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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 623020, 9 pages
A Review of Offshore Wave Energy Extraction System
Engineering Research Center of Motion Control of Ministry of Education, Southeast University, Nanjing 210096, China
Received 28 June 2013; Accepted 30 August 2013
Academic Editor: Fabrizio Marignetti
Copyright © 2013 Zhongxian Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Offshore wave energy can be easily predicted and is proved to be much better than other forms of ocean energy such as shoreline wave, near-shore wave, and tides. Research on offshore wave energy extraction has been carried out in many countries to meet the growing demand for clean energy and reduce the impact on natural environment. This paper reviews the development of offshore wave energy extraction systems in the recent decade. Several aspects are introduced, including a global wave energy resource assessment, offshore wave energy extraction technologies, and the interaction between wave and floating buoy as well as linear generators. Although various offshore wave energy extraction systems have been proposed and even tested, it is difficult to decide which is the best one. In fact, design of floating buoy and linear generators plays an important role in the operational efficiency of offshore wave energy extraction system. This review provides some useful guidelines for future studies in this field.
Currently petroleum and coal resources count the majority of world energy supply. However, consumption of petroleum and coal resource is the main cause of serious environmental problems such as acid rain and global warming. Thereby the Kyoto protocol has been approved in 1997. In addition, the use of nuclear energy may also lead to environmental problems and safety issues. For example, one of the most disastrous earthquakes on record hit Japan and brought about radiation leakage from Fukushima Daiichi Nuclear Power Plant in 2011. Therefore, clean and renewable energy is increasingly needed to meet the economy development and reduce the impact on natural environment in the near future.
Wave energy, a source of renewable energy, has the advantages of a high energy density and persistence and, therefore, is a competitive candidate for energy supply. It is estimated that the total amount of ocean wave energy is 2000 TWh/year, which amounts to about 10 percent of the total electricity generated worldwide in 2005 [1, 2]. Ocean wave energy along European west coast is estimated to be able to meet the electricity demand in Western European countries . There are various methods of wave energy extraction to realize the application by human beings [4–6]. Research and development (R&D) programmes on wave energy extraction are conducted in a number of countries, such as Norway, Denmark, Portugal, Sweden, USA, and Australia [7–10]. Following the targets for greenhouse gas emissions reduction and the growing consumption of energy, many researchers from electrical engineering, mechanical engineering, and hydrodynamics are going into this research field.
Despite a wide variety of technologies and more than one thousand patents for wave energy extraction system, which are generally classified according to working principle (attenuator, point absorber, and terminator) and location (shoreline, near-shore, and offshore), wave energy extraction is a hydrodynamic and mechanical process including complex wave phenomena (radiation and diffraction) and nonlinear oscillations, especially for the offshore wave energy extraction systems. This explains why many wave energy extraction systems are at the R&D or theoretical stage , with only very few of which have been installed and tested in waves. The point absorber PowerBuoy Prototype, designed by Ocean Power Technologies (OPT) Inc. and installed off the Hawaii coast, USA, represents one of the leading offshore wave energy extraction systems that are currently operating . Another example for the leading offshore wave energy extraction system is Pelamis, installed at Agučadoura Wave Park, Portugal, and represents one of the technologies for wave energy extraction with a high power capture rate . Provided that suitable methods are applied in the design, construction, operation, and maintenance, offshore wave energy would be a promising renewable energy.
Electrical generators are the conception of power takeoff (PTO) of wave energy extraction systems which should allow conversion of wave energy into usable electrical power. The method of PTO depends on the location of wave energy extraction station, but the general method of obtaining electrical power is through conventional rotary generators or linear generators . However, the characteristics of wave such as wave period, wave height, and seasonal variation cause the variability of energy absorption [15, 16]. Accordingly, designing a suitable generator for wave energy extraction system in certain sea site is very necessary. In addition, the survivability of electrical generators in extreme conditions (e.g., typhoon or hurricane) is another issue that should be considered.
The layout of the rest of the paper is as follows. The second section is about wave energy resource in the world. The third part is about technologies for offshore wave energy extraction system, and the forth part is theoretical analysis of interaction between wave and floating buoy. Before the last section of conclusions, some linear generators of wave energy extraction systems are discussed in the fifth section.
2. Wave Energy Resource
Wave energy is produced by the effect of wind on surface water and is, therefore, indirectly considered as one type of solar energy. In fact, the time-averaged energy flow is concentrated when solar energy is converted into wind energy, and wave energy is even more concentrated when wind blows [17, 18]. Therefore, the availability of wave energy is much higher than that of wind energy and solar energy . Wave energy consists of kinetic energy and potential energy, which arise from the motion of waves. The total amount of wave energy mainly depends on the characteristics of wave such as wave height, wave period, location, and seasonal variation. In general, the stored energy per unit wave surface in deep water (approximately a depth exceeding half of the wavelength) is proportional to the wave height squared, which can be described by the following equation [15, 18]: where is the stored energy per unit wave surface (J/m2), is the mass density of wave (1030 kg/m3), is the acceleration of gravity (kg/m3), and is the progressive harmonic plan wave height (m). According to linear theory and superposition principle [20, 21], a real sea wave may be characterized as energy spectrum and the stored energy can be equally divided between kinetic energy and potential energy.
Assessment of wave energy resource is one of the important prerequisite work for wave energy extraction system designing and prototype testing. Actually, (1) is not enough for the assessment of wave energy resource. The assessment should include the characteristics of wave (e.g., wave height, wave period, water depth, and seasonal variation) and the location of wave energy extraction system (e.g., channel, reefs, harbor, and coast). In 1991, European Commission started a project to investigate the characteristics of wave energy and produced some recommendations for prototype testing . The WERATLAS, funded by European Commission and considered as a reference for wave energy extraction system construction, proposed a proper numerical wind-wave modeling to describe the detailed characteristics of waves at 85 points off the Atlantic and Mediterranean coast of Europe .
Generally, the annual mean wave energy in offshore (20100 kW/m in the areas of moderate-to-high latitudes) is much more than that in shoreline and near shore. Figure 1 shows the global distribution of annual mean wave energy density [24–27]. A large seasonal variation makes southern hemisphere (e.g., southern coasts of South America, western coasts of Europe, Africa, Australia, and New Zealand) a competitive candidate for the location of wave energy extraction station.
3. Offshore Wave Energy Extraction Technologies
The advantage of offshore wave energy extraction system lies in that a great deal of wave energy and economic benefits can be obtained through a high energy density in deep water [28, 29]. However, construction and maintenance of offshore wave energy extraction system are expensive and difficult due to the complex sea condition. The system may be subject to strong wave impulsive load (e.g., typhoon or hurricane) and thereby damaged by peak pressures. Since 95% of energy in offshore wave is between water surface and 7 m under water surface [28, 29], the objective of this section is to briefly review the technologies in offshore wave energy extraction system.
Offshore wave energy extraction systems are basically oscillating floating bodies, and the horizontal dimensions of these floating bodies are usually smaller than one wavelength. The idea of converting offshore wave energy into electrical energy has witnessed a significant development in recent years. Some important examples of offshore wave energy extraction systems are given below.
3.1. Single-Body Floating Systems
An early example of single-body floating system is a floating buoy connected to a linear permanent magnet generator of seabed-fixed device through a rope, and the rope is kept tight by a spring under the linear permanent magnet generator, as shown in Figure 2 [30–32]. Spring obtains wave energy during half a wave cycle (wave from trough to crest) and drives linear permanent magnet generator to produce electrical energy in another half of the wave cycle (wave from crest to trough). One advantage of this system is that the floating buoy’s nature angular frequency in heave can be matched with the incident wave angular frequency. A full-scale single-body floating system (the radius of floating buoy is equal to 3 m) was constructed at a depth of 25 m, 2 km off the Swedish west coast, and tested in 2007 . In the years to come, an array of single-body floating systems will be deployed at the same site to evaluate the concepts of technology, ecology, and economy.
The backward bent duct buoy, another single-body floating system (also known as an oscillating water column converter), was designed in Japan under the leadership of Yoshio Masuda. Figure 3 shows the sketch of a backward bent duct buoy . In comparison with the frontward facing duct buoy, the advantages of backward bent duct buoy are that the oscillating water column could be designed to resonance with incident waves, and a high energy conversion rate with low mooring force could be achieved . The backward bent duct buoy has been investigated in several countries (Japan, Korea, China, and so on) and installed in Japan and China. In the second half of 2006, a 12 m long prototype with a novel Walls turbine was installed off Ireland western coast .
3.2. Two-Body Floating Systems
The single-body floating systems may cause some problems because of the unstable distance between water surface and seabed-fixed device, especially under the condition of typhoon or hurricane. In addition, installation of the device on seabed is expensive and difficult. Two-body floating systems may be utilized instead, where wave energy can be obtained through the relative motion between two floating bodies. The characteristics of oscillating of floating body are analyzed theoretically in papers [31, 32]. One famous example of two-body floating systems is PowerBuoy (shown in Figure 4) designed by Ocean Power Technologies Inc. (an American company in Pennington, NJ, USA), and installed off the Spain’s northern coast with a capacity of 40 kW, in September 2008 . The PowerBuoy consists of two floating bodies, the outer one acts as a resonating body with incident waves and the inner one as a fixed reference. The resultant mechanical stroking between two floating bodies drives a generator to produce electrical energy via a hydroelectric turbine, and the produced electrical energy is delivered ashore by an underwater cable.
Besides, PowerBuoy can be designed for strong wave impulsive load (e.g., typhoon or hurricane). PowerBuoy’s sensors monitor the relative motion of two floating bodies and surrounding ocean waves continuously. In the case of strong wave impulsive load, the PowerBuoy will shut off and cease electrical energy production. The PowerBuoy will continue to produce electrical energy when the strong wave impulsive load has passed.
3.3. Multibody Floating Systems
The most successful wave energy extraction system based on multibody floating systems is Pelamis (shown in Figure 5), which represents one of the most widely-used offshore wave energy extraction systems with a high power capture/unit weight . This system is a semisubmerged articulated structure consisting of several floating buoys linked through hinged joints. The relative vertical and horizontal motions of floating buoys are resisted by hinged joints which are used to drive electrical generators via high pressure oil and hydraulic motors. A set of three Pelamis has been installed at the European Marine Energy Centre of Orkney (a capacity of 750 kW) to establish the first grid-connected offshore wave energy extraction system for commercial purposes between 2004 and 2007. The Aegir wave farm of Shetland is expected to increase its capacity (10 MW) by installing 13 Pelamis [36, 37].
4. Interaction between Wave and Floating Buoy
Study of the interaction between wave and floating body could benefit from previous investigations on the motion of ship in waves. This section will review the motion of floating buoy based on vertical wave force.
4.1. Added Mass and Damping of Floating Buoy
The hydrodynamic parameters such as added mass and damping play an important role in the study of motion of floating buoy, there exist a lot of numerical methods for calculating the two hydrodynamic parameters of floating buoy, for example, traditional wave source distribution method, finite element variation formulations, and integrovariational method . However, the above numerical methods are time consuming and complicated. In fact, the two hydrodynamic parameters of floating buoy can be simply calculated by the use of eigenfunctions, especially for the low-frequency motion . Therefore, a quick calculation method consists of parameters (e.g., water depth, radius of floating buoy, and its draft) and summary formulas for the two hydrodynamic parameters are proposed, and the calculation results are verified by some available experimental results .
It is expected that calculation of the two hydrodynamic parameters will optimize the dynamic performance of floating buoy design and increase the efficiency of offshore wave energy extraction system.
4.2. Vertical Wave Force on Floating Buoy
It is assumed that the dimensions of heaving buoy are smaller than incident wavelength, and the fluid is irrotational and incompressible and experiences variation in sinusoidal curve as time goes on. Then the linearized theory and potential energy theory are applied. Generally, the velocity potential of wave  can be expressed as where is incident potential, is diffracted potential, and is radiated potential.
From potential theory the vertical wave force on the wet surface (see Figure 6) can be written as where is hydrodynamic pressure, is vertical unit vector, is Froude-Krylov force vector, and is diffraction force vector . Consider
In (4) and (5), kg/m3 is the mass density of sea water, and is the angular frequency of sea wave. Equation (4) may be divided into one integral over the area and one integral over the area by area integral method , as shown in
In addition, the integral over the area can be transformed into one triple integral over the displaced water volume by divergence and Gauss’ theorem [15, 44] Therefore, where and are the acceleration and amplitude of floating buoy in terms of complex, respectively.
In order to calculate the diffraction force vector , it is not necessary to calculate the diffracted potential but the proportional coefficient of radiated velocity potential . From the Green’s theorem [3, 15], the diffraction force vector can be expressed as
4.3. Motion Equation of Floating Buoy
As shown in Figure 6, the floating buoy is subject to three forces, namely, the vertical wave force , the radiation force , and the hydrostatic buoyancy force . According to Newton’s law, the motion equation of floating buoy in heave may be written as where is the weight of floating buoy. According to linear theory, the radiation force is proportional to the so-called radiation impedance of floating buoy, and the hydrostatic buoyancy force is proportional to the excursion of floating buoy from its equilibrium position, both of which can be written as where is the speed of floating buoy in heave . In terms of complex amplitude () and small-body approximation the speed of floating buoy in heave may be written as where and are added mass and damping of floating buoy, respectively.
Figure 7(a) shows a two-body floating system oscillating in heave. The wave propagates in sinusoidal trace, at the wave height of 1.4 meters and wave period of 5 seconds. Both of the diameters of outer floating buoy and damper plate (at the bottom of inner floating buoy) are equal to 2.4 m. The function of damper plate is to increase the damping effect on inner floating buoy by the surrounding water. The depths of submergence of outer and inner floating buoys are shown in Figure 7(a). From the above theory of interaction between wave and floating buoy, the speed curves of outer and inner floating buoys in heave are shown in Figure 7(b). Based on this concept of relative motion between outer and inner floating buoys, a two-body floating system with a novel permanent magnet tubular linear generator rated at 5 kW will be installed off the eastern coast of China, in the second half of 2013.
5. Linear Generators
The ultimate product of wave energy extraction system is electrical energy, which is produced from various kinds of electrical generators (e.g., conventional rotating generators or linear generators) and delivered into a grid [45–49]. Electrical generator is one of most important devices determining the operation efficiency of wave energy extraction system. In the case of conventional rotating generators, a linear-to-rotary conversion device (e.g., air turbine, water turbine, or hydraulic motor) is needed to convert the linear motion of wave into a uniform rotary motion [50, 51]. Although the first linear generator has been proposed since over 100 years ago in the USA , and linear generators have been designed for wave energy extraction systems since the late 1970s , there are still very few kinds of linear generators that have been tested in sea waves. In recent years, the term “direct-drive wave energy extraction system” emerges, which indicates coupling the wave’s speed and linear generator directly without any pneumatics or complex linear-to-rotary conversion systems. Thus, the complex conversion device is avoided and the mechanical loss is, therefore, decreased.
5.1. Two-Sided Permanent Magnet Linear Generator
Archimedes Wave Swing  is a fully submerged wave energy extraction system and consists of three parts: a two-sided permanent magnet linear generator, a basement (bottom part), and a floater (upper part), as shown in Figure 8. When a wave crest is above the AWS, the floater is pushed down by the added pressure of water, and when a wave trough is above it, the floater is moved up by the reduced pressure of water. The motion of floater is resisted by a two-sided permanent magnet linear generator, and the sketch of this two-sided permanent magnet linear generator is shown in Figure 9 . There are several advantages of a two-sided permanent magnet linear generator:(i)high force density, (ii)reasonable work efficiency,(iii)permanent magnet material is cheap,(iv)the electricity is only restricted in stator.
The AWS is the first wave energy extraction system, which is equipped with a permanent magnet linear generator, installed and tested in sea waves.
5.2. Permanent Magnet Tubular Linear Generator
A novel three-phase permanent magnet tubular linear generator (PMTLG) with Halbach array was proposed for wave energy extraction system by Southeast University, China, in 2010 . One significant advantage of PMTLG is that assistant teeth are adopted to minimize the detent force and optimize the dynamic performance of wave energy extraction system. Figure 10 shows the structure of PMTLG. With the assistant teeth, up to 70% of detent force is reduced. A wave energy extraction system equipped with a PMTLG has been designed and tested in China under the supporting of National Natural Science Foundation of China (NSFC), as shown in Figure 11. The test results indicate that a large amount of wave energy (3–5 KW/m) can be obtained from the East China Sea and the South China Sea, which is quite considerable because China possesses a long coastline of over 18,000 km.
Besides, a new linear switched reluctance generator was proposed for wave energy conversion by University of Beira Interior, Portugal, in 2012 . The numerical analysis and optimization results showed that the proposed linear switched reluctance generator was high force density, robustness, and easy design and installation.
6. Discussions and Conclusions
Although many studies have analyzed offshore wave energy extraction systems theoretically and a few kinds of prototype have been tested in wave tank or real sea, some R&D financial supports from governments are still necessary for the construction and maintenance of the extraction system in harsh environment. In order to ensure a full-scale offshore wave energy extraction system absorbing wave energy maximally, the geometry and size of certain floating buoy should be designed to resonance with incident waves. For this reason, a larger size and capacity of linear generators are needed in design and construct (D&C).
Offshore wave energy extraction systems are still far from maturity. To develop a grid-connected and commercial offshore wave energy extraction system is not an easy task. Many difficulties and issues are still to be solved. Researchers in related fields should cooperate to promote technological development and avoid repetitive mistakes. It is believed that high quality research results would lead to a better working efficiency and economic benefit for the offshore wave energy extraction system.
This review shows the current status of offshore wave energy extraction technologies. The interaction between wave and floating body, as well as linear generators, is also illustrated.
Conflict of Interests
The authors declared that they have no conflict of interests to this paper.
This work was financially supported by the National Natural Science Foundation of China (Grant no. 41076054), Special Foundation for State Oceanic Administration of China (GHME2011GD02), and the Support of Science and Technology project from Jiangsu Provincial (BE2012138).
- B. Drew, A. R. Plummer, and M. N. Sahinkaya, “A review of wave energy converter technology,” Proceedings of the Institution of Mechanical Engineers A, vol. 223, no. 8, pp. 887–902, 2009.
- V. C. Tai, P. C. See, S. Merle, and M. Molinas, “Sizing and control of the electric power take off for a buoy type Point absorber wave energy converter,” in Proceedings of the International Conference on Renewable Energies and Power Quality, Granada, Spain, March 2012.
- J. Brooke, Wave Energy Conversion, Elsevier, New York, NY, USA, 2003.
- M. E. McCormick, Ocean Wave Energy Conversion, Wiley, New York, NY, USA, 1981.
- Engineering Committee on Oceanic Resources and Working Group on Wave Energy Conversion, Wave Energy Conversion, Elsevier, New York, NY, USA, 2003.
- S. Petroncini, Introducing wave energy into the renewable energy marketplace [M.S. thesis], University of Edinburgh, Edinburgh, UK, 2000.
- L. Bergdahl, “Review of research in Sweden,” in Proceedings of the Wave Energy Workshop, Cork, Ireland, October 1992.
- G. Fredrikson, “IPS wave power Buoy Mark IV,” in Proceedings of the Wave Energy Workshop, Cork, Ireland, October 1992.
- K. Nielsen and N. I. Meyer, The Danish Wave Energy Programme, EWEC, Patras, Greece, 3rd edition, 1998.
- Officers of World Energy Council, Survey of Energy Resources, Interim Update 2009, London, UK, 2009.
- M. Previsic, “E21 EPRI assessment offshore wave energy conversion devices,” Report E21 EPRI WP-004-US-Rev 1, Electric Power Research Institute, Palo Alto, Calif, USA, 2004.
- Ocean Power Technologies (OPT) Inc, Recent News, http://www.oceanpowertechnologies.com.
- L. Lin and H. T. Yu, “Offshore wave energy generation devices: impacts on ocean bio-environment,” Acta Ecologica Sinica, vol. 32, pp. 117–122, 2012.
- M. A. Mueller, “Electrical generators for direct drive wave energy converters,” IEE Proceedings, vol. 149, no. 4, pp. 446–456, 2002.
- J. Falnes, Ocean Waves and Oscillating Systems, Cambridge University Press, Cambridge, 2002.
- M. Lucia, M. H. Anne, and F. Peter, “A method for EIA scoping of wave energy converters-based on classification of the used technology,” Environmental Impact Assessment Review, vol. 32, no. 1, pp. 33–44, 2012.
- N. N. Panicker, “Power resource estimate of ocean surface waves,” Ocean Engineering, vol. 3, no. 6, pp. 429–439, 1976.
- J. Falnes, “A review of wave-energy extraction,” Marine Structures, vol. 20, no. 4, pp. 185–201, 2007.
- R. Pelc and R. M. Fujita, “Renewable energy from the ocean,” Marine Policy, vol. 26, no. 6, pp. 471–479, 2002.
- Y. Goda, Random Seas and Design of Maritime Structure, University of Tokyo Press, Tokyo, Japan, 1985.
- M. J. Tucker, Waves in Ocean Engineering: Measurement, Analysis, Interpretation, Ellis Horwood, New York, NY, USA, 1991.
- T. Pontes, D. Mollison, J. C. Borge, L. Cavaleri, and G. A. Athanassoulis, “Evaluation of the wave energy resource,” in Proceedings of the Workshop on Wave Energy R&D, Cork, Ireland, 1993.
- M. T. Pontes, “Assessing the European wave energy resource,” Journal of Offshore Mechanics and Arctic Engineering, vol. 120, no. 4, pp. 226–231, 1998.
- J. R. Joubert, An investigation of the wave energy resource on the South African coast, focusing on the spatial distribution of the south west coast [M.S. thesis], University of Stellenbosch, Stellenbosch, South Africa, 2008.
- S. Barstow, M. Gunnar, D. Mollison, and J. Cruz, The Wave Energy Resource, Springer, Berlin, Germany, 2008.
- M. T. Pontes, L. Cavaleri, and D. Mollison, “Ocean waves: energy resource assessment,” Marine Technology Society Journal, vol. 36, no. 4, pp. 42–52, 2002.
- S. F. Barstow, O. Haug, and H. E. Krogstad, “Satellite altimeter data in wave energy studies,” in Proceedings of the 3rd International Symposium on Ocean Wave Measurement and Analysis (WAVES '97), vol. 2, pp. 339–354, November 1997.
- L. Duckers, “Wave energy,” in Renewable Energy, Oxford University Press, Oxford, UK, 2nd edition, 2004.
- U. A. Korde, “Control system applications in wave energy conversion,” in Proceedings of the MTS/IEEE Conference and Exhibition (OCEANS '00), vol. 3, pp. 1817–1824, September 2000.
- R. Waters, M. Stålberg, O. Danielsson et al., “Experimental results from sea trials of an offshore wave energy system,” Applied Physics Letters, vol. 90, no. 3, Article ID 034105, 3 pages, 2007.
- V. Ferdinande and M. Vantorre, “hydrodynamics of ocean wave energy utilization,” in The Concept of A Bipartite Point Absorber, Springer, Berlin, Germany, 1986.
- J. Falnes, “Wave-energy conversion through relative motion between two single-mode oscillating bodies,” Journal of Offshore Mechanics and Arctic Engineering, vol. 121, no. 1, pp. 32–38, 1999.
- Y. Masuda, L. Xianguang, and G. Xiangfan, “High performance of cylinder float backward bent duct buoy (BBDB) and its use in European seas,” in Proceedings of the 1st European Wave Energy Symposium, pp. 323–337, 1993.
- Y. Masuda and T. Kuboki, “Prospect of economical wave power electric generator by the terminator backward bent duct buoy (BBDB),” in Proceedings of the 12th International Offshore and Polar Engineering Conference, pp. 26–31, May 2002.
- Ocean Energy Inc, Recent News, http://www.oceanenergy.ie/.
- F. Zabihian and A. S. Fung, “Review of marine renewable energies: case study of Iran,” Renewable and Sustainable Energy Reviews, vol. 15, no. 5, pp. 2461–2474, 2011.
- A. F. D. O. Falcão, “Wave energy utilization: a review of the technologies,” Renewable and Sustainable Energy Reviews, vol. 14, no. 3, pp. 899–918, 2010.
- R. W. Yeung, “Added mass and damping of a vertical cylinder in finite-depth waters,” Applied Ocean Research, vol. 3, no. 3, pp. 119–133, 1981.
- C. J. R. Garrett, “Wave forces on a circular dock,” Journal of Fluid Mechanics, vol. 46, no. 1, pp. 129–139, 1971.
- T. Sabuncu and S. Calisal, “Hydrodynamic coefficients for vertical circular cylinders at finite depth,” Ocean Engineering, vol. 8, no. 1, pp. 25–63, 1981.
- N. J. Baker, Linear generators for direct drive marine renewable energy converters [Ph.D. thesis], University of Durham, Durham, UK, 2003.
- F. E. Gardner, “Learning experience of AWS pilot plants test offshore Portugal,” in Proceedings of the 6th European Wave Energy Conference, pp. 149–154, 2005.
- L. H. Holthuijsen, Waves in Oceanic and Coastal Waters, Cambridge University Press, Cambridge, UK, 2007.
- R. Haberman, Applied Partial Differential Equation: With Fourier Series and Boundary Value Problems, Addison Wesley, Upper Saddle River, NJ, USA, 4th edition, 2004.
- J. Ribeiro and I. Martins, “Development of a low speed linear generator for use in a wave energy converter,” in Proceedings of the International Conference on Renewable Energies and Power Quality, Granada, Spain, 2010.
- N. J. Baker, M. A. Mueller, and P. R. M. Brooking, “Electrical power conversion in direct drive wave energy converters,” in Proceedings of the 5th European Wave Energy Conference, Cork, Ireland, 2003.
- N. J. Baker, M. A. Mueller, and E. Spooner, “Permanent magnet air-cored tubular linear generator for marine energy converters,” in Proceedings of the 2nd IEE International Conference on Power Electronics, Machines and Drives (PEMD '04), pp. 862–867, Edinburgh, UK, April 2004.
- M. Eriksson, J. Isberg, and M. Leijon, “Hydrodynamic modelling of a direct drive wave energy converter,” International Journal of Engineering Science, vol. 43, no. 17-18, pp. 1377–1387, 2005.
- V. D. Colli, P. Cancelliere, F. Marignetti, R. Di Stefano, and M. Scarano, “A tubular-generator drive for wave energy conversion,” IEEE Transactions on Industrial Electronics, vol. 53, no. 4, pp. 1152–1159, 2006.
- S. Raghunathan, “The wells air turbine for wave energy conversion,” Progress in Aerospace Sciences, vol. 31, no. 4, pp. 334–386, 1995.
- L. C. Rome, L. Flynn, E. M. Goldman, and T. D. Yoo, “Biophysics: generating electricity while walking with loads,” Science, vol. 309, no. 5741, pp. 1725–1728, 2005.
- M. Eriksson, Modelling and experimental verification of direct drive wave energy conversion-Buoy-generator dynamics [Ph.D. thesis], Uppsala University, Uppsala, Sweden, 2007.
- H. Yu, C. Liu, B. Yuan, M. Hu, L. Huang, and S. Zhou, “A permanent magnet tubular linear generator for wave energy conversion,” Journal of Applied Physics, vol. 111, no. 7, Article ID 07A741, 3 pages, 2012.
- M. R. A. Calado, P. M. C. Godinho, and S. J. P. S. Mariano, “Design of a new linear generator for wave energy conversion based on analytical and numerical analyses,” Journal of Renewable and Sustainable Energy, vol. 4, no. 3, Article ID 033117, 11 pages, 2012.