Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011 June 19-24, 2011, Rotterdam, The Netherlands

OMAE2011-49

POWER ABSORPTION MEASURES AND COMPARISONS OF SELECTED WAVE ENERGY CONVERTERS

´ Aurelien Babarit Jorgen Hals Jorgen Krokstad ´ Laboratoire de Mecanique des Fluides Adi Kurniawan Statkraft CNRS UMR6598 Torgeir Moan PO Box 200, Lillekaer Ecole Centrale de Nantes Centre for Ships and Ocean Structures 0216 Oslo 1, rue de la Noe Norges Teknisk-Naturvitenskapelige Universitet Norway 44300 Nantes Otto Nielsens v. 10 Email: [email protected] France 7491 Trondheim Email: [email protected] Norway Email: [email protected] [email protected]

ABSTRACT

INTRODUCTION In the last decade many projects for the development of wave energy converters (WECs) have emerged all over the world, and especially in Europe. Some of the proposed designs are very similar 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 available information is usually limited to sketches, pictures and animations, and in some cases also dimensions and system layout. Only few quantitative figures on the estimated or measured energy conversion are presently known. The converted useful energy represents the income side of a wave energy project. It may be estimated once the external dimensions, working principle, machinery function and local wave resource are known. On the cost side the picture becomes more complex, with contributions from design, fabrication, installation, 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 uncertainties. In order to provide a benchmark for the income potential of wave energy converters, the energy absorption for a representative selection of converter designs has been estimated. Such a

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 selfreacting two-bodies device, a pitching device, and a floating OWC device. They are inspired by concepts which are currently under development. For each of these concepts, a numerical Wave To Wire (W2W) model is derived. Numerical estimates of the energy delivery 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 assessed 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 significant Power Take Off force. By comparing these criteria, one gets a better idea of the advantages and drawbacks of each of the studied concepts. 1

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agreed that all costs after installation (from Owner’s development cost to Periodic Levelized Overhaul and Replacement Cost) are proportional to this Total Plant Cost. So, for sake of comparison 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 good criterion. The higher the mooring loads, the more expensive the mooring system will be. It will also impact the installation cost. Therefore, the significant mooring force could be a good criterion, 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:

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 aiming at comparing different WEC’s principles on a quantitative basis. In [1], 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 experimental analysis), the selected WECs and the criteria used for comparison.

CRITERIA FOR COMPARISON OF WAVE ENERGY CONVERTERS The ultimate criterion for ranking WECs is the cost of electricity 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 fabrication, O& M, investment cost, insurances, to decommissioning. The power can be assessed using numerical modeling or experimental tests, with a certain degree of accuracucy that one should be aware of. The cost depends on many components. According to [2], they are:

- Energy absorption - Energy absorption / tons of displacement - Energy absorption / square meters of wetted surface - Energy absorption / unit of significant PTO force

- Absorber structure. - Power Take Off system. - Mooring. - 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 - Commissioning - Interest during Construction - Annual Scheduled O&M Cost - Annual Unscheduled O&M Cost - Annual Insurance Cost - Periodic Levelized Overhaul and Replacement Cost

CONSIDERED WAVE ENERGY CONVERTER TECHNOLOGIES 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 surface. 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 structure. 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 [3] and Waters [4], as well

Let the sum of the costs from the Absorber structure to the Installation Cost be the Total Plan Cost (TPC). Usually, it is 2

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TABLE 1. SYSTEM PARAMETERS OF THE SEABASED

Property

Value

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

m3

mass of the buoy

1000

kg

Wire stiffness

450000

Stroke length

1.8

m

1898

kg

Significant wetted surface

42

m2

Significant mass

31

tons

Mass of the translator FIGURE 1. SKETCH OF THE HEAVING BUOY REACTING AGAINST THE SEABED

Unit

kg/m

Tab. summarises the parameters. Heaving self-reacting two-bodies device It consists in an axi-symmetric, self-reacting point absorber, operating in the heave mode. 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 Wavebob WEC 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 [8], it is specified 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 [9]. 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 unknown parameters. 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-

FIGURE 2. COMPONENTS OF THE SEABASED WEC

as a series of articles, [5–7]. Some material has also been gathered from web pages on the internet. For the connection between the buoy and the machinery unit, steel wire with plastic coating is assumed. The wire stiffness is 450 kN/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 1.8 m, 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 42 m2 . 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. 3

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TABLE 2. HEAVING SELF-REACTING SYSTEM PARAMETERS

Property

Value

Unit

Outer diameter (torus)

20

m

Inner diameter (torus)

10

m

Draft (torus)

2

m

278

m3

Diameter at WL (float)

8

m

Draft (float)

50

m

4680

m3

Stroke length

6

m

Wetted surface

2120

m2

Total mass

4958

tons

Displacement (torus)

Displacement (float)

Pitching device on a floating platform This device consists in four hinged flaps which are all connected 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 3. SKETCH OF THE SYSTEM

FIGURE 5. SKETCH OF THE PITCHING SYSTEM

Dimensions of the system were obtained from [10] and from pictures and data found on the internet [11]. The width of the system is 25 m. 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 displacement 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-

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 m2 . The wetted surface of the float is about 1700 m2 . The total wetted surface is then 2120 m2 . Tab. 2 summarises the parameters which were used. 4

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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 generator. The motion of the water column relative to 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 from stalling. The design considered in this study is inspired by the OE Buoy which is developed by Ocean Energy Ltd. in Ireland [13]. 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 6. ARTISTIC VIEW OF THE LANGLEE WAVE ENERGY CONVERTER TABLE 3. PITCHING DEVICE PARAMETERS

Property

Value

Unit

Width (flap)

9.5

m

Draught (flap)

8.5

m

2

m

Displacement (flap)

185

m3

Length (Frame)

25

m

Width (Frame)

25

m

Draught (Frame)

12

m

Displacement

673

m3

Significant wetted surface

2160

m2

Significant mass

1410

tons

Thickness (flap)

FIGURE 7. SKETCH OF THE FLOATING OWC DEVICE

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 m2 . The wetted surface of the float is about 1240 m2 . The total significant wetted surface considered here is then 2160 m2 . 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 proposed by Masuda [12]. It has a submerged opening aligned downstream of the incident wave propagation direction. It has a single air chamber and is

FIGURE 8. 1/4 SCALE MODEL OF THE OEBUOY AT SEA

Losses, with the effect of reducing the body motions and 5

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TABLE 4. FLOATING OWC DEVICE PARAMETERS

Property

Value

in the accumulators in case of a hydraulic PTO. Mooring systems were represented by linear springs adjusted 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. [20] was used as the main reference. 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 coefficients from 0 to twice their nominal values and measuring the influence on the energy absorption. End stops were modelled by springs with large stiffness coefficient which becomes active when the motion violates the amplitude constraints. Power matrices of each WEC were determined by simulating their responses for each sea state over a period of 1200 s. For each sea state, the PTO parameters were optimised in order to maximise the energy absorption. The optimisation was made using brute force. No control mechanisms or strategies in order to increase the energy absorption were implemented, only optimisation 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-domain model, which is developed by assuming linear losses, linearising the air compressibility relationship, as well as assuming that there is no limit for the pressure in the air chamber. 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 [21]. Statistics for EMEC and Lisboa comes from [22]. For Belmullet, it comes from the Irish Marine Institure [23]. Tab. 5 shows the mean level of wave power resource at each of these sites.

Unit

Length

50

m

Width

24

m

Draft

13

m

Height of submerged opening

8

m

Significant wetted surface

3800

m2

Significant mass

1800

tons

the volume flow available to the turbine, are included. External restoring forces are contributed by moorings, whose contribution is assumed to be a small stiffness in surge. In this study we assume a linear pressure-volume flow relationship for the air turbine, where it is possible to tune the load resistance of the turbine. This parameter has been optimised in this study to maximise the energy absorption. The displacement of the device is 1800 m3 and its wetted surface is 3800 m2 . For a fair comparison with the other devices, we have not included the inner wetted surface of the device. Tab. 4 summarises the parameters.

METHODOLOGY For each one of the first three WECs, a Wave to Wire model was developed in 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 [14] or Achil3D [15]. The force applied by the PTO systems was modelled as linear. 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 solutions, the PTO behaviour might 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 [16] that a PTO with a linear behaviour allows to maximise the energy absorption when its coefficients are properly tuned. With irregular waves, a linear PTO with parameters optimised for each sea state still gives power absorption close to maximum [17]. One could note also that the PTO system can be controlled in order to behave linearly [18], or that with proper settings of the PTO parameters one can achieve about the same level of energy absorption [19]. 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

TABLE 5. MEAN ANNUAL WAVE POWER RESOURCE AT EACH SITE

6

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

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Power matrix of the heaving buoy (kW) 7

10 9 8 7 6 5 4 3 2 1

Height [m]

6

EMEC

5 4 3 2

Belmullet

1 5

Yeu island

10 Period [s]

15

Power matrix of the heaving two bodies sytem (kW)

SEM-REV 7

1000 900 800 700 600 500 400 300 200 100

6 Height [m]

Lisboa

5 4 3 2

FIGURE 9. LOCATION OF CONSIDERED SITE FOR ASSESSMENT OF ANNUAL ENERGY ABSORPTION

1 5

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) shows the results of these calculations. A range instead of a value is given for the power absorption of the three first WECs, because of uncertainties associated with the numerical modelling.

10 Period [s]

15

Power matrix of the pitching device (kW) 7

1000 900 800 700 600 500 400 300 200 100

Height [m]

6 5 4 3 2 1 5

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]

10 Period [s]

15

FIGURE 10. CALCULATED POWER MATRICES OF THE HEAVING 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 efficiencies and other energy losses have to be taken into account.

One can see that the level of power absorption on a site where the wave resource is about 25kW/m is typically: 7

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Power matrix of the floating OWC

Absorbed energy per unit of mass 5 1000 900 800 700 600 500 400 300 200 100

Height [m]

6

4

2

5

10 Period [s]

4 3 2 1 0

15

1

2

3 Site

4

5

Absorbed energy per unit of wetted surface

FIGURE 11. POWER MATRIX OF THE FLOATING OWC

3

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 case with the pitching device because an increase 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. However, it does not mean that this option must be disregarded because its cost is also likely to be hundred times smaller than for the other WECs.

2

1

0

1

2

3 Site

4

5

Absorbed energy per unit of PTO force 6 5 4 3 2

Criteria Fig. 12 shows the comparison of the criteria between each WEC. 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 devices than for the other two ones. Particularly, the heaving twobodies system is penalised by its large displacement. However, one should note that all this mass is not necessarily costly structural 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 criteria was not calculated for the OWC. Tab. 7 summarises the ranking of WECs for each criteria.

1 0

1

2

3 Site

4

5

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.

CONCLUSION 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 wetted surface and per unit of PTO force. Using numerical modelling, estimation of their range are calculated and comparisons are provided. 8

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TABLE 7. SUMMARY OF THE RANKING OF WECS FOR EACH CRITERIA. 1 IS FOR THE BEST.

Criteria

Power

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

REFERENCES [1] Nielsen, K., and al., 2002. Bølgekraftprogram. Afslutningsrapport, RAMBØLL, Teknikerbyen 31, 2830 Virum, Denmark. [2] Previsic, M., Siddiqui, O., and Bedard, R., 2004. EPRI Global E2I Guidelines, Economic Assessment Methodology for Offshore Wave Power Plants. Tech. rep., Electric Power Research Institute. [3] Eriksson, M., 2007. “Modelling and experimental verification of direct drive wave energy conversion – Buoygenerator dynamics”. PhD Thesis, Uppsala Universitet. [4] Waters, R., 2008. “Energy from Ocean Waves – Full Scale Experimental Verification of a Wave Energy Converter”. PhD Thesis, Uppsala Universitet. [5] Bostrom, C., Lejerskog, E., Stalberg, M., Thorburn, K., and Leijon, M., 2009. “Experimental results of rectification and filtration from an offshore wave energy system”. Renewable Energy, 34(5), May, pp. 1381–1387. [6] Bostrom, C., Waters, R., Lejerskog, E., Svensson, O., Stalberg, M., Stromstedt, E., and Leijon, M., 2009. “Study of a wave energy converter connected to a nonlinear load”. IEEE Journal of Oceanic Engineering, 34(2), April, pp. 123–127. [7] Tyrberg, S., Stlberg, M., Bostrom, C., Waters, R., Svensson, O., Stromstedt, E., Savin, A., Engstrom, J., Langhamer, O., Gravrkmo, H., Haikonen, K., Tedelid, J., Sundberg, J., and Leijon., M., 2008. “The lysekil wave power project – status update”. In Proceedings of the 10th World Renewable Energy Converence (WREC). Glasgow (UK). [8] www.wavebob.com. Website of wavebob company, accessed september, 9th, 2010. [9] www.seapower.ie/news2.php. Website accessed september, 9th, 2010. [10] Pecher, A., Kofoed, J., Espedal, J., and Hagberg, S., 2010. “Results of an experimental study of the langlee wave energy converter”. In Proceedings of the 20th International Offshore and Polar Engineering Conference. Beijing, China. [11] www.langleewavepower.com. Website of the langlee company, accessed november, 1st, 2010. [12] Masuda, Y., Kimura, H., Liang, X., Gao, X., Mogensen, R. M., and Anderson, T., 1996. “Regarding bbdb wave power generating plant”. In Proceedings of the Second European Wave Power Conference, G. Elliot and K. Diamantaras, eds., pp. 1–3. [13] www.oceanenergy.ie/index.html. Accessed december, 2010. [14] G.Delhommeau, 1993. “Seakeeping codes aquadyn and aquaplus”. In Proceedings of the 19th WEGEMT School, Numerical Simulation of Hydrodynamics: Ships and Offshore Structures. [15] Babarit, A., 2008. Achil3D v2.0 : User Manual. Tech. rep.,

per mass Power per surface Power per PTO force Absorbed power per unit

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%. PTO parameters 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.

ACKNOWLEDGMENT This study was made in collaboration between Ecole Centrale de Nantes, the Centre for Ships and Ocean Structures (CeSOS) and Statkraft. Thanks go to Statkraft for their financial support. Aur´elien Babarit would also like to thank CeSOS for hosting him during the realisation of the study. 9

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[16] [17]

[18]

[19]

[20] [21] [22]

[23]

Laboratoire de M´ecanique des Fluides - CNRS UMR6598, Ecole Centrale de Nantes. Falnes, J. Ocean Waves and oscillating systems. Linear interactions including wave energy extraction. Hals, J., 2010. “Modelling and and phase control of waveenergy converters”. PhD Thesis, NTNU - Trondheim, Norwegian University of Science and Technology. Henderson, R., 2006. “Design, simulation and testing of a novel hydraulic power take-off system for the pelamis wave energy converter”. Renewable Energy, 31(2), February, pp. 271–283. Josset, C., Babarit, A., and Cl´ement, A., 2007. “A waveto-wire model for the searev wave energy converter”. Proceedings of the Institution of Mechanical Engineers Part M-Journal of Engineering for the Maritime Environment, 221(2), pp. 81–93. Molin, B., 2002. Hydrodynamique des structures offshore, Guides Pratiques sur Les Ouvrages En Mer. TECHNIP. candhis.cetmef.developpement durable.gouv.fr. Accessed may, 2010. Nielsen, K., and Pontes, T., 2010. Generic and Site related wave data. Final technical report, OES-IEA Document No: T02-1.1. www.marine.ie. Accessed may, 2010.

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OMAE2011-49

POWER ABSORPTION MEASURES AND COMPARISONS OF SELECTED WAVE ENERGY CONVERTERS

´ Aurelien Babarit Jorgen Hals Jorgen Krokstad ´ Laboratoire de Mecanique des Fluides Adi Kurniawan Statkraft CNRS UMR6598 Torgeir Moan PO Box 200, Lillekaer Ecole Centrale de Nantes Centre for Ships and Ocean Structures 0216 Oslo 1, rue de la Noe Norges Teknisk-Naturvitenskapelige Universitet Norway 44300 Nantes Otto Nielsens v. 10 Email: [email protected] France 7491 Trondheim Email: [email protected] Norway Email: [email protected] [email protected]

ABSTRACT

INTRODUCTION In the last decade many projects for the development of wave energy converters (WECs) have emerged all over the world, and especially in Europe. Some of the proposed designs are very similar 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 available information is usually limited to sketches, pictures and animations, and in some cases also dimensions and system layout. Only few quantitative figures on the estimated or measured energy conversion are presently known. The converted useful energy represents the income side of a wave energy project. It may be estimated once the external dimensions, working principle, machinery function and local wave resource are known. On the cost side the picture becomes more complex, with contributions from design, fabrication, installation, 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 uncertainties. In order to provide a benchmark for the income potential of wave energy converters, the energy absorption for a representative selection of converter designs has been estimated. Such a

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 selfreacting two-bodies device, a pitching device, and a floating OWC device. They are inspired by concepts which are currently under development. For each of these concepts, a numerical Wave To Wire (W2W) model is derived. Numerical estimates of the energy delivery 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 assessed 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 significant Power Take Off force. By comparing these criteria, one gets a better idea of the advantages and drawbacks of each of the studied concepts. 1

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agreed that all costs after installation (from Owner’s development cost to Periodic Levelized Overhaul and Replacement Cost) are proportional to this Total Plant Cost. So, for sake of comparison 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 good criterion. The higher the mooring loads, the more expensive the mooring system will be. It will also impact the installation cost. Therefore, the significant mooring force could be a good criterion, 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:

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 aiming at comparing different WEC’s principles on a quantitative basis. In [1], 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 experimental analysis), the selected WECs and the criteria used for comparison.

CRITERIA FOR COMPARISON OF WAVE ENERGY CONVERTERS The ultimate criterion for ranking WECs is the cost of electricity 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 fabrication, O& M, investment cost, insurances, to decommissioning. The power can be assessed using numerical modeling or experimental tests, with a certain degree of accuracucy that one should be aware of. The cost depends on many components. According to [2], they are:

- Energy absorption - Energy absorption / tons of displacement - Energy absorption / square meters of wetted surface - Energy absorption / unit of significant PTO force

- Absorber structure. - Power Take Off system. - Mooring. - 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 - Commissioning - Interest during Construction - Annual Scheduled O&M Cost - Annual Unscheduled O&M Cost - Annual Insurance Cost - Periodic Levelized Overhaul and Replacement Cost

CONSIDERED WAVE ENERGY CONVERTER TECHNOLOGIES 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 surface. 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 structure. 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 [3] and Waters [4], as well

Let the sum of the costs from the Absorber structure to the Installation Cost be the Total Plan Cost (TPC). Usually, it is 2

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TABLE 1. SYSTEM PARAMETERS OF THE SEABASED

Property

Value

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

m3

mass of the buoy

1000

kg

Wire stiffness

450000

Stroke length

1.8

m

1898

kg

Significant wetted surface

42

m2

Significant mass

31

tons

Mass of the translator FIGURE 1. SKETCH OF THE HEAVING BUOY REACTING AGAINST THE SEABED

Unit

kg/m

Tab. summarises the parameters. Heaving self-reacting two-bodies device It consists in an axi-symmetric, self-reacting point absorber, operating in the heave mode. 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 Wavebob WEC 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 [8], it is specified 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 [9]. 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 unknown parameters. 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-

FIGURE 2. COMPONENTS OF THE SEABASED WEC

as a series of articles, [5–7]. Some material has also been gathered from web pages on the internet. For the connection between the buoy and the machinery unit, steel wire with plastic coating is assumed. The wire stiffness is 450 kN/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 1.8 m, 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 42 m2 . 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. 3

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TABLE 2. HEAVING SELF-REACTING SYSTEM PARAMETERS

Property

Value

Unit

Outer diameter (torus)

20

m

Inner diameter (torus)

10

m

Draft (torus)

2

m

278

m3

Diameter at WL (float)

8

m

Draft (float)

50

m

4680

m3

Stroke length

6

m

Wetted surface

2120

m2

Total mass

4958

tons

Displacement (torus)

Displacement (float)

Pitching device on a floating platform This device consists in four hinged flaps which are all connected 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 3. SKETCH OF THE SYSTEM

FIGURE 5. SKETCH OF THE PITCHING SYSTEM

Dimensions of the system were obtained from [10] and from pictures and data found on the internet [11]. The width of the system is 25 m. 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 displacement 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-

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 m2 . The wetted surface of the float is about 1700 m2 . The total wetted surface is then 2120 m2 . Tab. 2 summarises the parameters which were used. 4

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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 generator. The motion of the water column relative to 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 from stalling. The design considered in this study is inspired by the OE Buoy which is developed by Ocean Energy Ltd. in Ireland [13]. 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 6. ARTISTIC VIEW OF THE LANGLEE WAVE ENERGY CONVERTER TABLE 3. PITCHING DEVICE PARAMETERS

Property

Value

Unit

Width (flap)

9.5

m

Draught (flap)

8.5

m

2

m

Displacement (flap)

185

m3

Length (Frame)

25

m

Width (Frame)

25

m

Draught (Frame)

12

m

Displacement

673

m3

Significant wetted surface

2160

m2

Significant mass

1410

tons

Thickness (flap)

FIGURE 7. SKETCH OF THE FLOATING OWC DEVICE

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 m2 . The wetted surface of the float is about 1240 m2 . The total significant wetted surface considered here is then 2160 m2 . 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 proposed by Masuda [12]. It has a submerged opening aligned downstream of the incident wave propagation direction. It has a single air chamber and is

FIGURE 8. 1/4 SCALE MODEL OF THE OEBUOY AT SEA

Losses, with the effect of reducing the body motions and 5

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TABLE 4. FLOATING OWC DEVICE PARAMETERS

Property

Value

in the accumulators in case of a hydraulic PTO. Mooring systems were represented by linear springs adjusted 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. [20] was used as the main reference. 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 coefficients from 0 to twice their nominal values and measuring the influence on the energy absorption. End stops were modelled by springs with large stiffness coefficient which becomes active when the motion violates the amplitude constraints. Power matrices of each WEC were determined by simulating their responses for each sea state over a period of 1200 s. For each sea state, the PTO parameters were optimised in order to maximise the energy absorption. The optimisation was made using brute force. No control mechanisms or strategies in order to increase the energy absorption were implemented, only optimisation 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-domain model, which is developed by assuming linear losses, linearising the air compressibility relationship, as well as assuming that there is no limit for the pressure in the air chamber. 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 [21]. Statistics for EMEC and Lisboa comes from [22]. For Belmullet, it comes from the Irish Marine Institure [23]. Tab. 5 shows the mean level of wave power resource at each of these sites.

Unit

Length

50

m

Width

24

m

Draft

13

m

Height of submerged opening

8

m

Significant wetted surface

3800

m2

Significant mass

1800

tons

the volume flow available to the turbine, are included. External restoring forces are contributed by moorings, whose contribution is assumed to be a small stiffness in surge. In this study we assume a linear pressure-volume flow relationship for the air turbine, where it is possible to tune the load resistance of the turbine. This parameter has been optimised in this study to maximise the energy absorption. The displacement of the device is 1800 m3 and its wetted surface is 3800 m2 . For a fair comparison with the other devices, we have not included the inner wetted surface of the device. Tab. 4 summarises the parameters.

METHODOLOGY For each one of the first three WECs, a Wave to Wire model was developed in 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 [14] or Achil3D [15]. The force applied by the PTO systems was modelled as linear. 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 solutions, the PTO behaviour might 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 [16] that a PTO with a linear behaviour allows to maximise the energy absorption when its coefficients are properly tuned. With irregular waves, a linear PTO with parameters optimised for each sea state still gives power absorption close to maximum [17]. One could note also that the PTO system can be controlled in order to behave linearly [18], or that with proper settings of the PTO parameters one can achieve about the same level of energy absorption [19]. 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

TABLE 5. MEAN ANNUAL WAVE POWER RESOURCE AT EACH SITE

6

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

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Power matrix of the heaving buoy (kW) 7

10 9 8 7 6 5 4 3 2 1

Height [m]

6

EMEC

5 4 3 2

Belmullet

1 5

Yeu island

10 Period [s]

15

Power matrix of the heaving two bodies sytem (kW)

SEM-REV 7

1000 900 800 700 600 500 400 300 200 100

6 Height [m]

Lisboa

5 4 3 2

FIGURE 9. LOCATION OF CONSIDERED SITE FOR ASSESSMENT OF ANNUAL ENERGY ABSORPTION

1 5

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) shows the results of these calculations. A range instead of a value is given for the power absorption of the three first WECs, because of uncertainties associated with the numerical modelling.

10 Period [s]

15

Power matrix of the pitching device (kW) 7

1000 900 800 700 600 500 400 300 200 100

Height [m]

6 5 4 3 2 1 5

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]

10 Period [s]

15

FIGURE 10. CALCULATED POWER MATRICES OF THE HEAVING 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 efficiencies and other energy losses have to be taken into account.

One can see that the level of power absorption on a site where the wave resource is about 25kW/m is typically: 7

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Power matrix of the floating OWC

Absorbed energy per unit of mass 5 1000 900 800 700 600 500 400 300 200 100

Height [m]

6

4

2

5

10 Period [s]

4 3 2 1 0

15

1

2

3 Site

4

5

Absorbed energy per unit of wetted surface

FIGURE 11. POWER MATRIX OF THE FLOATING OWC

3

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 case with the pitching device because an increase 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. However, it does not mean that this option must be disregarded because its cost is also likely to be hundred times smaller than for the other WECs.

2

1

0

1

2

3 Site

4

5

Absorbed energy per unit of PTO force 6 5 4 3 2

Criteria Fig. 12 shows the comparison of the criteria between each WEC. 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 devices than for the other two ones. Particularly, the heaving twobodies system is penalised by its large displacement. However, one should note that all this mass is not necessarily costly structural 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 criteria was not calculated for the OWC. Tab. 7 summarises the ranking of WECs for each criteria.

1 0

1

2

3 Site

4

5

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.

CONCLUSION 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 wetted surface and per unit of PTO force. Using numerical modelling, estimation of their range are calculated and comparisons are provided. 8

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TABLE 7. SUMMARY OF THE RANKING OF WECS FOR EACH CRITERIA. 1 IS FOR THE BEST.

Criteria

Power

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

REFERENCES [1] Nielsen, K., and al., 2002. Bølgekraftprogram. Afslutningsrapport, RAMBØLL, Teknikerbyen 31, 2830 Virum, Denmark. [2] Previsic, M., Siddiqui, O., and Bedard, R., 2004. EPRI Global E2I Guidelines, Economic Assessment Methodology for Offshore Wave Power Plants. Tech. rep., Electric Power Research Institute. [3] Eriksson, M., 2007. “Modelling and experimental verification of direct drive wave energy conversion – Buoygenerator dynamics”. PhD Thesis, Uppsala Universitet. [4] Waters, R., 2008. “Energy from Ocean Waves – Full Scale Experimental Verification of a Wave Energy Converter”. PhD Thesis, Uppsala Universitet. [5] Bostrom, C., Lejerskog, E., Stalberg, M., Thorburn, K., and Leijon, M., 2009. “Experimental results of rectification and filtration from an offshore wave energy system”. Renewable Energy, 34(5), May, pp. 1381–1387. [6] Bostrom, C., Waters, R., Lejerskog, E., Svensson, O., Stalberg, M., Stromstedt, E., and Leijon, M., 2009. “Study of a wave energy converter connected to a nonlinear load”. IEEE Journal of Oceanic Engineering, 34(2), April, pp. 123–127. [7] Tyrberg, S., Stlberg, M., Bostrom, C., Waters, R., Svensson, O., Stromstedt, E., Savin, A., Engstrom, J., Langhamer, O., Gravrkmo, H., Haikonen, K., Tedelid, J., Sundberg, J., and Leijon., M., 2008. “The lysekil wave power project – status update”. In Proceedings of the 10th World Renewable Energy Converence (WREC). Glasgow (UK). [8] www.wavebob.com. Website of wavebob company, accessed september, 9th, 2010. [9] www.seapower.ie/news2.php. Website accessed september, 9th, 2010. [10] Pecher, A., Kofoed, J., Espedal, J., and Hagberg, S., 2010. “Results of an experimental study of the langlee wave energy converter”. In Proceedings of the 20th International Offshore and Polar Engineering Conference. Beijing, China. [11] www.langleewavepower.com. Website of the langlee company, accessed november, 1st, 2010. [12] Masuda, Y., Kimura, H., Liang, X., Gao, X., Mogensen, R. M., and Anderson, T., 1996. “Regarding bbdb wave power generating plant”. In Proceedings of the Second European Wave Power Conference, G. Elliot and K. Diamantaras, eds., pp. 1–3. [13] www.oceanenergy.ie/index.html. Accessed december, 2010. [14] G.Delhommeau, 1993. “Seakeeping codes aquadyn and aquaplus”. In Proceedings of the 19th WEGEMT School, Numerical Simulation of Hydrodynamics: Ships and Offshore Structures. [15] Babarit, A., 2008. Achil3D v2.0 : User Manual. Tech. rep.,

per mass Power per surface Power per PTO force Absorbed power per unit

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%. PTO parameters 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.

ACKNOWLEDGMENT This study was made in collaboration between Ecole Centrale de Nantes, the Centre for Ships and Ocean Structures (CeSOS) and Statkraft. Thanks go to Statkraft for their financial support. Aur´elien Babarit would also like to thank CeSOS for hosting him during the realisation of the study. 9

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[16] [17]

[18]

[19]

[20] [21] [22]

[23]

Laboratoire de M´ecanique des Fluides - CNRS UMR6598, Ecole Centrale de Nantes. Falnes, J. Ocean Waves and oscillating systems. Linear interactions including wave energy extraction. Hals, J., 2010. “Modelling and and phase control of waveenergy converters”. PhD Thesis, NTNU - Trondheim, Norwegian University of Science and Technology. Henderson, R., 2006. “Design, simulation and testing of a novel hydraulic power take-off system for the pelamis wave energy converter”. Renewable Energy, 31(2), February, pp. 271–283. Josset, C., Babarit, A., and Cl´ement, A., 2007. “A waveto-wire model for the searev wave energy converter”. Proceedings of the Institution of Mechanical Engineers Part M-Journal of Engineering for the Maritime Environment, 221(2), pp. 81–93. Molin, B., 2002. Hydrodynamique des structures offshore, Guides Pratiques sur Les Ouvrages En Mer. TECHNIP. candhis.cetmef.developpement durable.gouv.fr. Accessed may, 2010. Nielsen, K., and Pontes, T., 2010. Generic and Site related wave data. Final technical report, OES-IEA Document No: T02-1.1. www.marine.ie. Accessed may, 2010.

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