Energy calculations

The energy available from barrage is dependent on the volume of water. The potential energy contained in a volume of water is:

E=1/2 Apgh²
where:
h is the vertical tidal range,
A is the horizontal area of the barrage basin,
ρ is the density of water = 1025 kg per cubic meter (seawater varies between 1021 and 1030 kg per cubic meter) and
g is the acceleration due to the Earth's gravity = 9.81 meters per second squared.

The factor half is due to the fact, that as the basin flows empty through the turbines, the hydraulic head over the dam reduces. The maximum head is only available at the moment of low water, assuming the high water level is still present in the basin.

Example calculation of tidal power generation

Assumptions:
Let us assume that the tidal range of tide at a particular place is 32 feet = 10 m (approx)
The surface of the tidal energy harnessing plant is 9 km² (3 km × 3 km)= 3000 m × 3000 m = 9 × 106 m²
Specific density of sea water = 1025.18 kg/m³

Mass of the water = volume of water × specific gravity
= (area × tidal range) of water × mass density
= (9 × 10⁶ m² × 10 m) × 1025.18 kg/m³
= 92 × 10⁹ kg (approx)

Potential energy content of the water in the basin at high tide = ½ × area × density × gravitational acceleration × tidal range squared
= ½ × 9 × 10⁶ m² × 1025 kg/m³ × 9.81 m/s² × (10 m)²
=4.5 × 1012 J (approx)

Now we have 2 high tides and 2 low tides every day. At low tide the potential energy is zero.
Therefore the total energy potential per day = Energy for a single high tide × 2
= 4.5 × 1012 J × 2
= 9 × 1012 J

Therefore, the mean power generation potential = Energy generation potential / time in 1 day
= 9 × 1012 J / 86400 s
= 104 MW

Assuming the power conversion efficiency to be 30%: The daily-average power generated = 104 MW * 30% / 100%
= 31 MW (approx)

A barrage is best placed in a location with very high-amplitude tides. Suitable locations are found in Russia, USA, Canada, Australia, Korea, the UK. Amplitudes of up to 17 m (56 ft) occur for example in the Bay of Fundy, where tidal resonance amplifies the tidal range.

Economics

Tidal barrage power schemes have a high capital cost and a very low running cost. As a result, a tidal power scheme may not produce returns for many years, and investors may be reluctant to participate in such projects.

Governments may be able to finance tidal barrage power, but many are unwilling to do so also due to the lag time before investment return and the high irreversible commitment. For example the energy policy of the United Kingdom recognizes the role of tidal energy and expresses the need for local councils to understand the broader national goals of renewable energy in approving tidal projects. The UK government itself appreciates the technical viability and siting options available, but has failed to provide meaningful incentives to move these goals forward.

Mathematical modelling of tidal schemes

In mathematical modelling of a scheme design, the basin is broken into segments, each maintaining its own set of variables. Time is advanced in steps. Every step, neighbouring segments influence each other and variables are updated.

The simplest type of model is the flat estuary model, in which the whole basin is represented by one segment. The surface of the basin is assumed to be flat, hence the name. This model gives rough results and is used to compare many designs at the start of the design process.

In these models, the basin is broken into large segments (1D), squares (2D) or cubes (3D). The complexity and accuracy increases with dimension.

Mathematical modelling produces quantitative information for a range of parameters, including:
Water levels (during operation, construction, extreme conditions, etc.)
Currents
Waves
Power output
Turbidity
Salinity
Sediment movements

Global environmental impact

A tidal power scheme is a long-term source of electricity. A proposal for the Severn Barrage, if built, has been projected to save 18 million tonnes of coal per year of operation. This decreases the output of greenhouse gases into the atmosphere.

If fossil fuel resources decline during the 21st century, as predicted by Hubbert peak theory, tidal power is one of the alternative sources of energy that will need to be developed to satisfy the human demand for energy.

Operating tidal power schemes

The first tidal power station was the Rance tidal power plant built over a period of 6 years from 1960 to 1966 at La Rance, France. It has 240 MW installed capacity.
The first tidal power site in North America is the Annapolis Royal Generating Station, Annapolis Royal, Nova Scotia, which opened in 1984 on an inlet of the Bay of Fundy. It has 18 MW installed capacity.
The first in-stream tidal current generator in North America (Race Rocks Tidal Power Demonstration Project) was installed at Race Rocks on southern Vancouver Island in September 2006. The next phase in the development of this tidal current generator will be in Nova Scotia.
A small project was built by the Soviet Union at Kislaya Guba on the Barents Sea. It has 0.5 MW installed capacity. In 2006 it was upgraded with 1.2MW experimental advanced orthogonal turbine.
Jindo Uldolmok Tidal Power Plant in South Korea is a tidal stream generation scheme planned to be expanded progressively to 90 MW of capacity by 2013. The first 1 MW was installed in May 2009.
1.2 MW SeaGen system became operational in late 2008 on Strangford Lough in Northern Ireland.