Numerical benchmarking study of a selection of wave energy converters

TL;DR: In this article, the mean annual power absorption of a selection of eight Wave Energy Converters (WECs) with different working principles is derived based on numerical modeling. But, despite very different working principle and dimensions, power performance of the selected devices vary much less than the average power absorption.

About: This article is published in Renewable Energy.The article was published on 2012-05-01 and is currently open access. It has received 578 citations till now. The article focuses on the topics: Wave power & Root mean square.

Summary

1. Introduction

• In the last decade many projects for the development of wave energy converters (WECs) have emerged in places all around the world, especially in Europe.
• The second aim is to compare the selected technologies with reference to a set of quantitative measures that can be related with costs.
• One must notice the Danish Wave Energy Research program [2] which resulted in estimates of energy absorption and cost estimates for 15 different WECs.
• Annual absorbed energy per unit of characteristic PTO force.
• That is why there has not been any attempt to derive them in this study.

2.1. Devices

• Eight devices with different working principles and/or dimensions were considered in the case studies.
• Details on dimensions and parameters which were used can be found in [5] .
• The geometry and configuration of each of the eight devices were inspired by the design of well-known wave energy converters currently under development by different technology companies.
• It should however be noted that there may be significant and important differences both in geometry and configuration between the devices studied here and their inspirators, thus also the performance may differ.

2.1.1. Small bottom-referenced heaving buoy (Bref-HB)

• This wave energy converter is inspired by the Seabased WEC which is currently in development in Sweden.
• The device consists of an axi-symmetric buoy with ellipsoidal cross section floating on the ocean surface.
• The machinery consists of a linear generator placed inside a steel hull mounted on a concrete ballast structure.
• A simplified sketch of the system and its main dimensions and parameters are shown in the device summary sheet, Fig. 12 .N o t e that, for this device, the anchoring system is an essential component as it provides the reaction point.
• Therefore, it was included in the characteristic surface area and characteristic mass measures for the system.

2.1.2. Bottom-referenced submerged heave-buoy (Bref-SHB)

• This wave energy converter is inspired by the Ceto WEC which is currently being developed in Australia and France.
• The working principle of this device is close to the previous one.
• The main differences are that the buoy has a diameter twice as large, that it is fully submerged and that the PTO system is hydraulic.
• Fig. 13 shows simplified sketch of the system, as well as a table giving the main dimensions and parameters.
• The characteristic surface area was estimated to be about 220 m 2 and the characteristic mass to be about 200 tonnes.

2.1.3. Floating two-body heaving converter (F-2HB)

• This system is inspired by the Wavebob WEC which is currently under development in Ireland.
• Fig. 3 shows a picture of the 1/4th scale model of the Wavebob, which was tested at sea in the Galway bay in Ireland.
• The hydraulic PTO system is driven by the relative motion between the two bodies.
• The role of the mooring system is to counteract drift and current forces.
• The characteristic mass is then about 5700 tonnes and the wetted surface area about 2100 m 2 .

2.1.4. Bottom-fixed heave-buoy array (B-HBA)

• This system is inspired by the Wavestar WEC, under development in Denmark.
• In Fig. 4 the test section currently being tested at Hanstholm in Denmark is shown with its buoys and platform in survival mode.
• The jack-up structure stands on the seabed and provides a fixed reference to the floats.
• Each one is connected to the main structure via an arm and a hinge.
• The characteristic surface area was estimated to about 4350 m 2 and the characteristic mass to about 1600 tonnes.

2.1.5. Floating heave-buoy array (F-HBA)

• This system is inspired by the Pontoon Power Converter, under development in Norway.
• The total buoyancy force from the buoys is balanced by net gravity forces of the bridge and the ballast baskets.
• As the submerged structure is an essential part of the system, it was included in the mass and surface area measures.
• This device is a simple pitching flap, oscillating about a fixed axis close to the sea bottom, and so is suitable for shallow and intermediate water depth.
• It has a hydroelectric machinery system, where a pump placed at the rotating shaft pumps pressurised hydraulic oil to a shoreline station.

2.1.7. Floating three-body oscillating flap device (F-3OF)

• This device is inspired by the Langlee WEC, currently under development in Norway.
• It consists of 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.
• The characteristic mass of the flaps and supporting structure is then estimated to about 1600 tonnes.

2.1.8. Floating oscillating water column (F-OWC)

• The floating oscillating water column device is a particular type of OWC device known as the backward bent duct buoy (BBDB) first proposed by Masuda [6] .
• The water column has a submerged opening aligned downstream of the incident wave propagation direction.
• The device is constructed of thin steel walls enclosing the water column.
• The motion of the water column relative to the OWC body creates oscillating pressure in the chamber and air flow through the turbine.
• The characteristic mass is about 1800 tonnes and its characteristic external surface area is estimated to about 6500 m 2 .

2.2. Sites

• As the level of mean wave energy transport varies from one place to another, it is important to consider several sites with different wave resource in order to evaluate the influence this has on the benchmarking performance measures.
• For the SEM-REV and Yeu island sites, the data come from the ANEMOC data base.
• 2 Statistics for the EMEC and Lisbon come from [7] .
• Deep water was assumed for the numerical simulations.
• Therefore, shallow-water wave data was generated assuming that for each wave frequency component of each sea state, 90% of the energy is transferred from deep to shallow water depths (13e20 m).

3.1. Numerical model

• As the scatter diagrams are available (or processed to be available at the water depth of interest), the problem reduces to determining the power matrix of each device.
• For each device, a numerical Wave to Wire time-domain model was built.
• They have as many rows as the device has degrees of freedom.
• F V is a damping force that depends quadratically on the velocities, and which aims at taking into account the effect of viscous losses.
• Models and modelling assumptions used for these force terms are explained in more detail in the following sections.

3.1.1. Wave-structure interaction

• For modelling waves and waveestructure interaction, linear potential flow theory was used.
• For wave energy application, the agreement between linear theory and experiments is usually good in small to moderate sea states, as it has been shown in many studies; see [10e14] for examples.
• In addition, the authors assumed that waves are mono-directional.
• The mooring system of floating devices might well allow some alignment of the devices with the wave direction, and for bottomfixed devices refraction at shallow water tends to align the wave crests with the coastline.
• The hydrodynamic functions K and the coefficients F ex and m N were calculated using the BEM (Boundary Element Methods) codes WAMIT [18] or Aquaplus [19] .

3.1.2. Quadratic damping force

• In many cases, linearity and irrotationality assumptions of linear potential flow theory are likely to be violated.
• Neglecting this would in these cases lead to numerical prediction of unrealistically large amplitude of motions, and thereby also energy absorption.
• Drag coefficients were estimated based on that knowledge.
• In the case of hydraulic PTO, a Coulomb damping model was used.
• In the present study the first of the spectrum measurement approach is assumed, where the PTO parameters are optimised for each state.

3.1.4. End-stop forces

• Some of the considered devices have end stops, which were implemented in the numerical model by adding springs with large stiffness coefficients.
• They become active as soon as the amplitude of the motion is larger than the amplitude constraint.
• This was formulated as follows: EQUATION in which K es is the stiffness coefficient of the end stop spring; uð,Þ is the element-wise Heaviside step function and X es is the amplitude constraint vector.

3.1.5. Mooring force

• In [32] and [33] , it was shown that at least for slack-moored heave-buoy systems the influence of the mooring system on the energy absorption is negligible.
• Therefore, mooring systems were represented by simple linear springs adjusted to keep the device in place with minimum influence on the power absorption.

3.2. Implementation and verification

• For each particular device (except the floating heave-buoy array), the corresponding equation of motion was derived.
• The numerical models are available from the authors upon request.
• In the particular case of the floating heave-buoy array, the commercial SIMO software [38] was used.
• More illustration and discussion on how to use SIMO features to model PTO system, end stops and wires for multibody WEC may be found in [32] .

4. Results & discussion

• Using the Wave to Wire models, the power matrices of each device were computed.
• Therefore, results are reported only for the case of the linear PTO model, except for the floating heave-buoy array for which only Coulomb damping was considered.
• From one device to another, depending on the site, one can see that mean annual power absorption figures are very different, ranging from 2 to almost 800 kW.
• It is worth noticing that an increase in the available wave power resource does not necessarily mean an increase in mean annual absorbed power, as can be seen in the case of devices 5 and 7 for the Lisbon and Yeu sites.
• Large variations are also found on capture width ratios from one device to another, ranging from 4% for the small bottomreferenced heaving buoy to 70% for the bottom-fixed oscillating flap.

4.1. Estimation of uncertainties

• It relies on mathematical models for each component of the device, which are based on several assumptions and approximations.
• In the particular case of strong sea states, it is expected that the deviation between the response of the actual device and its numerical model can be large.
• Therefore, it is expected that even if the numbers are not perfectly exact, the trends observed in comparisons between each technology should be correct.
• Another damping coefficient is also introduced with the effect of reducing the volume flow through the mean internal water surface.
• Uncertainty limits were obtained by taking these damping coefficients to be zero and twice the nominal values.

4.2. Performance measures

• Consider first the capture width ratios in Figs. 12e19.
• Here it is worth noticing that the capture width ratios the authors obtained are in agreement with the ones which were found in [2] .
• It illustrates well the wide diversity in wave energy concepts.
• So if one takes the ratio of annual absorbed energy and characteristic mass, then the differences between the devices are considerably reduced.
• That leaves us with volume stroke, which is area times stroke length.

4.3. Parametric studies on maximum PTO power and rated power

• In the wave energy community, there are sometimes discussions on how the rated power of a device, and the resulting capacity factor (defined as the ratio of the averaged power to the rated power) should be defined.
• The incident wave is irregular with peak period 9 s and significant height 2.5 m.
• One can can see that the instantaneous absorbed power stays within the range between 0 and 2 MW which has been set as the maximum power of the PTO system in this case.
• As the authors can see, the settings for the maximum absorbed power and the rated power influence the mean annual output power.
• Therefore, the rule of thumb would be here that the capacity factor of a WEC should be at least about 0.2.

5. Conclusion

• Eight wave energy converters with different working principle have been considered, and their performance at five prospective locations have been estimated.
• Uncertainties in the numerical model were discussed and error bars were derived for each performance measure.
• Matrices of absorbed power per sea state and estimates of the annual absorbed energy were given for each considered device, at each location.
• The average capture width ratio varies only weakly between different sites.
• The annual absorbed energy per characteristic surface area was found to be typically about 1 MWh/m 2 , with exception for the Instantaneous power (kW) PTO rated power (kW) PTO mean power (kW) WEC rated power (kW) Fig. 22 .

Figures

Fig. 8. 1/4 scale model of the OE buoy at sea.

Fig. 10. Scatter diagrams of wave data statistics for, from top to bottom, SEM-REV, EMEC, Yeu island, Lisbon, Belmullet.

Fig. 9. Sites from which annual wave data statistics were taken.

Fig. 13. Summary sheet for the bottom-referenced submerged heave-buoy (Bref-SHB).

Fig. 17. Summary sheet for the bottom-fixed oscillating flap (B-OF).

Table 1 Mean annual wave power level in function of site and water depth.

Fig. 12. Summary sheet for the small bottom-referenced heaving buoy (Bref-HB).

Fig. 16. Summary sheet for the floating heave-buoy array (F-HBA).

Fig. 1. Components of the Seabased WEC.

Fig. 20. Mean annual absorbed power in function of applied drag coefficient ratio for the self-reacting two-body heaving device.

Fig. 15. Summary sheet for the bottom-fixed heave-buoy array (B-HBA).

Fig. 11. PTO force vs velocity when PTO is linear, Coulomb damping and approximate Coulomb damping.

Fig. 4. Picture of the test section of the Wavestar WEC.

Fig. 5. Artistic view of the Pontoon Power Converter WEC.

Fig. 3. 1/4 scale model of the Wavebob at sea.

Fig. 2. Picture of the unveiling of the Ceto buoy.

Fig. 21. Comparison of performance measures for the eight considered devices. The calculations were made using wave statistics for the Yeu site. Filled red bars indicate that the computation was made using time domain models, whereas the unfilled bars indicate solution in the frequency domain. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 19. Summary sheet for the floating oscillating water column (F-OWC).

Fig. 14. Summary sheet for the floating two-body heaving converter (F-2HB).

Fig. 22. Instantaneous and mean absorbed power by the floating two-body heaving device, in an irregular wave of peak period 9 s and significant height of 2.5 m. Also shown is the maximum PTO power and the rated power.

Table 2 Effect of limiting the instantaneous power or the mean rated power on the mean annual power absorption for some of the considered devices.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Numerical benchmarking study of a selection of wave energy converters" ?

In this paper, the authors compare the performance of different wave energy converters with reference to a set of quantitative measures that can be related with costs. 

Q2. How can the wave excitation force be written?

Using linear potential theory, the pressure force resulting from waveestructure interaction can be written as the sum of a wave excitation force Fex and a radiation force Frad ¼ mN €XR t 0 Kðt sÞ _XðsÞdt. 

Q3. What is the effect of reducing the volume flow through the mean internal water surface?

Another damping coefficient is also introduced with the effect of reducing the volume flow through the mean internal water surface. 

Q4. How many devices were evaluated for potential deployment in the US?

In [3], energy delivery and costs of 8 devices were assessed for potential deployment in a pilot plant in the US regarding energy production and costs. 

Q5. What are the main reasons why the cost estimates are hampered?

As long as the technical solutions are uncertain or unknown on a detailed level, cost estimates are inevitably hampered by large uncertainties. 

Q6. How can the power absorbed by the PTO system be smoothed?

It has to be smoothed, e.g. by using energy storage components such as hydraulic accumulators, flywheels, batteries [41] or super-capacitors [42]. 

Q7. How many kW/m is the wave resource for this site?

For this site, the wave resource is also of the order25 kW/mwhich can be considered as a reasonable average for wave energy resources. 

Q8. How can one obtain an estimate of the wave energy absorption of a particular device?

An estimate of the wave energy absorption of a particular device at a particular location can be obtained by multiplying the power matrix of this device with the scatter diagrams of wave statistics at this location.