The energy absorption of the wave energy converters (WEC) characterized by a limited stroke length - like the point absorbers developed at Uppsala University-depends on the sea level variation at the deployment site. In coastal areas characterized by high tidal ranges, the daily energy production of the generators is not optimal. The study presented in this paper quantifies the effects of the changing sea level at the Wave Hub test site, located at the south-west coast of England. This area is strongly affected by tides: the tidal height calculated as the difference between the Mean High Water Spring and the Mean Low Water Spring in 2014 was about 6.6 m. The results are obtained from a hydro-mechanic model that analyzes the behaviour of the point absorber at the Wave Hub, taking into account the sea state occurrence scatter diagram and the tidal time series at the site. It turns out that the impact of the tide decreases the energy absorption by 53%. For this reason, the need for a tidal compensation system to be included in the design of the WEC becomes compelling. The economic advantages are evaluated for different scenarios: the economic analysis proposed within the paper allows an educated guess to be made on the profits. The alternative of extending the stroke length of the WEC is investigated, and the gain in energy absorption is estimated.
The wave energy converter developed at Uppsala University (Uppsala, Sweden) consists of a linear generator placed on the seabed and driven by the motion of a buoy on the water surface. The buoy is connected to the moving part of the linear generator, the translator, which is made of ferrite magnets. The translator moves vertically inducing voltage in the windings of a fixed component, the so-called stator. The energy conversion of the linear generator is affected by the sea state and by variations of mean sea level. The sea state influences the speed and the stroke length of the translator, while the variation of tidal level shifts the average position of the translator with respect to the center of the stator. The aim of this study is to evaluate the energy absorption of the wave energy converter at different locations around the world. This goal is achieved by developing a hydromechanic model which analyses the optimum generator damping factor for different wave climates and the power absorbed by the generator, given a fixed geometry of the buoy and a fixed stroke length of the translator. Economic considerations regarding the optimization of the damping factor are included within the paper. The results suggest a nominal damping factor and show the power absorption losses at various locations, each of them characterized by a different wave climate and tidal range. The power losses reach up to 67% and in many locations a tidal compensation system, included in the design of the wave energy converter, is strongly motivated.
A directly coupled linear permanent magnet generator of longitudinal flux-type is investigated. The generator will be used for power take-off in a wave energy converter. A combined field- and circuit model, solved by a time stepping finite element technique, is used to model and analyse the electromagnetic behaviour of the machine. A large number of simulations form the basis of a design study where the influence of armature current level, number of cables per slot, and pole width is investigated with respect to efficiency, generator size, and the load angle. A case study is performed for a chosen generator design. The electromagnetic behaviour is examined both for nominal load and for overloads. The generator has a nominal output power of 10 kW for a constant piston speed of 0.7 m s(-1). The electromagnetic efficiency at nominal load is 86.0%, the load angle 6.6 degrees, and the power fluctuation 1.3%. At 300% overload the load angle barely exceeds 12 degrees and the cable temperature is below 25 degrees C provided that the stator back is thermally connected to the sea water. The numerical calculations have been verified for small speeds by experiments.
Future commercial installation of wave energy plants using point absorber technology will require clusters of tens up to several hundred devices, in order to reach a viable electricity production. Interconnected devices also serve the purpose of power smoothing, which is especially important for devices using direct-driven power take off. The scope of this paper is to evaluate a method to optimize wave energy farms in terms of power production, economic viability and resources. In particular, the paper deals with the power variation in a large array of point-absorbing direct-driven wave energy converters, and the smoothing effect due to the number of devices and their hydrodynamic interactions. A few array geometries are compared and 34 sea states measured at the Lysekil research site at the Swedish west coast are used in the simulations. Potential linear flow theory are used with full hydrodynamic interactions between the buoys. It is shown that the variance in power production depends crucially on the geometry of the array and the number of interacting devices, but not significantly on the energy period of the waves.
In a future energy system based on renewable energy sources, wave energy will most likely play a role due to its high energy potential and low intermittency. The power production from parks of wave energy converters of point absorber type has been extensively studied. This is also the case for the wave energy resource at many coastal areas around the globe. Wave energy has not yet reached a commercial level, and a large variety of technologies exist; therefore, an established method to calculate the technical potential for wave energy has still not been established. To estimate the technical potential of wave energy conversion, some approximations inevitably need to be taken due to the systems high complexity. In this study, a detailed mapping of the wave climate and simulation of large arrays of hydrodynamically cross‐coupled wave energy converters are combined to calculate the technical potential for wave energy conversion in the Swedish exclusive economic zone. A 16‐year wave data set distributed in a 1.1 km × 1.1 km grid is used to calculate the absorbed energy from a park of 200 generic point absorbers. The areas with best potential have an average annual energy absorption of 16 GWh for the selected wave energy park adapted to 1 km2 when using a constant damping, while the theoretical upper bound is 63 GWh for the same area.
It is well known that the energy transport of ocean waves propagates with the group velocity and that the energy decreases exponentially with depth. Expanding this theory, we will derive expressions for the energy transport as a function of depth and the total instantaneous transport's development over time for waves in waters of finite depth. Solutions to the Laplace equation are found for plane-parallel polychromatic waves with linearized boundary conditions. A time series of wave elevation collected at Uppsala University's wave energy research test site is chosen to present the results. Solutions for waters of both infinite and arbitrary depths are presented and compared. The solutions are convolution-type integrals with the wave elevation where we have found efficient ways to calculate the kernels. The difference in group velocity between finite depth and infinite depth and its impact on the energy transport is clearly seen in the results. 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. We further show that the total instantaneous energy transport can actually have a direction that is opposite to the direction of the waves as observed from a reference frame fixed to the seabed.
In many wave energy concepts, power output in the MW range requires the simultaneous operation of many wave energy converters. In particular, this is true for small point-absorbers, where a wave energy farm may contain several hundred devices. The total performance of the farm is affected by the hydrodynamic interactions between the individual devices, and reliable tools that can model full farms are needed to study power output and find optimal design parameters. This paper presents a novel method to model the hydrodynamic interactions and power output of very large wave energy farms. The method is based on analytical multiple scattering theory and uses time series of irregular wave amplitudes to compute the instantaneous power of each device. An interaction distance cut-off is introduced to improve the computational cost with acceptable accuracy. As an application of the method, wave energy farms with over 100 devices are studied in the MW range using one month of wave data measured at an off-shore site.
Large arrays of wave energy converters of point-absorber type are studied using an approximate analytical model. The model is validated against a numerical method that takes into account full hydrodynamic interactions based on linear potential flow theory. The low computational cost of the analytical model enables parameter studies of parks in the MW range and includes up to over 1000 interacting devices. The model is actuated by irregular wave data obtained at the Swedish west coast. In particular, focus is on comparing park geometries and improving park configurations to minimize the power fluctuations.
One of the major challenges in constructing effective and economically viable wave energy parks is to reduce the large fluctuations in power output. In this paper, we study different methods of reducing the fluctuations and improve the output power quality. The parameters studied include the number of devices, the separating distance between units, the global and local geometries of the array, sea state and incoming wave direction, and the impact of including buoys of different radii in an array. Our results show that, e. g., the fluctuations as well as power per device decrease strictly with the number of interacting units, when the separating distance is kept constant. However, including more devices in a park with fixed area will not necessarily result in lowered power fluctuations. We also show that varying the distance between units affects the power fluctuations to a much larger extent than it affects the magnitude of the absorbed power. The fluctuations are slightly lower in more realistic, randomized geometries where the buoys tend to drift slightly off their mean positions, and significantly lower in semi-circular geometries as opposed to rectangular geometries.
The damping effect, induced inside the linear generator, is a vital factor to improve the conversion efficiency of wave energy converters (WEC). As part of the mechanical design, the translator mass affects the damping force and eventually affects the performance of the WEC by converting wave energy into electricity. This paper proposes research on the damping effect coupled with translator mass regarding the generated power from WEC. Complicated influences from ocean wave climates along the west coast of Sweden are also included. This paper first compares three cases of translator mass with varied damping effects. A further investigation on coupling effects is performed using annual energy absorption under a series of sea states. Results suggest that a heavier translator may promote the damping effect and therefore improve the power production. However, the hinder effect is also observed and analyzed in specific cases. In this paper, the variations in the optimal damping coefficient are observed and discussed along with different cases.
Within the Lysekil wave energy research project at the Swedish west coast, more than ten Wave Energy Converters (WECs) prototypes have been developed and installed in an ocean based test site. Since 2006 various experiments have been conducted and the generated electricity was delivered to shore at a nearby island. While experiments are essential for the development of wave energy converters, theoretical studies and simulations are an important complement – not only in the search for advanced designs with higher efficiency, but also for improving the economic viability of the studied concepts. In this paper a WEC model is presented. The model consists of three subsystems: i) the hydrodynamic source, ii) the linear generator model, and iii) the electrical conversion system. After the validation with the experimental results at the research site, the generator model is connected to three passive load strategies – linear resistive load, passive rectification and resonance circuit. The paper focuses on analysing the operation of the model coupled with three load cases. The results prove that the WEC model correctly simulates the linear generator developed in the Lysekil Project. Moreover, the comparison among different load cases is made and discussed. The results gives an indication of the efficiency of energy production as well as the force ripples and resulting mechanical loads on the wave energy converters.
Wave energy converters (WECs), which are designed to harvest ocean wave energy, have recently been improved by the installation of numerous conversion mechanisms; however, it is still difficult to find an appropriate method that can compromise between strong environmental impact and robust performance by transforming irregular wave energy into stable electrical power. To solve this problem, an investigation into the impact of varied wave conditions on the dynamics of WECs and to determine an optimal factor for WECs to comply with long-term impacts was performed. In this work, we researched the performance of WECs influenced by wave climates. We used a permanent magnet linear generator (PMLG)-based WEC that was invented at Uppsala University. The damping effect was first studied with a PMLG-type WEC. Then, a group of sea states was selected to investigate their impact on the power production of the WEC. Two research sites were chosen to investigate the WEC's annual energy production as well as a study on the optimal damping coefficient impact. In addition, we compared the WEC's energy production between optimal damping and constant damping under a full range of sea states at both sites. Our results show that there is an optimal damping coefficient that can achieve the WEC's maximum power output. For the chosen research sites, only a few optimal damping coefficients were able to contribute over 90% of the WEC's annual energy production. In light of the comparison between optimal and constant damping, we conclude that, for specific regions, constant damping might be a better choice for WECs to optimize long-term energy production.
Several recently developed concepts for economically viable conversion of ocean wave energy are based on large arrays of point absorbers. Simulations of the hydrodynamic interactions between devices in wave energy parks provide guidelines for optimal configurations with regard to maximizing produced electricity while minimizing fluctuations and costs. Parameters that influence the performance include the geometrical lay-out of the park, the number of wave energy converters and their dimensions and separating distance, as well as the wave climate and the incoming wave spectral characteristics. However, the complexity of the simulations increases rapidly with growing number of interacting units, and simulations become a severe challenge that calls for new methods. Here we address the problem of rapid phase oscillations appearing in the simulation of large arrays of point absorbers using potential theory for the structure–fluid interaction. We do this by analytically integrating out the factors that are causing the oscillations. Our group has successfully utilized this method to model parks with up to 1000 point absorbers.
Potential theory is used to derive closed-form expressions for the energy flux in propagating polychromatic surface gravity waves for water of infinite depth. The energy flux vector has been obtained as convolution-type integrals of the wave-elevation time series at one point on the surface. An expression for the integrated flux through a vertical surface is also given. It is shown that the integrated flux cannot be negative at any instant in time.
The ocean are largely an untapped source of energy. However, compared to other energies, power fluctuations for ocean waves are small over longer periods of time. This paper present a grid-oriented approach to electricity production from ocean waves, utilizing a minimal amount of mechanical components.
Reliable simulation tools are necessary to study the performance and survivability of wave energy devices, since experiments are both expensive and difficult to implement. In particular, survivability in nonlinear, high waves is one of the largest challenges for wave energy, and since the wave loads and dynamics are largely model dependent, each device must be studied separately with validated tools. In this paper, two numerical methods based on fully nonlinear computational fluid dynamics (CFD) are presented and compared with a simpler linear method. All three methods are compared and validated against experimental data for a point-absorbing wave energy converter in nonlinear, high waves. The wave energy converter consists of a floating buoy attached to a linear generator situated on the seabed. The line forces and motion of the buoy are studied, and computational cost and accuracy are compared and discussed. Whereas the simpler linear method is very fast, its accuracy is not sufficient in high and extreme waves, where instead the computationally costly CFD methods are required. The OpenFOAM model showed the highest accuracy, but also a higher computational cost than the ANSYS Fluent model.
A challenge while applying latching control on a wave energy converter (WEC) is to find a reliable and robust control strategy working in irregular waves and handling the non-ideal behavior of real WECs. In this paper, a robust and model-free collaborative learning approach for latchable WECs in an array is presented. A machine learning algorithm with a shallow artificial neural network (ANN) is used to find optimal latching times. The applied strategy is compared to a latching time that is linearly correlated with the mean wave period: It is remarkable that the ANN-based WEC achieved a similar power absorption as the WEC applying a linear latching time, by applying only two different latching times. The strategy was tested in a numerical simulation, where for some sea states it absorbed more than twice the power compared to the uncontrolled WEC and over 30% more power than a WEC with constant latching. In wave tank tests with a 1:10 physical scale model the advantage decreased to +3% compared to the best tested constant latching WEC, which is explained by the lower advantage of the latching strategy caused by the non-ideal latching of the physical power take-off model.
This paper introduces a model-free, "on-the-fly" learning control strategy for arrays of energy converters with adjustable generator damping. The devices are arranged so that they are affected simultaneously by the energy medium. Each device uses a different control strategy, of which at least one has to be the machine learning approach presented in this paper. During operation all energy converters record the absorbed power and control output; the machine learning device gets the data from the converter with the highest power absorption and so learns the best performing control strategy for each state. Consequently, the overall network has a better overall performance than each individual strategy. This concept is evaluated for wave energy converter (WEC) with numerical simulations and experiments with physical scale models in a wave tank. In the first of two numerical simulations, the learnable WEC works in an array with four WECs applying a constant damping factor. In the second simulation, two learnable WECs were learning with each other. It showed that in the first test the WEC was able to absorb as much as the best constant damping WEC, while in the second run it could absorb even slightly more. During the physical model test, the ANN showed its ability to select the better of two possible damping coefficients based on real world input data.