A methodology for production and cost assessment of a farm of wave energy converters

To generate a substantial amount of power, Wave Energy Converters (WECs) are arranged in several rows or in a ‘farm’. Both the power production and cost of a farm are lay-out dependent.In this paper, the wave power redistribution in and around three farm lay-outs in a near shore North Sea wave climate, is assessed numerically using a time-dependent mild-slope equation model. The modelling of the wave power redistribution is an efficient tool to assess the power production of a farm. Further, for each lay-out an optimal (low cost) submarine cable network is designed. The methodology to assess the power production and cost of a farm of WECs is applied to the Wave Dragon Wave Energy Converter (WD–WEC). The WD–WEC is a floating offshore converter of the overtopping type, which captures the water volume of overtopped waves in a basin above mean sea level and produces power when the water drains back to the sea through hydro turbines.It is observed that the cable cost is relatively small compared to the cost of the WD–WECs. As a result, WD–WECs should be installed in a lay-out to increase power production rather than decrease cable cost, taking spatial and safety considerations into account. WD–WECs arranged in a single line produce the highest amount of power, but require an available sea area with a large width (51 km). Installing a single line of WD–WECs in front of a farm of wind turbines increases the time window for accessing the wind farm (applied to Horns Rev II – significant wave height smaller than 1–2 m during 8 h at minimum) by 9–14%.     

Prototype testing of the wave energy converter wave dragon

The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power.In the period from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57×27 m wide and 237 tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world's first offshore wave energy converter.The prototype is fully equipped with hydro turbines and automatic control systems, and is instrumented in order to monitor power production, wave climate, forces in mooring lines, stresses in the structure and movements of the Wave Dragon.In the period May 2003 to January 2005 an extensive measuring program has been carried out, establishing the background for optimal design of the structure and regulation of the power take off system. Planning for deployment of a 4 MW power production unit in the Atlantic by 2007 is in progress.     

Numerical modeling of the effects of wave energy converter characteristics on nearshore wave conditions

Modeled nearshore wave propagation was investigated downstream of simulated wave energy converters (WECs) to evaluate overall near- and far-field effects of WEC arrays. Model sensitivity to WEC characteristics and WEC array deployment scenarios was evaluated using a modified version of an industry standard wave model, Simulating WAves Nearshore (SWAN), which allows the incorporation of device-specific WEC characteristics to specify obstacle transmission. The sensitivity study illustrated that WEC device type and subsequently its size directly resulted in wave height variations in the lee of the WEC array. Wave heights decreased up to 30% between modeled scenarios with and without WECs for large arrays (100 devices) of relatively sizable devices (26 m in diameter) with peak power generation near to the modeled incident wave height. Other WEC types resulted in less than 15% differences in modeled wave height with and without WECs, with lesser influence for WECs less than 10 m in diameter. Wave directions and periods were largely insensitive to changes in parameters. However, additional model parameterization and analysis are required to fully explore the model sensitivity of peak wave period and mean wave direction to the varying of the parameters.     

Measurements of overtopping flow time series on the Wave Dragon,wave energy converter

A study of overtopping flow series on the Wave Dragon prototype, a low crested device designed to maximise flow, in a real sea, is presented. This study aims to fill the gap in the literature on time series of flow overtopping low crested structures. By comparing to a simulated flow the characteristics of the overtopping flow are discussed and the simulation algorithm is tested. Measured data is shown from a storm build up in October 2006, from the Wave Dragon prototype situated in an inland sea in Northern Denmark. This wave energy converter extracts energy from the waves, by funnelling them to run-up a ramp and overtop into a reservoir. This water is stored at a higher level than the average sea surface, before being discharged through hydro turbines. The waves, device sea handling and overtopping flow are measured by pressure transducers ahead of, beneath and in the device. Comparisons of the distribution and correlation show that the measurements support the use of the algorithm for generating a simulated flow.     

On the park effect in arrays of oscillating wave energy converters

This paper aims to provide guidelines for designing the layout of arrays of oscillating Wave Energy Converters (WECs) based on a review of the literature of wave interactions and park effect in WEC arrays that has been published over the past 30 years.First, the fundamentals of wave energy absorption by oscillating bodies are summarised, and the principal differences between the park effect in arrays of wave energy converters and wind turbines are highlighted. Then, the numerical approaches commonly used to deal with WEC arrays are outlined briefly and their limitations are discussed. It is argued that, at present, only Boundary Element Methods (BEM) are capable of the appropriate analysis. Finally, previous work on wave interactions and park effect in WEC arrays is reviewed. Similar trends are found in these studies, which allow conclusions to be drawn regarding the significance of the park effect as a function of the number of WECs in the array and their spacing. Based on these conclusions, the following tentative guidelines are proposed:For small arrays of conventional devices (fewer than 10 devices of typical dimension 10–20 m) with usual layouts (regular or shifted grids with separating distance of order 100–200 m), the park effect appears to be negligible. For larger arrays (more than 10 devices), a negative park effect seems to be increasingly important with increasing number of rows (the lines of WECs perpendicular to the incident wave direction). Therefore, the number of rows should remain as small as possible, with a separating distance as large as possible. For arrays of non-conventional WECs (WECs of typical dimensions much larger than 10–20 m), no information has been found. However, trends similar to the previous cases could be expected, provided that aspect ratios are maintained.     

Wave electricity production in Italian offshore: A preliminary investigation

In this paper the feasibility of wave energy exploitation off the Italian coasts is investigated. At this aim, the energy production and the performance characteristics of three of the most promising and documented wave energy converters (AquaBuOY, Pelamis and Wave Dragon) are estimated for two of the most energetic Italian locations. The sites are Alghero, on the western coast of Sardinia and Mazara del Vallo, on the Sicily Strait and they have respectively an average annual wave power of 10.3 kW/m and 4 kW/m, and an available annual wave energy of 90 MWh/m and 35 MWh/m.The energy production of the hypothetical wave farms is calculated based on the performance matrices of the wave energy converters (WECs) and on 21 years of wave buoy records, covering the period from 1990 to 2011. The estimated capacity factors are low (between 4% and 9%) compared to the ones obtained for the same wave energy converters in other locations and are affected by a strong seasonal variability. This indicates that the considered WECs are oversized with respect to the local wave climate and that a more efficient energy conversion would be obtained if they were downscaled according to the typical wave height and period of the study sites. As a consequence of the optimization of the device scale, at Alghero the deployment of 1:2.5 AquaBuOY, Pelamis or Wave Dragon devices would result in capacity factors around 20% and in a quite constant energy production throughout the year. In fact, the size reduction of the wave energy converters allows to capture the energy of the small waves which would otherwise be lost with the original WECs.The results of the present work suggest that deploying classic wave energy converters in Italian seas would not be cost effective but if the devices could accommodate a proper downscaling, their performance in energy conversion would become economically attractive also for some Italian locations.     

Model predictive control of sea wave energy converters – Part II: The case of an array of devices

This paper addresses model predictive control (MPC) of highly-coupled clusters of sea wave energy converters (WECs). Since each WEC is not only a wave absorber but also a wave generator, the motion of each WEC can be affected by the waves generated by its adjacent WECs when they are close to each other. A distributed MPC strategy is developed to maximize the energy output of the whole array and guarantee the safe operation of all the WECs with a reasonable computational load. The system for an array is partitioned into subsystems and each subsystem is controlled by a local MPC controller. The local MPC controllers run cooperatively by transmitting information to each other. Within one sampling period, each MPC controller performs optimizations iteratively so that a global optimization for the whole array can be approximated. The computational burden for the whole array is also distributed to the local controllers. A numerical simulation demonstrates the efficacy of the proposed control strategy. For the WECs operating under constraints explored, it is found that the optimized power output is an increasing function of degree of WEC–WEC coupling. Increases in power of up to 20% were achieved using realistic ranges of parameters with respect to the uncoupled case.     

基于风电场海域海况的波能浮子阵列发电功率优化

[目的]为了响应国家集约用海,发展清洁能源,助力碳中和,对海上风电-波浪能装置多能融合模式进行初步分析,对波能浮子进行优化设计,以获得更高的功率输出。[方法]依据势流理论,对漂浮式风机平台-波能浮子阵列进行仿真计算,分析浮子的外形尺寸和固有周期对浮子的输出功率的影响。[结果]仿真结果表明：同一固有周期下,波能浮子越扁平,波能浮子阵列的总发电功率越大,且浮子的经济性差异很小。对于海况下,不同固有周期的波能浮子阵列经济性差异较大,因此要综合分析考虑。[结论]在已知海域海况条件下,可以通过对波能浮子固有周期和外形尺度进行优化设计,使波能浮子获得更高的功率输出,提高单位海域能量产出。     

An investigation of the impacts of climate change on wave energy generation: The Wave Hub,Cornwall, UK

In this paper a generic methodology is presented that allows the impacts of climate change on wave energy generation from a wave energy converter (WEC) to be quantified. The methodology is illustrated by application to the Wave Hub site off the coast of Cornwall, UK. Control and future wave climates were derived using wind fields output from a set of climate change experiments. Control wave conditions were generated from wind data between 1961 and 2000. Future wave conditions were generated using two IPCC wind scenarios from 2061 to 2100, corresponding to intermediate and low greenhouse gas emissions (IPCC scenarios A1B and B1 respectively). The quantitative comparison between future scenarios and the control condition shows that the available wave power will increase by 2–3% in the A1B scenario. In contrast, the available wave power in the B1 scenario will decrease by 1–3%, suggesting, somewhat paradoxically, that efforts to reduce greenhouse gas emissions may reduce the wave energy resource. Meanwhile, the WEC energy will yield decrease by 2–3% in both A1B and B1 scenarios, which is mainly due to the relatively low efficiency of energy extraction from steeper waves by the specific WEC considered. Although those changes are relatively small compared to the natural variability, they may have significance when considered over the lifetime of a wave energy farm. Analysis of downtime under low and high thresholds suggests that the distribution of wave heights at the Wave Hub will have a wider spread due to the impacts of climate change, resulting in longer periods of generation loss. Conversely, the estimation of future changes in joint wave height-period distribution provides indications on how the response and power matrices of WECs could be modified in order to maintain or improve energy extraction in the future.     

Wave energy potential along the western Portuguese coast

An assessment of nearshore wave energy resource along the Portuguese coast is presented, focusing on identify appropriate locations for testing and developing Wave Energy Converter (WEC) for commercial exploit. The analysis covers the whole west seaside, to which a partition defined by 7 linear sections parallel to the coastline at 50 m depth was considered. Available wave energy at each linear sector was calculated from nearshore wave parameters, using as input the offshore wave conditions provided by a 15-year ocean wind-wave model simulation and considering a simplified but well-established analytical procedure for shoreward wave transformation. Two alternative measures of the nearshore wave energy resource were considered, the standard omni-directional wave power density and the more restricted normally-directed wave energy flux.Offshore wave direction combine to shoreline orientation proved to be determinant on the evaluation of the wave energy resource in each section, since sectors of the shoreline directly facing the offshore annual average wave direction have limited reduction in available wave energy as compare to offshore values. Independently of the wave energy measured criteria used, the analysis suggests that the sector from Peniche to Nazaré is the more suitable location for nearshore wave energy exploitation, with annual wave energy around 200 MWh m⁻¹, closely followed by the adjacent sector from Nazaré to Figueira da Foz.     

Experimental study of the functionality of a semisubmersible wind turbine combined with flap-type Wave Energy Converters

In the present paper the functionality of the Semisubmersible wind energy and Flap-type wave energy Converter (SFC) is examined experimentally. In order to study the functionality of the SFC, the focus is on operational environmental conditions. SFC is a combined concept that utilizes offshore wind energy and ocean wave energy for power production. Details are presented as far as the physical modelling of the wind turbine with the use of a redesigned small-scale rotor and of the Power Take-Off mechanism of the Wave Energy Converters (WECs) with the use of a configuration that is based on a mechanical rotary damper. Tests with quasi-static excitation, motion decay, regular and irregular waves without and with wind that is uniform are conducted on an 1:50 scale physical model. The experimental data are compared with numerical predictions obtained by a fully coupled numerical model using Simo/Riflex tool. A good agreement is observed between experimental and numerical predictions. The combined operation of WECs doesn't affect the tension of mooring lines nor the acceleration of nacelle and the bending moment in tower's base. The produced power of the WECs of the SFC and consequently the functionality of the SFC is estimated.     

Increases in the average power output of wave energy converters using quiescent period predictive control

The potential of controlling wave energy converters, (WEC), by deterministic prediction of large damaging waves is introduced and shown to offer very substantial increases in the annual average power output of such devices. Results obtained for idealised WEC models show that the potential exists for this increase to be at least a factor of two. Numerical simulations of actual dynamical models for both point absorbers and directionally sensitive devices employing practical control strategies show that most of this potential can actually be realised. The control of large scale wave farms using quiescent period predictive control is likely to be most cost effective using master/slave WEC systems. To achieve the computational savings that will allow this strategy analytic approximations are required for the response of WECs with time varying coefficients, preliminary forms of these have also been introduced.     

Improving the assessment of wave energy resources by means of coupled wave-ocean numerical modeling

Sea waves energy represents a renewable and sustainable energy resource, that nevertheless needs to be further investigated to make it more cost-effective and economically appealing. A key step in the process of Wave Energy Converters (WEC) deployment is the energy resource assessment at a sea site either measured or obtained through numerical model analysis. In these kind of studies, some approximations are often introduced, especially in the early stages of the process, viz. waves are assumed propagating in deep waters without underneath ocean currents. These aspects are discussed and evaluated in the Adriatic Sea and its northern part (Gulf of Venice) using locally observed and modeled wave data. In particular, to account for a “state of the art” treatment of the Wave–Current Interaction (WCI) we have implemented the Simulating WAves Nearshore (SWAN) model and the Regional Ocean Modeling System (ROMS), fully coupled within the Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) system. COAWST has been applied to a computational grid covering the whole Adriatic Sea and off-line nested to a high-resolution grid in the Gulf of Venice. A 15-year long wave data set collected at the oceanographic tower “Acqua Alta”, located approximately 15 km off the Venice coast, has also been analyzed with the dual purpose of providing a reference to the model estimates and to locally assess the wave energy resource. By using COAWST, we have quantified for the first time to our best knowledge the importance of the WCI effect on wave power estimation. This can vary up to 30% neglecting the current effect. Results also suggest the Gulf of Venice as a suitable testing site for WECs, since it is characterized by periods of calm (optimal for safe installation and maintenance) alternating with severe storms, whose wave energy potentials are comparable to those ordinarily encountered in the energy production sites.     

Electricity generation from wave power in Canada

The performance of three different types of wave energy converters (WECs) is evaluated at hundreds of Canadian locations using wave activity data made available by the Marine Environmental Data Service of Canada. Two Atlantic and three Pacific locations are found where at least one of these devices operates with a capacity factor of greater than 20%, while also being located close to urban/industrial centers. The economics of a nominal 25 GWh wave power plant are investigated at these five locations and compared among the three WEC types using two indicators: the 25-year life-cycle cost, and the required price of electricity for a 10-year simple payback period. The lowest required electricity price for a 10-year payback is $0.089/kWh, and occurs at a location near the Hibernia Oil Platform using the AquaBuOY WEC. The highest annual capacity factor is 32.1%, which occurs near the Hibernia Oil Platform when using the WaveDragon WEC. The 25-year life-cycle cost evaluations suggest that wave power plants at locations near Ucluelet, St. John's, and the Hibernia Oil Platform could all be profitable using either the AquaBuOY or the WaveDragon if a price of electricity between $0.10 and $0.15/kWh can be secured, depending on location and device.     

Power performance of wind energy converters characterized as stochastic process: applications of the Langevin power curve

The power performance of a wind energy converter (WEC) commonly refers to the relation between the input source and the electrical output, i.e. the input wind speed u and the electrical power output P. The International Electrotechnical Commission defined a so‐called power curve P(u) that quantifies this relation. Recently, a novel approach was introduced based on the short‐time dynamical response of the WEC to high‐frequency wind fluctuations. The dynamical behavior of the WEC is quantified by a drift field and the corresponding Langevin power curve (LPC). We present three applications of our method to wind energy based on the LPC. The first application consists of testing the power performance of WECs using LIDAR wind measurements. We then extend this test to the monitoring of the WEC performance over time. Finally, we apply the LPC to a simulation model for a WEC as a tool to characterize its performance. These applications illustrate the flexibility of the LPC as a relevant tool for performance testing and monitoring. Copyright © 2011 John Wiley & Sons, Ltd.     

Two improvements to the dynamic wake meandering model: including the effects of atmospheric shear on wake turbulence and incorporating turbulence build‐up in a row of wind turbines

The dynamic wake meandering (DWM) model is an engineering wake model designed to physically model the wake deficit evolution and the unsteady meandering that occurs in wind turbine wakes. The present study aims at improving two features of the model:

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Observations of wind turbine wakes and surface roughness effects on wind flow variability

Wind data collected at nine meteorological towers at the Goodnoe Hills MOD-2 wind turbine site were analyzed to characterize the wind flow over the site both in the absence and presence of wind turbine wakes. Free-flow characteristics examined were the variability of wind speed and turbulence intensity across the site as a function of wind direction and surface roughness. The nine towers' data revealed that scattered areas of trees upwind of the site caused pronounced variations in the wind flow over the site. At two towers that were frequently downwind of an extensive grove of trees, up to 30% reductions in wind speed and a factor of 2 to 3 increase in turbulence intensity were measured. A substantial increase in the magnitude of the wind gusts, as well as a considerable decrease in the mean wind speed, was observed when a tower was downwind of the trees.Wind turbine wake characteristics analyzed included the average velocity deficits, wake turbulence, wake width, wake trajectory, vertical profile of the wake, and the stratification of wake properties as a function of the ambient wind speed and turbulence intensity. The wind turbine rotor disk spanned a height of 15 m to 107 m. The nine towers' data permitted a detailed analysis of the wake behavior at a height of 32 m at various downwind distances from 2 to 10 rotor diameters (D). The relationship between velocity deficit and downwind distance was surprisingly linear, with average maximum deficits ranging from 34% at 2 D to 7% at 10 D. Largest deficits were at low wind speeds and low turbulence intensities. Average wake widths were 2.8 D at a downwind distance of 10 D. Implications for turbine spacing are that, for a wind farm with a 10-D row separation, array losses would be significantly greater for a 2-D than a 3-D spacing because of incremental effects caused by overlapping wakes. Other interesting wake properties observed were the wake turbulence (which was greatest along the flanks of the wake). the vertical variation of deficits (which were greater below hub height than above), and the trajectory of the wake (which was essentially straight).     

The influence of heat on the 3D-transition of the von Kármán vortex street

The wake behind a horizontally mounted heated cylinder with circular cross-section is visualised using an electrochemical tin precipitation method. In the experiments Re_D and Ri_D, both based on main stream properties, were set to 117 and varied between 0 and 1.5, respectively. The wake becomes 3D from Ri_D≈0.3. For small Richardson values (Ri_D<1), the warm fluid is initially collected in the coherent vortex structures shed from the cylinder. Further downstream thermal plumes originate from these structures. For larger Richardson values (Ri_D>1), the upward buoyancy force seems to prevent the formation of the coherent vortex structures and the plumes are already formed close behind the cylinder. The spanwise positions at which the plumes originate, are determined by the occurrence of 3D flow structures at the rear end of the cylinder. The distance between these structures is typically 1.8D and independent of the Richardson number.