In-stream hydrokinetic technology has been under development for the past several decades. Most of the research and engineering has been related to device development and optimization, impacts to aquatic systems, and the development of particular sites. Unfortunately, little research has been funded to advance the understanding of a systems approach for in-stream hydrokinetic potential. Several publications provide an overview of the state of knowledge for in-stream hydrokinetics (e.g., Khan et al., 2009; Kosnik, 2008).
Hydropower in one form or another has been in use for over 2,000 years, beginning with the use of water wheels to power machinery and leading to today’s applications of hydropower from conventional dams to produce electricity (USBR, 2009). Hydropower can be classified by plant size (e.g., micro, mini, small, large); by the technology (e.g., impounded, pump storage, hydrokinetic), or by use in the energy sector to meet demand (e.g., peak-load, base-load). In general, hydropower generation broadly describes the process of converting potential or kinetic energy of stored or flowing water contained in rivers and streams into electricity. For any given stream segment (shown in Figure 6-1), the potential energy head Ep at any location is z1 + d1, where z is the distance from the datum to the streambed and d is the water depth. The kinetic energy head is defined by the velocity head at the section, v12/2g, where g is gravity, and the total energy head is the sum of potential and kinetic energy heads, E1 = z1 + d1 + v12/2g. The energy gradeline along a stream (EGL) is the graphical representation of total energy at any point along the stream length. As seen in Figure 6-1,
FIGURE 6-1 Stream flow energy definition. HGL is the hydraulic gradient line, which corresponds to the water surface line (WSL).
the loss of energy head (hL) long the stream is energy slope (also known as the friction slope) multiplied by distance, or , where the friction slope Sf is approximated by use of Manning’s equation, n is the Manning’s roughness coefficient, Rh is the hydraulic radius, and AL is the channel length.
Conventional impounded hydropower works by recovering energy that would have been lost due to friction in a free-flowing stream or river (Figure 6-2). Specifically, as water flows from the stream into the impounded reservoir, the velocity is reduced as the depth of water increases, reducing the velocity head and the associated friction loss. In a deep reservoir the velocity, and therefore the friction loss per unit length, approaches zero near the dam. Therefore, the total available energy head at the dam location is approximately equal to the potential energy head, Ep = z + d.
More recently, the potential for recovery of hydrokinetic energy in streams has attracted increasing attention. In-stream hydrokinetic energy is recovered by deploying a single turbine unit or an array of units in a free-flowing stream (see Figure 6-3 for centerline view of a turbine array along a river reach). It is notable that the water surface will continue to rise in the upstream direction along the array until a new equilibrium normal depth is achieved due to the impedance of the devices. The distance required to reach the new equilibrium depth is approximately the water depth times the bottom slope, so the new depth will not be reached if the array is shorter than this. This back effect is expected to propagate further upstream from the array field; its distance is dependent on the overall water surface rise at the array, which itself is dependent on the density of deployed turbine units.
Whether in a conventional or in-stream deployment, the turbine captures a swept area of the rotor and converts flowing water velocity into power. Hydrokinetic power density of free-flowing rivers and streams is proportional to the cube of the fluid velocity and is usually expressed in the following (or similar) form:
where P is the power, A is the cross-sectional area, p is the water density, Ce is an efficiency factor, and v is the water velocity. Ce is used to account for limiting factors that will impact the realizable total power extraction from a site, including cut-in/cut-out speeds (Figure 6-4), usable cross-sectional area (top, bottom, sides), and impacts to riverine environments. Estimates of the maximum extractable energy that minimizes environmental impact range from 10 to 20 percent of the naturally available physical energy flux (Black & Veatch Consulting, 2004; Bryden et al., 2004). Several in-stream hydrokinetic developers suggest using Ce = 0.3, which was also used by the in-stream assessment group (EPRI, 2012).
FIGURE 6-4 Turbine output versus flow velocity. SOURCE: Hagerman and Polagye, 2006.
One challenge with hydrokinetic power is that flow around a single device or an array becomes very three-dimensional and is not easily assessed with commonly used one-dimensional hydraulic analysis. Each turbine imparts resistance to the flow, resulting in a potential redistribution of high velocities to other portions of the channel as well as a small increase in water surface elevation, creating a backwater condition that extends upstream. To fully understand the flow redistribution and back effects, higher order (two- or three-dimensional) mathematical models or field testing is required.
Given that the power density varies with velocity cubed, power density can be readily calculated for a site once the velocity distribution is known. It has been noted (e.g., by Hagerman and Polagye, 2006) that the distribution rather than mean values of velocities must be used for the power density estimation, because the cube of the mean current velocity is not the same as the mean of the cubed current velocity.
The number and spacing of turbine units on the footprint of a project location have been estimated using turbine spacing across the channel with a 0.5D to 3D gap between turbines and a longitudinal spacing of 10D to 15D, where D is the turbine diameter.
The in-stream assessment group developed its analysis of the in-stream hydrokinetic energy resource by first examining the river reaches available in the United States. Using the NHD Plus1 suite of data sets, the assessment group identified stream networks in the contiguous United States with mean annual discharge greater than 1,000 cubic feet per second (cfs). The resource assessment group then used this set of stream networks and slope data available from NHD Plus to estimate the theoretical in-stream resource for each stream segment:
where y is the specific weight of water (weight per unit volume), Q is the mean annual discharge, and H is the vertical elevation change calculated as stream segment slope multiplied by length.
To estimate the technical resource, the group evaluated the following expression at five locations (four on the lower Mississippi River and one on the Kuskokwim River in Alaska), using a simplified geometry, for seven river slopes and seven discharges:
where ξ is the machine efficiency (assumed to be 0.3), p is the density of water, V is the velocity (modified to account for flow resistance effects of the turbine array deployment on the water depth), N is the number of turbines in the river segment, and Ar is the swept area of the turbine. These calculations developed device array configurations for the 5th percentile flow, assumed the average recovery factor across all discharges for a given river reach was equal to the recovery factor for the mean flow, and assumed that device diameter D equaled 80 percent of the average depth with lateral and longitudinal device spacing of 0.5D and 5D, respectively. The in-stream assessment group then used these five river sites to calculate a recovery factor, RF, defined as the ratio of technical to theoretical resource. A simple expression was then developed from the Mississippi sites to relate the RF to discharge and slope (although this expression has little dependency on slope), and this parameterized expression was used to estimate the technical resource for all stream segments. A similar approach was applied to Alaska; however, given the lack of river slope information, it relied upon the relationship of RF to discharge. The theoretical and technical resources were then summed for different areas and presented online in the National Renewable Energy Laboratory (NREL) River Atlas2 for each segment.
The committee benefited from presentations by the in-stream resource assessment group3,4,5,6,7 and also reviewed a July 2012 draft of the final report (EPRI, 2012). It is the committee’s opinion that the theoretical resource estimate is based on reasonable data, methodologies, and analysis; however, the estimate of technical resources is flawed by the RF
3 P. Jacobson, T. Ravens, and K. Cunningham, “Assessment of U.S. in-stream hydrokinetic energy resources,” Presentation to the committee on February 8, 2011.
4 P. Jacobson, T. Ravens, G. Scott, and K. Cunningham, Electric Power Research Institute, “Methodology and preliminary results for assessment of U.S. in-stream hydrokinetic energy resources,” Presentation to the committee on September 27, 2011.
5 P. Jacobson, T. Ravens, G. Scott, and K. Cunningham, Electric Power Research Institute, “Methodology and preliminary results for assessment of U.S. in-stream hydrokinetic energy resources,” Presentation to the committee on December 12, 2011.
6 P. Jacobson, Electric Power Research Institute, “Assessment and mapping of the riverine hydrokinetic energy resource in the continental United States,” Presentation to the committee on April 9, 2012.
7 Scott, G., Virginia Tech University, “Validation and GIS display of river in-stream resources,” Presentation to the committee on April 9, 2012.
approach described in the previous section and the omission of other important factors, most important being the statistical variation of stream discharge. Insufficient data were provided in the in-stream resource assessment group’s final report to reproduce the calculations of recovery factor for the stated example conditions. As noted earlier, Hagerman and Polagye (2006) assert that the distribution of velocities must be used for the power density estimation rather than the mean values, because the cube of the mean current velocity is not the same as the mean of the cubed current velocity. The committee encourages future efforts in in-stream resource assessment to estimate the distribution of technically recoverable resource across the range of flows at all locations. This is particularly important as rivers and streams exhibit large annual and interannual variation in flow. Future work could focus on developing an estimate of channel shape for each stream segment and then, using the flow statistics for each segment along with an assumed array deployment, directly calculating the technically recoverable resource based on equation 3 (above) over the range of expected flows.
Given the lack of existing deployments of in-stream hydrokinetic arrays as well as the proprietary nature of this industry, little or no field or laboratory data exist to validate the assessment group’s methodology. However, a number of checks could be completed with respect to the reasonableness of the approaches. For example, although considerable effort was expended to develop a methodology to estimate back effects using a modified Manning’s resistance coefficient to account for the resistance that a turbine array will impart on flowing water, limited information is reported with respect to evaluation of the practicality and reasonableness of applying this methodology at various stream conditions. A two- or three-dimensional computational model would be more appropriate to assess the flow resistance effects of the turbine on the flow. The validation effort would also have been stronger if it had focused on questions regarding RF, such as the group’s assertion that slope contributes little to RF. A more thorough assessment of both modified Manning’s coefficient and RF will be necessary to ascertain the validity of these approaches.
Estimate of In-Stream Power Potential
Overall, the in-stream resource assessment group estimates the theoretical resource to be 1,433 TWh/yr and the technically recoverable in-stream resource to be 101.2 TWh/yr. The technical resource is largest
in the Mississippi, Alaska, Pacific Northwest, Ohio, and Missouri hydrologic regions. These rivers alone account for 95.3 TWh/yr, or ∼95 percent of the estimated technically available resource. Given that the largest portion of the resource is estimated within these five hydrologic regions, further testing of the approach in these areas is needed. Also, it is noteworthy that the recovery factor for the hydrologic regions varies from a few percent to nearly 24 percent for the Lower Mississippi region, raising doubt about the effectiveness of the recovery factor approach.
As a simple estimate of RF’s upper bound, one can assume a dimensionless flow depth h and a unit height D (equal to 0.8 x h), and a spacing between units of 2D. For a rectangular portion of a channel with a width of 3D, the swept area of the machine is ∼0.5, the total flow area is 2.4, and the share of flow captured is ∼20 percent. Factoring in turbine efficiency (∼30%), lost area along sloping channel edges with depth less than D, lost flow area above the depth h when flows are above the minimum flow, and energy lost to friction along the longitudinal distance, the RF approaches 2-10 percent (arguably 5% or lower). The committee is concerned that RF is not necessarily defensible based on the above arguments.
Last, there are many limiting factors to be considered that will reduce the realizable in-stream hydrokinetic energy production. These factors include but are not limited to ice flows and freeze-up conditions, transmission issues, debris flows, potential impacts to aquatic species (electromagnetic stimuli, habitat, movement and entrainment issues), potential impact to sites with endangered species, suspended and bedload sediment transport, lateral stream migration, hydrodynamic loading during high flow events, navigation, recreation, wild and scenic designations, state and national parklands, and protected archeological sites. These considerations will need to be addressed to further estimate the practical resource that may be available.
After reviewing the in-stream resource assessment report, the online information database, and additional information presented by the assessment group during committee meetings, it is the committee’s opinion that the estimate of the theoretical resource is based upon a reasonable approach and provides an upper bound to the available resource; however, the estimate of the technical resource is flawed by the assessment group’s recovery factor approach and the omission of other important factors, most importantly the statistical variation of stream discharge. A more thorough assessment of both modified Manning’s coefficient and the recovery factor used by the in-stream assessment group is needed to ascertain the usefulness of these approaches. Further work
is required with respect to the approach to estimate the technically recoverable resource before it will have value as an estimate to guide in-stream hydrokinetic development.
Recommendation: Future work on the in-stream resource should focus on a more defensible estimate of the recovery factor, including directly calculating the technically recoverable resource by (1) developing an estimate of channel shape for each stream segment and (2) using flow statistics for each segment and an assumed array deployment. The five hydrologic regions that comprise the bulk of the identified in-stream resource should be tested further to assure the validity of the assessment methodologies. In addition, a two- or three-dimensional computational model should be used to evaluate the flow resistance effects of the turbine on the flow.