Within a wave energy converter's operational bandwidth, device operation tends to be optimal in converting mechanical energy into a more useful form at an incident wave period that is proximal to that of a power-producing mode of motion. Point absorbers, a particular classification of wave energy converters, tend to have a relative narrow optimal bandwidth. When not operating within the narrow optimal bandwidth, a point absorber's response and efficiency is attenuated. Given the wide range of sea-states that can be expected during a point absorber's operational life, these devices require a means to adjust, or control, their natural response to maximize the amount of energy absorbed in the large population of non-optimal conditions. In the field of wave energy research, there is considerable interest in the use of non-linear control techniques to this end. Non-linear control techniques introduce time-varying and state dependent control parameters into the point absorber motion equations, which usually motivates a computationally expensive numerical integration to determine the response of the device - important metrics such as gross converted power and relative travels of the device's pieces are extracted through post processing of the time series data. As an alternative, the work presented in this thesis was based on a closed form perturbation based approach for analysis of the response of a device with periodically-varying control parameters, subject to regular wave forcing, in the frequency domain. The proposed perturbation based method provides significant savings in computational time and enables the device's response to be represented in a closed form manner with a relatively small number of solution components - each component is comprised of a complex amplitude and oscillation frequency. This representation of the solution was found to be very concise and descriptive, and to lend itself to the calculation of gross absorbed power and travel constraint violations, making it extremely useful in the automated design optimization process; the methodology allows large number of design iterations, including both physical design and control variables, to be evaluated and conclusively compared. In the development of the perturbation method, it was discovered that the device's motion response can be calculated from an in nite series of second order ordinary differential equations that can be truncated without destroying the solution accuracy. It was found that the response amplitude operator for the generic form of a solution component provides a means to gauge the device's response to a given wave input and control parameter variation, including a gauge of the solution process stability. It is unclear as of yet if this is physical, a result of the solution process, or both. However, for a given control parameter set resulting in an unstable solution, the instability was shown to be, at least in part, a result of the device's dynamics. If the stability concerns can be addressed through additional constraints and updates to the wave energy converter hydrodynamic parameters, the methodology will expand on the commonly accepted boundaries for wave energy converter frequency domain analysis methods and be of much practical importance in the evaluation of control techniques in the field of wave energy converter technology. / Graduate

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.

A prototype point absorber style wave energy converter has been proposed for deployment off the West coast of Vancouver Island near the remote village of Hotsprings Cove in Hesquiaht Sound; a site identified as having significant wave energy potential. The proposed design consists of two components, a long unique cylindrical spar and a concentric toroid float. To serve ongoing wave energy converter (WEC) dynamics modelling and control research in support of that project, an experimental facility for small scale physical model testing is desired at UVIC. In the immediate term, the facility could be used to determine the hydrodynamic coefficients over a range of wave frequencies. Refined estimates of the hydrodynamic coefficients would be exploited in the optimisation of the WEC geometry. To date, WEC research at UVIC has neglected the frequency dependence of the hydrodynamic coefficients, relying on limited experimental results to provide a single frequency invariant set of coefficient estimates. / Graduate / 0791 / 0547 / 0548 / mercedes.baylis@hotmail.com

As the world’s need for electricity increases, so does its demand for sustainable energy with low to no greenhouse gas emissions. One of these renewable sources of energy is the Ocean which is one of the world’s largest and most predictable energy source, where the extraction of energy can be from waves or tidal current, with zero greenhouse gas emissions during production. A company which works with wave energy is Waves4Power which has developed the wave energy buoy WaveEL.WaveEL is comprised of a buoy which is eight meters in diameter with a 36 meters long vertical cylinder which goes through the buoy. In the cylinder is a piston that oscillates in pace with the waves and generates electricity. Between the piston and the cylinder wall is a gap where the water can move from one side of the piston to the other in pace with the piston’s oscillations. The gap is called the leakage clearance. The leakage clearance effect on the flow resistance is the focus of this master thesis as something which has not been studied before in scientific articles for similar wave energy buoys or in other fields.The aim of the master thesis is to improve the understanding of how the water flow, because of the leakage clearance in the WaveEL buoy, affects the force which the piston is subjected to, and in turn how much electricity can be generated. As it is a complex system the focus will be to determine the dynamic flow resistance parameter because of the leakage clearance and the changes to the dynamic flow resistance parameter as the dimensions of the piston is varied.The leakage clearance effect on the flow resistance has been studied with the help of Computational Fluid Dynamics (CFD) in the software COMSOL Multiphysics 6.0 in two different models. In the first model, model A, the piston is locked in different positions in the cylinder and the pressure at the bottom of the cylinder varies to reflect the motion of the waves. For the second model, model B, the piston is allowed to move vertically in the cylinder due to a set force which reflects the motion of the waves.The dynamic flow resistance parameter for model A is lower at higher Reynolds number and within an interval between 0.4 and 1.6 within the working area. Outside of the working area the dynamic flow resistance parameter is lower at a higher Reynolds number and higher than in the working area at an interval between 0.7 and 45.For model B, the dynamic flow resistance parameter has only been calculated for the working area and is within an interval of 0.1 and 7, the value for the dynamic flow resistance parameter is low when the Reynolds number is high. Dissimilar to model A where the piston is locked into position, the piston oscillates in model B. There is a phase shift between the velocity of the piston and the velocity of the water, which leads to the piston being subjected to a larger force than in model A at lower water velocities. This is one of the reasons why the dynamic flow resistance parameter is higher in model B than model A at low Reynolds number. As model B calculates the dynamic flow resistance parameter based on the relative velocity between the piston and the water, the dynamic flow resistance parameter becomes lower than for model A at higher Reynolds number.For the performed sensitivity analysis, the results shows that a more advantageous value on the dynamic flow resistance parameter can be achieved by altering the dimensions of the piston. A more advantageous result was achieved for example when the rounded edge on the piston became sharper or when the leakage clearance width was increased by 10%. If this master thesis work is to be extended, the studies should focus on elaborating model B either more in depth or with values derived from experiments from the WaveEL buoy for a more realistic model and thus determine a more accurate dynamic flow resistance parameter.The results from the sensitivity analysis justifies a future study where the dynamic flow resistance parameter should be investigated with greater variations of the piston diameters, as this can increase the flow resistance and thus generate more electricity. However, it should be investigated in relation to the cost of manufacture, to obtain the ultimate design which generates maximum electricity for a reasonable manufacturing cost. / Allt eftersom värdens elektricitetsbehov ökar, ökar också efterfrågan på förnybar energi med låga eller inga växthusgasutsläpp. En av dessa förnybara energikällor är havet som anses vara en av världens största och mest förutsägbara energikällor, där utvinningen av energi kan ske från vågor eller tidvattenströmmar, med noll växthusgasutsläpp under produktion. Ett av företagen som arbetar med vågenergi är Waves4Power som har utvecklat vågenergibojen WaveEL.WaveEL består av en boj som är åtta meter i diameter med en 36 meter lång vertikal cylinder som går igenom bojen. I cylindern finns en kolv som oscillerar i takt med vågorna och genererar elektricitet. Mellan kolven och cylinderväggen finns en spalt där vatten kan förflytta sig från ena sidan av kolven till den andra i takt med att kolven oscillerar, denna spalt kallas läckspalten. Läckspaltens påverkan på flödesmotståndet är någonting som tidigare inte har studerats i andra vetenskapliga artiklar för likartade vågenergibojar eller inom andra branscher och är därför fokus för detta examensarbete.Syftet med examensarbetet är att förbättra förståelsen hur vattenflödet till följd av läckspalten i WaveEL-bojen påverkar kraften som kolven utsätts för, vilket i sin tur påverkar hur mycket elektricitet som genereras. Eftersom det är ett komplext system kommer focus vara att fastställa den dynamiska flödesmotstånds parametern till följd av läckspalten och förändringarna i den dynamiska flödesmotstånds parametern när dimensionerna på kolven varieras.Läckspaltens påverkan på flödesmotståndet har studerats med hjälp av Computational Fluid Dynamics (CFD) med programvaran COMSOL Multiphysics 6.0 i två olika modeller. I den första modellen, modell A, är kolven låst i olika positioner i cylindern och trycket vid botten av cylindern varierar för att efterlikna vågrörelser. För den andra modellen, modell B, tillåts kolven röra sig vertikalt i cylindern genom en bestämd kraft som efterliknar vågrörelserna.Resultatet från modell A visar att flödesmotståndet befinner sig mellan 0,4 och 1,6 inom arbetsområdet och utanför arbetsområdet är den dynamiska flödesmotståndsparametern större än i arbetsområdet, här är den dynamiska flödesmotstånds parametern mellan 0,7 och 45. Oberoende av kolvens position i bojen sjunker den dynamiska flödesmotståndsparametern i takt med att Reynolds talet ökar.För modell B har den dynamiska flödesmotstånds parametern endast beräknas för arbetsområdet och ligger inom intervallet 0,1 och 7, där ett lågt värde på den dynamiska flödesmotstånds parametern fås när Reynolds talet är högt. Tillskillnad mot modell A där kolven är låst i sin position, oscillerar kolven i modell B. Det finns en fasvridning mellan kolvens och vattnets hastighet, vilket innebär att kolven utsätts för en större kraft i modell B än i modell A vid låga vattenhastigheter. Det är en av anledningarna till att den dynamiska flödesmotstånds parametern är högre i modell B vid låga Reynolds tal. Eftersom modell B beräknar ut den dynamiska flödesmotstånds parametern med hjälp av den relativa hastigheten mellan kolven och vattnet blir den dynamiska flödesmotståndsparametern lägre än för modell A högre Reynolds tal.För den genomförda känslighetsanalysen visar resultatet att ett mer fördelaktigt värde på den dynamiska flödesmotsstånds parametern kan uppnås vid förändring av kolvens dimensioner. Exempelvis uppnåddes ett mer fördelaktigt resultat när den avrundade kanten på kolven blev skarpare eller när bredden på läckspalten ökades med 10%. Om detta examensarbete ska utökas bör studierna fokusera på att utveckla modell B antingen mer på djupet eller med värden härledda från experiment från WaveEL-bojen för en mer realistisk modell och därmed en mer exakt bestämning av den dynamiska flödesmotstånds parametern.Resultatet från känslighetsanalysen motiverar en framtida studie där den dynamiska flödesmotstånds parametern bör undersökas med kraftigare dimensions variationer på kolven, eftersom detta kan komma att öka flödesmotståndet och således generera mer elektricitet. Dock behöver de undersökas i relation med tillverkningskostnaderna, för att hitta den ultimata design som genererar maximalt med elektricitet vid en rimlig tillverkningskostnad.

Denna rapport ämnar undersöka de vanligast förekommande typerna av teknologier för vågkraftverk (eng. Wave Energy Converter, WEC) teknologier för att jämföra de olika konceptens förmåga att absorbera vågenergi. Koncept som undersöks är punktabsorbatorer och oscillerande vattenkolumner. I denna rapport används de vanligt använda engelska översättningarna point absorber och oscillating water column (OWC). Beräkningar görs för de olika koncepten i liknande vågförhållanden för att kunna jämföra den energi som kan utvinnas. I rapporten sker beräkningar under optimala vågförhållanden. Vågorna antas vara linjära och vågkraftverken antas vara i fas med vågens svängningsrörelse. Den vågdata som använts är uppmätt utanför Belmullet i Irland. Beräkningar görs på vågor med en signifikant våghöjd på 1,25 m och en periodtid på 7,5 s. Det görs även beräkningar på den största uppmätta förekommande vågen. I huvudsak används effektberäkningar enligt en modell som Kjell Budal. Syftet är att grafiskt och numeriskt jämföra den teoretiska och faktiska maxeffekt som kan utvinnas ur respektive våg. Resultatet från undersökningen visar att den största bidragande faktorn till en hög energiutvinning beror på bojens volym. Volymen måste anpassas för de vågförhållanden som finns där bojen ska placeras.Vid beräkningar av en OWC med tvärsnittsarea på 19 m2 visar det sig att den effekt som kan utvinnas av en luftkammare med tillhörande turbin är ungefär 10 kW, 1/30 av de 300kW som kan utvinnas av en point absorber. En OWC består dock sällan utav en ensam luftkammare utan ofta i en array med ett flertal luftkammare med separata turbiner för att öka effekten. / This report intends to examine the most common types of wave energy converter technologies to compare the different concepts' ability to absorb wave energy. Concepts being investigated are point absorbers and oscillating water columns (OWC). Calculations are made for the different concepts in the same wave conditions to be able to compare the energy that can be extracted. In the report, calculations are made under optimal wave conditions. The waves are assumed to be linear and the wave energy converter is assumed to be in phase with the oscillating motion of the wave. The wave data used is measured outside Belmullet in Ireland. Calculations are made on waves with a significant wave height of 1.25 m and a period time of 7.5 s. Calculations are also made on the largest measured wave present. In essence, power calculations are used according to a model developed by Kjell Budal and with the help of this be able to graphically and numerically compare the theoretical and actual maximum power that can be extracted from each scale. The results from the survey show that the largest contributing factor to high energy recovery is due to the volume of the buoy. The volume must be adapted to the wave conditions that exist where the buoy is to be placed.When calculating an OWC with a cross sectional area of 19 m2, it turns out that the power that can be extracted from an air chamber with an associated turbine is approximately 10 kW, 1/30 of the 300 kW that can be extracted by one point absorber. However, an OWC rarely consists of a single air chamber but often in a construction with several air chambers with separate turbines to increase the power.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: As a renewable energy source, wave energy has the potential to contribute to the increasing global demand for power. In South Africa specifically, the country’s energy needs may easily be satisfied by the abundance of wave energy at the South-West coast of the country. Commercially developing and utilizing wave energy devices is not without its challenges, however. The ability of these devices to survive extreme weather conditions and the need to achieve cost-efficacy while achieving high capacity factors are but some of the concerns. Constant changes in wave heights, lengths and directions as well as high energy levels and large forces during storm conditions often lead to difficulties in keeping the complexity of the device down, avoiding over-dimensioning and reaching high capacity factors. The point absorber device developed as part of this research is based on an innovation addressing the abovementioned issues. An approach is followed whereby standard "offthe- shelf" components of a proven hydraulics technology are used. The size of the device is furthermore adaptable to different wave climates, and the need for a control system is not necessary if the design parameters are chosen correctly. These characteristics enable low complexity of the device, excellent survivability and an exceptionally high capacity factor. This may lead to low capital as well as low operationand maintenance costs. In this paper the working principle of this concept is presented to illustrate how it utilises the available wave energy in oceans. The results obtained from theoretical tests correlate well with the experimental results, and it is proven that the device has the ability to achieve high capacity factors. As the device makes use of existing, "off-the-shelf" components, cost-efficient energy conversion is therefore made feasible through this research. / AFRIKAANSE OPSOMMING: As ’n hernubare/ herwinbare energiebron bied golfenergie die potensiaal om by te dra tot die bevrediging van die stygende globale energie-navraag. In spesifiek Suid-Afrika kan die oorvloed van beskikbare golfenergie aan die Suid-Weskus van die land gebruik word om aan die land se energiebehoeftes te voldoen. Betroubaarheid en oorlewing in erge weerstoestande, koste-effektiwiteit en die behaal van hoë kapasiteitsfaktore is beduidende struikelblokke wat oorkom moet word in die poging om ’n golfenergie-omsetter wat kommersieël vervaardig kan word, te ontwikkel. Daarby dra voortdurende veranderings in golfhoogtes, -lengtes en -rigtings sowel as hoë energievlakke en groot kragte tydens storms by to die feit dat dit moeilik is om die kompleksiteit van die stelsel laag te hou. Dit terwyl daar voorkom moet word dat die toestel oorontwerp en verhoed word dat hoë kapsiteitsfaktore bereik word. Die puntabsorbeerder-toestel wat in hierdie navorsing ontwikkel is, bestaan uit ’n ontwerp wat spesifiek ontwikkel is om die bogenoemde probleme aanspreek. ’n Unieke benadering is gevolg waardeur standaard, maklik-bekombare komponente gebruik is en die komponent-groottes ook aangepas kan word volgens golfgroottes. Indien die ontwerpsdimensies akkuraat gekies word, is die moontlikheid verder goed dat ’n beheerstelsel nie geïmplementeer hoef te word nie. Hierdie eienskappe verseker lae stelselkompleksiteit, uitstekende oorlewingsvermoë en ’n uitstaande kapasiteitsfaktor. Lae kapitaal- sowel as onderhoudskostes is dus moontlik. Die doel van hierdie dokument is om die werking van die konsep voor te stel en teoreties sowel as prakties te evalueer. Die resultate van teoretiese toetse stem goed ooreen met eksperimentele resultate, en dit is duidelik dat die toestel hoë kapasiteitsfaktore kan behaal. Aangesien die toestel verder gebruik maak van bestaande komponente wat alledaags beskikbaar is, word die koste-effektiewe omsetting van golfenergie dus moontlik gemaak deur hierdie navorsing.

The AOE Accumulated Ocean Energy Inc. (AOE) wave energy converter (WEC) is a cascaded pneumatic system, in which air is successively compressed through three point absorber devices on the way to shore; this air is then used to drive an electricity generator. To better quantify the performance of this device, this thesis presents a dynamically coupled model architecture of the AOE WEC, which was developed using the finite element solver ProteusDS and MATLAB/Simulink. This model is subsequently applied for the development and implementation of control in the AOE WEC. At each control stage, comprehensive power matrix data is generated to assess power production as a function of control complexity. The nature of the AOE WEC presented a series of novel challenges, centered on the significant residency time of air within the power take-off (PTO). As a result, control implementation was broken into two stages: passive and active control. The first stage, passive control, was realized as an optimization of eight critical PTO parameters with the objective of maximizing exergy output. After only 15 generations, the genetic algorithm optimization led to an increase of 330.4% over an initial, informed estimate of the optimal design, such that the annually-averaged power output was 29.37 kW. However, a disparity in power production between low and moderate energy sea-states was identified, which informed the development of an active control strategy for the increase of power production in low energy sea-states. To this aim, a recirculation-based control strategy was developed, in which three accumulator tanks were used to selectively pressurize and de-pressurize the piston at opportune times, thereby increasing the continuity of air throughput. Under the influence of active control, sea-states with significant wave heights between 0.75 m – 1.75 m, which on average encompass 55.93% of the year at the Amphitrite Bank deployment location, saw a 16.3% increase in energy production. / Graduate / 2018-08-18

The waves traveling on the surface of the world’s oceans carry atremendous amount of energy. The ability to convert this energy forhuman use has the potential to help solves the worlds energy problem. Adirect-drive linear generator point absorber is a wave energy converter(WEC) that aims to reduce the complexity of the overall system andshelter the most vulnerable parts of the system by placing them on theseabed. This concept builds around the buoy moving up and down indifferent sea-states which leads to a correlating vertical movement of thestroke in the generator resulting in the conversion of mechanical energyto power. This report aims to explore the possibility to use the open codeWEC-Sim to model the Uppsala University direct-drive linear generatorWEC in extreme sea states and to identify the resulting extreme loads. Theconstructed WEC-Sim model constrained the buoys motion in heave andsurge and limited its range of motion by modeling the generators upperend-stop spring. Simulations were run for different sea-states and theresulting forces on the system were analyzed. The peak line force for thedifferent sea states was calculated and compared to previous studies. Theresults validated the model as they showed a good correlation for mostsea-states. It was only for larger significant wave heights that there was adivergence compared to the results in previous studies.

There is a demand for renewable energy in today’s society. Wave energy is a nearly untapped source of renewable energy. Ocean Harvesting Technologies AB (OHT) is currently developing a device that can be used to convert wave energy into electricity. The device is a Wave Energy Converter of the type point absorber. Their concept is a floating buoy that is connected to the seafloor via a Power Take-Off (PTO) unit. The PTO unit is equipped with generators, which are used to convert kinetic energy of the buoy into electricity. The objective of this thesis is to control the generators to optimize the performance of the system. OHT was interested in knowing how their system performs under the influence of a controller based on MPC. Hence an MPC-controller is constructed in this thesis. The developed controller functions by predicting the states (position and velocity) of the buoy over a finite time (e.g. $5s$). Then the controller uses the predictions to find a control force that makes the system behave optimally for the next $5$ seconds. A requirement from the company is that the controller should find the control force based on how the buoy is predicted to move in 3 Degrees Of Freedom (DOF). Further, the controller should be able to operate in real-time. To meet the company’s requirements, the following is done. A linear 3ODF model of the system is derived. This is used to predict the states of the buoy in the controller. An MPC algorithm is constructed. In this, the linear model and constraints of the system are included. Then, a simulation environment is built. This is including a non-linear model of OHT’s system. The performance of the controller is tested in the simulation environment. Real-time implementation is an important aspect of the controller. The computational time required by the controller is measured in the simulations. The results imply that the controller stands a chance of being real-time implementable. However, make sure that it can be run in real-time it should be tested on the control unit that OHT plans to use in their system. A linear model of the system is used in the controller to predict the future states o the buoy. It is important that the predictions are accurate for the controller to control the system in an optimal way. Hence, the validity of the linear model is investigated. The controller is managing to predict some states better than others. However, the controller is doing a fine job with controlling the system in terms of generated power. Thus the linear model is considered to be valid for the application. An advantage with controllers based on MPC is the simplicity of tuning the controller. Changes of settings in the controller have a predictable effect on the results. For the settings found in this thesis, the system is performing fine in terms of power generation. However, more work is needed to find more optimal settings.

As worldwide energy consumption continues to increase, so does the demand for renewable energy sources. The total available wave energy resource for the United States alone is 2,640 TWh/yr; nearly two thirds of the 4,000 TWh of electricity used in the United States each year. It is estimated that nearly half of that available energy is recoverable through wave energy conversion techniques. In this thesis, a two-body 'point absorber' type wave energy converter with a mechanical power-takeoff is investigated. The two-body wave energy converter extracts energy through the relative motion of a floating buoy and a neutrally buoyant submerged body. Using a linear frequency-domain model, analytical solutions of the optimal power and the corresponding power-takeoff components are derived for the two-body wave energy converter. Using these solutions, a case study is conducted to investigate the influence of the submerged body size on the absorbed power of the device in regular and irregular waves. Here it is found that an optimal mass ratio between the submerged body and floating buoy exists where the device will achieve resonance. Furthermore, a case study to investigate the influence of the submerged body shape on the absorbed power is conducted using a time-domain numerical model. Here it is found that the submerged body should be designed to reduce the effects of drag, but to maintain relatively large hydrodynamic added mass and excitation force. To validate the analytical and numerical models, a 1/30th scale model of a two-body wave energy converter is tested in a wave tank. The results of the wave tank tests show that the two-body wave energy converter can absorb nearly twice the energy of a single-body 'point absorber' type wave energy converter. / Master of Science