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.     

Wave energy conversion under constrained wave-by-wave impedance matching with amplitude and phase-match limits

This paper investigates an approach to limit the fullness of ‘tuning’ provided by wave-by-wave impedance matching control of wave energy devices in irregular waves. A single analytical formulation based on the Lagrange multiplier approach of Evans [1] is used to limit the velocity amplitude while also limiting the closeness of the phase match between velocity and exciting force. The paper studies the effect of the present technique in concurrently limiting the device velocity and the required control/actuation force. Time domain application requires wave-profile prediction, which here is based on a deterministic propagation model. Also examined in the time domain is the effect of possible violation of the displacement constraint, which for many designs implies impacts at hard stops within the power take-off mechanism. Time domain simulations are carried out for a 2-body axisymmetric converter (with physical end-stops) in sea states reported for a site off the US east coast. It is found that the approach leads to effective power conversion in the less energetic sea states, while as desired, considerable muting of the optimal response is found in the larger sea states. Under the assumptions of this work, the end-stop collisions are found to have a minor effect on the power conversion. The present approach could be used to guide the design of power take-off systems so that their displacement stroke, maximum force, and resistive and reactive power limits are well-matched to the achievable performance of a given controlled primary energy converter.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

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.     

Dynamic analysis of wave energy converter by incorporating the effect of hydraulic transmission lines

A heaving-buoy wave energy converter equipped with hydraulic power take-off is studied in this paper. This wave energy converter system is divided into five subsystems: a heaving buoy, hydraulic pump, pipelines, non-return check valves and a hydraulic motor combined with an electric generator. A dynamic model was developed by considering the interactions between the subsystems in a state space form. The transient pressures caused by starting/stopping the buoy or closing/opening the check valves were predicted numerically using the established model. The simulation results show that transmission line dynamics play a dominant role in the studied wave energy converter system. The length of the pipeline will not only affect the amplitude of the transient pressures but also affect the converted power. The variation of the time-averaged converted electric power with the pipeline length is estimated using the simulation method for the buoy exposed to one irregular sea state. Finally, it is suggested how reduced power efficiency due to the pipelines may be ameliorated.     

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.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

Investigation on the energy absorption performance of a fixed-bottom pressure-differential wave energy converter

In this article, we investigate the energy absorption performance of a fixed-bottom pressure-differential wave energy converter. Two versions of the technology are considered: one has the moving surfaces on the bottom of the air chambers whereas the other has the moving surfaces on the top. We developed numerical models in the frequency domain, thereby enabling the power absorption of the two versions of the device to be assessed. It is observed that the moving surfaces on the top allow for easier tuning of the natural period of the system. Taking into account stroke limitations, the design is optimized. Results indicate that the pressure-differential wave energy converter is a highly efficient technology both with respect to energy absorption and selected economic performance indicators.     

Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters

To date the estimation of long-term wave energy production at a given deployment site has commonly been limited to a consideration of the significant wave height H_s and mean energy period T_e. This paper addresses the sensitivity of power production from wave energy converters to the wave groupiness and spectral bandwidth of sea states. Linear and non-linear systems are implemented to simulate the response of converters equipped with realistic power take-off devices in real sea states. It is shown in particular that, when the converters are not much sensitive to wave directionality, the bandwidth characteristic is appropriate to complete the set of overall wave parameters describing the sea state for the purpose of estimating wave energy production.     

Difference-frequency wave loads on a large body in multi-directional waves

The second-order difference-frequency wave forces on a large three-dimensional body in multi-directional waves are computed by the boundary integral equation method and the so-called FML formulation (assisting radiation potential method). Semi-analytic solutions for a bottom-mounted vertical circular cylinder are also developed to validate the numerical method. Difference-frequency wave loads on a bottom-mounted vertical cylinder and stationary four legs of the ISSC tension-leg platform (TLP) are presented for various combinations of incident wave frequencies and headings. These force quadratic transfer functions (QTF) can directly be used in studying slowly varying wave loads in irregular short-crested seas described by a particular directional spectrum. From our numerical results, it is seen that the slowly varying wave loads are in general very sensitive to the directional spreading function of the sea, and therefore wave directionality needs to be taken into account in relevant ocean engineering applications. It is also pointed out that the uni-directionality of the sea is not necessarily a conservative assumption when the second-order effects are concerned.     

Extreme value prediction of inundation drag force with and without current

This paper deals with drag forces due to irregular waves on a vertical slender structure in the splash zone, i.e. in the vicinity of still-water free surface, by considering the inundation effect due to instantaneous wave elevation. The force turns out to be a third-order quantity with respect to wave elevation. The focus of this paper is however limited to extreme value prediction of this force in stochastic waves. Based upon a transformation of random variables and use of the Rice formula, the mean up-crossing rate of inundation drag force is obtained in the frequency domain both by direct numerical integration and asymptotic evaluation for high levels using the Laplace method. The extreme value distribution of this force is then established by the Poisson probability law assuming independent up-crossing events. The proposed method agrees very well with time-domain simulations both for the mean up-crossing rate and the extreme value prediction. The effect of correlation between wave elevation and horizontal water particle velocity and the presence of current have been studied.     

Second-order drift force response of offshore guyed towers

An iterative frequency domain method of analysis is presented for determining the response behaviour of Guyed Offshore Towers to low-frequency, second-order wave drift forces generated in a random sea environment. For the response analysis, the tower is idealized as a shear beam with a rotational spring at the bottom support. The guylines are replaced by a non-linear spring. The second-order drift force is considered to be proportional to the square of the wave elevation and is simulated using a drift force coefficient and the time history of a slowly varying wave envelope in random sea. The responses due to drift forces are obtained in frequency domain by incorporating the non-linearities produced due to non-linear guy lines. An example problem is solved under different random sea states to compare the response behaviour of the tower obtained by the second-order wave force, the first-order wave force and a combination of the two.     

Wave actions on the side caissons of the Venice gates

The present study originates from a construction problem found in the planned deployment of the side caissons of the Venice gates barrier. Each of these caissons is made to float, then sunk into a lateral trench and jointed to the soil at its bottom. As a result, a C-shaped channel forms between the vertical caisson surfaces and the surrounding trench. Incoming storm waves propagating from the sea can then induce forced oscillations in this C-channel. An analytical model based on the method of matched asymptotics is developed in order to obtain the free surface oscillations in the channel, caused by a grazing incident wave. The resonant response of the basin and the amplification factors are then determined. From the free surface elevation, the pressure field and hence the total forces are also found. The analysis moves on to irregular wave motion. The analytical solution enables us to compute the dynamic actions, showing that their magnitude can be significant, due to the excitation of different resonant modes.     

非线性铰接浮体波能转换器的动力学特性研究

针对传统铰接浮体波能转换器捕获效率低、频带窄的瓶颈,提出一种新型高效波能捕获仿生非线性连接结构。该连接结构具有转动负刚度效应,可起到被动相位控制作用,提高系统的波能捕获效率。首先,基于海蛇脊柱骨结构的柔性约束机理,设计了一种高效波浪能捕获仿生连接结构,该结构由球窝结构、球头、翅状突出物和类肌肉柔性结构组成;其次,基于线性波浪理论和Cummins 方程,建立两模块非线性波能转换器的动力学模型,并采用谐波平衡法解析求解非线性控制方程;最后,开展了数值模拟研究,分析了规则波激励下该新型波能转换器的波能转换特性。结果表明：通过引入新型高效仿生连接结构,可有效降低系统的等效固有频率;当连接器的负刚度结构调整到合适参数时,系统的弹性力可以在纵摇相平面上形成一个椭圆势阱,其椭圆势阱的长轴接近铰接浮体系统相对纵摇运动的模态方向,由此驱动两个模块的相对纵摇运动趋于反相,起到被动相位控制的作用。     

Phase control through load control of oscillating-body wave energy converters with hydraulic PTO system

Oscillating bodies constitute an important class of wave energy converters, especially for offshore deployment. Phase control by latching has been proposed in the 1970s to enhance the wave energy absorption by oscillating bodies (especially the so-called point absorbers). Although this has been shown to be potentially capable of substantially increasing the amount of absorbed energy, the practical implementation in real irregular waves of optimum phase control has met with theoretical and practical difficulties that have not been satisfactorily overcome. The present paper addresses the case of oscillating-body converters equipped with a high-pressure hydraulic power take-off mechanism (PTO) that provides a natural way of achieving latching: the body remains stationary for as long as the hydrodynamic forces on its wetted surface are unable to overcome the resisting force (gas pressure difference times cross-sectional area of the ram) introduced by the hydraulic PTO system. A method of achieving sub-optimal phase-control is developed, based on the theoretical time-domain modelling of a single-degree of freedom oscillating body in regular and irregular waves, by adequately delaying the release of the body in order to approximately bring into phase the body velocity and the diffraction (or excitation) force on the body, and in this way get closer to the well-known optimal condition derived from frequency-domain analysis for an oscillating body in regular waves.     

基于多星融合高度计数据的中国海波浪能资源评估

Wave energy resources are abundant in both offshore and nearshore areas of the China's seas. A reliable assessment of the wave energy resources must be performed before they can be exploited. First, for a water depth in offshore waters of China, a parameterized wave power density model that considers the effects of the water depth is introduced to improve the calculating accuracy of the wave power density. Second, wave heights and wind speeds on the surface of the China's seas are retrieved from an AVISO multi-satellite altimeter data set for the period from 2009 to 2013. Three mean wave period inversion models are developed and used to calculate the wave energy period. Third, a practical application value for developing the wave energy is analyzed based on buoy data. Finally, the wave power density is then calculated using the wave field data. Using the distribution of wave power density, the energy level frequency, the time variability indexes, the total wave energy and the distribution of total wave energy density according to a wave state, the offshore wave energy in the China's seas is assessed. The results show that the areas of abundant and stable wave energy are primarily located in the north-central part of the South China Sea, the Luzon Strait, southeast of Taiwan in the China's seas; the wave power density values in these areas are approximately 14.0–18.5 k W/m. The wave energy in the China's seas presents obvious seasonal variations and optimal seasons for a wave energy utilization are in winter and autumn. Except for very coastal waters, in other sea areas in the China's seas, the energy is primarily from the wave state with 0.5 m≤H s≤4 m, 4 s≤T e≤10 s where H s is a significant wave height and T e is an energy period; within this wave state, the wave energy accounts for 80% above of the total wave energy. This characteristic is advantageous to designing wave energy convertors(WECs). The practical application value of the wave energy is higher which can be as an effective supplement for an energy consumption in some areas. The above results are consistent with the wave model which indicates fully that this new microwave remote sensing method altimeter is effective and feasible for the wave energy assessment.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.     

HF radar data quality requirements for wave measurement

HF radar wave measurements are presented focussing on theoretical limitations, and thus radar operating parameters, and quality control requirements to ensure robust measurements across a range of sea states. Data from three radar deployments, off the west coast of Norway, Celtic Sea and Liverpool Bay using two different radar systems, WERA and Pisces, and different radio frequency ranges, are used to demonstrate the wave measurement capability of HF radar and to illustrate the points made. Aspects of the measurements that require further improvements are identified. These include modifications to the underlying theory particularly in high sea states, identification and removal of ships and interference from the radar signals before wave processing and/or intelligent partitioning to remove these from the wave spectrum. The need to match the radio frequency to the expected wave peak frequency and waveheight range, with lower radio frequencies performing better at higher waveheights and lower peak frequencies and vice versa, is demonstrated. For operations across a wide range of oceanographic conditions a radar able to operate at more than one frequency is recommended for robust wave measurement. Careful quality control is needed to ensure accurate wave measurements.     

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.