POWER ABSORPTION MEASURES AND COMPARISONS OF SELECTED WAVE
Laboratoire de M
ecanique des Fluides
Ecole Centrale de Nantes
1, rue de la Noe
Centre for Ships and Ocean Structures
Norges Teknisk-Naturvitenskapelige Universitet
Otto Nielsens v. 10
PO Box 200, Lillekaer
In this study, a selection of Wave Energy Converters (WECs)
with different working principle is considered. It comprises
a heaving device reacting against the seabed, a heaving self-
reacting two-bodies device, a pitching device, and a ﬂoating
OWC device. They are inspired by concepts which are currently
For each of these concepts, a numerical Wave To Wire
(W2W) model is derived. Numerical estimates of the energy de-
livery which one can expect are derived using these numerical
models on a selection of wave site along the European coast.
This selection of wave site is thought to be representative with
levels of mean annual wave power from 15 to 88 kW/m.
Using these results, the performance of each WEC is as-
sessed not only in terms of yearly energy output, but also in
terms of yearly absorbed energy/displacement, yearly absorbed
energy/wetted surface, and yearly absorbed energy per unit sig-
niﬁcant Power Take Off force. By comparing these criteria, one
gets a better idea of the advantages and drawbacksof each of the
In the last decade manyprojectsfor the developmentof wave
energy converters (WECs) have emerged all over the world, and
especially in Europe. Some of the proposeddesigns are very sim-
ilar to each other, at least from a hydrodynamical point of view.
In other cases the designs may have more particular features.
For devices that have been publicly announced, the avail-
able information is usually limited to sketches, pictures and an-
imations, and in some cases also dimensions and system layout.
Only few quantitative ﬁgures on the estimated or measured en-
ergy conversion are presently known.
The converted useful energy represents the income side of a
wave energy project. It may be estimated once the external di-
mensions, working principle, machinery function and local wave
resource are known. On the cost side the picture becomes more
complex, with contributions from design, fabrication, installa-
tion, operation, maintenance and eventually decommissioning.
As long as the technical solutions are uncertain or unknown on
a detailed level, cost estimates are inevitably hampered by large
In order to provide a benchmark for the income potential of
wave energy converters, the energy absorption for a representa-
tive selection of converter designs has been estimated. Such a
2011 by ASME
Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering
June 19-24, 2011, Rotterdam, The Netherlands
benchmark may later serve as a premise, setting the upper limits
to the cost for a design to be viable.
To our knowledge, there are only few published studies aim-
ing at comparing different WEC’s principles on a quantitative
basis. In , results of energy absorption and cost estimates are
given for 15 different WECs. They were obtained through tank
test experiments. One of the result of this study is the averaged
measured capture width ratio in irregular waves. They all fall
in the range [4-30%]. The present study distinguishes from this
previous study by the used methodology (numerical against ex-
perimental analysis), the selected WECs and the criteria used for
CRITERIA FOR COMPARISON OF WAVE ENERGY
The ultimate criterion for ranking WECs is the cost of elec-
tricity per kilowatthour. One could notice that it does not depend
on the size of the system, so it does not tell if large or small
systems are better.
This criterion depends basically on two quantities:
- The output power
- The cost of the system, including everything from fabrica-
tion, O& M, investment cost, insurances, to decommission-
The power can be assessed using numerical modeling or ex-
perimental tests, with a certain degree of accuracucy that one
should be aware of. The cost depends on many components. Ac-
cording to , they are:
- Absorber structure.
- Power Take Off system.
- Electrical Interconnection.
- Grid Interconnection.
- Substation to Substation Upgrade Cost.
- Communication, Command and Control.
- Installation Cost.
- Owners development Cost.
- Spares Provisioning
- General Facilities and Engineering
- Financial Fees
- Interest during Construction
- Annual Scheduled O&M Cost
- Annual Unscheduled O&M Cost
- Annual Insurance Cost
- Periodic Levelized Overhaul and Replacement Cost
Let the sum of the costs from the Absorber structure to the
Installation Cost be the Total Plan Cost (TPC). Usually, it is
agreed that all costs after installation (from Owner’s develop-
ment cost to Periodic LevelizedOverhaul and Replacement Cost)
are proportional to this Total Plant Cost. So, for sake of compar-
ison it is enough to compare the TPC between devices.
Let us discuss now criteria which could affect the cost of the
components of the TPC.
Roughly, one could say that the absorber structure cost will
depend on its displaced mass. However, this criterion is not fair
when most of the mass is water or concrete ballasts like it is the
case for some WECs. To take into account for this, one could
also consider the wetted surface of the WEC, which could give a
better idea of the structural costs (steel) of the structure.
When it comes to the PTO, it is well known that for the same
amount of output power, the higher the velocity the cheaper the
PTO system. Conversely, the higher the PTO forces, the more
expensive the PTO system will be. Therefore, the amount of
absorbed energy per unit of signiﬁcant PTO force should be a
The higher the mooring loads, the more expensive the moor-
ing system will be. It will also impact the installation cost.
Therefore, the signiﬁcant mooring force could be a good crite-
rion, but it was not retained in this study because the modelling
of the moorings was rough.
The mean output power per WEC is also relevant, because
the higher it is the less the number of WECs will have to be
installed for a given power rating.
Finally, the retained criteria for comparisons of the selected
WECs in this study are:
- Energy absorption
- Energy absorption / tons of displacement
- Energy absorption / square meters of wetted surface
- Energy absorption / unit of signiﬁcant PTO force
CONSIDERED WAVE ENERGY CONVERTER TECH-
Heaving buoy reacting against the seabed
This wave energy converter is inspired by the Seabased
WEC. It consists of a circular buoy ﬂoating on the ocean sur-
face. Through a wire it is connected to a machinery unit standing
at the sea bottom. The machinery consists of a linear generator
placed inside a steel hull mounted on a concrete ballast struc-
ture. A simpliﬁed sketch of the system is shown in Fig. 1, and a
picture including the different components is found in Fig. 2.
The design considered in this study is derived from the one
that has been extensively studied at Uppsala university. The
shape of the buoy is assumed to be circular with ellipsoidal cross
section. The system parameters used in the present study has
thus been obtained mainly from publication by this group, and
includes the PhD theses of Eriksson  and Waters , as well
2011 by ASME
FIGURE 1. SKETCH OF THE HEAVING BUOY REACTING
AGAINST THE SEABED
FIGURE 2. COMPONENTS OF THE SEABASED WEC
as a series of articles, [5–7]. Some material has also been gath-
ered from web pages on the internet.
Forthe connectionbetween the buoyand the machineryunit,
steel wire with plastic coating is assumed. The wire stiffness is
450kN/m. In the present study, the line is modelled as massless.
The total stroke length of the translator before the end stop
springs are engaged is 1.8m, i.e. the maximum amplitude from
the mid-position is 0.9 m. Energy absorption by the Power Take
Off system is modelled by a linear damping on the translator part
of the generator. The damping coefﬁcient is the main parameter.
In this study, it has been optimised for each sea state in order to
maximise the energy absorption.
The wetted surface of the buoy + the surface of the casing
of the generator is about 42m
. The mass of the anchors as well
as the mass of the buoy and the generator was considered for
the mass of system, because it is an essential component of the
system. It is estimated about 31 tons.
TABLE 1. SYSTEM PARAMETERS OF THE SEABASED
Property Value Unit
crossectional shape of the buoy ellipsoidal
long axis 1.5 m
short axis 0.63 m
draft 0.63 m
height 1.26 m
displacement 2.83 m
mass of the buoy 1000 kg
Wire stiffness 450000 kg/m
Stroke length 1.8 m
Mass of the translator 1898 kg
Signiﬁcant wetted surface 42 m
Signiﬁcant mass 31 tons
Tab. summarises the parameters.
Heaving self-reacting two-bodies device
It consists in an axi-symmetric, self-reacting point absorber,
operating in theheavemode. It is composed of two bodies sliding
one along each other. A simpliﬁed sketch of the system is shown
in Fig. 3. The bigger and deeper body is referred to the Float
while the shallower one is referred to the Torus. This WEC is
inspired by the WavebobWEC which is currently in development
in Ireland by the Wavebob company. Fig. 4 shows a picture of
the 1/4th scale model of the Wavebob which was tested at sea in
the Galway bay in Ireland.
Dimensions of the system were estimated from pictures or
data found on the internet. On Wavebob’s website , it is spec-
iﬁed that the diameter of the torus is about 20 meters. Using
that length as a reference, other dimensions were estimated from
pictures of the 1/17th scale model found in .
The PTO system is modelled as a linear spring+damper. In
addition, the possibility of tuning the natural frequencies of the
system by transferring some of the mass from the ﬂoat to the
torus has been considered. This will not affect the equilibrium
position of both torus and ﬂoat if the PTO provides a static force
which compensates the difference between gravity and buoyancy
forces. The PTO is then characterised by three unknownparame-
ters. They were optimised for each sea state in order to maximise
the energy absorption.
As the system is a self - reacting device, the weight of the
moorings and anchors are supposed to be small. They are not
taken into account in the estimation of the total mass of the sys-
2011 by ASME
FIGURE 3. SKETCH OF THE SYSTEM
FIGURE 4. 1/4 SCALE MODEL OF THE WAVEBOB AT SEA
tem. Hence, the overall mass is equal to the displacement, i.e
4958 tons. The wetted surface of the torus is about 420 m
wetted surface of the ﬂoat is about 1700 m
. The total wetted
surface is then 2120 m
Tab. 2 summarises the parameters which were used.
TABLE 2. HEAVING SELF-REACTING SYSTEM PARAMETERS
Property Value Unit
Outer diameter (torus) 20 m
Inner diameter (torus) 10 m
Draft (torus) 2 m
Displacement (torus) 278 m
Diameter at WL (ﬂoat) 8 m
Draft (ﬂoat) 50 m
Displacement (ﬂoat) 4680 m
Stroke length 6 m
Wetted surface 2120 m
Total mass 4958 tons
Pitching device on a ﬂoating platform
This device consists in four hinged ﬂaps which are all con-
nected to the same frame. Via PTO systems, the relative motion
between each ﬂap and the main frame is converted into useful
energy. A simpliﬁed sketch of the system is shown in Fig. 5. It
is inspired by the Langlee WEC. Fig. 6 shows an artistic view of
a full scale Langlee WEC.
FIGURE 5. SKETCH OF THE PITCHING SYSTEM
Dimensions of the system were obtained from  and from
pictures and data found on the internet . The width of the
system is 25m.
The PTO system is supposed to behave like an ideal linear
damper + spring system proportional to the relative pitch motion
of the ﬂaps. As in the previous case, it is not necessary that the
mass of each individual component of the system (ﬂaps, frame)
balances its own displacement. Only the overall mass and dis-
placement must be balanced. It means that the ﬂaps can have
a positive buoyancy, if it is balanced by additional mass in the
frame part of the system. This provides a way of tuning the nat-
2011 by ASME
FIGURE 6. ARTISTIC VIEW OF THE LANGLEE WAVE EN-
TABLE 3. PITCHING DEVICE PARAMETERS
Property Value Unit
Width (ﬂap) 9.5 m
Draught (ﬂap) 8.5 m
Thickness (ﬂap) 2 m
Displacement (ﬂap) 185 m
Length (Frame) 25 m
Width (Frame) 25 m
Draught (Frame) 12 m
Displacement 673 m
Signiﬁcant wetted surface 2160 m
Signiﬁcant mass 1410 tons
ural frequency in pitch of the ﬂaps.
As in the previous case, the PTO is characterised by three
unknown parameters. They were optimised in order to maximise
the energy absorption.
The displacement of each ﬂap is equal to 185 tons and the
displacement of the frame is 670 tons. Hence, the overall mass is
1410 tons. The wetted surface of each ﬂap is about 890 m
wetted surface of the ﬂoat is about 1240 m
. The total signiﬁcant
wetted surface considered here is then 2160 m
Tab. 3 summarises the parameters which were used.
Floating OWC device
This device is a particular type of OWC device known as the
backward bent duct buoy(BBDB) ﬁrst proposedby Masuda .
It has a submerged opening aligned downstream of the incident
wave propagation direction. It has a single air chamber and is
free to move in six degrees of freedom. The device is constructed
of thin walls enclosing the water column. The PTO system is
provided by means of an air turbine connected to an electric gen-
erator. The motion of the water column relativeto the OWC body
creates oscillating pressure in the chamber and air ﬂow through
the turbine. A relief valve provides a way to keep the pressure
in the air chamber within acceptable limits to prevent the turbine
The design considered in this study is inspired by the OE
Buoy which is developed by Ocean Energy Ltd. in Ireland .
Fig. 8 shows a picture of the 1/4th scale model of the OE Buoy
which was tested at sea in Galway Bay in Ireland. A simpliﬁed
sketch of the system is shown in Fig. 7.
FIGURE 7. SKETCH OF THE FLOATING OWC DEVICE
FIGURE 8. 1/4 SCALE MODEL OF THE OEBUOY AT SEA
Losses, with the effect of reducing the body motions and
2011 by ASME
TABLE 4. FLOATING OWC DEVICE PARAMETERS
Property Value Unit
Length 50 m
Width 24 m
Draft 13 m
Height of submerged opening 8 m
Signiﬁcant wetted surface 3800 m
Signiﬁcant mass 1800 tons
the volume ﬂow available to the turbine, are included. External
restoring forces are contributed by moorings, whose contribu-
tion is assumed to be a small stiffness in surge. In this study we
assume a linear pressure-volume ﬂow relationship for the air tur-
bine, whereit is possible to tune the load resistance of the turbine.
This parameter has been optimised in this study to maximise the
The displacement of the device is 1800 m
and its wetted
surface is 3800 m
. For a fair comparison with the other devices,
we have not included the inner wetted surface of the device. Tab.
4 summarises the parameters.
For each one of the ﬁrst three WECs, a Wave to Wire model
was developedin the time domain. The waves and ﬂuid-structure
interactions were modelled using linear potential theory, and the
waves were assumed to be mono-directional. Hydrodynamic
functions and coefﬁcients were calculated using the BEM codes
WAMIT, Aquaplus  or Achil3D .
The force applied by the PTO systems was modelled as lin-
ear. Depending on the considered WEC, it can include a spring
and a mass term as well as a damping term. This linear modelling
of the PTO is usual in the wave energy ﬁeld. In technical solu-
tions, the PTO behaviourmight depart from this linear behaviour.
For instance, with hydraulic systems, the PTO behaviour will be
more of the Coulonb damping type. However, it is well known
from the early work of energy pioneers  that a PTO with a
linear behaviour allows to maximise the energy absorption when
its coefﬁcients are properly tuned. With irregular waves, a lin-
ear PTO with parameters optimised for each sea state still gives
power absorption close to maximum . One could note also
that the PTO system can be controlled in order to behave lin-
early , or that with proper settings of the PTO parameters
one can achieve about the same level of energy absorption .
In this study, the PTO parameters were optimised for each
state. This kind of control is known as slow control. It can easily
be achieved since it requires only the knowledge of the current
sea state. Technically, it can be achieved by varying the pressure
in the accumulators in case of a hydraulic PTO.
Mooring systems were represented by linear springs ad-
justed to keep the device in place with minimum inﬂuence on
the power absorption.
Rough representation of viscous losses were included where
they are expected to have strong inﬂuence. Drag coefﬁcients
were based on available information.  was used as the main
Estimation of drag coefﬁcients was identiﬁed as the main
source of inaccuracies in the models. Uncertainties associated
with these inaccuracies were assessed by varying the drag coef-
ﬁcients from 0 to twice their nominal values and measuring the
inﬂuence on the energy absorption.
End stops were modelled by springs with large stiffness co-
efﬁcient which becomes active when the motion violates the am-
Power matrices of each WEC were determined by simulat-
ing their responses for each sea state over a period of 1200s. For
each sea state, the PTO parameters were optimised in order to
maximise the energy absorption. The optimisation was made us-
ing brute force. No control mechanisms or strategies in order to
increase the energy absorption were implemented, only optimi-
sation of PTO parameters.
For the OWC system, the time-domain model is still under
development. For the time being, results are presented from a
linear frequency-domainmodel, which is developedby assuming
linear losses, linearising the air compressibility relationship, as
well as assuming that there is no limit for the pressure in the air
Using the derived power matrix, the absorbed energy over
a year was calculated based on annual wave statistics from ﬁve
locations offshore Western Europe, see Fig. 9.
Wave data statistics for SEM-REV and Yeu island comes
from the ANEMOC data base . Statistics for EMEC and Lis-
boa comes from . For Belmullet, it comes from the Irish Ma-
rine Institure . Tab. 5 shows the mean level of wave power
resource at each of these sites.
TABLE 5. MEAN ANNUAL WAVE POWER RESOURCE AT
Site Wave power resource (kW/m)
1. SEM-REV 14.8
2. EMEC 21.8
3. Yeu island 26.8
4. Lisboa 37.5
5. Belmullet 80.6
2011 by ASME
FIGURE 9. LOCATION OF CONSIDERED SITE FOR ASSESS-
MENT OF ANNUAL ENERGY ABSORPTION
RESULTS AND DISCUSSION
Power matrices and energy absorption
Fig. 10 and 11 shows the power matrices of the four WECs
computed with the Wave to Wire models.
Using these power matrices and annual wave statistics, the
mean annual power absorption at each site was derived. Table (6)
showsthe results of these calculations. A range instead of a value
is givenfor the powerabsorption of the three ﬁrst WECs, because
of uncertainties associated with the numerical modelling.
TABLE 6. MEAN ANNUAL WAVE POWER ABSORPTION OF
EACH WEC ON EACH SITE
Site Heaving Two heaving Pitching Floating OWC
buoy bodies system device
1 [1.3-1.9] [63-110] [70-100] [105-190]
2 [2.2-3.4] [100-180] [150-225] [195-330]
3 [2.6-4.] [150-270] [185-275] [255-420]
4 [2.8-4.2] [160-280] [150-220] [265-470]
5 [4.0-6.0] [300-520] [220-320] [520-970]
One can see that the level of power absorption on a site
where the wave resource is about 25kW/m is typically:
5 10 15
Power matrix of the heaving buoy (kW)
5 10 15
Power matrix of the heaving two bodies sytem (kW)
5 10 15
Power matrix of the pitching device (kW)
FIGURE 10. CALCULATED POWER MATRICES OF THE HEAV-
ING BUOY, THE HEAVING TWO BODIES SYSTEM AND THE
SELF REACTING PITCHING SYSTEM
- 3kW for the heaving buoy.
- 200kW for the heaving two-bodies system
- 200kW for the pitching device.
- 300kW for the ﬂoating OWC.
It corresponds with capture width ratio of respectively
4%,40%, 32% and 47%. These capture width ratio are based
on the width of the devices. It is recalled that these numbers
correspond with energy absorption. For energy output, PTO efﬁ-
ciencies and other energy losses have to be taken into account.
2011 by ASME
5 10 15
Power matrix of the floating OWC
FIGURE 11. POWER MATRIX OF THE FLOATING OWC
One can see that for all WECs except the pitching device,
the energy absorption increases with the available wave power
resource. It is not the casewith the pitching device because an in-
crease in the level of available power resource corresponds with
an increase of the period of the waves. Since the bandwidth of
the pitching device is narrower than the other devices, as one can
see on Fig. 10, it results in a decrease of the energy absorption
for site 4 in comparison to site 3, despite higher wave resource.
The order of magnitude of power absorption is much smaller
for the heaving buoy than for the other WECs. It is normal, since
this WEC is hundred of times smaller than the other ones. How-
ever, it does not mean that this option must be disregarded be-
cause its cost is also likely to be hundred times smaller than for
the other WECs.
Fig. 12 shows the comparison of the criteria between each
The ﬁrst criteria is the absorbed power per unit of mass. One
can see that it is much better for the pitching and the OWC de-
vices than for the other two ones. Particularly, the heaving two-
bodies system is penalised by its large displacement. However,
one should note that all this mass is not necessarily costly struc-
tural mass. Most of it could be cheap water ballast.
The second criteria is the absorbed power per unit of wetted
surface. One can see that the results are much closer ones to
the others for this criteria at the four ﬁrst sites. For the highest
energetic sea state, the OWC and the heaving two bodies system
have better criteria than the two other ones. The heaving buoy is
last for all sites.
The last criteria is the absorbed power per unit of PTO force.
The pitching device has the advantage for this one, followed by
the heaving buoy and the heaving two bodies system. This crite-
ria was not calculated for the OWC.
Tab. 7 summarises the ranking of WECs for each criteria.
1 2 3 4 5
Absorbed energy per unit of wetted surface
1 2 3 4 5
Absorbed energy per unit of PTO force
1 2 3 4 5
Absorbed energy per unit of mass
FIGURE 12. COMPARISONS OF CRITERIA. THE RED BARS
ARE FOR THE HEAVING BUOY, THE GREEN BARS ARE FOR
THE HEAVING TWO-BODIES SYSTEM, THE BLUE ONES ARE
FOR THE PITCHING DEVICE AND THE BLACK ONES ARE FOR
THE FLOATING OWC.
In this study, four wave energy converters with different
working principle were considered. Criteria for their objective
comparison are discussed and the following ones are selected:
absorbed power per WEC unit, per unit of mass, per unit of wet-
ted surface and per unit of PTO force. Using numerical mod-
elling, estimation of their range are calculated and comparisons
2011 by ASME
TABLE 7. SUMMARY OF THE RANKING OF WECS FOR EACH
CRITERIA. 1 IS FOR THE BEST.
Criteria Heaving Two heaving Pitching Floating
buoy bodies system device OWC
3 4 2 1
4 1 1 3
2 3 1 N/A
4 2 2 1
Numerical models were developed in order to be able to
compute the power matrices of each WEC, and then the absorbed
power. They were developed in the time domain in order to be
able to deal with non linear terms such as the viscous losses in
the equation of motion. With the used methodology, the viscous
losses could not be calculated explicitly, so they were modelled
as additional drag terms, for which the coefﬁcients were based
on available information. Sensitivity analysis were carried out in
order to assess the effect of errors in the estimation of the drag
coefﬁcients. It has been shown to be about 30%.
PTOparameters being unknown,they are optimised for each
sea state in order to maximise the energy absorption. The mean
annual absorbed power at 5 different locations over the west
coast of Europe was calculated using the numerical models, and
the criteria were derived.
Comparisons of criteria between the WECs showed that the
criteria absorbed power per unit of wetted surface and PTO force
are rather similar for each WEC, despite very different working
principle. However, the criteria absorbed power per unit and per
unit of mass were shown to be very different.
Hopefully, these criteria can be related with costs. Using
appropriate weighting, one can derive a ranking for these WECs
and then select the one which has the lowest cost of energy.
This study was made in collaboration between Ecole Cen-
trale de Nantes, the Centre for Ships and Ocean Structures (Ce-
SOS) and Statkraft. Thanks go to Statkraft for their ﬁnancial
support. Aur´elien Babarit would also like to thank CeSOS for
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2011 by ASME