Numerical benchmarking study of a selection of Wave Energy Converters

Transcription

1 Numerical benchmarking study of a selection of Wave Energy Converters Aurélien Babarit Ecole Centrale de Nantes, France Jorgen Hals, Adi Kurniawan, Made J. Muliawan, Torgeir Moan NTNU, Norway Jorgen Krokstad Statkraft, Norway

2 Motivations > Many projects for wave energy conversion currently under development all over the world. > Limited available information: sketches, pictures and animations. Only few quantitative figures > Lack of quantitative figures makes difficult the comparison between WECs concept

3 Aims of the study What can be the power of typical Wave Energy Converters? How do these typical WECs compare? Which criteria should be used?

4 Highlights Criteria for benchmarking of WECs are proposed 8 WECs are considered, based on different sizes and working principles Power matrices are estimated using numerical modelling. Annual energy absorptions are estimated at 5 different locations and uncertainties are discussed. Benchmarking criteria are compared and conclusions are drawn. > This study should serve as a benchmark for power capture to increase the understanding of different converter types to highlight the differences between them to indirectly indicate a limit to the allowed cost for viability

5 Criteria for comparison > The true criterion is cost of kwh. > kwh (power production) can be assessed in different manners (numerical or experimental modelling) > Cost is difficult (impossible?) to assess at this stage. Must be replaced by cost indicators.

6 Selected cost indicators > Ratio of energy absorption to characteristic mass Balance of power absorption to structure cost Significant mass = displaced mass + mooring system > Ratio of energy absorption to characteristic surface Balance of power absorption to structure cost > Ratio of energy absorption to RMS of PTO force Balance of power absorption to PTO cost > Mean annual power absorption Income side of COE The higher the power absorption per unit, the less the installation cost

7 Case studies (1/2) 1. Small bottom reference heaving buoy D ~ 3 m Mass* = 31 t Surf. = 42 m² 2. Bottomreferenced submerged heavebuoy D ~ 7 m Mass* = 200 t Surf. = 220 m² 3. Floating two body heaving converter 4. Bottom fixed heave buoy array D ~ 20 m Mass = 4900 t Surf. = 2100 m² L ~ 70 m Mass = 1600 t Surf. = 4350 m² *including estimated mass of a gravity based foundation

8 Case studies(2/2) 5. Floating heave buoy array 6. Bottomfixed oscillating flap B ~ 132 m Mass = 5233 t Surf. = 4750 m² B ~ 26 m Mass* = 3800 t Surf. = 2200 m² 7. Floating three body oscillating flaps 8. Floating Oscillating Water Column B ~ 25 m Mass = 1400 t Surf. = 2200 m² B ~ 24 m Mass = 1800 t Surf. = 6500 m² *including estimated mass of a gravity based foundation

9 Inspired by: (1/2) 1. Small bottom reference heaving buoy D ~ 3 m Mass* = 31 t Surf. = 42 m² 2. Bottomreferenced submerged heavebuoy D ~ 7 m Mass* = 200 t Surf. = 220 m² 3. Floating two body heaving converter 4. Bottom fixed heave buoy array D ~ 20 m Mass = 4900 t Surf. = 2100 m² L ~ 70 m Mass = 1600 t Surf. = 4350 m² *including estimated mass of a gravity based foundation

10 Inspired by: (2/2) 5. Floating heave buoy array 6. Bottomfixed oscillating flap B ~ 132 m Mass = 5233 t Surf. = 4750 m² B ~ 26 m Mass* = 3800 t Surf. = 2200 m² 7. Floating three body oscillating flaps B ~ 25 m Mass = 1400 t Surf. = 2200 m² 8. Floating Oscillating Water Column B ~ 24 m Mass = 1800 t Surf. = 6500 m² *including estimated mass of a gravity based foundation

11 Numerical models > Numerical model consists in solving the following (formal) equation of motion: Wave structure interaction Mass matrix Excitation force 1 MX F μ X K X K X C A X - X X - X 2 F K X F t t t d ex 0 H D 0 0 PTO force Radiation force F B X K X PTO PTO PTO Optimised for each sea state (slow control) K PTO >= 0 Hydrostatic force PTO M es Mooring force End stops force Drag force Estimated from available litterature

12 Verification / validation > Two independent implementations (frequency vs time domain) > Comparisons with publicly available information whenever possible: RAOs, capture width ratios Generally very good agreement

13 Power matrices (1/2) 1. Small bottom reference heaving buoy 2. Bottom referenced submerged heave buoy 3. Floating two body heaving converter 4. Bottom fixed heave buoy array

14 Power matrices (2/2) 5 Floating heave buoy array 6. Bottom fixed oscillating flap 7. Floating three body oscillating flaps 8. Floating Oscillating Water Column

15 Mean annual power absorption at 5 European sites > Mean annual power absorption is the product of power matrix with the scatter diagram of wave resource at a given location

16 Estimates of mean annual power absorption 1. Small bottom referenced heave buoy 2. Bottom referenced submerged heave buoy Capture width ratio 3. Floating two bodies heaving (=hydrodynamic converter efficiency) is less varying with site than mean power 4. Bottom fixed heave buoy array 5. Floating heave buoy array 6. Bottom fixed oscillating flap 7. Floating three body oscillating flaps 8. Floating oscillating water column SEMREV EMEC Yeu Lisboa Belmullet Mean power (kw) Capture width ratio 3.6% 4.2% 4.1% 3.1% 2.1% Mean power (kw) 8.8** 18.5** 22** 19** 31** Capture width ratio 9%** 13%** 13%** 8%** 6%** Mean power (kw) Capture width ratio 27% 29% 36% 27% 23% Mean power (kw) 127.** 225.** 280.** 303.** 612.** Capture width ratio 14%** 16%** 17%** 12%** 12%** Mean power (kw) Capture width ratio 11% 11% 11% 6.4% 3.9% Mean power (kw) 211.** 348.** 440.** 513.** 981.** Capture width ratio 61%** 68%** 72%** 58%** 52%** Mean power (kw) Capture width ratio 14% 20% 20% 11% 7% Mean power (kw) 147.* 262.* 337.* 367.* 745.* Capture width ratio 41%* 50%* 52%* 41%* 38%* Few kws ~20 kws ~200 kws ~300 kws ~400 kws ~400 kws ~100 kws ~300 kws * Frequency domain results ** Finite water depth calculations

17 Uncertainties in numerical models Linear wave theory and wave-body interaction Agreement is usually good in small to moderate seas. Discrepancies in large sea states, or near resonances. Experience shows that linear theory overpredicts energy absorption in these cases. Effect of directionality: Effect of directionality has been shown to be less than 10% in case of the SEAREV, limited directionality on considered sites, refraction will align waves for shallow water devices, moorings will allow alignment for floating devices No significant contribution to uncertainties Simplified mooring representation (spring stiffness) Litterature shows that the effect of moorings on the power absorption is negligible No significant contribution to uncertainties Simplified machinery forces (linear PTO or Coulomb damping) Litterature shows that energy absorption can be slighlty overpredicted. No significant contribution to uncertainties Viscous effects assessed by quadratic drag force terms Difficult to estimate accurately the drag coefficient. Larger source of uncertainties Results are upper estimates

18 Uncertainties in numerical models > Uncertainties associated with modelling of viscous effects estimated via sensitivity analysis. > Uncertainty is typically [ -25%, +25%]. Never found to be higher than 30%, whatever the device +27% -25%

19 Comparison of power absorption at Yeu > Very different levels of power absorption, well illustrates the wide diversity of WECs > Max to min ratio of 140 between bigger and smaller device. > Is this ratio as high for the other cost indicators?

20 Comparison of power to mass ratio at Yeu > Energy to mass ratio varies only from 0.3 to 1.6 (factor about 5) despite completely different devices. > Roughly, the order of energy to characteristic mass ratio is 1MWh/tonne

21 Comparison of power to surface ratio at Yeu > Max to min ratio of energy to surface is about 1.3, excluding the case of the bottom fixed flap. > Indicator is more than two times larger for the bottom fixed oscillating flap. It Indicates that the bottom fixed oscillating flap makes better use of its surface. > Typical order of energy to surface ratio is 1MWh/m² (2MWh/m² for the bottom fixed flap)

22 Comparison of power to PTO force at Yeu > Little variations with devices > Not surprising as it is related with stroke length > Order of 2MWh/kN

23 Conclusions > A benchmarking study of power absorption from a selection of typical wave energy devices. > Mean annual power absorption from 2kW to 800 kw depending on the device and site illustrates the wide diversity of WECs concepts. However, energy to dimension-related parameters are varying much less: Energy to mass ratio was found to be about 1MWh/tonne Energy to surface ratio was found to be about 1MWh/m² (2MWh/m² for bottom fixed flap) Energy to PTO force ratio about 2MWh/kN > Capture width ratio weakly depends on site. It could be used to make rough assessment of energy absorption.

24 Lessons learnt > Initial plot: not to identify the best solution, but at least to be able to discard some of the selected technologies. > Conclusions show that at the end of the day, they are all worth the same (regarding the selected criteria). > Actual cost of electricity of Wavestar is 1 /kwh. Recently, Oyster announced a similar cost (800 /MWh). It agrees with the conclusions. Probably it will be similar for the other devices. > Recently, radically new ideas have been proposed, based on deformable structures (Anaconda, AWS). Do they have better power measures (I believe so)?

25 Acknowledgements: > This research was carried out as part of the Statkraft Ocean Energy Research Program, sponsored by Statkraft ( The financial support is gratefully acknowledged. > Thanks also go to all the developers and associates who have shared information and discussed the results with us: namely Halvar Gravrakmo from Uppsala University, Thomas Soulard and Jochem Weber from Wavebob, Julius Espedal from Langlee and Øyvind Rogne from NTNU, Morten Kramer from DTU and Enrique Vidal Sanchez from Wavestar, Marco Alves from the Wave Energy Centre, Giovanni Mattarolo and Marc Andreewsky from EDF and Arnaud Vazeille from EDF EN, and Nils Myklebust from Pontoon Power Converter.

26 Thank you for your attention