A modified spectral-domain (SD) model is introduced in this study to address the nonlinear hydrostatic restoring force for heaving wave energy converters (WECs) with non-uniform cross-sectional areas. Distinguished from previous SD models, the modified SD model collectively includes the effects of incident wave elevation and buoy displacement, through the utilization of the multi-variate stochastic linearization method. The proposed SD model is verified against results obtained from a corresponding nonlinear time-domain (TD) model. Subsequently, a comprehensive comparison is carried out between the modified SD model, the other two existing SD models and the linear frequency-domain (FD) model. The nonlinear TD model is considered as the accuracy reference in this comparison. Various environmental and operational inputs, such as sea states, Power Take-Off (PTO) parameters, and buoy drafts, are systematically taken into account in the comparison. Additionally, the computational efficiency of each model is evaluated.

The results suggest that the modified SD model demonstrates significantly enhanced accuracy in cases where hydrostatic force nonlinearity intensifies, compared to the existing SD models and the FD model. Throughout the entire domain of the simulation cases, the maximum relative error of the modified SD model to the nonlinear TD model is below 5 %, while it is 20 % for the FD model and approximately 15 % for the two existing SD models. Moreover, the modeling accuracy of the FD model and existing SD models could be strongly disturbed by the variation of the environmental and operational inputs. Comparatively, the modified SD model is associated with much more stable accuracy. Nevertheless, the modified SD model only requires a modest increase in computational load compared to the FD model and existing SD models and it is still thousands of times faster than the nonlinear TD model.@en

Wave energy is considered one of the most potential renewable energy. In the last two decades, many wave energy converters (WECs) have been designed to harvest energy from the ocean. Different power take-off systems are developed to maximize the power generation of WECs. However, the estimation of the power matrix of the WECs and annual power generation on the different sites is much more complex. A lot of simulations or experiments are required to obtain the power matrix of one specific WEC. To solve this problem, this paper proposes an active learning Kriging approach to estimate the WEC power matrix with less computational cost or experiment test. The efficiency of the proposed approach is demonstrated by two analytic problems and a point absorber WEC. The results show the proposed approach can efficiently and accurately estimate the power matrix of the WECs. Using the proposed ALK-PE approach, less than one-fifth of simulations or experiments are required to construct the whole power matrix of WECs at all the sea states, and the mean absolute percentage error is around 1%.

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An adjustable draft point absorber was recently proposed as a novel approach to improve power absorption with constrained power take-off (PTO) capacities. The key feature of the novel wave energy converter (WEC) concept is to adjust the buoy draft by regulating the ballast water inside the buoy, which aims to enable variation of the natural frequency of the WEC. Although previous research has shown benefits for the energy absorption stage, the impact of the draft adjustment on the power conversion efficiency and overall performance has not been examined yet. Therefore, a wave-to-wire model is established to provide an in-depth insight into the systematic performance of the adjustable draft point absorber integrated with a linear permanent magnet generator. Both a nonlinear hydrodynamic model and an analytical generator model are derived, thus the complete process from the wave power input through the whole WEC system to the usable electricity is covered. Based on the established model, wave-to-wire responses of the novel concept are obtained and analyzed. The negative effects of the draft adjustment on the stroke and overlap between the stator and translator are demonstrated. Moreover, a comparison is made between this novel WEC and conventional fixed draft WEC, and both regular and irregular wave states are considered. The results show that the adjustable draft system could increase not only the absorbed power but also the generator conversion efficiency. In specific conditions, the delivered electrical power of the adjustable draft WEC was over 20 % and 10 % higher than a traditional fixed draft system for regular and irregular waves respectively.

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Wave-to-Wire models play an important role in the development of wave energy converters. They could provide insight into the complete operating process of wave energy converters, from the power absorption stage to the power conversion stage. In order to cover a set of relevant nonlinear effects, wave-to-wire models are predominately established in the time domain. However, the low computational efficiency of time-domain modeling is hindering the extensive application of wave-to-wire models, especially in early-stage design and optimization where a large number of iterations are required. To address this issue, a spectral-domain wave-to-wire model is proposed, and the nonlinear effects are incorporated by stochastic linearization. This model can significantly reduce the computational load and maintain good accuracy. The reference concept studied in this paper is defined as a heaving point absorber coupled with a linear permanent-magnet generator. Four representative nonlinear effects involved in both the hydrodynamic stage and the electrical stage of the concept are considered. The proposed model is verified against a corresponding nonlinear time-domain wave-to-wire model, and a good agreement is observed. The relative error of the proposed spectral-domain wave-to-wire model is around 2 % in typical operational regions and is still within 7 % for wave states with large significant wave heights, regarding the estimate of the power conversion efficiency. Meanwhile, the computational load of the spectral-domain wave-to-wire model is reduced by 2 to 3 orders of magnitudes compared with the conventional time-domain approach. Finally, a case study of tuning the PTO damping to maximize power production is conducted to demonstrate the performance of the proposed spectral-domain wave-to-wire model.

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Ocean wave energy has a huge potential to make a contribution to global energy transition. However, the high Levelized Cost of Energy (LCOE) is currently a big hurdle to the development of wave energy converters (WECs). This thesis is motivated to improve the techno-economic competitiveness of WECs. It focuses on the effects of systematic sizing of WECs. "Systematic sizing" is reflected in this thesis by considering the effects of sizing on the two main components of WECs, namely the buoy and PTO system. The main body of this thesis starts with a literature review. First, it is intended to provide an overview of current wave energy technologies and the application of power take-off (PTO) systems. Secondly, the studies relevant to sizing of WECs are reviewed, and sizing methods used in the context are discussed and compared. It indicates that the existing studies mainly focus on the effects of buoy sizing and there is a lack of consideration of PTO sizing. In addition, the sizing methods based on the Budal diagram and Froude scaling can only be used to conduct sizing of buoy but the influence of PTO sizing cannot be covered. Numerical simulation can be applied to take into account both effects of buoy sizing and PTO sizing, but it is usually associated with low computational-efficiency. As sizing can be regarded as a kind of optimization which normally requires a number of iterations, an efficient method is beneficial for accelerating the design process of WECs. Followed up by the literature review, Chapter 3 to Chapter 7 of this thesis are dedicated to accomplishing two main research objectives...@en

The demand for renewable energies is rising due to climate goals and high oil prices. Not only the established renewable sources like wind and solar are interesting to exploit. There is a vast amount of energy stored in the world’s oceans. To harvest this energy, one needs a Wave Energy Converter (WEC). There
are already some prototype WECs tested around the world but there is no leading design that proves to be a cost-effective way to convert this energy to electricity.

A company from the Netherlands, Dutch Wave Power, also tries to build a cost-effective device to harvest the ocean’s energy. Their design consists of a floating tube or cylinder that converts the heave and sway motion into a pitch motion. This pitch motion drives a generator which generates electrical power. The generator is connected to the outer wall of the float and rotates as the float pitches. Inside the generator is a shaft that is kept in place by an inside pendulum. Dutch Wave Power validated their concept with experimental tests in a wave flume. The next step in the development is a numerical model. This model
gives insight into the effects that influence the dynamics and power production of the WEC. Secondly, a numerical model eliminates the need for new experimental tests each time a design parameter is changed.

The numerical model estimates the dynamics of the WEC. The BEM software NEMOH is used to estimate the diffraction and radiation forces coefficients. A state-space approximation of the Cummins equation is used to capture the memory effect of the radiation forces. The Froude-Krylov forces are fully non-linear and are evaluated for each time step. Lastly, some friction and drag forces are included. The PTO system is described as a linear damper. The numerical model is validated with experimental tests executed by Dutch Wave Power.

Next, the numerical model is adapted to also estimate the hydrodynamics in irregular waves. The irregular waves used in this thesis are based on a JONSWAP spectrum. Using the parameters of the JONSWAP spectrum, a sea-state with the desired significant wave height and peak period can be generated. The
Froude-Krylov and the diffraction forces are estimated based on the principle of superposition. With this irregular wave model, a power matrix is constructed for a WEC with twice the size that was used in the experimental tests. This power matrix gives an indication of the ideal operational wave conditions, where the efficiency of the WEC is the highest, and it makes it enables the possibility to compare the performance of the WEC at different sea-states.

A crucial part of wave energy converters (WECs) is the power take-off (PTO) mechanism, and PTO sizing has been shown to have a considerable impact on the levelized cost of energy (LCOE). However, as a dominating type of PTO system in WECs, previous research pertinent to PTO sizing did not take modeling and optimization of the linear permanent magnet (PM) generator into consideration. To fill this gap, this paper provides an insight into how PTO sizing affects the performance of linear permanent magnet (PM) generators, and further the techno-economic performance of WECs. To thoroughly reveal the power production of the WEC, both hydrodynamic modeling and generator modeling are incorporated. In addition, three different methods for sizing the linear generator are applied and compared. The effect of the selection of the sizing method on the techno-economic performance of the WEC is identified. Furthermore, to realistically reflect the relevance of PTO sizing, wave resources from three European sea sites are considered in the techno-economic analysis. The dependence of PTO sizing on wave resources is demonstrated. @en

The power take-off (PTO) system is a main component in wave energy converters (WECs), and it accounts for a notable proportion in the total cost. Sizing the PTO capacity has been proven to be significant to the cost-effectiveness of WECs. In the numerical modeling, the PTO size is normally represented by a force constraint. Therefore, to accurately evaluate the power performance of WECs with various PTO sizes, it is necessary to take the PTO force limitation, a nonlinear effect, into consideration. In this paper, a computationally-efficient spectral domain model of the PTO force saturation is developed for a heaving point absorber, and the nonlinear term is included by statistical linearization. For comparison, a frequency domain and nonlinear time domain model are implemented, and the developed spectral model is verified with the results of the nonlinear time domain model. Compared with the frequency domain model, the spectral domain model remarkably reduces the relative errors in predicting the power performance of WECs with force constraints, while the computational demand is much lower than the nonlinear time domain model. Furthermore, a case study is conducted to size the PTO capacity for reducing the levelized cost of energy (LCOE) in a chosen wave site. Three different numerical models are applied respectively. The frequency domain model could lead to a misestimate of the optimal PTO capacity, with a maximum relative error on the prediction of the annual energy production (AEP) of 24%. In contrast, the spectral domain model indicates the same optimal PTO size with the time domain modeling, and its relative errors on the prediction of the AEP are within 4.3%.

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The Power Take-Off (PTO) rating of Wave Energy Converters (WECs) is generally much higher than the average extracted power. Scientific literature has indicated that downsizing the PTO capacity to a suitable level is beneficial for improving the techno-economic competitiveness. In this paper, a novel design, namely the adjustable draft system, is proposed for point absorbers to implement PTO downsizing. A frequency domain model is established to calculate the performance of the proposed device. From frequency domain analysis, two potential advantages are identified by installing the adjustable draft system. Firstly, the excitation force can be controlled by adjusting the buoy draft, which could be utilized to reduce the required PTO force. This is helpful for downsizing the PTO capacity. Secondly, the relevant natural frequency of the point absorber can be adapted to the operating wave states by varying the buoy draft, which improves the power absorption. A nonlinear approach is adopted specifically for the spherical buoy to include the nonlinear Froude–Krylov force and viscous drag force. The results show that the nonlinear forces have a significant influence on the power absorption when operating close to resonance regions. However, the advantages resulting from the proposed system still can be observed while considering the nonlinear forces. The power absorption can be improved by 27% and 12% in particular cases of regular and irregular wave states respectively.

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A spectral domain model is established to analyze the performance of a recently proposed wave energy concept, namely the adjustable draft point absorber. The non-linear hydrostatic force is incorporated in the spectral domain model. To improve the accuracy of the proposed model, the incident wave elevation is considered in the statistic linearization of the non-linear term. The proposed model is verified by the results obtained by the non-linear time domain simulations. The results suggest that the proposed spectral domain model could include the non-linear hydrostatic force while maintaining a higher computational efficiency than the non-linear time domain model. Based on the proposed model, the power performance of the adjustable draft WEC is identified. Furthermore, a techno-economic analysis is performed to reveal the benefits of the adjustable draft WEC for a given European sea site. The results show that the adjustable draft WEC is associated with higher power absorption in powerful sea states compared with the conventional fixed draft WEC. In addition, the adjustable draft system could contribute to the improvement of the annual energy production as well as the reduction of the levelized cost of energy of WECs.

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Currently, the techno-economic performance of Wave Energy Converters (WECs) is not competitive with other renewable technologies. Size optimization could make a difference. However, the impact of sizing on the techno-economic performance of WECs still remains unclear, especially when sizing of the buoy and Power Take-Off (PTO) are considered collectively. In this paper, an optimization method for the buoy and PTO sizing is proposed for a generic heaving point absorber to reduce the Levelized Cost Of Energy (LCOE). Frequency domain modeling is used to calculate the power absorption of WECs with different buoy and PTO sizes. Force constraints are used to represent the effects of PTO sizing on the absorbed power, in which the passive and reactive control strategy are considered, respectively. A preliminary economic model is established to calculate the cost of WECs. The proposed method is implemented for three realistic sea sites, and the dependence of the optimal size of WECs on wave resources and control strategies is analyzed. The results show that PTO sizing has a limited effect on the buoy size determination, while it can reduce the LCOE by 24% to 31%. Besides, the higher mean wave power density of wave resources does not necessarily correspond to the larger optimal buoy or PTO sizes, but it contributes to the lower LCOE. In addition, the optimal PTO force limit converges at around 0.4 to 0.5 times the maximum required PTO force for the corresponding sea sites. Compared with other methods, this proposed method shows a better potential in sizing and reducing LCOE. @en

Downsizing the Power Take-off (PTO) rating has been proven to be beneficial for decreasing the Levelized Cost of Energy (LCOE) of wave energy converters (WECs). However, the linear permanent magnet (PM) generator has not yet been modelled and optimized in detail in previous feasibility studies. This paper extends the study of the PTO downsizing to further investigate the influence of the linear PM generator sizing on a WEC's techno-economic performance. The generator is sized for providing different maximum forces, and the effect of sizing on the generator performance is presented. The efficiency map of the selected linear generator design is applied to evaluate the annual energy production (AEP) and finally identify its influence on the techno-economic performance of a WEC.

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PTO (Power Take-off) systems in WECs (Wave Energy Converters) are generally overrated with regard to the average extracted power, which is not economically favourable. However, there is no explicit and agreed approach on how to limit the absorbed power without damaging WECs. In this work, a generic point absorber and direct drive PTO are used as research objects. A frequency domain model and a cost model are established. Two possible approaches for downsizing PTO rating are investigated. The first approach is established by switching the control strategy of WECs between reactive control and passive control for making a compromise between extracted power and PTO rating. Alternatively, a novel design is proposed by integrating an adjustable draft system of buoy to release the excessive absorbed power. Based on the results, the performance of these two approaches are investigated and the techno-economic performance of these two approaches are compared.

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A significant percentage of the offshore wind resource is located in waters deeper than 60m. Therefore, several floating offshore wind turbines (FOWT) have been conceived in recent years. In deep waters, it seems logical to also harvest wave energy. One of the options to harness both resources is to use a floating offshore hybrid wind-wave energy converter (FOHWWEC), which physically combines a FOWT with a wave energy converter (WEC). Different studies have addressed the functionality, feasibility, optimization, control and survivability of FOHWWEC concepts. The majority considers a proven FOWT substructure to fit a certain type of WEC. Dynamic analyses in both, frequency and time domains, and laboratory experiments with models have been done. Nevertheless, the investigated studies have not considered the FOHWWEC concept as part of an extensive design space. In other words, they have not attempted to explore and compare the myriad design configurations that are possible in that space. Besides this, few studies have been able to deliver a comprehensive understanding on how certain parameters, intrinsic and extrinsic to the FOHWWEC system, influence its performance. The present study is the start of that space exploration and understanding. Three FOHWWEC design configurations (DC), based on the substructure stability principle, are proposed. Vertical cylinders are used as substructure and two spherical point absorbers are connected through a PTO without mechanical spring to the cylinder supporting the WT. The objective is to compare their performances, based on two variables: the annual average absorption width and the maximum standard deviation of the horizontal nacelle acceleration. Besides this, three draft levels are considered and their impact in the performance is also analyzed. The hydrodynamic analysis of the FOHWWEC with parked WT is performed in the frequency domain. Hydrodynamic coefficients and wave-excitation forces are obtained from the BEM solver NEMOH. The software FOHWWEC Analysis program, developed by the author, solves the EoMs and calculates the performance variables. The North Sea is the selected region and a JONSWAP spectrum has been applied. The results indicate that the design configuration 3 (DC3) FOHWWECs have a wave power absorption mechanism based on the heave resonance of both, substructure and WECs. This mechanism is more efficient than DC1 and DC2's mechanisms. This allows to maximize the absorption width. Besides this, DC3 FOHWWECs can also minimize the nacelle accelerations (DC3-D2 case). The effect of the draft on both performance variables differs depending on the DC. Wide-ranging deductions from the results can be summarized as follows. It is reasonable to design a FOHWWEC as a whole system, considering both, wind and wave power generation from the beginning. Using an existing substructure means to lose performance improvement opportunities. It is also reasonable to select a buoyancy-stabilized substructure for the design. This allows to reach the most efficient wave power absorption mechanism, while providing the required flexibility to thoroughly explore and find the balance between design parameters such as WPA, displacement, draft, size and position of the WECs, mooring, among others.

In this paper, a fair evaluation method of WECs (Wave Energy Converters) is established based on frequency domain simulation. In this fair evaluation, size optimization and downsizing of PTO (Power Take-Off) capacity are included to minimize the Cost of Energy for the concerned wave location. Based on this fair evaluation, a techno-economic evaluation of a generic point absorber is conducted for a specific wave location, and two different control strategies of PTO are considered. The results show that this fair evaluation method can contribute to the improvement of techno-economic performance of WECs. Furthermore, a comparison among three different size optimization methods of WECs is performed.@en