Logo: to the web site of Uppsala University

On March 13^th, 2006, the Division of Electricity at Uppsala University deployed its first wave energy converter, L1, in the ocean southwest of Lysekil. L1 consisted of a buoy at the surface, connected through a line to a linear generator on the seabed. Since the deployment, continuous investigations of how L1 works in the waves have been conducted, and several additional wave energy converters have been deployed.

This thesis is based on ten publications, which focus on different aspects of the interaction between wave, buoy, and generator. In order to evaluate different measurement systems, the motion of the buoy was measured optically and using accelerometers, and compared to measurements of the motion of the movable part of the generator - the translator. These measurements were found to correlate well. Simulations of buoy and translator motion were found to match the measured values.

The variation of performance of L1 with changing water levels, wave heights, and spectral shapes was also investigated. Performance is here defined as the ratio of absorbed power to incoming power. It was found that the performance decreases for large wave heights. This is in accordance with the theoretical predictions, since the area for which the stator and the translator overlap decreases for large translator motions. Shifting water levels were predicted to have the same effect, but this could not be seen as clearly.

The width of the wave energy spectrum has been proposed by some as a factor that also affects the performance of a wave energy converter, for a set wave height and period. Therefore the relation between performance and several different parameters for spectral width was investigated. It was found that some of the parameters were in fact correlated to performance, but that the correlation was not very strong.

As a background on ocean measurements in wave energy, a thorough literature review was conducted. It turns out that the Lysekil project is one of quite few projects that have published descriptions of on-site wave energy measurements.

Surface gravity waves in the world’s oceans contain a renewable source of free power on the order of terawatts that has to this date not been commercially utilized. The division of Electricity at Uppsala University is developing a technology to harvest this energy. The technology is a point absorber type wave energy converter based on a direct-driven linear generator placed on the sea bed connected via a line to a buoy on the surface.

The work in this thesis is focused mainly on the energy transport of ocean waves and on increasing the transfer of energy from the waves to the generator and load. Potential linear wave theory is used to describe the ocean waves and to derive the hydrodynamic forces that are exerted on the buoy. Expressions for the energy transport in polychromatic waves travelling over waters of finite depth are derived and extracted from measured time series of wave elevation collected at the Lysekil test site. The results are compared to existing solutions that uses the simpler deep water approximation. A Two-Body system wave energy converter model tuned to resonance in Swedish west coast sea states is developed based on the Lysekil project concept. The first indicative results are derived by using a linear resistive load. The concept is further extended by a coupled hydrodynamic and electromagnetic model with two more realistic non-linear load conditions.

Results show that the use of the deep water approximation gives a too low energy transport in the time averaged as well as in the total instantaneous energy transport. Around the resonance frequency, a Two-Body System gives a power capture ratio of up to 80 percent. For more energetic sea states the power capture ratio decreases rapidly, indicating a smoother power output. The currents in the generator when using the Two-Body system is shown to be more evenly distributed compared to the conventional system, indicating a better utilization of the electrical equipment. Although the resonant nature of the system makes it sensitive to the shape of the wave spectrum, results indicate a threefold increase in annual power production compared to the conventional system.

The search for new solutions for the generation of energy is becoming more and more important for our future. Big arguments and disagreements on e.g. the questions of gas transport or the dependence on energy supplied by other countries raise demands on the development of new forms of alternative energy resources. Wave power is one of the main sources of renewable energy due to the high power density stored in ocean waves.

Nevertheless, the dynamic forces of waves are so large that serious questions popped up on how to design a system which could work even in an unfavourable wave climate or could at least retain working capabilities after big storms without significant damages.

This thesis studies the reliability of the mechanical parts of a linear direct driven permanent magnet generator. The results of offshore experiment where strain gauge sensors instrumented on the capsule and the inner framework structure are presented. Stress estimation analyses using strain gauges are carried out. A method for measuring forces and moments in the mechanical structure of the WEC is developed.

Evaluation of the lateral force acting on the outer structure is a key factor for the design and construction of the WEC. A method for the measurement of the lateral force acting on the capsule has been developed.

A study of the inclination angle between the Wave Energy Converter and the floating buoy has been carried out.

The aim of this work is to contribute to the development of wave energy conversion system, and especially to the estimation of structural loads which are important for the survivability of the system under hard sea states.

This work is a step that may influence future design of wave energy devices in terms of material aspect, survivability in a hard wave climate and cost-effective renewable energies.

Different wave power technologies are in development around the world in different stages of prototype testing. So far only a few devices have been deployed offshore at full scale for extended periods of time. Little data is published about how these different devices perform.

This thesis presents results from experiments with the full-scale offshore wave energy converters at the Lysekil research site on the Swedish west coast. The theories, experiments, measurements, performance evaluations and developments of the submerged transmission in the direct driven permanent magnet linear generator are in focus. The reciprocating submerged transmission fulfills the purpose of transmitting the absorbed mechanical wave energy through the capsule wall into the generator, while preventing the seawater from entering the capsule and reducing the life time of the converter.

A measuring system with seven laser triangulation sensors has been developed to measure small relative displacements between piston rod and seal housing in the submerged transmission with excellent accuracy for the purpose of evaluating both functional behavior and successive wear in-situ. A method for calculating relative tilt angles, azimuth angles, differential tilt angles, and successive wear in the submerged transmission has been developed. Additional sensors systems have been installed in the converter enabling correlation and a thorough investigation into the operating conditions of the transmission and the converter. The thesis presents unique results from the measurements. A data acquisition system transmits the signals from the converter on the seabed to an onshore measuring station. Results are presented in time-, frequency- and the time-frequency domain.

The results have given important information for further development of the submerged transmission, which is important to the survivability of the system. The thesis describes the status of research, and is a step that may influence future designs of wave energy devices for reaching survivability and a cost-effective renewable energy system.

This thesis presents how experimental results, from wave power research performed offshore at the Lysekil research site, were obtained. The data were used to verify theoretical models as well as evaluate the feasibility of wave power as a future sustainable energy source.

The first experiments carried out at the research site was the measurement of the force in a line where one end was connected to a buoy with a diameter of 3 m and the other end to a set of springs with limited stroke length. The system is exposed to high peak forces compared to average forces. The maximum measured force in the line, when the buoy motion is limited by a stiff stopper rope is ten times the average force in that particular sea state.

The experiment performed on the first wave energy converter tested at the Lysekil Research Site is described. The infrastructure of the site is presented where the central connection point is the measuring station. The key finding is that it is possible to transform the motions of ocean waves into electrical energy and distribute it to land.

Many wave energy converters must be interconnected if large amounts of energy are to be harvested from the waves. The first submerged substation intended for aggregation of energy from wave power converters is described, with focus on the measurement and control system placed inside the substation. During this experiment period the generators were equipped with many different sensors; these measurements are explained in the thesis.

The system that aggregates power from the studied wave energy converter is regularly exposed to peak power of up to 20 times the maximum average output from the converter.

Vertical and horizontal movement of the buoy has been measured in different ways. The result is that the vertical displacement of the buoy can be measured with a simple accelerometer circuit but it is much more complicated to measure the horizontal displacement. A special method for measuring the horizontal displacement has been implemented by measuring the strain in the enclosure and the force in the line.

Den här avhandlingen berättar om hur experimenten vid Lysekils forskningsområde för vågkraft har utförts. Insamlade mätdata har använts för att verifiera teoretiska samband som modulerats vid Elektricitetslära, Uppsala universitet. De teoretiska och praktiska resultaten har visat på att vågkraft har förutsättningarna att implementeras som en hållbar framtida energikälla. Intressanta mätmetoder har utvecklas och påfrestningarna  på utrustningin och dess samband med medel effekten har studerats.

Wave energy converters of point absorber type have been developed and constructed. Full scale experiments have been carried out at sea and electricity has been successfully delivered. Linear permanent magnet generators together with a subsea substation and buoys of various geometric shapes have been investigated theoretically and experimentally. The design has in large extent an electronic approach, keeping the mechanical part of it as simple as possible, due to the long life span and reliability of electric components.

Because of the nature of a linear generator, the internal translator with permanent magnets has a limited stroke length which will be reached when the buoy is exposed to large wave heights. Internal springs at the top and bottom of the generator prevent the translator from hitting the generator hull. Inertial forces due to the mass and velocity of the translator and the buoy and its heave added mass compresses the spring. The added mass is a rather large part of the total moving mass. Simulations of a converter with a vertical cylindrical buoy and with a toroidal buoy were conducted, as well as real sea experiments with converters with cylindrical buoys of two different sizes and a toroidal buoy. The overloads are likely to affect the design and service life of the generator, the buoy and the wire which interconnects them.

Buoy shapes with as much excitation force as possible and as little heave added mass as possible were sought. A toroidal buoy caused less overloads on the generator at sea states with short wave periods and relatively large wave height, but for sea states with very long wave periods or extremely high waves, the magnitude of the overloads was mainly determined by the maximum displacement of the buoy.

Snap loads on the interconnecting wire, as the slack wire tensed up after a very deep wave trough, were found to be greater but of the same order of magnitude as forces during the rest of the wave cycle.

During a 4 day period at various wave conditions, two converters with cylindrical buoys proved efficiency between 11.1 % and 24.4 %. The larger buoy had 78 % larger water plane area than the other buoy which resulted in 11 % more power production. Short wave period was beneficial for the power production.

Infinite frequency heave added mass was measured for a cylindrical buoy at real sea and found to be greater than the linearly calculated theoretical added mass.

The thesis presents results from synchronous linear wave energy converters developed at Uppsala University. A study is done on closed stator slots and a study presenting offshore data focusing on the power absorption from a wave energy converter (WEC). The first step in studying the closed slots has been done during no-load, to study the magnetic flux path from the permanent magnets and to study the forces in the linear generator. The initial studies show a reduction in cogging force and a reduction in harmonics in the magnetic flux density in the air-gap. It also shows an increase of the total flux entering the stator and an increase in flux leakage. The study has been done with FEM simulations and compared with analytical calculations.

The second study was done to investigate the power absorption of a WEC in upward and downward motion in relation to the volume of the buoy and mass of the system. The experimental results were compared with a static model focusing on the limit in the absorption. As expected from the model, the WEC absorbs more energy in the upward direction. Also indications of snatch load were observed. Within this thesis, results from a comparison study between two WECs with almost identical electrical properties and the same volume of the buoy, but with different height and diameter have been presented. Moreover, experimental studies including the conversion step between AC to DC have been done.

The work done in this thesis is a part of a larger wave power project at Uppsala University. Where everything between the energy absorption from the waves to the connection to the electrical grid is studied. The project has a test-site at the west coast of Sweden near the town Lysekil, where wave energy research has been carried out since 2004.

Ocean wave energy can be harnessed and converted into electric energy nowadays. This provides a possibility for populations that live on islands or along coastlines to utilize the renewable and safe power produced by ocean waves. Point absorbing wave energy converter (WEC) is one example of such devices for electrical power production from ocean waves. It is composed of a floating buoy on the water surface, and a linear generator that sits on seabed and is connected with the buoy via a line. Electricity is generated when the buoy moves up and down in the waves.

The geometry and dimensions of the floating buoy have dominant influences on the energy absorption. This thesis introduces an equivalent electric circuit for modelling the  hydrodynamic interaction between the wave and a cylindrical buoy. The model allows a rapid assessment of the velocity, force in the connection line and output power, by which the system design and optimization can be performed faster and easier.

The electric circuit model is based on the WEC's dynamic force analysis, and the electric components' parameters are determined from analytical approximations of the hydrodynamic coefficients. The simulation results of the equivalent circuit for one typical wave climate in Lysekil has been presented, and the results indicate a good fitting with former experimental results.

The thesis also includes a hydrodynamic study for a torus shaped buoy, which aims at  applying a theoretical background for a force measurement experiment. A comparison has been conducted between the torus buoy and two similar cylindrical buoys. Preliminary WAMIT simulation results demonstrate that the force in the connection line will be 5% bigger by using the torus buoy. It is also found that the torus buoy is advantageous for its larger excitation force and smaller added mass. A brief introduction of the 500kN force measurement system and the communication test have been introduced as well.

The motion of ocean waves can be captured and converted into usable electricity. This indicates that wave power has the potential to supply electricity to grids like wind or solar power. A point absorbing wave energy converter (WEC) system has been developed for power production at Uppsala University. This system contains a semi-submerged buoy on the water surface driving a linear synchronous generator placed on the seabed. The concept is to connect many small units together, to form a wave farm for large-scale electricity generation.

A lot of effort has gone into researching how to enhance the power absorption from each WEC unit. These improvements are normally done separately for the buoy, the generator or the electrical system, due to the fact that modelling the dynamic behavior of the entire WEC system is complicated and time consuming. Therefore, a quick, yet simple, assessment tool is needed. 

This thesis focuses on studying the use of the equivalent circuit as a WEC system modelling tool. Based on the force analysis, the physical elements in an actual WEC system can be converted into electrical components. The interactions between the regular waves, the buoy, and the Power Take-off mechanism can be simulated together in one circuit network. WEC performance indicators like the velocity, the force, and the power can be simulated directly from the circuit model. Furthermore, the annual absorbed electric energy can be estimated if the wave data statistics are known.

The linear and non-linear equivalent circuit models developed in this thesis have been validated with full scale offshore experimental results. Comparisons indicate that the simplest linear circuit can predict the absorbed power reasonably well, while it is not so accurate in estimating the peak force in the connection line. The non-linear circuit model generates better estimations in both cases. To encourage researchers from different backgrounds to adapt and apply the circuit model, an instruction on how to establish a non-linear equivalent circuit model is supplied, as well as on how to apply the model to accelerate the decision making process when planning a WEC system.

This thesis studies wave energy converters developed at Uppsala University. The wave energy converters are of point absorbing type with direct driven linear generators. The aim has been to study generator design with closed stator slots as well as offshore experimental studies.

By closing the stator slots, the harmonic content in the magnetic flux density is reduced and as a result the cogging forces in the generator are reduced as well. By reducing these forces, the noise and vibrations from the generator can be lowered. The studies have shown a significant reduction in the cogging forces in the generator. Moreover, by closing the slots, the magnetic flux finds a short-cut through the closed slots and will lower the magnetic flux linking the windings.

The experimental studies have focused on the motion of the translator. The weight of the translator has a significant impact on the power absorption, especially in the downward motion. Two different experiments have been studied with two different translator weights. The results show that with a higher translator weight the power absorption is more evenly produced between the upward and downward motion as was expected from the simulation models. Furthermore, studies on the influence of the changing active area have been conducted which show some benefits with a changing active area during the downward motion. The experimental results also indicate snatch-loads for the wave energy converter with a lower translator weight.

Within this thesis results from a comparative study between two WECs with almost identical properties have been presented. The generators electrical properties and the buoy volumes are the same, but with different buoy heights and diameters. Moreover, experimental studies including the conversion from AC to DC have been achieved.

The work in this thesis is part of a larger wave power project at Uppsala University. The project studies the whole process from the energy absorption from the waves to the connection to the electrical grid. The project has a test-site at the west coast of Sweden near the town of Lysekil, where wave energy systems have been studied since 2004.

Ocean wave energy is considered to be one of the important potential renewable energy resources for sustainable development. Various wave energy converter technologies have been proposed to harvest the energy from ocean waves. This thesis is based on the linear generator wave energy converter developed at Uppsala University. The research in this thesis focuses on the foundation optimization and the power absorption optimization of the wave energy converters and on the wave climate modelling at the Lysekil wave converter test site.

The foundation optimization study of the gravity-based foundation of the linear wave energy converter is based on statistical analysis of wave climate data measured at the Lysekil test site. The 25 years return extreme significant wave height and its associated mean zero-crossing period are chosen as the maximum wave for the maximum heave and surge forces evaluation.

The power absorption optimization study on the linear generator wave energy converter is based on the wave climate at the Lysekil test site. A frequency-domain simplified numerical model is used with the power take-off damping coefficient chosen as the control parameter for optimizing the power absorption. The results show a large improvement with an optimized power take-off damping coefficient adjusted to the characteristics of the wave climate at the test site.

The wave climate modelling studies are based on the wave climate data measured at the Lysekil test site. A new mixed distribution method is proposed for modelling the significant wave height. This method gives impressive goodness of fit with the measured wave data. A copula method is applied to the bivariate joint distribution of the significant wave height and the wave period. The results show an excellent goodness of fit for the Gumbel model. The general applicability of the proposed mixed-distribution method and the copula method are illustrated with wave climate data from four other sites. The results confirm the good performance of the mixed-distribution and the Gumbel copula model for the modelling of significant wave height and bivariate wave climate.

The Division for Electricity of Uppsala University is developing a wave power concept. The energy of the ocean waves is harvested with wave energy converters, consisting of one buoy and one linear generator. The units are connected in a submerged substation. The mechanical design is kept as simple as possible to ensure reliability.

The submerged substation includes power electronics and different types of electrical power components. Due to the high cost of maintenance operations at sea, the reliability of electrical systems for offshore renewable energy is a major issue in the pursuit of making the electricity production economically viable. Therefore, proper thermal management is essential to avoid the components being damaged by excessive temperature increases.

The chosen cooling strategy is fully passive, and includes no fans. It has been applied in the second substation prototype with curved heatsinks mounted on the inner wall of the pressurized vessel. This strategy has been evaluated with a thermal model for the completed substation. First of all, 3D-CFD models were implemented for selected components of the electrical conversion system. The results from these submodels were used to build a lumped parameter model at the system level.

The comprehensive thermal study of the substation indicates that the rated power in the present configuration is around 170 kW. The critical components were identified. The transformers and the inverters are the limiting components for high DC-voltage and low DC-voltage respectively. The DC-voltage—an important parameter in the control strategy for the WEC—was shown to have the most significant effect on the temperature limitation.

As power diodes are the first step of conversion, they are subject to large power fluctuations. Therefore, we studied thermal cycling for these components. The results indicated that the junction undergoes repeated temperature cycles, where the amplitude increased with the square root of the absorbed power.

Finally, an array of generic heat sources was optimized. We designed an experimental setup to investigate conjugate natural convection on a vertical plate with flush-mounted heat sources. The influence of the heaters distribution was evaluated for different dissipated powers. Measurements were used for validation of a CFD model. We proposed optimal distributions for up to 36 heat sources. The cooling capacity was maximized while the used area was minimized.