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).