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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)


ation under grant agreement No 308991.

WP2 Deliverable 2.4

Modelling


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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


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]


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


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.


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


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


), 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


. 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


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


. 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.


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


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


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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[37] W. F. Marion, B. Kroposki, K. Emery, J. Del Cueto, D. Myers, and C. Osterwald, “Validation of photovoltaic module energy ratings procedure at NREL,” National Renewable Energy Laboratory, Golden, Colorado, NREL/TP-520-26909, 1999.

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[39] M. A. Munoz, F. Chenlo, and M. C. Alonso-García, “Influence of Initial Power Stabilization Over Crystalline-Si Photovoltaic Modules Maximum Power,” Prog.

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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.


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.


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.


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.


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.


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.


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


practice

> 100 kWp: Must

have

After communication failure, the datalogger

resends all not sent information

automatically.

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Data

collection


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


practice

Datalogger sends only new information to

the servers.

In order to avoid high communication costs and delay in data processing.

Data

collection


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


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


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


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.

WP2 Deliverable 2 - Home - Performance Plus · 1 INTRODUCTION ... σPR Uncertainty on the...

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