Power Take-off Damping Research Articles

Hydrodynamic performance evaluation of a wave energy converter with two concentric vertical cylinders by analytic solutions and model tests

In this paper, the hydrodynamic performance of a two-concentric-cylindrical-body WEC (Wave Energy Converter) is investigated through a systematic parametric study by using analytical solutions and model tests. The two-body WEC generates power by LEG (linear electric generator) through the relative heave motion between the inner and outer buoys. In order to maximize the relative heave motions between the two buoys, resonance of each buoy was used. As a means of finding its maximum hydrodynamic efficiency, the matched eigenfunction expansion method (MEEM) was applied to obtain the analytic solutions under the assumption of linear potential theory. The numerical results are validated through comparisons with a series of model tests conducted by authors in a 2-D wave tank at Jeju National University. Based on the case study, several design strategies that can further enhance the PTO (Power take-off) efficiency are proposed, including the optimal PTO damping and intentional mismatching of heave natural frequencies of the two buoys and the peak frequency of target wave spectrum. The intentional mismatching strategy, in particular, can increase high-quality extracted power for broader wave conditions, which is a big advantage in designing the proposed WEC-LEG system.

Scaling and air compressibility effects on a three-dimensional offshore stationary OWC wave energy converter

Understanding the hydrodynamic performance of an Oscillating Water Column (OWC) wave energy converter is essential for further improving the device efficiency. Most experimental measurements are performed at small scales where air compressibility can be ignored. In this paper, scaling and air compressibility effects on the performance of an offshore stationary OWC wave energy converter are studied in a 3D numerical wave tank. A Computational Fluid Dynamics (CFD) model based on the RANS equations and the VOF surface capturing scheme is developed and validated against physical measurements of a 1:50 model-scale OWC. Following the validation stage, the CFD model is utilized to investigate scaling and air compressibility effects on the performance of an OWC by comparing five different scales from 1:50 up to full-scale and modelling air as both compressible and incompressible. Other parameters that are considered include the impact of varying the power take-off (PTO) damping, wave height and period, underwater geometry, and the effect of air chamber height. Results reveal that at full-scale air compressibility is important and can induce about 12% reduction in the maximum efficiency predicted at model-scale under regular waves at the resonant frequency and the optimum PTO damping. Air compressibility effects slightly reduce as the extracted pneumatic power increases. In order to consider full-scale air compressibility effects while testing a small OWC model scaled using Froude’s similitude law, the full-scale air chamber volume is best scaled with the square of the scale factor rather than cubic to predict the device performance with errors of less than 1.2%. In this manner, this work contributes to the full-scale development of OWCs by better understanding the differences from small physical model-scales.

A study on a novel two-body floating wave energy converter

This paper proposes a novel wave energy converter (WEC), which is needed for monitoring the marine environment. The converter is composed of two oscillating bodies: a floating sphere connected to a heavy submerged sphere using a tight rope and a power take off (PTO) system mounted in the floater. Energy is converted from the relative motion between the differently oscillating bodies caused by the action of the waves. The model was first tested in the frequency domain to optimize the geometry and mechanical parameters, and subsequently, a time domain model was built for simulation of a multi-DOF motion system. In the frequency domain research, a constraint was first added to the two-body WEC to address the problem of the small value of the optimized PTO damping. The state space approximation method was employed during the time domain simulation, and external forces acting on the bodies due to the tight rope were deduced. The motions of the system and power absorbed by the converter under regular and irregular waves were analyzed in detail. Finally, experiments were conducted on a scaled model, and the results show that the total power efficiency was more than 20%.

Optimal Configurations of Wave Energy Converter Arrays with a Floating Body

Abstract An array of floating point-absorbing wave energy converters (WECs) is usually employed for extracting efficiently ocean wave energy. For deep water environment, it is more feasible and convenient to connect the absorbers array with a floating body, such as a semi-submersible bottom-moored disk, whose function is to act as the virtual seabed. In the present work, an array of identical floating symmetrically distributed cylinders in a coaxial moored disk as a wave energy device is proposed The power take-off (PTO) system in the wave energy device is assumed to be composed of a linear/nonlinear damper activated by the buoys heaving motion. Hydrodynamic analysis of the examined floating system is implemented in frequency domain. Hydrodynamic interferences between the oscillating bodies are accounted for in the corresponding coupled equations. The array layouts under the constraint of the disk, incidence wave directions, separating distance between the absorbers and the PTO damping are considered to optimize this kind of WECs. Numerical results with regular waves are presented and discussed for the axisymmetric system utilizing heave mode with these interaction factors, in terms of a specific numbers of cylinders and expected power production.

Performance of arrays of direct-driven wave energy converters under optimal power take-off damping

It is well known that the total power converted by a wave energy farm is influenced by the hydrodynamic interactions between wave energy converters, especially when they are close to each other. Therefore, to improve the performance of a wave energy farm, the hydrodynamic interaction between converters must be considered, which can be influenced by the power take-off damping of individual converters. In this paper, the performance of arrays of wave energy converters under optimal hydrodynamic interaction and power take-off damping is investigated. This is achieved by coordinating the power take-off damping of individual converters, resulting in optimal hydrodynamic interaction as well as higher production of time-averaged power converted by the farm. Physical constraints on motion amplitudes are considered in the solution, which is required for the practical implementation of wave energy converters. Results indicate that the natural frequency of a wave energy converter under optimal damping will not vary with sea states, but the production performance of a wave energy farm can be improved significantly while satisfying the motion constraints.

Coordinated Control of Wave Energy Converters Subject to Motion Constraints

In this paper, a generic coordinated control method for wave energy converters is proposed, and the constraints on motion amplitudes and the hydrodynamic interaction between converters are considered. The objective of the control problem is to maximize the energy converted from ocean waves, and this is achieved by coordinating the power take-off (PTO) damping of each wave energy converter in the frequency domain in each sea state. In a case study, a wave energy farm consisting of four converters based on the concept developed by Uppsala University is studied. In the solution, motion constraints, including constraints on the amplitudes of displacement and velocity, are included. Twelve months of sea states, based on measured wave data at the Lysekil test site on the Swedish west coast, are used in the simulation to evaluate the performance of the wave energy farm using the new method. Results from the new coordinated control method and traditional control method are compared, indicating that the coordinated control of wave energy converters is an effective way to improve the energy production of wave energy farm in harmonic waves.

부유식 풍력-파력발전 플랫폼과 탑재된 파력발전기와의 단방향 연성 운동 해석

In this study, a six degree-of-freedom motion analysis of a wind-wave hybrid platform equipped with numerous wave energy converters (WECs) was carried out. To examine the effect of the WECs on the platform, an analysis of one-way coupling was carried out, which only considered the power take-off (PTO) damping of the static WECs on the platform. The equation of motion of a floating platform with mooring lines in the time domain was established, and the responses of the one-way coupled platform were then compared with the case of a platform without any coupling effects from the WECs. The hydrodynamic coefficients and wave exciting forces were obtained from the 3D diffraction/radiation pre-processor code WAMIT based on the boundary element method. Then, an analysis of the dynamic responses of the floating platform with or without the WEC effect in the time domain was carried out. All of the dynamics of a floating platform with multiple wind turbines were obtained by coupling FAST and CHARM3D in the time domain, which was further extended to include additional coupled dynamics for multiple turbines. The analysis showed that the PTO damping effect on platform motions was negligible, but coupled effects between multiple WECs and the platform may differentiate the heave, roll, and pitch platform motions from the one without any effects induced by WECs.

Hydrodynamic performance of a pile-restrained WEC-type floating breakwater: An experimental study

In this paper, a system which integrates an oscillating buoy type wave energy converter with a vertical pile-restrained floating breakwater is introduced. A preliminary experimental study on the hydrodynamic performance of the system is carried out in a wave flume under the action of regular waves. A current controller-magnetic powder brake system is used to simulate the power generation system. The design is verified against published results. The power-take off damping characteristics are investigated, and the current controller-magnetic powder brake system can simulate the (approximate) Coulomb damping force very well. The effects of various parameters, including wave period and wave height, dimensions of the system and excitation current, on the hydrodynamic performance are investigated. Results indicate that the power take-off damping force, draft and relative width between the floating breakwater and the wavelength have a significant influence on the hydrodynamic performance of the system. A range can be observed for which the capture width ratio of the system can achieve approximately 24% while transmission coefficient was kept lower than 0.50 with the proper adjustment of power take-off damping force, and the floating breakwater performs in an effective manner. The new concept provides a promising way to utilize wave energy cost-effectively.

Effect of inclination on oscillation characteristics of an oscillating water column wave energy converter

Oscillating water column (OWC) wave energy converters are adopted in many marine applications such as buoys. This research investigates how inclination-induced changes in motion affect the oscillation characteristics of an OWC. As the collector of the OWC wave energy converter is inclined, the direction of motion of the water column is also inclined because it is constrained by collector walls. To investigate this idea, we developed a mechanical 1-degree-of-freedom oscillator model of an inclined OWC. The usefulness of the mechanical model was confirmed in a water tank test with OWCs inclined at 90° (vertical), 45°, and 18.4°. We then investigated the effect of inclination on the resonance period and the optimum power take-off damping of the OWC. The resonance period was mainly prolonged by the reduced restoring force as the motion direction changed. The optimum power take-off damping of an inclined OWC equaled the radiation damping, as observed in vertical OWCs. Finally, we varied the air chamber volume and observed much smaller effects than when varying the inclination. We conclude that changing the direction of motion affects the oscillation characteristics of OWCs mostly because of the reduction of gravity restoring force.

Experimental and numerical comparisons of hydrodynamic responses for a combined wind and wave energy converter concept under operational conditions

The spar torus combination (STC) concept is a combined wind and wave energy converter concept that is composed of a spar floating wind turbine and a torus-shaped, heaving-body wave energy converter (WEC). The WEC is installed on the spar floater. Wave power can be absorbed by a power-take off (PTO) system through the relative heave motions between spar and torus. Numerical model was established to predict dynamic responses of the STC concept ​under different sea states. To validate the numerical model, a model test of the STC concept under operational conditions was performed. A two-body physical model at a 1:50 scaling ratio was built. A series of tests were performed to assess the performance of the concept. During the tests, different PTO damping levels were applied. When large power output was achieved, air compressibility of the PTO damper in the model matters, making relevant a suitable nonlinear PTO modeling in the numerical simulations. Wind conditions were considered to model the effect of the thrust force on the rotor using a wind drag disc. Numerical and experimental results are presented and compared. Good agreements are achieved.

Computational Modeling of Rolling Wave-Energy Converters in a Viscous Fluid1

The performance of an asymmetrical rolling cam as an ocean-wave energy extractor was studied experimentally and theoretically in the 70s. Previous inviscid-fluid theory indicated that energy-absorbing efficiency could approach 100% in the absence of real-fluid effects. The way viscosity alters the performance is examined in this paper for two distinctive rolling-cam shapes: a smooth “Eyeball Cam (EC)” with a simple mathematical form and a “Keeled Cam (KC)” with a single sharp-edged keel. Frequency-domain solutions in an inviscid fluid were first sought for as baseline performance metrics. As expected, without viscosity, both shapes, despite their differences, perform exceedingly well in terms of extraction efficiency. The hydrodynamic properties of the two shapes were then examined in a real fluid, using the solution methodology called the free-surface random-vortex method (FSRVM). The added inertia and radiation damping were changed, especially for the KC. With the power-take-off (PTO) damping present, nonlinear time-domain solutions were developed to predict the rolling motion, the effects of PTO damping, and the effects of the cam shapes. For the EC, the coupled motion of sway, heave and roll in waves was investigated to understand how energy extraction was affected.

Wave Loads on a Point-Absorbing Wave Energy Device in Extreme Waves

The survivability of a 1:20 scale point-absorbing Wave Energy Converter (WEC) model is considered in extreme wave tests with focused waves embedded in regular wave backgrounds and with time series of irregular waves. The wave heights were many times higher than the maximal stroke length of the device. Three different float geometries were used in the tests. The peak loads were measured and compared for extreme waves embedded in background waves with a range of periods and phase relations and with different values of Power Take-Off (PTO) damping.

Numerical modeling of power take-off damping in an Oscillating Water Column device

An Oscillating Water Column (OWC) is a wave energy converter consisting of a partially submerged chamber with an air column over the water column. The work done by the air column under excitation by the incident waves is used to generate electrical energy through a power take-off (PTO) device. The air column is under pressure due to the damping from the PTO device and this pressure is essential for the extraction of wave energy using the OWC. The relationship between the PTO damping and the hydrodynamic efficiency of the OWC provides more insight into the wave energy extraction using an OWC.In this paper, two-dimensional Computational Fluid Dynamics (CFD) simulations are used to investigate the response of the OWC under different values of damping from the PTO device. The PTO damping on the chamber is represented using a linear pressure drop law with the permeability coefficient derived from Darcy’s equation for flow through porous media. The model is validated by comparing the numerical results to experimental data. The influence of the PTO damping on the chamber pressure, the free surface motion, the velocity of the vertical motion of the free surface and the hydrodynamic efficiency of the OWC is studied. The hydrodynamic efficiency is calculated as the ratio of the power delivered at the vent of the OWC to the incident wave power. It is found that the PTO damping needed to attain the maximum OWC hydrodynamic efficiency increases with increasing incident wavelength. The formation of stagnation zones in the water due to high velocities for lower values of PTO damping is found to reduce the hydrodynamic efficiency.

Dynamic modelling of Spar-Buoy oscillating water column wave energy converter

The main objective of this research is to develop an experimentally validated numerical wave power prediction tool for an offshore Spar-Buoy oscillating water column (OWC) wave energy converter (WEC). The numerical tool should be able to predict the spar heave motion and the water column oscillations inside the structure, in order to estimate the power absorber and evaluate the device performance. A two-degree-of-freedom mechanical oscillation model was adopted. The model considers the power take-off (PTO) damping and the stiffness due to air compressibility inside the pneumatic chamber. Experiments were performed in order to calculate the damping coefficients and to validate the predicted results. PTO mechanism was experimentally modelled by orifice plate located on top of the OWC model. Different orifice areas were used to allow the examination of the PTO damping effect on the hydrodynamic behaviour of the system.

선형발전기가 탑재된 파랑에너지 추출장치 설계 -I. 파력 부이 설계

Design procedure of WEC (wave energy converter) using the heaving motion of a floating cylinder- type buoy coupled with LEG (linear electric generator) system is introduced. It is seen that the maximum power can actually be obtained at the optimal conditions (cPTO=bT, ω = ωN ). Then, based on the developed theory, several design strategies are proposed to further enhance the maximum PTO (power take off), which includes the inten- tional mismatching with the heave natural frequency, which is 15% higher value than the peak frequency of input velocity spectrum. By using the intentional mismatching strategy, the generated power is actually increased and the corresponding draft as well as the required PTO damping value is significantly reduced, which is a big advantage in manufacturing the WEC with practical LEG (linear electric generator) system.

Multi-objective optimum design of a buoy for the resonant-type wave energy converter

This paper deals with the resonant type of wave energy converter (WEC) and the determination method of its geometric parameters, which were obtained to construct a robust and optimal structure. The optimization problem is formulated with the objectives of simultaneously maximizing the absorbed power output, which is mainly related to optimal power take-off damping, and minimizing the production cost by the volume of the required sheet plate using a weighting method. The constraints are composed of the response surfaces that indicate the resonance period (heave, pitch) and the meta-center height of the buoy. The signal-to-noise ratio calculated from the normalized multi-objective results with the weight factor can be used to help select the robust design level. In order to obtain a sample data set, the motion responses of the power buoy were analyzed using a commercial code based on the boundary element method. We present the Pareto-optimal set to reveal the relationship between the power and the volume of a sheet plate. Lastly, the power efficiency of the WEC with the optimum design variables is estimated as the captured wave ratio resulting from the absorbed power. The result of the WEC design is economically optimal and satisfies given constraints.

The method of imbedded Lagrangian element to estimate wave power absorption by some submerged devices

A simple approach is described to estimate the wave power absorption potential of submerged devices known to cause wave focusing and flow enhancement. In particular, the presence of a flow-through power take-off (PTO) system, such as low-head turbines, can be accounted for. The wave radiation characteristics of an appropriately selected Lagrangian element (LE) in the fluid domain are first determined. In the limit of a vanishing mass, the LE reduces to a patch of distributed normal dipoles. The hydrodynamic coefficients of this virtual object are then input in a standard equation of motion where the effect of the PTO can be represented, for example, as a dashpot damping term. The process is illustrated for a class of devices recently proposed by Carter and Ertekin (2011), although in a simplified form. Favorable wave power absorption is shown for large ratios of the LE wave radiation coefficient over the LE added mass coefficient. Under optimal conditions, the relative flow reduction from the PTO theoretically lies between 0.50 and \(1/\sqrt 2 \approx 0.71\), with lower values corresponding to better configurations. Wave power capture widths, the sensitivity of results to PTO damping and sample spectral calculations at a typical site in Hawaiian waters are proposed to further illustrate the versatility of the method.

Heaving displacement amplification characteristics of a power buoy in shoaling water with insufficient draft

The resonance power buoy is a convincing tool that can increase the extraction efficiency of wave energy. The buoy needs a corresponding draft, to move in resonance with waves within the peak frequency band where wave energy is concentrated. However, it must still be clarified if the buoy acts as an effective displacement amplifier, when there is insufficient water depth. In this study, the vertical displacement of a circular cylinder-type buoy was calculated, with the spectrum data observed in a real shallow sea as the external wave force, and with the corresponding draft, according to the mode frequency of normal waves. Such numerical investigation result, without considering Power Take-Off (PTO) damping, confirmed that the area of the heave responses spectrum can be amplified by up to about tenfold, compared with the wave energy spectrum, if the draft corresponds to the peak frequency, even with insufficient water depth. Moreover, the amplification factor of the buoy varied, according to the seasonal changes in the wave spectra.

Frequency/time domain modeling of a direct drive point absorber wave energy converter

Two different methods to model a point absorber wave energy converter (WEC) with direct drive linear power take-off (PTO) are proposed in the present study: the frequency domain (FD) method and the time domain (TD) method. In the FD analysis, the frequency response function (FRF) of the WEC device is obtained via the equation of motion, and the expressions of power capture width in regular and random waves are derived as well. In the TD modeling, based on a state space approximation of the convolution term in the motion equation, both regular wave and random wave simulations are carried out. The regular wave simulation results indicate that the state space approximation is sufficiently accurate and the capture width reaches the maximum in the vicinity of the natural frequency. In the random wave simulations, the effects of buoy size, the PTO damping and wave climate on the power capture width are discussed in detail, which leads to the conclusion that the capture widths are influenced by the natural frequency of the WEC device, peak frequency of the wave spectrum, the amplitude of FRF and PTO damping. Furthermore, the increase of the capture width is at the cost of a relatively large buoy size and PTO damping when control is not included.

근사기법을 활용한 공진형 파력발전 부이의 발전량 추정 및 최적설계

This paper deals with the resonant type of a WEC (wave energy converter) and the determination method of its geometric parameters which were obtained to construct the robust and optimal structure, respectively. In detail, the optimization problem is formulated with the constraints composed of the response surfaces which stand for the resonance period(heave, pitch) and the meta center height of the buoy. Use of a signal-to-noise ratio calculated from normalized multi-objective results with the weight factor can help to select the robust design level. In order to get the sample data set, the motion responses of the power buoy were analyzed using the BEM (boundary element method)-based commercial code. Also, the optimization result is compared with a robust design for a feasibility study. Finally, the power efficiency of the WEC with the optimum design variables is estimated as the captured wave ratio resulting from absorbed power which mainly related to PTO (power take off) damping. It could be said that the resultant of the WEC design is the economical optimal design which satisfy the given constraints.