Power Take-off Research Articles

Experimental and numerical analysis of power take-off control effects on the dynamic performance of a floating wind-wave combined system

The integration of wave energy converters (WEC) into floating offshore wind turbines (FOWT) is regarded as a promising approach for comprehensively harnessing deep-sea energy and reducing the levelized cost of energy. This study aims to investigate the WEC power take-off (PTO) control effects on the dynamic performance of a floating wind-wave combined system, wherein three heaving-type WECs are integrated into a semi-submersible FOWT. In particular, the hydraulic PTO is modelled as a Coulomb damping system to enable a more realistic analysis. The aero-hydro-servo-elastic-mooring coupled numerical simulations and 1:50 wave basin experimental data demonstrate good agreement. It is observed that wave power production varies significantly with different control settings, potentially reaching 24.0 % of the overall hybrid energy production with proper control parameters. Furthermore, platform pitch oscillation generally shows a decreasing trend with increasing damping forces under below-rated and rated conditions, while showing minimal influence when above-rated. Conversely, tower base damage equivalent load (DEL) tends to initially decrease and subsequently increase across all examined conditions. This consistent convexity indicates the potential use of DEL as a performance index for optimising PTO control. In summary, power increment, motion reduction, and load mitigation could be achieved concurrently with appropriate control design. For instance, an extra 0.48 MW wave power could be produced under the rated condition, while a 10.4 % reduction in tower base DEL and a 6.57 % mitigation in platform pitch oscillation could also be achieved at the same time.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

High-fidelity numerical modelling of a two-WEC array with accurate implementation of the PTO system and control strategy using DualSPHysics

In order for Wave Energy Converters (WECs) to become economically viable they will have to be installed closely together in so-called WEC arrays. When WECs are placed closely together they influence each other’s motion, which is challenging to implement in a numerical model. The accurate modelling of WECs in WEC arrays is crucial for their further development into cost-effective renewable energy converters. This paper presents the study of numerical modelling of an array of two heaving WECs (a two-WEC array) placed in close proximity of each other in order to increase their interaction effect. The numerical model uses DualSPHysics, a Smoothed Particle Hydrodynamics (SPH) based software to model wave-WEC interaction, coupled to Project Chrono for the modelling of the Power Take-Off (PTO) system and the friction. First, a series of numerical system identification tests are simulated: a free-decay test of an isolated WEC, radiation tests and an excitation test. During the radiation test one WEC is moved by an external force with a chirp-up noise signal, while the other WEC is kept still. This allows the computation of the impedance matrix, and thereby also the hydrodynamic coefficients of the two-WEC array, which has not been done before in SPH. Results were validated with experimental data from the WECfarm test campaign. Secondly, a series of numerical dynamic tests are simulated of the two-WEC array in regular and irregular waves. In the experimental test campaign a friction force caused by the motor and gearbox was counteracting the WEC’s motion, so a friction compensation (FC) force was added to cancel out this friction. This friction and FC force was numerically modelled by adding a novel implementation in Project Chrono. Furthermore, a novel global control strategy was implemented using Project Chrono, in which the PTO force on each WEC depends on the velocity of both WECs. Overall, good to very good agreement was found in terms of heave and free surface elevation when comparing numerical to experimental results.

Experimental and numerical study on the integration of a built-in wave energy converter(BIWEC) and floating platform

Nowadays generating electricity continuously in real waves over extended periods is a big challenge due to harsh ocean environment for wave energy converters (WECs). In this study, in order to enhance the reliability of WEC, a novel BIWEC which can form an integrated system by combing with existing floating platforms is proposed. This design method provides a robust mechanism for using wave energy efficiently and has been validated through the numerical simulations and physical model experiments of integrated systems. In addition, a comprehensive study and analysis on the coupling dynamic characteristics of the integrated system, as well as the influence of different power take-off (PTO) parameters on the power generation performance of BIWEC are conducted. Furthermore, using the typical wave conditions in the South China Sea (2–10 s wave period and 2 m wave height) as an example, the capture power and capture width ratio of BIWEC under various effective motion strokes and mass ratios are investigated. The research results indicate that the BIWEC has the characteristics of dual resonance frequencies, a wide range of wave frequency capture, and high energy conversion efficiency, and the results of the physical experiments are consistent with those of numerical simulations, validating the reliability of the physical experiments. In the physical experimental tests, the average mechanical efficiency of the BIWEC model is 49.17%. The research results presented in this paper have significant implications for the further promoting of commercialization of WEC.

Optimization of power take-off system settings and regional site selection procedure for a wave energy converter

Ocean wave energy stands as a crucial component in the quest for sustainable and renewable energy sources, essential in the global effort to mitigate climate change. However, a significant challenge in this field is optimizing the efficiency of Wave Energy Converters (WECs) on a regional scale, particularly Oscillating Surge Wave Energy Converters (OSWECs). This challenge stems from the complex, nonlinear interactions between ocean waves and these devices, necessitating precise tuning of Power Take-Off (PTO) system settings and optimal placement for the highest possible performance and stability. To address this challenge, our study introduces the Hill Climb - Explorative Grey Wolf Optimizer (HC-EGWO), a novel algorithm combining local search and swarm-based global optimization strategies. This hybrid approach effectively balances exploration and exploitation in the solution space, leading to more optimal PTO settings for OSWECs. Alongside this algorithmic development, we conduct a thorough feasibility analysis based on the constraints of the flap’s maximum angular motion. This ensures the optimized OSWEC operates within safe and efficient limits. In a comparative analysis with the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), the artificial Gorilla Troops Optimizer (GTO), and different implementations of the GWO, our results show an improvement in power output, with the HC-EGWO method achieving up to a 3.31% increase over other variations of the GWO and 45% increase compared to all the methods. The findings of this study not only demonstrate the effectiveness of the HC-EGWO method but also provide strategic insights for the deployment of OSWECs in areas like the South Caspian Sea, where unique environmental factors imply careful consideration in the site selection process.

Improving the OWC Wave Energy Converter Power Take-Off Efficiency throughout Experimental and Numerical Characterisation of an SCIG

The increasing interest in the use of renewable energy technologies is directing attention towards the potential contribution of marine energy technologies, especially ocean wave energy, to world energy demand. While open-sea demonstrations of full-scale devices have been carried out to validate several technologies, the focus now is shifting to optimising the components for efficiency and reliability. The efficiency of the electrical generator plays a crucial role in wave-to-wire numerical models for converting wave energy into usable electricity. It provides essential data that enables the industry to reduce technical risks and uncertainties. Wave-to-wire models typically simplify the generator’s efficiency through assuming a single curve based on the load. This curve is usually provided by the machine manufacturers for the nominal rotational speed. However, the rotational speed varies in the case of air turbines used in OWC devices. Therefore, to accurately estimate decision variables derived from these models, a comprehensive efficiency map is necessary. This map should demonstrate the performance at different rotational speeds and loads, as it directly influences the estimation of key parameters. The main objective of the present work is to improve the generator behaviour of an OWC for different generator operation regimes. For this purpose, a numerical model of the generator’s efficiency will be developed throughout the segregation of losses and validated experimentally. Finally, an optimal control law will be presented to maximise the electrical power output of the wave energy converter, considering the efficiency of both the generator and the turbine.

Two-Way Coupling Simulation of Fluid-Multibody Dynamics for Estimating Power Generation Performance of Point Absorber Wave Energy Converters

The objective of the present study is to develop and validate a two-way coupling simulation method between viscous fluid and multibody dynamics to estimate the power generation performance of point absorber wave energy converters. For numerical analysis of fluid dynamics, an enhanced density correction model was proposed to improve the accuracy and stability of the pressure calculation in DualSPHysics, an open-source code based on smoothed particle hydrodynamics (SPH). Through 2D hydrostatic and wave generation simulations, it was seen that the relative error in the average pressure was reduced from 11.81% to 1.64%. In addition, an interaction interface was developed to enable coupling simulation with RecurDyn, a commercial software for the simulation of multibody dynamics. Simulations were performed for a 3D single-body cylinder with a simple shape and a two-body floating wave energy converter (WEC) in regular waves, varying the linear damping coefficient of the power take-off (PTO) system to verify the proposed coupling simulation method for fluid-multibody dynamics. The results were benchmarked against experimental data, revealing a relative error of 1.05% with the experimental results when employing a high damping coefficient for the PTO system. Furthermore, to improve the efficiency of the two-body WEC, two design modifications were suggested; their impact on power generation performance improvement was examined. The developed method is anticipated to contribute to research aiming to enhance the power generation efficiency of various wave power devices with multiple elements and joints, pending further validation and refinement of the simulation approach.

Structural strength analysis of a rotary drum mower during harvesting

A Rotary Drum Mower (RDM) is a tractor-mounted mechanism used for harvesting green fodder crops. It faces dynamic forces from rough field surfaces and cutting resistance, posing design challenges and potential failures. This study aims to present a well-designed procedure for analysing the structural strength of an RDM during harvesting, employing both experimental and engineering simulation methods. A specific harvesting scenario was created to simulate realistic load conditions. Experimental testing and advanced computer-aided engineering (CAE) simulations were conducted. Tractor Power Take-off (PTO) torque measurements during harvesting revealed values of 231.07 Nm, 264.44 Nm, and 269.39 Nm at speeds of 8.56 km h-1, 12.6 km h-1, and 16.23 km h-1, respectively. Finite element analysis (FEA) was conducted to determine stress levels in the RDM components (RDM165-A-004, RDM165-B-003, and RDM165-B-004). The FEA stress results ranged from 5.070 MPa to 20.600 MPa, 13.800 MPa to 28.600 MPa, and 5.400 MPa to 27.550 MPa, respectively. Experimental testing yielded stress results ranging from 2.127 MPa to 18.600 MPa, 14.618 MPa to 33.229 MPa, and 8.838 MPa to 31.248 MPa, respectively. The comparison between experimental and FEA results showed reasonable correlation. FEA visual outputs provided insights into the maximum equivalent stress and deformation distributions on the RDM, with no indications of failure in the machine's structure observed in either the experimental or numerical analyses. In conclusion, this study demonstrates that the machine analysed operates safely under harvesting conditions. Moreover, the combination of experimental and advanced CAE methodologies presented in this research offers a valuable approach for future investigations into the complex stress and deformation evaluations of rotary drum mowers.

Implementation and optimization of hydraulic wave energy generation system.

Wave energy is one of the primary sources of marine energy, representing a readily available and inexhaustible form of renewable clean energy. In recent years, wave energy generation has garnered increasing attention from researchers. To study wave energy generation technology, we have constructed a real wave energy generation system and designed wave simulation and hydraulic energy storage systems. The wave simulation system is mainly composed of a frequency converter and an electric boost pump, while the hydraulic energy storage system consists of a hydraulic control unit and hydraulic motors. Corresponding mathematical models have been established to investigate the characteristics of wave energy generation. Specifically, a mathematical model for wave input using the double-parameter JONSWAP wave spectrum has been created for wave simulation in the wave simulation system. For the hydraulic energy storage system, known as the Power Take Off (PTO) system, mathematical models have been developed for double-acting hydraulic cylinders, energy storage devices, and precise displacement hydraulic motors, taking into consideration fluid Reynolds numbers and leakage. During the generation of wave energy, there is a problem of prolonged power interruption when wave conditions are unfavorable, which hinders continuous power generation. To address this issue, a system structure with an energy storage unit and two parallel generator sets, as well as a power operation optimization scheme, have been proposed. This system structure and optimization approach efficiently and reasonably utilize wave energy, achieving the goal of uninterrupted power supply in the hydraulic wave energy generation system.

A Numerical Investigation of the Hydrodynamic Performance of a Pitch-Type Wave Energy Converter Using Weakly and Fully Nonlinear Models

In this study, the performance of a wave energy converter (WEC) rotor under regular and irregular wave conditions was investigated using 3D nonlinear numerical models. Factors such as the power take-off (PTO) load torque, wave periods, spacing of multiple WEC rotors, and wave steepness were analyzed. Two models were employed: a weakly nonlinear model formulated by incorporating the nonlinear restoring moment and Coulomb-type PTO load torque based on the potential flow theory, and a fully nonlinear model based on computational fluid dynamics. The results show that the average power estimated by both numerical models is consistent, with a wave steepness of 0.03 for the range of one-way and two-way PTO load torques, except for the deviations observed in the long range of the one-way PTO load torque. Furthermore, the average power of the WEC rotor under the applied PTO load torque exhibits a quadratic dependency, regardless of the wave steepness. In addition, adopting a one-way PTO load torque was more efficient than adopting a two-way PTO load torque. Therefore, the fully nonlinear model demonstrated its ability to handle a high degree of nonlinearity, surpassing the limitations of the weakly nonlinear model, which was limited to moderate wave steepness.

Small-scale field experiment on wave forces on a U-OWC breakwater

A small-scale field experiment is conducted on a U-Oscillating Water Column (U-OWC) incorporated into a model of caisson breakwater at the Natural Ocean Engineering Laboratory (NOEL) laboratory of Reggio Calabria (Italy). The U-OWC or REWEC (REsonant Wave Energy Converter) is a device belonging to the family of Oscillating Water Columns (OWCs), characterized by the introduction of a U-duct. Such a device is innovative, absorbing a high percentage of incoming sea energy and, then, to produce electricity via a Power-Take-Off (PTO). The aim of the present study is the investigation of the wave pressures and forces acting on the U-OWC monolithic coastal defense structure. Moreover, the structural response of the U-OWC structure is also investigated under the occurrence of wave crests, by calculating the hydrodynamic forces realized in the active parts of the U-OWC. It is shown as a global additional force is realized, which contributes to increase the overall stability of the structure. Considering the wave loads acting on the U-OWC caisson, the post-process of the overall dataset recorded during the real field experiment at NOEL laboratory reveals the occurrence of both quasi-static loading (non-breaking), and of impact loading (impulsive) due to wave breaking. Thus, a systematic analysis is pursued in order to identify the loading cases acting on the U-OWC breakwater. When high non-breaking sea waves interact with the breakwater, “Quasi-Standing (QS)” wave pressures and forces occur at modified structure with two peaks of equal intensity. Instead, the impact of extreme breaking waves against the U-OWC structure generates asymmetrical wave pressure records beneath the wave crests, with two peaks with different intensity: the first one greater than the second one. In these cases, “Slightly Breaking (SB)” wave forces and “Impact Loads (IL)” are identified. Wave pressure distributions and forces acting on the U-OWC model are, then, investigated for the three classes of wave loads. Moreover, the probability of occurrence of maximum positive peak forces is determined from the experimental dataset, given a number of parameters. In particular, when QSWs occur, the maxima peak forces are recorded for deeper water depths dn, d’ and a, at given significant wave height HSi. Instead, for SBWs and ILs, the extreme wave loads are realized, when the most severe sea states occur with higher HSi , and for decreasing water depth dn. d’ and a. Then, the influence both of the length of the berm and of the width of the U-duct in the front structure is considered. When the dimensions of both structural elements is reduced, the maxima wave forces occur in a fixed recorded sea state. Then, the Quasi-Determinism (QD) nonlinear model at the U-OWC breakwater is introduced for evaluation of Quasi-Standing wave loads, showing a good agreement among analytical and experimental results. Finally, the Goda's model is applied to calculate the wave pressure distributions acting on the external walls of the U-OWC model. The theoretical results given by the Goda's formulae are compared with experimental data, overestimating experimental results for both QSWs and SBWs and, significantly, underestimating IL conditions.

Design, modeling and performance analysis of a deformable double-float wave energy converter for AUVs

Autonomous underwater vehicles (AUVs) are one of the most important means of ocean exploration. However, the restricted energy supply poses a significant challenge to the advancement and practical application of AUVs. Based on the structural characteristics, this paper proposes a novel AUV, which integrates a deformable double-float wave energy converter (WEC), called DFWEC-AUV. The DFWEC empowers the AUV to capture wave energy to supply itself by oscillating double-float form in power generation mode. The structural design, focusing on the deformable float (DeF) and the onboard damping plate (DP), and the working principle, including mode switching and energy capture, are firstly introduced. Then, a double-float dynamic model of DFWEC-AUV oscillating in regular waves is established to reveal the energy capture mechanism in both frequency-domain and time-domain. Finally, the influence of the presence of DP, structural parameters (diameter of DP and deployment angle of DeF) and power take-off (PTO) system damping coefficient on the dynamic response characteristics and energy capture performance is analyzed. In addition, to verify the effectiveness of the performance analysis, a comparative simulation of parameter optimization is carried out under actual wave excitation. The results show that the addition of onboard DP is able to effectively enhance the energy capture performance of DFWEC-AUV, as well as increase the energy capture bandwidth. Moreover, the larger the diameter of the DP is, the greater the performance improvement of DFWEC-AUV is. Conversely, increasing the deployment angle of the DeF does not necessarily lead to better power capture performance. Additionally, it is observed that waves of a particular period are consistently associated with an optimal PTO damping coefficient, which leads to superior power capture performance. In comparative simulation, the energy capture performance of DFWEC-AUV after parameter optimization is increased by 4.7 times.

Innovative Design of a Sea Wave Energy Harnesser

The aim of this research is to design and develop a simple, light and cost-effective wave energy conversion device. The mass to power ratio is of importance to achieve high working efficiency. In addition proper control concept is proposed for various sea wave conditions to manage the system optimally. . their operation. This research addresses the above two problems by considering the system mechanical structure and schemes designed to achieve optimal control. Methods employed to achieve maximum power output are inevitably non-causal and require prediction of the shape of the incident waves. The potential wave resource in South Africa is enormous as there are over 2000 km of coastline with an annual wave height average of 2-3 m. One of the most efficient wave energy extractor is the hinged wave energy converter (HIWEC) whereby the wave force is applied to a responsive mechanism able to resist the working force of the waves. The hinged mechanism used in this project is of the power take-off (PTO) type. The PTO captures the wave energy and then between the wave’s time intervals transfers it to be converted and stored. Control of the response of the HIWEC can be achieved through active tuning of the PTO. As wave energy is intermittent, the supplied electrical power will show strong variations unless an energy storage system is available. The energy storage system consists of several series connected gas accumulators, placed in the hydraulic circuit to produce a smoothing effect.

A 3D BEM-Coupled Mode Model for the Performance Analysis of Wave Energy Converter Parks in Nearshore-Coastal Regions

Estimation on the production capacity of wave energy converter arrays (WECs) of the type of simple floaters deployed in nearshore locations highly depends on the evaluation of their performance. The latter also depends on various factors, including the dimensions and inertial characteristics of the devices, their relevant positioning, and the power take-off (PTO) system characteristics. Studying the system operation, based on the prevailing sea conditions in the region considered for deployment, can ensure that such WEC farms are sized and designed in an effective way. Furthermore, the wavelength and propagation direction of incoming wave fields can be significantly impacted by wave-seabed interactions in coastal areas, which can alter the WECs’ response pattern and ultimately the array’s power output. In this work, a 3D BEM hydrodynamic model is proposed aiming to assess the energy-capturing capacity of WEC arrays, accounting for the hydrodynamic interactions between various identical floating devices, as well as the local seabed topography. The model is supplemented by a Coupled Mode System (CMS) to calculate the incident wave field propagating over variable bathymetry, in order to simulate realistic nearshore environments. Finally, a case study is performed for an indicative geographical area, north of the coast of the island of Ikaria, located in the Eastern Aegean Sea region, where the wave potential is high, using long-term data. The latter study highlights the applicability of the proposed method and suggests its usage as a tool to support optimal WEC park design.

Integrated Design and Optimization of a Direct Drive Axial Flux Permanent Magnet Generator for a Tidal Turbine

The C-GEN is a novel topology of direct drive air-core permanent magnet generator being developed at University of Edinburgh [1]. The topology has many benefits such as; absence of cogging torque, reduced mass and ease of manufacturing. A 20 kW prototype test rig and 15kW machine for a wind turbine has been manufactured and tested previously. Initial sizing studies for wind turbines indicate that the C-GEN concept will be up to 50% lighter than conventional iron cored PM direct drive generators [1]. In addition to the applications wind turbines, C-GEN technology can also be implemented for marine energy power take-off systems. To investigate that, a feasibility study is being undertaken in collaboration with two wave and two tidal energy companies. In this paper, design and optimization method of an axial flux permanent magnet generator for a tidal energy converter device has been investigated. An analytical optimization tool is designed that combines electromagnetic, structural and thermal aspects of the machine design. A genetic algorithm optimization method has been utilized based on the operation conditions of generator and pre-defined constraints on dimensions and material limitations. The output of the analytical design tool is compared with the electromagnetic FEA simulations. The results showed that proposed analytical calculation method is consistent with FEA results

Design and Performance Evaluation of an Enclosed Inertial Wave Energy Converter with a Nonlinear Stiffness Mechanism

In order to enhance the power generation efficiency and reliability of wave energy converters (WECs), an enclosed inertial WEC with a magnetic nonlinear stiffness mechanism (nonlinear EIWEC) is proposed in this paper. A mathematical model of the nonlinear EIWEC was established based on the Cummins equation and the equivalent magnetic charge method, and the joint simulations were carried out using MATLAB/Simulink 2020 and AMESim 2020 softwares. The effect of the magnetic nonlinear stiffness mechanism (NSM) on the performance of the EIWEC system was investigated. The results show that the nonlinear negative stiffness property of NSM can significantly improve the motion response and output power of EIWEC under low-frequency waves. Compared to EIWEC without NSM (linear EIWEC), nonlinear EIWEC has a higher generation efficiency and wider frequency bandwidth. Additionally, the effects of linear spring, internal mass body, and hydraulic power take-off (PTO) system parameters on the energy conversion capability of the system were analyzed to provide a reference for the design of nonlinear EIWECs. In general, the proposed nonlinear EIWEC could provide good development potential for the scale utilization of wave energy resources.

Theoretical modeling of a co-located system with a floating wind platform and vertical truncated cylinders array

Combined floating offshore wind turbines (FOWTs), wave energy converters (WECs), and floating solar photovoltaics (FPVs) systems have the potential to provide cost-effective solutions for offshore multi-energy complementation and structure protection. In this study, a theoretical model based on the potential flow theory and eigenfunction matching method is utilized to study wave diffraction and radiation by a co-located system, in which the main components of the wind platform and WECs are made of vertical cylindrical floats. Based on the displacement constraint matrix, coupled equations of motion are developed to calculate the kinematic response of the co-located systems. After running the convergence analysis and model validation, the present model is employed to perform a multiparameter impact analysis. Case studies are presented to clarify the effects of the WEC radius, draft, layout, power take-off (PTO) system, and incident wave heading and frequency on the hydrodynamic coefficient, wave energy capture width, and motion response of the wind platform. Our findings highlight that several factors play a crucial role in the performance of the co-located system, more importantly, that the theoretical model developed in this study is capable of effectively predicting the wave-structure interactions in wave fields, making it applicable to future wave farm projects.

Nonlinear dynamics of a heaving spar-floater system integrated with inerter pendulum vibration absorber power take-off for wave energy conversion

A power take-off based on the inerter pendulum vibration absorber (called IPVA-PTO) is integrated with a spar-floater system to study its hydrodynamic response suppression and wave energy conversion capabilities in regular waves. The hydrodynamics of the spar-floater system is computed using the boundary element method with linear wave theory. With the wave height and wave frequency as the bifurcation parameters, it is found that the system can undergo two bifurcations: period-doubling bifurcation around the first resonance frequency (spar mode) and secondary Hopf bifurcation around the second resonance frequency (floater mode). The period-doubling bifurcation results in an energy transfer between the spar-floater system and the IPVA-PTO for small electrical damping values. As a result, the IPVA-PTO system simultaneously reduces the maximum response amplitude operator (RAO) of the spar and increases the normalized capture width in comparison with the optimal linear benchmark. Experiments performed on a “dry” single-degree-of-freedom system integrated with the IPVA-PTO where the base excitation is substituted for the wave excitation verify the simultaneous performance enhancement due to the period-doubling bifurcation. The system performance beyond the period-doubling bifurcation is also experimentally investigated. On the other hand, as the wave height approaches and passes the secondary Hopf bifurcation, the pendulum responses transition from primary harmonic responses to quasi-periodic responses to rotations. When the rotations occur, the IPVA-PTO system increases the maximum normalized capture width threefold to fivefold compared with the optimal linear benchmark, yet slightly increases the RAO around the second resonance frequency. Nevertheless, the RAO remains smaller than the global maximum RAO of the optimal linear benchmark. Finally, parametric studies are performed to study the effects of parameters on the bifurcations. It is observed that by varying the electrical damping, the wave height required for achieving the period-doubling bifurcation can be changed significantly, which can be exploited to stabilize the spar.

Achieving optimum power extraction of wave energy converters through tunable mechanical components

Wave energy converters (WECs) play a significant role in harnessing the vast potential of marine renewable energy. To enhance the power extraction of WECs, it is necessary but challenging to design the parameters of the WECs for the time-varying wave conditions. This research explores the utilization of tunable mechanical components within both the power take-offs (PTO) and wave capturing structures. We first briefly review the tunable mechanisms and then conduct a theoretical analysis of their applications for maximizing power extraction under regular and irregular wave conditions. The study investigates the impact of PTO stiffness and inertance on power extraction through an analytical approach. The results reveal that both parameters exhibit a monotonic effect within specific frequency ranges, and showed the optimum power extraction can be achieved through the tunable mechanical components. Furthermore, the research highlights the importance of designing the frequency tuning limit for two-body WECs to coincide with the desired wave conditions, as it enables all PTO parameters to achieve an optimal power output. Based on the analysis, the paper gives insightful suggestions on the design of PTO and WEC systems, including mass ratio between the two bodies, mooring stiffness, and other relevant parameters. It is found that the tuning through the mechanical component can be significant for the single-body WEC yet less effective for the two-body WEC especially at irregular wave conditions.

Hydroelastic theory for offshore floating plates of variable flexural rigidity

We present a theoretical model of the hydrodynamic behaviour of a floating flexible plate of variable flexural rigidity connected to the seabed by a spring/damper system. Decomposition of the response modes into rigid and bending elastic components allows us to investigate the hydroelastic behaviour of the plate subject to monochromatic incident free-surface waves of constant amplitude. We show that spatially dependent plate stiffness affects the eigenfrequencies and modal shapes, with direct consequences on plate dynamics and wave power extraction efficiency. We also examine how plate length and Power Take-Off (PTO) distribution affect the response of the system and its consequent absorbed energy. This work highlights the need to improve existing models of flexible floating energy platforms, especially given their importance in the Offshore Renewable Energy (ORE) sector.