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In 2012 National Grid, the company responsible for managing the electricity transmission network in the UK, estimated that the UK's energy grid can accommodate up to 22 GW of solar PV generation. Managing such a level of PV penetration on the grid will require advancements in our understanding of the combined energy production of distributed PV. Here we present the results of a study into the length scales over which PV generation time series become decorrelated, a crucial statistic in order to accurately model how PV penetration in the electricity grid impacts at Low, Medium and High Voltage (Transmission) network levels. Using a database containing thousands of real PV generation time series, we have employed simplified geostatistical techniques such as an empirical pseudo-semivariogram with exponential fit in order to study the decorrelation length of PV generation on a half hourly resolution. The decorrelation length under clear-sky conditions is found to extend beyond 350 km, whilst under variable sky conditions PV generation time series are found to decorrelate after 15 km. We have qualitatively identified the presence of stochastic decorrelation at all length scales.
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Quantifying PV fleet output variability in the UK:
Consequences for Distribution Network Operators
Jamie Taylor
*
, Jonathan Leloux
, Aldous M. Everard
, Julian Briggs
, Dr Alastair Buckley
,
Sheffield Solar, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
Instituto de Energía Solar, Universidad Politécnica de Madrid, Spain
*
Corresponding Author jamie.taylor@sheffield.ac.uk
Abstract
In 2012 National Grid, the company responsible for managing the electricity transmission
network in the UK, estimated that the UK’s energy grid can accommodate up to 22 GW of solar
PV generation. Managing such a level of PV penetration on the grid will require advancements
in our understanding of the combined energy production of distributed PV. Here we present the
results of a study into the length scales over which PV generation time series become
decorrelated, a crucial statistic in order to accurately model how PV penetration in the electricity
grid impacts at Low, Medium and High Voltage (Transmission) network levels. Using a
database containing thousands of real PV generation time series, we have employed simplified
geostatistical techniques such as an empirical pseudo-semivariogram with exponential fit in
order to study the decorrelation length of PV generation on a half hourly resolution. The
decorrelation length under clear-sky conditions is found to extend beyond 350 km, whilst under
variable sky conditions PV generation time series are found to decorrelate after 15 km. We
have qualitatively identified the presence of stochastic decorrelation at all length scales.
Introduction
In 2012 National Grid, the company
responsible for managing the electricity
transmission network in the UK, estimated
that the UK’s energy grid can
accommodate up to 22 GW of solar PV
generation, but acknowledged that to do so
would “make balancing the existing grid
infrastructure significantly more challenging
in its current form” [1]. As such, electricity
Distribution Network Operators (DNOs)
need to be able to integrate a growing
photovoltaic (PV) generation into their
energy grids. One of their challenges is to
achieve the highest levels of reliability while
minimizing the capital expenditure
(CAPEX) associated with the extension of
their network capacities, and the
operational expenditure (OPEX)
associated with the intermittent nature of
PV power output. DNOs and researchers in
the field of electrical grids still lack a precise
knowledge of the dynamics of PV output
power fluctuations. DNOs currently cope
with this problem by oversizing their
network, and by limiting the PV power to be
integrated. There is a need for a better
understanding of the power fluctuations of
distributed PV fleets, with particular
attention to the correlation between the
power outputs of each PV system. This
paper explores the
correlation/synchronicity between PV
generation time-series using an ensemble
of several thousands of real systems. We
apply simplified geostatistical techniques in
order to identify the spatial separation of PV
systems beyond which the generation
becomes decorrelated. The conclusions of
this study will be highly relevant for anyone
wishing to simulate distributed PV
penetration on an electrical grid, since we
effectively set an upper limit on the length
scale over which a single PV generation
time series can be considered
representative at other locations.
The data-set used in this analysis
comprises PV generation data from more
than 1000 PV systems across the UK, of
varying temporal resolutions (5-min to 30-
min), with historic data spanning up to
seven years [2].
Data and Method
Distributed PV generation data is collected
via the Microgen Database website [2], with
PV owners using the site as a portal to
upload readings and in return receiving free
monthly Performance Ratio (PR) analysis
and peer-to-peer performance checking in
the form of interactive maps. The majority
of the high resolution data used in this
particular study is measured by the
inverters and is collected from commercial
data donors who own/monitor hundreds of
systems using automated transfers.
The complete data-set of Microgen
Database comprises PV generation data
from more than 7000 PV systems across
the UK (see Figure 1), at various temporal
resolutions (typically 10-min, 30-min, daily
or monthly), with historic data spanning up
to seven years, although most of the PV
systems were installed after 2011. The
data-set is supplied by a combination of
homeowners and commercial sources and
includes both domestic and commercial
scale installations between 0.7 and 69 kW
p
with a wide range of orientation and tilt
angles.
To minimise the influence of shading on the
pairwise comparisons used throughout, we
only consider readings in the summer
months between 08:00 and 16:00 GMT
each day. To isolate effects due to clear-
sky conditions, we break the pairwise
comparisons up by day such that days can
be subjected to basic classification as
clear-sky (CS), variable sky (VS) or
overcast (OC). Classification as CS or OC
is automatic and uses a modified version of
the algorithm developed by Reno et al. [3],
whilst VS encompasses all days not
classified as CS or OC. Typical time series
under each condition can be seen in figure
1. To maximise the system pairs that can
be considered, we group systems
according to their orientation and tilt and
then only compare pairs from within a
single group, but ultimately include all
pairwise comparisons on the pseudo-
semivariograms (hereafter we will just say
“semivariogramfor the sake of simplicity)
i.e. the points on the semivariogram do not
necessarily have similar orientation and tilt,
but the individual systems that form the pair
do. We have also utilised all sub-30-minute
resolution data by down-sampling the
higher resolution data where the interval is
a factor of 30 minutes. In such instances,
the mean power over the 30-minute interval
is used.
Figure 1: Top window shows 30-min normalised
power generation on a typical CS day overlaid
with a typical VS day whilst the bottom window
shows the corresponding power fluctuations.
To characterise the problem, we first
consider the Pearson correlation coefficient
of PV power generation time series
between pairs of PV systems on a half-
hourly timescale as a function of the
distance between the systems.
We have then employed a method similar
to that of Elsinga et al. [4] in order to
produce empirical semivariograms. In this
context, the semivariogram plots the
variance in the power fluctuations of pairs
of PV systems in the time dimension as a
function of the spatial separation between
systems. By applying an exponential fit to
the semivariogram we are able to calculate
the decorrelation length scale as the point
at which the variance reaches 95% of the
sill, . The parameter is known as the
‘nugget’, and reveals information about the
decorrelation of generation power
fluctuations due to factors other than pair
separation, for example differences in the
orientation, tilt or system design of two
paired systems. The exponential fit takes
the form of equation 1, such that the
decorrelation length is  (equation 2).
In order to generate our semivariograms,
we first normalise the power readings to the
system peak power (kW
p
). All systems
used in the analysis are relatively new (less
than 5 years old) and so unlike Elsinga we
do not consider there to be any relevant
degradation in the system peak power. The
normalised power readings are converted
to power fluctuations for each system such
that the power fluctuation at time t is the
difference between the powers at time t+1
and t [5]. We then compare the systems on
a pairwise basis and calculate the variance
in the  dimension which, as Elsinga
demonstrates, gives a measure of the
temporal correlation. Finally, we measure
the standard deviation of this variance,

,
and plot it against the spatial separation of
the systems in question.

is therefore a
measure of the temporal decorrelation, a
concept which is explained in more detail
by Elsinga. Equation 1 is a generalisation
of the one used by Elsinga, which allows us
to take into account a nugget effect [6].




(1)



 (2)
Results and Discussion
Figure 1 demonstrates how the temporal
correlation of PV generation varies as a
function of distance for 30-min data.
Separations on a length scale less than or
equal to the approximate length scale of
low voltage (LV) networks show a
coefficient close to 1, indicating a very high
degree of correlation. The correlation
varies considerably for length scales
between those approximating LV and
medium voltage (MV) network limits, which
for the purposes of this report are taken as
1 and 10 km respectively. Crucially, below
1 km separation generation for similarly
oriented systems is totally correlated. LV
networks lie in this spatial limit and should
be modelled appropriately. Between 1 km
and 10 km separation there is a drop in
correlation which requires further
investigation in order to establish whether
the generation should still be considered
temporally correlated in this spatial range.
This graph is useful for demonstrating the
decorrelation of the generation over
distance, but cannot effectively quantify the
critical length scales.
Figure 2: Correlation between generation time-
series of PV systems at a range of length scales
(30-min time scale).
In Figure 3 we show how temporal
correlation varies with sky conditions in the
UK. As in the Netherlands [4], the
exponential fit is not appropriate under CS
conditions since

is low over all pair
separations, suggesting that under CS
conditions 30-min power fluctuations in PV
generation are correlated over separations
of up to 350 km. This requires that both
systems in each pair experience a CS day.
Figure 3: Empirical semivariogram showing
temporal correlation of power fluctuations under
CS and VS conditions.
The Variable Sky condition is explored in
more detail in figure 4. This day of VS data
corresponds to the day with the median
decorrelation length of all days sampled
and may be considered reasonably
representative of the VS condition. The
exponential fit reveals the decorrelation
length for 30-min power fluctuations under
VS conditions to be 15.6 ± 0.3 km. The
nugget for this semivariogram is 0.034, or
20% of the sill, which is 0.17. This nugget
reveals that there is a degree of
decorrelation in the power fluctuations due
to factors other than the spatial separation
of the system pair.
Figure 4: Empirical semivariogram showing temporal correlation of 30-minute power fluctuations between
system pairs. The data is taken from 2012-07-07, which is found to yield the median decorrelation length
for the 13 VS days sampled.
This decorrelation is much smaller than that
due to the spatial separation and so the
decorrelation length can be identified
accurately. Referring back to figure 2, the
decorrelation length we have calculated
corresponds to a correlation coefficient of
around 0.75. The decorrelation length scale
for the VS condition is higher than that
reported in the Netherlands of 5 km, but this
can be explained by the fact that this was
measured on a 15 minute time scale, and
one expects the decorrelation to increase
as the time interval increases since high
frequency events such as fast moving
passing clouds are less important.
Whilst the data in figure 4 can be accurately
fitted using the model in equation 1, it’s
important to note that there is dispersion of
points around the fit which implies that
some close systems will experience a high
degree of decorrelation whilst some very
distant systems will experience a high
degree of correlation. Generally these
systems are not problematic for DNOs
since they are a minority. In fact, the
decorrelation of close systems can benefit
the local LV and MV grid by reducing the
impact of high amplitude power
fluctuations, effectively dispersing the
power fluctuation. The highly correlated
distant systems will generally be on
different MV networks and so their impact
will be minimal. With regards to simulations
of PV penetration on an electrical grid, this
dispersion suggests some degree of
stochastic decorrelation should be
introduced to the generation time series of
all systems. Future studies will examine the
residuals of the exponential fit in order to
study this effect.
Conclusion
We have assessed the decorrelation length
of 30-min PV generation power fluctuations
under CS conditions to be at least 350 km.
This result suggests that on a clear-sky
day, a single PV generation time series can
be used to represent the generation from
other identical systems within a loci of 350
km, provided both experience CS
conditions. We have concluded that under
VS conditions, the equivalent decorrelation
length is 15 km, such that, on a variable-sky
day, a single PV generation time series can
only be considered representative of other
nearby identical systems within a loci of 15
km. This result is highly relevant in
simulating PV energy flows on an electrical
grid since it implies that systems on an LV
and small MV networks can be considered
to have synchronised generation with some
stochastic temporal decorrelation.
Acknowledgments
The Microgen Database is a public-
industry-academic collaboration providing
solar photovoltaic performance data for use
across the UK PV supply chain. The
Sheffield Solar project is funded by the
EPSRC (Solar Energy for Future Societies:
EP/I032541/1; Wise PV: EP/K022229/1)
and The University of Sheffield.
Thanks to Maria-Madalina Opincaru for her
role as database admin.
The work of Jonathan Leloux has been
partially financed by the European
Commission within the project PV CROPS
under the 7th Framework Program (Grant
Agreement nº 308468).
References
[1]
UK Department of Energy and Climate
Change, “UK Renewable Energy
Roadmap Update 2012,” 27 December
2012. [Online]. Available:
https://www.gov.uk/government/uploads/sy
stem/uploads/attachment_data/file/80246/
11-02-
13_UK_Renewable_Energy_Roadmap_Up
date_FINAL_DRAFT.pdf. [Accessed 20 03
2015].
[2]
Sheffield Solar, “Microgen Database,”
Sheffield Solar - University of Sheffield,
[Online]. Available: http://www.microgen-
database.org.uk/.
[3]
M. J. Reno and W. van Sark, “Global
Horizontal Irradiance Clear Sky Models:
Implementation and Analysis,” Sandia
National Laboratories (SANDIA REPORT
SAND2012-2389), Albuquerque, New
Mexico, March 2012.
[4]
B. Elsinga and W. van Sark, “Spatial
power fluctuation correlations in urban
rooftop photovoltaic systems,” Progress in
Photovoltaics: Research and Applications,
2014.
[5]
J. Marcos, L. Marroyo, E. Lorenzo, D.
Alvira and E. Izco, “Power output
fluctuations in large scale pv plants: One
year observations with one second
resolution and a derived analytic model,”
Progress in Photovoltaics: Research and
Applications, vol. 19, no. 2, pp. 218-227,
March 2011.
[6]
J. P. Chilès and P. Delfiner, Geostatistics:
Modeling Spatial Uncertainty, John Wiley
& Sons, 2009.
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Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis
  • M J Reno
  • W Van Sark
M. J. Reno and W. van Sark, "Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis," Sandia National Laboratories (SANDIA REPORT SAND2012-2389), Albuquerque, New Mexico, March 2012.