getting to large-scale solar integration
considered fluctuation time
scale is an important parameter specifying whether the
observed variability occurs in
a matter of seconds, minutes
or hours.
Myth: Fluctuations Are
an obstacle to Large-
Scale Deployment
The 3.5-megawatt PV
power plant in Springerville, Ariz., operated by the
Tucson Electric Power Co.,
occasionally exhibited the
type of variability illustrated
in the top part of figure 1
when analysts evaluated
1-minute ramp rates. The
high-frequency rampings up
and down caused by passing
clouds raised concerns with
the utility company: What if
PV penetration reached a sizeable fraction
of Tucson Electric’s production? Would this
single-plant observation translate into massive utility-scale power rampings of the sort
shown in the top part of figure 1? Would the
utility have to plan for an expensive infrastructure upgrade to mitigate such variability?
The Springerville data were widely publicized, with the implication that regional solar
output may be just as variable and impossible to manage. This issue prompted the
U.S. Department of Energy (DOE) and the
California Solar Initiative to identify PV variability as a top research priority in the context
of high PV penetration.
Copyright © 2011 by the American Solar Energy Society Inc. All rights reserved.
the short-term variability issue can be addressed
by combining the output from many systems
that are physically separated some distance.
This empirical evidence can be explained by
what is one of the most important contributions
of probability theory: the law of large numbers.
Mathematically, if the short-term output time series of
two locations experiencing
a similar level of variability
are uncorrelated (i.e., if they
vary independently from each
other), the resulting variability of the ensemble should be
1/√ 2 times that of a single
location (Mills and Wiser,
Hoff and Perez). This simple
mathematical formulation can
be extended to N locations.
For instance the variability
of 400 identical uncorrelated
PV plants should amount to 5
percent (1/√400) of a single
plant’s variability and the PV
output converges to the average system output.
Therefore, the key question to ask is what is the correlation between the fluctuations of different solar power plants distributed
over a considered utility grid or feeder?
Intuitively we know that if two plants are
very near each other, they will have nearly
the same view of the sky and will vary in
almost perfect sync; that is, their correlation
is high and their variability will not cancel
out. Intuitively, we also sense that locations
that are far apart do not vary in short-term
synchronicity, because clouds have many
shapes and structures and it would be a
rare occurrence when two distant locations
experience identical cloud patterns evolving
in sync. We also intuitively sense that the
considered fluctuation time scale — from
seconds to hours — will affect correlation,
hence the cancellation or not of the resulting
variability at that considered time scale. Consider a large weather front where regional
conditions would switch from clear to overcast. In such instance, short-term up-down
ramps of less than a few minutes occurring
during cloud cover buildup would very likely
cancel out among dispersed regional plants,
but the longer-term ramps of an hour or more
Over the last few years, concerted efforts to
observe, understand and quantify the influence
of distance and time scale on variability smoothing have brought us to a point where we now
figure 2: Recent studies find the correlation of the fluctuations between two sites to be a
predictable function of distance, time scale and cloud speed. This graphic illustrates the
influence of fluctuation time scale (top) and cloud speed (bottom) upon the correlation
of the fluctuations between site pairs in two locations.
50 September/October 2011 SOLAR TODA Y solartoday.org
Fact: It Is All About
Time and Space
The data in the top part of figure 1 are very
real, and there is no doubt that conditions
can be highly variable at any given location.
Empirical evidence, however, is showing that
the output aggregated over several locations
tends to mitigate the short-term variability
problem.
The bottom part of figure 1 presents the
same irradiance data as in the top part of the fig-
ure, with the only difference being that the irradi-
ance is measured at 25 locations in a 4-square-
kilometer (1.5-square-mile) grid rather than at a
single location. The figure clearly illustrates that
figure 3: As evidenced by the variability of a New York City
single site vs. citywide variability, fluctuations decrease as
the number and spacing of distributed systems increases.
