Energy and Human Ambitions on a Finite Planet, 2021a

11 Hydroelectric <strong>Energy</strong> 176
Box 11.1: Why So Efficient?
Achieving 90% efficiency is superb! Electric motors <strong>and</strong> generators 14
can be > 90% efficient in converting between mechanical energy
(rotation) <strong>and</strong> electrical energy. When coupled with low-friction
turbines, dams just have very little loss—unlike thermal sources
where most of the energy is unavoidably lost (for reasons covered in
Sec. 6.4; p. 88).
Example 11.2.1 To compute the power available from a hydroelectric
plant, we need to know the height of the reservoir <strong>and</strong> the flow rate of
water—usually measured in cubic meters per second. The density of
water is, conveniently, 1,000 kg/m 3 (Figure 11.3), so that if we consider
a dam having a flow rate of 2,000 m 3 /s <strong>and</strong> a reservoir height of 50 m,
we can see that every second of time will pass 2 × 10 6 kg of water, 15
<strong>and</strong> the associated potential energy is mgh ≈ 10 9 J. If each second
delivers 1 GJ of energy, the power available is 1 GJ/s, or 1 GW. At an
efficiency of 90%, we get to keep 900 MW of electrical power.
The largest hydroelectric facility in the world is the Three Gorges Dam
in China, rated at an astounding 22.5 GW. The largest in the U.S. is the
Gr<strong>and</strong> Coulee on the Columbia River, producing a maximum of 6.8 GW.
The iconic Boulder Dam (a.k.a. Hoover Dam) is just over 2 GW.
14: Fundamentally, motors <strong>and</strong> generators
are nearly identical in concept <strong>and</strong> construction.
1 m 3
1,000 kg
Figure 11.3: One cubic meter of water has a
mass of 1,000 kg.
15: Flow rate times density gives mass per
second: 2,000 m 3 /s times 1,000 kg/m 3
2 × 10 6 kg/s
Look at the Wikipedia page on
largest hydroelectric power stations
[66] for a complete list.
Note that flow rates vary seasonally with rainfall, so that dams cannot
always operate at full capacity. In fact, the U.S. has about 80 GW of
capacity installed, but operates at an annual average of about 33 GW.
This implies a typical “capacity factor” around 40%.
Definition 11.2.1 A capacity factor is the ratio of actual performance
over time to the peak possible performance—or average output divided by
maximum output, expressed as a percentage.
Example 11.2.2 Boulder (Hoover) Dam on the Colorado River is listed
in [66] as having a capacity of 2,080 MW <strong>and</strong> an annual production of
4.2 TWh. What is its capacity factor?
We just need to turn the 4.2 TWh in a year into an average delivered
power. Following the definition of a watt-hour, we note that all we
really have to do is divide 4.2 × 10 12 Wh 16 by the number of hours in
a year: 24 times 365, or 8760.
16: 1 TWh is 10 12 Wh.
4.2 × 10 12 Wh/8760 h ≈ 480 MW average power. Dividing this by
2,080 MW (max capacity) gives a 23% capacity factor.
As we saw in Fig. 7.5 (p. 108) <strong>and</strong> Table 10.3 (p. 170), hydroelectricity
in the U.S. accounts for 2.7% of the nation’s total energy consumption,
corresponding to about 33 GW of production. Globally, hydroelectric
production averaged 477 GW in 2017. By comparison, Table 10.2 (p. 168)
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.