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.     

Analysis of dynamic effects relevant for the wear damage in hydraulic machines for wave energy conversion

The present paper deals with a mathematical model of a heaving-buoy Wave Energy Converter (WEC) equipped with high-pressure hydraulic power take-off machinery for energy conversion. This model is based on linear hydrodynamic theory, and a hybrid frequency-time domain model is used to study the dynamics of the heaving-body exposed to an irregular incident wave. For the power take-off system, end-stop devices are provided to protect the hydraulic machinery when the buoy is exposed to severe sea states. The model also takes into account the lubricated friction force and pressure drops of orifice flow through the valves in the hydraulic system. All the forces mentioned in the hydraulic power take-off machinery have non-linear features. A complete non-linear state space model for the WEC system is presented in this study.The WEC system was numerically simulated for different cylinder lengths under a fixed volume. The effect of fluid compressibility in the cylinder has been investigated in the mathematical model. High frequency oscillations (HFOs) caused by the compressibility of the fluid are displayed in the time series and in corresponding power spectra, and variation is shown for different cylinder sizes. Piston ring and cylinder bore wear damage is estimated by using Archard’s equation on the basis of the simulation results. A comparison of these results with a performance of an identical WEC system which neglects fluid compressibility has been done in this work. It shows that although the spectral power is small, HFO can make a large contribution to both the ring and cylinder bore wear. For the purpose of wear prediction, oscillations at or below the wave frequency and HFO may be equally important.     

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 sub-optimal control and the spectral wave climate on the performance of wave energy converter arrays

A linear hydrodynamic model is used to assess the sensitivity of the performance of a wave energy converter (WEC) array to control parameters. It is found that WEC arrays have a much smaller tolerance to imprecision of the control parameters than isolated WECs and that the increase in power capture of WEC arrays is only achieved with larger amplitudes of motion of the individual WECs. The WEC array radiation pattern is found to provide useful insight into the array hydrodynamics. The linear hydrodynamic model is used, together with the wave climate at the European Marine Energy Centre (EMEC), to assess the maximum annual average power capture of a WEC array. It is found that the maximum annual average power capture is significantly reduced compared to the maximum power capture for regular waves and that the optimum array configuration is also significantly modified. It is concluded that the optimum configuration of a WEC array will be as much influenced by factors such as mooring layout, device access and power smoothing as it is by the theoretical optimum hydrodynamic configuration.     

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.     

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.     

Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment

This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment.     

Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.     

Numerical study for vegetation effects on coastal wave propagation by using nonlinear Boussinesq model

The vegetation has important impacts on coastal wave propagation. In the paper, the sensitivities of coastal wave attenuation due to vegetation to incident wave height, wave period and water depth, as well as vegetation configurations are numerically studied by using the fully nonlinear Boussinesq model. The model is based on the implementation of drag resistances due to vegetation in the fully nonlinear Boussinesq equation where the drag resistance is provided by the Morison’s formulation for rigid structure induced drag stresses. The model is firstly validated by comparing with the experimental results for wave propagation in vegetation zones. Subsequently, the model is used to simulate waves with different height, period propagating on vegetation zones with different water depth and vegetation configurations. The sensitivities of wave attenuation to incident wave height, wave period, water depth, as well as vegetation configurations are investigated based on the numerical results. The numerical results indicate that wave height attenuation due to vegetation is sensitive to incident wave height, wave period, water depth, as well as vegetation configurations, and attenuation ratio of wave height is increased monotonically with increases of incident wave height and decreases of water depth, while it is complex for wave period. Moreover, more vegetation segments can strengthen the interaction of vegetation and wave in a certain range.     

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。     

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.     

Declutching control of a wave energy converter

When hydraulic power take off (PTO) is used to convert the mechanical energy of a wave energy converter (WEC) into a more useful form of energy, the PTO force needs to be controlled. Continuous controlled variation of the PTO force can be approximated by a set of discrete values. This can be implemented using either variable displacement pumps or several hydraulic cylinders or several high pressure accumulators with different pressure levels. This pseudo-continuous control could lead to a complex PTO with a lot of components. A simpler way for controlling this hydraulic PTO is declutching control, which consists in switching on and off alternatively the wave energy converter's PTO. This can be achieved practically using a simple by-pass valve. In this paper, the control law of the valve is determined by using the optimal command theory. It is shown that, theoretically when considering a wave activated body type of WEC, declutching control can lead to energy absorption performance at least equivalent to that of pseudo-continuous control. The method is then applied to the case of the SEAREV wave energy converter, and it is shown than declutching control can even lead to a higher energy absorption, both in regular and irregular waves.     

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.     

Wave force on vertically submerged circular thin plate in shallow water

The paper presented is a solution of shallow water wave force, using small amplitude linear wave theory on two-dimensional vertically submerged circular thin plates under three different configurations: (1) a surface-piercing circular thin plate, (2) a submerged circular thin plate, and (3) a bottom-standing circular thin plate. Finally Morison's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore on uniformly sloping bottom. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force by single particle, total horizontal force and moment with respect to the wave amplitude are obtained at different depth of water and at different wave period. It is observed that the force and moment are converging with the increase of wave period and the gradients of force and moment with respect to the wave amplitude are extremely high for lower wave period.     

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.     

鹰式一号波浪能装置频域运动分析与优化设计

波浪能发电装置的波能转换通常分为两级能量转换:第一级能量转换是波浪作用下波浪能装置部件发生相对运动驱动PTO做功捕获波浪能;第二级能量转换为将捕获的波浪能转换为电能。其中一级波浪能转换系统的优化设计是提高波浪能装置能量转换效率的重要手段和关键技术。波浪作用下波浪能装置的运动与PTO做功运动相互耦合和影响,本文通过对不同波浪要素环境下、不同PTO阻尼下波浪能装置的频域运动模拟,以迎波宽度比为尺度对波浪能装置的一级能量转换系统进行优化设计,获得波浪能装置的最优做功阻尼,为实型装置负载加载设计提供设计依据,提高波浪能装置能量转化效率。鹰式一号波浪能装置的实海况运动证明,通过对一级能量转换系统的优化设计,能够有效提高装置的发电效率和提高装置对波浪响应频带宽度。     

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.     

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.     

Wave interactions with multiple-row curtainwall-pile breakwaters

In this study, a mathematical model has been developed that can compute various hydrodynamic characteristics of a multiple-row curtainwall-pile breakwater. To examine the validity of the developed model, laboratory experiments have been conducted for double- and triple-row breakwaters with various combinations of drafts of curtain walls, porosities between piles, and distances between rows. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. As a whole, the transmission coefficient decreases with an increase in relative water depth, whereas the reflection coefficient, normalized run-up and force exhibit an opposite trend in their variations. With fixed values of the draft of the curtain wall and the porosity of lower perforated part of the first row of a double-row breakwater, as these values of the second row increase and decrease, respectively, the transmission coefficient decreases, as expected. On the other hand, their effects on wave reflection, run-up, and wave force change with the relative depth. As for the distance between the rows, the transmission coefficient becomes a maximum when it is about one half of the wave length, suggesting that this condition should be avoided to achieve the advantage of the breakwater in reducing wave transmission. It is shown that for prototype breakwaters, on an average, the transmission coefficient would be smaller than 0.3 for wave periods less than 6.0 s, and it would be about 0.45 even for the wave period of 9.0 s, although there would be a variation depending on the geometry of the breakwater. It is also shown that wave transmission is significantly reduced by multiple-row breakwaters compared with a single-row breakwater, while the difference between double-row and triple-row breakwaters is marginal. Finally, engineering monograms are provided for double-row breakwaters to be used in practical engineering applications of the breakwaters.