Fundamentals of Tidal Energy

At a basic level, the gravitational pull of the sun and the moon on the Earth's oceans produces a twice daily rise and fall in water depth at northern and southern latitudes (semi-diurnal tide). As the depth of the open ocean rises, water floods into estuaries and then, as the depth falls, ebbs back out. The relative declination between celestial bodies can also set up a once daily variation, such that successive high and low tides are not of the same strength (mixed, mainly semi-diurnal tide). In addition to these daily variations, there is a fortnightly variation dependent upon the relative alignment of the sun and the moon with the Earth. When their gravitational fields act in opposition, the amplitude of the tides and currents is weakest, and when they act in concert tides and currents are strongest. This cycle has a 14.8 day period, with weak tides referred to as 'neap tides' and strong tides as 'spring tides'. Finally, the relative separation between the earth, sun, and moon gives rise to a seasonal variation with the strongest annual tides occurring twice yearly around the equinoxes and weakest around the solstices. Therefore, the tides are both intermittent and variable.

Since the motion of the earth, moon, and sun are well characterized, and tidal energy is derived from these gravitational interactions, it is possible to predict the tides far in advance. Currents are predictable to the first order, though not as predictable as tides (Polagye et al. 2010). This is in contrast to wind energy, which derives from uneven heating of the earth's crust and is, therefore, as "predictable" as the weather. The tides exactly repeat on an 18.6 year cycle (the tidal epoch). Since these motions are periodic, the underlying structure of tides or currents may be represented as a superposition of harmonic functions, or constituents. Depending on the relative strength of the semidiurnal (twice daily) and diurnal (once daily) constituents, a tidal energy site may be classified into one of four regimes by its form factor, or Formhazl, (F) which is the ratio of the amplitudes of the diurnal (K1+O1) to the semidiurnal (M2+S2) constituents. The four classifications are described as follows:

  • Semidiurnal - two high and low waters each day of approximately the same height. (F: 0-0.25)
  • Mixed, mainly semidiurnal - two high and low waters each day, but with significant inequality in height and timing. (F: 0.25-1.5)
  • Mixed, mainly diurnal - either one high and low water each day or two high and low waters with significant inequality in the height and timing. (F: 1.25-3.0)
  • Diurnal - one high and low water each day of approximately the same height. (F>3.0)

Most potential hydrokinetic tidal energy sites have a semidiurnal or mixed, mainly diurnal regime.

While tidal currents ebb and flood around the world, hydrokinetic tidal energy requires extreme currents to generate cost-effective power. In oceanographic terms, currents of 1 m/s are exceptionally strong, but currents at the most promising hydrokinetic sites may regularly exceed 4 m/s. There are two mechanisms which can give rise to such currents and both are the result of a phase difference in the tide across relative constrictions.

The first is when a narrow channel connects two large bodies of water in which the tides are out of phase. The phase difference generates a driving head across the constriction. In this case, the water flowing through the channel is negligible in comparison to the volume of water in the adjacent bodies. Deception Pass, connecting Skagit Bay to the Strait of Juan de Fuca, is an example of this type of site in Washington.

The second is when a narrow channel connects one part of an embayment to another. In this case, frictional power dissipation across the channel gives rise to a phase difference, which generates a driving head. Coming full circle, the driving head leads to strong currents, which are the mechanism for frictional power dissipation. However, in this case, the water elevation landward of the channel is dependent on the volume of water passing through the channel. Admiralty Inlet, separating Puget Sound from the Strait of Juan de Fuca, and Tacoma Narrows, separating the South Sound from the Main Basin, are examples of this type of site in Washington.

Both cases require relatively narrow channels connecting large bodies of water (though the larger the exchange between these two bodies, the less severe the constriction must be to support tidal energy generation). By their nature, such constrictions are relatively small-scale topographic features. Therefore, strong tidal currents tend to be very localized, which is in contrast to wind or wave energy, where the resource is relatively uniform over a large area.

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Site Characteristics

Desirable tidal energy sites have a number of key characteristics, though the strength of the currents is only necessary requirement.

A common measure of the intensity of the hydrokinetic resource is kinetic power density (W/m2) which is given by:

In the above equation, is the density of seawater (nominally 1024 kg/m3) and u is the time-varying speed (m/s).

For the purposes of feasibility assessment, kinetic power density is often reported as an annual average. The minimum economic threshold for site development is around 1 kW/m2 and for outstanding sites the kinetic power density may exceed 5 kW/m2. While power density is a common measure of resource intensity, it is also important to account for large scale turbulence, which could place considerable stress on the device and support structure. In addition, currents are ideally bi-directional (180o degree difference between ebb and flood) with limited vertical shear. Further characterization metrics are discussed in Gooch et al. (2009).

A water depth of 30-40 m is optimal for device deployment, but depths up to 80 m can be accommodated by existing foundation technology. A level bedrock seabed is preferred, but it is possible to install turbines on other substrates (e.g. cobbles, consolidated sediments) or on minor slopes.

The power generated by turbines must be interconnected with the electrical grid. Transmission lines (115 kV) near a load center may be able to accept up to 100 MW of power from a tidal energy installation, but distribution lines (15 kV) may be able to accept less than 5 MW.

Ideally, tidal sites have few existing uses or are large enough to accommodate existing uses and tidal energy. Commercial shipping, fishing, and diving are all examples of existing uses which might conflict with tidal energy.

The environmental characteristics of a site are of tremendous interest to the public and regulatory agencies, but often difficult to quantify. In particular the noise or flow alterations related to turbine operation may trigger avoidance or aggregation behavior in fish and marine mammals. Since there are only a handful of device demonstrations presently operating around the world, these near-field effects has not yet been studied in detail. Tidal power extraction may also lead to changes in the far-field; that is, alter the estuary-wide tidal regime. This has broad implications for biological processes (e.g. sediment transport, dissolved oxygen), particularly when the ecosystem is already stressed.

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Devices

Only a brief overview of in-stream devices is given here. A descriptive database of tidal energy devices and projects is maintained by the United States Department of Energy. While there are a number of device variants, the leading designs have a horizontal axis; that is, the axis of rotation is along the same principle axis as the fluid flow. Like wind turbines, the motion of water over the blades generates a lifting force that acts to rotate the blades. An electrical generator converts this rotation to electricity, which is transmitted to the shore via a power cable. The axial force on the rotor is resisted by a support structure either embedded in the seabed (e.g. pile foundation) or held in place by its mass (gravity foundation). The support structure also serves to elevate the rotor out of the slowest region of the boundary layer. The designs of the blades and drive train (gearbox, generator) borrow heavily from the wind industry, and foundation technology is adapted from offshore oil and gas structures.

In contrast to wind turbines, which may be over 100 m in diameter, the largest proposed tidal turbines are no more than 20 m across. This reflects both the more limited depth of tidal channels and the larger stresses due to the relatively higher density of seawater (1024 kg/m3) compared to air (1.2 kg/m3). Most designs for utility-scale turbines call for a peak electrical output on the order of 1-2 MW per device. Smaller devices, which are more suitable for remote, distributed generation, are also being developed.

In order to prevent blade damage due to cavitation, the tip speed of the turbine rotor is generally restricted to 10-12 m/s. For utility-scale turbines, this limits the rate of blade rotation to around 10 RPM. In contrast, the propellers on large ships rotate at about 100 RPM. Research could allow for higher, more efficient, tip speed ratios, but this might also increase the hazard posed to fish and marine mammals.

The power curve for a hypothetical tidal turbine with blade pitch control is shown below with a constant efficiency of 50%, cut-in speed of 1 m/s, and rated speed of 2.5 m/s. Three operating states are possible.

  1. Below cut-in speed: The water speed is insufficient to rotate the blades and the turbine generates no power. Typical cut-in speeds are between 1 and 2 knots (0.5-1 m/s).
  2. Between cut-in and rated speed: The turbine extracts power in proportion to the kinetic power incident over its swept area . The constant of proportionality is the extraction efficiency. For variable pitch turbines this is roughly constant over a range of velocities.
  3. Above rated speed: Constant power is extracted from the flow by changing blade pitch with current speed.

The extracted power is related to the generated power by the balance of system efficiency, which includes the efficiency of the gearbox, generator, and power transmission back to shore.

Wind turbines have a fourth operating regime defined by a cut-out speed, above which the turbine blades are feathered to avoid damage during periods of extremely high winds. Since tidal currents are largely predictable, there is no tidal analogue to extreme weather.

Device utilization is quantified by the capacity factor, defined as the ratio of average power extracted to power extracted at rated speed. Feasibility studies indicate that the lowest cost of energy for tidal turbines would be achieved with capacity factors between 30 and 40% depending on the particulars of the tidal regime. Therefore, the selection of the rated speed is an economic decision.

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Key Issues

There are a number of key issues which must be resolved if hydrokinetic tidal energy is to be developed in an responsible manner. These include:

  • Uncertainty in the practically receoverable resource (balancing available power against competiting uses, maximum device density, and environmental impacts).
  • The effect of certain site-specific characteristics, such as turbulence and shear on device operation and survivability.
  • Cumulative environmental effects of large arrays, including disruption of natural circulatory processes and migration routes for fish and marine mammals.
  • Maximum packing density for devices, in order to make effective use of a localized resource.
  • Long-term survivability of devices in a marine environment, including reduced performance due to bio-fouling.

Several of these areas are being addressed by Center research.

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