. Given the

position of the mass-point of the kite p(φ,β) not in

the desired path, we determine the closest point to the

desired path (A). Then, a reference target B is deﬁned

as the point distancing L from A in a forward direction

along the path. An auxiliary vector

is computed

between p and B (see Figure 5).

Finally, we compute the angle (γ) between the kite

velocity ˙p and

, which serves as a reference to the

desired heading direction adjustment, so that the de-

sired path is rejoined at B. In order to control the an-

gle (γ) towards zero, we act on the roll angle ψ using a

proportional controller: ψ(t) = Kγ(t). The kite trajec-

tory control through the heading directions, acting on

the roll angle using a proportional controller has been

shown to be an adequate steering command (Fagiano

et al., 2014).

A B

˙p

Figure 5: Trajectory Controller.

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

536

4 HANDLING WIND GUST

Although the trajectory controller system is resilient

enough to support certain strong wind velocities, the

resultant tether tension force might be overwhelming

for the kiteline or other components. Therefore, for

security purposes, a method to handle wind gusts in a

robust way is crucial.

The chosen response strategy for wind velocities

that we consider above the safety limit consists in el-

evating the kite towards the zenith, to an equilibrium

inclination and centring it (i.e. φ=0), by controlling

the roll angle ψ (see Figure 7). Also, the tether reel-

ing is stopped and the angle of attack is set to a high

value, guaranteeing a low lift force and a high drag,

stalling and decelerating the kite. The low lift force

minimizes the tether tension and the stalling avoids

uncontrollable movements.

When the wind velocity returns to lower values,

the system resumes the normal production or retrac-

tion phase, depending on which phase was interrupted

by the wind gust.

Simulation results are described in the next sec-

tion.

5 SIMULATION RESULTS

We consider the simulation parameters of the kite sys-

tem deﬁned in table 2.

Table 2: Simulation Parameters.

Parameter Value

ρ 1.2 kgm

−3

10 ms

−1

g 9.8 m s

−2

m 0.7 kg

A 0.28 m

The aerodynamic coefﬁcients were obtained by

making a linear regression from data in (UIUC, 2018).



(α) = 0.3 + 0.1α, 0 < α < 12

(α) = 9.9 − 0.7α, 12 < α < 15

(α) = 0.012 + 0.01α

For the simulations we use the software Simulink,

where we build the model presented above and design

the controllers.

5.1 Fixed Tether Length

We start by simulating how the kite reacts to a wind

gust when the tether is on a ﬁxed length. As we can

see in Figure 7, the kite follows the prescribed path

and when the gust begins, the kite elevates to an equi-

librium inclination and is centred in φ. When the wind

velocity returns to normal values, the kite descends

and resumes to follow the desired path.

As we can see in Figure 8, when the gust mode

is activated, the tether force is small, as is desirable

when handling strong winds. In this simulation we

have ﬁrst a wind velocity of 10 m s

−1

, then we in-

crease the velocity to 30 m s

−1

, above the wind gust

threshold, and ﬁnally we reduce it to 20 ms

−1

5.2 Complete Production Cycle

Now we see an example of a complete production cy-

cle, with the reel-out and reel-in of the tether. As we

can see on ﬁgure 9, as the kite rises and a wind gust

occurs, the reeling out of the tether is stopped and the

kite is elevated to an equilibrium point, returning to

the trajectory as wind velocities return to lower val-

ues.

On ﬁgure 11 we can see the state variables (r,φ,β).

We clearly see the wind gust occurring between

[200,250]s, as r stays constant, φ goes to zero and the

elevation angle β rises. On ﬁgure 12 we can see the

control variables, and as supposed, during the wind

gust we have a high angle of attack (α) and ψ is zero

since the kite is centered on φ = 0. Finally, on ﬁgure

10, we can see energy is produced during the reel-

out phase, and a negligible amount is spent during the

reel-in phase. During the gust mode, energy is neither

produced or spent.

6 CONCLUSIONS

Using a 3D dynamic simulation model of a kite power

system, considering the forces acting on it, we de-

velop here a method to control the kite to follow a

pre-deﬁned path. The prescribed path is deﬁned only

by the minimum and maximum values of φ and β,

independently of the tether length and reel in veloc-

ity. The steering controller in the production path-

following phase is based on the adjustment of the roll

angle (ψ), working with a constant angle of attack.

Although this procedure has shown itself robust for

high wind speeds, a safety mode to avoid excessive

strain on the tether and other components was devel-

oped.

A Trajectory Controller for Kite Power Systems with Wind Gust Handling Capabilities

537

Figure 6: Simulink System.

Figure 7: Kite reacting to wind gust.

Figure 8: Tether force.

The angle of attack plays an important roll to bal-

ance both drag and lift aerodynamic forces and the

resultant tether tension. In the event of wind gusts,

we adjust the angle of attack to an appropriate value

that decreases the tether tension. Moreover, at the

same time the kite is driven towards the zenith where

it can handle the excessive energy contained in the

wind gust.

Figure 9: Trajectory example with wind gust.

ACKNOWLEDGEMENTS

We acknowledge the support of FEDER/-

COMPETE2020/NORTE2020/POCI/PIDDAC/-

MCTES/FCT funds through grants SFRH/BPD/-

126683/2016, PTDC-EEI-AUT-2933-2014|16858–

TOCCATA, and 02/SAICT/2017-31447|POCI-01-

0145-FEDER-031447|FCT–UPWIND.

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