Characterizing spatiotemporal irradiance variability is important for the
successful grid integration of increasing numbers of photovoltaic (PV) power
systems. Using 1

The number of photovoltaic (PV) power systems has drastically increased in
many regions of the world during the last decade, reaching a total nominal
capacity of more than 178

Recent studies of PV-related variability have analyzed power spectra of PV
systems and solar irradiance

While satellite-derived irradiance data are convenient for the analysis of
large spatiotemporal scales, comprehensive data sets for local short-term
variability are time consuming and expensive to collect. They are needed but have not previously been available

To fill the gap in understanding of small-scale spatial and temporal
variability in irradiance, we use an extensive experimental data set of global
horizontal irradiance (GHI) field samples from two measurement campaigns to
characterize sub-minute variability of clear-sky index for distances between
tens of meters and about 10 km. A high temporal resolution of
1

The data sets on which this study's analyses are based originate from two
extensive measurement campaigns performed during the HD(CP)

The first field campaign with these instruments took place near Jülich,
Germany (50.9

The geometry of the pyranometer locations for the Melpitz and Jülich
campaigns, as well as a histogram of all sensor pair distances

Panels

Taking into account the final data sets' high temporal resolution of
1

The available global horizontal irradiance (GHI) at any given point on the
Earth's surface is subject to influences from both astronomical and
atmospheric processes. As for the former, the apparent movement of the
Sun relative to Earth gives rise to diurnal and seasonal variations in GHI. These
variations are accurately predictable and not large on short timescales of
seconds or minutes. On the other hand, weather-related contributions to
irradiance variability are manifold and complex, and present on all timescales.
For instance, the growth, motion, and decay of clouds can affect the
seasonal cycle in GHI (e.g., winter tends to be cloudier than summer in
mid-latitude low-lying land), and the rapid succession of sunlight exposure
and cloud shadow in conditions dominated by fair-weather cumulus generates
stochastic variability on short timescales (seconds–minutes)

In order to distinguish the cloud-induced fluctuations from the
slowly evolving, astronomically determined apparent motion of the Sun, a GHI
time series

While all atmospheric influences on GHI variability are included in

The lowest values of

To characterize the modulation of

To illustrate the wide range of cloud influences on

Examples of different spatiotemporal variability in clear-sky index

Summary statistics used to visualize data spread throughout this study.

The 15 min window in Fig.

In order to assess the character of irradiance variability conditioned on sky
type, we group subsets of similar sky conditions by means of two simple
statistics. Specifically, we compute the sample arithmetic mean

These two statistical measures allow an intuitive characterization of the
prevailing sky type that a sensor has been subjected to for a limited time,
by quantifying the average and spread of the respective 15 min window in its
time series. A kernel density estimate (KDE) of the joint probability density
function (PDF) of

In the low variability range

Kernel density estimate (KDE) of the joint probability density
function (PDF) of mean

The quantities

The resulting distributions of spatial autocorrelation functions

Pairs of sensors with very high

Spatial two-point correlation coefficients

For further analyses, and consistent with the manually selected exemplary
periods previously shown in Fig.

overcast (A1 and B1),

clear (D1 and E1), and

mixed (A3 through E5).

Under overcast conditions, correlation coefficients remain

The

The previously discussed properties of the observed

PDFs of

Statistics of clear-sky index increments

All PDFs are characterized by a narrow central peak – corresponding to a
high probability of very small increments – surrounded by broad tails in
which the PDF decreases slowly. With increasing

Under overcast conditions, the central peaks of the distributions are
generally prominent and the tails are not particularly pronounced. The PDFs
of clear skies also have a strong central peak but display broad flat tails
(higher than for overcast conditions), representing the rare large excursions
evident in Fig.

A measure of the extent of the tails of the PDF is the probability

While changes in increment variability are reflected by changes of

The differences between the single-sensor increment statistics and the
distributions of areal averages in Fig.

Conditioned on the previously defined classification scheme of sky types,
summary statistics of

Spatial two-point correlation coefficients

A useful measure of increment correlation structure is the decorrelation
length scale

In accord with previous studies published by

Increment decorrelation length scales

In addition to the statistics of the measured data, each panel of
Fig.

The ranges of the model results are in broad agreement with the summary
statistics of the two field campaigns and the general decrease of spatial
correlation with increasing distance is reproduced well. However, differences
between overcast and clear-sky conditions are evident, as the former tends to
coincide with the upper region of the model range (corresponding to high

Finally, the bottom panels (Fig.

Averaging clear-sky index increments from different sensors provides an
estimate of the output variability of an ensemble of PV installations at
multiple locations. In order to assess the effect of area averaging on
variability as a function of averaging area

Three representative realizations of randomly selected circles
falling within the study domain, using circle radii of 1.25

The time series of

Normalized standard deviations

Variability in averaged clear-sky index decreases much more slowly with
averaging area than does variability in increments. The decrease of
variability with averaging area is also more rapid for shorter increment
times than longer increments, and less rapid for overcast conditions than
other sky types. For both

When considering the implications of clear-sky index variability for PV power,
the short-term sky type classifications used throughout this study can be
linked to distinct PV power fluctuation levels as in

The relationship between measured irradiance and PV power also includes a
smoothing effect, because the area of a pyranometer is very small compared to
that covered by a PV system's panels. Thus, the larger the spatial footprint
of a considered set of PV systems, the more pronounced the smoothing effect
will be, and the lower the necessary temporal resolution of the data may
become. When considering many interconnected PV systems in a very large
area, e.g., all of Europe, spatial smoothing appreciably reduces the necessary
temporal resolution of data (the European Energy Exchange, for example, uses
15 min time steps for electricity trading). At the other end of scale,

There are substantial differences between the variability characteristics of
single utility-scale PV plants covering relatively small areas, and fleets of
distributed systems with similar total capacities, but spanning relatively
large areas

With the continual global increase of PV power systems and the inherent
weather-induced volatility of their power output, characterizing the
underlying irradiance variability in both space and time is important for the
planning and reliable operation of future power grids. In the present study,
we analyzed spatiotemporal field characteristics of clear-sky index and
sub-minute

By means of a simple classification scheme based on clear-sky index
statistics, we identified overcast, clear, and mixed sky conditions, and
subsequently analyzed sub-minute

The corresponding spatial autocorrelation structures of

As a proxy for the smoothing effects of distributed PV, spatial averaging was
shown to effectively mitigate relative variability in

These initial characterizations of PV-related clear-sky index variability
during HOPE can be extended to consider other issues of relevance to solar PV
power generation. For example, a more refined analysis of the two-point
spatial autocorrelation structures of

The pyranometer network measurements are hosted on the HD(CP)

We thank Andreas Macke at the Leibniz Institute for Tropospheric Research
TROPOS (Leipzig, Germany) for sharing the pyranometer network data sets of the
HD(CP)