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3E
WP2 Deliverable 2.4
Best Practice Guide On Uncertainty in PV
Mauricio Richter, K
John Kalisch, Thomas Schmidt, Elke Lorenz (UOL)
This project has received funding from the European Union’s Seventh Programme for research, technological development
and demonstration under grant agreement No
3E – UNIVERSITY OF OLDENBURG
30/01/2015 – Version Final
Checked by John Kalisch
Approved by Achim Woyte
WP2 Deliverable 2.4
Best Practice Guide On Uncertainty in PV Modelling
Mauricio Richter, Karel De Brabandere (3E)
John Kalisch, Thomas Schmidt, Elke Lorenz (UOL)
This project has received funding from the European Union’s Seventh Programme for research, technological development
ation under grant agreement No 308991.
WP2 Deliverable 2.4
Modelling
This project has received funding from the European Union’s Seventh Programme for research, technological development
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In this work, the uncertainties introduced by the different elements in the photovoltaic
(PV) energy conversion chain are reviewed and translated into best practice guidelines
on uncertainty in PV modelling and monitoring of grid-connected PV systems. The
guidelines for uncertainty assessment in PV modelling will help developers and investors
in managing the financial risks of an investment in photovoltaic systems. Moreover, the
monitoring guidelines will help them to monitor accurately and in a robust and effective
way the plant indicators that are required to be able to assess and improve the
operational performance of the plants during their lifetime.
The first part of this work reviews the different uncertainties linked to the measurements
and modelling of the solar resource and PV components. Moreover, the uncertainties of
the different meteorological and PV system design models developed within the
Performance Plus project are reviewed.
The second part of this document provides guidelines on the correct combination of the
different uncertainties affecting both, the PV modelling and the monitoring of PV systems.
Typical values for practical application are provided.
The third part of this work provides guidelines for uncertainty assessment in PV
modelling and monitoring of grid-connected PV systems. These guidelines reflect the
current state-of-the-art in monitoring and photovoltaic plant performance assessment as
represented in various standards and research results.
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BEST PRACTICE GUIDE ON UNCERTAINTY IN
PV MODELLING Operational PV system Modelling – D2.4
CONTENTS
SUMMARY. ......................................................................................................... 2
ABBREVIATIONS AND SYMBOLS ................................................................................. 4
1 INTRODUCTION ........................................................................................ 6
2 METHODOLOGY ........................................................................................ 7
2.1 UNCERTAINTY METRICS .............................................................................. 7
2.2 COMBINATION OF UNCERTAINTY .................................................................... 7
3 UNCERTAINTIES OVER THE PV MODELLING CHAIN ................................................ 9
3.1 UNCERTAINTIES IN THE SOLAR RESOURCE ......................................................... 9 3.1.1 LONG-TERM RESOURCE ASSESSMENT .............................................................. 9
3.1.2 MEASUREMENT UNCERTAINTIES ................................................................... 11
3.1.3 MODEL UNCERTAINTIES ............................................................................ 12
3.1.4 SHORT TERM RESOURCE ASSESSMENT (FORECASTING) ........................................ 15
3.2 UNCERTAINTIES IN THE PV MODELLING ......................................................... 17
3.2.1 UNCERTAINTY CHAIN ............................................................................... 17
3.2.2 PV MODULE TEMPERATURE MODEL ................................................................ 17
3.2.3 PV ARRAY MODEL ................................................................................... 18
3.2.4 PV INVERTER MODEL ............................................................................... 19
3.2.5 OTHER FIELD RELATED UNCERTAINTIES .......................................................... 19
4 OVERALL ASSESSMENT OF UNCERTAINTY ........................................................ 21
4.1 PROPAGATION OF UNCERTAINTY .................................................................. 21
4.2 VALUES FOR PRACTICAL APPLICATION ............................................................ 24
4.2.1 MONITORING ........................................................................................ 24
4.2.2 MODELLING .......................................................................................... 24
5 BEST PRACTICE GUIDELINES ....................................................................... 26
5.1 MONITORING GUIDELINES ......................................................................... 26
5.2 GUIDELINES FOR UNCERTAINTY ASSESSMENT IN PV MODELLING ............................. 26 6 CONCLUSIONS....................................................................................... 28
REFERENCES .................................................................................................... 29
ANNEX: MONITORING GUIDELINES ........................................................................... 32
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Latin Abbreviations and Symbols
AC Alternating Current
CMV Cloud Motion Vector
Cnst Temperature independent constant
CPP Cloud Physical Properties
c-Si Crystalline Silicon
DC Direct Current
E Energy
ECMWF European Center for Medium-Range Weather Forecasts
G Irradiation
GHI Global Horizontal Irradiation
GPOA Irradiation in plane-of-array
GSTC Irradiation at Standard Test Conditions (i.e., 1000 Wh/m2)
HC-1 HelioClim-1
HC-3 HelioClim-3
I Current
ISC Short Circuit Current
JCGM Joint Committee for Guides on Metrology
KMI Koninklijk Meteorologisch Instituut van België
KNMI Koninklijk Nederlands Meteorologisch Instituut
LC Array capture losses
LID Light Induced Degradation
LS System losses
MAE Mean Absolute Error
MBE Mean Bias Error
n Number of samples
NASA National Aeronautics and Space Administration
NREL National Renewable Energy Laboratory
nmae Normalized mean absolute error
nmbe Normalized mean bias error
nrmse Normalized root mean squared error
NWP Numerical Weather Prediction
P Power
PN Nominal power
POA Plane-of-array
PR Performance Ratio
PV Photovoltaic
PVGIS Photovoltaic Geographical Information System
RandNorm Normally distributed random components
RandUni Uniformly distributed random components
RMSE Root Mean Squared Error
Rseries Series resistance
Rshunt Shunt resistance
SIS Smart Irradiation Service
SW Wind speed
SystNorm Normally distributed systematic components
SystUni Uniformly distributed systematic components
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Tcell Cell temperature
Tmod Module temperature
U Expanded uncertainty
uc Combined uncertainty
V Voltage
WMO World Meteorological Organization
YA Array yield
Yf System yield
Yr Reference yield
Greek Symbols �� Actual quantity ��� Estimated quantity �̅� Average value
∆t Sampling interval
σAv Uncertainty on the availability
σC-AC Uncertainty on AC cable losses
σC-DC Uncertainty on DC cable losses
σclim Uncertainty on climate variability
σE Uncertainty on the estimated energy output
σfld Uncertainty on PV field related losses ��� Uncertainty on the estimated plane-of-array irradiation
σInv Uncertainty on inverter modelling
σirr Uncertainty on irradiation quantification
σPOA Uncertainty on conversion to the plane-of-array
σPR Uncertainty on the calculated performance ratio of the system
σPVarr Uncertainty on PV array modelling
σTmp Uncertainty on module temperature modelling
σYA Uncertainty on the calculated array yield
σYf Uncertainty on the calculated system yield
σYr Uncertainty on the calculated reference yield
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The uncertainty quantification
managing the financial risk of an
is subject to the uncertainties introduced by each element in the
first and most important element is the solar resource. Apart from uncertainties related
with the measurement and/or estimation of the solar resource, also the long
variability of the resource must be
performance of the various components affecting the energy
also the simulation procedures used to estimate the energy
subject to uncertainties and must be
quantification of all uncertainties in data inputs and modelling procedures
developers and investors to contain
Figure 1 illustrates the energy flow in a grid
the main energy conversion steps taking place within the system
collection of measured and calculated parameters
parameters is linked to an uncertainty
document.
FIGURE 1: ENERGY FLOW IN A G
The uncertainty quantification of solar energy yield calculations is
managing the financial risk of an investment in photovoltaic system. The
is subject to the uncertainties introduced by each element in the PV modelling chain. The
lement is the solar resource. Apart from uncertainties related
with the measurement and/or estimation of the solar resource, also the long
variability of the resource must be taken into account. Furthermore, variations on the
s components affecting the energy yield are quantified. Finally,
also the simulation procedures used to estimate the energy yield of a
subject to uncertainties and must be considered. Thus, the correct
uncertainties in data inputs and modelling procedures
contain the financial risks.
illustrates the energy flow in a grid-connected photovoltaic system describing
the main energy conversion steps taking place within the system. A limited but
nd calculated parameters is shown in Figure
linked to an uncertainty as it will be explained in the next sections of this
: ENERGY FLOW IN A GRID-CONNECTED PHOTOVOLTAIC SYSTEM
calculations is important for
. The yield estimation
modelling chain. The
lement is the solar resource. Apart from uncertainties related
with the measurement and/or estimation of the solar resource, also the long-term
. Furthermore, variations on the
quantified. Finally,
of a PV plant are
correct identification and
uncertainties in data inputs and modelling procedures allows
connected photovoltaic system describing
limited but selected
gure 1. Each of these
as it will be explained in the next sections of this
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The uncertainties of the different steps in the modelling chain are classified in three main
groups: uncertainties in the solar resource, uncertainties in the PV modelling and
uncertainties due to additional losses occurring in the field.
2.1 UNCERTAINTY METRICS
The term “uncertainty” used in this report refers to the root mean square error (RMSE)
associated with the estimation of a quantity. The RMSE is composed of a systematic part
(MBE, Mean Bias Error) and a non-systematic part (σ, standard deviation of the error)
which represents the random contributions to the error around the mean value. The
definition of these accuracy measures are presented below in equations (1) to (8), where �� is the actual quantity, ��� the estimated one, ��� the average value and the variable n is
the number of samples. The RMSE, MBE and MAE are normalized over the average value ��� and presented as nrmse, nbme and nmae respectively.
��� = �1�� ���� − ������
(1)
��� = 1�� ���� − �����
(2)
��� = 1�� ����� − ������
(3)
���� = ���� + �� (4)
��� = 1�� ����
(5)
� !"# = ��� ���$ (6)
�!%# = ��� ���$ (7)
!&#(�) !&*+,#-) = ��� /0111$ (8)
2.2 COMBINATION OF UNCERTAINTY
When neglecting correlations or assuming independent variables, the general rule of
propagation of uncertainties u3, u5 for a given function 6(7, 8) is presented in equation (9).
This equation is an estimation of the standard deviation of the function 6(7, 8), assuming
that u3, u5 are small compared to the partial derivatives.
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When calculating uncertainties after summing or averaging a set of values, special care
must be taken to deal properly with the random and systematic components of
uncertainty. The random uncertainty components reduce with the sample size as a result
of the law of large numbers, whereas the systematic uncertainty components are not
affected by the sample size. The recommended way to deal with both uncertainty
components when summing or averaging a set of values can be summarized in the
following equations based on the recommendations of the Join Committee for Guides in
Metrology (JCGM) [1]. When the uncertainty sources can be considered independent, the
combined standard uncertainty uA is calculated using equation (10). The combined
expanded uncertainty U is then calculated by multiplying the combined standard
uncertainty with a coverage factor. Considering the 95% confidence interval of a
Gaussian distribution, this coverage factor is 1.96. Therefore, the final equation to obtain
the expanded uncertainty U is presented in equation (11).
9: = B; &�-CDEFG2 =� + ; &�-I��J√3 =� +⋯� + N�8"OCDEF:2 P� + N�8"OI��Q√3 P� +⋯
(10)
R = 1.96 ∙ 9: (11)
Where:
� = number of samples
&�-CDEF = normally distributed random components
&�-I�� = uniformly distributed random components
�8"OCDEF = normally distributed systematic components
�8"OI�� = uniformly distributed systematic components
9: = combined uncertainty
R = expanded uncertainty
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3.1 UNCERTAINTIES IN THE
3.1.1 LONG-TERM RESOURCE ASSESS
Long-term trends
Different sources of solar radiation are available worldwide. Amongst others, measured
values, interpolated values and estimated va
available as, e.g., data from meteorological i
SatelLight, PVGIS, NASA, etc.
methods and, sometimes, covering differ
irradiance due to pollution and
irradiation for a typical year
in central Europe a significant
thanks to reduced pollution.
Brussels) where irradiation data from different sources are synthesized (
Figure 3). Similar trends have been reported in
Significant differences can be observed when comparing the databases between each
other or against reference meteorological observations.
a large extent on the source of the data
FIGURE 2: COMPARISON OF DIFF
HORIZONTAL IRRADIATION IN BRUSSELS, BELG
FROM THE ROYAL METEOROLOG
NCERTAINTIES OVER THE PV MODELLING CHAIN
NCERTAINTIES IN THE SOLAR RESOURCE
TERM RESOURCE ASSESSMENT
Different sources of solar radiation are available worldwide. Amongst others, measured
values, interpolated values and estimated values derived from satellit
data from meteorological institutes, Meteonorm, SoDa
, NASA, etc. These databases use irradiation data obtained by different
sometimes, covering different periods. Given the long term variations of
irradiance due to pollution and/or climate change, the time period used to estimate the
irradiation for a typical year often has an important influence (up to 10% and more). E.g.
nt brightening trend has been observed since the mid
reduced pollution. This is visible in the following figures for
where irradiation data from different sources are synthesized (
). Similar trends have been reported in [2], [3] and [4]
Significant differences can be observed when comparing the databases between each
other or against reference meteorological observations. Thus, the uncertainty depend
on the source of the data and the reference period used.
: COMPARISON OF DIFFERENT DATABASES PROVIDING YEARLY VALUES
ON IN BRUSSELS, BELGIUM WITH GROUND MEASURED DATA (BLACK LIN
ROLOGICAL INSTITUTE OF BELGIUM (KMI)
MODELLING CHAIN
Different sources of solar radiation are available worldwide. Amongst others, measured
lues derived from satellite models are
nstitutes, Meteonorm, SoDa HC-3, SolarGIS,
These databases use irradiation data obtained by different
long term variations of
climate change, the time period used to estimate the
influence (up to 10% and more). E.g.
since the mid 1980s
This is visible in the following figures for Uccle (near
where irradiation data from different sources are synthesized (Figure 2 and
[4] amongst others.
Significant differences can be observed when comparing the databases between each
he uncertainty depends to
.
IDING YEARLY VALUES FOR GLOBAL
URED DATA (BLACK LINE)
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FIGURE 3: COMPARISON OF DIFF
FOR GLOBAL HORIZONTAL IRRADIATION IN BRU
(BLACK LINE) FROM THE ROYAL METEOROLOG
LINE REPRESENTS THE 10 YEARS MOVING AVER
Long-term variability
When comparing yearly values to the long
presented above, the climate variability, calculated as the standard deviation (σ) of 60
years of Global Horizontal Irradiation (
average the standard deviation of yearly sums of
(based on a period of 18 years from 1985 to 2004).
are observed mostly for arid climatic regions.
were identified along coasts and in mountainous regions
dependencies must be accounted for
illustration, Table 1 presents an overview of the variability (σ) of
Meteonorm [6] for some weather
TABLE 1: VARIABILITY OF THE ANNUAL
SITES IN EUROPE.
Weather station
Madrid / Barajas (WMO nr: 82210)Roma/Ciampino (WMO nr: 162390)Bern-Liebefeld (WMO nr: 66310)Cabauw (WMO nr: 63480)Uccle(WMO nr: 64470) London Weather C. (WMO nr: 37790)Hamburg (WMO nr: 101410)Helsinki-Airport (WMO nr: 29740)
The variability of the resource has a stochastic behaviour (i.e.
Therefore, when evaluating the
can be used depending on the purpose of the analysis. The two different
defined based on whether one wants to assess the risk associated
: COMPARISON OF DIFFERENT DATABASES PROVIDING "MEAN IRRADIAT
L IRRADIATION IN BRUSSELS, BELGIUM WITH GROUND MEASURED DATA
E ROYAL METEOROLOGICAL INSTITUTE OF BELGIUM (
10 YEARS MOVING AVERAGE (MA) OF KMI DATA
When comparing yearly values to the long-term average, for the example
presented above, the climate variability, calculated as the standard deviation (σ) of 60
years of Global Horizontal Irradiation (GHI), is 6%. Similar studies e.g.
average the standard deviation of yearly sums of GHI is mostly in the range of 4% to 6%
period of 18 years from 1985 to 2004). Standard deviation values below 4%
or arid climatic regions. On the other extreme, values up to 10%
were identified along coasts and in mountainous regions. This shows that
accounted for when analysing the solar resource variability.
presents an overview of the variability (σ) of GHI
for some weather stations located across Europe.
ANNUAL GLOBAL HORIZONTAL IRRADIATION (GHI) FOR
Variability (σ) of GHI
Madrid / Barajas (WMO nr: 82210) 4.5% Roma/Ciampino (WMO nr: 162390) 4.0%
nr: 66310) 4.6% Cabauw (WMO nr: 63480) 5.7%
6.4% London Weather C. (WMO nr: 37790) 7.1% Hamburg (WMO nr: 101410) 6.6%
Airport (WMO nr: 29740) 4.6%
The variability of the resource has a stochastic behaviour (i.e.,
hen evaluating the economic value of a PV plant, two different approaches
can be used depending on the purpose of the analysis. The two different
ther one wants to assess the risk associated with the cash flow
IDING "MEAN IRRADIATION" VALUES
GROUND MEASURED DATA
STITUTE OF BELGIUM (KMI) – THE BLACK
term average, for the example from Uccle
presented above, the climate variability, calculated as the standard deviation (σ) of 60
), is 6%. Similar studies e.g. [5], show that in
is mostly in the range of 4% to 6%
Standard deviation values below 4%
, values up to 10%
that the geographic
when analysing the solar resource variability. As
as extracted from
RADIATION (GHI) FOR DIFFERENT
non systematic).
fferent approaches
can be used depending on the purpose of the analysis. The two different approaches are
with the cash flow
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the uncertainty due to yearly variations in the solar resource is considered.
For risk analysis (i.e., the risk associated with the cash flow during a single year), the
variability of the annual solar resource may become the main source of uncertainty.
When calculating the lifetime accumulated income instead, the uncertainty due to the
variability of the annual solar resource has a relatively small effect, as years with less
irradiation are generally compensated for by other years with more irradiation. Moreover,
when calculating the total energy yield over the lifetime of a PV plant, the systematic
components are the main source of uncertainty (i.e., their effect does not change from
year to year over the system lifetime).
3.1.2 MEASUREMENT UNCERTAINTIES
The total hemispherical solar radiation (beam and diffuse) is typically measured with
thermopile pyranometers, photodiode pyranometers or silicon sensors.
The performance of a solar irradiation measurement device in operation is correlated to
a number of parameters. Therefore, uncertainties in the measured irradiance can be
expected if the conditions differ significantly from calibration conditions. Most irradiance
measurement devices come with a maximal uncertainty interval specified by the
manufacturer. This value in turn, comes from several factors that contribute to the
overall uncertainty of the measurements.
The different contributions to the uncertainty of the ground-based irradiance
measurements from a thermopile pyranometer are explained in detail in [7], [8], [9] and
listed here below:
• Calibration uncertainty
• Drift over time
• Directional response (as a function of the azimuth and the zenith angle)
• Offset originated by the thermal radiation
• Offset originated by the temperature change
• Temperature dependency of the sensitivity
• Non linearity
• Spectral response
• Tilt response
• Long time drift of the measuring system
• Error of the analog to digital converter of the measuring unit
All the contribution factors listed above, must be combined using the procedure
described in section 2, i.e., following the methodology described by the Join Committee
for Guides in Metrology (JCGM) [1]. Uncertainty values for different pyranometers
(classified according the ISO 9060 as described in [8]) are presented in Table 2.
For thermopile pyranometers, the different uncertainty components are most often
specified by the manufacturer, whereas for silicon sensors usually only a gross
uncertainty value is provided. For example, for the Si-13TC-T-K the manufacturer
(Mencke & Tegtmeyer GmbH) specifies a total uncertainty in the measurement of
irradiance of ± 5%, expressed as the error of a device with temperature compensation
compared to a pyranometer within the operating range of -20°C to 70°C and vertical
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[11], also came with a reported "accuracy" of ± 5% of final value. In the case of the
ISET sensor from IKS Photovoltaik GmbH [12], a relative measurement uncertainty ≤
±4% for crystalline material and ≤ ± 5% for amorphous is reported.
A test developed by PHOTON magazine [13] compared several pyranometers / irradiance
sensors against one reference secondary standard device (Kipp & Zonen - CM 21). The
results represent the deviation of the total irradiation registered during a period of
almost one year, starting in November 2009 until final September 2010. The results
from the deviation of the measurements obtained for the most relevant silicon-based
sensors when compared with the reference as described in [13] are in the same order of
magnitude.
As stated e.g. in [14], [15], on average, the annual irradiation measured by crystalline
silicon sensors is 2% – 4% less than the irradiation measured by pyranometers. This
happens amongst others since crystalline silicon sensors have a flat surface and, thus,
are subject to higher reflection losses. In contrast, pyranometers have virtually no
directional error due to the geometry of the dome. Moreover, a flat surface suffers more
from dirt accumulation and hence, potentially higher soiling losses, than a dome
geometry.
The use of amorphous silicon sensors as a reference for calculating performance ratios is
not recommended since, amongst others, their poor long-term stability and their
significantly higher dependency on air mass and weather type.
Table 2 shows typical uncertainty values for the different types of instruments for
measuring the solar radiation.
TABLE 2: TYPICAL EXPANDED UNCERTAINTY VALUES (95% CONFIDENCE INTERVAL) FOR THE
DIFFERENT TYPES OF INSTRUMENTS FOR MEASURING THE SOLAR RADIATION
Device Expanded systematic
uncertainty (U)
Secondary standard pyranometer ~ ±2%
First class pyranometer ~ ±5%
Second class pyranometer ~ ±10%
Silicon sensor ~ ±5% - ±8%
3.1.3 MODEL UNCERTAINTIES
Satellite estimations
As presented in the Performance Plus Deliverable D2.3 “Engineering models for PV
system operations” [16], an extensive assessment of different satellite derived solar
radiation products ([17]) found that for latitudes from 20° to 60° and various climate
conditions, the standard deviation of the bias varies from 2% to 5% for the global
irradiance at yearly resolution. Results of a similar study [18], where data from five
irradiation sources was used for 18 sites in Europe, show similar values ranging from
1.47% to 5.82% at yearly resolution. As an example, Figure 4 shows the percentage
difference between the estimations of SoDa HC-3 for the Benelux region when compared
with meteorological stations from the Royal Netherlands Meteorological Institute (KNMI)
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the yearly mean error remains within a range of ±5%, in the
Netherlands, yearly mean errors exceeding 8% were found.
FIGURE 4: PERCENTAGE DIFFERE
BENELUX REGION DURING 2011. (RED MEANS O
UNDERESTIMATION)
Some alternative data source
alternatives is the Smart Ir
combining satellite and g
methodology. Another alternative
Physical Properties (CPP) algorith
analysis and results presented in
are summarized below in Table
TABLE 3: ROOT MEAN SQUARED
WITH GROUND DATA FROM 204 WEATHER STATIO
Belgium and The
Netherlands
(44 sites)
France
(160 sites)
Belgium, The Netherlands
and France
(204 sites)
Figure 5 shows the overall validation results and comparison of the presented
alternatives compared with measured data from the 204 weather stations. Both
CPP show a significantly higher accur
for daily values to almost 50% reduction for yearly values.
algorithm is slightly better than the
on-site pyranometer still provide
and the Royal Meteorological Institute of Belgium (KMI). Whereas for most of Benelux,
the yearly mean error remains within a range of ±5%, in the northern part of the
Netherlands, yearly mean errors exceeding 8% were found.
: PERCENTAGE DIFFERENCE BETWEEN SATELLITE (HC-3) AND GROUND STATIO
G 2011. (RED MEANS OVERESTIMATION OF SODA HC-
data sources were investigated in [16]. One of the proposed
alternatives is the Smart Irradiation Service (SIS), which reduces the uncertainty by
ground measured data through a kriging
alternative are the satellite irradiance estimates from the Cloud
) algorithm developed at KNMI (Dutch Weather Service)
analysis and results presented in [16], where the different alternatives are compared,
Table 3.
: ROOT MEAN SQUARED ERROR (RMSE) OF VARIOUS SATELLITE REFERE
M 204 WEATHER STATIONS IN BELGIUM, FRANCE AND THE NETHERLAND
SoDa HC-3 CPP
Hourly 24% 20% Daily 14% 10% Monthly 8% 4% Yearly 6% 2% Daily 14% 10% Monthly 8% 5% Yearly 6% 3%
Belgium, The Netherlands Daily 14% 10% Monthly 8% 5% Yearly 6% 3%
shows the overall validation results and comparison of the presented
alternatives compared with measured data from the 204 weather stations. Both
show a significantly higher accuracy than HC-3, with ca. 30% reduction of the
for daily values to almost 50% reduction for yearly values. The accuracy of the
algorithm is slightly better than the CPP algorithm, while measurements from a reliable
pyranometer still provide the most accurate data.
Whereas for most of Benelux,
northern part of the
3) AND GROUND STATIONS IN THE
-3 AND BLUE MEANS
One of the proposed
reduces the uncertainty by
round measured data through a kriging-of-difference
satellite irradiance estimates from the Cloud
m developed at KNMI (Dutch Weather Service). The
ent alternatives are compared,
OUS SATELLITE REFERENCES COMPARED
E AND THE NETHERLANDS
SIS
19% 8% 3% 2% 9% 4% 2% 9% 4% 2%
shows the overall validation results and comparison of the presented
alternatives compared with measured data from the 204 weather stations. Both SIS and
3, with ca. 30% reduction of the RMSE
The accuracy of the SIS
algorithm, while measurements from a reliable
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FIGURE 5: ROOT MEAN SQUARE ERROR (RMSE) OF VARIOUS SATELLITE REFERENCES COMPARED
WITH GROUND DATA FROM 204 WEATHER STATIONS IN BELGIUM, FRANCE AND THE NETHERLANDS
AND STANDARD RMSE ON PYRANOMETER DATA.
Conversion to the plane of the array
The conversion of the Global Horizontal Irradiance (GHI) to the plane-of-array (POA)
Irradiance requires two major steps: first, the GHI is split into its components, i.e.,
horizontal diffuse irradiance and horizontal direct irradiance, by the use of a
decomposition model; subsequently the diffuse, direct and ground reflected irradiance
components are transformed to the POA and recombined again in order to obtain the
global irradiance in the POA.
Different combinations of decomposition methods and algorithms for the horizontal to
the POA conversion were evaluated and the results presented in [16]. The results of the
validation using more than two years of five minutes data measurements from two
secondary standard pyranometers at a site in France is summarized in Table 4.
The validation shows that the highest overall accuracy was obtained using the Skartveit
decomposition algorithm in combination with the Hay and Davis conversion algorithm
with a normalized root mean square error (nrmse) of 4.8% for hourly resolution. Similar
values are reported in literature as e.g. in [19] where 4.5% for the Perez model is
reported and 5.4% for the Hay model.
TABLE 4: VALIDATION OF THE DIFFERENT ALGORITHM COMBINATIONS (ANALYZED PERIOD: MAY
2010 TO JANUARY 2013).
Hay Isotropic Muneer Perez
nrmse
Erbs 28.8% 28.8% 28.9% 18.7%
Ruiz_G0 5.1% 5.8% 5.3% 6.3%
Ruiz_G2 5.4% 5.4% 5.6% 6.4%
Skartveit 4.8% 6.6% 4.8% 5.2%
nmbe
Erbs -14.7% -14.8% -14.7% -9.7%
Ruiz_G0 1.1% -1.3% 1.5% 2.7%
Ruiz_G2 1.3% -1.0% 1.7% 2.8%
Skartveit 0.0% -2.5% 0.4% 1.4%
nmae
Erbs 17.3% 17.3% 17.3% 11.3%
Ruiz_G0 3.4% 3.8% 3.5% 4.3%
Ruiz_G2 3.5% 3.6% 3.6% 4.3%
Skartveit 3.0% 4.2% 3.1% 3.5%
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The performance, the abilities and the forecast uncertainties of irradiance predictions depend on a wide variety of parameters, e.g. the data base (respectively the model), forecast horizon, spatial resolution (grid space and averaging), temporal resolution (averaging), seasonal conditions and the prevailing weather conditions. Forecasting methods using different models and data basis have an individual optimal forecast range, both in time and space. Figure 6 shows the absolute RMSE of the irradiance forecast as a function of the forecast horizon, see [20]. This comparison is made for the European Centre for Medium-Range Weather Forecasts (ECMWF), Persistence model, Cloud-Motion Vectors (CMV) and a combined forecast, i.e., ECMWF combined with CMV.
FIGURE 6: RMSE FOR A SINGLE SITE AS FUNCTION OF FORECAST HORIZON FOR ECMWF-BASED,
CLOUD-MOTION VECTORS (CMV), COMBINED FORECAST (ECMWF + CMV) AND PERSISTENCE.
Figure 6 shows that the better the spatial resolution of the forecast model, the lower the time horizon of the forecast and vice versa. When it comes to forecasts of large areas, spatial averaging effects lead to smoothing of the errors, because forecast errors of single sites partly compensate each other. For example the mean RMSEs for the area of Germany are smaller by a factor of approximately 3 compared to the single site RMSEs.
Forecasts based on Numerical Weather Predictions (NWP)
The ECMWF provides forecasts with a spatial resolution of 0.25° x 0.25° and a temporal resolution of 3 hours. Therefore it is not able to resolve small scale clouds and their effect on irradiance, but weather systems. This forecast data is especially important for the planning and operation of solar systems and its grid integration. In the time horizon of 5 to 48 hours ahead forecasts based on NWP data are the first choice for single model forecasts. For shorter horizons (below 5 hours) the other forecasting schemes have lower uncertainties.
Forecasts based on satellite cloud motion vectors (CMV)
Meteosat Second Generation provides satellite data with a spatial resolution of approximately 1.2 km x 2 km and a temporal resolution of 15 minutes. The information on clouds and on the surface irradiance are derived using the algorithm by [21]. Cloud motion vectors (CMV) are derived from analyzing subsequent images and used to forecast the surface irradiance.
For the time horizon of 1 to 4 hours the CMV forecasting scheme outperforms the other
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accurate than the CMV forecasts due to the use of inwith minor measurements errors as inputconditions.
Combined forecast
The combination of NWP and the created forecast. Both data sources are considered with an optimized weighting depending on the forecast horizon. This approach reduces both, the frequency distribution of forecast errors as well
Forecasts based on sky imagers
Forecasts based on sky imagery are limited to very local areas and very short time ranges. In general this method can only consider clouds for the forecast, that are also viewed by the camera.
The uncertainty of sky image based forecasts and the forecast horizon depend on a large variety of factors: e.g. cloud height, cloud type, cloud convection, cloud formation, wind speed, wind direction, solar elevation as well as the geometry between the pothe camera, position of the sun and position of the clouds.
FIGURE 7: SURFACE IRRADIANCE
FORECAST (RED) AND THE IN-SITU MEASUREMENTS (B
Figure 7 shows an example of the sky imager based forecast of the next 22 minutes (red graph). The forecast has a binary characteristic, allowing valuestypical clear sky or the overcast irradiance.
Common forecast horizons are in the range of 10 to 25 minutes. Typically an area of up to 10 km around the imager can be detected. The cloud pixel resolution is in the range of several meters or higher.
Forecast uncertainties for the first few minutes might be high, because clouds in the circumsolar region are hard to detect.
For clear sky and overcast conditions a parameterization) has the same or even smaforecasting method based on sky imagery can only complement the other forecasting models by improving short-conditions.
single model forecasts. In the sub-hourly range forecasts of persistenceforecasts due to the use of in-situ ground measured irradiances
with minor measurements errors as input and the general persistence
and CMV forecast is used to improve the overall performance of the created forecast. Both data sources are considered with an optimized weighting depending on the forecast horizon. This approach reduces both, the frequency distribution of forecast errors as well as the maximum forecast errors.
Forecasts based on sky imagers
Forecasts based on sky imagery are limited to very local areas and very short time ranges. In general this method can only consider clouds for the forecast, that are also
The uncertainty of sky image based forecasts and the forecast horizon depend on a large variety of factors: e.g. cloud height, cloud type, cloud convection, cloud formation, wind speed, wind direction, solar elevation as well as the geometry between the pothe camera, position of the sun and position of the clouds.
: SURFACE IRRADIANCE AS FUNCTION OF FORECAST HORIZON FOR A SK
SITU MEASUREMENTS (BLUE).
shows an example of the sky imager based forecast of the next 22 minutes (red graph). The forecast has a binary characteristic, allowing values to be fixed to the typical clear sky or the overcast irradiance.
Common forecast horizons are in the range of 10 to 25 minutes. Typically an area of up to 10 km around the imager can be detected. The cloud pixel resolution is in the range of
Forecast uncertainties for the first few minutes might be high, because clouds in the circumsolar region are hard to detect.
For clear sky and overcast conditions a persistence model (e.g. irradiance parameterization) has the same or even smaller forecasting errors. Therefore the forecasting method based on sky imagery can only complement the other forecasting
-term and small-scale irradiance forecasts for broken cloud
persistence models are more situ ground measured irradiances
persistence of the weather
forecast is used to improve the overall performance of the created forecast. Both data sources are considered with an optimized weighting depending on the forecast horizon. This approach reduces both, the frequency
Forecasts based on sky imagery are limited to very local areas and very short time ranges. In general this method can only consider clouds for the forecast, that are also
The uncertainty of sky image based forecasts and the forecast horizon depend on a large variety of factors: e.g. cloud height, cloud type, cloud convection, cloud formation, wind speed, wind direction, solar elevation as well as the geometry between the position of
AST HORIZON FOR A SKY IMAGER BASED
shows an example of the sky imager based forecast of the next 22 minutes (red to be fixed to the
Common forecast horizons are in the range of 10 to 25 minutes. Typically an area of up to 10 km around the imager can be detected. The cloud pixel resolution is in the range of
Forecast uncertainties for the first few minutes might be high, because clouds in the
model (e.g. irradiance ller forecasting errors. Therefore the
forecasting method based on sky imagery can only complement the other forecasting scale irradiance forecasts for broken cloud
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3.2.1 UNCERTAINTY CHAIN
Different performance models are used
that a PV system can produce.
mathematical formulations, approach and
for the simulation. Moreover, t
temperature, array orientation, module and inverter performance,
for additional losses such as soiling, mismatch, cabling, e
and therefore have to be properly accounted for and combined
available algorithms result in uncertainties in the order of
The smaller value obtained from
model uncertainty of ±3%, an irradiation model uncertainty of
uncertainty of ±1%, but does not account for
shows the different steps in the
FIGURE 8: UNCERTAINTIES RELATE
The uncertainties on the environmental conditions are relatively large when estimating
the PV energy yield. It is expected that the system scenario approach, developed in D1.3
“WHAT-IF experimental validation and extended framework: A system scenario appro
[23], may prove to be well suited to increase the accuracy of forecasted
Further work is planned on investigating and evaluating the potential improvement
brought by this model reduction
In the following sections, the most important contributions to the uncertainty in
modelling are summarized.
3.2.2 PV MODULE TEMPERATURE MODEL
The model presented in [24]
ambient conditions. However, since the model requires a
power, it is not ideal to be used as engineering model for
Therefore, a simplified module temperature model was developed and presented in
The results of the validation are presented in
models with increasing complexity
speed are neglected, resulting in a
only dynamics are neglected
model III, only wind speed is neglected, res
NCERTAINTIES IN THE PV MODELLING
RTAINTY CHAIN
Different performance models are used in the industry to predict the amount of energy
produce. These models can differ significantly in their underlying
, approach and in the amount of data (assumptions)
Moreover, the large amount of input parameters as e.g. irradiation,
temperature, array orientation, module and inverter performance, user
as soiling, mismatch, cabling, etc. have inherent uncertainties
and therefore have to be properly accounted for and combined. Even the use of the best
result in uncertainties in the order of ±3.75% to
obtained from [19] (±3.75%), is calculated considering a
3%, an irradiation model uncertainty of ±2% and an inverter
, but does not account for other field-related uncertainties.
ferent steps in the PV modelling chain that are subject to uncertainties.
UNCERTAINTIES RELATED TO THE DIFFERENT STEPS IN THE PV MODEL
The uncertainties on the environmental conditions are relatively large when estimating
. It is expected that the system scenario approach, developed in D1.3
IF experimental validation and extended framework: A system scenario appro
, may prove to be well suited to increase the accuracy of forecasted
Further work is planned on investigating and evaluating the potential improvement
model reduction approach.
In the following sections, the most important contributions to the uncertainty in
TEMPERATURE MODEL
[24], is especially suited to analyse non-steady and non
ambient conditions. However, since the model requires a large amount of computational
power, it is not ideal to be used as engineering model for PV system operations.
Therefore, a simplified module temperature model was developed and presented in
validation are presented in Table 5, where four different regression
increasing complexity are compared. In model I, both dynamics and wind
, resulting in a multivariate linear regression model
only dynamics are neglected, resulting in a multivariate nonlinear regression model
, only wind speed is neglected, resulting in a multivariable linear dynamic
to predict the amount of energy
in their underlying
(assumptions) required
he large amount of input parameters as e.g. irradiation,
user-defined values
inherent uncertainties
Even the use of the best
±3.75% to ±5% [19], [22].
(±3.75%), is calculated considering a PV array
2% and an inverter
related uncertainties. Figure 8
modelling chain that are subject to uncertainties.
TEPS IN THE PV MODELLING CHAIN
The uncertainties on the environmental conditions are relatively large when estimating
. It is expected that the system scenario approach, developed in D1.3
IF experimental validation and extended framework: A system scenario approach”
, may prove to be well suited to increase the accuracy of forecasted PV energy yield.
Further work is planned on investigating and evaluating the potential improvement
In the following sections, the most important contributions to the uncertainty in PV
steady and non-uniform
amount of computational
system operations.
Therefore, a simplified module temperature model was developed and presented in [16].
different regression
, both dynamics and wind
multivariate linear regression model. In model II,
linear regression model. In
multivariable linear dynamic
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model is taken into account, resulting in a multivariable nonlinear dynamic regression
model with a (Koyck) geometric distributed lag scheme and V a constant.
TABLE 5: RMSE ([K]) FOR THE DIFFERENT MODELS AT DIFFERENT SAMPLE TIMES
Sample time
(minutes)
Model I Model II Model III Model IV
1’ 1.94 1.75 1.49 1.02 5’ 1.79 1.54 1.5 1.04 30’ 1.49 1.16 1.45 1.04
A literature review shows that model IV is extremely accurate compared to the state of
the art. The very low RMSE of ca. 1 K is significantly lower than what has been reported
in literature, e.g. [25], [26], [27], [28], [29].
3.2.3 PV ARRAY MODEL
Different PV array simulation programs that are available in the market use different PV
module models to predict the energy yield of PV systems. A comparison study of
different PV module models performed by [19], including three different models for
crystalline silicon modules, found error values in the order of ±1% to ±3%. A similar
value of ±3% is reported by [30]. The predicted performance, independently from the
model, is based on input measurements of irradiance and temperature and, therefore,
the uncertainties in these input variables have to be correctly accounted for through the
rule of propagation of uncertainty. As stated by [19], the ±1% to ±3% values are
including irradiation model errors but are not considering the additional system losses
such as soiling, mismatch, etc. For a broader analysis of the uncertainties linked to these
additional system losses, refer to section 3.2.5.
A sensitivity analysis of the electrical model from [24] is shown in Figure 9. The model
parameters (solar cell temperature (Tcell), Ideality factor, Short-circuit current (Isc),
series resistance (Rseries), temperature independent constant (Cnst) and shunt resistance
(Rshunt) are sequentially either increased or decreased by 10% compared to the
calibrated value, while the remaining parameters were kept constant. The results of the
sensitivity analysis are presented in Figure 9, where the effect in power output is shown.
The effects of radiative thermal losses are not embedded in the model yet, which
increases the error on clear sky days. The temperature of the silicon is overestimated
and hence the simulated operating voltage (and power) is lower than the real one. This
issue is currently being addressed by IMEC within WP1 and significant improvements in
the model are expected.
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FIGURE 9: SENSITIVITY ANALYSIS FOR THE MODEL PARAMETERS. SOLAR CELL TEMPERATURE
(TCELL), IDEALITY FACTOR, SHORT-CIRCUIT CURRENT (ISC), SERIES RESISTANCE (RSERIES),
TEMPERATURE INDEPENDENT CONSTANT (CNST) AND SHINT RESISTANCE (RSHUNT).
3.2.4 PV INVERTER MODEL
Compared with the other models in the PV modelling chain, the inverter model is subject
to smaller uncertainties. Typical uncertainty values are in the order of ±0.2% to ±0.5%
[31], [32]. The uncertainty of the inverter measured efficiency is given by the combined
uncertainty of the DC and AC power measurements. As shown by [31] the measurement
uncertainty of each efficiency value strongly depends on the actual power reading
relative to full scale. The overall measurement uncertainty of the inverter efficiency is in
the range between ±0.2% to ±0.6% of reading based on a 95% confidence interval,
being in average ±0.22% for actual power readings at full scale, ±0.29% at 50% of full
scale and ±0.45% at one quarter of full scale [31].
Although the load-dependent efficiency is covered by using a weighted average
methodology like the European efficiency, the voltage dependency is not always taken
into account. According to [31], the dependency of the efficiency with DC voltage is less
than 1% for most inverters with maximum efficiency of 97% or higher. Nevertheless,
transformer-less inverters with maximum efficiency values smaller than 95% exhibit a
significantly higher voltage dependency of around 2.5%. Photon magazine has been
testing the efficiency dependency of most commercial inverters, with contour plots of the
efficiency as a function of DC voltage and power to be found in each monthly issue.
The inverter model presented in [16] is based on [33] and is able to capture the
variations in electrical efficiency over the full range of operating conditions (i.e., different
power levels and input voltages). As described in [33], validation results show that the
model error (RMSE) of such a model is typically smaller than 0.2%.
3.2.5 OTHER FIELD RELATED UNCERTAINTIES
Additional losses that occur in the field are due to soiling, mismatch caused by row-to-
row shading and/or due to module tolerances, degradation, snow, reflection, DC and AC
cabling losses, availability, etc. These additional losses are typically based on
assumptions and therefore are thus subject to uncertainties that have to be quantified.
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below.
PV module soiling is caused, amongst others, by pollution, bird droppings, accumulation
of dust and/or pollen and its impact is strongly site dependent [34]. As a result, the
effect of dirt and soiling on the PV energy yield is difficult to model or extrapolate from
case studies and therefore a standard deviation of 2% is often assumed [35]. In
temperate regions with year-through rain, soiling losses are typically between 0% to 4%,
whereas in arid regions with seasonal dry periods and dust, extreme soiling losses up to
25% have been reported [22], [36]. This suggests that losses due to soiling could be
estimated by considering the rainfall information for the site and the cleaning schedule.
The uncertainty of soiling loss is estimated between ±0.4% for regularly cleaned
systems with more than 800 mm of yearly rainfall up to 2.5% or more for systems
located on a site with less than 200 mm of yearly rainfall.
Furthermore, the nameplate power of a PV module frequently differs from the measured
power. Most manufacturers have a nameplate band of 5 Wp which results in
approximately 2.5% variation from the best to the worst module, i.e., ±1.25%
uncertainty. In addition, flash tests that are carried out by independent test facilities
typically guarantee the measured values to ±2% [22]. Other authors, as e.g. [35],
consider a ±3% uncertainty based on typical tolerances usually given by module
manufacturers. A validation study of energy rating procedures [37] found uncertainties
for selected reference days in the order of ±5% for crystalline modules. This ±5%
uncertainty represents the combination of the uncertainties in measuring and modelling
of voltage, current, irradiance, module temperature and module power.
The degradation of c-Si PV modules is the result of the combination of two phenomena:
An initial decrease in efficiency that happens within the first few days of exposure, which
is known as Light Induced Degradation (LID); and a long-term, gradual decrease in
efficiency over the years [35]. An extensive analytical review made by NREL [38], shows
that the long-term yearly degradation for c-Si PV modules is around 0.5% with a related
uncertainty in the order of ±0.25%. The initial degradation that occurs within the first
days of exposure, is in the order of 0.16% with an uncertainty of ±1.7% and 1.31%
with an uncertainty of ±0.8% for multi-crystalline and mono-crystalline (p-type)
respectively [39].
Some other effects as e.g. snow, shading, reflection, DC and AC cabling, transformer
and availability also have an impact on the energy yield and therefore, have a related
uncertainty. For example, [35] takes a conservative value of ±5% of uncertainty due to
these additional factors.
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4.1 PROPAGATION OF UNCERTAINTY
The correct identification and quantification of the related uncertainty is especially
important when calculating the total real/expected energy yield of a grid-connected PV
system for financial risk assessment purposes. In the following a distinction will be made
between up-front estimation and ex-post (or hindsight) evaluation of system yield
and/or performance. The modelling uncertainties in up-front estimation are replaced by
measurement uncertainties of the monitoring system in ex-post evaluation. As shown in
the previous sections, the PV energy yield quantification/estimation is subject to several
uncertainties introduced by the different elements in the PV chain. An overview of the
energy flow in a grid-connected PV system with the uncertainties related to each
conversion step is shown in Figure 10. The uncertainties shown in Figure 10 are
classified in three main groups as described in Table 6.
TABLE 6: UNCERTAINTIES CLASSIFICATION
Group Uncertainty
Uncertainties in the solar resource
Climate variability (σClim)
Irradiation quantification (σIrr)
Conversion to the plane-of-array (σPOA-conv)
Uncertainties in the PV modelling
Temperature model (σTmp)
PV array model (σPVarr)
Inverter modelling (σInv)
Other field related uncertainties
PV field related uncertainties (σfld)
DC cabling (σC-DC)
AC Cabling (σC-AC)
Availability (σAv)
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FIGURE 10: ENERGY FLOW DIAGRA
THE MEASURED/CALCULATED PARAMETER
Figure 10 highlights the importance
uncertainties in the different steps
measured/expected energy production
Performance Ratio (PR), which quantifies the overall efficiency of energy conversion of
the PV system. The PR represent
reference yield Yr and should be accompan
on the uncertainty in the final yield
Energy output of a PV system
The energy output of a PV plant is calculated by integrating the product of voltage
current I (at maximum power) over a period as described in
� = � W(O) ∙ 0(O. ∙ ∆YY
Where ∆Y is the sampling interval.
The uncertainty of the energy
and voltage V for the case of a monitoring system
energy output E from a PV
models used and on external variables specific to the site as described in section
: ENERGY FLOW DIAGRAM IN A GRID-CONNECTED PHOTOVOLTAIC SYSTEM.
CALCULATED PARAMETERS AND IN RED THE RELATED UNCERTAINTIES
the importance of the correct identification and quantification of
uncertainties in the different steps in the PV energy conversion.
expected energy production or system yield Yf, is reported
, which quantifies the overall efficiency of energy conversion of
represents the ratio between the system yield
should be accompanied by an uncertainty, which
uncertainty in the final yield Yf and reference yield quantification
Energy output of a PV system (E)
plant is calculated by integrating the product of voltage
(at maximum power) over a period as described in equation (
is the sampling interval.
The uncertainty of the energy E depends on the uncertainty of the measured
for the case of a monitoring system. In contrast, when modelling th
PV system, the uncertainty depends on the combination of
models used and on external variables specific to the site as described in section
IC SYSTEM. IN BLACK,
ATED UNCERTAINTIES
of the correct identification and quantification of
. In general, the
together with the
, which quantifies the overall efficiency of energy conversion of
between the system yield Yf and the
which in turn depends
reference yield quantification Yr.
plant is calculated by integrating the product of voltage V and
(12).
(12)
measured current I
In contrast, when modelling the
s on the combination of
models used and on external variables specific to the site as described in section 3.
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The final system yield Yf is defined
nominal system power PN as described in equation
Z[ � �\C
The uncertainty of the final yield
measurements only. The nominal system power
thus not subject to uncertainties. Remark that this contracted value may differ from the
real nominal (STC) power of the
modules is subject to uncertainties as described above
modelling the uncertainty of the produced energy
Performance Ratio (PR)
The overall performance of the
calculating the ratio between the final system yield
reference yield is derived from the measured/
(GPOA) over the period and the irradiation at Standard Test Conditions (
Wh/m2 as described in equation
ZE � /]^_/`ab
\ � Z[ZE Figure 11 shows the uncertainty dependencies of the different
presented above. The dashed
the energy quantification/estimation
post evaluation) or modelled
FIGURE 11: FACTORS INFLUENCING
INDICATORS
defined as the ratio between the produced energy
s described in equation (13) below.
The uncertainty of the final yield �cd is determined by the uncertainty in the energy
measurements only. The nominal system power PN represents a contracted value and is
thus not subject to uncertainties. Remark that this contracted value may differ from the
real nominal (STC) power of the PV modules. In contrast to PN, the STC power of the
modules is subject to uncertainties as described above, which are accounted for when
modelling the uncertainty of the produced energy E.
(PR)
of the PV system is evaluated using equation
calculating the ratio between the final system yield Yf and the reference yield
is derived from the measured/estimated irradiation in the plane
over the period and the irradiation at Standard Test Conditions (
as described in equation (14).
shows the uncertainty dependencies of the different PV performance indicators
The dashed line in Figure 11 highlights the fact that the uncertain
estimation, depends on whether the system is monitored
modelled (up-front estimation).
FACTORS INFLUENCING THE UNCERTAINTIES OF PV PLANT PERFORMANCE
as the ratio between the produced energy E and the
(13)
is determined by the uncertainty in the energy
represents a contracted value and is
thus not subject to uncertainties. Remark that this contracted value may differ from the
he STC power of the PV
are accounted for when
equation (15), by
and the reference yield Yr. The
estimated irradiation in the plane-of-array
over the period and the irradiation at Standard Test Conditions (GSTC), i.e., 1000
(14)
(15)
performance indicators
fact that the uncertainty in
whether the system is monitored (ex-
PLANT PERFORMANCE
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4.2.1 MONITORING
When monitoring the actual energy production of a PV plant, the uncertainty on the
energy yield depends on the energy measurement device used by the monitoring system.
This can be either a dedicated energy meter or direct inverter energy readings. For the
case of dedicated energy meters, uncertainties in the order of magnitude of ±0.2% to
±0.5% are expected for class 0.2 or class 0.5 devices [14] [40], [41]. On the other hand,
if direct measurements from the inverter are used, a higher uncertainty in the order of
±3% is expected, as typically stated by inverter manufacturers, e.g. [42]. However,
other sources such as the monthly inverter assessments of Photon magazine show that,
in reality, errors of the inverter direct readings can be much lower than specified by the
manufacturer, with typical values in the order of ±1% to ±2%.
The uncertainty of the reference yield �ce is the result of the uncertainty of the solar
resource quantification in the plane-of-array ��� , which depends on the source, i.e.,
pyranometer, silicon sensor or satellite, as presented in section 3.1. For up-front
estimations, the climate variability (stochastic behaviour) has to be considered as well
and therefore the resulting uncertainty increases. Special care must be taken when
classifying each uncertainty as either systematic or variable (stochastic). Whereas
stochastic deviations vary from year to year, the impact of systematic deviations is the
same every year again for a certain system. The yearly variation in solar irradiation is a
good example of a stochastic deviation. On the other hand, deviations in yield due to
system characteristics occur each year again and are thus systematic.
Finally, the resulting uncertainty on the PR calculation is the combination of the final
system yield uncertainty σ5g and reference yield σ5h uncertainty as shown in equation
(16).
�]i � �;1ZE ∙ �cd=� + N Z[ZE� ∙ �ceP�
(16)
Considering the values presented in section 3 for the final system yield uncertainty σ5g and reference yield uncertainty σ5h, the combined uncertainty in yearly PR calculations is
typically between ± 2.5% and ± 3% for a good monitoring system (e.g. dedicated
energy meter and secondary standard pyranometer on site measuring the POA
irradiation and properly calibrated and maintained). The combined uncertainty on the
calculated PR can go up to around ±4% to ±6% when using lower accuracy irradiation
measurement devices (e.g. silicon sensor) or satellite estimations (based on the values
presented in section 3.1.3) and direct inverter readings.
4.2.2 MODELLING
When estimating the energy output of a grid-connected PV system, the uncertainty �j depends on the different models used and on external variables specific to the site as
discussed in section 3.2. For the typical range of values presented in section 3.2, the
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shown in equation (17) following equation (9), is in the order of ±6% to ±8%.
�j � 6��]klee , �m�n , �opQ� (17)
The uncertainty on the PV array output �]klee in turn depends on the uncertainties on the
resource quantification σqrr , the uncertainty on the conversion to the plane-of-array
model �]^_ (when the use of a transposition model is required as shown in section 3.1.3),
the temperature model uncertainty �aFs and the uncertainty on the nominal STC power �]tuv. The field related uncertainties is the result of the combination of all uncertainties
due to additional losses occurring in the field as described in section 3.2.5, i.e., soiling,
mismatch caused by row-to-row shading and/or due to module tolerances, degradation,
snow, reflection, DC and AC cabling losses, availability, etc.
The uncertainty in the resulting modelled performance ratio PR is then calculated in the
same way as explained before using equation (16).
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5.1 MONITORING GUIDELINES
The accuracy of a measurement instrument varies depending on its nature and quality
and on the parameter being measured. Therefore, no monitoring system is perfect and
there will always be a level of uncertainty. Acceptable tolerances for measurement
accuracy must be established. The monitoring guidelines are presented in Table 7 in the
Annex. This guidelines will help PV plant operators to monitor accurately and in a robust
and effective way the plant indicators required for assessing and improving the
operational performance of the plants during their lifetime. These guidelines reflect the
current state-of-the-art in monitoring and photovoltaic plant performance assessment as
represented in various standards and research results [43], [44], [45].
5.2 GUIDELINES FOR UNCERTAINTY ASSESSMENT IN PV MODELLING
The ability to accurately estimate the generated energy output from a grid-connected PV
system is crucial. However, as discussed in section 3.2, no model is perfect and there is
always a related uncertainty, which must be correctly assessed and reported. Besides
being crucial for financial risk assessment purposes, the uncertainty has a direct impact
on the ability to detect operational problems, especially when detecting performance
variations that are smaller than the measurement uncertainty of the parameters that
define the performance [45], [46].
The following guidelines when assessing the uncertainty in PV modelling, should be
followed:
• The uncertainty of the different elements in the PV modelling chain should be
assessed separately e.g. uncertainty of radiation separately from uncertainty of
the PV module performance model. Moreover, it is recommended to measure the
solar irradiation with the highest possible accuracy and always assess the
magnitude of the measurement uncertainty.
• The models must be validated only using normal operation conditions, i.e.,
performance and weather data during specific abnormal weather conditions or
during faults should be removed from the datasets.
• To validate a model, different sites with different conditions should ideally be
considered. However, one should be careful and follow the monitoring guidelines
presented in the previous section for each of the validation sites since they must
be monitored in the same way and following the same standards to ensure a
correct comparison between the different sites.
• The assessment period should ideally last one full year in order to include all
possible weather characteristics (seasons). However if a long-term measurement
campaign is not possible, at least it is recommended to include both solstices in
order to cover the full range of solar elevation angles.
• The PV array should be correctly characterized and clearly described, i.e., the
system design (e.g. inclination angle, azimuth, wiring diagrams with correct
lengths) must be documented. Moreover, the performance data of the PV
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i.e., no assumptions or generic devices should be used.
• All PV performance models rely on weather data; mainly on solar irradiation and
ambient temperature data. As shown in section 3.1, these can be measured
locally or estimated by satellite or from a nearby station. The uncertainty of these
data will depend on the methods used and therefore special care must be taken
when selecting the measurement devices. For a PV performance model validation
and uncertainty assessment, it’s recommended to use the highest possible
accuracy in all weather related data. Furthermore, as shown in section 3.2.2, the
module temperature model accuracy can be improved with wind speed
measurements and therefore, the higher the accuracy of the wind speed data, the
lower the uncertainty of the module temperature model.
• For PV performance model validations, the AC energy output of the array must be
measured as minimum requirement. Ideally DC measurements (i.e., DC current
and voltage) should also be made. They are useful not only for model validation
but also for fault detection as shown in Performance Plus deliverable D4.2
“Monitoring intelligence for predictive performance quantification” [47].
• It is recommended to use a standard method to assess the uncertainty of each of
the elements of the PV modelling chain that allows the identification of random
and systematic errors as explained in section 2. Moreover, to allow a clearer
identification and understanding of why and where the model deviates from the
measurements, different approaches are proposed as e.g. the residuals method
[46] or a sensitivity analysis of the models to different input parameters.
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The uncertainty quantification of solar energy yield calculations is important for
managing the financial risks of an investment in a photovoltaic system. Quantifying the
energy yield is subject to several uncertainties introduced by the different elements in
the PV model chain. In this document, a distinction is made between the uncertainties
related with up-front estimations and ex-post (or hindsight) evaluation of system yield
and performance. The modelling uncertainties in up-front estimation are replaced by
measurement uncertainties of the monitoring system in ex-post evaluation.
The most important element in the contribution to the total combined uncertainty is the
measurement and/or estimation of the solar resource. This uncertainty is the result of
the uncertainty of the solar resource quantification in the plane-of-array ��� , which
depends on the source, i.e., pyranometer, silicon sensor or satellite. For up-front
estimations, the climate variability (stochastic behaviour) has to be considered as well
and, therefore, the resulting uncertainty increases. Special care must be taken when
classifying each uncertainty as either systematic or variable (stochastic).
When estimating the energy output of a grid-connected PV system (up-front
calculations), in addition to the uncertainty on the estimation of the solar resource, the
uncertainty depends on the different models used and on external variables that are
specific to the site, such as soiling, mismatch caused by row-to-row shading and/or due
to module tolerances, degradation, snow, reflection, DC and AC cabling losses,
availability, etc. It has been shown that even when using the best available algorithms
for estimating the energy yield of a PV system, uncertainties in the order of ±3.75% and
±5% are expected.
When monitoring the actual energy yield of a PV plant (ex-post or hindsight calculation),
the uncertainty depends on the energy measurement device used by the monitoring
system. When calculating PV performance indicators as, e.g., performance ratio, the
resulting uncertainty is the combination of the energy yield uncertainty and the
uncertainty in the solar resource quantification. The combined uncertainty is calculated
using the rule of propagation of uncertainty. It has been shown, that the combined
uncertainty in yearly PR calculations is typically between ±2.5% and ±3% for a good
monitoring system, e.g., a properly maintained dedicated energy meter and secondary
standard pyranometer on site measuring the POA irradiation. The combined uncertainty
on the calculated PR can go up to around ±4% to ±6% when using lower accuracy
irradiation measurement devices (e.g. silicon sensor) or satellite estimations and direct
inverter readings.
The guidelines for uncertainty assessment in PV modelling and the monitoring guidelines
presented in this document, will help developers, investors and plant operators to
manage the financial risks and improve the operational performance of the plats during
their lifetime.
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ANNEX: MONITORING GUIDELINES TABLE 7: BEST PRACTICE GUIDELINES FOR SOLAR MONITORING OF GRID-CONNECTED PHOTOVOLTAIC SYSTEMS
Topic Subtopic Criteria Requirement Explanation Monitoring Irradiation All plants: Best
practice
> 100 kWp: Must
have
On-site good-quality measurement of in-
plane irradiation, preferably with a
crystalline silicon solar cell sensor
On-site measurements are recommended for PV systems greater than 100 kWp.
The type of sensor (silicon sensor or pyranometer) will depend on the purpose of
the monitoring and the required accuracy of measurements. It is important that
the solar cell sensor provides stability over time. Therefore a crystalline silicon
solar cell is required. Crystalline silicon sensors are advantageous when verifying
the PV plant's STC power. However, they are subject to a higher uncertainty (in
the range of ± 5%) compared to pyranometers. The use of amorphous silicon
sensor is not recommended due to their instability over time.
Monitoring Irradiation > 100 kWp: Best
practice
Individual sensors should be located in-
plane of each array in case of different array
orientations.
The conversion of the Global Horizontal Irradiance (GHI) to the plane-of-array
(POA) is subject to a typical uncertainty in the order of 3 - 5% (depending on the
orientation and location). By measuring the irradiation in the plane of each sub-
array on a PV system with more than one array orientations, this uncertainty is
eliminated.
Monitoring Irradiation All plants: Best
practice
> 1 MWp: Must have
At least 1 in-plane pyranometer of ISO
Secondary Standard quality or First Class
quality.
Pyranometers are recommended when the performance of the PV plant is to be
compared with performance figures estimated in the energy yield assessment.
The higher the quality of the pyranometer, the lower the uncertainty will be.
Monitoring Irradiation > 1 MWp: Best
practice
Horizontal irradiation measurements. On-site horizontal irradiation data allows comparison with e.g. standard
meteorological data from other locations. In addition, it can be used to assess
the health of the other in-plane sensors.
Monitoring Irradiation All plants: Best
practice
> 100 kWp: Must
have
Access to an independent irradiation
reference supplied by a nearby weather
station or derived from satellite data.
Independent irradiation reference allows for irradiation sensor benchmarking
and independent reporting: minimal monthly granularity and correlation with
local data required.
Monitoring Irradiation All plants: Must have Irradiation sensors must be placed on the
least shaded location and in accordance
It is important that the sensor is not impacted by shadow - particular attention
shall be given for early morning and late afternoon hours. Furthermore, the
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with manufacturer guidelines (i.e. fixation
and cabling).
sensor should be co-planar with the array since a small error on the orientation
of the sensor (tilt - azimuth), can result in a virtual time offset between the
production measurements and the irradiation measurement.
Monitoring Irradiation All plants: Must have Preventive maintenance and calibration of
the sensors in accordance to the
manufacturers guidelines
The accuracy if the irradiation measurement will drift in time if the sensor is not
subject to a maintenance and calibration plan. It is recommended to combine
the maintenance and calibration instructions of the manufacturer with the
cleaning strategy of the PV plant itself. Calibration reports, maintenance plans
and intervention reports should be stored in a central document management
system that is accessible to all involved stakeholders.
Monitoring Irradiation All plants: Best
practice
Automated access to in-plane on-site
irradiation data from a high-quality satellite
irradiation data provider. 15 minute
granularity and daily update frequency.
For recurring performance assessment purposes.
Monitoring Irradiation All plants: Best
practice
Digital communication between sensor and
datalogger
Analogue signal output and data collection can be a source of errors: conversion
boxes, cabling specifications, calibration factors to be applied.
Monitoring Irradiation All plants: Must have The irradiance is sampled at minimum 1'
resolution
Irradiation data can be highly variable. 15' instantaneous sampling can be
sufficient for monthly reporting purposes, but is not sufficient for daily
operations and detailed performance analysis purposes.
Monitoring Irradiation All plants: Best
practice
The irradiance should be sampled ideally at
15'' or higher resolution.
Short interval sample data can provide more accurate estimations over larger
periods of time. A high sample resolution is recommended for parameters that
vary directly with irradiance.
Monitoring Module
temperature
> 100 kWp: Best
practice
> 1 MWp: Must have
At least 1 module temperature
measurement per module type and per
integration type, sampled at minimum 1'
resolution
The direct measurement of the module temperature is recommended where
access to the rear of the module is possible. The temperature sensor should be
sticked with appropriate and stable thermal conductive glue to the middle of the
backside of the module in the middle of the array table, positioned in the centre
of a cell, away from the junction box of the module . The installation should be in
accordance with manufacturer guidelines (e.g. respecting cabling instructions
towards the dataloger). The accuracy of the temperature sensor, including signal
conditioning should be < ± 1 °C.
Monitoring Module
temperature
> 1 MWp: Best
practice
> 5 MWp : Must have
Measurement of module temperature at
different places across the PV array.
For large arrays, the module temperature should be measured for a module in
the centre of the array and for modules at edge locations where temperature
variation is expected.
Monitoring Meteorological
data
> 1 MWp: Best
practice
A local meteorological station is installed
measuring at least ambient temperature
The local meteorological station should be installed in accordance with the
manufacturers guidelines. The ambient temperature measurements should not
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> 5 MWp : Must have and wind speed at minimum 1' resolution. be affected by irradiance and therefore the use of solar radiation shield is
recommended (the shield also protects the sensor from the cooling effect from
the wind). For PV systems > 10 MWp, it's recommended to install one
meteorological station per each 25 Hectares.
Monitoring Meteorological
data
> 100 kWp: Best
practice
> 10 MWp: Must have
Automated data collection of independent
hourly meteo data (ambient temperature,
wind speed, snow coverage) from an
independent meteo source.
On-site meteorological station are subject to local phenomena and installation
specific results. Data from an independent meteo-station is less subject to this
while also being more stable and robust with respect to long term drift.
Therefore, both for performance assessment as for detailed analysis purposes, it
is recommended to enable automated data collection from a nearby
independent meteo reference.
Monitoring Stringbox > 100 kWp: Best
practice
> 1 MWp: Must have
All PV arrays with PV arrays > 8 kWp that
are not subject to DC input current
monitoring at inverter level, should have
current monitoring at string box level. The
minimal parameter requirement is current
measurement using 15" sampling and 15'
averaging at datalogger.
Recommended to increase up-time and for timely detection of faults.
Monitoring Inverter All plants: Best
practice
> 10 kWp: Must have
At AC level, collect energy data instead of
instantaneous power. Store and send
cumulative values instead of punctual or
daily cumulative values
In case of gaps in data collection or data communication, power measurements
will reduce the available information at aggregated level.
Monitoring Inverter All plants: Best
practice
> 10 kWp: Must have
Collect all inverter alarms Inverter alarms are a valuable source of information for fault detection,
organisation of the maintenance and even setting up preventive maintenance
actions.
Monitoring Inverter > 10 kWp: Best
practice
Collect all inverter alarms in accordance
with original manufacturers format
Some on-site dataloggers will transform the inverter alarms to a datalogger
specific category and thus reduce the amount of information available. This
should be avoided/
Monitoring Inverter > 10 kWp: Must have Monitor all control settings of the plant at
inverter level and grid injection level if
available.
Many plants apply control settings for local grid regulation or electricity price
optimisation. These settings need to be monitoring for reasons of contractual
reporting or performance assessment.
Monitoring Inverter > 10 kWp: Best
practice
Collect all inverter labels: serial number,
inverter ID, inverter input labels
In order to avoid mistakes in the configuration of the monitoring, it is
recommended that the monitoring solution captures automatically the device
configuration information. This also allows for inverter replacement detection.
Monitoring Inverter All plants: Best Measurement of the input DC voltage and For ad-hoc performance analysis purposes e.g. to allow the analysis of PV array
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practice
> 10 kWp: Must have
current to the inverter based on a <1"
sampling and <15' averaging.
performance, root cause analysis or possible MPP-tracking problems, the input
DC voltage and current need to be measured and stored separately.
Monitoring Inverter All plants: Best
practice
Measurement of inverter temperature if
there is risk of potential overheating
If there is considered to be a risk of inverter overheating, it is advisable to
measure the inverter temperature using a suitable thermocouple so that the
requirement for additional ventilation can be assessed.
Monitoring Energy meter All plants: Best
practice
> 100 kWp: Must
have
Automated collection of meter data with at
least daily frequency and 15' granularity.
Energy meter data is required for invoicing purposes but also serves as an
independent reference versus the inverter yield for benchmarking, analysis
purposes and loss detection. A high accuracy energy meter for the total output
of the plant with an uncertainty of ± 0.5% is required for plants > 100 kWp and
highly recommended for all plants.
Monitoring Energy meter > 100 kWp: Best
practice
Data collection via digital meter
communication or via smart meter reading
service.
Pulse meter readings via dataloggers can be subject to faults in cabling and
configuration while they will still not serve the invoicing purposes. Therefore it is
strongly recommended to use a smart meter reading service.
Monitoring Energy meter All plants: Best
practice
Send total cumulative values instead of
punctual or daily cumulative values.
Punctual or daily cumulative values will reduce performance analysis possibilities
in case of data gaps. Pulses could be missed and accuracy of the measurement is
depending on the pulse frequency.
Monitoring AC circuit All plants: Best
practice
> 500 kWp: Must
have
Monitor AC switch positions as for
(sub)plants
Monitoring AC circuit All plants: Best
practice
Monitor AC switch positions
Data
collection
Datalogger All plants: Best
practice
> 100 kWp: Must
have
Datalogger stores at least 1 week of data
and must have a built-in battery to allow for
alerting in case of power shut down.
Data storage is required to prevent data loss during communication network
outages.
Data
collection
Datalogger > 100 kWp: Best
practice
Datalogger stores 6 months of data and has
a built-in battery to allow for alerting in
case of power shut down.
The amount of storage needed depends on the expected time for repair the
network outage. An amount of storage that is equals to two times the highest
recorded communications outage is recommended. Typically 3 months of
storage are installed. Six months of storage is recommended.
Data
collection
Datalogger All plants: Best
practice
> 100 kWp: Must
have
After communication failure, the datalogger
resends all not sent information
automatically.
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Data
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Datalogger All plants: Best
practice
> 100 kWp: Must
have
Direct data connection from the site to the
monitoring servers.
A direct connection to a monitoring server with an SLA guarantees continuous
data access. If data passes via alternative monitoring servers without SLA, (e.g.
monitoring portal of the inverter manufacturer), this SLA can no longer be
guaranteed.
Data
collection
Datalogger > 100 kWp: Best
practice
Datalogger sends only new information to
the servers.
In order to avoid high communication costs and delay in data processing.
Data
collection
Datalogger > 100 kWp: Best
practice
Datalogger sends 1 aggregate and
compressed file for all connected devices.
In order to reduce the delay in file transfer and processing.
Data
collection
Datalogger All plants: Best
practice
> 100 kWp: Must
have
Automatic firmware updates of the
datalogger are disabled.
Firmware updates are subject to acceptance procedure with the monitoring
service.
Data
collection
Datalogger All plants: Best
practice
Datalogger should allow for sampling at
minimum 15" granularity and data
collection of maximum 15' averages.
Data
collection
Datalogger All plants: Must have Data format of file must respect standards
and has to be clearly documented.
Data
collection
Datalogger All plants: Best
practice
While 15' granularity of the data collection
and storage is considered as requirement,
5' granularity or higher is considered as best
practice.
Monitoring Documentation All plants: Best
practice
As-built files of the monitoring installations,
manuals and configuration information of
the installed devices, should be stored in a
central document management store that is
accessible to all involved stakeholders.
Data
collection
Documentation All plants: Best
practice
As-built files of the monitoring installations
should include at least a LAN diagram
providing a description of devices installed,
location of devices, interconnections, IP
configuration.
Data
collection
Communication > 500 kWp: Best
practice
Stable wired LAN connection.
Data Communication > 500 kWp: Best Industrial router that allows for GPRS or
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collection practice satellite communication back-up in case
LAN connection fails.
Data
collection
Communication All plants: Best
practice
> 500 kWp: Must
have
If GPRS signal < -108 dBm, foresee signal
amplifier or additional antenna's to reach
the required level. Foresee satellite
communication as a back-up.
Data
collection
Communication All plants: Must have The mobile communication subscription
should not expire in time and should allow
for the data quantity foreseen.
Data
collection
Communication All plants: Must have Ensure physical distance between (DC or
AC) power cables and communication
cables
Data
collection
Communication All plants: Must have Ensure that communication cables are
protected from direct sunlight
Data
collection
Communication All plants: Must have Ensure cables with different polarities are
clearly distinguishable (label or colour) for
avoiding polarity connection errors.
Data
collection
Communication All plants: Must have Specifications of cables and connectors.