A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC) operating in a nonlinear multidirectional random sea are rigorously investigated. The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter. This is a new approach, and, as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea, avoids the inaccuracies resulting from using a first order linear wave model in the simulation process. The predicted results have been systematically analyzed and compared, and the advantages of using this new approach have been convincingly substantiated.     

Hydrodynamic Analysis and Power Conversion for Point Absorber WEC with Two Degrees of Freedom Using CFD

Point absorber wave energy device with multiple degrees of freedom (DOF) is assumed to have a better absorption ability of mechanical energy from ocean waves. In this paper, a coaxial symmetric articulated point absorber wave energy converter with two degrees of freedom is presented. The mechanical equations of the oscillation buoy with power take-off mechanism (PTO) in regular waves are established. The three-dimensional numerical wave tank is built in consideration of the buoy motion based upon the CFD method. The appropriate simulation elements are selected for the buoy and wave parameters. The feasibility of the CFD method is verified through the contrast between the numerical simulation results of typical wave conditions and test results. In such case, the buoy with single DOF of heave, pitch and their coupling motion considering free (no PTO damping) and damped oscillations in regular waves are simulated by using the verified CFD method respectively. The hydrodynamic and wave energy conversion characteristics with typical wave conditions are analyzed. The numerical results show that the heave and pitch can affect each other in the buoy coupling motion, hydrodynamic loads, wave energy absorption and flow field. The total capture width ratio with two coupled DOF motion is higher than that with a single DOF motion. The wave energy conversion of a certain DOF motion may be higher than that of the single certain DOF motion even though the wave is at the resonance period. When the wave periods are high enough, the interaction between the coupled DOF motions can be neglected.     

Maximizing the Absorbed Power of A Point Absorber Using An FA-Based Optimized Model Predictive Control

This paper presents an extended model predictive controller for maximizing the absorbed power of a point absorber wave energy converter. Owing to the great influence of controller parameters upon the absorbed power, the optimization of these parameters is carried out for the first time by a firefly algorithm (FA). Error, the difference between output velocity of buoy and input wave speed which leads to power maximization in the optimized MPC is compared with the classical MPC. Simulation results indicate that given the high accuracy and acceptable speed of the algorithm, it can adjust the parameters of the controller to the point where system error decreased effectively and the absorbed energy increased about 4 MW.     

On a new wave energy absorber

It is a commonly held opinion that only a forced resonance is possible between random wind-generated waves and wave energy absorbers; the forced resonance being pursued by means of devices for phase control. We show, instead, that it is possible to obtain an impressive natural resonance between random wind-generated waves and a new kind of absorber beneath the sea level. The proof is given through a small scale field experiment. This finding should enable us to defend coasts with a very low environmental impact and to use breakwaters for converting large quantities of wave energy into electric power.     

Artificial reef effect and fouling impacts on offshore wave power foundations and buoys – a pilot study

Little is known about the effects of offshore energy installations on the marine environment, and further research could assist in minimizing environmental risks as well as in enhancing potential positive effects on the marine environment. While biofouling on marine energy conversion devices on one hand has the potential to be an engineering concern, these structures can also affect biodiversity by functioning as artificial reefs. The Lysekil Project is a test park for wave power located at the Swedish west coast. Here, buoys acting as point absorbers on the surface are connected to generators anchored on concrete foundations on the seabed. In this study we investigated the colonisation of foundations by invertebrates and fish, as well as fouling assemblages on buoys. We examined the influence of surface orientation of the wave power foundations on epibenthic colonisation, and made observations of habitat use by fish and crustaceans during three years of submergence. We also examined fouling assemblages on buoys and calculated the effects of biofouling on the energy absorption of the wave power buoys. On foundations we demonstrated a succession in colonisation over time with a higher degree of coverage on vertical surfaces. Buoys were dominated by the blue mussel Mytilus edulis. Calculations indicated that biofouling have no significant effect in the energy absorption on a buoy working as a point absorber. This study is the first structured investigation on marine organisms associated with wave power devices.     

A three-dimensional wave field over a bidirectionally periodic ripple bottom

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the second order so that the Bragg resonance effect of the ripple bottom on the free-surface wave can be analyzed. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is avoided. This theory is successfully verified by reducing to simpler situations. Then, the analytical results for the special case of a unidirectional sinusoidal bottom are compared with experimental data for validation.     

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber’s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.     

渗透海床上矩形Bragg防波堤对波浪反射的研究

与海床不可渗透的情况相比,波浪在可渗透海床上传播时会发生波能衰减。本文将基于可渗透海床上一维修正型缓坡方程,建立方程求解的有限差分模型。将通过与不可渗透海床上矩形Bragg防波堤对波浪反射系数解析解的对比,验证有限差分模型的正确性和适用性。将进一步研究海床可渗透情况下,海床的渗透性参数、坝体的相对宽度、数量、浸没度对波浪反射系数的影响及其与海床不可渗透情况下的差异。本文研究发现,Bragg共振发生时的反射系数随坝体数量的增多而增大,随海床渗透性参数和坝体浸没度的增大而减小,并且存在一个坝体相对宽度值会使Bragg共振反射达到最大。相较于海床不可渗透的情况,发生Bragg共振反射的波浪频率几乎相同,但反射系数减小,而且零反射（或全透射）现象不再存在。     

点吸收式波浪能发电装置姿态特性分析

点吸收式波浪能发电装置是一种最简单的振荡体式波浪能发电装置, 但其安装成本高、生存能力较差。本文针对点吸收式波浪能发电装置的姿态稳定性问题, 开展了其在波浪作用下的运动姿态和发电功率之间的关系研究。首先介绍了点吸收波浪能发电装置的工作原理; 然后,根据我国南海海域的自然资源条件, 划定波况范围, 利用相似理论在实验室中模拟波浪参数,选定工况, 建立模型, 设计测量系统, 开展物理模型试验; 最后, 利用试验结果分析了发电装置的最佳发电周期、波高对装置发电功率的影响, 装置姿态对发电功率的影响等。本文为点吸收式波浪能发电装置设计及测试提供了参考。     

基于时间反转理论的聚焦Lamb波结构损伤成像

从理论和实验上研究了时间反转法在频散和多模式的Lamb波结构健康检测方面的应用.当Lamb波在包含有损伤的板类结构中传播时,损伤的存在表现为一个被动波源.采用分布式传感器网络,基于传递函数的观点,通过推导由损伤这个被动波源产生的时间反转波场幅值的表达式,证实了当观察点位于损伤位置时,时间反转波场的幅值最大.为验证时间反转方法的聚焦效应,提出了一种适合于分布的激励/接收传感器网络的成像方法,该方法可以对损伤定位并近似确定损伤尺寸.结合有限元的实验结果显示了Lamb波检测信号的能量可在损伤处聚焦,表明时间反转     

Hydrodynamic performance of a pile-supported OWC breakwater: An analytical study

A pile-supported OWC breakwater is a novel marine structure in which an oscillating water column (OWC) is integrated into a pile-supported breakwater, with a dual function: generating carbon-free energy and providing shelter for port activities by limiting wave transmission. In this work we investigate the hydrodynamics of this novel structure by means of an analytical model based on linear wave theory and matched eigenfunction expansion method. A local increase in the back-wall draft is adopted as an effective strategy to enhance wave power extraction and reduce wave transmission. The effects of chamber breadth, wall draft and air chamber volume on the hydrodynamic performance are examined in detail. We find that optimizing power take-off (PTO) damping for maximum power leads to both satisfactory power extraction and wave transmission, whereas optimizing for minimum wave transmission penalizes power extraction excessively; the former is, therefore, preferable. An appropriate large enough air chamber volume can enhance the bandwidth of high extraction efficiency through the air compressibility effect, with minimum repercussions for wave transmission. Meanwhile, the air chamber volume is found to be not large enough for the air compressibility effect to be relevant at engineering scales. Finally, a two-level practical optimization strategy on PTO damping is adopted. We prove that this strategy yields similar wave power extraction and wave transmission as the ideal optimization approach.     

Estimating the potential of ocean wave power resources

The realistic assessment of an ocean wave energy resource that can be converted to an electrical power at various offshore sites depends upon many factors, and these include estimating the resource recognizing the random nature of the site-specific wave field, and optimizing the power conversion from particular wave energy conversion devices. In order to better account for the uncertainty in wave power resource estimates, conditional probability distribution functions of wave power in a given sea-state are derived. Theoretical expressions for the deep and shallow water limits are derived and the role of spectral width is studied. The theoretical model estimates were compared with the statistics obtained from the wave-by-wave analysis of JONSWAP based ocean wave time-series. It was shown that the narrow-band approximation is appropriate when the variability due to wave period is negligible. The application of the short-term models in evaluating the long-term wave power resource at a site was illustrated using wave data measured off the California coast. The final example illustrates the procedure for incorporating the local wave data and the sea-state model together with a wave energy device to obtain an estimate of the potential wave energy that could be converted into a usable energy resource.     

Research of Power Take-off System for “Sharp Eagle Ⅱ” Wave Energy Converter

The "Sharp Eagle" device is a wave energy converter of a hinged double floating body. The wave-absorbing floating body hinges on the semi-submerged floating body structure. Under the action of wave, the wave-absorbing floating body rotates around the hinge point, and the wave energy can be converted into kinetic energy. In this paper, the power take-off system of "Sharp Eagle II" wave energy converter(the second generation of "Sharp Eagle") was studied, which adopts the hydraulic type power take-off system. The 0-1 power generation mode was applied in this system to make the "Sharp Eagle II" operate under various wave conditions. The principle of power generation was introduced in detail, and the power take-off system was simulated. Three groups of different movement period inputs were used to simulate three kinds of wave conditions, and the simulation results were obtained under three different working conditions. In addition, the prototype of "Sharp Eagle II" wave energy converter was tested on land and in real sea conditions. The experimental data have been collected, and the experimental data and simulation results were compared and validated. This work has laid a foundation for the design and application of the following "Sharp Eagle" series of devices.     

Dynamic Performance Analysis of the Tuned Heave Plate System for Semi-Submersible Platform

Logistical supply is costly for the deepwater oil and gas exploitation, thereby it is necessary to develop a novel power supply solution to improve the offshore structure’s self-holding capacity. The two-body point absorbers, as a renewable energy device, have achieved a rapid development. Heave plate is used to constrain the truss’s motion in the two-body point absorber, and the floater moves along the truss up and down. This two-body point absorber can be considered to be an essentially mass-spring-damper system. And it is well known that the heave plates have been widely used in the Spar platform to suppress the heave motions. So if the two-body point absorber can be modified to combine with offshore floating structures, this system can not only offer electric power to support operations or daily lives for the platform, but also control the large motions in the vertical plane. Following this concept, a novel tuned heave plate (THP) system is proposed for the conventional semi-submersible platform. In order to investigate the dynamic performances of the single THP, two experiments are conducted in this paper. First, the hydrodynamic coefficients of the heave plates are studied, and then the THP experiments are carried out to analyze its dynamic performance. It can be concluded that this THP is feasible and achieves the design objective.     

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.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Stochastic control of wave energy converters with constrained displacements for optimal power absorption

An semi-analytical solution is derived for the optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the displacement. At first the control force is derived during states, where the displacement constraint is active. This results in an open-loop control law dependent on the external wave load on the absorber. Next, the analytical solution for the optimal control in the unconstrained state is indicated, which turns out to be of the closed loop type with feedback from the present displacement and acceleration and from future velocities. The derived control law contains an undetermined constant, which is calibrated at the interface to the previous constrained state. The approach requires the estimation of the wave load during the constrained states, and the prediction of the future velocity response during unconstrained states. An algorithm has been devised in the paper for handling these problems. The theory has been validated against numerical solutions obtained by nonlinear programming.     

双浮子点吸收式波能转换装置参数研究

点吸收式波能转换装置是具有较好应用前景的一种波浪能开发利用装置,其参数设计直接影响到波浪能开发利用的可行性与有效性。作者针对青岛斋堂岛目标海域海况,通过数值模拟首先应用单因素敏感性分析法分析了双浮子点吸收式波能转换装置的结构尺寸、锚固形式、波流夹角、PTO阻尼、PTO刚度等参数对装置俘能功率的独立影响规律。之后考虑多参数的综合影响,通过运用稳健设计方法,以上述参数为控制因子并确定合理的变动水准,将俘能功率作为评价标准,选取合理的正交实验L矩阵,得到了不同参数组合情况下的装置俘能功率并进行统计分析。结果表明,浮子尺寸、PTO阻尼、波流夹角对装置俘能功率影响较大,而PTO刚度、锚链与铅垂线夹角、锚链与波浪在水平面内的夹角对俘能功率影响不明显。提出的参数研究方法可为其他海域点吸收式波能转换装置参数设计提供参考。     

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.