To Sofia List of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I Engström, J., Waters, R., Stålberg, M., Strömstedt, E., Eriksson, M., Isberg, J., Henfridsson, U., Bergman, K., Asmussen, J., and Leijon, M., "Offshore experiments on a direct-driven Wave Energy Converter", Proc. of the 7th European Wave and Tidal Energy Conference, Porto, Por- tugal, (2007) II Waters, R., Engström, J., Isberg, J., and Leijon, M., "Wave climate off the Swedish west coast", Renewable Energy 34(6), 1600-1606, (2009) III Tyrberg, S., Stålberg, M., Boström, C., Waters, R., Svens- son, O., Strömstedt, E., Savin, A., Engström, J., Langhamer, O., Gravråkmo, H., Haikonen, K., Tedelid, T., Sundberg, J., and Leijon, M., "The Lysekil Wave Power Project: Status update", Proceedings of the 10th World Re- newable Energy Conference, WREC, Glasgow, UK, (2008) IV Langhamer, O., Wilhelmsson, D., and Engström, J., "Arti- ficial reef effect and fouling impacts on offshore wave power foundations and buoys - a pilot study", Estuarine, Coastal and Shelf Science 82(3), 426-432, (2009) V Leijon, M., Waters, R., Rahm, M., Svensson, O., Boström, C., Strömstedt, E., Engström, J., Tyrberg, S., Savin, A., Gravråkmo, H., Bernhoff, H., Sundberg, J., Isberg, J., Ågren, O., Danielsson, O., Eriksson, M., Lejerskog, E., Bolund, B., Gustafsson, S., and Thorburn, K., "Catch the Wave to Electricity: The Conversion of Wave Motion to Electricity Using a Grid-Oriented Approach", IEEE Power & Energy Magazine 7(1), 50-54, (2009) VI Engström, J., Eriksson, M., Isberg, J., and Leijon, M., "Wave Energy Converter with enhanced amplitude re- sponse at frequencies coinciding with Swedish west coast sea states by use of a supplementary submerged body", Journal of Applied Physics 106(6), 064512-5, (2009) VII Isberg, J., Engström, J., and Leijon, M., "Depth variation of energy transport in fluid gravity waves" Journal of Re- newable and Sustainable Energy 2(2), 023104, (2010) VIII Tyrberg. S., Svensson, O., Kurupath, V., Engström, J., Strömstedt, E., and Leijon, M., ”Wave Buoy and Translator Motions - On-Site Measurements and Simulations, IEEE Journal of Oceanic Engineering, 36(3), 377-385, (2011) IX Li, W., Engström, J., Hai, L., Bontemps, S., Waters, R., Isberg, J., and Leijon, M., "Optimization of the Dimensions of a Gravity-based Wave Energy Converter Foundation Based on Heave and Surge Forces", Proc. of the 9th Euro- pean Wave and Tidal Energy Conference, Southampton, UK, (2011) X Lejerskog, E., Gravråkmo, H., Savin, A., Strömstedt, E., Tyrberg, S., Haikonen, K., Krishna, R., Boström, C., Rahm, M., Ekström, R., Svensson, O., Engström, J., Ekergård, B., Baudoin, A., Kurupath, V., Hai, L., Li, W., Sundberg, J., Waters, R., and Leijon, M., "Lysekil Research Site, Swe- den: A Status Update" Proc. of the 9th European Wave and Tidal Energy Conference, Southampton, UK, (2011) XI Engström, J., Isberg, J., Eriksson, M., and Leijon, M., "To- tal instantaneous energy transport in polychromatic fluid gravity waves at finite depth", Submitted to Journal of Re- newable and Sustainable Energy (2011) XII Engström, J., Isberg, J., Eriksson, M., and Leijon, M., "Properties of the energy transport for plane-parallel poly- chromatic surface gravity waves in waters of arbitrary depth", Submitted to IEEE Journal of Oceanic Engineer- ing, (2011) XIII Kurupath, V., Engström, J., Ekergård, B., Isberg, J., and Leijon, M., "Modelling and Simulation of Linear Wave En- ergy Converter", Submitted to IET Renewable Power Gen- eration, (2011) XIV Engström, J., Kurupath, V., Isberg, J., and Leijon, M., "A resonant Two Body System for a point absorbing Wave En- ergy Converter with direct-driven linear generator", Ac- cepted for publication in Journal of Applied Physics, (02 November 2011) Other contributions by the author that is not included in the thesis. XV Langhamer, O., Wilhelmsson, D., and Engström, J., “De- velopment of invertebrate assemblages and fish on offshore wave power”, Proc. of the ASME 28th International Confer- ence on Ocean, Offshore and Arctic Engineering, OMAE 2009, OMAE2009-79239, Honolulu, USA XVI Boström. C., Svensson. O., Rahm. M., Lejerskog. E., Savin. A., Strömstedt, E., Engström, J., Gravråkmo, H., Haiko- nen, K., Waters, R., Björklöf, D., Johansson, T., Sundberg, J., and Leijon, M., "Design proposal of electrical system for linear generator wave power plants" Presented at the 35th Annual Conference of the IEEE-Industrial-Electronics- Society (IECON 2009), Porto, Portugal, (2009) XVII Gravråkmo, H., Leijon, M., Strömstedt, E., Engström, J., Tyrberg, S., Savin, A., Svensson, O., and Waters, R., "De- scription of a torus shaped buoy for wave energy point ab- sorber", Presented at the conference Renewable Energy 2010, Yokohama, Japan, (2011) Reprints were made with permission from the respective publishers. Contents Introduction...................................................................................................17 1.1. Wave energy conversion...................................................................17 1.2. Wave energy......................................................................................19 1.2.1 Wave energy resource.................................................................19 1.2.2. Wave energy transport properties..............................................20 1.3. Wave energy conversion devices......................................................21 1.3.1. Point absorber............................................................................22 1.3.2. Two-body point absorber...........................................................23 1.4 Aim of the thesis................................................................................23 2. The Lysekil wave energy project..............................................................25 2.1 The Lysekil test site............................................................................25 2.2 The technology...................................................................................27 3. Theory of energy in ocean waves and energy absorption for a point absorber.........................................................................................................30 3.1 Potential linear wave theory...............................................................30 3.2 Ocean wave spectrum.........................................................................32 3.3 Energy transport of ocean waves........................................................34 3.4 Energy absorption for a point absorber..............................................36 3.4.1 Energy absorption for a two-body point absorber......................39 4. Methods to calculate the energy of ocean waves and modelling the point absorber.........................................................................................................40 4.1. Wave climate and sea states..............................................................40 4.1.1 Wave data measured at the Lysekil test site...............................40 4.1.2 Hindcast model wave data..........................................................41 4.1.3 Empirical spectra........................................................................41 4.2. Energy transport of ocean waves at finite depth...............................41 4.2.1. Depth variation of the energy transport.....................................42 4.2.2. Total instantaneous energy transport.........................................42 4.3 Point absorber model..........................................................................45 4.3.1 Defining the geometry................................................................45 4.3.2 Calculation of hydrodynamic coefficients..................................46 4.3.3 Point absorber model with linear damping.................................47 4.3.4 TBS point absorber model with non-linear damping..................49 5. Results and discussion..............................................................................55 5.1. Wave climate at the Swedish west coast...........................................55 5.3. Energy transport of ocean waves at finite depth...............................58 5.3.1. Depth variation of energy transport...........................................58 5.3.2. Total instantaneous energy transport.........................................59 5.4. TBS point absorber model.................................................................63 5.4.1. Linear damping..........................................................................63 5.4.2. Non-linear damping...................................................................65 5.4.2.1 Grid connection.......................................................................70 6. Conclusions...............................................................................................75 7. Suggestions for future work......................................................................76 8. Summary of Papers...................................................................................77 9. Svensk sammanfattning............................................................................83 10. Acknowledgements.................................................................................86 Bibliography.................................................................................................88