Linear Power Take-off System Research Articles

Hydrodynamic Analysis of a Breakwater-Integrated Heaving-Buoy-Type Wave Energy Converter with an Optimal Artificial Damping Scheme

A three-dimensional frequency-domain numerical wave tank (FR-NWT) based on the Rankine panel method was developed. An optimal artificial damping zone (ADZ) scheme was first applied to the FR-NWT to prevent reflection waves from the end walls. Parametric studies of ramp function shape with artificial damping coefficients and damping zone length were conducted to find a proper damping scheme for the frequency domain program. Applying both the Sommerfeld radiation condition and the ADZ scheme to the frequency domain program can reduce the length of the ADZ to less than one wavelength. The FR-NWT developed by the authors was used to calculate the hydrodynamic response of a hemispherical-heaving buoy wave energy converter (WEC) integrated with a seawall-type breakwater of infinite length. A linear power take-off system was used to calculate power generation of the WEC. The global motion of the WEC combined with the breakwater was up to 1.85 times greater than that of the WEC without the breakwater. Moreover, the capture width ratio of the WEC increased approximately 3.67 times more than that of the WEC without the breakwater.

A numerical study of a taut-moored point-absorber wave energy converter with a linear power take-off system under extreme wave conditions

Probably the biggest challenge for wave energy is to ensure survival in harsh offshore conditions, in order to reduce costs for offshore repair operations and downtime, and achieve economic viability. This work presents a reliable numerical tool that can be used to study the dynamics and survivability of wave energy converters in violent wave conditions, possibly cutting down the costs of experimental campaigns. Within the Smoothed Particle Hydrodynamics framework, this research identifies a detailed procedure to model a taut-moored point-absorber wave energy converter together with its inherent power take-off device, which seamlessly exploits its functions of energy harvesting and load bearing. A validation of the DualSPHysics code is provided by contrasting the numerical outcome with a thorough set of data obtained in physical tests with extreme waves, showing that the time-integrated numerical model can capture with good accuracy all the physics involved. The computational fluid dynamics tool is employed to perform a survivability study, modeling high-return period wave conditions for marine structures, and providing guidelines on how to create the numerically best setup to be used for design purposes. A real-like irregular sea state representation, comprising 500 waves, was used to draw insightful indications for the structure optimization to increase the structure’s life expectancy, or conversely, to reduce the initial and operational costs.

Performance analysis of a coast – OWC wave energy converter integrated system

In this paper, a cylindrical dual-chamber oscillating water column (OWC) wave energy converter semi-embedded in a coastline or breakwater is proposed. A theoretical model based on linear potential flow theory is developed to evaluate the power absorption performance of the integrated system in the finite water depth. According to the matched eigenfunction expansions, the fluid domain is divided into five sub-domains and unknown coefficients in the diffraction and radiation problems are separately solved by matching the velocity and pressure between adjacent sub-domains. A linear power take-off system considering air compressibility is adopted to connect air volume flux with the chamber pressure. The reliability of this model is assessed by general identities (i.e., far-field relations). Then the model is performed to investigate the effects of wave conditions, draft, breadth and opening angle of the chambers on the wave power extraction. It is shown that the proposed integrated system can improve the total hydrodynamic efficiency in both regular and irregular waves.

Theoretical investigation on integrating a torus oscillating body with a concentric perforated cylindrical system

In this paper, the hydrodynamic performance of a hybrid wave energy extraction (HWEE) system consisting of a torus oscillating body (OB) and a concentric perforated cylindrical system was investigated based on the linear potential flow theory. A linear power take-off system is assumed to extract wave power. To solve the diffraction and radiation problems, a theoretical model was proposed using the methods of separation of variables and eigenfunction matching. Through a contrastive study, it was found that the model with an arc-shaped perforated outer cylinder performs better than the model with a partially perforated outer cylinder in terms of effective bandwidth of capture width ratio and the hydrodynamic horizontal forces acting on them. The HWEE system with an arc-shaped perforated outer cylinder was studied particularly and optimized by examining the effect of several main design parameters, including the incident wave angle, the porosity and opening angle of the arc-shaped perforated outer cylinder, as well as the exterior radius and draft of the torus OB. It was also found that the torus OB has no negative effects on the stability of the concentric perforated cylindrical system, at least in terms of the horizontal wave forces acting on the structures.

Performance enhancement of a vibration energy harvester via harmonic time-varying damping: A pseudospectral-based approach

Energy harvesting technologies are attracting increasing attention in the last decades, mainly thanks to the rapid advancement of sensors miniaturization, wireless sensors network, the internet of things, and the growing awareness on energy efficiency. The main objective of current research on energy harvesters is to enlarge the natural response bandwidth in order to increase the otherwise insufficient performance away from resonance. While popular approaches consider the inclusions of specific nonlinearities, this paper investigates the benefits of time variations of the damping coefficient of a linear power take-off system. A rigorous mathematical framework is firstly introduced, based on optimal control and pseudospectral decomposition, providing proofs and conditions for the existence of an unique optimal solution. Furthermore, a convenient algebraic formulation for the calculation of the steady-state response is provided, applicable to a wider family of time-varying systems. Such a tool is used to extensively study harmonic variations of the control damping parameters, discussing various combinations of orders and orthogonal terms. The optimization is first performed unconstrained, then forcing passivity, hence considering both active and semi-active controls. It is found that, in both cases, the best performance is achieved with damping variations at twice the exciting frequency, including both cosine and sine terms in the control law, while lower and higher harmonics are of less relevance.

Performance analysis of a point-absorber wave energy converter with a single buoy composed of three rigidly coupled structures

A single-body point absorber system is analysed to improve its power absorption at a finite water depth. The proposed wave energy converter consists of a single floating body coupled to a direct-drive power take-off system placed on the seabed. The structure of a cylindrical buoy with large draft is changed by a single body composed of three structures rigidly coupled, reducing its volume and improving its frequency-dependent hydrostatic parameters that are obtained through a numerical analysis tool called NEMOH. The undamped natural frequency of the oscillating system is tuned to a specified wave period and the performance of the WEC system is obtained assuming a linear Power Take-Off system. In time domain, the performance of the WEC device is carried-out under a regular (sinusoidal) and irregular incident wave profile. Comparing the performance of the WEC system using the cylindrical and the proposed buoy outcomes that the system with the proposed buoy is able to absorb more energy from incident waves with a wider frequency range, whereas the oscillating system is kept as simple as possible.

Numerical analysis of a new multi-body floating wave energy converter with a linear power take-off system

Abstract A floating wave energy converter (FWEC) with central buoy (CB), circumferentially connected by a set of four, smoothly-finished tubular floats is proposed. The central buoy and floats are connected rigidly at one end while the other end is hinged, enabling a relative motion. The rotation of floats about the CB represents the energy extraction mode of the device. Float shapes of five different configurations, including a newly-proposed ‘bean float,’ are investigated to estimate their power outputs with linear PTO. FWEC remains afloat and re-centered using taut-moored tethers. The frequency-domain model is utilized to determine the hydrodynamic coefficients of the device, assuming a Potential Wave Theory (PWT). The research evaluates the impact of the obtained hydrodynamic coefficients on the average power absorbed by the FWEC. The influence of a linear power take-off (PTO) system on the average power output of FWEC is studied by optimization of the damping coefficients for the encountered regular waves. Further, time-domain analysis is carried out on the ‘bean float’ - FWEC configuration using an open-source computer-aided engineering tool called WEC-Sim (Wave Energy Converter Simulator), and MATLAB® - Simulink® implementing nonlinear buoyancy and Froude-Krylov forces.

Two-mode WEC-type attachment for wave energy extraction and reduction of hydroelastic response of pontoon-type VLFS

Proposed herein is a two-mode wave energy converter-type attachment to the fore edge of pontoon-type very large floating structures (VLFSs) for wave energy extraction and reduction of hydroelastic response. This attachment consists of floating horizontal and submerged vertical plates that are connected to the VLFS with hinges and linear power take-off systems. The use of both floating horizontal and submerged vertical plates combines the superior performances of floating plates in extracting wave energy from short waves (T < 5 s) and of submerged vertical plates in extracting wave energy from intermediate and long waves (T > 7 s). When deployed in sites where 5 s ≤ T ≤ 7 s, the two-mode attachment yields a larger power production than the sole usage of floating plates or the sole usage of submerged vertical plates. Interestingly, the two-mode attachment also combines the superior performance of submerged vertical plates in reducing hydroelastic response for relatively short waves (T < 7 s) and the superior performance of floating plates in reducing hydroelastic response for relatively long waves (T ≥ 9 s). Moreover, this two-mode attachment furnishes a good balance between extracting wave energy and reducing hydroelastic response of VLFS for the same wave period.

Wave power extraction from multiple oscillating water columns along a straight coast

The integration of oscillating water column (OWC) wave energy converters into a coastal structure (breakwater, jetty, pier, etc.) or, more generally, their installation along the coast is an effective way to increase the accessibility of wave power exploitation. In this paper, a theoretical model is developed based on the linear potential flow theory and eigenfunction matching method to evaluate the hydrodynamic performance of an array of OWCs installed along a vertical straight coast. The chamber of each OWC consists of a hollow vertical circular cylinder, which is half embedded in the wall. The OWC chambers in the theoretical model may have different sizes, i.e. different values of the radius, wall thickness and submergence. At the top of each chamber, a Wells turbine is installed to extract power. The effects of the Wells turbine together with the air compressibility are taken into account as a linear power take-off system. The hydrodynamic and wave power extraction performance of the multiple coast-integrated OWCs is compared with that of a single offshore/coast-integrated OWC and of multiple offshore OWCs. More specifically, we analyse the role of the incident wave direction, chamber size (i.e. radius, wall thickness and submergence), spacing between OWCs and number of OWCs by means of the present theoretical model. It is shown that wave power extraction from the coast-integrated OWCs for a certain range of wave conditions can be significantly enhanced due to both the constructive array effect and the constructive coast effect.

Capture Performance of A Multi-Freedom Wave Energy Converter with Different Power Take-off Systems

Among the wave energy converters (WECs), oscillating buoy is a promising type for wave energy development in offshore area. Conventional single-freedom oscillating buoy WECs with linear power take-off (PTO) system are less efficient under off-resonance conditions and have a narrow power capture bandwidth. Thus, a multi-freedom WEC with a nonlinear PTO system is proposed. This study examines a multi-freedom WEC with 3 degrees of freedom: surge, heave and pitch. Three different PTO systems (velocity-square, snap through, and constant PTO systems) and a traditional linear PTO system are applied to the WEC. A time-domain model is established using linear potential theory and Cummins equation. The kinematic equation is numerically calculated with the fourth-order Runge-Kutta method. The optimal average output power of the PTO systems in all degrees of freedom are obtained and compared. Other parameters of snap through PTO are also discussed in detail. Results show that according to the power capture performance, the order of the PTO systems from the best to worst is snap through PTO, constant PTO, linear PTO and velocity-square PTO. The resonant frequency of the WEC can be adjusted to the incident wave frequency by choosing specific parameters of the snap through PTO. Adding more DOFs can make the WEC get a better power performance in more wave frequencies. Both the above two methods can raise the WEC’s power capture performance significantly.

Analyzing the Near-Field Effects and the Power Production of an Array of Heaving Cylindrical WECs and OSWECs Using a Coupled Hydrodynamic-PTO Model

The Power Take-Off (PTO) system is the key component of a Wave Energy Converter (WEC) that distinguishes it from a simple floating body because the uptake of the energy by the PTO system modifies the wave field surrounding the WEC. Consequently, the choice of a proper PTO model of a WEC is a key factor in the accuracy of a numerical model that serves to validate the economic impact of a wave energy project. Simultaneously, the given numerical model needs to simulate many WEC units operating in close proximity in a WEC farm, as such conglomerations are seen by the wave energy industry as the path to economic viability. A balance must therefore be struck between an accurate PTO model and the numerical cost of running it for various WEC farm configurations to test the viability of any given WEC farm project. Because hydrodynamic interaction between the WECs in a farm modifies the incoming wave field, both the power output of a WEC farm and the surface elevations in the ‘near field’ area will be affected. For certain types of WECs, namely heaving cylindrical WECs, the PTO system strongly modifies the motion of the WECs. Consequently, the choice of a PTO system affects both the power production and the surface elevations in the ‘near field’ of a WEC farm. In this paper, we investigate the effect of a PTO system for a small wave farm that we term ‘WEC array’ of 5 WECs of two types: a heaving cylindrical WEC and an Oscillating Surge Wave Energy Converter (OSWEC). These WECs are positioned in a staggered array configuration designed to extract the maximum power from the incident waves. The PTO system is modelled in WEC-Sim, a purpose-built WEC dynamics simulator. The PTO system is coupled to the open-source wave structure interaction solver NEMOH to calculate the average wave field η in the ‘near-field’. Using a WEC-specific novel PTO system model, the effect of a hydraulic PTO system on the WEC array power production and the near-field is compared to that of a linear PTO system. Results are given for a series of regular wave conditions for a single WEC and subsequently extended to a 5-WEC array. We demonstrate the quantitative and qualitative differences in the power and the ‘near-field’ effects between a 5-heaving cylindrical WEC array and a 5-OSWEC array. Furthermore, we show that modeling a hydraulic PTO system as a linear PTO system in the case of a heaving cylindrical WEC leads to considerable inaccuracies in the calculation of average absorbed power, but not in the near-field surface elevations. Yet, in the case of an OSWEC, a hydraulic PTO system cannot be reduced to a linear PTO coefficient without introducing substantial inaccuracies into both the array power output and the near-field effects. We discuss the implications of our results compared to previous research on WEC arrays which used simplified linear coefficients as a proxy for PTO systems.

Analysis for wave power capture capacity of two interconnected floats in regular waves

The most representative of raft-type wave energy converters (WECs) is one composed of two interconnected floats, which uses the relative rotation between the floats to drive a Power Take-Off (PTO) system, achieving power capture from ocean waves. This paper presents a fundamental investigation into the wave power capture capacity of two interconnected floats with arbitrary float length. Linear hydrodynamics of the interconnected floats and a linear PTO system are employed, which enables us to carry out a frequency-domain analysis. Analytical formulas are derived of an optimized PTO damping and PTO stiffness/inertia for maximizing wave energy conversion in regular waves with/without consideration of relative rotary motion constraints due to the restraints of pump stroke or/and collision problem between the floats. The analytical model is then employed to examine the influence of fore-and-aft float length ratio, PTO system and float rotary inertia radius on the power capture capability of the two interconnected floats. It is concluded that for general wave conditions and specified total float length, two interconnected floats with the fore one properly shorter than the aft one possess high capacity in power absorption.

Comparative study on power capture performance of oscillating-body wave energy converters with three novel power take-off systems

Converting persistent and renewable wave energy into electricity has been a research focus in recent years. The oscillating-body wave energy converter (WEC) is a promising approach, especially for offshore areas. However, conventional oscillating-body WECs with linear power take-off (PTO) systems are less efficient under off-resonance conditions and have a narrow power capture bandwidth, which has inhibited the commercial application of wave energy. In order to enhance the power capture performance, this study examined oscillating-body WECs with three new types of PTO systems: bistable impulsive PTO, coupled linear PTO, and coupled bistable PTO. Governing equations for the heave motion of a WEC were established based on the linear potential theory by coupling the buoy and PTO systems and were numerically calculated with the fourth-order Runge–Kutta method. The influence of PTO parameters such as the spring constant, stable equilibrium position, and mass ratio on the power capture ratio was investigated. The differences among the WECs with different PTOs were analysed to determine the optimum device. Compared with the linear PTO system, the WEC with the bistable impulse PTO system enhanced the power capture ratio for low-frequency regular waves, and WECs with coupled linear or coupled bistable PTO systems increased the power capture ratio for low-frequency regular waves and expanded the power capture spectrum bandwidth when proper PTO parameters were applied.

Hydrodynamic performance of concentric arrays of point absorbers

The behaviour of arrays of 12 heaving point absorbers in concentric arrangements is numerically assessed in a frequency domain model. The floaters are attached to a central cylindrical bottom-mounted structure. Each point absorber is restricted to the heave mode and is assumed to have its own linear power take-off system consisting of an external damping coefficient enabling power extraction and a supplementary mass coefficient tuning the point absorber to the incoming waves. The external damping and supplementary mass coefficients are optimized to maximize the power absorption by each floater in the array, with a restriction on the total control force that can be applied on the floaters. Various concentric arrangements with different radii and number of concentric circles are analysed to determine the most efficient among them. Moreover, the influence of the presence of a central bottom-mounted pillar and the effect of change in its dimension and shape on the power absorption are also studied.

Power Takeoff Optimization for Maximizing Energy Conversion of Wave-Activated Bodies

This paper presents a fundamental investigation on optimizing the power takeoff (PTO) for maximizing wave energy conversion of the wave-activated bodies (WABs) wave energy converters. In this research, two relative heave motions are taken for capture power, and a linear PTO is considered in the primary analysis. For such a linear dynamic system, the frequency-domain analysis can be carried out, and an analytical formula can be derived for the optimized frequency-dependent PTO damping coefficient, which can be used to determine an optimized PTO damping for maximizing wave energy conversion in regular waves. However, when an optimized PTO is required for maximizing energy conversion from ocean waves, the PTO damping optimization may be very different and much less certain, because it may be based on one of many characteristic periods of the given sea state and the dependency may change from different sea states. For this reason, the optimized PTO damping coefficient for a given sea state must be studied carefully. Another important aspect of the research is to examine whether an optimized nonlinear PTO can take more energy out from waves than that of an optimized linear PTO. For this purpose, the maximized capture powers by the optimized linear and nonlinear PTOs are compared using the time-domain analysis. It has been shown from the examples that the maximized capture power by a nonlinear PTO system may exceed that by the linear PTO, but only marginally (less than 1%). Hence, it can be generally concluded that the maximized power using a linear PTO system can be a very good indicator for the device in extracting the maximal energy from waves regardless of the linear or nonlinear PTO in actual use. This conclusion may help simplify the analysis of the wave energy converters in terms of the energy production as well as the device optimization for improving energy conversion capacity.

Maximum Wave Energy Conversion by Two Interconnected Floaters

Interconnected floaters could use relative rotations around connection joints to drive a power take-off (PTO) system, such that the ocean wave energy can be converted into a useful energy. In this paper, our attention is on the PTO optimization for the interconnected floaters. A fully linear dynamic system, including the linear hydrodynamics of the interconnected floaters and a linear PTO system, is considered. Under assumptions of linear theory, we present a mathematical model for evaluating the maximum wave energy conversion of two interconnected floaters based on the three-dimensional wave radiation–diffraction theory. The model is validated by comparison of the present results with the published data, and there is a good agreement. The model can be employed to calculate the maximum power absorbed by the interconnected floaters under motion constraints due to the restraints of pump stroke or/and collision problem between the floaters. The influence of wave frequency, PTO system, floater rotary inertia radius, and motion constraints on the power capture capability of the two interconnected floaters is also examined. It can be concluded that enlarging the rotary inertia of each floater by using mass nonuniform distribution can be seen as an alternative way of adding PTO inertia. The maximum relative power capture width of the two interconnected floaters with optimized PTO system under constraints is much smaller than that without any motion constraints for long waves.

Power capture performance of an oscillating-body WEC with nonlinear snap through PTO systems in irregular waves

Compared with solar and wind energy, wave energy is a kind of renewable resource which is enormous and still under development. In order to utilize the wave energy, various types of wave energy converters (WECs) have been proposed and studied. And oscillating-body WEC is widely used for offshore deployment. For this type of WEC, the oscillating motion of the floater is converted into electricity by the power take off (PTO) system, which is usually mathematically simplified as a linear spring and a damper. The linear PTO system is characteristic of frequency-dependent response and the energy absorption is less powerful for off resonance conditions. Thus a nonlinear snap through PTO system consisting of two symmetrically oblique springs and a linear damper is applied. A nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two oblique springs to the original length of both springs. JONSWAP spectrum is utilized to generate the time series of irregular waves. Time domain method is used to establish the motion equation of the oscillating-body WEC in irregular waves. And state space model is applied to replace the convolution term in the time domain motion equation. Based on the established motion equation, the motion response of both the linear and nonlinear WEC is numerically calculated using 4th Runge–Kutta method, after which the captured power can be obtained. Then the influences of wave parameters such as peak frequency, significant wave height, damping coefficient of the PTO system and the nonlinear parameter γ on the power capture performance of the nonlinear WEC is discussed in detail. Results show that compared with linear PTO system, the nonlinear snap through PTO system can increase the power captured by the oscillating body WEC in irregular waves.