Tidal Power Generation
A strange feature of Tidal Power is that everyone thinks it is a good idea, but few seem able to make it work (commercially).
There are a great number of grant-funded starter companies that research away for decades but never get to linking into the national 'grid'. One is reminded of a sardonic remark about anti-cancer research: that "there are as many people who live by cancer as die by cancer". Rather than give up a wonderful outdoor life on a Scottish island and return to university, they think up another plan and put in another research-grant application.
The exploitation of water to generate electricity is quite old. William Armstrong was using hydroelectricity to illuminate his house in Northumberland back in 1878, letting water flow out of his lake down an Archimedean screw. And H.J. Rogers began generating electricity on a grander scale at what is known as "the world's first hydroelectric power plant", at Appleton, Wisconsin, on 30 September, 1882. Countries like Norway, Switzerland and New Zealand generate nearly all their electricity by such schemes. But they all use fresh water falling under gravity, from a height (to which it was raised by solar evaporation). Tidal power is much scarcer.
There are two ways of describing the cost of hydroelectricity; (a) ignoring the initial capital costs (counting only maintenance), and (b) including the capital costs. The latter is more just, but it only becomes possible to calculate when the lifetime of the installation is known. Which may be why we are often told how cheap hydroelectricity is. Like all the renewables, the input energy, the 'fuel', is free. The ongoing cost involves only maintenance (oiling, painting, cleaning the filters). Thus, it is said [1] that:
"at US$ 0.05/kWh, hydroelectricity remains the lowest-cost source of electricity worldwide, according to a recent report by the International Renewable Energy Agency, entitled 'Renewable Power Generation Costs in 2017'."
Once built, the only costs are servicing and maintenance, for the fuel is free. But building is expensive. It has been calculated that to build a hydroelectric dam and install turbines costs around £4000 per kiloWatt of installed power, falling slightly with increasing size [2]. This means that, if the installation lasts 4,000 hours and we ignore maintenance, we are producing electricity at the cost of £1 per kWh unit. To get the cost down to 1p per unit, the life must be ≧ 400,000 hr, or 46 years.
Such lifetimes have been easily achieved with freshwater systems, and many exist around the world producing low cost electricity. What is it, then, that puts up the engineering costs of tidal power; perhaps the salt water and the stressful marine environment? Let us look at some examples, but first at why tidal power is so tempting.
The immense amount of energy in tides
Tidal flows contain two forms of energy: potential energy in the change in height, and kinetic energy in the movement of mass. Both depend linearly on the mass (m) of water involved.
Potential energy (E(p)) depends linearly on the height through which the water falls.
E(p) = mgh
(where g is the constant acceleration due to gravity, h is height in metres.)
Kinetic energy (E(k)) is represented by:
E(k) = ½ mv^2
and therefore on the square of the velocity (v). (Some [3,4] say on the cube of velocity! Perhaps they are applying the formula used by wind turbine engineers [5].) With tidal-stream generation there is little or no fall of mass, just the lateral momentum of the tide flowing past the turbine; like viscous and massive 'wind'.
Many people have noted the immense amount of kinetic energy involved in the tides that flow round many of the coasts in the world. Dragged round, of course, by the relatively sluggish rotation of the moon round the earth and the much faster rotation of the earth on its axis; for of course the earth rotates on its axis once in 24 hours (23.93 hours in sidereal time, for in our 'day' the earth rotates a tiny bit more than 360º, more like 361º), while the moon circumscribes the earth in 27.3 days.
The energy involved in the twice-daily flow of water through Cook Straight between the North and South Islands of New Zealand) is estimated [6] at 12 GWatt, more that enough for the whole of New Zealand. A couple of engineering firms have been eying it up for a decade, but no electricity has yet been made. Kaipara Harbour [6] in the north of the North Island of New Zealand is another promising site, as it fills and empties 7960 million cubic metres of sea water daily through a channel only 6 km wide.
(Why does the earth spin? And rotate round the sun for that matter; ditto the moon about the earth? These are presumed to be residual rotational energies possessed by the matter from which the solar system was formed. It is a baffling thought, but belief in this theory is bolstered by noting that nearly all the planets and moons spin in the same direction and roughly in a plane. Looking down on that plane from the 'north', they all spin anticlockwise (except Uranus and Venus). If you are wondering if these residual spins are gradually running down due to friction, as water rushes up and down our estuaries, the answer is 'yes they are, but not by very much'. According to Wikipedia, the length of our day has increased from 21.9 hours to 24 hours in the last 620 million years. As yet 'Man' has not increased, by a noticeable fraction, the frictional dissipation of rotational momentum. The tides will survive us, and our grandchildren.)
Sea water may impose problems,
Tidal power has been harnessed since the dark ages, driving costal water mills as water flowed into or out of tidal ponds. It is a little surprising that there are so few successes and so many failures in harnessing this energy for the generation of electricity. When it comes to sea water, extra problems seem to arise, like corrosion, and storm-damage.
Tidal Successes [6]
1. Rance River project in Brittany, France (Usine marémotrice de la Rance).
Construction took five years and was completed in 1966. In the following year a road was built across the barrage linking the towns of Dinard and Saint-Malo, and the output was connected to the national grid. The plant cost some €94.5 million (in Francs, of course) and, at an annual output of approximately 500 GWh, is said to have taken 20 years to pay for itself.
The cost of electricity production is currently quoted as "€0.12/kWh", but it is not clear what assumed lifetime goes into that calculation .
2. Sihwa Lake Barrage, South Korea.
This barrage (completed 2011) was built with the primary purpose of land reclamation. The cost (US$ 560 million) should be recouped in 10-11 years as the generated energy is 552 GWh per annum. (552 million units, at 10c per unit, is 55.2 million US$ per year.)
Tidal Failures [6]
The "world's first commercial-scale and grid-connected tidal stream generator" – by SeaGen in Strangford Lough, Northern Ireland, built 2008, and decommissioned in 2019, cost 12 M£ and generated a total of 11.6 GWh in its lifetime. As there are a million kiloWatthours (kWh) in a gigaWatthour (GWh), we see that the tidal stream electricity cost roughly £1 per kWh. This technology is still in the developmental stage.
A proposed tidal power project to be located in the Kaipara Harbour was approved in 2011 and put on hold in 2013. The project planned an ultimate size of 200MW at a cost of $600 million. Suppose it achieved 60MW for 100,000 hours (producing 6000 GWh) the produced electricity costs $0.1 per kWh, and would take 11.4 years to pay the up front capital cost. But the developer Crest Energy gave up and sold the project to Todd Energy.
Conclusions
Big tidal projects require deep pockets; maybe government investment.
It is sad that the successful Rance Barrage has not been followed up more energetically, though admittedly it was not till 1990 that it could be said unequivocally to be a success.
Tidal Stream generation has not yet become commercial, but should develop from its present experimental status.
References
[1] https://www.hydroreview.com/business-finance/hydropower-remains-the-lowest-cost-source-of-electricity-globally/
[2] https://www.renewablesfirst.co.uk/hydropower/hydropower-learning-centre/how-much-do-hydropower-systems-cost-to-build/
[3] https://en.wikipedia.org/wiki/Ocean_power_in_New_Zealand#Tidal_power
[4] http://large.stanford.edu/courses/2018/ph240/peterson2/
[5] https://www.engineeringtoolbox.com/wind-power-d_1214.html
[6] Wikipedia
