08.b Boek sewtha.pdf

If we imagine extracting 10% of this incident energy, and if the conversion and transmission processes are 50% efficient, the average power delivered would be 5 kWh per day per person. This is a tentative first guess, made without specifying any technical

Figure 14.6. The average incoming power of lunar tidal waves crossing these two lines has been measured to be 250 GW. This raw power, shared between 60 million people, is 100 kWh per day per person.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

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details. Now let’s estimate the power that could be delivered by three specific solutions: tide farms, barrages, and offshore tidal lagoons.

Tidal stream farms One way to extract tidal energy would be to build tide farms, just like wind farms. The first such underwater windmill, or “tidal-stream” generator, to be connected to the grid was a “300 kW” turbine, installed in 2003 near the northerly city of Hammerfest, Norway. Detailed power production results have not been published, and no-one has yet built a tide farm with more than one turbine, so we’re going to have to rely on physics and guesswork to predict how much power tide farms could produce. Assuming that the rules for laying out a sensible tide farm are similar to those for wind farms, and that the efficiency of the tide turbines will be like that of the best wind turbines, table 14.7 shows the power of a tide farm for a few tidal currents. Given that tidal currents of 2 to 3 knots are common, there are many places around the British Isles where the power per unit area of tide farm would be 6 W/m2 or more. This power per unit area can be compared to our estimates for wind farms (2–3 W/m2 ) and for photovoltaic solar farms (5–10 W/m2 ). Tide power is not to be sneezed at! How would it add up, if we assume that there are no economic obstacles to the exploitation of tidal power at all the hot spots around the UK? Chapter G lists the flow speeds in the best areas around the UK, and estimates that 9 kWh/d per person could be extracted.

Barrages Tidal barrages are a proven technology. The famous barrage at La Rance in France, where the tidal range is a whopping 8 metres on average, has produced an average power of 60 MW since 1966. The tidal range in the Severn Estuary is also unusually large. At Cardiff the range is 11.3 m at spring tides, and 5.8 m at neaps. If a barrage were put across the mouth of the Severn Estuary (from Weston-super-Mare to Cardiff), it would make a 500 km2 tide-pool (figure 14.8). Notice how much bigger this pool is than the estuary at La Rance. What power could this tide-pool deliver, if we let the water in and out at the ideal times, generating on both the flood and the ebb? According to the theoretical numbers from table 14.4, when the range is 11.3 m, the average power contributed by the barrage (at 30 W/m2 ) would be at most 14.5 GW, or 5.8 kWh/d per person. When the range is 5.8 m, the average power contributed by the barrage (at 8 W/m2 ) would be at most 3.9 GW, or 1.6 kWh/d per person. These numbers assume that the water is let in in a single pulse at the peak of high tide, and let out in a single pulse at low tide. In practice, the in-flow and out-flow would be spread over a few hours, which would reduce the power delivered a little.

speed power density (m/s) (knots) (W/m2 ) 0.5 1 2 3 4 5

1 2 4 6 8 10

1 8 60 200 500 1000

Table 14.7. Tide farm power density (in watts per square metre of sea-floor) as a function of flow speed. (1 knot = 1 nautical mile per hour = 0.514 m/s.)

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

14 — Tide

The current proposals for the barrage will generate power in one direction only. This reduces the power delivered by another 50%. The engineers’ reports on the proposed Severn barrage say that, generating on the ebb alone, it would contribute 0.8 kWh/d per person on average. The barrage would also provide protection from flooding valued at about £120M per year.

Tidal lagoons Tidal lagoons are created by building walls in the sea; they can then be used like artificial estuaries. The required conditions for building lagoons are that the water must be shallow and the tidal range must be large. Economies of scale apply: big tidal lagoons make cheaper electricity than small ones. The two main locations for large tidal lagoons in Britain are the Wash on the east coast, and the waters off Blackpool on the west coast (figure 14.9). Smaller facilities could be built in north Wales, Lincolnshire, southwest Wales, and east Sussex. If two lagoons are built in one location, a neat trick can be used to boost the power delivered and to enable the lagoons to deliver power on demand at any time, independent of the state of the tide. One lagoon can be designated the “high” lagoon, and the other the “low” lagoon. At low tide, some power generated by the emptying high lagoon can be used to

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Figure 14.8. The Severn barrage proposals (bottom left), and Strangford Lough, Northern Ireland (top left), shown on the same scale as the barrage at La Rance (bottom right). The map shows two proposed locations for a Severn barrage. A barrage at Weston-super-Mare would deliver an average power of 2 GW (0.8 kWh/d per person). The outer alternative would deliver twice as much. There is a big tidal resource in Northern Ireland at Strangford Lough. Strangford Lough’s area is 150 km2 ; the tidal range in the Irish Sea outside is 4.5 m at springs and 1.5 m at neaps – sadly not as big as the range at La Rance or the Severn. The raw power of the natural tide-pool at Strangford Lough is roughly 150 MW, which, shared between the 1.7 million people of Northern Ireland, comes to 2 kWh/d per person. Strangford Lough is the location of the first grid-connected tidal stream generator in the UK.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

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pump water out of the low lagoon, making its level even lower than low water. The energy required to pump down the level of the low lagoon is then repaid with interest at high tide, when power is generated by letting water into the low lagoon. Similarly, extra water can be pumped into the high lagoon at high tide, using energy generated by the low lagoon. Whatever state the tide is in, one lagoon or the other would be able to generate power. Such a pair of tidal lagoons could also work as a pumped storage facility, storing excess energy from the electricity grid. The average power per unit area of tidal lagoons in British waters could be 4.5 W/m2 , so if tidal lagoons with a total area of 800 km2 were created (as indicated in figure 14.9), the power generated would be 1.5 kWh/d per person.

Beauties of tide Totting everything up, the barrage, the lagoons, and the tidal stream farms could deliver something like 11 kWh/d per person (figure 14.10). Tide power has never been used on an industrial scale in Britain, so it’s hard to know what economic and technical challenges will be raised as we build and maintain tide-turbines – corrosion, silt accumulation, entanglement with flotsam? But here are seven reasons for being excited about tidal power in the British Isles. 1. Tidal power is completely predictable; unlike wind and sun, tidal power is a renewable on which one could depend; it works day and night all year round; using tidal lagoons, energy can be stored so that power can be delivered on demand. 2. Successive high and low tides take about 12 hours to progress around the British Isles, so the strongest currents off Anglesey, Islay, Orkney and Dover occur at different times from each other; thus, together, a collection of tide farms could produce a more constant contribution to the electrical grid than one tide farm, albeit a contribution that wanders up and down with the phase of the moon. 3. Tidal power will last for millions of years. 4. It doesn’t require high-cost hardware, in contrast to solar photovoltaic power. 5.

Moreover, because the power density of a typical tidal flow is greater than the power density of a typical wind, a 1 MW tide turbine is smaller in size than a 1 MW wind turbine; perhaps tide turbines could therefore be cheaper than wind turbines. 6. Life below the waves is peaceful; there is no such thing as a freak tidal storm; so, unlike wind turbines, which require costly engineering to withstand rare windstorms, underwater tide turbines will not require big safety factors in their design. 7. Humans mostly live on the land, and they can’t see under the sea, so objections to the visual impact of tide turbines should be less strong than the objections to wind turbines.

Figure 14.9. Two tidal lagoons, each with an area of 400 km2 , one off Blackpool, and one in the Wash. The Severn estuary is also highlighted for comparison.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

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Mythconceptions Tidal power, while clean and green, should not be called renewable. Extracting power from the tides slows down the earth’s rotation. We definitely can’t use tidal power long-term. False. The natural tides already slow down the earth’s rotation. The natural rotational energy loss is roughly 3 TW (Shepherd, 2003). Thanks to natural tidal friction, each century, the day gets longer by 2.3 milliseconds. Many tidal energy extraction systems are just extracting energy that would have been lost anyway in friction. But even if we doubled the power extracted from the earth–moon system, tidal energy would still last more than a billion years.

Notes and further reading page no.

Tide: 11 kWh/d Wave: 4 kWh/d Deep offshore wind: 32 kWh/d

Food, farming, fertilizer: 15 kWh/d Gadgets: 5 Light: 4 kWh/d

82 The power of an artificial tide-pool. The power per unit area of a tide-pool is derived in Chapter G, p311. – Britain is already supplied with a natural tide-pool . . . known as the North Sea. I should not give the impression that the North Sea fills and empties just like a tide-pool on the English coast. The flows in the North Sea are more complex because the time taken for a bump in water level to propagate across the Sea is similar to the time between tides. Nevertheless, there are whopping tidal currents in and out of the North Sea, and within it too. 83 The total incoming power of lunar tidal waves crossing these lines has been measured to be 100 kWh per day per person. Source: Cartwright et al. (1980). For readers who like back-of-envelope models, Chapter G shows how to estimate this power from first principles.

Heating, cooling: 37 kWh/d

Jet flights: 30 kWh/d

84 La Rance generated 16 TWh over 30 years. That’s an average power of 60 MW. (Its peak power is 240 MW.) The tidal range is up to 13.5 m; the impounded area is 22 km2 ; the barrage 750 m long. Average power density: 2.7 W/m2 . Source: [6xrm5q]. 85 The engineers’ reports on the Severn barrage. . . say 17 TWh/year. (Taylor, 2002b). This (2 GW) corresponds to 5% of current UK total electricity consumption, on average.

Shallow offshore wind: 16 kWh/d Hydro: 1.5 kWh/d

Biomass: food, biofuel, wood, waste incin’n, landfill gas: 24 kWh/d

PV farm (200 m2/p): 50 kWh/d

PV, 10 m2/p: 5

Car: 40 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

86 Power per unit area of tidal lagoons could be 4.5 W/m2 . MacKay (2007a).

Figure 14.10. Tide.