Buoy and Generator Interaction with Ocean Waves

To Magdalena Front cover: The buoy of the wave energy converter L3. In the background, Klam- merskär and the observation tower. June 2009. Back cover: The rubber dinghy Bullen, which has made many trips to and from Klammerskär, with and without the author. In the background, the southern marker buoy for the Lysekil research site can be seen. July 2011. List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Leijon, M., Boström, C., Danielsson, O., Gustafsson, S., Haikonen, K., Langhamer, O., Strömstedt, E., Stålberg, M., Sundberg, J., Svensson, O., Tyrberg, S., and Waters, R. “Wave Energy from the North Sea: Experiences from the Lysekil Research Site”. Surveys in Geophysics, Vol. 29, Issue 3, pp. 221–240, May 2008. II Tyrberg, S., Stålberg, M., Boström, C., Waters, R., Svensson, O., Strömstedt, E., Savin, A., Engström, J., Langhamer, O., Gravråkmo, H., Haikonen, K., Tedelid, J., Sundberg, J., and Leijon, M. “The Lysekil Wave Power Project: Status Update”. Proceedings of the 10th World Renewable Energy Congress, WREC, Glasgow, UK, pp. 1061–1066, July 2008. III Leijon, M., Waters, R., Stålberg, M., Svensson, O., Boström, C., Ström- stedt, E., Engström, J., Tyrberg, S., Savin, A., Gravråkmo, H., Bern- hoff, 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 Motions to Electric- ity Using a Grid-Oriented Approach”. IEEE Power & Energy Magazine Vol. 7, Issue 1, pp. 50–54, January/February 2009. IV Tyrberg, S., Gravråkmo, H., Leijon, M. “Tracking a Wave Power Buoy Using a Network Camera — System Analysis and First Results”. Pro- ceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering (peer-reviewed), OMAE, Honolulu, USA, June 2009. V Tyrberg, S., Waters, R., and Leijon, M. “Wave Power Absorption as a Function of Water Level and Wave Height: Theory and Experiment”. IEEE Journal of Oceanic Engineering, Vol. 35, Issue 3, pp. 558–564, July 2010. VI Boström, C., Lejerskog, E., Tyrberg, S., Svensson, O., Waters, R., Savin, A., Bolund, B., Eriksson, M., and Leijon, M. “Experimental Results From an Offshore Wave Energy Converter”. Journal of Offshore Mechanics and Arctic Engineering, Vol. 132, Issue 4, pp. 041103-1–041103-5, November 2010. VII Tyrberg, S., Svensson, O., Kurupath, V., Engström, J., Strömstedt, E., and Leijon, M. “Wave Buoy and Translator Motions — On-site Mea- surements and Simulations”. IEEE Journal of Oceanic Engineering, Vol. 36, Issue 3, pp. 377–385, July 2011. VIII Lejerskog, E., Gravråkmo, A., Savin, A., Strömstedt, E., Tyrberg, S., Haikonen, K., Krishna, R., Boström, C., Rahm, M., Ekström, R., Svens- son, O., Engström, J., Ekergård, B., Baudoin, A., Kurupath, V., Hai, L., Li, W., Sundberg, J., Waters, R., and Leijon, M. “Lysekil Research Site, Sweden: A Status Update”. Proceedings of the 9th European Wave and Tidal Energy Conference (peer-reviewed), EWTEC11, Southamp- ton, UK, September 2011. IX Lindroth, S. and Leijon, M., “Offshore Wave Power Measurements - a Review”, Renewable & Sustainable Energy Reviews, in press, available online, DOI:10.1016/j.rser.2011.07.123, September 2011. X Lindroth, S. and Leijon, M., “Spectral Parameters and Wave Energy Converter Performance”, Manuscript, October 2011.

Reprints were made with permission from the publishers. The author has also contributed to the following papers, not included in the thesis. Paper A is a conference version of Paper VI. For Paper B the contribution of the author was minor, and the scope differs somewhat from the rest of the papers.

A Boström, C., Lejerskog, E., Tyrberg, S., Svensson, O., Waters, R., Savin, A., Bolund, B., Eriksson, M., and Leijon, M. “Experimental results from an offshore wave energy converter”. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering (peer-reviewed), OMAE, Estoril, Portugal, June 2008. B Gravråkmo, H., Leijon, M., Strömstedt, E., Engström, J., Tyrberg, S., Savin, A., Svensson, O., Waters, R., “Description of a Torus Shaped Buoy for Wave Energy Point Absorber”. Proceedings of Renewable Energy 2010, Yokohama, Japan, June/July 2010. Received Best Paper Award. Contents

1 Introduction ...... 11 1.1 Wave energy and ways to capture it ...... 11 1.2 Working in engineering science ...... 12 1.3 Aims of the thesis ...... 13 2 Background ...... 15 2.1 The Lysekil Project ...... 15 2.2 Timeline ...... 15 2.3 Theory ...... 18 2.3.1 Describing waves ...... 18 2.3.2 Linear generators ...... 21 3 Ocean Measurements ...... 23 3.1 History and development of wave power measurements ...... 23 3.2 The fundamental difﬁculties ...... 24 3.3 The work at Klammerskär ...... 25 3.3.1 Successes and failures ...... 26 3.4 Interpreting measurements ...... 27 3.4.1 Comparing measurements with incoming waves ...... 29 4 WEC Performance ...... 31 4.1 Deﬁning performance ...... 31 4.2 Controlling the variables ...... 32 4.2.1 AC/DC load and sea state ...... 33 4.2.2 Water level and wave height ...... 34 4.2.3 Spectral shape ...... 34 5 Summary of Papers ...... 37 6 Conclusions ...... 43 6.1 Measurements and buoy/generator motion ...... 43 6.2 WEC Performance ...... 44 7 Acknowledgements ...... 45 8 Svensk sammanfattning ...... 47 References ...... 49

Abbreviations and nomenclature

Abbreviation Meaning AC Alternating Current DC Direct Current GPS Global Positioning System L1–9 Wave energy converter 1–9 LRS The Lysekil Research Site WEC Wave Energy Converter

Symbol Unit Entity Φ Wb Magnetic ﬂux ρ kg/m3 Density E V Electromotive force H m Wave height

Hm0 m Signiﬁcant wave height J W/m Energy transport N - Number of coil turns S( f ) m2/Hz Variance spectral density T s Period

T−10 s Energy period Tp s Peak period f Hz Frequency

f0 Hz Fundamental frequency f−10 Hz Energy frequency fp Hz Peak frequency g m/s2 Gravitational constant 2 k mk m Hz Spectral moment number k t s Time w m Water level

1. Introduction

1.1 Wave energy and ways to capture it The ever increasing need for energy in the world and the dangers of further use of fossil fuels have put a focus on renewable energy technologies. That there is a vast amount of energy in ocean waves has been known for a long time (see e.g. [1,2]), and this also becomes very evident to anyone who spends time out at sea. The exact amount of power available from waves is impossible to determine, since it depends on the performance of the technology chosen, but an estimation that about 1 TW continuously descends on the coastlines of the world was made in [3]. Regardless of the precision in that statement, it is clear that our oceans carry enough energy for wave power to be interesting to study further. Numerous projects have tried to harvest the energy in waves. There are quite a few projects still active around the world, the most famous of which is possibly the Pelamis [4, 5]. Some other concepts that are, or have been, active in recent years are the Wave Dragon [6], the Archimedes Wave Swing [7], Oceanlinx [8], the Ocean Energy Buoy [9], the Oregon State University project [10] and the Backward Bent Duct Buoy [11]. Further projects, past and present, can be found in a recent review by Falcão [12]. Historically, most attempts have failed in creating a technology that can survive the harsh ocean wave climates, or in designing a technology that is economically viable. There are some considerable advantages in using wave energy in comparison to other intermittent energy sources, such as wind and solar energy. But there are also some fundamental difﬁculties. On the positive side, wave energy is a concentrated form of energy, since waves absorb the energy from winds blowing over large areas. This also means that waves, in comparison with winds, are more predictable and more evenly distributed in time. Even if the wind abates, waves will keep rolling in for some time. The major difﬁculty of tapping into the huge energy resource of ocean waves is the large variations of the powers and forces involved. For a system to be sustainable, it needs to produce electricity at average wave climates, but still survive harsh weathers and storms. There is therefore a risk of ending up with systems that are either too bulky to be economically viable, or conversely, too fragile to survive in the long run. The Lysekil project, run by the Division of Electricity at Uppsala University, is an attempt to design a wave energy system which is sturdy enough, without becoming too expensive.

11 (b)

(a) (c)f Figure 1.1: A classiﬁcation of wave energy devices. (a) Wave activated bodies, (b) Overtopping devices, (c) Oscillating water columns [13].

Systems for wave energy conversion can be classified in many different ways. In Fig. 1.1, wave energy devices have been categorized based on their working principle. These are wave activated bodies, overtopping devices, and oscillating water columns. The first of these describes systems where the motion of the waves is directly transferred to the Wave Energy Converter (WEC). Examples of this technology include the Pelamis mentioned above. Overtop- ping devices let water run up a slope into a reservoir, from where the potential energy is converted using a low-head turbine. The Wave Dragon is an example of such a technology. Oscillating water columns use a fluctuating air pressure above the ocean surface to drive a turbine. One way to achieve such a varying air pressure is to partially submerge a pipe into the water. The Backward Bent Duct Buoy is an example of a technology using an oscillating water column. The technology used in the Lysekil project can be classified as a wave activated body. It is also a point absorber, meaning that the width of the WEC is small in comparison to the wave length.

1.2 Working in engineering science Engineering science differs from natural science in some senses. Whereas natural science is mainly concerned with understanding and explaining natural phenomena, engineering science also strives to create new systems, new ob- jects, or new solutions, based on knowledge gained in natural science. Thus, engineering science is an iterative process of gathering knowledge, making design choices, constructing solutions, and then again gathering knowledge about how the constructed system works in the surrounding environment. This knowledge may be used to draw conclusions that can be transferred to other scientiﬁc disciplines, but it may also form the base for new designs, new ideas and new solutions.

12 The work with the wave energy system at the Division of Electricity is an example of the engineering process described above. Theories of wave dynamics, electromagnetism and mechanics have been used together with existing solutions within power electronics and mechanical engineering to de- velop a system that has then been deployed in the ocean. The workings of this human-made system, and its interaction with the sea, have then been the focus of our studies. As we have learned more and more, we have been able to take steps towards more efﬁcient wave energy converters, and we have also been able to draw several conclusions on the workings of our system in relation to different natural and engineering parameters. The extent to which these conclusions can be applied to general cases may vary, but regardless of this, the work gives us the foundation needed to take further steps, and to ﬁnd the next questions to ask.

1.3 Aims of the thesis Describing work within engineering science, this thesis does not follow one single straight line, as such a line does not exist, now or in the future. Rather, it is composed of a number of papers describing work within the same general area, but with slightly different focuses. The general aim of the papers is to increase the understanding of wave–buoy–generator interaction in a wave power plant, so that the performance can be increased. This broad aim can be translated to a number of more specific questions to be answered: • How can we measure buoy and generator motion? • How does the buoy behave in the waves? • How do the motions of the waves, the buoy and the generator relate? • What electrical and oceanic parameters impact the performance of a wave energy converter? How can this impact be described? • To what extent can we simulate and predict the performance of a wave energy converter? Due to the nature of engineering science, the answers to the questions above may give very different results. Some answers will stimulate new theories, others will be used to confirm simulations, and others still could provide input for mechanical solutions. Certain answers, finally, will not lead anywhere. However, it is in the process of working with the questions that we find a good path, and it is often afterwards that the big picture can be distinguished, rather than before.

2. Background

2.1 The Lysekil Project The Lysekil wave energy project was initiated with simplicity as a guiding principle, since the harsh conditions at sea mean that complex systems have a high risk of failure, and are associated with high maintenance costs. The idea of simplicity meant that direct drive (i.e. without gearboxes or energy stor- age) was favoured, and led to the wave energy converter concept illustrated in Fig. 2.1. The buoy follows the motion of the waves and the line transmits this motion to the translator in the linear generator, where electricity is produced. The chosen system means that the most complex part (the generator) is placed on the seabed, away from the extreme forces of the waves. The direct drive means that the system becomes more robust, but also that it is impossible to transmit the converted electricity directly to the grid, since voltages will vary both in amplitude and frequency. There is a need for an intermediate step, where the voltages from several WECs are rectiﬁed, added together and then inverted again to the grid frequency. The experimental work within the project has taken place both at the Ångström Laboratory in Uppsala and out at sea near Lysekil on the West Coast, at the Lysekil Research Site (LRS). A sea chart of the area, from Paper IV, can be found in Fig. 2.2. The site is also described in more detail in Paper I and II. Eight licentiate theses [14–21] and seven doctoral theses [13, 22–27] have been published regarding the Lysekil project. The research covers many different topics, such as power electronics, generator technology, hydrodynamics, wave resource descriptions, structural mechanics, measurement systems and environmental impact.

2.2 Timeline Paper II and VIII give an overview of the Lysekil project history, on several different areas. In addition to this, Paper I and III describe the main ideas behind the project, and go into some more detail. For a better understanding of the timing of different steps, a brief time line is also presented here:

2002–2004 • The project is started during the spring of 2002.

15 Buoy

Line Sealing 9m Endstopspring

Stator

Translator

Retracting springs Endstopspring Foundation

Figure 2.1: The wave energy converter L3 (left), and a schematic description of the concept (right). Adapted from Paper VII.

• Investigations are made of the bottom conditions at LRS during the summer of 2003. • A laboratory version of the linear generator is ﬁnished in December 2003. • A wave measuring buoy is deployed at LRS in April 2004. • The National Maritime Administration deploys buoys to mark LRS to the public in October 2004.

2005 • An experimental setup to measure forces on a cylindrical buoy is deployed at LRS in March. • The four ﬁrst “biology buoys” are deployed at LRS during the fall. The purpose of these is to study the environmental impact of installing buoys and foundations in an otherwise empty ocean area. • The construction of the ﬁrst wave energy converter, L1, is started.

2006 • A measurement station is built on Härmanö, close to LRS, during the ﬁrst months of the year.

16 Figure 2.2: The Lysekil Research Site and its surroundings. The dash-dotted line rep- resents the power cable from the wave park to shore. The dots surrounded by the dashed line represent wave energy converters and biology buoys. From Paper IV.

• L1 is deployed at LRS on the 13th of March, and the ﬁrst set of experimental data from the generator is gathered.

2007 • Additional biology buoys are deployed. • In July, a tower is erected on the islet of Klammerskär, near the research site, to form the base for a future observation system. A picture of the research site, taken from the tower, can be seen in Fig. 2.3.

Figure 2.3: The Lysekil research site, as seen from the observation tower. From Pa- per VI.

17 2008 • A toroidal buoy is attached to L1 in May, to investigate if the design can help decrease the peak forces on the generator. • In July, a network camera is installed in the tower on Klammerskär, en- abling real time observation of the park from Uppsala. • During the fall and winter, WECs number two and three (L2 and L3) are ﬁnished and transported to Lysekil.

2009 • L2 and L3 are deployed at LRS in February. • In March, the substation is deployed at LRS. • In October, WEC number four (L9)1 is deployed. • In connection to the deployment of L9, L2 and L3 are also taken out of the water for maintenance.

2010–2011 • During the summer of 2010, additional biology buoys are deployed. Many of the buoys from the ﬁrst round have come loose in harsh winter storms. • In November 2010, WECs number ﬁve through eight (named L4, L5, L7 and L8) are deployed, but without buoys. • In April of 2011, buoys are attached to L7 and L8.

2.3 Theory The theoretical background for this work comes from several different branches. Some of the main concepts will be outlined here, but for a thorough understanding the reader is advised to existing literature within each ﬁeld. References are given at the end of the sections.

2.3.1 Describing waves The most detailed way to describe waves is through a time series of the ocean surface displacement, see Fig. 2.4(a). However, for long time periods it is more convenient to present waves using summary statistics. Using Fourier analysis, it is possible to decompose the time series of surface elevation into its frequency components and to calculate the so-called variance spectral density function S( f ) (sometimes simply called the wave spectrum). The discrete

1The enumeration of the WECs may seem strange, but is a result from them being numbered in the design phase, rather than in the construction phase.

18 wave spectrum is defined as 2 2|zn| S(n f0) ≡ , (2.1) f0 where zn are the complex Fourier coefficients corresponding to the surface displacement time series, and f0 is a fundamental frequency, determined by the measurement frequency and the length of the measurement. The wave spectrum corresponding to the time series in Fig. 2.4(a) can be seen in Fig. 2.4(b). The unit on the y-axis (m2/Hz) may seem somewhat odd but can be under- stood as a measure of the energy content for each frequency. Thus, the spectrum shows us what frequencies carry the most energy. It also says something about the total energy for the sea state, as this is related to the area under the graph. In the case of ocean waves, the energy content is usually described as power per meter wave front, or energy transport J. In other words, J is a measure of how much energy on average passes below one meter of ocean surface, paral- lel to the wave crest, per second. For a sinusoidal wave, this can be described with the relation ρg2 J = TH2, (2.2) 32π where ρ is the density of the water, g is the gravitational constant, T is the period of the wave and H is the wave height (the vertical distance from wave trough to wave peak). For a more complex wave, such as the one in Fig. 2.4(a), the concepts of period and wave height are not as clear since the amplitude and the frequency of the wave vary. To find meaningful definitions, the wave spectrum is therefore used. However, it is first necessary to introduce the spectral moments. These moments mk are defined as Z ∞ k mk ≡ f S( f )d f . (2.3) 0

The zeroth moment m0 is the easiest one to grasp conceptually, since it is equal to the area under the graph in Fig. 2.4(b). Using the zeroth and negative first moments, the energy period T−10 and the significant wave height Hm0 are defined as m−1 √ T−10 ≡ , Hm0 ≡ 4 m0. (2.4) m0

These deﬁnitions may seem somewhat strange, but they lead to a fairly straightforward expression for the energy transport for waves such as the one in Fig. 2.4(a): ρg2 J = T H2 . (2.5) 64π −10 m0

19 0.1

0.05

−0.05

Surface elevation (m) −0.1

0 20 40 60 80 100 120 Time (s) (a) Time series representation.

0.01 /Hz) 2 0.008

0.006

0.004

0.002

Spectral density (m 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency (Hz) (b) Spectral density representation, S( f ).

0.8

0.6

0.4

Frequency (Hz) 0.2

0 20 40 60 80 100 120 Time (s) (c) Wavelet scalogram representation. Figure 2.4: Different ways to present wave data. Adapted from Paper X.

This equation assumes that the deep water approximation is valid, which usually means that the water depth must be larger than half the wavelength of the waves. Fig. 2.4(c) shows a wavelet scalogram. This is an alternative way to represent waves and gives information both on the frequency content and the time distribution of the energy. The colour in the scalogram corresponds to energy, and the x-axis and y-axis display time and frequency respectively. The scalogram is produced using dilations and translations of a so-called mother wavelet on the original signal. The mother wavelet is a fast decaying wave form whose shape can be varied depending on the application. In the case of ocean engineering the Morlet wavelet is often used [28], see Fig. 2.5.

20 1

0.5

−0.5

−1 −4 −3 −2 −1 0 1 2 3 4 Figure 2.5: The Morlet wavelet, at arbitrary scale.

A more thorough introduction to wave theory and spectra can be found in [29] and [30]. Several papers have also been published on the use of wavelets in ocean engineering; see for example [31–34].

2.3.2 Linear generators The purpose of a generator is to convert mechanical energy into electric energy. Most conventional generators are of the rotating kind, but the system studied in this thesis uses a linear generator. However, the principles of electric energy conversion do not differ, and a linear generator consists of the same key components as its rotating sibling. Fig. 2.6 shows a schematic illustration of a rotating and a linear generator. Both generators have a moving part (the rotor/translator) and a static part (the stator). Magnets with alternating magnetic direction are mounted on the moving part. All generators are based on Faraday’s law, which states that a changing magnetic field in a coil will induce an electromotive force E in that coil: dΦ E = −N . (2.6) dt N is the number of coil turns and Φ is the magnetic flux. The changing magnetic field can come from a motion of the coil, a motion of the magnet or a change of magnetic flux density. In Fig. 2.6 the magnets are of the permanent kind, but electromagnets can also be used, which allows for control of the magnetic field. In a rotating generator, N in Eq. 2.6 remains constant. In a linear generator however, there is a possibility for the translator to move out of the stator, resulting in a decrease of the active area, i.e. the area where the stator and the translator overlap, see Fig. 2.6. This means that the voltage will drop, and that the dynamics of the generator will change. The impact will among other things depend on the stator and translator lengths, the stroke length of the translator, the equilibrium position of the translator, and the load connected to the generator. Paper V is an investigation of this effect.

21 Stator

Permanentmagnet

Rotor Conductor

Airgap

Translator

Stator Figure 2.6: A rotating and a linear generator [13].

For a more thorough description of generators and electromagnetic theory, see e.g. [35–37]. Linear generators have been investigated thoroughly by e.g. [22].

22 3. Ocean Measurements

Papers IV, VII and IX all have perspectives on ocean measurements. Paper IV describes the setup of a visual observation system, Paper VII presents its outcome and compares it to that of a fundamentally different system, and Pa- per IX gives a broad background on other measurements that have been made in the wave power society.

3.1 History and development of wave power measurements The earliest article reviewed in Paper IX is from the mid seventies, although wave power research is much older (the first patent was filed in 1799 [38]). It is possible to see some developments in equipment and technology from the seventies until today, but many basic methods and sensors also remain. The greatest change is probably the speed with which information can be transferred and stored, along with some fundamentally new measurement technologies, such as the Global Positioning System (GPS). Although the number of projects on wave power over the years is large (probably in the order of hundreds), only a few were found to have published measurements on offshore tests. Among measurements commonly made are: wave height (measured in nearly all projects), electric output, air pressure, mooring forces and device motion. Accelerometers, pressure sensors, and strain gauges were popular sensors in the seventies, and remain so today. To give a rough idea of the progress of wave energy sea trials, Fig. 3.1 and 3.2 have been compiled, based on the material reviewed in Paper IX. Fig. 3.1 shows the number of papers with descriptions of ocean measurements published per year. This is an indication of the academic activity related to sea trials. It can be seen that the rate of publications is fairly even until about 2005, when there is a clear increase. This could be seen as a trend that follows the current focus on renewable energy. However, a large part of this increase can be attributed to a few academically very active groups (e.g. the Wave Dragon and the Lysekil project), so caution must be exercised when making predictions for the future. Fig. 3.2 is also based on the material from Paper IX. Here, the year of the first publication from each project is plotted, which means that the number of publications from each project is not reflected. Projects that have mentioned

23 15

0 1975 1980 1985 1990 1995 2000 2005 2010 Figure 3.1: Number of yearly publications that are describing ocean measurements, and are referenced in Paper IX.

0 1975 1980 1985 1990 1995 2000 2005 2010 Figure 3.2: Number of ﬁrst publications per year from all projects referenced in Pa- per IX. sea trials but not described any measurements are also included. The ﬁgure gives an indication to the progress of sea trials in general, regardless of academic priorities. In is interesting to note that the increase at year 2005 that was seen in Fig. 3.1 can be seen here too. The most recent European Wave and Tidal Energy Conference, which is the major conference within wave energy, took place in the early fall of 2011. This was too late for the publications from the conference to be included in Paper IX. A few papers presented details on measurements from offshore ocean tests however and could be mentioned here: [39] regarding the BOLT point absorber, [40] regarding the CETO unit, [41] regarding a version of the Ocean Energy Buoy, [42] regarding the Oyster, and [43] regarding the Lysekil project.

3.2 The fundamental difficulties In order to understand why relatively few projects have presented measurements on ocean trials, it might be valuable to reflect on the difficulties in making offshore measurements. As the aim of any wave energy project is

24 to capture incoming energy, the sites are almost always energetic and at times impossible to access. This means that (i) the window of opportunity for installation and maintenance is short, (ii) the conditions in which the measurement system is to operate are harsh, (iii) nearby stationary points are rare, (iv) the chances of regularly checking if the system works are small, (v) the possibility of using wired communications with the device is low, and (vi) the opportunity of long-time controlled testing on site is virtually non-existent. Finally there is a need for the system to be self-sufficient on energy if regular exchanges of batteries are to be avoided. Keeping the above difficulties in mind, it is perhaps not surprising that the number of reported offshore wave power measurements remains fairly low. Most projects have run across unexpected difficulties, such as malfunction- ing sensors, mooring failures, biofouling, leakages, destroyed equipment, and even theft of sensors (see for example [44]). It must also be remembered that not all projects have an interest in present- ing their results. Much research is performed within companies, which limits the need or drive for publishing results. Other projects may have performed measurements that are in principle open, but lack funding or sufficient results for publishing.

3.3 The work at Klammerskär The observation station on Klammerskär is an example of an offshore/near- shore measurement station. The setup of the station is thoroughly described in Paper IV. Some additional comments will be given here, to complete the picture. As was stated above, most often a wave energy developer will not have the possibility to perform measurements on her/his device from a stationary point, as most tests are made offshore. In the case of the Lysekil project, however, there were two small islets south of the research site; Western and East- ern Klammerskär, on which an observation tower could be placed. The purpose of such a tower was primarily to enable observation of the site in harsh weathers. There was also a secondary objective: to see if the motion of the buoy could be tracked optically during operation. Thus, planning for a tower began in 2006. Several permits were needed: the consent of the land owner, a building permit, an exception from the coastal protection rule, and a permit for camera surveillance. By the summer of 2007, all permits had been granted, and the tower was erected on Western Klammerskär in July 2007. During the fall and coming spring, the tower was equipped with an energy system, a 3G modem for communication, and ﬁnally the camera. Some images from the installation of the tower can be seen in Fig. 3.3. In the rightmost image, the camera can be seen at the top of the tower. In the middle of the tower, there are four solar cell panels installed. The control

25 Figure 3.3: Setup of the observation system. Left: casting the foundation. Middle: the empty tower. Right: equipment installed. equipment, the batteries, and the communication system are also installed in the middle of the tower.

3.3.1 Successes and failures Klammerskär is little more than some rocks sticking out of the water, and at high waves the site is very hostile. Two images taken by the camera pointing straight down can be seen if Fig. 3.4. The ﬁrst one is taken on a calm day, and the second one on a day when moderate waves are coming in. On such a day it is impossible to access the tower. As the conditions on Klammerskär are harsh, the strain on the tower and the equipment has been heavy. Twice, installed wind turbines have been wrecked and had to be dismounted. The ﬁrst time it was due to the waves destroying the dump load, leading to the turbine spinning out of control. The second time

Figure 3.4: Two images taken by the camera at Klammerskär, on a calm day and on a day with moderate waves.

26 Northernmarkerbuoy L9

Biologybuoys Southernmarkerbuoy

Figure 3.5: The Lysekil research site, iced in. February 11th, 2010.

it was possibly a lightning strike that destroyed the turbine, or the control equipment that kept it from spinning too fast. At that time, melted pieces of metal could be found inside the turbine housing after taking it apart. Other things that have broken are: the ladder in the tower, the ﬁrst electric cabinet, the heavy duty metal bars that held the cabinet, and the grounding cable. Naturally, the strain on the installed WECs has been equally heavy. Fig. 3.5 shows a panoramic picture of LRS on February 11th 2010, where almost the entire site was frozen in. In spite of the weather challenges L9 survived the winter of 2010. More- over, the camera, as well as the communication equipment and the rest of the electric system, has worked since installation in 2008, virtually without any maintenance. Managing to make something not break may seem like a petty success, but in this business it is far from a small step.

3.4 Interpreting measurements Paper VII compares measurements of buoy motion from the observation tower with measurements made inside the buoy, for the wave energy converter L3. Having independent measurements of the same thing is a luxury for anyone working in an uncontrolled environment. Even so, interpreting the measurements can be very difﬁcult. There is no “ground truth”, against which data can be compared. Instead, it is necessary to try to use sound judgement, and to

27 1.5 Surface elevation 1 Cumulative mean 0.5

−0.5 Position (m) −1

−1.5 0 10 20 30 40 50 Time (s) Figure 3.6: Sample wave and its cumulative mean.

be observant of what assumptions are the most critical for the results. As an example, in the case of Paper VII, the filtering of the accelerometer signals is of great importance, as is the assumption that the buoy is primarily moving perpendicular to the line of sight of the camera. The accelerometer signals have to be integrated to obtain position. This in- tegration introduces a drifting error, which needs to be removed. In Paper VII this was done using a sliding mean filter and then subtracting the calculated mean from the signal. The width of the sliding mean window was set to 21 s. Essentially, this means that any oscillation with a period longer than 21 s is removed. Choosing a narrower window would have meant filtering away more of the motion, and conversely; choosing a wider window would have filtered away less. The choice of the size of the window is not obvious, and different values give different ranges of resulting buoy motion. Fig. 3.6 gives an illustration to the motive for choosing a value of 21 s. The red graph shows the surface elevation for 50 s of the measurement period. The blue dashed graph shows the cumulative mean of the surface elevation, which tends to zero as the window for the mean increases. This figure is just an example, but is fairly typical for the sea state at the time. When the window reaches approximately 20 s, the main oscillations of the mean have died out, and only small variations remain. The energy period at the time was approximately 7 s, and a value roughly corresponding to three periods, or 21 s, was decided upon. The assumption that the buoy is primarily moving perpendicular to the line of sight of the camera is clearly a simplification of the reality. However, it is reasonable that the motion to/from the camera is small. This is due to the camera being roughly south of the buoy, with waves coming in mainly from the west. It is also reasonable to assume that the motion to/from the camera is of fairly small importance for the resulting calculated vertical motion of the buoy. This is due to the fact that the camera is only 14 m above the ocean surface, while being approximately 250 meters away from the buoy. This is a challenge when it comes to getting good photos of the buoy in high waves. But at the same time, it is a strength when estimating vertical motion, since this motion is almost perpendicular to the line of sight for the camera.

28 3.4.1 Comparing measurements with incoming waves There is another difficulty when it comes to interpreting data obtained from ocean trials, which comes into play when motion data is compared to the incoming waves: it is in principle impossible to measure the wave that actually reaches the WEC, for two reasons. First, it is impossible to measure the waves at exactly the same location as the WEC. However small the distance between measurement unit and the WEC is, the waves measured may differ somewhat from the waves reaching the WEC. Therefore, it is necessary to make an estimation of whether it is reasonable that the waves within a given area are relatively stationary in space. At the Lysekil research site, the bottom is fairly flat, and the distances between the wave measurement buoy and the WECs are relatively small in comparison to the size of the site. Furthermore, the main part of the waves are coming from one direction (west). Therefore, the conditions for stationarity were deemed to be fulfilled. The second reason that it is impossible to measure the wave that actually reaches the WEC is that the WEC is absorbing energy and radiates waves. Thus, what is measured is essentially the incoming wave plus the wave gener- ated by the WEC. In a laboratory environment, it would be possible to measure the (stationary) wave before inserting the WEC, and then measure the motion of the WEC separately. This cannot be done in an ocean environment. How- ever, since the power absorbed by the WEC is very small in relation to the power passing within a few buoy lengths, this effect was deemed negligible.

4. WEC Performance

For a developer of a wave energy device, deployment of the ﬁrst unit in the ocean is a clear and major milestone. Such a deployment gives invaluable experiences of the practicalities and challenges associated with working at sea. It also gives the developer a chance to evaluate how the device works in real waves, rather than in a controlled laboratory environment. The aim of the evaluation will be to answer questions on how the performance of the device varies with certain parameters. Papers V, VI, and X all include investigations on how the WECs at LRS perform depending on electrical and oceanic parameters. Before going into the results of these papers, however, it is important to clarify what is meant by performance when it comes to wave energy.

4.1 Defining performance Describing the performance of a WEC is far from trivial. This is partly due to an immaturity of the subject, where different developers have chosen different ways of describing their devices, but also due to the complexity of ocean waves. For assessments with the purpose of comparing different projects, protocols have been suggested [45,46], and may be accepted by the wave energy community in the future. These protocols aim at giving proper estimates of the produced electricity over a year, based on a specific site, and on (scaled) measurements for different combinations of wave parameters. If the aim is to describe how the performance of a single device changes with one or several parameters, it may be more straightforward to present figures on (i) absorbed power, (ii) the ratio of absorbed power to incoming power, or (iii) capture width. However, all of these descriptions have their limitations and caution must be exercised when using them. Absorbed power is perhaps the easiest parameter to understand. However, it is important to specify where in the energy conversion chain this power is located. A hydrodynamic absorption of e.g. 10 kW is very different from having 10 kW in a hydraulic system, or in an electric load. In this thesis, absorbed power refers to power dissipated in the windings of the generator, in the sea cable, and in the load onshore. It is therefore somewhat less than what is removed from the waves, since mechanical losses and iron losses in the generator are not accounted for.

31 The ratio of captured power to incoming power is sometimes referred to as absorption, or relative absorption. It may be given without a unit, or in per cent. It is important to stress that relative absorption is not the same as efficiency, since efficiency relates to losses. The energy in a wave which is not absorbed by a WEC is not lost, as it can be absorbed at another point. This is different from e.g. resistive losses in a generator, which cannot be utilized. It is also worth pointing out that the width of the WEC defines the amount of incoming power. Changes in WEC width will therefore also result in changes in relative absorption, unless the absorbed power changes in the same way. Capture width is defined as the absorbed power by the device, divided by the incoming power per meter wave front. This measure is given in meters and has been recommended by some as it provides a robust and normalized measure of WEC performance [45], if combined with information on WEC size. In comparison with the relative absorption, it is less likely that the capture width will be confused with efficiency, since the unit is not per cent. The downside is that it is slightly less straightforward. All of the parameters above can be suitable when describing how the performance of a WEC changes with a certain variable. However, it is important to keep in mind that neither of the parameters say anything about how “good or bad” the WEC is in absolute terms, unless they are combined with knowledge of WEC size, need for maintenance, rated power, generator efficiency, ability to handle overloads, etc.

4.2 Controlling the variables Testing at sea has its advantages and its disadvantages. One of the disadvantages is that the incoming waves cannot be controlled. In a wave tank it is possible to subject your model WEC to specific combinations of significant wave height and energy period, as well as sea states with defined spectral shapes. In the ocean you have to wait and see what Mother Nature serves you. How- ever, if sufficiently long series of measurements can be acquired, the natural variations in sea state will give a relatively complete set of conditions. Much unlike the sea state, the electric setup is something that can be controlled completely. Varying the electric parameters essentially means varying the damping of the device, i.e. how the generator will resist the motion of the buoy. In this thesis, the variations of electrical parameters are limited to using different loads, and switching between AC and DC systems for longer periods. In principle, however, it is possible to make electrical changes on time scales in the millisecond region. There are many other parameters that have also been varied in the Ly- sekil project, but that are not covered in this thesis. For instance, cylindrical, toroidal and discus shaped buoys have been tested. Different types of DC

32 25 9.2 Ω 9.2 Ω 9.2Ω trendline 9.2Ω trendline 13.8 Ω 4 13.8 Ω 20 13.8Ω trendline 13.8Ω trendline 27.5 Ω 27.5 Ω 27.5Ω trendline 27.5Ω trendline 15 3

10 2 Absorbed power(kW) Relativeabsorption(%) 5 1

0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 Significantwaveheight(m) Significantwaveheight(m) (a) (b) Figure 4.1: Absorption as a function of signiﬁcant wave height, for a DC system. Adapted from Paper VI.

setups have been tried, and ﬁnally there are signiﬁcant differences in the generator design of the later WECs, as compared to L1–L3.

4.2.1 AC/DC load and sea state The first results from L1 were presented in 2007 [47]. During the first set of measurements the generator was directly connected to a resistive load. The results showed that the absorbed power increased in more energetic sea states, as expected. They also indicated that there should exist an optimal electric load, regardless of sea state (i.e. combination of significant wave height and energy period). The value of this load was found to lie between 2.2 Ω and 10 Ω. Paper VI builds upon the results from [47], as it investigates the variations in performance for L1 for a DC-connected load. Connecting the load after rectification means that no current will flow through the load until the voltage of the generator reaches the DC level of the system. This in turn means that the system will not be continuously damped, as was the case above. The damping will be approximately zero until the translator has reached sufficient speed. This is a substantially more complex situation, and the results from Paper VI are not quite as clear as those from [47]. Fig. 4.1, from Paper VI, shows the relative and absolute absorption as a function of wave height for three different loads. The trend lines in Fig. 4.1 (a) indicate that the relative absorption peaks for slightly different wave heights for each load. Fig. 4.1 (b) shows that the load with the highest absorbed power is not the same for all wave heights. The data points are quite scattered however, and there is a lack of data for high wave heights for the 13.8 Ω load, so there is a high level of uncertainty. Further investigations were made by the primary author of Paper VI, and can be found in [48].

33 f

(a) (b) (c)f Figure 4.2: Different translator-stator geometries. (a) Long translator, (b) Long stator, (c) Geometry of L1.

4.2.2 Water level and wave height One of the design choices for the generator is the length of the translator relative to the stator. This choice is a balance between performance and economy. In the extreme case, a very long translator (longer than any incoming wave height) would mean that the active length (the length for which translator and stator overlap) would never decrease, see Fig. 4.2, case (a). However, this would make for a very large and not very economical generator since the magnets are an expensive component. Making the stator very long instead (case (b)) would also result in a constant active area, but at the prize of a higher cost, as well as increased impedance in the stator windings. In L1, a middle way was chosen, and the respective lengths of stator and translator were set to 1.26 m and 1.87 m. This has been illustrated in case (c) in Fig. 4.2. For a set generator geometry, whether or not the translator will move out of the stator is dependent on the magnitude of the oscillating motion, but also on the equilibrium position of the translator inside the stator. These two entities are dependent on the incoming wave height and the water level. In an attempt to quantify the impact a theoretical expression was derived in Paper V, and was compared to experimental data. Fig. 4.3 from said paper shows the results. The relative absorption has been plotted as a function of signiﬁcant wave height Hm0 and still water level w. The theoretically expected performance is plotted as a surface. It was found that the theoretic values follow the experimental data qualitatively in the Hm0-direction, but that the correlation in the w-direction is less clear.

4.2.3 Spectral shape Typically, WEC performance is presented in scatter diagrams for combinations of T−10 and Hm0. However, when studying data from L1 for sea states where T−10 and Hm0 were kept roughly constant, large variations in perfor-

34 0.25

0.2

0.15

0.1

Relativeabsorption 0.05

-0.8 2.5 -0.4 1.5 2 0 0.4 1 0.8 0 0.5 Stillwaterlevel w (m) Significantwaveheight Hm0 (m) Figure 4.3: Absorption as function of signiﬁcant wave height and still water level. Adapted from Paper V.

mance were found. Such variations have been suggested to be caused by variations in spectral width [49]. Therefore in Paper X a number of parameters describing spectral width were tested against the performance data to investigate any correlations. The two best indicators were found to be κ and ε1, deﬁned as Z ∞ √ 1 i2 f m /m κ = S( f )e π 0 2 d f , (4.1) m0 0

rm1m−1 ε1 = 2 − 1. (4.2) m0

Variations of these parameters accounted for roughly 40% of the variations in WEC performance for a load of 4.9 Ω, using a linear ﬁt. Another parameter that relates to the shape of the spectrum, and that could be used to explain the performance variations for constant T−10 and Hm0, is the peak period Tp. The peak period corresponds to the peak frequency fp, i.e. the frequency for which S( f ) has its maximum. If this period differs substantially from the energy period (Fig. 4.4), it is an indication that the spectrum might be double peaked or skewed. This could mean that a large portion of the available energy in the waves is carried by frequencies that are not captured by the WEC. Fig. 4.5 from Paper X shows a scatter diagram of performance and energy period for 42 measurements on L1 where the energy period was between 3.5 s and 4.0 s. It can be seen that the six lowest absorption values have a peak period which is greater than 6.0 s or lower than 3.5 s. It therefore

35 0.05 /Hz)

2 0.04

0.03

0.02

0.01 Spectral density (m 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Frequency (Hz) Figure 4.4: A double peaked spectrum, where T−10 = 3.99 s (corresponding to f−10 = 0.25 Hz) and Tp = 6.10 s (corresponding to fp = 0.16 Hz).

Absorption (%) 5

0 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Peak period (s) Figure 4.5: Scatter diagram of absorption and peak period Tp. Adapted from Paper X. seems as if the poorest performances in the data set can be explained using Tp. However, there is still quite some variation in the remaining values, and there are also data points with high absorption for which Tp is close to, or even below, 3.5 s.

36 5. Summary of Papers

This thesis is based on ten papers, presented in their full length at the end. A short summary is given here.

PAPER I Wave Energy from the North Sea: Experiences from the Lysekil Research Site A very thorough description of the ﬁrst years of the Lysekil project can be found in this paper, both on the technology used and the process of installing the ﬁrst WEC. The paper covers all parts of the project: from a brief introduction of wave energy projects around the world to describing the properties of LRS and the results on wave characteristics, electrical systems, absorption and environmental impact. The author coordinated the texts from the other authors, and contributed with the description of the observation tower, as well as the actual installation of the tower. This paper is published in Surveys in Geophysics Vol. 29, Issue 3, May 2008.

PAPER II The Lysekil Wave Power Project: Status Update This paper presents a more brief, but slightly more updated, description of the status of the Lysekil project as it was in 2008, as compared to Paper I. A lot of the material in this paper is covered in Paper I as well, but the focus here is more on the work performed by the author, i.e. the effect of varying water levels and the installation of the observation system. The author performed most of the writing of this paper, based on the information provided by the people who had carried out the experiments within each ﬁeld. The work of installing the observation tower mentioned in section 4.6 was also carried out by the author.

37 This conference paper is published in the Proceedings of the 10th World Re- newable Energy Conference and was orally presented by the author in Glas- gow, UK, in July 2008.

PAPER III Catch the Wave to Electricity: The Conversion of Wave Motions to Electricity Using a Grid-Oriented Approach In this paper, the main ideas behind the Lysekil project are introduced, together with a short summary of the process of carrying out the project. Com- pared to Paper I and II, the focus here is on what philosophies led to the chosen system, rather than detailed descriptions of the technology. The author contributed to a major revision of this paper and took part in the submission process. This paper is published in IEEE Power & Energy Magazine, Vol. 7, Issue 1, January/February 2009.

PAPER IV Tracking a Wave Power Buoy Using a Network Camera - System Analysis and First Results In the summer of 2008, a camera system was installed at Klammerskär, south of LRS. In this paper, the work with this system is described, and an analysis is made of the ﬁrst series of pictures from the camera. The wave power buoy has been photographed during operation, and using image analysis on these pictures, buoy motions have been extracted. The values (±0.5 m maximum vertical motion) correspond fairly well to what would be expected based on the sea state during the image sequence (Hm0 = 0.82 m). The strengths and weaknesses of the system are analyzed in the paper, concluding that some work remains on quantifying the accuracy and synchronizing the images to the measurements of voltages in the linear generator. In general the system has worked well. The author performed most of the work in this paper. This conference paper is published in the peer-reviewed Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering and was orally presented by the author in Honolulu, USA, in June 2009.

38 PAPER V Wave Power Absorption as a Function of Water Level and Wave Height: Theory and Experiment Since the translator will move partly out of the stator at high amplitudes of motion, resulting in a decreased active area, it is reasonable to assume that the WEC performance is dependent on the equilibrium position of the translator as well as stroke magnitude. The former is affected by the water level at the site, and the latter is affected by the size of the incoming waves. In this article, a theoretical model was presented to describe the performance of the wave energy converter L1 as a function of significant wave height and water level. The model was matched against experimental data from LRS. Experimental and theoretical values exhibit similar characteristics, especially with changing significant wave heights. It is therefore likely that the declining values of relative absorption at high significant wave heights are due to the decrease of the active area. For changing water levels, it is more difficult to draw any conclusions. The author performed most of the work in this paper. This paper is published in IEEE Journal of Oceanic Engineering, Vol. 35, Issue 3, July 2010.

PAPER VI Experimental Results From an Offshore Wave Energy Converter This paper describes an experiment with rectiﬁcation of the voltage of the wave energy converter L1 at LRS. Absorbed power and relative absorption as a function of wave height and electric DC load was plotted. The relative absorption was found to have peaks at different wave heights for different loads. This indicates that there is not a single optimal load for all signiﬁcant wave heights. The author contributed with section 2, as well as Fig. 3b and 3d, and helped out in the review of the paper. This paper is published in Journal of Offshore Mechanics and Arctic Engi- neering, Vol. 132, Issue 4, November 2010.

PAPER VII Wave Buoy and Translator Motions — On-Site Measurements and Simulations In the process of improving the concept in the Lysekil project, it is important to be able to quantify and predict several different entities in the wave energy

39 converters. This paper has an engineering focus, and is aimed at comparing different ways of measuring buoy motion, as well as relating these measurements to simulations made in Simulink. Buoy motion was measured using a land based optical system, and a buoy based accelerometer system. The measurements were found to correlate well in the vertical direction. However, in the horizontal direction the difference was substantial. The main reason for this was that the buoy rotation about its axis of symmetry was not measured. In a ﬁrst comparison, the simulations and the measurements showed good agreement. The author organized the work in this paper, wrote most of the text, and produced all ﬁgures except for Fig. 11. The author also performed the measurements of buoy motion through optical measurements, and the subsequent analysis. This paper is published in IEEE Journal of Oceanic Engineering, Vol. 36, Issue 3, July 2011.

PAPER VIII Lysekil Research Site, Sweden, A Status Update This paper presents an up-to-date description of the Lysekil project. Together with Paper II, it gives a brief overview of the project from start to present. The author made a minor contribution to the writing of the paper. This conference paper is published in the peer-reviewed Proceedings of the 9th European Wave and Tidal Energy Conference and was presented by Erik Lejerskog in Southampton, UK, in September 2011.

PAPER IX Offshore Wave Power Measurements - a Review In the process of developing a wave power concept, it is important to learn from previous successes and failures, not least when moving into the ocean for testing. In this paper, a thorough review of measurements made in offshore wave power trials has been made. The purpose of the review is to ﬁnd out what has commonly been measured, and how these entities have been measured. Such information can help present and future wave energy projects in their design of measurement systems, and could also be used when preparing protocols and standards for testing. Twenty projects were reviewed, where the earliest one took place in the 1970s. Wave height was an almost universal measurement among the projects, although the technologies used differed somewhat. Other common measurements included voltages, device motion and mooring forces. It is clear that it is

40 far from trivial to measure any entity at sea, and many of the projects reported on sensor failures and other unforeseen events. The author performed most of the work in this paper. This paper is in press for publication in Renewable & Sustainable Energy Reviews and is available online. DOI: 10.1016/j.rser.2011.07.123.

PAPER X Spectral Parameters and Wave Energy Converter Performance Studying performance data from L1 it can be seen that for measurements with similar summary statistics T−10 and Hm0 there are values for relative absorption that vary from 5% to 25%. It therefore seems probable that the properties of the sea state that are not captured using T−10 and Hm0 have an effect on how a WEC performs. It has been proposed in the literature that the width of the wave spectrum is one such property. In this paper, six parameters that describe spectral width have been tested against performance data to look for correlations. In addition to this, the performance data was tested against peak period and standard deviation of peak frequency, as found through wavelet analysis. It was found that out of the parameters tested, κ and ε1 displayed the strongest correlation. Even this correlation was not very strong however, and did only exhibit an r2-value of 0.39 in a linear ﬁt for L1 connected to a 4.9 Ω load. It was also found that the lowest absorption values were connected to the lowest and highest Tp-values. The author performed most of the work in this paper, which is an unsub- mitted manuscript.

6. Conclusions

The main conclusions in this thesis can be divided into two broad categories: conclusions regarding measurements and buoy/generator motion, and conclusions regarding WEC performance.

6.1 Measurements and buoy/generator motion • Although many ocean experiments have been made within the field of wave power, published descriptions of measurements are fairly rare. However, an increase can be seen in recent years. • Almost everyone who has published descriptions of ocean measurements have also reported on problems encountered in the marine environment. • Wave height, electric power and air pressure are the most common measurements in sea trials of wave energy devices. Pressure transducers are the most common specific sensors. • The buoy motion of L3 is not symmetrical, due to the constraint of the buoy being attached to the generator. The observed motion is skewed, whereas a free motion would be expected to be circular or elliptical. • The installed camera system on Klammerskär works for motion measurement, even though the conditions are far from ideal in terms of distances camera–buoy, tough weather, and wave sheltering. • The gathered accelerometer data for buoy motion matches the image data from the camera, but the results are dependent on proper filtering. • Buoy rotation about the vertical axis cannot be neglected in accelerometer measurements. • Horizontal motion of the buoy does not contribute in any significant way to the motion of the translator. • Dual measurements of buoy motions are recommended if possible. Opti- cal measurements make the interpretation of results easier, although the present system needed a lot of manual work. This has been remedied by adding markers to later versions of the buoy. • In a first evaluation, the simulations of buoy and translator motion match the measured results. • The range of motion in the translator is slightly less than for the buoy. This is expected, since the translator is bound by its end stops.

43 6.2 WEC Performance • The theoretical model for the expected performance variation with the variation of water levels and wave height seems to qualitatively predict the de- cline of performance for increasing wave heights. Variations in water level were not captured as clearly by the model. • Out of the ten parameters related to spectral width or shape studied in Pa- per X, κ and ε1 were found to be the best indicators for performance variation for set values of signiﬁcant wave height and energy period. However, they only explained about 40% of the variations for performance of L1 connected to a 4.9 Ω load, which indicates that there may be other factors affecting performance as well. • The lowest performance values in the studied set were connected to the highest and the lowest values of the peak period.

44 7. Acknowledgements

First, I would like to thank my supervisor Mats Leijon for letting me be a part of this project. It has been stimulating, challenging, varying and fun all the way, and I am impressed by your belief in us PhD students. Looking back at all the things I have gotten the chance to do in this job, it seems almost unreal. Thank you to my assistant supervisor Jan Isberg for always being around and giving answers regarding theoretical issues. To all of our financiers: thank you for your support – it gives us a chance to pursue this research. Thank you also to Uppsala University for financing my PhD studies. To all the great people in the Wave Group: thanks for all the fun times in Uppsala, Lysekil, and at conferences around the world. It has been a privilege to work with you all, and I wish you the greatest of luck in the future. To my room mates, past and present: Olle Svensson, Remya Krishna, Mag- nus Rahm and Rafael Waters, thank you for talks, laughs, scientific exchange, and general support. Olle, thank you for your help in everything concerning measurement technology and electronics - including, but not limited to, the workings of guitar pickups and microphones. Remya, thank you for giving me insight into the details of Indian weddings and cooking. Magnus and Rafael, thank you for good food and good wine, for all the great non-work times, for guiding me into the Division, and for the great little band Electric Acoustics. Rafael, thank you also for all the other music we have shared, and for many hours of conversation on the way to or from Lysekil. Jörgen Nilsson, thank you for the help with making Klammerskär a working measuring station. Without your practical talents it would never have become operational, and without your swimming capabilities we would still have been stuck on that rock. Thank you also to Jens Engström, Kalle Haikonen, Fredrik Bülow, Jenny Tedelid, Nils Englund and Erik Back who on different occasions have help me out on Klammerskär. Mårten Grabbe, Staffan Lundin, Cecilia Boström, Magnus Rahm, Johan Bladh, Olle Svensson, Katarina Yuen, Rafael Waters, Jens Engström and Jo- han Lundin, thank you for proofreading my thesis and the last paper. I ap- preciate very much your feedback. Thanks are also given to the people who contributed in my beer-for-errors program, among which Marcus Berg and Anders Goude are the most notorious. Staffan Lundin, thank you for being a living LATEX dictionary, to whom no coding problem is too small to investigate. Katarina Yuen, thank you for great talks, and for helping me to take some steps

45 in figuring out just what engineering science is about. Johan Bladh, thank you for good lunch times and for sharing my bike interest. Thank you Gunnel Ivarsson, Thomas Götschl, Ingrid Ringård, Christina Wolf, Elin Tögenmark and Maria Nordengren for all the support in adminis- trative issues. Without you I would have been lost on numerous occasions. Ulf Ring, thanks for the invaluable help with construction issues, and the non- invaluable help with coming up with bad jokes. Thank you Tommy Carlsson, at Klubban in Fiskebäckskil, for practical help in the field. To all the fantastic people at the Division of Electricity: thank you for great discussions on scientific and worldly issues, laughs, lunch talks, fika, Friday beer, Basic Cooking, Blodomloppet, Raid Uppsala, Christmas parties, ski trips to Orsa, and the numerous events with the Division choir. Thanks to you all, coming to work has been something to look forward to every single day. To my family: thank you for all the support and love. Finally, to my fabulous wife Magdalena: thank you for being there and letting me be there with you. Thank you for your patience, your wisdom, and your great sense of humor. You make my days and my future bright.

46 8. Svensk sammanfattning

Bakgrunden till den här avhandlingen är arbetet med Lysekilsprojektet, vilket drivits vid avdelningen för elektricitetslära sedan 2002. Inom projektet har ett antal vågkraftverk installerats i havet sydväst om Lysekil. Principen för vågkraftverken är att en boj vid ytan rör sig med vågorna, och förmedlar rörelsen till en bottenplacerad linjärgenerator via en lina. Den genererade spänningen från ﬂera sådana vågkraftverk likriktas, sammanläggs i ett ställ- verk på botten, växelriktas igen och transformeras innan den förs iland via en sjökabel. Installationen av det första vågkraftverket, som döpts till L1, följde på ett stort teoretiskt och experimentellt arbete där systemet simulerats, försöksplat- sen undersökts och en försöksuppställning installerats för att mäta krafter på bojen. Sedan installationen genomförts har L1 och senare vågkraftverk varit i bruk i sammanlagt över två år. En mängd vetenskapliga undersökningar har genomförts i olika delar av projektet, och har resulterat i ett stort antal pub- licerade artiklar. En företeelse som varit viktig att förstå har varit hur vågkraftverken presterar i olika vågklimat, och för olika elektriska parametrar. I den här avhandlingen har L1:s prestanda undersökts för varierande våghöjder och vattenstånd, samt för varierande vågspektra, det vill säga vågklimat med olika sammansättning av periodiska vågor. Avhandlingen innehåller också resultat över hur prestandan varierar med olika elektriska laster i ett likriktat system. Att ändra den elektriska lasten innebär att generatorns benägenhet att bromsa in bojens rörelse förändras. Det visar sig att den absorberade effekten i relation till den inkommande effekten minskar för ökande våghöjder. Detta är i överensstämmelse med teorin, eftersom stora rörelser hos bojen ger stora utslag i generatorn, vilket i sin tur innebär att generatorns aktiva area minskar tillfälligt. Skiftande vattennivåer, och därmed skiftande jämviktslägen i generatorn, förutspåddes ha samma ef- fekt, men en sådan variation var svårare att se i praktiken. Man kan se att prestandan för L1 (mätt över en halvtimme) varierar kraftigt, även för vågklimat med samma statistiska parametrar (våghöjd och period). Därför undersöktes kopplingen mellan prestanda och ett antal parametrar som beskriver spektral bredd, det vill säga i vilken utsträckning energin i vågorna är utspridd på olika frekvenser. Viss koppling hittades, men även de parametrar som var starkast kopplade till prestandan förklarade bara ungefär 40 % av variationen. Kopplingen mellan topperioden, motsvarande den frekvens som

47 bär mest av energin i vågklimatet, och prestandan undersöktes också. Resul- tatet var att för tillfällen då topperioden (som beror på var vågspektrumets maxvärde uppträder) avvek från energiperioden (som påverkas av vågspek- trumets form) var också prestandan lägre. För ett likriktat system verkar det som att generatorns optimala dämpning varierar med våghöjden. Dock saknades mätpunkter för vissa laster i höga vågor, varför det är svårt att dra några deﬁnitiva slutsatser. Som bakgrund till resultaten ovan beskriver avhandlingen mätningar av boj- rörelser till havs för olika mätsystem, och ger en historik över havsbaserade vågkraftsmätningar i andra projekt. Datainsamling till havs är svår att genom- föra, vilket också visat sig genom att tämligen få projekt genom åren valt att, eller kunnat, redovisa mätningar. Inom Lysekilprojektet har bojens rörelse mätts med två olika system: ett landbaserat optiskt system och ett accelero- metersystem i bojen. Resultaten från systemen överensstämmer i huvudsak, och deras styrkor och svagheter kompletterar varandra. Generatorns rörelse mättes också under samma tidsperiod, och fanns vara något mindre än bojens rörelse. Detta är ett förväntat resultat, eftersom generatorns rörelse är begrän- sad av ändstopp i övre och nedre läget. Slutligen jämfördes bojens och generatorns rörelser med simuleringar. Vid en första utvärdering visade sig dessa ge tillfredsställande resultat.

48 References

[1] S. H. Salter, “Wave power,” Nature, vol. 249, pp. 720–724, 1974.

[2] D. Mollison, O. P. Buneman, and S. H. Salter, “Wave power availability in the NE atlantic,” Nature, vol. 263, pp. 223–226, 1976.

[3] J. Falnes and J. Løvseth, “Ocean wave energy,” Energy Policy, October 1991.

[4] C. Retzler, “Measurements of the slow drift dynamics of a model Pelamis wave energy converter,” Renewable Energy, vol. 31, pp. 257–269, 2006.

[5] R. Henderson, “Design, simulation, and testing of a novel hydraulic power take- off system for the Pelamis wave energy converter,” Renewable Energy, vol. 31, pp. 271–283, 2006.

[6] J. Tedd and J. Kofoed, “Measurements of overtopping ﬂow time series on the Wave Dragon, wave energy converter,” Renewable Energy, vol. 34, pp. 711– 717, 2009.

[7] M. Prado, F. Neumann, M. Damen, and F. Gardner, “AWS results of pilot plant testing 2004,” in Proceedings of the 6th European Wave and Tidal Energy Con- ference, EWTEC05, Glasgow, UK, pp. 401–407, 2005.

[8] R. Alcorn, S. Hunter, C. Signorelli, R. Obeyesekera, T. Finnigan, and T. Denniss, “Results of the Testing of the Energetech Wave Energy Plant at Port Kembla on October 26, 2005,” tech. rep., Energetech Australia Pty Limited, 2005.

[9] D. O’Sullivan, J. Grifﬁths, M. G. Egan, and A. W. Lewis, “Development of an electrical power take off system for a sea-test scaled offshore wave energy device,” Renewable Energy, vol. 36, no. 4, pp. 1236–1244, 2011.

[10] D. Elwood, A. Schacher, K. Rhinefrank, J. Prudell, S. Yim, E. Amon, T. Brekken, and A. von Jouanne, “Numerical modeling and ocean testing of a direct-drive wave energy device utilizing a permanent magnet linear generator for power take-off,” in Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2009, Honolulu, USA, pp. 817–824, 2009.

[11] K. Toyota, S. Nagata, Y. Imai, and T. Setoguchi, “Research for evaluating performance of OWC-type Wave Energy Converter “Backward Bent Duct Buoy”,” in Proceedings of the 8th European Wave and Tidal Energy Conference, EWTEC09, Uppsala, Sweden, pp. 901–913, 2009.

49 [12] A. F. de O. Falcão, “Wave energy utilization: A review of the technologies,” Renewable and Sustainable Energy Reviews, vol. 14, no. 3, pp. 899 – 918, 2010.

[13] R. Waters, Energy from Ocean Waves. Full Scale Experimental Veriﬁcation of a Wave Energy Converter. PhD thesis, Uppsala University, Division of Electricity, 2008.

[14] I. Ivanova, Simulation of Linear Permanent Magnet Octagonal Generator for Sea Wave Energy Conversion. Licentiate thesis, Uppsala University, Division of Electricity, 2004.

[15] M. Eriksson, Electromechanical Dynamics of a Direct Drive Wave Energy Con- verter. Licentiate thesis, Uppsala University, Division of Electricity, 2004.

[16] K. Thorburn, Modelling new generators for wave energy conversion and hy- dropower upgrading. Licentiate thesis, Uppsala University, Division of Elec- tricity, 2004.

[17] C. Boström, Electrical System of a Wave Power Plant. Licentiate thesis, Uppsala University, Division of Electricity, 2008.

[18] J. Engström, Hydrodynamic Modeling of the Energy Conversion from Ocean Waves to Electricity. Licentiate thesis, Uppsala University, Division of Electric- ity, 2009.

[19] S. Tyrberg, Studying Buoy Motion for Wave Power. Licentiate thesis, Uppsala University, Division of Electricity, 2009.

[20] H. Gravråkmo, Buoy for linear wave energy converter. Licentiate thesis, Upp- sala University, Division of Electricity, 2011.

[21] R. Krishna, Multilevel Inverter for Wave Power Conversion. Licentiate thesis, Uppsala University, Division of Electricity, 2011.

[22] O. Danielsson, Wave Energy Conversion, Linear Synchronous Permanent Mag- net Generator. PhD thesis, Uppsala University, Division of Electricity, 2006.

[23] K. Thorburn, Electric Energy Conversion Systems: Wave Energy and Hy- dropower. PhD thesis, Uppsala University, Division of Electricity, 2006.

[24] M. Eriksson, Modelling and Experimental Veriﬁcation of Direct Drive Wave Energy Conversion. Buoy-Generator Dynamics. PhD thesis, Uppsala University, Division of Electricity, 2007.

[25] O. Langhamer, Wave energy conversion and the marine environment: Coloniza- tion patterns and habitat dynamics. PhD thesis, Uppsala University, Division of Electricity, 2009.

[26] M. Rahm, Ocean Wave Energy: Underwater Substation System for Wave Energy Converters. PhD thesis, Uppsala University, Division of Electricity, 2010.

50 [27] C. Boström, Electrical systems for wave energy conversion. PhD thesis, Uppsala University, Division of Electricity, 2011.

[28] G. Nolan, J. V. Ringwood, and B. Holmes, “Short term variability off the west coast of Ireland,” in Proceedings of the 7th European Wave and Tidal Energy Conference, EWTEC07, Porto, Portugal, 2007.

[29] J. Falnes, Ocean Waves and Oscillating Systems. Cambridge University Press, 2002.

[30] L. H. Holthuijsen, Waves in Oceanic and Coastal Waters. Cambridge University Press, 2007.

[31] P. C. Liu, “Is the wind wave frequency spectrum outdated,” Ocean Engineering, vol. 27, pp. 577–588, 2000.

[32] S. R. Massel, “Wavelet analysis for processing of ocean surface wave records,” Ocean Engineering, vol. 28, no. 8, pp. 957–987, 2001.

[33] M. C. Huang, “Wave parameters and functions in wavelet analysis,” Ocean En- gineering, vol. 31, no. 1, pp. 111 – 125, 2004.

[34] M. Elsayed, “An overview of wavelet analysis and its application to ocean wind waves,” Journal of Coastal Research, vol. 26, no. 3, pp. 535–540, 2010.

[35] I. Boldea, Synchronous Generators. Taylor & Francis Group, 2006.

[36] R. K. Wangsness, Electromagnetic Fields. New York City, New York, USA: John Wiley & sons, 2 ed., 1986.

[37] K. E. Hallenius, Elektriska maskiner (Electrical Machines). Liber Läromedel, 1980.

[38] D. Ross, Power from the waves. Oxford University Press, 1995.

[39] I. K. Bjerke, J. Sjolte, E. Hjetland, and G. Tjensvoll, “Experiences from ﬁeld testing with the BOLT wave energy converter,” in Proceedings of the 9th Euro- pean Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[40] R. Caljouw, D. Harrowﬁeld, L. Mann, and J. Fievez, “Testing and model evaluation of a scale CETO unit,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[41] F. Thiebaut, D. O’Sullivan, P. Kracht, S. Ceballos, J. López, C. Boake, J. Bard, N. Brinquete, J. Varandas, L. M. C. Gato, R. Alcorn, and A. W. Lewis, “Testing of a ﬂoating OWC device with movable guide vane impulse turbine power take- off,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[42] J. Skelton, G. Bryans, and K. Doherty, “The learning and development process of the Oyster wave energy converter,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

51 [43] O. Svensson, E. Strömstedt, A. Savin, and M. Leijon, “Sensors and measurements inside the second and third wave energy converter at the Lysekil research site,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[44] Y. Masuda, T. Kuboki, and X. Liang, “Wave power use for island power sup- ply by a Backward Bent Duct Buoy,” in Proceedings of the Annual Offshore Technology Conference, Houston, Texas, USA, vol. 1, pp. 527–536, 1997.

[45] E. D. Tietje, III, M. Folley, S. Beatty, M. Raftery, and P. Ricci, “Standardized performance assessment of wave energy converters,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[46] C. Johnstone, T. McCombes, A. S. Bahaj, L. Myers, B. Holmes, J. P. Kofoed, and C. Bittencourt, “Equimar: Development of best practices for the engineering performance appraisal of wave and tidal energy convertors,” in Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 2011.

[47] R. Waters, M. Stålberg, O. Danielsson, O. Svensson, S. Gustafsson, E. Strömst- edt, M. Eriksson, J. Sundberg, and M. Leijon, “Experimental results from sea trials of an offshore wave energy system,” Applied Physics Letters, vol. 90, p. 034105 (3 pages), 2007.

[48] C. Boström, R. Waters, E. Lejerskog, O. Svensson, M. Stålberg, E. Strömstedt, and M. Leijon, “Study of a wave energy converter connected to a nonlinear load,” IEEE Journal of Oceanic Engineering, vol. 34, no. 2, pp. 123–127, 2009.

[49] J.-B. Saulnier, A. Clément, A. F. D. O. Falcão, T. Pontes, M. Prevosto, and P. Ricci, “Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters,” Ocean Engineering, vol. 38, no. 1, pp. 130–147, 2011.