Jtam-A4.dvi

JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

53, 1, pp. 195-207, Warsaw 2015
DOI: 10.15632/jtam-pl.53.1.195

PERFORMANCE ASSESSMENT OF A 2 DOF GYROSCOPIC WAVE

ENERGY CONVERTER

Alessandro Battezzato

Center for Space Human Robotics, Istituto Italiano di Tecnologia, Torino, Italy

Giovanni Bracco, Ermanno Giorcelli, Giuliana Mattiazzo

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy

e-mail: giovanni.bracco@polito.it

Wave Power is one of the most investigated energy sources today. So far, several devices
have been tested and built up to the pre-commercial stage. ISWEC (Inertial Sea Wave
Energy Converter) has developed at the Politecnico di Torino, exploiting gyroscopes to
extract wave energy. It allows power extraction without using any moving part immersed
intowater.Thepreviousversionof ISWECpresented 1DOF(DegreeOfFreedom), therefore
requiring alignment of the device to the incomingwave; this paper describes a novel version
of ISWEC, with 2 DOFs and consequently able to absorb power from every wave direction.
The kinematics and the dynamics of the device are investigated, in order to compare the
1 DOF and the 2 DOF architectures from the point of view of the extracted power. The
resulting simulations show that the 1 DOF prototype is more efficient when aligned with
the incoming wave, while the behavior of the 2 DOF device is substantially independent of
the wave direction. Such a difference of the performances is quantified and discussed along
with considerations on the design and realization of the full-scale prototype.

Keywords: gyroscope, wave power, flywheel, hydrodynamics, renewable energy

1. Introduction

Ocean is a wide source of different kinds of energies such as tides, marine streams, salinity
gradients, temperature gradients and wave power. Wave power is the discipline studying the
extraction of energy from seawaves. Until now,wave power is still a developing technology, even
though research on sea power exploitation began in the early stages of the 19th century. At the
time of writing, the field is growing with great interest from the big players of industry (Chen
et al., 2013). Consistent investments have been made on the sector and several devices already
reached the pre-commercial stage.

The Wave Energy Converters (WECs) proposed until now exploit different physical princi-
ples. This results in a variety of morphologies and sizes of the devices. WECs can be classified
according to their position with respect to the sea (floating, tethered or submerged) and to
their dimensions compared to the incomingwave: point absorbers, having dimensions negligible
with respect to the wave length, attenuators, with their length comparable to the wave length,
and terminators, having width comparable with the wave length. WECs can also be classified
according to the working principle: Oscillating Water Columns (OWC), oscillating bodies and
overtopping devices (Falcão, 2010; Torre-Enciso et al., 2010; Sorensen and Friis-Madsen, 2010;
Le Crom et al., 2009; Lucas et al., 2007; Pizer et al., 2005).

The OWC is one of the first WECs ever investigated: since 1940 in Japan Masuda has
designed and built several prototypes operating in real sea conditions. TheOWC is a terminator
composed of a submerged concrete or steel structure, open below thewater level. The oscillating

196 A. Battezzato et al.

motion of the internal water level produced by the incident waves forces the air contained inside
the chamber to flow through a turbine driving an electrical generator. Since the turbine must
be bidirectional, theWells turbine is themost used in this kind ofWECs. Several realizations of
OWCwere completed, among which the Pico plant, Azores, Portugal in 1999 and the LIMPET
plant in Islay island, Scotland in 2000. Afloating version of theOWCwas realized by the project
OSPREY in UK, 2005.

The class of oscillating bodies includes floating devices and submerged devices. Dexawave
(DK) and Pelamis (UK) are two floating devices exploiting the wave induced relative motion
of two or several floating bodies to produce energy. In the joints connecting the bodies, there
is an energy conversion system composed of hydraulic rams acted by the relative motion of the
bodies, a hydraulic circuit to stabilize the oil flow coming from the alternatemotion of the rams
and a hydraulic motor driving the electric generator. The energy conversion system is usually
referred to as Power Take Off – PTO. Another oscillating body device is the AWS (UK). It is
a submerged device composed by a fixed part moored to the seabed and a vertical sliding cap
separated with an air chamber. As waves approach the device, the hydrostatic pressure on the
top of the cap changes making it oscillate vertically and acting linear electric generators. The
stiffness of the air chamber can be changed to tune the device on the incoming wave.

The last category of overtopping devices is represented mainly by terminators: they convey
waves ona slopeand collectwater onan elevated reservoir: theproductionof energy is performed
by returning the water to the sea level through a low-head turbine coupled with a generator.
An example of realization of the machine is represented by the Danish projectWave Dragon.

One of the problems to be solved in a WEC is the so called “reaction problem” (French,
2006): in order to extract power from the sea surface with a force, a reaction to that force
must be provided. In his analysis, French highlighted that the reaction force can be given in
four different ways: reacting on a large structure bigger than the wavelength and therefore
hydrodynamically stable, reacting to the seabed, reacting on a mass that is part of the WEC
and reacting against a part of the sea. Except for the third choice, the other possibilities imply
the use ofmechanical parts inmotion while immersed into sea water or spray and thus the need
of expensive solutions such as reliable seals and corrosion protection techniques. In this article,
the system ISWEC (Inertial SeaWave EnergyConverter) is proposed. ISWECuses a gyroscope
to create an internal inertial reaction able to harvest wave power without exposed mechanical
parts. In fact, ISWEC externally presents as a monolithic float: the float rocks in reaction to
the incoming wave and the gyroscopic system is sealed inside.

The rotor dynamics is a discipline continuously investigated due to its several applications
(Ładyżyńska-Kozdraś and Koruba, 2012; Baranowski, 2013). The use of its inertial effects to
harvest wave power was investigated on a 1 degree of freedom ISWEC device (Bracco, 2012;
Bracco et al., 2010, 2011) proving its power absorption capacities. The 1 DOF device so far
proposed and investigated is unidirectional, meaning that the system must be aligned with the
incoming wave in order to absorb the maximum power, while the power absorption drastically
decreaseswhendiverging fromthis preferreddirection.Toovercome this problem, anovel 2DOF
ISWEC device has been derived: now the gyroscope can freely rotate about two orthogonal
axes, in order to decrease and ideally neglect the influence of the wave direction. This paper
deals with the investigation of the 2 DOF ISWEC system, in order to determine its power
conversion capabilities and its multi-directionality effectiveness. To perform such analysis, a
robotic approach is taken into account: first of all, the position of each linkage of themechanism
is described through the definition of a number of reference frames and proper DOFs, then
the velocities are investigated and finally the dynamical equations are written according to
the Lagrangian approach. Once the extracted power is analytically expressed, an optimization
process is carried out in order to find values of the coefficients of the stiffness and damping
elements of the ISWEC prototype maximizing the extracted power itself. Finally, a number

Performance assessment of a 2 DOF gyroscopic wave... 197

of simulations have been launched, in order to investigate the theoretical effectiveness of the
optimized 2 DOF prototype for the varying wave direction. The final results permit one to
take important design considerations and proper choices towards the realisation of a full scale
prototype of the ISWEC.

2. ISWEC working principle

As shown in Fig. 1, the ISWEC is a floating Wave Energy Converter externally appearing as a
monolithic hull with a slack mooring to the sea bed.

Fig. 1. ISWEC external view

Inside the ISWEC, there is a gyroscope that is carried on a 1 DOF or a 2 DOF (gimbal)
structure. In the 2 DOF system, the flywheel is carried on a gimbal allowing the flywheel to
precess with two degrees of freedom ε and λ. The PTOs (Power-Take-Off, the device converting
mechanical energy into electrical energy) in the representation of Fig. 2 are linear devices linked
to the inner platform of the gimbal and the hull.

Fig. 2. The 2 DOF ISWEC

The working principle of the device can be summarized in three main steps:

• The waves tilt the buoy

• Due to stiffness of thePTO, a fraction of this rotation is transmitted to the inner platform
of the gimbal perturbing the gyroscope

• Thanks to the inertial effect, the gyro starts its precession. By damping the precession and
restoring the initial condition, the PTOs produce energy.

The job of the PTOs is both to link the gyro to the gimbal and to damp the motion of the
gyro to extract energy. In Fig. 2, they are considered as four linear actuators but they can also
be rotary motors. In the second case, they are coupled directly on the axis of motion to damp,
their shaft on the mobile part and their carter on the still part. In this configuration, there are

198 A. Battezzato et al.

no restrains to the angles performed by the gimbal, and the gyro can freely rotate around the
two axis. Such a system, as shown in the next Sections, is omni-directional.
On the other hand, in the 1 DOF version shown in Fig. 3, the system must be pointed

towards the waves and in response to pitch motion of the float the systems precesses around
the coordinate ε driving in rotation a PTO. By controlling the PTO (Bracco et al., 2009) the
extraction of energy from the waves is achieved.

Fig. 3. The 1 DOF ISWEC

2.1. Equations of motion

The first step to study the kinematical and dynamical behavior of the ISWEC architecture
consists in assigning a coordinate reference system to each body composing the system. In fact,
given a reference system attached to a body, then the position and orientation of the body are
completely defined if the position and orientation of the reference system are known. First of
all, it is necessary to place a fixed reference system, referred to asCS0, whose axis z0 is directed
vertically. The direction fromwhich thewave is arriving is identified by the axis y0′ belonging to
CS0′, a reference system obtained fromCS0 through rotation of the angle β about z0 ≡ z0′. The
system CS1 is associated with the frame which carries the gyroscope: it is obtained from CS0
through rotation of the angle δ about the axis x0′ belonging toCS0′. Then, the flywheel is linked
to the frame through a pair of rings. The reference system named asCS2 is associated with the
external ring: it can be obtained from CS1 through rotation of the angle ε about y1 ≡ y2. On
the other side, the reference system CS3 is linked to the internal ring: it is obtained from CS2
through rotation of the angle λ about x2 ≡ x3. Finally, the reference system CS4 is associated
with the flywheel: it is obtained from CS3 through rotation of the angle ϕ about z3 ≡ z4. The
coordinate reference systems are represented in Fig. 4.

Fig. 4. Representation of the coordinate reference systems: (a) fromCS0 toCS1, (b) fromCS1 toCS4

Performance assessment of a 2 DOF gyroscopic wave... 199

Once the reference systems associated with the whole mechanism have been defined, then
it is possible to study the kinematics of the system. Given the previously introduced reference
systems, the following rotation matrices between successive reference systems can be expressed,
where jAi is the matrix that permits one to pass from a genericCSi toCSj

0
A0′ = rot(z0,β) =







cβ −sβ 0
sβ cβ 0
0 0 1







1
A2 = rot(y1,ε)=







cε 0 sε
0 1 0
−sε 0 cε







0′
A1=rot(x0′,δ)rot(z1,−β)=







1 0 0
0 cδ −sδ
0 sδ cδ













cβ sβ 0
−sβ cβ 0
0 0 1






=







cβ sβ 0
−sβcδ cβcδ −sδ
−sβsδ cβsδ cδ







2
A3 = rot(x2,λ)=







1 0 0
0 cλ −sλ
0 sλ cλ







3
A4 = rot(z3,ϕ) =







cϕ −sϕ 0
sϕ cϕ 0
0 0 1







(2.1)

In the previous (2.1) and in the following, letters c and s stand for cosine and sine respectively.
Moreover, if jAi in (2.1) is the rotation matrix between CSi and CSj, then the transposes of
(2.1) give the iAj rotation matrices between CSj andCSi.
The analysis of the velocities and accelerations of the ISWEC system is limited to the study

of the angular terms; in fact, given the previous description of the whole architecture, no linear
translations are taken into account in themodeling of the system. In the following equations, the
notation ii, ji and ki refers to the unit vectors respectively directed along the axes xi, yi and zi
of the systemCSi.Moreover, the apex i that precedes a generic vector

ia indicates that vector a
is expressed in the reference system CSi. When not specified, in the following, the vectors are
intended as expressed inCS0. The angular velocity ωi of the i-th reference system is

1
ω1 = δ̇

1A0′
0′i0′

2
ω2 =

2A1(ε̇
1j1+

1
ω1)

3
ω3 =

3A2(λ̇
2i2+

2
ω2)

3
ω4 = ϕ̇

3k3+
3
ω3

(2.2)

Time derivatives of (2.2) lead to the angular accelerations that are here reported

1
ω̇1 = δ̈

1A0′
0′i0′

2
ω̇2 =

2A1(ε̈
1j1+ ε̇

1
ω1×

1j1+
1
ω̇1)

3
ω̇3 =

3A2(λ̈
2i2+ λ̇

2
ω2×

2i2+
2
ω̇2)

3
ω̇4 = ϕ̈

3k3+ ϕ̇
3
ω3×

3k3+
3
ω̇3

(2.3)

Each velocity vector in (2.2) and (2.3) is expressed in its own reference system, except forω4 and
its time derivative, which are expressed in CS3. This is due to the axial symmetry hypothesis
of link 4, as explained in the following.
The successive step consists in the dynamical analysis of the ISWEC system; the reference

systems previously defined are supposed to be central, i.e. the inertial tensor of each body
with respect to the body reference system is diagonal and the origin of the coordinate system
coincides with the center ofmass. Hence, the inertial tensor of the i-th bodywith respect to the
i-th coordinate system is

i
Ii =







Ixi 0 0
0 Iyi 0
0 0 Izi






(2.4)

Each tensor is diagonal and constant only when expressed in its coordinate system; the only
exception is the flywheel that presents a diagonal inertial tensor also when expressed in CS3
due to its axial symmetry

200 A. Battezzato et al.

3
I4 =

3
A4
4
I4
3
A
⊤

4 =







cϕ −sϕ 0
sϕ cϕ 0
0 0 1













Ix4 0 0
0 Iy4 0
0 0 Iz4













cϕ sϕ 0
−sϕ cϕ 0
0 0 1






=







Ixy4 0 0
0 Ixy4 0
0 0 Iz4







(2.5)

where Ix4 = Iy4 = Ixy4. To solve the dynamics of the system, the Lagrangian approach can
be applied. To manage the problem, it is fundamental to properly define the unknowns of the
system. In fact, given the previously introduced angles, it is important to notice that some of
themwill be considered as given, while the other are unknowns and have to be calculated. First
of all, in the current model, the sea conditions are imposed: thus, the angle δ and its time
derivatives as well as angle β are known. Also the angle of rotation of the flywheel ϕ and its
derivatives are supposed to be imposed by the motor: in particular, the flywheel rotates at a
constant velocity ϕ̇, which leads to ϕ̈=0. Thus, the only unknowns in the currentmodel of the
system are the two passive angles ε and λ and their time derivatives. It is important to point
out that elastic and viscous elements are applied to the revolute joint between the frame and
the external ring described by the rotational stiffness constant and the damping ratio kε and cε.
Analogously, the elastic and viscous elements are also applied to the revolute joint between the
external and the internal ring: the rotational stiffness constant is kλ and the damping ratio is cλ.
Moreover, ε0 and λ0 are the values of the angles in the two rotational joints where the torque
springs give the null response, while ε̇0 and λ̇0 are the rotational velocities where the torque
dampers give the zero torque.
In order towrite theLagrangian equations of the system, the generalized coordinates qi have

to be chosen: they are the angles ε andλ. The generic Lagrangian equation for a dynamic system
is the following

(∂T

∂q̇i

)

−
∂T

∂qi
+
∂V

∂qi
+
∂D

∂qi
=0 (2.6)

where T is the kinetic energy of the system, V is the potential energy and D is the dissipation
function. In the current ISWEC model, T has only rotational terms, V takes into account
the presence of the elastic elements, while the viscous terms are included in the dissipation
functionD. In fact it is

T =
1

2
1
ω
⊤

1
1
I1
1
ω1+

2
2
ω
⊤

2
2
I2
2
ω2+

2
3
ω
⊤

3
3
I3
3
ω3+

2
3ω4
⊤ 3
I4
3ω4 (2.7)

and

V =
kε

2
(ε−ε0)

2+
kλ

2
(λ−λ0)

2 D=
cε

2
(ε̇− ε̇0)

2+
cλ

2
(λ̇− λ̇0)

2 (2.8)

If, on the other hand, the PTO components are four linear parts like in the example shown in
Fig. 2, previous equations (2.8) change slightly. Given kε and cε the linear spring constant and
damping ratio of the elements connecting the frame to the external ring, and kλ and cλ the
linear spring constant and damping ratio of the elements connecting the frame to the internal
ring, then equations (2.8) can be substituted by the following (2.9)1 and (2.9)2, respectively

V =
kε

2
[(r1ε−r1ε 0)

2+(r2ε−r2ε 0)
2]+
kλ

2
[(r1λ−r1λ 0)

2+(r2λ−r2λ 0)
2]

D=
cε

2
[(ṙ1ε− ṙ1ε 0)

2+(ṙ2ε− ṙ2ε 0)
2]+
cλ

2
[(ṙ1λ− ṙ1λ 0)

2+(ṙ2λ− ṙ2λ 0)
2]

(2.9)

where rij = |pij −qij|, with i = 1,2, and j = ε,λ. The vector pij gives the position of the
connection point between the ring and the corresponding PTO element; the vector qij gives

Performance assessment of a 2 DOF gyroscopic wave... 201

the position of the connection point between the same PTO element and the external frame.
The terms rij 0 and ṙij 0 express the linear offset, respectively associated with the elastic and
damping effect. Thus, two Lagrangian equations (2.6), written with respect to q1 = ε and λ,λ̇
are

E1ε̈+E2ε̇+E3ε̇λ̇+E4λ̇+E5 =0 L1λ̈+L2λ̇+L3ε̇
2+L4ε̇+L5 =0 (2.10)

It is noteworthy that the coefficients are not constants but functions of the angles ε and λ, too.
The system composed by equations (2.10) can be solved through a numerical software and the
trend of the angles ε andλ, as well as the kinematics of thewhole system can be calculated from
the initial conditions. Afterwards, also some dynamical outputs can be calculated; for example
the torque Tϕ that the motor has to apply to the flywheel in order to maintain the constant
velocity ε̇ is

Tϕ =(I4ω̇4+ω4× I4ω4) ·k3 (2.11)

At the same time, the torque actions that are exerted on the flywheel along the joint axes, where
the elastic and viscous elements are applied, are

Tε =−cε(ε̇− ε̇0)−kε(ε−ε0) Tλ =−cλ(λ̇− λ̇0)−kλ(λ−λ0) (2.12)

2.2. The small scale prototypes

Most of the experimental work relative to the 1 DOF ISWEC has been carried out on the
small scale prototype shown in Fig. 5mainly at the Politecnico di Torino but using test facilities
of theUnivertities of Edinburgh andNaples. The prototype has a rated power of 2.2W (Bracco,
2010), its flywheel has a diameter of 180mm, a moment of inertia of 0.0174kgm2 and spins at
2000rpm.

Fig. 5. The 1 DOF prototype in the wave tank at the Institute of Energy Systems of the University of
Edinburgh, UK

The1DOFprototypehas beendesigned to exploit thewaves produced fromthewave tankat
the University of Edinburgh. The reference frequency of the wave tank when producing regular
waves is 1Hz (Taylor et al., 2003). In order to understandwhich angularmotions are transferred
to the float, a preliminary hydrodynamic analysis based on previous experimental works has
been carried out, suggesting that the float will rock with an amplitude of motion equal to 2deg.
That analysis was actually verified one year later with the tank tests (Bracco et al., 2010).
In order to compare the 1DOFand the 2DOFdevice, the 2DOFprototype shown in Fig. 6

has been built with the same inertial characteristics.
Apart from themechanical architecture, themain difference between the two devices stands

in thePTO.The 1DOFdevice uses an electric PTOcontrolled by a commercial driver, whereas
the 2DOFprototype has pneumatic PTOs simulators coupledwith springs, in which the action
is regulated bypneumatic resistances put in the inlet of the chambers.Thepneumatic equipment
has been chosen because of the lack of commercially available linear generators of the required
size. In any case at these small scales, it is common practice to damp the produced energywhile
concentrating on evaluating the amount of such energy to make full scale production analysis.

202 A. Battezzato et al.

Fig. 6. The 2 DOF prototypemodel

3. Results and simulations

A number of simulations has been performed in order to study the system behavior and to
optimize some design parameters. The goal of this optimization process for the 2 DOF ISWEC
is to maximize Pd, the average power extracted from the system by the dampers evaluated in
steady-state conditions. Accordingly with the 1 DOF tests, in the following simulations, the
sea wave is described by the equation δ = δ0 sin(ωt), where δ0 = 2deg and the frequency ω is
equal to 1Hz.While the inertial terms of the rings are neglected, the flywheel that rotates at a
constant rotational velocity of ϕ̇=2000rpm has Ixy4 =0.0166kgm

2 and Iz4 =0.0174kgm
2.

Moreover, the elastic and viscous offset constants ε0 and λ0, ε̇0 and λ̇0 that appear in the
preceding equations are all set to zero. In addition, to guarantee the isotropy of themechanism,
the damping and spring coefficients about the two passive rotational joints are equal: thus, in
the following it is cε = cλ = c and kε = kλ = k. Hence, the first simulations are set in order to
find themaximumofPd for varying c and k. The numerical code used for the simulations is the
MATLAB ODE45 implementing the Runge-Kutta algorithm with a variable step. The angle β
is set equal to 30deg. The results of these simulations are plotted in Fig. 7 – themaximumofPd
occurs at c = 0.11, k = 22. Hence, the maximization of the power extracted from the ISWEC
system leads to these elastic and damping coefficients.

Fig. 7. Optimization of the coefficients c and k

Finally, given the system with the optimized c and k coefficients, the steady-state periodic
trend of the kinematic and dynamic variables of the system is reported. Figure 8a shows the
input sea wave oscillation, i.e. the trend of angle δ; the angle β is set equal to 30deg. Figure 8b

Performance assessment of a 2 DOF gyroscopic wave... 203

reports a quite sinusoidal trend of the angles ε and λwhile Fig. 8c shows their time derivatives.
All those variables proved to behave sinusoidally or quasi-sinusoidally on the field c, k explored
in this work. Figure 8d presents the torque actions Tε and Tλ, expressed in (2.12)1 and (2.12)2,
respectively.

Fig. 8. (a) Time plot of the system input δ; (b) time plot of position of the system 2DOF; (c) time plot
of velocity of the system 2DOF; (d) time plot of the torque applied to the PTOs in the 2DOF system

Fig. 9. (a) Time plot of the torque applied to the motor in the 2 DOF system (null mean value);
(b) time plot of the instantaneous power absorbed by the dampers in the 2 DOF system

The torque that the motor has to supply to the flywheel – calculated in (2.11) – is shown
in Fig. 9a. Finally, Fig. 9b reports the sinusoidal trend of the instantaneous powerPd,inst whose
value is the sum of the power terms Pd,inst,ε and Pd,inst,λ dissipated on the two revolute joints

Pd,inst,ε = cε(ε̇− ε̇0)
2 Pd,inst,λ = cλ(λ̇− λ̇0)

2 (3.1)

204 A. Battezzato et al.

These equations are valid for the rotational PTO, however similar expression can be formulated
in the case of linear PTO components

Pd,inst,ε = cε[(ṙ1ε− ṙ1ε 0)
2+(ṙ2ε− ṙ2ε 0)

Pd,inst,λ = cλ[(ṙ1λ− ṙ1λ 0)
2+(ṙ2λ− ṙ2λ 0)

2]
(3.2)

Figure 10a shows the time plot of the PTO shaft position in the 1 DOF system. The total
instantaneous power output coming from the 2DOF system is relatively smooth, whereas in the
1 DOF device it presents a peak about double with respect to the average value (see Fig. 10b).
Therefore, the 1 DOF device could be mechanically simpler and cheaper to build, but the cost
of the power electronics able to smooth such a variable power output could be relevant in the
total economic balance.

Fig. 10. (a) Angle of precession ε of the 1 DOF systemworking in rated conditions; (b) time plot of the
instantaneous power absorbed by the damper in the 1 DOF systemworking in rated conditions

Using the optimal c and k coefficients, the wave sea direction angle β is varied. Thus, the
influence of th angle β on the trend of Pd is reported in Fig. 11. It can be seen that the
2 DOF model is practically insensitive to the wave direction from the Pd point of view. On
the other hand, the 1 DOF system shows a better power absorption when aligned with the
incomingwave (2.2Wagainst 1.32W), whereas themore waves come from the side, the smaller
is the absorbed power. From this analysis, the 2 DOF device results are convenient in the field
52deg<β< 128deg.

Fig. 11. Average absorbed power with respect to sea wave direction β

Performance assessment of a 2 DOF gyroscopic wave... 205

4. Full scale considerations

By scaling the results according to Froude, as it is common practice with floatingWECs (New-
man, 1977), the full scale parameters summarized in Table 1 are obtained. That scaling process
has beendoneusing the reference sea ofAlghero, Italy, described through thePierson-Moskowitz
(Vicinanza et al., 2009) spectrumwith thepeakperiodequal to 6.7s anda significantwaveheight
equal to 1.19m (2007 yearly average values). According to Froude and being the two prototypes
designed to work at the 1Hz wave, when they are compared to the real sea they are about 1:45
scaled (6.72 = 44.9). Table 1 shows that the two prototypes are representative of a full scale
system with power of the order of the MW. The gyroscope needed to harvest such power is
relatively big if scaled directly from the prototype. However, this value can be split in different
gyros in the case the unique disc is not feasible. The angles ε and δ are not recalled in Table 1
because, according to Froude, they are the same between the scaled prototype and the real
system (scale factor = 0). The losses to maintain the gyro in rotation in the two prototypes are
of the same order of magnitude of the produced power because of the small scale and the gyro
spinning in the atmosphere. However, at the time of writing, a 1:8 scaled prototype with rated
power 214W is under construction. The prototype uses standard ball bearings and a vacuum
chamber to reduce the gyro losses below 10% of the produced power (Bracco et al., 2010), and
from the preliminary analysis the same technology can be used in full scale devices to achieve
effective power production.

Table 1. Froude scaling to full scale

Froude scale
Prototype Full scale

factor

Power (2 DOF) 3.5 1.32W 0.81MW

Power (1 DOF) 3.5 2.2W 1.34MW

Angular momentum 4.5 3.48kgm2rad/s 1E+08kgm2rad/s

Gyro mass 3 1.2kg 110ton

Gyro speed −0.5 2000rpm 300rpm

Wave period 0.5 1s 6.7s

5. Conclusions

In this paper, the 2 DOF ISWEC gyroscopic wave energy converter is proposed and analyzed
in order to investigate its effectiveness with respect to similarly conceived 1 DOF ISWEC ar-
chitecture. Such a comparison has been carried out in terms of capability of power extraction
at variable direction of the incoming sea waves. In detail, once the kinematics and dynamics of
the novel device have been solved, the spring and damping coefficients of the PTO have been
investigated within the field of interest in order to maximize the absorbed power of the 2 DOF
prototype. Such an optimized configuration has been analyzed in the time domain and compared
with the performance of the 1 DOF ISWECwith the same inertial characteristics. The 1 DOF
system is more convenient in terms of the power output, producing 2.2W against the 1.32W of
the 2DOFdevice.However, the power output of the 2DOFsystem ismuchmore regular around
itsmean value,meaning less investments in power electronics smoothing systems.Moreover, the
2 DOF system proved to be truly omni-directional, whereas the 1 DOF system performs better
only if aligned with the incoming wave. Future works will deal with the translation of these re-
sults into effective design considerations, whichwill be a guideline towards the full scale ISWEC
prototype.

206 A. Battezzato et al.

Acknowledgements

The presentworkwas realized in collaborationwithENEAon the agreementwith theMinistero dello

Sviluppo Economico “Accordo di ProgrammaPAR 2013”.

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Manuscript received March 17, 2014; accepted for print August 27, 2014