Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1443
Numerical Modelling and Mechanical Studies on a Point Absorber Type Wave Energy Converter
YUE HONG
ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9731-6 UPPSALA urn:nbn:se:uu:diva-305650 2016 Dissertation presented at Uppsala University to be publicly examined in 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Wednesday, 7 December 2016 at 13:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Researcher Jørgen Hals Todalshaug (Norwegian University of Science and Technology).
Abstract Hong, Y. 2016. Numerical Modelling and Mechanical Studies on a Point Absorber Type Wave Energy Converter. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1443. 76 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9731-6.
Oceans cover two thirds of the Earth’s surface and the energy potential of ocean waves as a renewable energy source is huge. It would therefore be a tremendous achievement if the vast mechanical energy in waves was converted into a form of energy that could be used successfully by society. For years, scientists and engineers have endeavored to exploit this renewable energy by inventing various generators designed to transform wave energy into electrical energy. Generally, this sort of generator is called a Wave Energy Converter (WEC). In this thesis, the research is based on the WEC developed in the Lysekil Project. The Lysekil Project is led by a research group at Uppsala University and has a test site located on the west coast of Sweden. The project started in 2002. So far, more than ten prototypes of the WEC have been deployed and relevant experiments have been carried out at the test site. The WEC developed at Uppsala University can be categorized as a point absorber. It consists of a direct- drive linear generator connected to a floating buoy. The linear generator is deployed on the seabed and driven by a floating buoy to extract wave energy. The absorbed energy is converted to electricity and transmitted to a measuring station on land. The work presented in this thesis focuses on building a linear generator model which is able to predict the performance of the Lysekil WEC. Studies are also carried out on the damping behavior of the WEC under the impact of different sea climates. The purpose is to optimize the energy absorption with a specific optimal damping coefficient. The obtained results indicate an optimal damping for the Lysekil WEC which can be used for optimizing the damping control. Additionally, the impact two central engineering design features (the translator weight and the stroke length) are investigated. The aim is to find a reasonable structural design for the generator which balances the cost and the energy production.
Keywords: linear generator, point absorber, numerical modelling, power production, optimal damping
Yue Hong, Department of Engineering Sciences, Electricity, Box 534, Uppsala University, SE-75121 Uppsala, Sweden.
© Yue Hong 2016
ISSN 1651-6214 ISBN 978-91-554-9731-6 urn:nbn:se:uu:diva-305650 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-305650)
Dedicated to my parents
List of Papers
This thesis is based on the following papers, which are referred to in the text by their Roman numerals.
I Hong Y., Waters R., Boström C., Eriksson M., Engström J., Leijon M. (2014) Review on electrical control strategies for wave energy converting systems. Renewable and Sustainable Energy Reviews, 31:329–342 II Hong Y., Hultman E., Castellucci V., Ekergård B., Sjökvist L., Soman D. E., Krishna R., Haikonen K., Baudoin A., Lindblad L., Lejerskog E., Käller D., Rahm M., Strömstedt E., Boström C., Wa- ters R. and Leijon M. (2013) Status update of the wave energy re- search at Uppsala University. Proceedings of the 10th European Wave and Tidal Energy Conference, Aalborg, Danmark, 2-5 Sep- tember, EWTEC2013 III Parwal A., Remouit F., Hong Y., Francisco F., Castellucci V., Hai L., Ulvgård L., Li W., Lejerskog E., Baudoin A., Nasir M., Chat- zigiannakou M., Haikonen K., Ekström R., Boström C., Göteman M., Waters R., Svensson O., Sundberg J., Rahm M., Strömstedt E., Engström J., Savin A. and Leijon M. (2015) Wave energy research at Uppsala University and the Lysekil Research Site, Sweden: A status update. Proceedings of the 11th European Wave and Tidal Energy Conference, Nantes, France, 6-11 September, EW- TEC2015 IV Hong Y., Eriksson M., Castellucci V., Boström C., Waters R. (2016) Linear generator-based wave energy converter model with experimental verification and three loading strategies. IET Renew- able Power Generation, 10(3): 349-359 V Hong Y., Eriksson M., Boström C., Waters R. (2016) A study on the damping coefficient of a direct-drive type wave energy con- verter, conditionally accepted to Renewable Energy, September, 2016 VI Hong Y., Eriksson M., Boström C., Waters R. (2016) Impact of generator stroke length on energy production for a direct drive wave energy converter. Energies, 9: 730-742
Reprints were made with permission from the respective publishers.
Contents
1. Introduction ...... 13 1.1 Wave energy technologies ...... 13 1.1.1 Oscillating water column ...... 13 1.1.2 Overtopping devices ...... 14 1.1.3 Attenuators ...... 14 1.2 Lysekil Project ...... 15 1.2.1 Test site ...... 15 1.2.2 History ...... 15 1.2.3 Previous work with published thesis ...... 16 1.3 Aims of thesis ...... 18 2. Theory ...... 19 2.1 Ocean waves and energy spectrum ...... 19 2.2 Hydrodynamics model ...... 21 2.3 Electrical theory of linear generator model ...... 22 2.4 Load strategies for generator ...... 24 2.4.1 Linear load ...... 24 2.4.2 Passive rectification and filter ...... 25 2.4.3 Resonant rectification ...... 25 3. Material and Method ...... 27 3.1 Wave climates at test site ...... 27 3.2 Device parameters ...... 28 3.3 Simulation tools ...... 28 4. Linear Generator Model ...... 30 4.1 Validation of linear generator model ...... 30 4.2 Hydrodynamic wave ...... 32 4.3 Connection to load cases ...... 32 4.3.1 Resistive load ...... 33 4.3.2 Passive rectifier circuit ...... 34 4.3.3 Resonant circuit ...... 34 5. Optimal Damping Coefficient ...... 37 5.1 Different sea states and linear damping ...... 37 5.2 Sea state dependent power production ...... 38
6. Impact by Translator Mass ...... 41 6.1 Comparison between translator weights ...... 41 6.2 Power matrix and energy production ...... 45 7. Influence of Stroke Length ...... 48 7.1 Concept of stroke length ...... 48 7.2 Consequences of a limited stroke length ...... 48 7.3 Energy production at test sites 6 ...... 49 8. Discussion ...... 52 8.1 Reviews of control strategies and the Lysekil project ...... 52 8.2 The linear generator model ...... 52 8.3 Optimal damping coefficient ...... 54 8.3.1 Impact on power production ...... 54 8.3.2 Shift of optimal damping ...... 55 8.3.3 Energy production ...... 55 8.4 Impact by varying the mechanic designs ...... 56 8.4.1 Translator mass ...... 56 8.4.2 Stroke length ...... 58 9. Conclusions ...... 59 10. Future Work ...... 61 11. Summary of papers ...... 62 12. Svensk Sammanfattning ...... 65 13. Acknowledgement ...... 67 Bibliography ...... 70
Nomenclature and abbreviations
Chapter 2—Theory Chapter 2.1 Symbol SI unit Description � �� Frequency � � � Acceleration of gravity � � Wave height � � Significant wave height � �/� Energy flux � � � Spectral moment at the nth order � � Energy period � � � �/��� Wave power spectrum � � �/��� Bretschneider spectrum � �� � Density of the sea water � ���/� Angular frequency � ���/� Modal frequency for any given wave
Chapter 2.2 Symbol SI unit Description Damping force induced inside lin- � � ear generator � � Hydrostatic force � � Excitation force
� � Line force
� _ � Spring force on upper end stop
� _ � Spring force on lower end stop Impulse response function for the ℎ(�) − radiation impedance � �/� Spring constant of line Spring constant for the upper end � �/� stop Spring constant for the lower end � �/� stop � � Stroke length to upper end stop � � Stroke length to lower end stop � �� Mass of the buoy � �� Mass of the translator
Added mass in infinity frequency � �� ∞ limit � % Power capture ratio Absorbed wave power from the ab- � �� sorber � �� Wave power density � � Buoy position � � Translator position � ��/� Damping coefficient � � Diameter of the buoy
Chapter 2.3 Symbol SI unit Description Reactive area between translator � − and stator � � Open circuit voltage � � Voltage drop on Phase A � � Voltage drop on Phase B � � Voltage drop on Phase C � � Phase current flowing at A � � Phase current flowing at B � � Phase current flowing at C � 1/� Wave number � � Inductance Number of turns of the winding in- � − side the stator
� � Resistance of generator windings
� � Resistance of the sea cable
� � Load resistance � � Resistance Phase Voltage output from the gen- � � erator on phase A Phase Voltage output from the gen- � � erator on phase B Phase Voltage output from the gen- � � erator on phase C Voltage drop over the generator re- � � sistance
� � Voltage drop over the sea cable
� � Load voltage � �� � Density of the sea water � − Factor for calculating the A � − Factor for calculating the A � ��� Phase angle � � Wave length � �� Magnetic flux
� �� Magnitude of magnetic flux
Chapter 6—Impact by translator mass Symbol SI unit Description
� � The kinetic energy of the translator
� � The gravitational potential energy on the translator
� � The work done by the damping force
� � The work done by the force on the guiding line
Abbreviation Description AC Alternating Current DC Direct Current OWC Oscillating Water Column WEC Wave Energy Converter
1. Introduction
The concept of the Wave Energy Converter (WEC) was first introduced the 70s [1]. It was originally a navigation buoy [2], which was designed to be self- powered by transforming the wave mechanics into electricity. Since then, the concept has been developed into a variety of advanced applications and even deployed in a large-scale project [3, 4, 5]. With increasing knowledge and experience, expectations are growing for wave energy plants to be able to open up the ocean’s potential, and provide electricity by connecting to the grid. However, budgeting can be one of the trickiest parts of a project, especially with regards to the high cost of manufacturing, operating and maintaining a high power rating WECs [6]. Furthermore, to make the WECs competitive in the electricity market, it is necessary to be able to guarantee a stable power supply. In this introduction, I briefly categorize different types of WECs, in line with one of my review articles PAPER I. This is followed by an outline of the Lysekil project [7, 8] which my research proposal is a part of. Lastly, the re- search aim is specified.
1.1 Wave energy technologies Wave energy technologies vary wildly in the mechanical and electrical prin- cipal of operation [9]. In this study, the WEC devices are categorized based on their mechanics. More details and relevant electrical strategies can be found in PAPER I.
1.1.1 Oscillating water column The oscillating water column (OWC) device consists of a partially submerged chamber with a water column that rises and falls in response to the pressure from the ocean waves [10, 11]. Both the upward and downward movement of the column drive air through a turbine and the turbine drives a generator for electricity production. One of the typical OWC devices is the Pico Plant on the Azores in Portugal [12], see Figure 1.1(a).
13 1.1.2 Overtopping devices Overtopping devices are partially submerged wave energy converters with reservoirs for capturing wave crests and water turbines to produce electricity. The kinetic energy of the waves is converted into potential energy when in- coming waves are led up a ramp and water is collected in a reservoir [13]. The water returns to the ocean from the reservoir through water turbines, thus uti- lizing the potential difference between the ocean and the reservoir to generate electricity. The Wave Dragon [14, 15] deployed and tested offshore in Den- mark, as shown in Figure 1.1(b) is a famous example of an overtopping device.
(c) Pelamis with hydraulic conver- sion system [22].
(a)The Pico Plant located on Azores Island in Portugal [12].
(b)The wave Dragon tested in the sea [16]. (d)The direct drive WEC developed in the Lysekil Project (courtesy of Rafael Waters). Figure 1.1 Illustration on different types of WECs (reused from PAPER I).
1.1.3 Attenuators Attenuators are devices where the water physically pushes and induces motion in the WEC’s structure and energy is converted by dampening this motion [17, 18]. The devices are often constructions that float on and interact with the ocean waves without being physically fixed in place.
14 Attenuators can be categorized into two types: hinged attenuators and point absorbers [19]. a. Hinged attenuators Hinged attenuators consist of several parts linked horizontally by universal joints, allowing flexing movement in multiple directions. The Pelamis for in- stance, is a device that floats semi-submerged on the surface of the water and faces the direction of waves [20, 21], see Figure 1.1(c). As waves pass down the length of the machine and the sections bend in the water, the movement is converted into electricity via hydraulic systems. The power is then transmitted to the grid on the shore. b. Point absorbers Point absorbers are usually smaller than other WECs. Point absorbers are equipped with a floating part which enables a heave motion driven by the waves, and a generator which is connected to the floating structure and which converts the mechanics into electricity [23]. As illustrated in Figure 1.1(d), the Lysekil WEC developed in Sweden is a typical example [24].
1.2 Lysekil Project 1.2.1 Test site The Lysekil Project is one of the world’s ongoing wave energy research pro- jects, aiming to develop a WEC farm will full scale devices for Swedish con- ditions and study wave energy conversion [25]. This project is led by a re- search group from the division for electricity at Uppsala University [26]. The test site is located offshore, in Västra Götaland county, on the west coast of Sweden (58.18N, 11.37E). Several points make this location suitable as a test site [27]: a. A flat and wide sea bottom with an average depth of around 25 meters. This condition makes it possible to accommodate over 10 WECs. b. The nearby island Härmanö provides convenient transportation pos- sibilities and enables connection to the gird on the surrounding island. c. The nearby city of Lysekil has a well-equipped harbor and serves as a starting point for the deployments of WECs and other large scale equipment.
1.2.2 History The project started in 2002 [28] and has developed into a multi-physics plat- form for different research programs [29]. The project’s first WEC, named the L1, was installed and connected to an onshore load in March 2006 [30, 31].
15 During the last ten years, over ten different prototypes of the WECs and two marine substations [32, 33] have been deployed at the test site. The first generator (L1) was installed with the purpose of verifying the con- cept of the WEC. After the installation of the L2 and the L3 in 2009, the three generators were connected into a farm through a marine substation [34]. The converted electricity was transferred to an onshore measuring station. The L2 and the L3, had an updated measurement system, as well as an improved me- chanical design. At the end of 2009, a new linear generator, the L9, was de- ployed at the site [35]. The L9 had an updated design, aimed at obtaining a higher power production. In November 2010, four generators (L4, L5, L7 and L8) with various designs were installed. The L7 was connected to a resonant electrical circuit for rectification, while the L8 was connected to a diode rec- tifier. In 2015, three different generators (L10, L11 and L12) were launched as well as an advanced marine substation equipped with auxiliary control modules [36, 37, 38]. A variety of buoys have been developed and tested for the connection to the generators. So far, three types of buoys have been developed and investi- gated: cylindrical buoys, torus buoys and discus buoys [25, 39, 40]. Both force sensors and accelerometers have been installed in the buoys. A measuring station was built to provide a platform for the load tests [41]. From 2006 to 2008, the WECs were connected with resistive loads and a pas- sive rectified circuit [42, 43]. In 2010, a resonant circuit was designed to up- grade the power production [44, 45] and the electrical system has been con- tinually upgraded since then, currently e.g. hosting full AC/DC/AC conver- sion and grid connection. The project also has a number of ongoing interdisciplinary studies, such as studies on the cooling systems for the substations [46, 47, 48], remotely oper- ated vehicles [49] and buoys that can alter the length of the buoy line in re- sponse to sea level variations [50, 51]. All aim to improve the overall viability of the WEC concept. Furthermore, there are studies on different areas of en- vironmental impact [52, 53, 54]. An observation tower was built during 2007 and 2008 to monitor the test site as well as collecting wave data with the wave measuring buoys [55]. At the same time, biology buoys were deployed to study the biofouling and the impact from the WECs on the marine environ- ment [56].
1.2.3 Previous work with published thesis At present, 20 PhD theses have been published by the wave energy research group at Uppsala University. A brief summary of the contributions is provided here. Dr. Thorburn proposed an electrical approach on the concept of Wave En- ergy Conversion focused on the modelling of rectification and transmission of the generated electricity [57].
16 Extensive studies on the linear permanent magnet generator designed for the studied WEC concept was carried out by Dr. Danielsson [58]. Dr. Eriksson proposed and verified a hydrodynamic model on the interac- tion between the point absorbing type WEC and the ocean waves [59]. Dr. Waters main contribution was a mechanical design and the construction of the first full scale linear generator (the L1). Experiments on the prototype were carried out over several years. [60]. The environmental impact caused by the WEC on the marine ecosystem was carried out by Dr. Langhamer [61]. The first marine substation for electrical conversion and connection of up to three WECs in a small wave farm was designed by Dr. Rahm [62]. Dr. Lindroth performed research on the L1’s in the presence of changing water levels, wave heights and how the WEC behavior corresponded to the spectral shapes of different sea states [63]. A two-body system WEC was proposed by Dr. Engström, presenting a op- tion for enhancing the wave energy capture ratio [64]. Different load strategies of the WECs were studied by Dr. Boström both in modelling and experiments at the Lysekil test site [65]. Force measurements on the buoy and measurement systems in the substa- tion and measuring station were installed by Dr. Svensson [66]. Dr. Strömstedt studied the linear lead through for the WEC and performed extensive measurements on the WECs [67]. Dr. Andrej studied the reliability of the mechanical parts of the linear gen- erator as well as the lateral forces acting on the outer structure of the WEC [68]. A new type of linear generator equipped with ferrite permanent magnets was studied by Dr. Ekergård [69]. Dr. Ekström developed a marine substation, for up to 7 WECs, equipped with advanced measuring and control systems [70]. Dr. Gravråkmo investigated the point absorbing buoys with respect to their different geometry, size and hydrodynamic performance [40]. Dr. Haikonen conducted research on the radiated noise from the WEC and possible impact to the marine environment [71]. The electrical conversion of a three-level inverter from WEC to the grid was studied by Dr. Krishna [72]. Dr. Hai proposed an approach on equivalent circuit modelling to simulate the performance for the WEC developed in the project [73]. Dr. Lejerskog performed a study on the cogging forces generated inside the generator. He also studied new generator designs [74]. A sea level compensation system was developed by Dr. Castellucci aiming to optimize the energy extraction from the ocean waves in areas with high tides [75].
17 1.3 Aims of thesis My research aim has been focused on developing and using WEC models to study the energy conversion of the chosen WEC concept. The performance of the WECs is investigated by varying the mechanical design, aiming to opti- mize the energy absorption.
18 2. Theory
This chapter begins with a basic theory on the wave energy spectrum. The hydrodynamic theory is proposed in the second paragraph to illustrate the in- teraction between the waves and the WEC device. This theory is important to predict the WEC behavior and energy extraction by solving the mechanical relationships. The theory is applied when building the numeric model, as well as to perform the studies in Papers V and VI on the WEC device. Later in this chapter, the electrical theory on the linear generator is pro- posed and a WEC model is developed based on it. The theory is explained in paper IV. Furthermore, three load strategies for practical tests in the Lysekil project are presented and simulated with the proposed WEC models.
2.1 Ocean waves and energy spectrum Ocean waves, regarding as the irregular waves, can be defined by the wave height �, wave length � and wave period �, see Figure 2.1. On the premise that the linear theory is applicable [76] when the water depth ℎ > 2� [77], the irregular waves is concerned as a superposition of series of different frequen- cies. An analysis approach of the wave spectrum S � is commonly utilized to describe the real sea state, where � is the frequency [78]. The � moment if the spectral density in continuous form is interpreted in Equation (2.1), � = � � � �� (2.1) The significant wave height and average energy period are expressed respec- tively as below, � = 4 � (2.2) � = � � (2.3) According to (2.1) under the deep water condition [79], the energy flux for the real ocean waves could be then obtained: � = � � (2.4) where � is the density of the sea water and � is the acceleration of gravity.
19
Figure 2.1. a simple definition of the ocean wave’s characteristics with wave length , wave height and water depth .
ìIn addition, the" Bretschneider spectruma [80] is also used as one of the empir- ical approaches to describe the ocean waves, defined as below,
(2.5) ® ® ® • ¶ß ' ü•¶ß £¶ In Equation (2.5) where45 is the angular© ( frequency, is the modal fre- quency for any given0 wave.9 Figureú h¢ ¶ 2.2" gives™ an example of the Bretschneider : spectrum used for describing9 five different sea states. 9
! Figure 2.2. An example of Bretschneider spectrum describing the ocean waves by known wave period and significant wave height.!
20 2.2 Hydrodynamics model The mechanic interaction between a Wave Energy Converter and the waves is described in Equation (2.6). In this study, the floating buoy is restricted to the heave motion only. In Equation (2.6), � is the vertical position of the buoy and � is the translator position under excitation from the waves. The upper differential equation describes the interaction between the buoy and the waves, where � is the mass of the buoy, � is the added mass in infinity frequency limit, � is the time dependent excitation force, ℎ � is the im- pulse response function for the radiation impedance, � is the hydrostatic force and � is the line force.
� + � � = � � − ℎ � � � − � − � � , � − � � � � = � � , � + � � , � − � � + � _ + � _ (2.6) The lower differential equation describes the motion of the translator driven by the buoy, where � is the translator mass and � is the generator damping force. The end stops are springs with a high spring constant, denoted as � _ and � _ respectively in the equation. The line between the buoy and the translator is modelled as a stiff spring, which becomes active when the distance between buoy and translator becomes larger than the length of the line. The line force is modelled by Equation (2.7), where the spring constant is denoted as � .
� � − � �� � > � � � , � = (2.7) 0 ����
The upper and lower end stop forces are described in Equation (2.8) and (2.9). In the equations where � and � are the spring constant for the end stops, � and � are the stroke length to the upper and lower end stop respectively.
−� � − � �� � > � � � = (2.8) _ 0 ����
−� � − � �� � < −� � � = (2.9) _ 0 ����
The generator damping force is proportional to the translator speed with the damping coefficient �, is given by. � � = −�� (2.10)
21 The ratio between average absorbed power and the power transport towards the buoy is defined as the power capture ratio. The expression for the power capture ratio is given by, � = ×100% (2.11)
Where � is the average absorbed power by the buoy and � is given by, � = � � � (2.12)
where the buoy diameter is denoted by �, while � and � is the mean en- ergy period and the significant wave height respectively.
2.3 Electrical theory of linear generator model In the linear generator, the magnetic flux is generated by the permanent mag- nets on the translator. The flux is confined inside the magnetic path along the laminated steel sheets, enclosing the isolated conductors mounted on the stator [81]. Assuming that the magnetic flux has a sinusoidal form, the flux can be described as � = � ��� (�� + �) (2.13)