Ocean tides are a response to gravitational forces exerted by the Moon and the Sun. They include the rise and fall of the sea surface and the associated horizontal currents. The potential of tidal power for human use has long led to proposals that envision a barrage across the entrance of a bay that has a large range of height between low and high tides. A simple operating scheme is to release water trapped behind the barrage at high tide through turbines, generating power in a manner similar to a traditional hydropower facility.
In recent years, considerable attention has been paid to the direct exploitation of tidal currents using in-stream turbines rather than a barrage, in a manner similar to the way that wind turbines work. By way of scale comparison, a current v is equivalent to a hydraulic head of 0.5v2/g (where g is gravity), so that even a strong current of 3 m/s (∼10 ft/s) is equivalent to a hydraulic head of only 0.5 m (∼1.6 ft), which is considerably less head than a typical tidal range. Because the power produced by a turbine is related to the product of the head and the flow rate, it is clear that capturing tidal currents is considerably less effective than capturing the hydraulic head associated with even a modest tidal range. It is often claimed that in-stream turbines have less serious ecosystem impacts than barrages, though it is not at all clear that this is true for installations with the same average power output. In spite of these reservations, and because in-stream turbines could possibly be used in small-scale projects or in areas without a large tidal range, much work has gone into evaluating their potential.
The upper bound on the power from such an in-stream turbine is shown in Table 1.2 and is expressed by the Lanchester-Betz limit of 0.3pAv3, where p is water density, v is current speed, and A is the cross-sectional area across the blades (also referred to as the swept area).1 The power density equation shows that the turbine power is related to the cube of the current and demonstrates the advantage of deploying turbines in regions of strong current. As an example, if the cross-sectional area A is 100 m2 (∼ 1,075 ft2) and the current speed v is 3 m/s, the upper bound on the power from a turbine is 0.8 MW. The average power over a tidal cycle is, of course, less than that obtainable at the maximum current.
Several prototype turbines have been developed and tested in recent years, but tidal turbine technology has not yet reached convergence (as opposed to wind turbine technology, which has converged on a three-blade, horizontal-axis design). In the United States, there are multiple tidal turbine pilot projects under way, including the Verdant project in the East River in New York, which recently received approval from the Federal Energy Regulatory Commission (FERC); the Snohomish Public Utility project in Admiralty Inlet, Washington; and the Ocean Renewable Power Company (ORPC) project in Cobscook Bay, Maine, which has begun to deliver power to the grid. These projects demonstrate the variety of technology and the scales of power generation. In the East River, up to thirty 5-m diameter Verdant turbines will generate a nominal 35 kW each, using an open horizontal-axis design with variable yaw (Figure 2-1a). In Cobscook Bay, up to five 30-m-long ORPC turbines with a cross-flow helical design (Figure 2-1b) will have a total generation capacity of up to 300 kW (FERC, 2012). In Admiralty Inlet, two 6-m diameter OpenHydro turbines will have a nominal output of 150 kW of generation each, using a ducted horizontal-axis design with fixed pitch and yaw (Figure 2-1c). As with wind turbines or solar arrays, the actual average output will be much less than the nominal output (also known as “rated power” or “installed capacity") because the intensity of the resource varies greatly with time over a tidal cycle, even though it is predictable. Although site selection may be informed by the resource assessment reviewed below, it is expected that future projects and development will continue to require site-specific data collection.
1 The Lanchester-Betz limit is the maximum power which can be extracted by a turbine in an unbounded flow. If a turbine array occupies a significant fraction of the channel cross section, the flow is more constrained in going around the turbines than it would be in an unbounded flow. This partial blockage can cause an increase in the pressure on the turbines as well as force more flow through them, increasing the power, which ultimately approaches that from a barrage if the array blocks the entire channel cross section (Garrett and Cummins, 2007).
FIGURE 2-1 Turbine designs for U.S. tidal energy pilot projects. SOURCE: Verdant Power; Ocean Renewable Power Company; OpenHydro.
Another important consideration is the large-scale far-field back effect of an array of turbines. In addition to local flow disturbance around an individual turbine, drag associated with the presence of turbines will reduce large-scale flow. Open water currents will tend to avoid and flow around a region of extra drag associated with a turbine array, while the presence of turbines in confined channels will reduce the overall volume flux through the whole channel. The potential of a single turbine may be reasonably assessed using the natural flow, but the extra power from the addition of more turbines to an array will eventually be offset by the lower power due to reduction in flow from the turbines already present. The maximum power Pmax (the theoretical resource) that can be achieved can be assessed only after taking large-scale back effects into account.
The tidal resource assessment group conducted its tidal energy assessment study by developing a set of models to simulate all U.S. coastal regions and to estimate the maximum tidal energy based on predicted
tidal currents2,3 (Georgia Tech Research Corporation, 2011). The model used in the study was the three-dimensional Regional Ocean Modeling System (ROMS),4 which is often used in modeling studies of coastal oceanography and tidal circulation. The model was configured with eight vertical layers and set up for 52 model domains, with grid resolutions in the range of 350 m. Each domain included a section of coast or a particular bay, with offshore boundaries that included part of the adjacent continental shelf. The models were forced at their offshore boundaries by predicted tidal constituents, using the Advanced Circulation Model (ADCIRC) tidal database5 for the East Coast and Gulf of Mexico regions and the TPXO database6 for the West Coast region. River inflows and atmospheric forcing (such as wind) were not considered, and stratification and density-induced currents were not simulated. The landward model boundaries and bathymetry were defined using coastline data from the National Ocean Service of the National Oceanic and Atmospheric Administration (NOAA) and digital sounding data from NOAA’s National Geophysical Data Center. The effect of tidal flats was initially evaluated but not considered in the final model setup and runs.
The tidal resource assessment group calibrated the tidal models by adjusting the single friction coefficient to improve the comparison among model results, NOAA predictions of tidal elevation and currents, and limited observations of depth-averaged tidal currents. Model calibration parameters include harmonic constituents for tidal currents and water levels, maximum/minimum tidal currents, and high/low tides. An independent model validation was performed by the Oak Ridge National Laboratory (ORNL), which compared model predictions with observed tidal elevations and currents at selected stations that were not included in the calibration exercises7 (ORNL, 2011). Error statistics between model results and observed data were generated in this validation.
Model output was used (1) to provide an upper bound, Pmax , of the power available from tidal in-stream turbines for each bay and (2) to create a Web-based geographic information system (GIS) interface of quantities
2 K. Haas, Z. Defne, H.M. Fritz, and L. Jiang, Georgia Tech Savannah; S.P. French, Georgia Tech Atlanta; and B. Smith, Oak Ridge National Laboratory, “Assessment of energy production potential from tidal streams in the United States,” Presentation to the committee on November 15, 2010.
3 K. Haas, H.M. Fritz, and L. Jiang, Georgia Tech Savannah, “Assessment of tidal stream energy potential for the United States,” Presentation to the committee on February 8, 2011.
6 See http://www.esr.org/polar_tide_models/Model_TPXO71.html. Accessed June 21, 2011.
7 V.S. Neary, K. Stewart, and B. Smith, Oak Ridge National Laboratory, “Validation of tidal current resource assessment,” Presentation to the committee on February 8, 2011.
such as the local average power density (W/m8) in a vertical plane perpendicular to the average current at each model grid cell. Visualizations of average power density could, in principle, be used to estimate the power available from a single turbine or a few turbines (an array small enough not to have a significant back effect on the currents). The ArcView GIS database developed by the tidal resource assessment group was well designed and executed, and it allows for downloading of the tidal modeling results for further analysis by knowledgeable users. Based on the final assessment report, the assessment group produced estimates of the total theoretical power resource. However, this was done for complete turbine fences, which essentially act as barrages. The group did not assess the potential of more realistic deployments with fewer turbines, nor did they incorporate technology characteristics to estimate the technical resource base. It is clear, however, that the practical resource will be very much less than the theoretical resource.
Methodology and Validation
ROMS is a structured-grid, open-source coastal ocean model. It has performed well in the prediction of coastal circulation and tides in a large number of applications (e.g., Warner et al., 2005; Patchen, 2007; NOAA, 2011a). Finer grid resolution may be needed to represent bathymetry accurately in high tidal current regions. Increasing the grid resolution in local areas of a ROMS model often results in a significant increase of the total model grid size, owing to the structured-grid framework. In contrast, unstructured-grid models, which have greater flexibility for high grid resolution in complex waterways, could provide an alternative, especially for areas of complex geometry with high tidal energy (see, e.g., Patchen, 2007). An evaluation of the effect of grid resolution in the most promising high tidal energy regions would be a critical next step for future studies.
The location of the offshore boundary, partway out onto the continental shelf, is adequate for this effort, assuming that only a single turbine or a limited number of turbines is represented. Extension of the model boundary farther away to minimize the boundary effect (e.g., to the shelf edge [see, for example, Garrett and Greenberg, 1977]) may be necessary in the future if models are rerun with representations of a large turbine array that would be extensive enough to have a back effect on offshore tides. Estimates of available power may not be accurate without considering the effect of the locations of open boundaries. This question could be evaluated in future studies. Comparisons of model bathymetry to acoustic Doppler current profiler (ADCP) measurements at selected stations indicated
the bathymetric difference could be as large as 30 percent. Therefore, finer grid resolution and better accuracy of model bathymetry are critical for the improvement of model predictions.
According to the materials provided to the committee (Georgia Tech Research Corporation, 2011), the model tends to reproduce observed tidal elevations well. This is essential for the accurate prediction of the currents, but it may not be sufficient. It is possible for a model to reproduce tidal elevations well but still to have incorrect current patterns. Comparisons between predicted and observed currents indicated that errors associated with predicted currents may be 30 percent or more (ORNL, 2011). One of the main concerns surrounding the model calibration and validation efforts is the limited number of current observation stations used in the study—24 stations for model calibration and 15 for model validation (five stations are excluded because modeled and measured depths differ more than 30 percent), which means many of the 52 submodel domains do not contain any current data. Thus, the comparisons are more akin to spot-checking than actual validation, and comparisons are often poorest in the regions of most interest.
For example, at the site of the Snohomish Public Utility District pilot project in Admiralty Inlet, field data from the Northwest National Marine Renewable Energy Center shows a mean power density of 2 kW/m2, which can be compared to the mean power density of 0.8 kW/m2 given by the tidal resource assessment database. Field data also show a significant ebb dominance and directional asymmetry, in contrast to flood dominance and directional symmetry given by the resource maps.
The committee feels that efforts should have been focused on obtaining more observational data in the validation study rather than on producing a large metric of error statistics between model results and observations. It could be useful to consider more conventional model evaluation skill metrics used in the ocean modeling field (Warner et al., 2005; Patchen, 2007; NOAA, 2011a). Because power is related to the cube of current speed, errors of 100 percent or more occur in the prediction of tidal power density in many model regions. It is unclear whether model calibration through the adjustment of the single friction coefficient is more appropriate than adjustment or improvement of other factors, such as model bathymetry, grid resolution, or offshore boundary conditions. As noted by the tidal resource assessment group, errors in currents may be a consequence of inadequate model resolution rather than of an erroneous friction coefficient or uncertain forcing from the open boundary (ORNL, 2011).
Estimate of Available Tidal Power
One principal result of the tidal resource assessment is the maximum power, Pmax, extractable from the tidal currents in a bay or other locations with constricted flow. Pmax is the basis for the theoretical resource shown in the left column of Figure 1-1. Pmax would result from the use of a complete turbine fence across the entrance to the bay, but, owing to large-scale back effects, it is not the time-average of the horizontal kinetic energy flux, 0.5pv3, times the area of the vertical cross section of the entrance to the bay (e.g., Garrett and Cummins, 2007 and 2008). Instead, Pmax is given to a reasonable approximation by
where g is gravity, a is tidal amplitude (the height of high tide above mean sea level), and Qmax is the maximum volume flux into a bay in the natural state without turbines (Garrett and Cummins, 2008). Pmax increases with the tidal amplitude, a, and the surface area of the bay. For example, a tidal amplitude of 1 m (3.28 ft) would require more than 300 square kilometers (over 110 square miles) to produce 100 MW as an absolute maximum. This result is for a single tidal constituent. If the dominant tide is the twice-a-day lunar tide, Pmax is equivalent to the provision from each square meter of the bay’s surface of 0.3a2 watts if a is in meters. In an area with multiple tidal constituents, the potential power is greater than that available from the dominant tide alone (see, e.g., Garrett and Cummins, 2005). In the assessment, Pmax was based on all constituents that were extracted for each site. The result makes it clear why serious consideration of tidal power is generally limited to regions with a large tidal differential. As reviewed by Garrett and Cummins (2008), this formula for Pmax is also a reasonable approximation for the power available from a tidal fence across a channel that connects two large systems in which the tides are not significantly affected. In this case, a is the amplitude of the sinusoidal difference in tidal elevation between the two systems. In both situations, Pmax is the average of the power over the entire tidal cycle.
In the Pmax scenario, the fence of turbines is effectively acting as a barrage, so that Pmax is essentially the power available when all water entering a bay is forced to flow through the turbines. Pmax is thus likely to be a considerable overestimate of the practical extractable resource once other considerations, such as the extraction and socioeconomic filters shown in Figure 1.1, are taken into account. Reductions, even of the theoretical resource, can also occur in situations with more than one channel. In that case, installing turbines in one channel will tend to divert flow into other channels (Sutherland et al., 2007).
Lesser but still useful amounts of power could be obtained from turbines that are deployed in regions of strong current without greatly impeding a bay’s overall circulation. As mentioned earlier, a single turbine can extract no more than the Lanchester-Betz limit. A total power P requires a volume flux through the cross-sectional area of the turbines of P/(0.3pv2), so that even with a current speed of 3 m/s, the volume flux required for a power of 100 MW is nearly 40,000 m3/s (∼1.4 million ft3/s). Delivering such a flux would require a large number of turbines (for example, 120 turbines if each had a cross-sectional area of 100 m2, or 24 turbines of 25 m diameter if full-scale turbines were employed). Many more turbines would be needed for more typical smaller average currents. Deploying an extensive array of turbines would impact other marine resource uses, such as other sea-space uses and ecological services, and would necessitate extensive site-specific planning.
More importantly, a single turbine or a small number of turbines would not significantly affect preexisting tidal currents, but an array large enough to generate tens of megawatts would have near-field back effects that reduce the current that each individual turbine experiences. In theory, this back effect is allowed for in a complete tidal fence considered in the calculation of Pmax. However, other than for the case of a complete tidal fence, which results in estimates fairly close to the theoretical resource base, the tidal resource group’s assessment cannot be used to estimate directly the potential power of strong currents in specific bays if more than a few turbines are considered.
Nonetheless, an early group presentation to the committee (Haas et al., 2010) attempted to evaluate the technical resource based on Pk, the power that could be obtained if turbines of a specific swept area and efficiency were deployed at a specified spacing in regions satisfying specified minimum average current and minimum water-depth criteria, while assuming that any back effects on the currents would be small. This assumption is likely to be false, particularly if Pk is a significant fraction of Pmax. In that case, the turbines would have an effect on currents throughout the bay, and Pk would be an overestimate of the power available from the turbine array. If Pk is not a significant fraction of Pmax, circulation in other areas of the bay might not be greatly impacted, but local reductions in the currents would still be likely and could again cause Pk to be an overestimate. The group could consider choosing the lesser of Pk and Pmax as an estimate of the technical resource base. However, the committee notes that the tidal resource assessment group abandoned Pk and thereby any evaluation of the technical resource, because of the major uncertainties inherent in specifying parameters (personal communication to the committee from Kevin Haas, Georgia Institute of Technology, March 18, 2011).
Allowing for the back effects of an in-stream turbine array deployed in a limited region of a larger scale flow requires extensive further numerical modeling that was not undertaken in the present tidal resource assessment study and is in its early stages elsewhere (e.g., Shapiro, 2011). However, a theoretical study by Garrett and Cummins (2013) has examined the maximum power that could be obtained from an array of turbines in an otherwise uniform region of shallow water that is not confined by any lateral boundaries. The effect of the turbines is represented as a drag in addition to any natural friction. As the additional drag is increased, the power also increases at first, but the currents inside the turbine region decrease as the flow is diverted and, as in other situations, there is a point at which the extracted power starts to decrease. The maximum power obtainable from the turbine array depends strongly on the local fluid dynamics of the area of interest. Generally, for an array larger than a few kilometers in water shallower than a few tens of meters, the maximum obtainable power will be approximately half to three-quarters of the natural frictional dissipation of the undisturbed flow in the region containing the turbines. In deeper water, the natural friction coefficient in this result is replaced by twice the tidal frequency. For small arrays, the maximum power is approximately 0.7 times the energy flux incident on the vertical cross-sectional area of the array (Garrett and Cummins, 2013).
Estimates of the true available power must also take into account other uses of the coastal ocean and engineering challenges associated with corrosion, biofouling, and metal fatigue in the vigorous turbulence typically associated with strong tidal flows. This issue is discussed in greater detail in Chapter 7.
The assessment of the tidal resource assessment group is valuable for identifying geographic regions of interest for the further study of potential tidal power. However, although Pmax (suitably modified to allow for multiple tidal constituents) may be regarded as an upper bound to the theoretical resource, it is an overestimate of the technical resource, as it does not take turbine characteristics and efficiencies into account. More important, it is likely to be a very considerable overestimate of the practical resource as it assumes a complete fence of turbines across the entrance to a bay, an unlikely situation. Thus, Pmax overestimates what is realistically recoverable, and the group does not present a methodology for including the technological and other constraints necessary to estimate the technical and practical resource base.
The power density maps presented by the group are primarily applicable to single turbines or to a limited number of turbines that would not
result in major back effects on the currents. Additionally, errors of up to 30 percent for estimating tidal currents translate into potential errors of a factor of more than 2 for estimating potential power. Because the cost of energy for tidal arrays is very sensitive to resource power density, this magnitude of error would be quite significant from a project-planning standpoint. The limited number of validation locations and the short length of data periods used lead the committee to conclude that the model was not properly validated in all 52 model domains, at both spatial and temporal scales. Further, the committee is concerned about the potential for misuse of power density maps by end users, as calculating an aggregate number for the theoretical U.S. tidal energy resource is not possible from a grid summation of the horizontal kinetic power densities obtained using the model and GIS results. Summation across a single-channel cross section also does not give a correct estimate of the available power. Moreover, the values for the power across several channel cross sections cannot be added together.
The tidal resource assessment is likely to highlight regions of strong currents, but large uncertainties are included in its characterization of the resource. Given that errors of up to 30 percent in the estimated tidal currents translate into potential errors of more than a factor of 2 in the estimate of potential power, developers would have to perform further fieldwork and modeling, even for planning small projects with only a few turbines.
Recommendation: Follow-on work for key regions should take into account site-specific studies and existing data from other researchers. In regions where utility-scale power may be available, further modeling should include the representation of an extensive array of turbines in order to account for changes in the tidal and current flow regime at local and regional scales. For particularly large projects, the model domain extent should be expanded, probably to the edge of the continental shelf.
As discussed in Chapter 7, further work on tidal assessments might include additional filters to progress from theoretical resource estimates to estimates of the technical and practical resource bases. Given that DOE’s objective for the resource assessments is to produce estimates of the maximum practicable, extractable energy, it is clear that estimates of the practical resource base need to incorporate additional filters beyond those in the first column of the committee’s conceptual framework (Figure 1-1). To investigate this, one might consider a region of strong tidal currents in which there is also a large tidal range, such as Cook Inlet. Such an example could compare an in-stream tidal power scheme with a tidal
power scheme involving a barrage across the head of a bay or involving a lagoon enclosing a coastal area. The reasons for this include the following: (1) as noted above, even a current of 3 m/s is equivalent to a head of only 0.5 m, much less than would be available with a barrage or lagoon; (2) the construction of a lagoon should be much simpler than the installation of a large number of in-stream turbines in a region of strong currents; and (3) the overall environmental impact of a lagoon might be less than that of an array of turbines producing the same average power.