Energy and Human Ambitions on a Finite Planet, 2021a

16 Small Players 281
divide the energy available by the time over which we let out the water:
nominally 6 hours. 20 Collecting it all, we have:
20: Six hours is a typical time between high
tide <strong>and</strong> the next low tide.
P ε ΔE
Δt εmgh 2
Δt
ερAgh2 , (16.2)
2Δt
where g ≈ 10 m/s 2 is the acceleration due to gravity <strong>and</strong> ε is the efficiency
of converting gravitational energy into electrical energy.
Example 16.2.1 The Rance tidal capture station in France has a capture
area of A 22.5 km 2 , <strong>and</strong> a height capacity of 8 m. If operating off
of a 7 m high tide <strong>and</strong> draining for 6 hours, what is the expected
power delivered at an efficiency of 90% (as is typical for hydroelectric
power)?
Expressing A in square meters yields 22.5 × 10 6 m 2 . The time is
21,600 seconds, leading to a calculated value of 230 MW.
Only two large tidal facilities operate in the world today: Rance in France
(Example 16.2.1) has a rated capacity of 240 MW, <strong>and</strong> produces an average
of 57 MW. Thus the capacity factor is about 24% due to the fact that it
can only generate tidal power half the time 21 <strong>and</strong> not all high tides are at
the full design height. The h 2 in Eq. 16.2 indicates particular sensitivity
to height—due to the double-whammy that lower height means less
trapped mass <strong>and</strong> lower pressure head.
21: It has to spend half the time letting
water back in as the tide flows.
The other facility is Sihwa Lake in South Korea, a 254 MW facility that
came online in 2011. Much like Rance, <strong>and</strong> for the same reasons, its
capacity factor is 25%, averaging 63 MW. Its basin is 30 km 2 <strong>and</strong> has
similar operating height as the French installation. The Sihwa Lake
facility cost $560 million to build, making it $9 per average Watt of
delivered power. This puts it roughly in line with the cost of nuclear
power (page 256), <strong>and</strong> a little higher than utility-scale PV, currently.
Two other large tidal stations in the 300–400 MW capacity range are in
the works for the UK <strong>and</strong> Scotl<strong>and</strong>. But it’s not something that works
well everywhere: best suited for areas that have large tidal swings <strong>and</strong>
large inlets having narrow mouths that are easy to dam. It’s a niche
player now <strong>and</strong> always will be. After all, the 3 TW global budget for
tidal energy suggests that it is not an energy jackpot.
16.3 Ocean Currents
Steady currents throughout the volume of the ocean 22 are estimated to
total 5 TW (see Table 10.2; p. 168). This is not much more than total tidal
dissipation on the planet, at 3 TW. Already, we don’t hold out much
hope for an energy bonanza. Wind in the atmosphere, by contrast, has
22: . . . contrasted to the oscillating currents
from tides
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.