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Yield predictions are performed to predict the solar resource, the performance and the energy production over the expected lifetime of a photovoltaic (PV) system. In this study, we compare yield predictions and monitored data for 26 PV power plants located in southern Germany and Spain. The monitoring data include in-plane irradiance for comparison with the estimated solar resource and energy yield for comparison with predicted performance. The results show that because of increased irradiance in recent years (‘global brightening’) the yield predictions systematically underestimate the energy yield of PV systems by about 5%. Because common irradiance databases and averaging times were used for the yield predictions analysed in this paper, it is concluded that yield predictions for areas where the global brightening effect occurred in general underestimated the energy yield by the same magnitude. Using recent satellite-derived irradiance time series avoids this underestimation. The observed performance ratio of the analysed systems decreases by 0.5%/year in average with a relatively high spread between individual systems. This decrease is a main factor for the combined uncertainty of yield predictions. It is attributed to non-reversible degradation of PV cells or modules and to reversible effects, like soiling. Based on the results of the validation, the combined uncertainty of state of the art yield predictions using recent solar irradiance data is estimated to about 8%.
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29TH EU PVSEC, AMSTERDAM, THE NETHERLANDS, 2014
Yield predictions for photovoltaic power plants:
empirical validation, recent advances and remaining
uncertainties
Björn Müller*, Laura Hardt, Alfons Armbruster, Klaus Kiefer and Christian Reise
Fraunhofer ISE, Fraunhofer Institute for Solar Energy Systems, Heidenhofstraße 2, Freiburg 79110, Germany
ABSTRACT
Yield predictions are performed to predict the solar resource, the performance and the energy production over the expected
lifetime of a photovoltaic (PV) system. In this study, we compare yield predictions and monitored data for 26 PV power
plants located in southern Germany and Spain. The monitoring data include in-plane irradiance for comparison with the
estimated solar resource and energy yield for comparison with predicted performance. The results show that because of in-
creased irradiance in recent years (global brightening) the yield predictions systematically underestimate the energy yield
of PV systems by about 5%. Because common irradiance databases and averaging times were used for the yield predictions
analysed in this paper, it is concluded that yield predictions for areas where the global brightening effect occurred in general
underestimated the energy yield by the same magnitude. Using recent satellite-derived irradiance time series avoids this
underestimation. The observed performance ratio of the analysed systems decreases by 0.5%/year in average with a rela-
tively high spread between individual systems. This decrease is a main factor for the combined uncertainty of yield predic-
tions. It is attributed to non-reversible degradation of PV cells or modules and to reversible effects, like soiling. Based on
the results of the validation, the combined uncertainty of state of the art yield predictions using recent solar irradiance data
is estimated to about 8%. Copyright © 2015 John Wiley & Sons, Ltd.
KEYWORDS
PV systems; yield prediction; performance ratio; solar resource assessment; global dimming and brightening
*Correspondence
Björn Müller, Fraunhofer ISE, Fraunhofer Institute for Solar Energy Systems, Heidenhofstraße 2, 79110 Freiburg, Germany.
E-mail: bjoern.mueller@ise.fraunhofer.de
Received 7 July 2014; Revised 17 February 2015; Accepted 10 March 2015
1. INTRODUCTION
Since the beginning of the current millennium, commer-
cially operated photovoltaic (PV) systems have become a
common source of energy supply. PV power plants with
installed capacities of several hundred kilowatts to multiple
megawatts became possible especially because of the intro-
duction of xed feed-in tariffs for roof-top and free-
standing systems in Germany in 2004 [1], the year when
worldwide annual PV installations exceeded 1 GW for
the rst time [2]. In the following years, a growing number
of power plants were installed in Germany. In 2007 and
2008, a second country joined this development: Spain
saw something like a PV gold rushin these years with
massive installations of big PV power plants. Italy joined
with rst big installations in 2008. Since 2010, the number
of big PV power plants increased in various countries in
Europe and other regions all over the world.
Right from the beginning, an assessment of the ex-
pected energy yield was an essential precondition for the
nancing of PV power plants. This is especially true for
European countries with feed-in tariffs: because of xed
tariffs and guaranteed rights to feed in all energy produced,
one of the main uncertainties for an investment in a PV
power plant is the assessment of the expected energy pro-
duction within its lifetime or its investment time horizon.
This assessment is performed within a yield prediction.
In order to allow a better understanding of the following
sections, we will rst briey describe the steps involved
in such a prediction.
A yield prediction is an estimate of the total energy
production for a PV system at a specic site[3]. The pri-
mary aim is to predict the annual energy production over
the expected lifetime of the system. Usually, it is per-
formed at an early stage of a planned PV project. Yield
predictions can be partitioned in three main parts:
PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS
Prog. Photovolt: Res. Appl. (2015)
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/pip.2616
Copyright © 2015 John Wiley & Sons, Ltd.
an assessment of the solar resource;
modelling of the expected PV system energy output
based on the estimated meteorological values; and
an estimation of long-term changes in energy yield
over the expected lifetime of the system under
consideration.
For a solar resource assessment, the long-term average
solar radiation from the past (the reference period) is used
as an estimator for the availability of solar resources in the
future (the prediction period). Because long-term ground
measurements of solar radiation for a specic site are most
often not available, satellite-derived solar irradiance is
commonly used for the reference period (sometimes in
combination with interpolations of ground measurements).
PV system modelling can be described as a set of
models, methods and parameters to simulate the energy de-
livery of a PV system using the specications of the system
(PV modules, azimuth and tilt angle, inverters, wiring, etc.)
and meteorological values (solar irradiance, ambient or
module temperature, wind speed, etc.) for the location of
the system. Because usually no measurements are available
for a yield prediction, model parameters cannot be ex-
tracted from system performance data. Laboratory mea-
surements, data sheets or typical characteristics have to
be used instead. This is in contrast to PV system modelling
carried out in the context of system monitoring to compare
actual with expected system performance in order to detect
failures. For such purposes, previously measured meteoro-
logical parameters and system performance can be used to
calibrate simulation models. This difference is crucial
when comparing modelling errors and uncertainties re-
ported in publications that focus on PV system modelling
(refer to e.g. [47]).
Only a few publications on the combined uncertainties
of yield predictions are available so far [811]. Most of
them do not consider long-term effects in detail or lack a
comparison with measurement data from real PV systems.
Long-term effects that inuence the energy yield may ei-
ther be changes in system performance or changes in avail-
ability of the solar resource. Estimates of long-term
changes in system performance are usually based on an as-
sumption of expected degradation rates for the PV mod-
ules. On the other hand, changes in the solar resource are
often neglected or considered to be negligible [1113]. Re-
cent publications show, however, that this factor does need
to be considered [14].
In this paper, an empirical validation of yield predic-
tions against measured irradiance and measured energy
yields of commercially operated PV systems is presented.
For some of the systems, up to eight years of data are avail-
able. The present paper is a continuation of previous pub-
lications on validation of yield predictions [9,10]. Beside
some overall improvements, the longer time period of
available data is used to focus on the identication and
analysis of long-term effects and their inuence on valida-
tion results. The ndings will be used for an uncertainty as-
sessment of state of the art yield predictions.
2. VALIDATION OF YIELD
PREDICTIONS WITH
MEASUREMENTS
Fraunhofer Institute for Solar Energy Systems (ISE)
prepared some hundreds yield predictions for commer-
cially operated PV systems in the past 10 years. At the
same time, continuous performance monitoring of about
300 PV systems is performed. The intersection of PV
systems with both Fraunhofer ISE yield prediction and
monitoring is the basis for the validation of yield predic-
tions with monitored data in this section. The comparison
is performed for global irradiance in plane of array
(GPOA), performance ratio (PR) and specic energy yield
(Yield) of the systems.
2.1. Yield predictions and measured data
For the yield predictions under consideration, the simula-
tion programme INSEL [15] was used to model PV system
behaviour in the rst years; since about 2008, the in-house
simulation software ZENIT is used. As estimator for the
availability of solar resource in Germany, the rst predic-
tions used long-term mean irradiance values from the
period of 1980 to 2000, provided by the German meteoro-
logical service [Deutscher Wetterdienst (DWD); we will
refer to this data as DWD raster data[16] throughout
the paper]. Later predictions (since about 2007) used
DWD raster data for even longer time periods ranging up
to the year preceding the preparation date of the yield pre-
diction (also starting in 1980). For all sites outside of
Germany, annual mean irradiance values from University
of Oldenburg starting with the year 1997 were used.
Finally, since 2013, time series of irradiance and ambient
temperature provided by GeoModel Solar [17] are used
for all calculations inside or outside Germany. From the
beginning, all yield predictions included an uncertainty
assessment. Because these uncertainties are given as stan-
dard uncertainties (i.e. k= 1 with a condence interval of
68%), also all uncertainties within this paper are given as
standard uncertainties.
Monitoring data of PV systems used for the comparison
with yield predictions are obtained with common Fraunho-
fer ISE monitoring systems. The data are measured each
second, averaged to ve-minute intervals and stored by
an industrial data logger. Each night data are transferred
to the institute and undergo a set of plausibility and quality
checks.
For measurement of GPOA, silicon reference cells are
used. The cells are regularly calibrated at Fraunhofer ISE
CalLab with a calibration uncertainty of 1%. Because
reference cells exhibit similar physical properties com-
pared with PV modules of the same technology, they
measure the irradiance that is visibleto the PV mod-
ules. Taking additional sources of uncertainty (e.g. line-
arity and data acquisition system) into account, we
estimate the annual uncertainty for this measurement to
2-3%. However, yield predictions use broadband
Yield predictions for photovoltaic power plants B. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
irradiance data (with similar physical properties as
pyranometer measurements), which differ from reference
cell readings mainly because of different angular sensi-
tivity, spectral effects and soiling. To account for this
difference, the irradiance predicted in the yield predic-
tions was adjusted with predicted angular, soiling and
spectral losses and PR was recalculated accordingly. Al-
though this simple conversion routine seems to work
quite well (refer to [7]; Figure 2), it introduces additional
uncertainties. We estimate these uncertainties to about 1%,
leading to a combined uncertainty of about 3.5% for the
comparison of GPOA,
The uncertainties for the measurement of the energy
yield feed into the grid are estimated to about 1%.
Additional uncertainties for specic energy yield may
appear because of differences between nominal and ac-
tual installed power. Installed power cannot be deter-
mined without uncertainty: On the one hand, there is
the measurement uncertainty on the power at standard
test conditions (STC) of single PV modules. To date,
measurement uncertainties of as low as 0.8% for crystal-
line silicon PV modules can be achieved, whereas some
5-10 years ago, measurement uncertainties were in a
range of 1.5-2.5% ([18], uncertainties converted to stan-
dard uncertainties). On the other hand, not all modules
of a PV plant can be measured with low uncertainty as
achieved in an advanced laboratory. Therefore, the sam-
pling of modules introduces additional uncertainty [19].
In addition, initial stability aspects like light-induced
degradation (power loss of 02% after 20 kWh/m
2
for
crystalline silicon) need to be considered [20]. Taking
into account an additional 2% uncertainty for installed
STC power, the overall uncertainty for comparison of
specic yield may reach about 2%.
As a result, the uncertainty for comparison of PR is es-
timated to about 3.5 to 4%.
For a more detailed description of the monitoring sys-
tem, the irradiance correction and its validation by compar-
ison with pyranometer measurements please refer to Reich
et al. [7] and Müller et al. [10].
2.2. Systems available for the comparison
Yield predictions estimate the long-term yield of a system;
therefore, only systems that are measured for ve or more
calendar years are used. Consequently, the yield predic-
tions for those systems were prepared between the years
2004 and 2009. Measurement data from 2005 (the rst full
year of operation of the oldest systems) up to the year 2013
are used. For the comparison in this paper, annual data
availability of 98% is required (i.e. not more than about
one week out of a year may be missing). To ensure a fair
comparison, we excluded the whole year if only one mea-
surement quantity was missing, e.g. one year with a defec-
tive irradiance sensor that could not be repaired/exchanged
within one week, is completely excluded. After applying
this rule, PV systems with less than three years reliable op-
erating data remaining are excluded.
Based on these quality criteria, 38 systems are available
for comparison. In the next step of the selection procedure,
we identied systems for which the original specications
used for the yield prediction (e.g. installed DC power, azi-
muth angle or tilt angle) differ from those of the built sys-
tem. The following major deviations were identied:
Installed power differs by more than 10%: 2 systems.
Azimuth angle differs by more than 10°: 4 systems.
Tilt angle differs by more than 5°: 2 systems.
As a result, a further 7 systems were excluded from
comparison. The fact that 7 out of 38 systems (18%) are
not built as expected during the yield assessment study
clearly demonstrates the need for an integrated quality as-
surance for bankable PV investments [21].
From the remaining 31 systems, we excluded those in
which system failures (particularly inverter failures) re-
duced the number of available operating years below
three. This removes another 5 systems, at the end leaving
a batch of 26 systems for comparison. These systems
collectively provide 129 years of operating data. We ex-
cluded single years with system failures (11 years, equiv-
alent to 9%), resulting to a nal data set of 118 years.
For some systems, eight years of data, at minimum
(per denition) three years and in average 4.5 years per
system are available. Three of the systems are sun-
tracking systems (1-axis tracking), the others have xed
tilt angles in a range of 1530° in combination with az-
imuth angles ranging from southeast (150°) to southwest
(230°). Two systems are located in Spain, all other sys-
tems in Germany. The locations of these systems are
shown in Figure 1; more details for all systems are given
in Table I.
All systems are equipped with modules made of crystal-
line silicon cells and use silicon sensors for irradiance
measurements.
2.3. Validation
For the validation, annual relative differences between
measured and predicted values (GPOA, PR and energy
yield) are calculated. Furthermore, the overall difference
(referring to the entire measurement period) is calculated.
The results of the validation are shown in Figure 2. The
systems are sorted by their commissioning date (oldest sys-
tems on top).
Note that because the age of installations differ, the dif-
ferences shown in Figure 2 refer to unequally long operat-
ing periods (ranging from three to nine years, refer to
Section 2.2). Although the comparison is inuenced by
this fact (especially for GPOA and yield because of their
high year-to-year variations), the gure nevertheless shows
the current status of measurements compared with yield
predictions.
Figure 2 shows that measured GPOA is higher than pre-
dicted for almost all systems.
Yield predictions for photovoltaic power plantsB. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
In fact, the measured irradiance for 20 out of 26
systems is more than 3.5% above the prediction (which
is equal to the estimated uncertainty for the
comparison, refer to Section 2.1). This leads to an
overall mean difference of +4.9%. System nos. 22, 24
and 26 show a negative difference or extraordinary
Table I. Characteristics of the systems under consideration.
No.
Year of
installation
Nominal power
(kWp)
Mounting
concept
Tilt angle
(deg)
Orientation (deg, 180:
south)
Monitoring data available
(years)
1 2004 1890 1-axis tracking 0 8
2 2004 1925 1-axis tracking 0 6
3 2005 6262 1-axis tracking 0 5
4 2005 73 Fixed 30 174 8
5 2006 36 Fixed 30 184 5
6 2006 137 Fixed 25 183 6
7 2006 257 Fixed 25 227 4
8 2007 372 Fixed 24 170 5
9 2007 1012 Fixed 25 200 3
10 2007 279 Fixed 25 180 5
11 2007 973 Fixed 25 180 5
12 2007 763 Fixed 25 180 4
13 2007 1045 Fixed 30 182 5
14 2007 497 Fixed 25 157 3
15 2007 197 Fixed 25 208 3
16 2007 1553 Fixed 25 165 4
17 2008 1118 Fixed 25 180 5
18 2008 738 Fixed 24 152 5
19 2008 1202 Fixed 24 188 5
20 2008 400 Fixed 25 180 4
21 2008 421 Fixed 24 188 4
22 2008 638 Fixed 15 165 3
23 2008 926 Fixed 25 180 5
24 2008 787 Fixed 15 196 4
25 2008 1320 Fixed 15 170 3
26 2008 1103 Fixed 15 186 3
All systems are equipped with crystalline silicon modules. PV system nos. 22 and 24 are situated in Spain; all other systems in Germany (refer to Figure 1).
Figure 1. Locations of the PV systems.
Yield predictions for photovoltaic power plants B. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
small positive difference. Two of these systems (nos.
22 and 24) are the systems located in Spain with irra-
diance data from a different source and time period
used in the yield prediction (refer to Section 2.1). We
will analyse the reasons for these differences in Section
3.2. For now, it can be concluded that GPOA seems to
be systematically underestimated by the yield
predictions.
PR over all systems seems in line with the predictions.
The mean difference of -0.8% is clearly within uncer-
tainties of the PR comparison. However, for the rst half
of the systems (the older systems), PR seems to be slightly
overestimated.
System nos. 4, 6, 8 and 11 show negative differences of
more than 3.5% (the lower range of the estimated uncer-
tainty for PR comparison). The reason for this underesti-
mation is mainly because of a decrease of PR over time.
For the yield predictions, no decrease in PR or an estimate
of degradation effects was considered. So the difference of
the measured to the predicted PR tends to become more
negative from year to year. We will further analyse this
in Section 3.1.
As a consequence of higher irradiance and a slightly
lower than predicted PR, measured energy yield of the sys-
tems is approximately 4% above predictions. Single years
exceed the predicted long-term average energy production
by up to 18%. This big difference is a combined effect of
annual uctuations in solar resource (with deviations of
10 to +12 % from the measured mean) and underestimated
mean annual irradiance.
3. INVESTIGATION OF BIAS
DIFFERENCES
The results from the previous section naturally lead to the
question why the predicted energy yield is systematically
underestimated. Within this section, we will identify the
reasons for the observed systematic differences and try to
identify approaches to reduce them in future yield
assessments.
3.1. Long-term system stability
As stated in Section 2.3, the long-term decrease in PR in-
uences the differences shown in Figure 2.
To analyse this inuence, we computed change rates for
all systems under consideration. Note that we avoid the
term degradationhere to differentiate between changes
in performance caused by potentially reversible effects (e.
g. soiling) and non-reversible degradation of PV modules
or cells. A separation of these effects is not possible from
the data available for this paper. Details of the method
and the ltering procedure we used are given in Kiefer
et al. [22]. Figure 3 shows the histogram of the annual
change rates for PR.
Mean and median indicate a negative trend of about
0.5%/year. Five systems show a slightly positive change
rate (of up to 0.2%/year). The mean for all systems is
not inuenced (up to the rst digit) if for these systems
zero change rate would be assumed. Another ve
systems show a decrease of more than -1%/year.
Neglecting measurement uncertainties and reversible ef-
fects, this would mean that typical power guaranties of
PV module manufacturers (80% power after 20 years)
do not hold. There are no relevant differences between
monocrystalline (5 systems) and polycrystalline systems
(21 systems): the mean, the median and the range are
Figure 2. Measured values compared with predictions. The
blue bars show the differences over the entire measurement pe-
riod. The lines in light blue indicate the interannual variability; the
vertical line in orange indicates the mean difference. The mean
difference and the standard deviation for GPOA, PR and yield
are specied on the subplot titles.
Yield predictions for photovoltaic power plantsB. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
similar; however, the monocrystalline systems are older
in average.
An overview on the development of change rates de-
pending on operating time is given in Figure 4.
The results are basically in accordance with data
available in the literature: Jordan and Kurz [23] recently
published a comprehensive review on long-term perfor-
mance of PV modules and systems. They identify a me-
dian change rate of about -0.5%/year for polycrystalline
systems (for installations after 2000) and a change rate
of about -0.2%/year for monocrystalline systems. The
magnitude of the change rates found for the systems un-
der consideration here are similar, with the exception that
no differences between monocrystalline and polycrystal-
line systems were found. The fact that there is no differ-
ence between both technologies may indicate that other
effects like soiling dominate change rates; however, the
sample size is small.
As a sound separation in reversible and non-
reversible effects is not possible here, we use the calcu-
lated change rates to check their inuence on the
comparison of measured and predicted PR and energy
yield. To do so, the predicted annual energy yield and
PR are reduced by the individual change rates of the
systems. Note that this is not a realistic case for a yield
prediction because the change rates will be unknown
beforehand. However, it (nearly) removes time-
dependent changes from the comparison. The results
are shown in Figure 5.
Compared with Figure 2, this removes the negative
overall PR difference and reduces the shift especially for
the older systems. The remaining scatter can be attributed
to a combination of measurement uncertainties (monitoring
data, nominal to real STC power) and discrepancies in sys-
tem modelling within the yield predictions. However, only
for one system (no. 23), the difference exceeds the as-
sumed uncertainty for PR comparison of 3.5%.
Note that the difference between measured and pre-
dicted energy yield also has changed: the mean difference
of the measurements from the predictions is now above
5%. Because changes in PR are now included in predicted
values, this number is a measure for the real
Figure 3. Histogram of annual PR changes for the systems under consideration.
Figure 4. Changes in PR depending on operation years.
Yield predictions for photovoltaic power plants B. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
underestimation of the energy yield resulting from the un-
derestimation of the solar resource.
3.2. Solar resource
From Figure 2, it seems obvious that for the systems
that use (very long-term) DWD raster data, the solar re-
source is systematically underestimated by the yield
predictions. This data source was used for 24 out of
the 26 yield predictions analysed here (all German sys-
tems). However, because measurements of in plane irra-
diance performed with a reference cell are compared
with corrected irradiance in plane of array from the
yield prediction (refer to Section 2.1), the reason for
this difference is not easy to identify. Possible reasons
include the following:
(1) deviations of projected global horizontal irradiance
(GHI) and trueGHI in the reference period;
(2) deviations between mean irradiance in the refer-
ence period and irradiance in the measurement
period;
(3) deviations introduced by the transposition model
(and the composition of direct and diffuse irradiance
within the time series); and
(4) deviations from conversion of predicted (pyranometer-
based) irradiance to equivalent silicon sensor based ir-
radiance measurements.
Figure 5. Comparison of measurements against predictions using the calculated rate of change for the PR.
Yield predictions for photovoltaic power plantsB. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
Deviations from (1) cannot be evaluated directly, be-
cause measurements of GHI within the reference period
are not available. For an indirect evaluation, results from
the literature and from continuous quality assurance of so-
lar resource assessments at Fraunhofer ISE can be used.
Within this process, different sources of irradiance data
are regularly compared against ground measurements and
amongst each other. For irradiance data provided by
GeoModel Solar, the mean deviation compared with mea-
surements from 15 meteorological stations of the DWD for
the time period of 20052009 was found to be -0.7%. This
number quite well corresponds to ndings from the litera-
ture [24,25]. On the other hand, we compared GeoModel
data and DWD raster data for 94 locations in Germany
for the time period of 20032012 and found a mean devi-
ation of 0.1%. As a result, while deviations between mea-
sured and predicted irradiance may reach more than 5%
at some individual locations, a systematic deviation of
5% at distributed locations and for long time periods seems
very unlikely. This statement only applies for recent data,
though. The quality of DWD raster data for the period of
19802000 (which is available as a single mean value)
cannot be evaluated with these comparisons. It can be as-
sumed that the quality of more ancient satellite-derived ir-
radiance data is poorer compared with recent data: the
satellites (e.g. METEOSAT 1 starting in 1979 [26] up to
Meteosat Second Generation nowadays) as well as the
models and other input parameters used to derive irradiance
data drastically improved (refer to e.g. [2730). How-
ever, the procedure to generate raster data applied by
the DWD (refer to Riecke [16] for a description of the
procedure) uses (monthly) satellite-derived irradiance
and ground-measured irradiance from the DWD
observational network (currently about 30 distributed
stations equipped with pyranometers). Within this proce-
dure, satellite-derived irradiance is scaled to correspond
to the ground measurements and a spatial interpolation
is applied to ll all raster points with this scaled data.
This implies that the spatial mean of the ground
measurements is preserved, while the satellite data are
used to map the spatial variability. For a (mostly)
pyranometer-based spatial mean, we do not expect devi-
ations to true irradiance in the same time period in a
range of 5%. Therefore, we conclude that an underesti-
mation of irradiance in this order of magnitude for 24
distributed solar resource assessments cannot be attrib-
uted to deviations between DWD raster data and true
irradiance in the reference period.
Deviations from (2) can be evaluated by a comparison
of the mean irradiance in the reference period with irradi-
ance in the prediction period from the same data source.
For this comparison, annual DWD raster data are available
for the systems located in Germany. The result of this com-
parison is shown in Figure 6.
Figure 6 shows that annual mean deviations against the
predicted irradiance from the reference period are positive
for all years, but 2013. Only in the years 2010 and 2013,
there are cases were the deviation for a single location is
negative. The mean GHI in the years 20052013 for all lo-
cations is 5.1% higher than GHI in the reference period.
This order of magnitude is clearly in line with the underes-
timation of GPOA in the yield predictions.
The higher irradiance can be attributed to the following
reasons: as stated in Section 2.1, for the original yield pre-
dictions, long-term average values of up to 26 years from
the past were used to estimate solar irradiance on the hori-
zontal plane. However, solar irradiance is not necessarily
stable on such time scales and has in fact been shown to
Figure 6. Annual deviations to predicted GHI from the reference period for all 24 locations in Germany shown as coloured lines. The
mean annual deviation is shown as thicker black line.
Yield predictions for photovoltaic power plants B. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
follow long-term trends spanning multiple decades [31].
While from the 1950s up to the 1980s, a decline was ob-
served; since the mid-1980s, a gradual increase in solar ra-
diation was observed at many sites around the world. This
phenomenon is known as global dimming and brighten-
ing. A more detailed discussion of these trends and their
causes can be found in Wild, Wild et al. and Wild and
Schmucki [3234].
In Müller et al. [14], the inuence of these long-term
trends on solar resource assessments is analysed. From
measurements at 8 stations of the DWD distributed over
Germany, an average brightening trend of 3.3%/decade is
found for the years 19842010. To reduce the prediction
error in the presence of long-term trends, the authors rec-
ommend using irradiance data from the 10 most recent
years as a basis for solar resource assessments. Whereas
Müller et al. [14] uses a different data base (ground mea-
surements of GHI), it is estimated that the use of a 10-year
average will result in about 5% higher predictions com-
pared with predictions based on a 30-year average. This
is almost exact in accordance with the observed difference
for the yield predictions that use DWD raster data (with a
comparable time period of up to 26 years) from the present
study. Whereas this exact accordance will be accidentally,
this approach may have the potential to remove existing
bias differences for these systems. For the systems located
in Spain (nos. 22 and 24), the recommendations from the
aforementioned publication are fullled: they use 10 years
of data preceding the preparation date of the yield predic-
tion. The fact that these two systems show very low devi-
ations between measured and predicted GPOA (refer to
Figure 2) further supports this theory.
We will test this approach and update the existing yield
predictions with recent irradiance data in the next section.
An analysis of the remaining possible reasons for the devi-
ations of GPOA in the original predictions (points 3 and 4
from the beginning of the recent section) will also be
performed.
4. UPDATED YIELD PREDICTIONS
To update the yield predictions, irradiance time series pro-
vided by GeoModel Solar are used to recalculate the yield
predictions with the 10 most recent years preceding the
commissioning of the system.
For the recalculation, the PV module and inverter pa-
rameters from the original yield predictions are used.
Note that at least in part, different models had to be used
for the recalculation. For the original yield predictions
calculated with the simulation programme INSEL, the
two-diode model was applied for the simulation of PV
module behaviour and at least for the rst predictions a
polynomial interpolation to simulate inverter efciencies.
So new parameters had to be derived for the models
used for the recalculation (refer to Heydenreich [35] for
the module model and Schmidt and Sauer [36] for the
inverter model). For simulation of shading losses, not
all parameters necessary for the recent model used in
our software ZENIT could be derived from the old pre-
dictions (refer to Müller et al. [37] for more details on
the recent shading model). For that reason, the losses
predicted in the original predictions were used as loss
factors in the recalculation.
For conversion to GPOA, we applied two different
models: the Perez [38] and the Hay model [39]. On one hand,
these models show a good agreement with measurements at
different locations (especially at south oriented planes with
tilt angles 45°, which are typical for PV systems), and on
the other hand, the Perez model usually predicts higher irra-
diance than the Hay model [4046]. This makes a combina-
tion of these models valuable to estimate the inuence of
transposition models and their uncertainties.
The individual change rates for the PR as derived in
Section 3.1 are not adequate for a yield prediction, because
these change rates are not known in advance. Therefore,
the average change rate of -0.5%/year as computed in
Section 3.1 is assumed for all systems.
The comparison of measured data and updated yield
predictions are shown in Figure 7 using the Hay model
and in Figure 8 using the Perez model.
The most obvious nding from these results is the strong
inuence of the transposition model on the overall results:
measured GPOA and yield are slightly higher compared with
the prediction when the Hay model is used, whereas the
higher irradiance gains from GHI to GPOA predicted by
the Perez model lead to negative deviations. The predictions
of the Hay model are very close to most GPOA measure-
ments. Only for the rst three systems, which are the tracking
systems, the Perez model seems to predict lower differences.
Note, however, that this comparison does not allow for
a ranking of transposition models as measurement uncer-
tainties and possible systematic deviations from conver-
sion of predicted (pyranometer-based) irradiance to
equivalent silicon sensor-based irradiance measurements
cannot be separated based on available data.
Despite the inuence of the transposition models, it can
be concluded that the use of more recent irradiance data re-
duces bias differences of measured to predicted GPOA.
The mean difference is reduced as well as most differences
for single locations. Differences for 22 (16 for the Perez
model) out of 26 systems are within the estimated uncer-
tainty range of the comparison.
The observed differences for PR are low with a mean
difference around zero and standard deviations of about
2%. For system nos. 7 and 10, the differences are above
the estimated uncertainty. These differences, however, can
at least in part be attributed to deviations from the assumed
change rate of -0.5%/year. For the older systems (the sys-
tems on top of the gures), the differences again seem to
be more pronounced than for the newer systems. This can
be attributed to the fact that differences caused by devia-
tions from the assumed change rate cumulate over time.
As a result, the differences in energy yield are mainly
inuenced by the differences in GPOA and from devia-
tions to the change rate assumed.
Yield predictions for photovoltaic power plantsB. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
5. RESULTS AND DISCUSSION
The validation results and recalculated predictions from the
previous sections can be used to estimate uncertainties for
future yield predictions. However, for a complete uncer-
tainty analysis, different sources of uncertainty have to be
considered. Not all of these sources could be validated sep-
arately with measured data within this paper, because e.g.
measurements of GHI are not available or a separation be-
tween reversible and non-reversible effects on long-term
changes in performance is not possible. For this reason, ad-
ditional information from the literature is used to estimate
uncertainties for each separate source. The aim is to derive
uncertainties for lifetime energy yields of a typical PV sys-
tem in a moderate climate. Uncertainties for individual sys-
tems will differ from this estimate, depending on location
and characteristics of the system.
For long-term yield predictions and solar resource assess-
ments, not only uncertainties from possible deviations of
projected and trueGHI in the reference period have to be
considered. If there are long-term changes of solar
irradiance in the past, also uncertainties from possible de-
viations between solar irradiance in the reference and in
the prediction period (with unknown magnitude) have to
be taken into account. Evidence for the existence of such
long-term trends are not only found from ground measure-
ments of irradiance but also from ground measurements of
other meteorological quantities such as diurnal tempera-
ture ranges or sunshine duration [31] and satellite data
[47]. The ndings from the present paper further support
this assumption.
As no measurements are available, the uncertainty from
deviations between projected and true GHI in the reference
period cannot be estimated using data from the present
Figure 7. Results when using the Hay model and assuming a
change rate of -0.5%/year.
Figure 8. Results when using the Perez model and assuming a
change rate of -0.5%/year. [Correction added on 29 April 2015,
after rst online publication: Figure 8 previously duplicated
Figure 7, but this has been corrected.]
Yield predictions for photovoltaic power plants B. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
analysis. Based on literature [24,25] and own validations
(refer to Section 3.2), we estimate this uncertainty for a re-
cent 10-year reference period to about 3%. In the presence
of long-term irradiance trends that span multiple decades,
the use of longer and/or older reference periods (as carried
out in the original yield predictions) will likely increase the
uncertainty and add biases to the predictions. In case of a
recent brightening trend (the actual situation), longer
and/or older reference periods will underestimate current
irradiance conditions. Beside the ndings from the current
paper, examples for this underestimation can be found in
various other publications that compare GHI from different
data sources and time periods with recent ground measure-
ments, e.g. [24]; Table III and [48]; Table I. Note that the ad-
dition of biases and higher uncertainties should also occur
if a dimming trend exists (but result in an overestimation of
irradiance). In the case of stable irradiance conditions,
longer or shorter reference periods would not inuence un-
certainties. The only case, where a longer reference period
can provide a better estimator, is a trend reversal within
reference and prediction period (refer to Müller et al. [14]
for a more detailed discussion on this topic).
In Müller et al. [14], the resulting uncertainty of devia-
tions between GHI in the reference and in the prediction
period is estimated to about 3% based on historical mea-
surement data for sites in Germany. Because of changes
in the ratio of direct to diffuse irradiance, the uncertainty
for tilted planes is estimated to be about 4-5%. However,
dimming and brightening trends do show regional differ-
ences in their magnitude. According to Wild [31], the
highest brightening trends were observed for Germany,
with slightly lower trends for Spain and other parts of
Europe. An overview for the brightening trends is given
in Table II. Based on this, we estimate the typical uncer-
tainty on expected energy yields arising from possible
long-term changes in irradiance in the future to be about
3%. Because this uncertainty do not inuence initial years
in the prediction period (if recent irradiance data are used),
we include them as a long-term uncertainty.
The assessment of long-term performance stability
from Section 3.1 showed a negative trend of about -0.5%/
year. Especially for outdoor-measured PV systems, a differ-
entiation between non-reversible degradation of PV mod-
ules and possibly reversible effects like dust and soiling is
not possible for the systems under consideration and very
difcult to achieve in general. Soiling losses may be very
high especially in arid regions [49]; however, soiling also
has an inuence in moderate climates as found in Germany.
For negative change rates of more than 1%, the contribution
of reversible effects is likely to be higher. So a cleaning
concept may be an appropriate way to avoid such high de-
creases. For this reason, the uncertainty of the long-term
change rate is assumed to be about 0.5%/year (i.e. the ex-
pected change rate will be in a range of 0 to 1%). Over
an expected system lifetime of 20 years, this adds up to
the estimated uncertainty for the lifetime energy yield.
A summary of all estimated uncertainties and their
contribution to the overall combined uncertainty is given
in Table III. Note that the combined uncertainties are
calculated as the square root of the sum of squared indi-
vidual uncertainties. More advanced statistical modelling
Table II. Brightening trends for different regions of the world
(time period: 1980s to 2000s).
Region Brightening trend (%/decade)
Global 2.5
Europe 2.6
North America 3.0
Asia 2.1
Germany 3.4
Iberian Peninsula 2.4
Mean values of various sources given in Wild [31].
Table III. Estimated uncertainties and uncertainty contributions for a yield prediction of a typical crystalline silicon PV system in a
moderate (middle European) climate.
Estimation Contribution Sources/references
(Initial)Solar resource
GHI 3% [24,25]
Transposition to GPOA 3% [4046]
4.2% 58%
(Initial) PR modelling
System modelling 3% [47]
Nominal power 2% [1820]
3.6% 42%
Yield before long-term effects 5.6% 100% 48%
Long-term effects
Performance changes 5% 74% [23]
Solar resource trends 3% 26% [14]
5.8% 100% 52%
Lifetime energy yield 8.1% 100% [11]
Depending on the technology used, the uncertainties for PR modelling and long-term stability may be higher for thin-lm modules.
Yield predictions for photovoltaic power plantsB. Müller et al.
Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
techniques were used to combine uncertainties in
Thevenard and Pelland [11] and Drury et al. [8]. How-
ever, as long as variable uncertainties (with changing
daily, seasonal and annual magnitudes) are not combined
for individual modelling time steps, such techniques are
also imperfect. Nevertheless, a comparison of both ap-
proaches in Thevenard and Pelland [11] delivered similar
results.
For the initial assessment of GPOA, the estimated com-
bined uncertainty from Table III is about 4%. The compar-
ison of recalculated GPOA with measurements reveals
remaining differences of about 5% for individual locations.
The gap may be mainly attributed to the conversion of
pyranometer to sensor irradiance. For the same reason,
the theoretical uncertainties for initial PR modelling are
slightly higher than the observed differences from the
recalculation.
Differences between measured and predicted energy
yields are only slightly higher than for GPOA. They are
lower than the uncertainty estimations from Table III (with
about 8%). However, this is in line with expectations be-
cause the energy yield compared within this paper does
not cover the whole lifetime of the PV system but only
4.5 years in average. As a result, the observed differences
are expected to increase with time. For a nal validation
and uncertainty assessment, 2025 years of measurement
data would be required.
The uncertainties estimated within this paper are valid
for the lifetime energy yield of individual PV systems.
However, individual years may show much higher devia-
tions from predicted energy yields because of interannual
variations in solar resource. On the other hand, from the
overall comparison of all 26 PV systems, it seems evident
that the uncertainties for the prediction of an ensemble of
PV systems are lower compared with predictions for indi-
vidual systems.
All in all, it can be stated that estimated uncertainties
correspond with the ndings from the comparison of mea-
surements and recalculated yield predictions.
6. CONCLUSION
The combined uncertainty of the lifetime energy yield pre-
diction for a PV system is estimated to about 8%. Solar re-
source assessment and long-term changes in system
performance contribute the most to this uncertainty.
Yield predictions that use older irradiance data for solar
resource assessments may overestimate or underestimate
the energy yield of PV systems, systematically in regions
where trends in the solar resource can be observed. The
use of recent satellite-derived irradiance time series can
help to avoid such wrong assessments. More precise trans-
position models (and more precise irradiance measure-
ments) would further reduce uncertainties of GPOA
predictions.
A better understanding of regional soiling effects [50]
and factors inuencing PV module degradation [51]
could help to separate reversible and non-reversible com-
ponents of long-term system performance stability, mak-
ing it possible to further reduce prediction uncertainty.
Detailed on-site analyses, the development of site-
specic and system-specic cleaning and maintenance
concepts with the owners of the systems and additional
measurements of meteorological and environmental pa-
rameters for the systems under consideration would be
desirable.
ACKNOWLEDGEMENTS
The authors want to thank Anton Driesse (Photovoltaic
Performance Labs) for fruitful discussions, Wolfgang
Riecke (DWD) for details on DWD raster data and all em-
ployees at Fraunhofer ISE that helped to collect the data
over the years.
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Prog. Photovolt: Res. Appl. (2015) © 2015 John Wiley & Sons, Ltd.
DOI: 10.1002/pip
... Accurate simulations, proper methodologies for system analysis, and periodic monitoring are the practical methods to study PV systems. Yield calculations are necessary for feasibility investigations to select the optimal locations and calculate approximately the economic risks of the investments [13,14]. In this case, it should be noted that the simulation of PV technologies is classified as the energy rating including a presence of comparison among the real operational parameters of various modules under the standard conditions. ...
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Today, photovoltaic panels are used in various applications, and increasing their efficiency is of interest to many researchers. In this research, we try to increase the radiation density by increasing direct radiation to finally increase the energy production in photovoltaic power plants. The direct radiation amplification system is used to improve the photovoltaic efficiency. In this proposed system, energy and economics are analyzed by MATLAB software. Also, prototype testing and photovoltaic power plant testing are examined. The results show that by implementing this system in photovoltaic power plants, annual energy production can be increased. By adding this system to a photovoltaic power plant, the price of electricity produced in photovoltaic power plants will be increased from 13 ¢ ℎ ⁄ to 9 ¢ ℎ ⁄ , which shows a 31% reduction in the price of electricity per kilowatt-hour.
... In reference [6], the authors compare yield predictions and monitoring data for 26 PV power plants located in southern Germany and Spain. If rather old radiation databases are used, the model systematically underestimates PV production by about 5% due to increased irradiance in recent years. ...
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The simulation of photovoltaic installations is a major issue for their sizing, their smart grid operation, and their fault detection and diagnosis. In this article, we study in detail every step of the simulation chain, either from the global horizontal irradiance and the ambient temperature (i.e., 4 steps of simulation) or considering the global in-plane irradiance and the module operating temperature (i.e., 1 step of simulation). The average quality estimation of the models is made through the calculations of average annual error between estimations and measurements, from 2016 to 2020. We have shown that the most uncertain step is the conversion of the global irradiance in its diffuse and direct components (17.2%, 2 models tested). If the model goes up to the in-plane irradiance, the average annual error decreases to 5.3% (6 models tested). The photovoltaic module temperature calculation induces an error of less than 2°C (4 models tested with 2 configurations). Meanwhile, the photoelectrical conversion shows a 3.5% error, similar to the measurement uncertainties, considering as input, the modules temperature, and the in-plane irradiance. If the simulation goes from the global irradiance and the ambient temperature measured locally, the estimation leads to a 6.7% average annual error. If the local measurements are not available, we can use the closest meteorological station’s records (13 for our study), and the error becomes 12.1%. Finally, we can also use the satellite images that lead to a 15.2% error, for average per year. The impact of available input shows that modeling the DC photovoltaic production, using global horizontal irradiance and ambient temperature, gives rise to an error of 6.6% for local measurements, 12.1% for weather station measurements, and 15.2% for satellite images estimations. This article thus draws up a review of the existing models, allowing to calculate the DC production of a photovoltaic module, depending on the atmospheric conditions, and highlights the most precise or most critical steps, considering in situ and weather station ground-based measurements, and also estimation from satellite images. 1. Introduction Photovoltaic (PV) production mainly depends on the solar radiation incident on PV modules. Solar resource variability and uncertainty associated with the modeling of PV energy production are one of the most important factors that influence the grid stability (with wind turbines), regardless of the size of the power grid [1]. The ability to precisely predict the energy produced by PV systems is of great importance and has been identified as one of the key challenges for massive PV integration [2, 3]. It is also a milestone in the sizing step of PV installations. This can also be used for PV fault detection and diagnosis. This study focuses on evaluating the uncertainty on PV production estimation at each step of the modeling process. Each step is studied independently, and also its impact on the whole simulation chain is evaluated. Few articles study the impact of the uncertainty of the modeling process. We can cite [4] which examines the uncertainty in long-term PV system yield predictions by statistical modeling (using Solar Advisor Model software) of a hypothetical 10 MW crystalline silicon PV system in Toronto (Canada). In this case study, uncertainties were estimated to be about 3.9% for year-to-year climate variability, 5% for long-term average horizontal irradiation, 3% for estimation of the in-plane radiation, 3% for power rating of modules, 2% for losses due to dirt and soiling, 1.5% for losses due to snow, and 5% for other sources of error. By performing statistical simulations, it was found that the combined uncertainty is approximately 8.7% for the first year of operation and 7.9% for the average yield over the PV system lifetime. The study led by Sandia Laboratory [5] explains that the solar resource uncertainty (due to measurements, variability, spectrum...) is between 5 to 17%, the transposition of the horizontal irradiances to the in-plane irradiance is between 0.5 to 2%, the energy simulation and power plant losses induce uncertainty of 3 to 5%, and annual degradation uncertainty is about 0.5 to 1%. Using in situ ground-based measurements can reduce the uncertainty by up to 3.5%. In reference [6], the authors compare yield predictions and monitoring data for 26 PV power plants located in southern Germany and Spain. If rather old radiation databases are used, the model systematically underestimates PV production by about 5% due to increased irradiance in recent years. Using recent satellite-derived irradiance avoids this underestimation. According to them, the main factor for the uncertainty of yield predictions is the aging, that is to say, the observed decrease of performance ratio. In this study, it decreases by 0.5% per year on average with a relatively high spread between systems. This decrease is attributed to nonreversible degradations and reversible effects, like soiling. The conclusion is that the uncertainty of the state-of-the-art yearly yield predictions using recent solar irradiance data is estimated to about 8%. Only two publications compare the uncertainty of different photoelectric conversion models [7, 8]. Those two papers, written by the same authors, compare the annual PV yield prediction errors of four models: single-point efficiency, single-point efficiency with temperature correction, PVUSA (Photovoltaics for Utility Scale Applications), and single-diode model (SDM), against outdoor measurements for different grid-connected PV systems in Cyprus over a 4-year evaluation period. The best agreement between the modeled results and outdoor measurements for crystalline silicon PV technologies was obtained using SDM. The energy yield for thin-film technologies was more accurately predicted using the PVUSA model. Our approach in this paper is similar to indirect forecasts: first, we calculate (or measure) the solar global in-plane irradiance () and PV module operating temperature (), and then, using a PV performance model, we calculate the power produced at the maximum power point () [9]. Only the DC side of the photoelectric conversion is considered (no inverter). The different steps of the PV simulation are summarized in Figure 1, together with the considered models and the data sources.
... The second question has received particular attention in Germany (Müller et al., 2016), and is generally addressed by evaluating decadal trends in GHI (or, much more rarely, DNI) using either long periods of measurement at radiometric stations or modeled predictions based on different types of approaches: satellite-based models, reanalysis data, or empirical sunshine-based irradiation estimates. These decadal trends are often studied in the climatic context of dimming (downward GHI trend) or brightening (upward GHI trend). ...
Chapter
Various technical aspects of the measurement and modeling of the solar energy potential are addressed in this chapter to provide a solid understanding of the different steps involved in the practice of solar resource assessments. The information presented here represents the state of the art with regard to the availability of solar resource databases developed from satellite imagery or meteorological reanalysis, and their derivatives, such as solar resource maps or typical meteorological years. The fundamentals that are reviewed include measuring, modeling, and applying solar radiation resource data to meet various needs, such as site selection, solar system design and simulation, or financial projections.
... The novel simulation tools will be combined with better evaluation of technical uncertainties and their influence on financial models. These tools will build on previous pioneering developments by some partners of the project [4]. ...
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... The parameters of PV modules are known as ideality factor (n), series resistance (R s ), shunt resistance (R sh ), photocurrent (I ph ) and saturation current (I o ). Determination of these parameters is vital to predict and establish various strategies in the production of energy [21], establishing maximum power point trackers (MPPTs) [22][23][24], developing plug-in hybrid electric vehicles (PHEVs) [25] and addressing various issues in the PV plants operation [26][27][28][29]. Furthermore, these parameters are key factors affecting the value of photovoltaic parameters such as opencircuit voltage, short circuit current, fill factor and efficiency [10]. ...
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