Energy and Human Ambitions on a Finite Planet, 2021a

12 Wind <strong>Energy</strong> 190
wind is not always blowing, <strong>and</strong> its speed varies over wide ranges. In
this sense, wind is an intermittent power source. Just as for hydroelectric
installations, wind resources are characterized by a regionally-dependent
capacity factor, which is the ratio of energy delivered to what would
have been delivered if the generation facility operated at full capacity
at all times. Typical capacity factors for wind in the U.S. 18 are around
33%, <strong>and</strong> Figure 12.6 provides a visual sense for how this manifests in
the real world: pretty erratic.
18: Capacity factors for wind are smaller
than for hydroelectricity due to wind being
more variable than river flow.
Figure 12.6: One month of wind generation
from a 20 MW wind farm, illustrating the
intermittent nature <strong>and</strong> why capacity factors
are low [76]. The facility saturates at
maximum power late in the month, selflimiting
to avoid damage to the turbines.
©2010 Springer.
For very low wind speeds, 19 wind turbines do not have enough wind to
turn at all <strong>and</strong> sit still at zero output. Furthermore, a turbine is rated at
some maximum power output, which occurs at some moderately high
wind speed, 20 beyond which the generator risks damage—like “redlining”
a car’s engine. When the wind climbs above this maximum-rated
speed, the turbine is pegged at its maximum power—no longer following
a v 3 relation—<strong>and</strong> deliberately twists its blades 21 to be less efficient as
the wind speed grows so that it maintains constant (maximum) power
output. When the wind speed becomes large enough to endanger the
turbine, it will twist its blades parallel to the wind to allow the air to
pass without turning the rotor at all, so that it no longer spins while it
“rides out” the high winds. 22
19: . . . less than about 3 m/s; called the
“cut-in” velocity
20: . . . usually around 12–15 m/s
21: The blades are like long airplane wings
<strong>and</strong> are mounted so that they can be rotated
on an axis running the length of the blade,
allowing them to engage the wind at any
angle, thus varying efficiency.
22: A typical shut-off wind speed for turbines
is 20–30 m/s.
Figure 12.7: Actual data (thickly-clustered
black circles) of power delivered by a turbine
rated at 2 MW, as a function of wind
velocity. The red curve represents the theoretical
Betz limit of 59%, appearing as a
cubic function of velocity—as Eq. 12.2 dictates.
The better-matching blue curve corresponds
to an overall efficiency ε c p 0.44
(44%), <strong>and</strong> the green curve—which rolls
over from the cubic function <strong>and</strong> saturates
at higher velocities—is the manufacturer’s
expectation for the unit [77]. The “cut-in”
velocity for this turbine is around 3.5 m/s:
note the small step up from zero output
in the green curve. This turbine saturates
around 12 m/s: the green curve flattens out
<strong>and</strong> no black circles appear above the cutoff.
From ©2017 Wiley.
Figure 12.7 shows a typical power curve for a2MWturbine, on top
of which are drawn a cubic function of velocity at the theoretical Betz
limit (red curve), a cubic (blue) at 44% efficiency (ε 0.44), <strong>and</strong> the
green manufacturer’s curve [77]. Notice that the turbine performance
[77]: Fischer et al. (2017), “Statistical learning
for windpower: a modeling <strong>and</strong> stability
study towards forecasting”
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.