Modelling of a wave energy converter array with a nonlinear power take-off system in the frequency domain

This paper presents a nonlinear frequency domain model and uses this to assess the performance of a wave energy converter (WEC) array with a nonlinear power take-off (PTO). In this model, the nonlinear PTO forces are approximated by a truncated Fourier series, while the dynamics of the WEC array are described by a set of linear motion equations in the frequency domain, and the hydrodynamic coefficients are obtained with the boundary element method. A single heave absorber is firstly investigated to establish the accuracy of the new model in capturing the nonlinear behaviour of the pumping system. Subsequently, simulations of a 2D array with 18 WECs and a pillar in the centre (representing the tower of a wind turbine) are carried out to understand wave interference effects. Several optimisation strategies are proposed to improve the overall performance of the WEC array. These results demonstrate a computationally effective method for accounting for nonlinear effects in large WEC arrays. The proposed approach may potentially be applied for developing control algorithms for the adaptability of a 2D array to incoming wave excitation.     

Performance investigation of a two-raft-type wave energy converter with hydraulic power take-off unit

Raft-type wave energy converter (WEC) is a multi-mode wave energy conversion device, using the relative pitch motion to drive its hydraulic power take-off (PTO) units for capturing energy from the ocean waves. The hydraulic PTO unit as its energy conversion module plays a significant role in storing large qualities of energy and making the output power smooth. However, most of the previous investigations on the raft-type WECs treat the hydraulic PTO unit as a linear PTO unit and do not consider the dynamics of the hydraulic circuit and components in their investigations. This paper is related to a two-raft-type WEC consisting of two hinged rafts and a hydraulic PTO unit. The aim of this paper is to make an understanding of the dynamics of the hydraulic PTO unit and how these affect the performance of the two-raft-type WEC. Therefore, a combined hydrodynamic and hydraulic PTO unit model is proposed to investigate and optimize the performance of the two-raft-type WEC; and based on the simulation of the combined model, the relationships between the optimal power capture ability, the optimal magnitude of the hydraulic PTO force and the wave states are numerically revealed. Results show that an approximately square wave type hydraulic PTO force is produced by the hydraulic PTO unit, which causes the performance of the two-raft-type WEC not to be sinusoidal and the energy capturing manner different from that of the device using a linear PTO unit; moreover, there is an optimal magnitude of the hydraulic PTO force for obtaining an optimal power capture ability, which can be achieved by adjusting the parameters of the hydraulic PTO unit; in regular waves, the optimal power capture ability as well as the optimal magnitude of the hydraulic PTO force normalized by the wave height presents little relationship with the wave height, mainly depends on the wave period; in irregular waves, the trends of the optimal power capture ability and the normalized optimal magnitude of the hydraulic PTO force against the peak wave periods at different significant wave heights are generally identical and show a good correlation. All means that the hydraulic PTO unit of the two-raft-type WEC can be tuned to the wave states, and these would provide a valuable guidance for the optimal design of its hydraulic PTO unit.     

The effect of water depth on the performance of a small surging wave energy converter

The effect of water depth on the performance of a small surging wave energy converter (WEC) is investigated analytically, numerically and experimentally. It is shown that although the average annual incident wave power is significantly reduced by water depth, a large proportion of this reduction is due to the dissipation of highly energetic, but largely unexploitable seas. It is also shown that the power capture is related more closely to incident wave force than incident wave power. Experimental results demonstrate that both the surge wave force and power capture of a flap-type WEC increase in shallow water.     

On the capture width of wave energy converters

This paper extends the theory on capture width, a commonly used performance indicator for a wave energy converter (WEC). The capture width of a linear WEC is shown to depend on two properties: the spectral power fraction (a property introduced in this paper), which depends entirely on the sea state, and the monochromatic capture width, which is determined by the geometry of the WEC and the chosen power take off (PTO) coefficients. Each of these properties is examined in detail. Capture width is shown to be a measure of how well these two properties coincide. A study of the effects of PTO control on the capture width suggests that geometry control, a form of control that has not been the focus of much academic research, despite its use in the wave energy industry, deserves more attention. The distinction between geometry control and PTO control is outlined. While capture width is a valuable design tool, its limitations must be recognised. The assumptions made in the formulation of capture width are listed, and its limitations as a tool for estimating annual power capture of a WEC are discussed.     

Numerical implementation and sensitivity analysis of a wave energy converter in a time-dependent mild-slope equation model

Several Wave Energy Converters (abbreviated as WECs) have intensively been studied and developed during the last decade and currently small farms of WECs are getting installed. WECs in a farm are partly absorbing, partly redistributing the incident wave power. Consequently, the power absorption of each individual WEC in a farm is affected by its neighbouring WECs. The knowledge of the wave climate around the WEC is needed to predict its performance in the farm. In this paper a technique is developed to implement a single and multiple WECs based on the overtopping principle in a time-dependent mild-slope equation model. So far, the mild-slope equations have been widely used to study wave transformations around coastal and offshore structures, such as breakwaters, piles of windmills and offshore platforms. First the limitations of the WEC implementation are discussed through a sensitivity analysis. Next the developed approach is applied to study the wave height reduction behind a single WEC and a farm. The wake behind an isolated WEC is investigated for uni- and multidirectional waves; it is observed that an increase of the directional spread leads to a faster wave redistribution behind the WEC. Further the wake in the lee of multiple WECs is calculated for two different farm lay-outs, i.e. an aligned grid and a staggered grid, by adapting the performance of each WEC to its incident wave power. The evolved technique is a fast tool to find the optimal lay-out of WECs in a farm and to study the possible influence on surrounding activities in the sea.     

Design,Optimization and Numerical Modelling of A Novel Floating Pendulum Wave Energy Converter with Tide Adaptation

A novel floating pendulum wave energy converter(WEC) with the ability of tide adaptation is designed and presented in this paper.Aiming to a high efficiency,the buoy's hydrodynamic shape is optimized by enumeration and comparison.Furthermore,in order to keep the buoy's well-designed leading edge always facing the incoming wave straightly,a novel transmission mechanism is then adopted,which is called the tidal adaptation mechanism in this paper.Time domain numerical models of a floating pendulum WEC with or without tide adaptation mechanism are built to compare their performance on various water levels.When comparing these two WECs in terms of their average output based on the linear passive control strategy,the output power of WEC with the tide adaptation mechanism is much steadier with the change of the water level and always larger than that without the tide adaptation mechanism.     

Design, Optimization and Numerical Modelling of A Novel Floating Pendulum Wave Energy Converter with Tide Adaptation

A novel floating pendulum wave energy converter (WEC) with the ability of tide adaptation is designed and presented in this paper. Aiming to a high efficiency, the buoy''s hydrodynamic shape is optimized by enumeration and comparison. Furthermore, in order to keep the buoy''s well-designed leading edge always facing the incoming wave straightly, a novel transmission mechanism is then adopted, which is called the tidal adaptation mechanism in this paper. Time domain numerical models of a floating pendulum WEC with or without tide adaptation mechanism are built to compare their performance on various water levels. When comparing these two WECs in terms of their average output based on the linear passive control strategy, the output power of WEC with the tide adaptation mechanism is much steadier with the change of the water level and always larger than that without the tide adaptation mechanism.     

An approximate solution for the wave energy shadow in the lee of an array of overtopping type wave energy converters

In this study we investigate how the wave energy deficit in the lee of an array of overtopping type wave energy converting devices (WECs), redistributes with distance from the array due to the natural variability of the wave climate and wave structure interactions. Wave directional spreading has previously been identified as the dominant mechanism that disperses the wave energy deficit, reducing the maximum wave height reduction with increasing distance from the array. In addition to this when waves pass by objects such as an overtopping type WEC device, diffracted waves re-distribute the incident wave energy and create a complex interference pattern. The effect of wave energy redistribution from diffraction on the wave energy shadow in the near and far field is less obvious. In this study, we present an approximate analytical solution that describes the diffracted and transmitted wave field about a single row array of overtopping type WECs, under random wave conditions. This is achieved with multiple superpositions of the analytical solutions for monochromatic unidirectional waves about a semi-infinite breakwater, extended to account for partial reflection and transmission. The solution is used to investigate the sensitivity of the far field wave energy shadow to the array configuration, level of energy extraction, incident wave climate, and diffraction. Our results suggest that diffraction spreads part of the wave energy passing through the array, away from the direct shadow region of the array. This, in part, counteracts the dispersion of the wave energy deficit from directional spreading.     

Numerical modeling on hydrodynamic performance of a bottom-hinged flap wave energy converter

The hydrodynamic performance of a bottom-hinged flap wave energy converter(WEC) is investigated through a frequency domain numerical model.The numerical model is verified through a two-dimensional analytic solution,as well as the qualitative analysis on the dynamic response of avibrating system.The concept of "optimum density" of the bottom-hinged flap is proposed,and its analytic expression is derived as well.The frequency interval in which the optimum density exists is also obtained.The analytic expression of the optimum linear damping coefficient is obtained by a bottom-hinged WEC.Some basic dynamic properties involving natural period,excitation moment,pitch amplitude,and optimum damping coefficient are analyzed and discussed in detail.In addition,this paper highlights the analysis of effects on the conversion performance of the device exerted by some important parameters.The results indicate that "the optimum linear damping period of 5.0 s" is the most ideal option in the short wave sea states with the wave period below 6.0 s.Shallow water depth,large flap thickness and low flap density are advised in the practical design of the device in short wave sea states in order to maximize power capture.In the sea state with water depth of 5.0 m and wave period of 5.0 s,the results of parametric optimization suggest a flap with the width of 8.0 m,thickness of 1.6 m,and with the density as little as possible when the optimum power take-off(PTO) damping coefficient is adopted.     

Study of Hydrodynamic Characteristics of A Sharp Eagle Wave Energy Converter

According to Newton''s Second Law and the microwave theory, mechanical analysis of multiple buoys which form Sharp Eagle wave energy converter (WEC) is carried out. The movements of every buoy in three modes couple each other when they are affected with incident waves. Based on the above, mechanical models of the WEC are established, which are concerned with fluid forces, damping forces, hinge forces, and so on. Hydrodynamic parameters of one buoy are obtained by taking the other moving buoy as boundary conditions. Then, by taking those hydrodynamic parameters into the mechanical models, the optimum external damping and optimal capture width ratio are calculated out. Under the condition of the optimum external damping, a plenty of data are obtained, such as the displacements amplitude of each buoy in three modes (sway, heave, pitch), damping forces, hinge forces, and speed of the hydraulic cylinder. Research results provide theoretical references and basis for Sharp Eagle WECs in the design and manufacture.     

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.     

动力输出系统(PTO)对集成波能转换装置式防波堤消波性能及波能捕获率影响研究

针对波浪能转换装置(WEC)研究重点主要集中在能量捕获效率方面,而忽略其附带的消波功能的问题。基于Open FOAM程序,建立垂荡浮子式波浪能发电装置与桩式约束的浮式防波堤的集成系统(OBC-FB)。主要研究WEC中的重要组件动力输出系统(PTO)对集成系统波能捕获效率及消波性能的影响。分析流体黏性影响下线性PTO系统的最优PTO阻尼特性。开发非线性电磁阻尼模型与线性PTO系统性能进行比较。结果显示,考虑黏性影响下线性的最优PTO阻尼系数略大于无黏的理论值;适当增大PTO阻尼系数可以获得更大的波能捕获宽度比(CWR),从而可以保证装置单位特征尺寸的波能转换效率更高,同时可以在更宽波况范围保证消波性能;相较于线性PTO阻尼系统,非线性电磁PTO阻尼系统可以更好地兼顾波能捕获效率和消波性能。因此,在OBC-FB集成系统的优化设计中,PTO阻尼系统是一个重要的优化参数。     

Design and testing of a non-linear power take-off simulator for a bottom-hinged plate wave energy converter

Eddy current brakes provide a versatile way of simulating the power take-off system (PTO) in model testing of small scale wave energy converters (WECs). This type of PTO simulator is based on the principle that a conductive material moving in a magnetic field generates a braking force proportional to its velocity. A bottom-hinged pitching plate WEC model has been designed using an eddy current brake as a PTO simulator. A dedicated electric current source unit was developed to provide a controllable and reliable level of DC current intensity to feed the magnetic field generating coils. Using a real-time data acquisition and control, this unit can be used to impose non-linear damping PTO characteristic curves in several types of WEC models based on eddy current brakes. In the present case, this current source has been used to simulate a constant damping PTO on a small scale pitching WEC model that has been tested in the IST wave flume. Two different cases were considered: one corresponding to a surface piercing plate and another to a fully submerged plate. Experimental results are presented for plate motion and for non-dimensional capture width.     

Oscillating Body Design for A 3-DOF Wave Energy Converter

Ocean wave energy converters (WECs) are obtaining more and more attentions in the world. So far, many types of converters have been invented. Oscillating body systems are a major class of WECs, which typically have one degree of freedom (DOF), and the power absorption efficiency is not quite satisfactory. In this paper, a 3-DOF WEC is proposed and a simplified frequency-domain dynamic model of the WEC depending on the linear potential theory is conducted. The performances of three geometries of the oscillating body including the cone, the cylinder and the hemisphere have been compared, and the results show that the hemisphere is more suitable for the 3-DOF WEC. Subsequently, the relationship among the parameters of the hemisphere is established based on the equal natural frequencies of the heave and pitch (or roll) motions, and the results show that lowering the center of gravity leads to the better power absorption in the pitch (or roll) motion. In the end, the power matrixes of different sizes of the hemispheres under different irregular waves are obtained, which can give a size design reference for engineers.     

Connection Technology of HPTO Type WECs and DC Nano Grid in Island

Wave energy fluctuating a great deal endangers the security of power grid especially micro grid in island. A DC nano grid supported by batteries is proposed to smooth the output power of wave energy converters (WECs). Thus, renewable energy converters connected to DC grid is a new subject. The characteristics of WECs are very important to the connection technology of HPTO type WECs and DC nano grid. Hydraulic power take-off system (HPTO) is the core unit of the largest category of WECs, with the functions of supplying suitable damping for a WEC to absorb wave energy, and converting captured wave energy to electricity. The HPTO is divided into a hydraulic energy storage system (HESS) and a hydraulic power generation system (HPGS). A primary numerical model for the HPGS is established in this paper. Three important basic characteristics of the HPGS are deduced, which reveal how the generator load determines the HPGS rotation rate. Therefore, the connector of HPTO type WEC and DC nano grid would be an uncontrollable rectifier with high reliability, also would be a controllable power converter with high efficiency, such as interleaved boost converter-IBC. The research shows that it is very flexible to connect to DC nano grid for WECs, but bypass resistance loads are indispensable for the security of WECs..     

摆式波能转换装置水动力特性频域分析

基于势流理论,建立波浪与摆式波能转换装置作用的三维频域分析模型。应用数值模型对两种质量的摆式波能转换装置进行水动力分析,在考虑粘性阻尼作用的条件下,计算传动系统的最优扭阻系数。在最佳工况下,开展了波浪频率对摆板运动响应和俘获能量影响的系统研究,给出了波浪最佳频率范围、摆板振幅、能量俘获效率以及摆板表面的波动压强。     

Wave climate scatter performance of a cycloidal wave energy converter

A lift based cycloidal wave energy converter (WEC) was investigated using potential flow numerical simulations in combination with viscous loss estimates based on published hydrofoil data. This type of wave energy converter consists of a shaft with one or more hydrofoils attached eccentrically at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The operation of the WEC as a wave-to-shaft energy converter interacting with straight crested waves was estimated for an actual ocean wave climate. The climate chosen was the climate recorded by a buoy off the north-east shore of Oahu/Hawaii, which was a typical moderate wave climate featuring an average annual wave power P_W = 17 kWh/m of wave crest. The impact of the design variables radius, chord, span and maximum generator power on the average annual shaft energy yield, capacity factor and power production time fraction were explored. In the selected wave climate, a radius R = 5 m, chord C = 5 m and span of S = 60 m along with a maximum generator power of P_G = 1.25 MW were found to be optimal in terms of annual shaft energy yield. At the design point, the CycWEC achieved a wave-to-shaft power efficiency of 70%. In the annual average, 40% of the incoming wave energy was converted to shaft energy, and a capacity factor of 42% was achieved. These numbers exceeded the typical performance of competing renewables like wind power, and demonstrated that the WEC was able to convert wave energy to shaft energy efficiently for a range of wave periods and wave heights as encountered in a typical wave climate.     

Wave prediction using wave rider position measurements and NARX network in wave energy conversion

Several control methods of wave energy converters (WECs) need prediction in the future of wave surface elevation. Prediction of wave surface elevation can be performed using measurements of surface elevation at a location ahead of the controlled WEC in the upcoming wave. Artificial neural network (ANN) is a robust data-learning tool, and is proposed in this study to predict the surface elevation at the WEC location using measurements of wave elevation at ahead located sensor (a wave rider buoy). The nonlinear autoregressive with exogenous input network (NARX NN) is utilized in this study as the prediction method. Simulations show promising results for predicting the wave surface elevation. Challenges of using real measurements data are also discussed in this paper.     

Theoretical and Experimental Study of A Coaxial Double-Buoy Wave Energy Converter

The double-body heave wave energy converter(WEC) is one of the most conducive devices to absorb the wave energy from relative motion while the law of which is not well understood. This paper makes an in-depth study on this wave energy converter, by means of the combination of theoretical analysis and physical model experiment. The hydrodynamic characteristics and energy capture of the double-buoy under constant and linear Power Take-Off(PTO) damping are investigated. Influences of absolute mass and mass ratio are discussed in the theoretical model.Relative displacement amplitude and average power output are tested in the experiment to analyze the effect of the wave period and outer buoy's mass, while the capture width ratio(CWR) is also calculated. Results show that the wave period and mass of the buoys have a significant effect on the converter. Different forms of PTO damping have no influence on the optimal wave period and mass ratio of this device. It is recommended to select the double-buoy converter with a mass ratio of 0.80 and to place it in an area with the frequent wave period close to the natural period of the outer buoy to achieve the optimal energy capture.     

Design pressure distributions on the hull of the FLOW wave energy converter

This paper presents a procedure to calculate the design pressure distributions on the hull of a wave energy converter (WEC). Design pressures are the maximum pressure values that the device is expected to experience during its operational life time. The procedure is applied to the prototype under development by Martifer Energy (FLOW—Future Life in Ocean Waves).A boundary integral method is used to solve the hydrodynamic problem. The hydrodynamic pressures are combined with the hydrostatic ones and the internal pressures of the large ballast tanks. The first step consists of validating the numerical results of motions by comparison with measured experimental data obtained with a scaled model of the WEC. The numerical model is tuned by adjusting the damping of the device rotational motions and the equivalent damping and stiffness of the power take-off system. The pressure distributions are calculated for all irregular sea states representative of the Portuguese Pilot Zone where the prototype will be installed and a long term distribution method is used to calculate the expected maximum pressures on the hull corresponding to the 100-year return period.