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).