Power in ocean waves originates as wind energy that is transferred to the sea surface when wind blows over large areas of the ocean. The resulting wave field consists of a collection of waves at different frequencies traveling in various directions, typically characterized by a directional wave spectrum. These waves can travel efficiently away from the area of generation across the ocean to deliver their power to nearshore areas.
The theoretical resource estimate is a measure of how much energy flux is in the observed wave fields along the coasts. For the estimate of the theoretical resource, “wave power density” is usually characterized as power per length of wave crest; it represents all the energy crossing a vertical plane of unit width per unit time. This vertical plane is oriented along the wave crest and extends from the sea surface down to the sea-floor. To capture this orientation, wave power is expressed as a vector quantity (see Table 1-2), and accurate representation of its magnitude and direction requires the consideration of the full directional wave spectrum.
Because wave energy travels in a particular direction, care must be taken when interpreting maps that show wave power density as a function of location but do not indicate predominant wave directions. It also must be recognized that if the energy is removed by a wave energy device from the wave field at one location, less energy will necessarily be available in the shadow of the extraction device. It would not be expected that a second row of wave energy devices would perform the same as the first row of devices that the wave field encounters because the spacing between rows of typical wave extraction devices does not allow adequate
fetch to replenish the resource. This shadowing effect implies that one cannot estimate the theoretical resource as the sum of the wave power density over an area as one might do for solar energy. Note that the magnitude of this shadowing effect is likely to be highly dependent on the specific characteristics of the device (e.g., size, efficiency). Although there are some initial publications with rigorous analytical approaches for quantifying the effect of an arbitrary array of point absorber devices (e.g., Garnaud and Mei, 2010), shadowing effects due to actual devices are a topic of active research. The planning of any large-scale deployment of wave energy devices would require sophisticated, site-specific field and modeling analysis of the wave field and the devices’ interactions with the wave field. This step is essential to refine any estimate of theoretical wave resource into an estimate of the technical wave resource.
The wave resource assessment group from the Electric Power Research Institute (EPRI) and Virginia Tech was tasked by DOE with producing estimates of the potential wave resource in U.S. coastal waters. To estimate the theoretical wave resource, the assessment group utilized a hindcast of wave conditions that was assembled by the National Oceanic and Atmospheric Administration’s (NOAA’s) National Center for Environmental Prediction using WAVEWATCH III, a state-of-the-art global wave generation and propagation model. Although the model was recently expanded to introduce physical processes specific to intermediate and shallow water (dispersion and refraction), the version available at the time of the assessment was the deepwater version, restricting its validity in intermediate and shallow water. The accuracy of WAVEWATCH III predictions is relatively well outlined in the scientific literature; in particular, WAVEWATCH III is known to reproduce wave height quite well (Chawla et al., 2009). However, it was unclear to the committee how well the reconstructed spectra represented the observed spectra, especially because the spectral reconstruction was optimized only at deepwater stations. Model accuracy is questionable in water depth shallower than about 50 m.
The assessment group first addressed several potential issues related to the available hindcast (e.g., a data record of only 51 months and the lack of full spectral information at all grid points) and then generated parametric fits of wave frequency spectra for all points of interest. To produce maps of wave power density, it computed a sum of the power density associated with all spectral components at a given location, regardless of wave direction. This is equivalent to considering the wave energy flux (i.e., power density) impinging on a cylinder of unit diameter that extends over the entire water column. The total theoretical resource
was then computed by summation of these cylinders along an entire line of interest (such as a 50 m depth contour or a 50 nautical mile line).
The products of the wave resource assessment include a database of 51-month time series at 3-hour intervals of wave parameters that can be used to reconstruct the fitted frequency spectra, although directional spreading information is not available. In addition, the group provides maps of annual and monthly average wave conditions (such as wave power density, wave height, period, direction, shown in three-dimensional plots) in a geographic information system (GIS)1 presented by the National Renewable Energy Laboratory’s (NREL’s) Renewable Resource Data Center. Bulk numbers for the total available theoretical wave resource and the total technical resource for different regions and for the entire United States are presented in the assessment group’s written report (EPRI, 2011).
To produce an estimate of the technical wave resource, the assessment group adopted an approach based on analyzing the cumulative probability density function (PDF) of wave power converted by a wave-energy device of prescribed capacity as a function of wave height. For a given threshold operating condition (TOC) and maximum operating condition (MOC), the percentage of the wave power that can be recovered can be estimated as a function of the rated operating condition (ROC). Note that this approach considers several extraction filters (e.g., TOC, MOC, and ROC constraints) and simplifies or neglects others (e.g., efficiencies, device spacing). The group generated cumulative PDFs for sites along the U.S. coastline and estimated the technical wave resource using the TOC and MOC values specific to three devices (Archimedes Wave Swing, Pelamis, and Wave Dragon) for various ROC values.
Compared to the more rigorous approach taken to compute the theoretical resource, the technical resource estimate relies on considerably looser assumptions. In the report, many of the factors are bundled into a single “packing density” of power per kilometer of installed system and some simple assumptions about the range of conditions in which the installed system can operate. Inaccurate or overly optimistic assumptions in these evaluations could create misleading estimates of the technical resource. In fact, the numbers used by the wave assessment group indicate that the technical resource is between 30 percent and 90 percent of the theoretical resource, depending on location. These concerns are addressed in more detail below.
Methodology, Results, and Presentation
The committee benefited from three presentations by the wave resource assessment group2,3,4, and their final report (EPRI, 2011). The committee commented on the work of the assessment group on the basis of these materials and has identified concerns related to the suitability of the hindcast data set in shallow waters, the technique used to generate the aggregate theoretical resource, the lack of directional information, and the technology assumptions utilized for assessment of the total technical resource.
Shallow Water Bathymetry
At a resolution of 4 minutes globally, the WAVEWATCH III simulations cannot capture wave transformation effects due to bathymetric features over shorter spatial scales because the simulations cannot resolve such variability. However, these bathymetric effects are known to be important at depths shallower than approximately 50 m (Dean and Dalrymple, 1984). Shallow-water regions might be of significant interest to developers who seek to optimize the ratio of construction and operating costs to the expected extractable power (largely a function of cable cost/distance to the coast). The methodology used precludes providing site-specific information to such developers. Reliable site-specific information in shallow waters can only be produced using results from models with higher spatial resolution that include the consideration of shallow-water physics (e.g., shoaling, refraction, diffraction). The wave resource assessment group acknowledges that its results are not accurate in the shallower waters of the inner continental shelf, and as such the shallowest water depths analyzed are 50 m (or 20 m on the Atlantic coast, where the continental shelf is smoother and less steep). Areas where inaccuracies due to these bathymetric concerns are most prevalent are blanked out in the GIS. While these regions could be assessed in the future using a shallow-water model such as SWAN, the results of
2 P. Jacobson, Electric Power Research Institute, G. Hagerman, Virginia Tech, and G. Scott, National Renewable Electricity Laboratory, “Assessment and mapping of the U.S. wave energy resource,” Presentation to the committee on November 15, 2010.
3 G. Hagerman, Virginia Tech, and P. Jacobson, Electric Power Research Institute, “Meaning and value of U.S. wave energy resource assessments,” Presentation to the committee on February 8, 2011.
4 G. Hagerman, Virginia Tech, P. Jacobson, Electric Power Research Institute, and G. Scott, National Renewable Energy Laboratory, “Assessment and visualization of United States wave energy resource,” Presentation to the committee on September 27, 2011.
the present assessment are insufficient to initialize such a model because there is no available directional spectral information.
Validity of a Limited Dataset
An additional minor concern in the theoretical wave assessment is the limited statistical inference from the 51-month dataset. Although NREL conducted a “typicality” study to demonstrate the adequacy of the dataset, one could still argue whether the results of short time series are valid. A simpler approach could be to use confidence intervals to reflect the accuracy of the assessment. For example, when using a 20-year time series, the significant wave height representing a 50-year event on the East Coast is on the order of 8.5 m, with a 95 percent confidence interval between 7.5 and 9.5 m. This represents an expected theoretical power varying by a factor of 1.6 between the limits of the confidence interval; the mean value is accurate in a confidence interval of ±25 percent. Using a 51-month time series instead of 20 years significantly increases the range of the 95 percent confidence interval, although it could still be quantified.
Similarly, the occurrence of extreme events is not captured well in the 51-month time series, as acknowledged by the NREL validation group.5 As a result, the cumulative probability distribution curves might be less accurate for large waves. It is unclear how this affects the results, but an accurate evaluation of the confidence interval for extreme events will be needed to assess device survivability.
Scalar Power Density
A further concern related to the theoretical resource assessment is the use of the unit-circle approach. This approach has the potential to double-count a portion of the wave energy if the direction of the wave energy flux is not perpendicular to the line of interest or if there is significant wave reflection from the shore. This technique was the subject of criticism in the committee’s interim report (Appendix B). The assessment group responded to this point, and its final report correctly computes the wave-energy flux across lines parallel to the coast by integrating only the component of the wave energy flux vector that crosses the line (i.e., the normal component). It retains the results from the previous unit-circle approach in their report and shows that the line integral is 56-87 percent of the unit-circle estimate, depending on location (see Tables 2.16-2.19 in EPRI, 2011). Despite acknowledging the bias of the unit-circle approach for estimating
5 G. Scott, National Renewable Energy Laboratory. “Validation and display of wave energy resource estimates,” Presentation to the committee on February 8, 2010.
the total theoretical resource, the assessment group continued to use the summation of scalar power density at all unit circles rather than the perpendicular component of power density. Although this is consistent with various European wave resource assessments, it clearly overestimates the total theoretical resource.
In order to take into account the technical details of the wave extraction devices, the assessment group utilized the concept of recoverable power. While this concept is an interesting initial approach to the technically recoverable resource, it assesses only the available power to specific devices and should not be confused with the technical resource as defined in the committee’s conceptual framework. Recoverable power integrates the fundamental technical constraints based on wave frequency and wave height thresholds, as well as indirectly on the temporal variability, before loss in the mechanical and electrical power transformation. Hypothetical or selected devices are considered operational in given wave periods and significant wave height ranges, specific to the device’s characteristics.
A similar methodology was applied to the Energetech Oscillating Water Column in Rhode Island coastal waters (Grilli et al., 2004). By applying constraints including MOC and TOC as well as the observed temporal variability, an estimated recoverable technical power of 30 percent of the theoretical power was obtained. This is of comparable order of magnitude to the assessment group’s minimal packing density.
The committee agrees that the method provides a convenient correct bulk number of the recoverable power at an individual site but would like to strongly reiterate that (1) the method is a rough estimation and is therefore inaccurate and (2) the method does not represent the technically recoverable resource. The mechanical and electrical losses in the transformation processes and transmission significantly reduce the technical resource, typically to 15-25 percent of the recoverable power. Returning to the example above, the Energetech prototype would have had a technical power resource of just 4.5-7.5 percent of the incident wave’s theoretical power.
Capacity Packing Density
The group’s approach to recoverable power is highly dependent on the assumptions made in determining the devices’ rated power and density. Packing more devices perpendicular to the wave direction of propagation would ideally allow for the extraction of most of the power from the waves (the fraction not extracted by the first row of devices would
then be partially extracted by the second row, leaving a further reduced fraction to the third row, and so on). To estimate the fraction of recoverable power at a given point, the assessment group compared the power carried by the incident wave field to the estimated recoverable power assuming a priori a deployment of multiple devices, defined by their combination of rated power and density. This ad hoc approach prescribes such an array using a capacity packing density, specified as 10 kW, 15 kW, and 20 kW per meter. The capacity packing density is defined as “the maximum extractable power by the array of devices,” similar in concept to the rated power (maximum extractable power by a single device). The range of values chosen is based on characteristics of the Pelamis (Pelamis Wave Power) and Powerbuoy (Ocean Power Technologies) extraction devices.
Their results indicate that 29-93 percent of the theoretical resource could be captured. The assessment group assumed that the devices could be packed in a series of parallel rows perpendicular to the main incident wave direction. Such a packing process alters the wave field because of the extractive characteristics of the device and the interaction of the wave field with the device, and the quantification of those interactions and resulting wave field constitute an active field of research. A focus of this research is optimizing the device layout to maximize the fraction of power extracted by an array or multiple arrays of n devices compared to the power extracted by n independent devices. This ratio is known as the q factor and represents the interaction of the wave field with the specified device(s) (Borgarino, 2011). This q factor is not explicitly included in the group’s recoverable power estimate; however, its estimation could be implicit in the concept of capacity packing density.
One theoretical study on wave-device interaction modeled the Wave Dragon Energy Converter deployed in the highly energetic North Sea (Beels et al., 2009). It concluded that capturing 1 GW of power would require the deployment of either a 200-km-long single row of devices (5 kW/m) or a five-row staggered grid about 3 km wide and 150 km long (7 kW/m). Such capacity packing density values are significantly lower than those assumed by the assessment group. Furthermore, this result does not take into account that the recovered power must be transformed into electricity and then transmitted.
Figure 3-1 further clarifies the difference between the concepts of recoverable power and technical power. A wave energy facility will consist of many elements, such as the wave-motion absorber, the machinery to convert that motion to electrical energy, power conditioning, and power transmission. The wave-motion absorbing part of the device is unlikely to absorb more than a single-digit percentage of the incident wave energy for a typical point absorber (Falnes, 2007), but that limitation can be overcome by adding many devices, as described above. This is not
FIGURE 3-1 A comparison of the concepts of recoverable, technical, and practical power. The flowchart describes the filters adopted in each concept. TOC, MOC, and ROC stand for threshold operating condition, maximum operating condition, and rated operating condition.
necessarily cost effective but stays within the definition of the technical resource. However, all wave-energy conversion devices will have systems to convert energy from mechanical to electrical form and for electrical transmission needs. None of these systems are likely to operate at efficiencies much greater than 90 percent and will probably have more realistic efficiencies of 50-70 percent. This calls into question claims of wave energy facilities that capture 90 percent or more of the available energy. As emphasized in Figure 3-1, it is important to place these numbers in the appropriate framework.
The committee agreed that the assessed estimates of monthly or annual mean wave power were the primary metrics for validation. Inaccuracies in these estimates could result from two primary sources of error: (1) inaccuracies in the WAVEWATCH III simulations and (2) differences between the full and reconstructed wave spectra.
The NREL validation only examined average wave power estimates produced by the assessment group and did not address the validity of the spectral reconstruction.6 The committee found that the validation was generally lacking in rigor, especially given the paucity of available data. The 44 observational locations were insufficient relative to the gradients in power density shown in the assessment, with order of magnitude changes in power density between some locations without validation. More important, no skill metrics were given.
While little can be done to address this shortcoming in the near term, data from the Northeast Regional Association for Coastal Ocean Observing System,7 Scripps Institution of Oceanography’s Coastal Data Information Program buoys,8 and the network of the National Federation of Regional Associations for Coastal and Ocean Observing9 could be used to provide additional validation information in the future.
Perhaps more important, the NREL validation group calculated wave power using a simplified formulation that is valid only in deep water, while the wave resource assessment group used the full reconstructed spectrum for this estimate. Finally, the validation effort did not report any statistical measures that would quantify the agreement between observations and estimates, such as root-mean-square error values, R2 statistics, and the like.
The wave resource assessment, especially the GIS visualization, could prove useful to developers who are interested in identifying general regions for their particular wave energy conversion devices. However, the spatial resolution of the assessment is of necessity very coarse, and there are numerous extraction and practical filters that will likely dominate the actual development of marine and hydrokinetic resources. Site-specific analysis for wave-energy facilities will still be needed at candidate locations. Additional information about the potential temporal variability of electricity generation would also be needed for electricity system operators to integrate wave power into utility-scale electricity systems.
The theoretical wave resource assessment estimates are reasonable, especially for mapping wave power density, although the accepted unit-circle approach overestimates the aggregate total theoretical resource.
6 G. Scott, National Renewable Energy Laboratory. “Validation and display of wave energy resource estimates,” Presentation to the committee on February 8, 2010.
The estimates are limited by sparse data and the assumptions inherent in the WAVEWATCH III model. Most notably, the assessment is limited to deep-water locations (depths greater than 50 m on the U.S. West Coast and 20 m on the East Coast). While there has been a recent trend to envision wave energy extraction in deep water to avoid ecological impacts, there are several potential projects seeking shallow-water siting because it affords closer proximity to transmission lines and other logistical requirements. Devices may be placed in shallow-water areas because such siting also reduces construction and maintenance costs.
Recommendation: Any future site-specific studies in shallow water should be accompanied by a modeling effort that resolves the inner shelf bathymetric variability and accounts for the physical processes that dominate in shallow water (e.g., refraction, diffraction, shoaling, wave dissipation due to bottom friction and wave breaking).
The technical resource assessment is based on loose assumptions about how much average power is available from each kilometer of installed wave-energy conversion facility, indicating that nearly all of the available wave energy in some sites could be converted to electrical energy if enough wave-energy converters are installed. Since there will always be mechanical and electrical loss mechanisms, this seems unlikely. Conversion percentages from theoretical wave power to electricity on the grid are expected to be dramatically less than the 90 percent values that are reported as the recoverable resource. In addition, estimates of the current state of wave-energy technology are not based on proven devices.
Finally, although the optimal layout of wave farms designed to maximize wave power capture and minimize costs is still an open question, the footprint of the infrastructure required to recover 1 GW cannot be reduced to less than a row of devices more than 100 km long and parallel to the coast, given current levels of technology. Because of the high development and maintenance costs, low efficiency, and large footprint of wave converter technologies, such devices would be a sustainable option only for smaller-scale developments that are considerably less than 1 GW, ideally close to territories with limited demand, such as islands.