Uncertainty in wave energy resource assessment. Part 2: Variability and predictability

The uncertainty in estimates of the energy yield from a wave energy converter (WEC) is considered. The study is presented in two articles. The first article considered the accuracy of the historic data and the second article, presented here, considers the uncertainty which arises from variability in the wave climate. Mean wave conditions exhibit high levels of interannual variability. Moreover, many previous studies have demonstrated longer-term decadal changes in wave climate. The effect of interannual and climatic changes in wave climate on the predictability of long-term mean WEC power is examined for an area off the north coast of Scotland. In this location anomalies in mean WEC power are strongly correlated with the North Atlantic Oscillation (NAO) index. This link enables the results of many previous studies on the variability of the NAO and its sensitivity to climate change to be applied to WEC power levels. It is shown that the variability in 5, 10 and 20 year mean power levels is greater than if annual power anomalies were uncorrelated noise. It is also shown that the change in wave climate from anthropogenic climate change over the life time of a wave farm is likely to be small in comparison to the natural level of variability. Finally, it is shown that despite the uncertainty related to variability in the wave climate, improvements in the accuracy of historic data will improve the accuracy of predictions of future WEC yield.     

Wave resource assessment along the Cornish coast (UK) from a 23-year hindcast dataset validated against buoy measurements

Long-term knowledge of the wave climate of a potential wave energy site is essential for project planning and design, not only for an understanding of the resource variability, but also for the prediction of design wave conditions. The southwest region of the UK is at the forefront of the country's wave energy development, with two operational test sites. However, no detailed long-term resource assessment has yet been performed. This paper presents a long-term wave hindcast for southwest England, performed using the numerical wave model SWAN, with a particular focus on two energy device test facilities: ‘Wave Hub’ on the energetic and exposed north Cornwall coast, and ‘FaB Test’ on the more sheltered south coast. A high-resolution wave model suite, aimed at establishing nearshore wave hindcasts, is described and evaluated. The suite is run for a 23-year period, starting in 1989 and continuing to 2011. The hindcast is compared with measurement data and the results are analysed for the two test sites. Special attention is given to the implications of present hindcast errors and how the hindcast errors can be minimized.     

中国沿海风电施工窗口期及功效分析

海上风电建设施工难度大、风险高,成本极难控制,其中工期是最大的可变成本。适应平价上网时代海上风电降本增效要求,本研究基于实测数据比较ERA5、CCMPv2、NCEP这3种再分析风场在中国近海的质量,并对SWAN模式进行适应性修正,在此基础上根据25 a(1996—2020年)逐小时风浪数值后报数据对山东半岛南至广西海上风电桩基施工和风电机组安装窗口期及功效的时空分布进行评估,并结合关键海域具体风电场进行讨论。结果表明：ERA5数据的质量最优;修正SWAN模式后报波浪要素的准确性得到提升;可施工桩基及安装风电机组数据在研究海域具有显著的时空变化特征。     

Decadal variability of wave power production in the North-East Atlantic and North Sea for the M4 machine

We look at the variability of the power produced by the three-float M4 wave energy converter for locations in the North-East Atlantic and North Sea using the NORA10 hindcast data from 1958−2011. The aim is to investigate whether the produced power is also strongly affected by the climate variability (such as the North Atlantic Oscillations) in the winter, just as the ocean wave power resource as observed in previous studies. In this study, we demonstrate the use of proxy indices in combination with the climate indices to reconstruct a historic practical wave power climate from 1665−2005. We also conduct sensitivity studies to assess the changes in the practical wave power variability in response to perturbing the machine size, the power take-off coefficient, the response bandwidth and the power limit of the power take off. We find that the resultant temporal variation is still dominated by the climate variability. However, the overall variability important for power availability and energy supply economics is smaller than that of the ocean wave power resource because of the finite capture bandwidth of the M4 machine. The statistical methodology presented here is also potentially relevant to other wave energy converters in similar locations.     

Wave energy resources along the Hawaiian Island chain

Hawaii's access to the ocean and remoteness from fuel supplies has sparked an interest in ocean waves as a potential resource to meet the increasing demand for sustainable energy. The wave resources include swells from distant storms and year-round seas generated by trade winds passing through the islands. This study produces 10 years of hindcast data from a system of mesoscale atmospheric and spectral wave models to quantify the wind and wave climate as well as nearshore wave energy resources in Hawaii. A global WAVEWATCH III (WW3) model forced by surface winds from the Final Global Tropospheric Analysis (FNL) reproduces the swell and seas from the far field and a nested Hawaii WW3 model with high-resolution winds from the Weather Research Forecast (WRF) model capture the local wave processes. The Simulating Waves Nearshore (SWAN) model nested inside Hawaii WW3 provides data in coastal waters, where wave energy converters are being considered for deployment. The computed wave heights show good agreement with data from satellites and buoys. Bi-monthly median and percentile plots show persistent trade winds throughout the year with strong seasonal variation of the wave climate. The nearshore data shows modulation of the wave energy along the coastline due to the undulating volcanic island bathymetry and demonstrates its importance in selecting suitable sites for wave energy converters.     

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.     

Case study feasibility analysis of the Pelamis wave energy convertor in Ireland, Portugal and North America

The performance and economic viability of the Pelamis wave energy converter (WEC) has been investigated over a 20 year project time period using 2007 wave energy data from various global locations: Ireland, Portugal, USA and Canada. Previous reports assessing the Pelamis quote a disparate range of financial returns for the Pelamis, necessitating a comparative standardised assessment of wave energy economic indicators. An Excel model (NAVITAS) was created for this purpose which estimated the annual energy output of Pelamis for each location using wave height (H_s) and period (T_z) data, and produced financial results dependant on various input parameters. The economic indicators used for the analysis were cost of electricity (COE), net present value (NPV) and internal rate of return (IRR), modelled at a tariff rate of €0.20/kWh). Analysis of the wave energy data showed that the highest annual energy output (AEO) and capacity for the Pelamis was the Irish site, as expected. Portugal returned lower AOE similar to the lesser North American sites. Monthly energy output was highest in the winter, and was particularly evident in the Irish location. Moreover, the difference between the winter wave energy input and the Pelamis energy output for Ireland was also significant as indicated by the capture width, suggesting that Pelamis design was not efficiently capturing all the wave energy states present during that period. Modelling of COE for the various case study locations showed large variation in returns, depending on the number of WEC modelled and the initial cost input and learning curve. COE was highest when modelling single WEC in comparison to multiples, as well as when using 2004 initial costs in comparison to 2008 costs (at which time price of materials peaked). Ireland returned the lowest COE of €0.05/kWh modelling over 100 WEC at 2004 cost of materials, and €0.15/kWh at 2008 prices. Although favourable COE were recorded from some of the modelled scenarios, results indicated that NPV and IRR were not encouraging when using a €0.20/kWh tariff. It is recommended that a tariff rate of €0.30/kWh be considered for Ireland, and higher rates for other locations. In conclusion, Ireland had the most abundant wave energy output from the Pelamis. COE returns for Ireland were competitive for large number of WEC, even at peak costs, but it is recommended that careful analysis of NPV and IRR should be carried out for full economic assessment. Finally, a standardised method of COE reporting is recommended, using fixed WEC number or MW size, as well as standardised learning/production curves and initial costs, to facilitate confidence in investment decisions based on COE.     

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.     

Validation and uncertainty quantification of metocean models for assessing hurricane risk

A reliable metocean model, with its uncertainty quantified and its accuracy validated for conditions appropriate to assessing risk, is essential to understand the risk posed by hurricanes to offshore infrastructure such as offshore wind turbines. In this paper, three metocean models are considered, with the seastate predicted using the commercial software Mike 21, and the meteorological forcing defined by three conditions. The three conditions include (1) reanalysis data within and surrounding the hurricane, (2) predictions from the empirical Holland model within the hurricane and reanalysis data surrounding the hurricane, and (3) predictions from the empirical Holland model within the hurricane and wind‐free conditions surrounding the hurricane. The accuracy of the first metocean model is validated with (1) measurements of wind speed, wave height, wave period, and storm surge during 23 historical hurricanes from 1999 to 2012 and (2) a comparison to hindcast data from WaveWatch III, another numerical metocean model. The prediction performance of the second and third metocean models is then compared with that of the first to evaluate the impact of meteorological conditions on model predictions, as the third metocean model is necessary for risk analysis, where reanalysis data of meteorological conditions is not available. This study shows that the inconsistency between the modeling of meteorological conditions for risk assessment and for validation is influential for hurricanes with low maximum wind speeds, when model predictions are significantly better if the meteorological conditions surrounding the hurricane wind field are included. This study also shows that this inconsistency is effectively diminished when considering only events with high maximum wind speeds. Since high wind speeds are what is relevant to risk assessments, the third metocean model can be reasonably used to assess hurricane risk. Finally, the uncertainties, biases, and correlations of uncertainties in the model predictions for wind speed, wave height, wave period, and storm surge are quantified for the third metocean model, and a numerical example is constructed to illustrate the impact of including uncertainty on the assessment of risk to offshore infrastructure during hurricanes. The example demonstrates how uncertainty and correlation of uncertainty influence the size and shape of a 50‐year environmental contour of wind speed and wave height.     

鹰式二号波浪能装置的频域动态响应计算与负载优化设计

以鹰式二号波浪能发电装置为研究对象,基于捕获宽度达到最优为准则,通过对波浪中运动的装置建立频域运动方程,计算装置运动模态响应、获得最优负载阻尼和主要结构点受力等设计要素,并根据万山岛海域波浪条件开展能量转换系统负载设计、提供结构强度设计支持数据等。研究结果表明:在不同波况下装置获得捕获宽度对应的最优阻尼也不同;鹰式二号波浪能装置对于周期约2 s小周期波浪也具有良好的响应,捕获宽度达50%以上,在主要设计波况3~6 s最高捕获宽度达到300%,在万山岛海域波浪能试验场波况最高捕获宽度达到200%。     

Offshore and nearshore wave energy assessment around the Korean Peninsula

A wave resource assessment is presented for the region around the Korean peninsula. Offshore wave power was obtained from significant wave heights and peak periods, and wave directions hindcast for the period of 1979-2003. The spatial distributions for the seasonal and annual averaged wave power were obtained on a 1/6° grid covering the longitudes of 117-143°E and latitudes of 20-50°N. The highest monthly averaged wave power (25 kW/m) was observed on the southwestern side of the peninsula in winter. In order to obtain the wave power around Hongdo, numerical simulations were performed with respect to the monthly averaged waves. The correlation between the significant wave height and energy period was considered to adjust the nearshore wave power obtained by the numerical simulation. The correction procedure was validated from comparing the simulated data with wave buoy data.     

Evaluating winds and vertical wind shear from Weather Research and Forecasting model forecasts using seven planetary boundary layer schemes

The existence of vertical wind shear in the atmosphere close to the ground requires that wind resource assessment and prediction with numerical weather prediction (NWP) models use wind forecasts at levels within the full rotor span of modern large wind turbines. The performance of NWP models regarding wind energy at these levels partly depends on the formulation and implementation of planetary boundary layer (PBL) parameterizations in these models. This study evaluates wind speeds and vertical wind shears simulated by the Weather Research and Forecasting model using seven sets of simulations with different PBL parameterizations at one coastal site over western Denmark. The evaluation focuses on determining which PBL parameterization performs best for wind energy forecasting, and presenting a validation methodology that takes into account wind speed at different heights. Winds speeds at heights ranging from 10 to 160 m, wind shears, temperatures and surface turbulent fluxes from seven sets of hindcasts are evaluated against observations at Høvsøre, Denmark. The ability of these hindcast sets to simulate mean wind speeds, wind shear, and their time variability strongly depends on atmospheric static stability. Wind speed hindcasts using the Yonsei University PBL scheme compared best with observations during unstable atmospheric conditions, whereas the Asymmetric Convective Model version 2 PBL scheme did so during near‐stable and neutral conditions, and the Mellor–Yamada–Janjic PBL scheme prevailed during stable and very stable conditions. The evaluation of the simulated wind speed errors and how these vary with height clearly indicates that for wind power forecasting and wind resource assessment, validation against 10 m wind speeds alone is not sufficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Assessing sustainable forest biomass potential and bioenergy implications for the northern Lake States region,USA

Forestlands in the United States have tremendous potential for providing feedstocks necessary to meet emerging renewable energy standards. The Lake States region is one area recognized for its high potential of supplying forest-derived biomass; however, the long-term availability of roundwood harvests and associated residues from this region has not been fully explored. Better distribution and temporal availability estimates are needed to formulate emerging state policies regarding renewable energy development. We used a novel predictive methodology to quantify sustainable biomass availability and likely harvest levels over a 100-year period in the Lake States region. USDA Forest Inventory and Analysis estimates of timberland were combined with published growth and yield models, and historic harvest data using the Forest Age Class Change Simulator (FACCS) to generate availability estimates. Monte-Carlo simulation was used to develop probability distributions of biomass harvests and to incorporate the uncertainty of future harvest levels. Our results indicate that 11.27–15.71 Mt y⁻¹ dry roundwood could be sustainably harvested from the Lake States. Assuming 65% collection rate, 1.87–2.62 Mt y⁻¹ residue could be removed, which if substituted for coal would generate 2.12–2.99 GW h of electricity on equivalent energy basis while reducing GHG (CO₂e) emission by 1.91–2.69 Mt annually. In addition to promoting energy security and reducing GHG emissions, forest residues for energy may create additional revenues and employment opportunities in a region historically dependent on forest-based industries.     

Adaptability of a generic wave energy converter to different climate conditions

This study evaluates the influence of wave climate tunability on the performance of a generic Wave Energy Converter (WEC) for different climate scenarios. The generic WEC is assumed to be composed of an array of heaving, floating cylinders. In this study, two natural periods for the cylinders of 4 s and 8 s (typical of enclosed seas and the mean Atlantic swell, respectively) and a location-tunable cylinder are considered to evaluate the influence of tuning on the power performance of the cylinder. The WEC power matrix is computed using a frequency domain model, and the performance of the WEC is evaluated along the global coasts; the met-ocean data originated from the global reanalysis database (GOW) from Reguero et al. (2012). The performance of the WEC is evaluated using two parameters: the capture width ratio (CWR), which evaluates the efficiency of the converter at each location, and the kW/Ton (KWT) parameter, which evaluates the efficiency of the converter using “economic” terms. Tuning a converter for each location displayed a positive CWR; however, the KWT was low after WEC tuning because of the weight of the structures required to tune the converter that experiences high peak periods.     

Variability and uncertainty of wind power in the California electric power system

The California generation fleet manages the existing variability and uncertainty in the demand for electric power (load). When wind power is added, the dispatchable generators manage the variability and uncertainty of the net load (load minus wind power). The variability and uncertainty of the load and the net load are compared when 8790 MW of wind power are added to the California power system, a level expected when California achieves its 33% renewable portfolio standard, using a data set of 26,296 h of synchronous historic load and modeled historic wind power output. Variability was calculated as the rate of change in power generated by wind farms or consumed by the load from 1 h to the next (MW/h). Uncertainty was calculated as the 1 h ahead forecast error [MW] of the wind power or of the load. The data show that wind power adds no additional variability than is already present in the load variability. However, wind power adds additional uncertainty through increased forecast errors in the net load compared with the load. Forecast errors in the net load increase 18.7% for negative forecast errors (actual less than forecast) and 5.4% for positive forecast errors (actual greater than forecast). The increase in negative forecast errors occurs only during the afternoon hours when negative load forecasts and positive wind forecasts are strongly correlated. Managing the integration of wind power in the California power system should focus on reducing wind power forecast uncertainty for wind ramp ups during the afternoon hours. Copyright © 2013 John Wiley & Sons, Ltd.     

The stochastic seasonal behavior of energy commodity convenience yields

This paper contributes to the commodity pricing literature by consistently modeling the convenience yield with its empirically observed properties. Specifically, in this paper, we show how a four-factor model for the stochastic behavior of commodity prices, with two long- and short-term factors and two additional seasonal factors, may accommodate some of the most important empirically observed characteristics of commodity convenience yields, such as the mean reversion and stochastic seasonality. Based on this evidence, a theoretical model is presented and estimated to characterize the commodity convenience yield dynamics that are consistent with previous findings. We also show that commodity price seasonality is better estimated through convenience yields than through futures prices.     

点源影响下的SWAT模型非点源负荷核定方法

在多参数模型应用中,单纯以控制断面资料为标准进行校核易导致模型参数的不确定性,而估算点源和实际点源输入的误差将进一步加大此不确定性。为解决点源影响下流域污染负荷核定问题,提出采用断面水质校核与流域输出系数评价相结合的方法进行SWAT模型的率定和验证,并将其应用于鞍山市南沙河流域污染负荷的模拟中。结果表明,南沙河断面水质模拟结果符合污染物质输出规律,不同土地利用类型的输出系数计算结果合理,可见SWAT模型在以点源污染为主的流域同样具有较好的适用性。     

Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of Wave Dragon wave energy converters

Time-dependent mild-slope equations have been extensively used to compute wave transformations near coastal and offshore structures for more than 20 years. Recently the wave absorption characteristics of a Wave Energy Converter (abbreviated as WEC) of the overtopping type have been implemented in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus the incident wave power towards a ramp. The focussed waves run up the ramp and overtop in a water reservoir above mean sea level. The obtained potential energy is converted into electricity when the stored water drains back to the sea through hydro turbines. The wave reflectors and the main body (ramp and reservoir) are simulated as porous structures, exhibiting the same reflection, respectively absorption characteristics as obtained for the prototype Wave Dragon WEC. The wake effects behind a single Wave Dragon WEC are studied in detail for uni- and multidirectional waves. The shadow zone indicating the wake effect is decreasing with increasing directional spreading. The wake in the lee of a farm of five Wave Dragon WECs, installed in a staggered grid (3 WECs in the first row and 2 WECs in the second row), is calculated for three in-between distances of respectively D, 2D and 3D, with D the distance between the tips of the wave reflectors of a single WEC. As a result, a farm of five Wave Dragon WECs installed in a staggered grid with an in-between distance of 2D is preferred, when taking cost and spatial considerations into account.     

Numerical simulation of a submerged cylindrical wave energy converter

In this study, a numerical model based on the complete solution of the Navier–Stokes equations is proposed to predict the behavior of the submerged circular cylinder wave energy converter (WEC) subjected to highly nonlinear incident waves. The solution is obtained using a control volume approach in conjunction with the fast-fictitious-domain-method for treating the solid objects. To validate the model, the numerical results are compared with the available analytical and experimental data in various scenarios where good agreements are observed. First, the free vibrations of a solid object in different non-dimensional damping ratios and the free decay of a heaving circular cylinder on the free surface of a still water are simulated. Next, the wave energy absorption efficiency of a circular cylinder WEC calculated from the model is compared with that of the available experiments in similar conditions. The results show that tuning the converter based on the linear theory is not satisfactory when subjected to steep incident waves while the numerical wave tank (NWT) developed in the current study can be effectively employed in order to tune the converter in such conditions. The current NWT is able to predict the wave-body interactions as long as the turbulence phenomena are not important which covers a wide range of Reynolds and Keulegan-Carpenter numbers.