PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
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PROJECT
308468
PVCROPS
Photovoltaic Cost Reduction, Reliability, Operational
performance, Prediction and Simulation
Collaborative Project
FP7-ENERGY.2012.2.1.1
DELIVERABLE
D2.2
First version of the technical specifications for grid
connected PV systems
31/10/2014
Francisco Martínez, Eduardo Lorenzo
UPM
UPM
UPM, DIT, ONE, RTONE, ACCIONA, INGETEAM,
REDT
PUBLIC
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
TABLE OF CONTENTS
1
INTRODUCTION
1
2
COMMON QUALITY ASSURANCE PRACTICES AND PVCROPS
OPTIONS
3
2.1 PV modules data sources and guarantees.
3
2.2 Energy yield forecast and PV performance modelling.
4
2.3 Testing performance: PR and PRSTC.
5
2.4 Measurement of operation conditions: pyranometers, thermocouples and
reference devices.
8
3
2.5 Thermal (infrared) revisions: dealing with hot-spots.
10
THE PVCROPS QUALITY ASSURANCE PACKAGE
12
3.1 Project profitability and risk.
12
3.2 Quality assurance procedures.
14
3.2.1 Initial Yield Assessment.
14
3.2.2 On-site horizontal and effective solar radiation measuring campaigns. 15
4
3.2.3 Laboratory testing of PV module samples.
16
3.2.4 Commissioning testing of entire PV plants.
17
3.2.5 Operation surveillance.
18
TECHNICAL SPECIFICATIONS AND QUALITY CONTROLS FOR GRID
CONNECTED PV SYSTEMS
19
4.1 PV system layout.
20
4.2 Definitions.
21
4.3 Standards.
21
4.4 Technical requirements.
22
4.4.1 PV arrays.
22
4.4.2 Supporting structure.
24
4.4.3 Inverters.
25
4.4.4 LV/MV transformer, protection and measurement cells.
26
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
4.4.5 Measurement, monitoring and data acquisition.
26
4.4.5.1 Effective incident irradiance and cell temperature sensors.
26
4.4.5.2 Meteorological station.
27
4.4.5.3 SCADA.
28
4.4.6 Buildings and auxiliary services.
28
4.4.7 Grounding and lightning protection.
29
4.4.8 Safety and fire protection.
29
4.4.9 Civil works.
30
4.5 Quality control procedures.
31
4.5.1 Prior to installation.
31
4.5.2 Commissioning.
32
4.5.3 After one year of operation.
36
REFERENCES
38
ANNEX 1. PV ENERGY PERFORMANCE MODELLING INTO THE FRAME
OF QUALITY ASSURANCE OF PV POWER SYSTEMS
CONNECTED TO THE GRID
40
ANNEX 2. DEALING IN PRACTICE WITH HOT-SPOTS
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
1. INTRODUCTION
Technical Quality Assurance Procedures of PV systems connected to the grid look for
tightening expectations and realities, both in terms of energy production along the PV
plant lifetime.
Expectation is established, prior to the construction of the PV plant, by means of a
forecast simulation exercise modelling the energy yield under a baseline scenario
describing, both, the solar resource at the site and the PV plant electrical performance.
More in detail, the solar resource is modelled by means of temporal series of operation
conditions values, namely in-plane irradiance, G, and solar cell temperature, TC; while
the PV plant performance is modelled through its power response to these values, PAC =
PAC(G,TC). Once the PV plant is in routine operation, testing and monitoring campaigns
are performed to analyse the fulfilment of these models.
It must be emphasized that predicting the evolution of the operation conditions at the
PV plant site unavoidably rely on available meteorological data, is far of being an exact
science and no one can holds responsible for future weather evolution. However, the
performance of the PV plant is a matter of technical quality and strict responsibilities
which use to be endorsed to Engineering, Procurement and Construction Contractors,
EPCC, whom, in turns, requires responsibilities from PV module and inverter
manufacturers. Because of that, the technical specifications of the PV plant and of the
testing and monitoring must not be rigorous from a scientific point of view and, at the
same time, discriminant enough to result in clear PV plant acceptance/rejection
decisions.
A rapid PV market growth is observed from 2005. Less than 10 years have being
enough to achieve a total installed PV power above 100 GW. An important part of this
market develops under “Project Finance” schemes associated to compulsory “Due
Diligence” procedures, looking for assuring the technical quality of the PV plant and,
so, to guarantee the investment recovery. Because of that, addressing the bankability of
PV projects, through the modelling of its energetic yield followed by on-site measuring
campaigns, has become a common PV engineering task. Roughly speaking, most PV
plants currently in operation fulfil the energy production expectation established at the
design, so that it can be suspected that few can be added to the current state-of-art of
specifying the technical characteristics and the corresponding quality controls of PV
plants. However, this is far of being the case, as revealed by significant discrepancies
between different PV performance models, in-field testing procedures and
acceptance/rejection criteria coexisting at today market.
During the last ten years, the IES-UPM has offered quality control services (yield
assessments, in-field testing, irradiance sensor calibrations, failure diagnosis, etc.) to the
PV industry and has carried out on-site testing campaigns for more than 60 PV plants
totalling 300 MW, in close relation with EPCC and financial entities. The experience
thus gained has been extensively published in high reputation scientific journals1-14, has
led us to the conviction of that considerable improvements can still be expected in terms
of uncertainty reduction along the whole technical quality assurance process, and has
now provided the grounds for the elaboration of the Technical Specifications for Grid
Connected PV Systems and for the corresponding Quality Control Procedures presented
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
at this report. These are the specific objectives of the Work Packages 2 and 9 of the
PVCROPS project.
This report, first, summarizes today technical common quality assurance practices,
disclosing relevant feebleness and discussing corresponding solutions. Three questions
are particularly addressed: modelling the energy performance of PV generators in
adherence with PV manufacturer’s datasheet information, in-field testing of PV plants
with as low uncertainty as possible and how to deal in practice with hot-spots.
Once these technical questions are clarified, a complete quality control package is
developed. It extends to all the project phases and comprises the following steps:
-
Initial Yield Assessment.
-
On-site horizontal and effective solar radiation measuring campaigns.
-
Laboratory testing of PV module samples.
-
Commissioning testing of entire PV plants.
-
Operation surveillance.
The consistency of this package is better appreciated when understood as a progressive
uncertainty reduction process. Hence, uncertainty estimation and corresponding impact
on project profitability and risk are addressed.
Finally, the report presents a set of technical specifications and quality control
procedures of general application for large ground PV plants and BIPV systems.
Looking for direct market applicability, they are presented in such a way that they can
be easy adapted to the contractual frames regulating the construction of PV plants.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
2. COMMON QUALITY ASSURANCE PRACTICES AND
PVCROPS OPTIONS
Common quality assurance practices deserving further comments concerns:
2.1 PV modules data sources and guarantees.
PV modules are rated in power at the so called Standard Test Conditions, STC (G* =
1000 W/m2 and TC=25oC). However, their efficiency varies with irradiance and
temperature, so that, the power they deliver at other operation condition is given by:
𝑃𝐷𝐶 (𝐺, 𝑇𝐶 ) = 𝑃∗
𝜂 (𝐺,𝑇𝐶 )
𝜂∗
(1)
where the superscript * means STC, P* is the rated power and η means efficiency.
Because PV modules operate in a wide range of (G, TC) values, dealing with them
requires not only the rated power values but also information related with the efficiency
variation with irradiance and temperature. Obviously, in order to preserve the PV
modules performance guaranties, this information must be agreed with the PV module
manufactures.
Manufacturers provide datasheets for each PV module type. According with the
standard EN 50380 (“Datasheet and nameplate information for photovoltaic modules”)
they must contain:

The Nominal Operation Cell Temperature, NOCT.

Characteristic values for three points of the I-V curve (short circuit current, ISC,
open circuit voltage, VOC, and power and voltage at maximum power point, PDC
and VM) at two different (G, TC) conditions: at STC (G*, TC*) and at NOCT (G =
800 W/m2, TC = NOCT ≈ 45o C).

The efficiency reduction from STC to (G = 200 W/m2, TC*).

The temperature coefficients for open circuit voltage, β, and for short-circuit
current, α.
However, this norm is nowadays far of being generally respected. In contrast, despite
not required at EN 50380, all the datasheets we know include the value of the
temperature coefficient for power, γ. Our experience with today datasheets suggests two
main drawbacks:
1. Datasheets content is often not fully coherent. For example, there are two ways
of deriving P* values from I-V curves measured at other than STC conditions.
The one is to extrapolate to STC the full I-V curve in accordance with IEC60891, using α and β. The other consist on, first, obtain the maximum power of
the measured curve and, second, to extrapolate to STC only this value, using γ.
Ideally, both results should fully coincide. However, they usually differ about 23%, and our experience includes differences up to 5%. This can be a
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
consequence of differences on the characteristics of different specimens
belonging to the same PV module type. In fact, module to module parameter
variations has been pointed out as a significant source of uncertainty15, 16. As a
representative example, observed width ranges at a flash-list of 126 crystalline
silicon PV modules recently received at our laboratory are 3% for P*(which
corresponds to a common market tolerance), 6.4 % for ISC*, 1.2% for VOC*, 5.2%
for IM* and 5.4% for VM*.
2. Today standard guarantees are restricted to the value of P* while the rest of the
datasheet content is given by way of general information, but not particularly
intended to support efficiency quality controls. Because of that, guarantees on
other than P* values must be agreed with the PV modules manufacturer, prior to
the PV modules supply. The IES-UPM experience on the quality control of large
PV plants includes several cases of PV manufactures providing guarantees also
on γ values. This is important because thermal losses (due to TC≠TC*) use to be
particularly relevant at the energy balance of a PV plant.
Both, datasheet limitations and doubtful representativeness of data from particular
specimens, represent uncertainty sources for energy yield forecasts performed at the
project design. Uncertainty can be further reduced by fitting the performance model
with data directly measured at the concerned PV array. However, that can only be made
once the PV generator installation. Hence, after the responsibility guarantees chain has
been established. In practice, that often leads the involved EPCC to a rather unfair
position: to assume responsibilities on the full energy behavior of the PV array having
the only formal support of PV manufacturer guarantees on P* values. That demands to
enlarge the PV manufacturers’ commitment to also give guarantees on other than P*
values. This is likely easier when such values are directly obtained from datasheets (for
example, the NOCT and temperature coefficients) that when they are extracted from
other than PV manufacturers information (for example, the value of the parallel
resistance obtained from a I-V curve measured on a particular specimen at an
independent organization).
2.2 Energy yield forecast and PV performance modelling.
Energy yield forecast is more often performed by means of commercially available
software packages17 (www.pvresources.com). Most of them describe the PV behavior
by means of the so called 5 parameters one diode model equation. Required input data
for this model (series and shunt resistance, photocurrent, saturation current and diode
quality factor) are not found at the PV manufacturer datasheets. Instead, they are
derived from certain software authors assumptions from I-V curves measured on
particular specimens at independent testing organizations, which entail a risk of
breaking-off of the responsibility chain.
For example, PVsyst, maybe the most worldwide extensively used PV software, relies
on own suppositions for the parallel and series resistances or, if available, on I-V curve
databases from TISO (Swiss test center for PV modules) and from PHOTON (German
PV journal) and warns the user about the lack of PV manufactures commitment “…for
definitive simulations, the user is advised to carefully verify the library data with the
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
last manufacturer’s specifications… We drop out any responsibility about the integrity
and the exactness of the data and performance including in the library.” (Disclaimer at
the PVsyst User’s Guide). The same is found at the concerned databases: “The database
was compiled to the best of our knowledge and with the greatest possible accuracy. At
the same time, PHOTON cannot be held responsible from any damage that results from
the use of this database.” (Disclaimer at Photon database). The PVsyst authors have
even expressed their wishes of further PV manufactures commitment: “…These data are
key parameters of the model, and should be part of the module’s specifications in the
future.” 18. However, these data remain absent from the PV module manufacturer’s
engagement.
In order to overcome this problem, PVCROPS has reviewed available PV performance
models at the lights of, both, accuracy and adherence to datasheet information,
concluding that the model given by:
𝜂(𝐺,𝑇C )
𝜂∗
= [1 + 𝛾 · (𝑇C − 𝑇C∗ )][𝑎 + 𝑏
𝐺
𝐺∗
𝐺
+ 𝑐 · ln 𝐺∗ ]
(2)
is particularly convenient. This model describes thermal losses by means of γ, a value
which is always found at manufacturer datasheets. Moreover, the three parameters, a, b
and c, describing the efficiency dependence on irradiance are obtained from values
corresponding at two other than G* irradiance values, which must also be found at
datasheets, providing they comply with EN 50380.
Details on this reviewing research are found at Annex 1. The model has been included
at SISIFO, a PV simulation software developed at PVCROPS, free available at
www.pvcrops.eu, and it is used on the here proposed technical specifications for on-site
measuring campaigns.
2.3 Testing performance: PR and PRSTC.
Technical performance of grid connected PV plant is usually assessed by means of the
Performance Ratio, PR, observed along a given operation period. This index, defined in
IEC 61724 (“Photovoltaic system performance monitoring: guidelines for measurement,
data exchange and analysis”), is calculated as
𝑃𝑅 =
𝐸AC
∗ 𝐺T
𝑃N
∗
(3)
𝐺
where EAC is the energy effectively delivered to the grid, 𝑃𝑁∗ in the nominal power of the
PV generator, understood as the product of the number of PV modules multiplied by the
corresponding in-plate STC power, and GT is the in-plane yearly irradiation during that
period. The PR value can be directly calculated without any kind of modelling, because
EAC, 𝑃𝑁∗ and GT values are directly given by the billing energy meter of the PV plant, the
PV manufacturer datasheet (or the flash-list) and the integration of a solar irradiance
signal.
This mere PR lumps together avoidable and unavoidable losses. The first ones are due
to technical imperfections deriving on real performance below the nominal
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
characteristics announced by the EPCC or by the equipment manufacturers
(underrating, mismatching, under efficiency, etc.), while the second ones are intrinsic to
the functioning (thermal and irradiance efficiency losses) or to the design (shades and
inverter saturation) of the PV plant. Therefore, only avoidable losses are really related
with the technical quality of the PV plant. Nevertheless, this mere PR is still adequate
for qualifying that technical quality, providing that full year periods are considered.
This is because, for a given PV plant and site, the PR value tends to be constant along
the years, as much as the climatic conditions tend to repeat. This way, contractual
management of the PR only requires of an agreement on the guaranteed value (derived
from the initial yield simulation exercise and a margin of safety agreed among the
parties involved on the project), on the solar radiation measuring device (further
discussed on the next section of this report) and on the correction to account for longterm degradation effects. However, quality assurance procedures also include the
consideration of other than full year periods. Reception testing when the PV plant is put
into commissioning, and monthly production reporting are two relevant examples.
When sub-year periods are considered, the PR dependence on unavoidable and timedependent losses requires corresponding correction in order to properly qualify the
technical quality of a PV plant. Otherwise, the qualification result of a same PV plant
varies with the climatic conditions of the qualification period, which seems contrary to
the common sense. These losses are the ones derived from the efficiency variation with
temperature and irradiance, from intrinsic to PV design phenomena: shades and inverter
saturation, and from possible angular and spectral response differences between the PV
generator and the irradiance sensor. A convenient way of doing such correction is to
consider the so called Performance Ratio at Standard Test Conditions, PRSTC, which can
be properly understood as the PR of the same PV plant but corresponding to an
hypothetic period with the PV generator is permanently kept at STC (G = 1000 W/m2;
TC= 25oC). The PRSTC for a given period, ∆t, is given by:
PRt
(4)
PR STC,t 
 (1  E
u
u
)
where ∆E represents energy losses during the considered period and the subscript “u”
extends to all the unavoidable energy losses phenomena. All these losses must be
calculated from measured G and TC values, which require some kind of modelling. The
coherence of the full quality assurance process requires using the same PV performance
model that at the energy yield forecast. Otherwise, the assumptions of energy forecast
underlying are not properly verified.
Thermal losses are typically the most significant at the global energetic balance of a PV
plant. In energy terms, ∆𝐸 𝑇𝐶 ≠𝑇𝐶∗ , they result from weighting the power thermal losses,
∆𝑃𝑇𝐶 ≠𝑇𝐶∗ , by the incident irradiance. That is:
∆𝐸𝑇𝐶 ≠𝑇𝐶∗ =
∫∆t ∆𝑃𝑇 ≠𝑇∗ ·𝐺·dt
𝐶 𝐶
∫∆t 𝐺·dt
(5)
where ∆𝑃 𝑇𝐶 ≠𝑇𝐶∗ , in accordance with the here selected PV performance model, defined by
equation (2), is given by:
∆𝑃𝑇𝑐≠𝑇𝐶∗ = 𝛾 · (𝑇C − 𝑇C∗ )
(6)
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
As a representative example, Figure 1 shows the evolution of the weekly PR and PRSTC,
observed from March 2011 to February 2012, at a PV plant located in Navarra (Spain).
Thermal and irradiance losses have been calculated with the model defined by equation
(2), and the plant is free of shades and inverter saturation. Table 1 presents the
corresponding mean, maximum and minimum values for this year and also for the year
from March 2012 to February 2013. As expected, the PRSTC performs significantly
more constantly, roughly, ±3% versus ±15%. We believe this is a great benefit, in terms
of sound technical quality evaluation, in return for the pain of measuring not only G but
also TC and of performing rather simple modelling just based on PV manufactures
datasheet.
Figure 1. Observed evolution of the weekly PR and PRSTC, from March 2011 to February 2012, at a PV
plant located in Navarra (Spain).
PRW
PRSTCW
March 2011 – February 2012
Mean
Maximum
Minimum
1.06
0.85
0.93
(+12.8 %)
(-8.9 %)
0.97
0.94
0.95
(+2.3 %)
(-1 %)
March 2012 – February 2013
Mean
Maximum
Minimum
1.040
0.752
0.936
(+10.5 %)
(-18.7 %)
0.987
0.934
0.953
(+3.3 %)
(-1.9 %)
Table 1. Mean, maximum and minimum values of weekly PR and PRSTC values observed along two years
at a PV plant located in Navarra (Spain). PRSTC is significantly more stable than PR
It is worth mentioning that some projects have addressed technical quality on the basis
of observed PR values by considering a different guaranteed value for each month. The
12 reference PR values are established by a simulation exercise on the basis of solar
radiation and ambient temperature databases. However, the validity of this PR monthly
7
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
correction procedure is likely not general but restricted to particular climatic regions. In
fact, our results show weekly PR variations up to 5 % on the same month, which seem
not adequate for large scale PV plants qualification. Because of that, the here proposed
technical specifications for on-site measuring campaigns rely on the PRSTC concept.
2.4 Measurement of operation conditions: pyranometers, thermocouples
and reference devices.
Solar radiation databases provide input data for energy yield forecast in terms of
broadband (as seen by pyranometers) horizontal radiation. Then, energy yield forecast
requires transposition from horizontal to the plane of array and also correction for
angular, spectral and soiling losses. This way the so called effective (as seen by PV
generators) radiation is obtained.
However, when on-site testing of PR or PRSTC values, effective irradiance can be
directly measured by using a reference module of the same type of that the concerned
PV generator. This way, such correction and corresponding uncertainties (typically
about 3%) are fully avoided. Hence, reference modules are particularly suitable for
assessing the technical quality of PV plants. Nevertheless and despite this is
unanimously recognized at specialized laboratories7, 19-23 such modules are seldom used
at today commercial PV plants. A possible explanation is that reference modules are
understood as similar to reference cells. This is theoretically correct, because their
angular and spectral responses are the same. However, their practical use significantly
differs. A large variety of reference cells is found at the market, and some are nonstandardized and bad quality products (poorly encapsulated, suspicious calibrations,
etc.) often leading to unacceptable measurement errors24. That is in detriment of the
general reputation of reference devices and in favour to opt for pyranometers, which are
well standardized and good quality products. To make matter worse, reference modules
are not the object of routine market activities. Instead, they must be specifically
prepared which means stabilization followed by calibration. The stabilization
requirements are given at international standards IEC 61215 and IEC 61640. In any
case, this makes a minimum Sun exposition of 60 kWh/m2. It is worth mentioning that
round-robin tests performed in European laboratories have shown calibration accuracy
better than 2% for crystalline silicon modules25. It is also worth mentioning that
reference modules and PV generators response to dirt accumulation is the same: neither
the irradiance measured by the reference modules or the efficiency of the PV generators
are affected by isolated dirtiness as, for example, caused by depositions of birds.
As a representative example, Figure 2 shows the evolution of the weekly PR observed
from mid-June to end-July 2014 at a PV system located in Madrid. PRPYR and PRREF
represent the PR corresponding, respectively, to irradiation measured by a pyranometer
and by a reference module. The value of PRSTC with irradiation measured by a reference
module has also been included, PRSTC,REF. Table 2 shows the corresponding numerical
values. An improvement of up to 2% in accuracy is obtained by using a reference
module instead of a pyranometer.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Figure 2. Weekly PR observed from mid-June to end-July 2014 at a PV plant located in Madrid. PRPYR
and PRREF represent the PR corresponding, respectively, to irradiation measured by a pyranometer and by
a reference module. The value of PRSTC with irradiation measured by a reference module has also been
included.
Performance Ratio
PRPYR
PRREF
PRSTC,REF
Mean
0.775
0.801
0.880
Maximun
0.824
0.819
0.889
Minimun
0.726
0.784
0.870
Range
± 4%
± 2%
± 1%
Table 2. Main values corresponding to Figure 2. Using reference modules instead of pyranometers
improve the PR accuracy of up 2%.
On similar lines, the open circuit voltage of a reference PV module is in practice a better
indicator of TC that direct temperature measurements given by thermocouple glued to
the back of the modules. The VOC method, described at IEC 60904-5, avoids possible
thermocouple sticking failures and also the uncertainty associated to non-homogeneous
temperature distributions inside the PV modules. This is because the thermocouple is
glued to a single point while the open circuit voltage of the PV module integrates the
values corresponding to all the solar cells.
To summarize, reference Si-x modules are very good quality products (design approved
by IEC 61215, measurements normalized by IEC 60904-1) allowing in-field
measurements of PV generator characteristics with the lowest possible uncertainty. The
here proposed technical specifications rely on these devices.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
2.5 Thermal (infrared) revisions: dealing with hot-spots.
A hot-spot consists of a localized overheating in a photovoltaic (PV) module. It appears
when, due to some anomaly, the short circuit current of the affected cell becomes lower
than the operating current of the whole module and giving rise to reverse biasing, thus
dissipating the power generated by other cells as heat. Figure 3 shows two infrared (IR)
images of hot-spots. The anomalies that cause hot-spots can be external to the PV
module (shading or dust) or internal (micro-cracks, defective soldering, potential
induced degradation –PID). In general, when a hot-spot persists over time, it entails
both a risk for the PV module’s lifetime and a decrease in its operational efficiency.
(a)
(b)
Figure 3. Hot-spots in two modules. (a) General view of a tracker with hot-spots caused by PID. (b)
Hot-spot caused by micro-cracks. The operating temperature of the hot-spot is 87 ºC while the mean
temperature of the rest of the module is 53 ºC.
Hot-spots are relatively frequent in current PV generators and this situation will likely
persist as the PV technology is evolving to thinner wafers, which are prone to
developing micro-cracks during the manipulation processes (manufacturing, transport,
installation, etc.). Fortunately, they can be easily detected through IR inspection, which
has become a common practice in current PV installations. However, there is a lack of
widely accepted procedures for dealing with hot-spots in practice as well as specific
criteria referring to the acceptance or rejection of affected PV modules in commercial
frameworks. For example, the hot-spot resistance test included in IEC-61215
(Crystalline silicon terrestrial photovoltaic modules. Design qualification and type
approval) is successfully passed if the module resists the hot-spot condition for a period
of 5 hours, which suggests that this standard addresses transitory hot-spots, as those
caused by also transitory shading, but not permanent ones, caused by internal module
defects. Along the same lines, the IEC-62446 (Grid connected photovoltaic systems.
Minimum requirements for system documentation, commissioning tests and inspection)
only states: “A hot-spot elsewhere in a module usually indicates an electric problem
[…] In any case investigate the performance of all modules that show significant hotspots”. Furthermore, a draft of the IES-60904-12 (Photovoltaic devices: infrared
thermography of photovoltaic modules) clearly establishes how to capture, process and
analyse the IR images, but still does not set out any PV module acceptance/rejection
criteria. Not surprisingly, the IES-UPM experience includes many cases of EPCC and
PV module manufacturers requesting advice on how to proceed with collections of IR
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
images of affected modules, and whose corresponding contracts lacked the previsions to
ask a relevant question: which affected PV modules should be changed under the PV
manufacturer’s responsibility?
In order to ask this question, PVCROPS has investigated the hot-spot impacts on the
lifetime and on the operational efficiency of the affected module (that is, the efficiency
of the PV module when it is integrated at a PV generator and connected to an inverter
able of tracking the maximum power point of the assemble). First, hot-spots are
characterized by the temperature increase of this cell in relation to the non-defective
∗
ones and normalized to the STC irradiance, ∆𝑇𝐻𝑆
. Then, using observations on 200
affected modules as experimental support, the following acceptance/rejection criteria
are proposed:
1) If ∆𝑇𝐻𝑆 ∗ < 10°𝐶, to consider the module non-defective, except in the case that
one or more by-pass diodes are defective.
2) If ∆𝑇𝐻𝑆 ∗ > 20°𝐶, to consider the module defective.
3) If 10°𝐶 < ∆𝑇𝐻𝑆 ∗ < 20°𝐶, to consider all the modules with an effective power
loss (measured as a decrease in the operating voltage in relation to a nondefective module of the same string) that exceeds the allowable peak power
losses fixed at standard warranties defective.
It is worth mentioning that this procedure and acceptance/rejection criteria have already
been applied by the IES-UPM when mediating in hot-spot conflicts between module
manufacturers and EPCC during the last years. Details on this research are found at
Annex 2.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
3. THE PVCROPS QUALITY ASSURANCE PACKAGE
3.1 Project profitability and risk.
PV project investment requires estimate, both, profitability and risks. Profitability is
addressed by calculating the most probable value of the yearly energy production,
which is a key parameter for the baseline economic scenario. This value is typically
denoted as EP50, where “E” means yearly energy and “P50” means that this value is just
at the middle of the probability range. In other words, the probability of real energy
production exceeding this value equals the probability of being below it. In practice,
EP50 is just the direct result of a forecast simulation exercise, modelling the energy yield
with some dedicated software, under a solar climate scenario described by an available
solar radiation data base, a PV plant described by the technical information announced
by the equipment manufacturers (PV module, inverter and transformer datasheets) and
an allowable energy losses scenario agreed by the owner, the financing bank and the
EPCC in charge of the construction of the PV plant.
Risks derive from the fact that such simulation exercise relies on a set of suppositions
that do not necessarily will exactly be matched by later realities. For example, the solar
radiation in the years to come can be somewhat different of the solar radiation observed
in the past and that provided the grounds for the elaboration of the database. Differences
among initial suppositions and further realities are denoted, somewhat inappropriately,
as “errors” and are obviously unknown at the beginning of the project. Because of that,
they are treated as random variables, each defined by its corresponding mean and
standard deviation values, ε and σ, respectively. Table 3 lists the main reasons for such
differences, more properly defined as “uncertainty sources”
Assuming these uncertainty sources are independent each other, the expected yearly
energy production is properly described by means of a Gaussian distribution with
standard deviation, σT, given by:
𝑁
𝜎𝑇 = √∑ 𝜎𝑖2
1
where “i” extends to all identified uncertainty sources. Then, basic statistics allows
quantifying the risk, linking expected production and occurrence probability values. For
example, the EP90, i.e. the energy production value having 90% probability of being
exceeded by real production is given by:
𝐸𝑃90= 𝐸𝑃50 − 1.28𝜎𝑇
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Uncertainties
First Year
20 years
Database, σDB
Mean Bias Error and Root Mean Square Error of Yearly
Irradiation given at corresponding database.
Interannual variability, σAV
The range between the extreme
Yearly Global Irradiation values
observed along a period of 10 years
is understood as the 95%
confidence interval
No applicable
Long term trend, σDL
Non applicable
0,9% (Note 1)
Solar radiation, σSR = (σDB2 + σAV2+ σDL2)1/2
Transposition from horizontal to
tilt radiation and operation
temperature estimation , σOC
4% (Note 2)
Power response of PV system, σPR
2% (Note 3)
Simulation, σSIM = (σOC2 + σPR2)1/2
Initial STC of PV arrays, σIP
2% (Note 4)
Ageing, σAG
No applicable
1% (Note5)
STC Power of PV arrays, σSTC = (σIP2 + σAG2)1/2
Energy Yield, σT = (σRS2 + σSIM2+ σSTC2)1/2
Table 3. Main uncertainty sources affecting to energy yield values.
1
Solar Radiation is subject to decadal cycles and other long-term trends, due to atmospheric composition
(SOx emissions, volcanos, etc.). Available literature shows the magnitude of these trends varies with
location, between +0.05% e -0.3% per year. These two values can be understood as the upper and lower
limits of a 95% confidence interval, so that, under a Gaussian hypothesis, their difference is equal to 3.82
times the corresponding standard deviation. This way, the expected deviation after N years can be
estimated as a mean value decreasing with time, at a ratio of -0.125% per year (mean value among the
extremes), and a standard deviation increasing with time, at a ratio of 0.09% per year. For a period of 20
years, that leads to a decreasing of 1.25% with a standard deviation of 0.9%.
2
SISIFO includes models for broken down global horizontal radiation into its diffuse and direct radiation
components, for considering the anisotropic nature of the diffuse radiation, and for considering the dust
effect on the angular response of PV arrays. The uncertainty estimation derives from the comparison of
estimated values with values measured at several well maintained PV installations. This term also
considers the uncertainty on the operation temperature.
3
SISIFO relies on certain models for considering the PV array efficiency dependence on irradiance and
operation temperature, and also for considering the influence of the relative load on the efficiency of
inverters and transformers. These models include adjusting parameters which are fitted to the information
provided by equipment manufacturers. Uncertainty derives from possible differences between the real
performance and the performance described by this information, namely regarding the efficiency of PV
arrays.
4
This uncertainty component derives from possible differences between real and nominal STC values,
associated to power tolerance at manufacturing, and from light induced initial degradation.
5
According with available literature, the degradation margin observed for crystalline silicon varies
between 0.4 and 0.8% of loss of power per year. This way, degradation at the end of N years can be
estimated by a mean value decreasing with time, at a ratio of -0.6% per year (mean value among the
extremes), and a standard deviation increasing with time, at a ratio of 0.1 % per year. For a period of 20
years, that leads to a decreasing of 6 % with a standard deviation of 1 %.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Note the risk of failure associated to bet on EP90 is limited to 10%. Banks, which
typically are rather conservative entities, use to associate project financing to EP90
values. This is why facilities for calculating not only EP50 but also EP90 and other EPX
values are found in some simulation software: SISIFO, a free access tool developed in
PVCROPS, PVsyst, etc. Table 4 provides values for other risk levels, sometimes found
in PV project financing.
EPX = EP50 - ∆XσT
EPX (%)
∆X
50
0
75
0.67
80
0.84
90
1.28
95
1.96
99
2.58
Table 4. Coefficients for the calculation of different risk levels.
3.2 Quality assurance procedures.
Being the risks intimately associated to uncertainties, any quality assurance process can
be properly understood as a progressive uncertainty reduction process. Each particular
quality assurance step adds information related with a particular issue at the yield
estimation process. Obviously, that reduces associated uncertainty and risk. The
particular quality assurance procedures proposed at PVCROPS are as follows:
3.2.1
Initial Yield Assessment.
Estimating profitability and risks is the obvious first step of any quality assurance
process. As mentioned above, this is done in terms of EP50 and EP90 values. The first
results from a forecast performance exercise under given solar climate information,
PV array geometry, technical characteristic of selected components as announced
by their manufacturers and a certain allowable losses scenario. The second is
estimated by analysing the different uncertainties associated to each step at such
forecast exercise.
PVCROPS has developed SISIFO, a free access and open source simulation tool
(www.pvcrops.eu) able of EP50 and EP90 calculations and also economic evaluations
under different scenarios. SISIFO is based on cutting-edge modelling and is
supported by detailed comparison of simulated and monitored results at large PV
plants totalling more than 300 MW.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
3.2.2 On-site horizontal and effective solar radiation measuring
campaigns.
Dealing with solar radiation encompasses the largest uncertainty at Yield estimation
exercices. Currently available databases often result from certain atmospheric
models able to derive solar radiation estimations from satellite observations (given
in terms of colour intensity at different wavelengths for the pixel corresponding to a
concerned site). Such models include some parameters which are adjusted to fit
solar radiation measurements at specific existing ground meteorological stations
distributed over the concerned region. That assures the solar radiation estimates
encompass the minimum possible error for the ensemble of these control ground
stations sites, but not for the particular site where the PV plant is going to be
located, that can sometimes be located far from these sites. Hence, a certain
uncertainty must be associated to using a solar radiation database for a given site.
Obviously, the denser the control stations network and the closer the site to a
control station the lower the uncertainty. In fact, solar radiation databases use to
provide additional information allowing for the estimation of the standard deviation
values that must be associated to corresponding irradiation data content.
An obvious procedure for reducing such uncertainty consists on performing a solar
radiation measuring campaign directly at the concerned site and large enough to
provide statistically significant correction for the model at the back of the database.
For example, that can be made by comparing model estimates and ground
measurements in terms of daily irradiation along a full year. Then, a simple linear
fit provides a correction factor for each month, which is finally applied to the
database content, thus removing any possible bias in the long-term modelled data.
This is possible because, despite such database content is based on past
observations along 10 or more years, the correction reflects site climatic
peculiarities (altitude, humidity, etc.) that use to remain over the years.
In practice, that can hardly be made with free available solar radiation data bases,
because corresponding responsible (more often public meteorological services) do
not regularly provide actual solar radiation estimates but only long term past
averages. In fact, providing both past averages and actual estimates is the core
business of specialized companies, able of directly access satellite images and
derive solar radiation values by means of own dedicated models.
On-site measurement of the energy resource during a year is traditionally required
for assessing the bankability of wind energy parks. This practice is now expanding
to large PV plants and must be welcome, because it helps to reduce uncertainty and,
therefore, to increase confidence on PV technology. However, it should be adapted
to PV engineering peculiarities. Using pyranometers for global horizontal solar
radiation measurements instead of anemometers for wind speed ones is obviously
the first step, but additional refinements can be envisaged when considering that the
“fuel” that is converted to electricity by PV plants is not the solar radiation as seen
by an horizontal pyranometer (the basic instrument supporting solar radiation
databases) but the solar radiation incident on the PV array surface and filtered by
the spectral and angular responses of the particular PV module technology and also
by the dust accumulated on the modules surface (no perfectly cleaned sunglasses
can serve as a proper analogy for soiling and for this responses).
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Translation from horizontal to in-plane irradiances and spectral and angular
correction can be afforded by modelling, but at the price of some associated
uncertainty. Available literature26 shows that the best combination of models to
perform these tasks is not general but varies according with the characteristics of
the solar radiation at the site (diffuse/global ratio, turbidity, etc.), the orientation of
the PV array, the solar cell and cover glass technology, etc., making it difficult to
know what combination of models performs best at any given site. On-site
horizontal radiation with pyranometers and also effective radiation with reference
PV modules with the same orientation of the future PV array is an appealing
possibility for minimizing the uncertainty associated to such modelling. Even more,
that allows assessing even soiling, providing adequate maintenance during the
measuring campaign. It is opportune remembering that, despite to be scarcely
known at general solar radiation ambiences, reference PV modules are very good
quality products encompassing lowest possible uncertainty measurements when PV
systems are concerned.
3.2.3
Laboratory testing of PV module samples.
Independent laboratory testing of a representative PV module sample and
comparison with corresponding “flash-list” data is a common practice today for
controlling the power delivered by the PV manufacturers. However, even assuming
perfect coincidence, some uncertainty on PV module performance still persists.
On the one hand, c-Si modules are somewhat affected by so called Light Induced
Degradation, LID, which is a very rapid decrease in efficiency with the first few
days of exposure. Manufacturers use to provide positive tolerance for the power
rating of their products and also guaranties on that STC power will remain above
97% of the nominal value after the first year of exposure. Despite that represent a
kind of formal protection against excessive LID and other possible initial failures, it
is strongly recommended testing the representative modules sample not only “as
received” but also after an exposure above 60 kWh/m2. That assures the PV module
reaches the PV plant in proper conditions and also provides information for
estimating real LID rates. On the other hand, PV efficiency varies with irradiance
and temperature. Related information is usually provided at manufacturers’
datasheets, in terms of temperature coefficients and efficiency reduction from STC
to 200 W/m2. However, experience shows this information is sometimes of
doubtful representativeness. Therefore, it is also recommended testing the
irradiance and temperature performance of the modules control sample. That allows
detecting possible performance irregularities before PV modules reach the field and
provides more certain information that datasheets. Then, Yield assessment can be
refreshed with this new LID and performance data, and warning can be issued in
case of significant differences (above 2%) with initial results.
On other lines, it is worth considering testing also PV modules propensity to so
called Potential Induced Degradation, PID. This is a medium-term degradation
phenomenon sometimes observed in real PV arrays after few months of exposure.
Despite work in progress, PID is still not considered at the current version of IEC
61215 qualification standard. Meanwhile, propensity for PID can be quickly tested
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
(about a week) and preventive measures, like PV array grounding, can be adopted
at the PV system in case of modules result not PID free.
Finally, it is worth to taking advantage of laboratory testing to prepare reference PV
modules for further use as operation conditions sensors at the PV plant. As rule of
thumb, we propose two reference modules per MW, for irradiance and temperature,
respectively, plus four: two intended to keep on dark at the PV plant site, in order to
serve as reference for future degradation measurements, and two intended to spare
parts.
3.2.4
Commissioning testing of entire PV plants.
Commissioning testing represents a great chance for assuring the PV systems
already in operation fulfil their specifications and are free of threats for their
lifetime. In addition, it also represents a chance for in-depth characterization of PV
plant performance, which provides the grounds for careful operation surveillance.
The following test sequence is here recommended:
– STC power of individual modules. That can be made without removing the
selected modules from their definitive installation site. Better than 3%
accuracy is obtained by simultaneous tracing of I-V curves of the concerned
module and of a reference module located just close to it. Samples of about
20 – 30 modules per MW are considered to be representative.
– Visual and Infrared inspections of the PV arrays. Somewhat like persons
develop fever in case of illness, PV modules and other electric equipment
develop so called hot-spots in case of anomalies (micro-cracks, defective
soldering, bad contacts, etc.). Fortunately, they can be easily detected by
inspecting with IR cameras, which is now a common practice of PV
engineering. PVCROPS has investigated the hot-spots impact on, both, the
lifetime and the efficiency of the affected modules, and has proposed a set of
acceptance/rejection criteria for contractual dealing of this problem (see 2.5).
– PRSTC of the generation units. Large PV plants use to be composed by
several generation units, each injecting AC power to an internal AC grid. The
overall energy performance of each unit is properly characterised by
measuring the PRSTC along a representative period (about a week) of normal
operation. The PRSTC is a kind of Performance Ratio, but corrected to STC.
This correction requires measuring not only incident irradiance, as for the
mere PR, but also operation temperature and performing some calculations,
using the same PV performance model that involved at Initial Yield
Assessment. The outstanding benefit for this rather low added complexity is
that the PRSTC is neither time nor site dependent, so that it precisely qualify
the technical quality of the generation unit and of the entire PV plant.
– In-depth characterization of the generation units. The PRSTC lumps together
the performance of all the generation unit elements: PV array, inverter and
transformer. More in-depth characterization can be made at the price of
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
measuring not only irradiance, as for the mere PR, and operation temperature,
as for the PRSTC, but also measuring the DC and AC power responses on the
input and the output of the inverter, respectively. That must be done with
highly accurate power analysers and paying particular attention to DC current
measurements. The corresponding benefit is to clearly distinguishing between
the performance characteristics of the PV system components (STC power of
the PV array, efficiency dependence on temperature and irradiance, inverter
efficiency versus load) and also to observe the PV system behaviour in both
normal and abnormal operation (shades, inverter saturation, partial clouding,
etc.). All this information not only enjoy enthusiast engineers but also allow
for detailed energy losses analysis and, therefore, for advanced operation
surveillance.
3.2.5
Operation surveillance.
Large PV plants are often surveyed by SCADAS monitoring operational data and
alarms. Further analysis allows for daily, monthly and yearly reporting of the
operational energy balances. Following the cutting-edge procedures described
above (measuring irradiance and temperature by means of reference modules, not
only PR but also PRSTC determination, in-depth characterization during
Commissioning tests, periodic comparison on in-field reference modules with kept
on dark ones, etc.) and on comparing observed productions with estimated from
operation conditions, it is possible to detect and to diagnose hidden failures, and to
evaluate PV modules aging.
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4. TECHNICAL SPECIFICATIONS AND QUALITY
CONTROLS FOR GRID CONNECTED PV SYSTEMS
This section presents technical specifications and quality controls for the particular case
of a large PV plant connected to the medium voltage, MV, distribution grid and being
the object of a due diligence process linked to bank financing. We have selected this
case as particularly representative not only because it represents a significant share of
the global PV market but mainly because bankability contexts systematically require
rigorous quality assurance processes. PV projects of lower entity can also find here
inspiration, and simplify the proposed specifications and control methods in order to
cope with their own particularities (size, budget, technical risk, etc.).
It must be remembered that technical specifications and quality controls are intended to
assure that real energy production satisfies the expectation created by a dedicated Yield
Assessment carried out before the construction of the project. Additionally to the Solar
Resource Assessment, the input data for this study are the technical information
supplied by the EPCC and the baseline loss scenario agreed between all the parties
involved in the project (EPCC, investors and independent experts). This scenario
establishes the maximum allowable difference between the performance of the ideal
reference system and the real system to be constructed. This reference ideal means that
system performance is assumed to be optimal and all its components are assumed to
correspond exactly to the technical datasheets of the manufacturers.
Obviously, these Yield Assessment input data must be fully consistent with the
prescribed system technical specifications and also with the acceptance/rejection criteria
at corresponding quality controls. The modelling of PV generator performance, i.e. the
modelling of efficiency dependence on operation conditions, deserves particular
comment. As mentioned above, we advocate for the model defined by equation (2),
which parameters can be directly related with datasheet of the manufacturers, and we
have developed a free software (SISIFO) based on that model. However, other widely
used commercial software relying on the so called one-diode model which
corresponding 5 parameters are derived from assumptions or from I-V measurements
external to manufacturers. Over the paper, that entails a certain risk of breaking-off the
PV module guarantee chain, as clearly advised by these software authors. However,
especially when dealing with crystalline silicon generators and sunny places, both
models perform consistently and lead to similar results at corresponding Yield
Assessments, providing equivalent solar resource estimation models. This allow to
make somewhat compatible the use of software based on the one-diode model for initial
Yield Assessments with the use of equation (2) for calculating the PRSTC, which is
definitively better than the mere PR, for qualifying the technical quality at reception
essays.
On the other hand, it must be advised that technical specifications always require local
adaptation. In particular the physical conditions of the site, the national regulations and
the market circumstances should be taken into account. For example, the here proposed
specifications state that “support structures must be rigid and resistant to wind gusts up
to 150 km/h” and that “they must be done in aluminium or hot galvanized steel”.
However, a higher wind velocity can be required in regions affected by tornados, and
other materials like wood can also be accepted if corresponding market availability
entails lower prices. On the same lines, central inverter generally represents a cheaper
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
solution than distribute (string) inverters. However, the last can be preferred at building
integrated PV systems often affected by shades. The protection scheme and the inverter
features (power factor, response to abnormal voltage or frequency conditions, etc.) must
comply with particular national electric regulations.
4.1 PV system layout.
Figure 4 describes the basis electrical layout of a large PV plant. It is formed by several
generation units, each composed by PV arrays and inverters feeding, through
corresponding LV/MV transformers, an internal MV line which is connected to the
national grid at the Common Coupling Point CCP. In turns, each generation unit can be
composed by only one inverter or by the parallel of several inverters, each one with its
corresponding PV array (Figure 5).The PV plant also includes measuring and
monitoring devices (reference modules, standard meteorological stations, SCADA) and
auxiliary services (buildings, security systems, etc.).
Generation
Unit 1
P AC
P DC
PV Array
Inverter
Internal MV line
Connection point
Generation
Unit 2
.
.
LV/MV
Transformer
Energy
meter
Generation
Unit N-1
Power line
Protection and
measurement cell
Generation
Unit N
Figure 4 Basic electrical layout of the PV installation
1
1
:
:
N
N
(a) Only one inverter
(b) One inverter, N MPPT inputs
(c) N inverters in parallel
Figure 5. Acceptable alternatives for PV array-inverter.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
4.2 Definitions.
The STC power of the PV plant is here understood as the nominal power of the PV
arrays, i.e. the product of the total number of modules by the in-plate STC power given
at the datasheet of manufacturer. This can be different of the nominal power of the PV
plant, which is given by the maximum allowable power injected at the CCP.
On similar lines, the nominal power of the PV arrays can be different of the nominal
power of the inverter which is the maximum power at its output.
4.3 Standards.
All the components of the PV installation should fulfil the national standards and
international ones, guaranteeing quality, integrity and an optimal performance after its
installation.
Some standards affect to the specific devices of a PV installation: modules, arrays and
inverters. Particularly interesting are:
IEC 61215
Crystalline Silicon Terrestrial Photovoltaic Modules: Design
Qualification and Type approval
IEC 61646
Thin-Film Terrestrial Photovoltaic Modules: Design Qualification
and Type approval
IEC 61730
Photovoltaic Module Safety Qualification
IEC 60364-7-712
Electrical Installations of Buildings – Part 7-712: Requirements for
Special Installations or Locations Solar Photovoltaic (PV) Power
Supply Systems
More general devices (electric lines, cables, energy meters, buildings and protection
systems) should fulfil the national regulations in force. Particularly relevant are:
IEC 60555-2,-3
Disturbances in supply systems caused by household appliances
and similar electrical equipment - Part 2: Harmonics, Part 3:
Voltage fluctuations.
IEC 61727
Photovoltaic (PV) systems - Characteristics of the utility interface
IEC 62116
Test procedure of islanding prevention measures for utilityinterconnected photovoltaic inverters.
IEC 1024-1
Protection of structures against lightning. Part 1:General principles
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
IEC 62305-4
IEC 60309
Protection against lightning. Part 4: Electrical and electronic
systems within structures
Plugs, socket-outlets and couplers for industrial purposes – Part 1:
General requirements.
Other standards that must be taken into account, especially in the quality control
procedures, are:
IEC 62446
Grid connected photovoltaic systems – Minimum requirements for
system documentations, commissioning test and inspection.
IEC 61829
Crystalline silicon photovoltaic (PV) array: On-site measurement
of I-V characteristics.
IEC 60891
Photovoltaic devices – Procedures for temperatures and irradiance
corrections to measured I-V characteristics
IEC 61853-1
Photovoltaic (PV) module performance testing and energy rating:
Part1: Irradiance and temperature performance measurement and
power rating.
4.4 Technical requirements.
4.4.1
PV arrays.
1)
Each PV array must be formed by PV modules of the same manufacturer, type
and model.
2)
The PV modules must have certifications IEC 61215 or IEC 61646 if they are
crystalline silicon or thin-film, respectively.
3)
The PV modules must have certification IEC 61730.
4)
The PV modules must be resistant to Potential Induced Degradation (hereafter
PID).
NOTE. This question is being addressed in a new, still draft, version of IEC 61215.
Meanwhile, different laboratories use different test procedures, all of them able of detecting
the PV modules propensity to suffer PID.
5)
The plugs of all the modules, and also of all the cables between the modules
and the connection boxes, must be the same model to ensure good
connections. They must be placed in such a way that they are free of
accumulation of dust, sand or water to avoid short-circuits and/or premature
degradation.
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6)
7)
DC cables must be attached to the supporting structure or placed in trays to
avoid loose cables that could rub against objects such as roof tiles or sharp
structures that could damage their insulation or even provoke trip hazard.
The STC power measured in the input of each inverter must be equal or above
to 93% of the nominal power. In other words, the sum of the losses due to
initial degradation, mismatching and wiring cannot be above 7%.
NOTE: This value is proposed as an absolute maximum. Lower losses can be specified, in
particular with PV modules offering positive tolerance in rated power. Whichever the case,
this value must be consistent with the Yield Assessment baseline loss scenario
8)
The PV modules must not exhibit “hot spots” or “hot cells” when there is not
shade cast over them and the inverter is injecting to the grid normally.
9)
Preferably, as a protection measure against indirect contact, the PV arrays
(active poles) should not be earthed.
10) The expected operational ranges of PV array voltages and currents (VOC, ISC,
VM and IM) must agree with the technical specifications of the inverter.
11) All the strings, consisting of modules connected in series, must be protected
with fuses in both poles. String fuses must be rated (at 50ºC) between 2 and 4
times the modules STC short-circuit current, below the rated DC current of
module cables.
NOTE. Strictly, electric security at no-earthed PV arrays requires only one fuse. However, the
second fuse allows for easy string electrical separation from the rest of the PV array, which
can be useful for inspection and maintenance purposes. An intermediate solution consist on
protect one pole with a fuse and provide some easy isolation mean to the other pole.
12) The parallel association of strings must be done inside connection boxes
including the following elements:
a) All the string with operative fuses.
b) Overvoltage protection devices (operative surge arrestors) between both
positive and negative poles and earth (another one between poles is
optional).
NOTE: This is not strictly necessary if the cable that connects these boxes and the
inverter has a length lower than 20 m.
c) Load breaking switch to safely open the DC part in case of emergency.
d) Depending on the configuration, these devices can be integrated in the
inverter.
e) Fixed labels warning the risk of electric shock.
f) Poly-Methyl–Methacrylate (PMM) sheets for preventing direct contact
with live wires, fuses, busbars, etc.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
g) Individual labels for each cable, reporting about its polarity and its origin.
h) A blocking system in doors or covers for when they are open to avoid
damage due to wind gusts.
13) The elements inside the connection boxes should be correctly ordered and
disposed so that positive and negative poles are as separated as possible to
minimize the risk of direct contact.
14) All the fuses, surge arrestors and load breaking switches must fulfil the
standard IEC 60634-7-712.
15) The connection boxes must have (and respect) at least IP54, in accordance
with the standard IEC 60529, and must be resistant to UV radiation. So, cable
entering connection boxes must be correctly installed and sealed to not modify
this IP protection degree.
16) DC cables from connection boxes to inverter input must run in underground
tubes, with manholes separated no more than 15 meters. The extremes of the
tubes must be sealed once the tubes and cables are totally laid.
4.4.2
Supporting structure.
17) Supporting structures must be rigid and resistant to wind gusts up to 150 km/h
and to corrosion environments equal to or higher than C4, in accordance with
the standard ISO 9223.
18) Supporting structures must be done in aluminium or hot dipped galvanized
steel. The installation procedures must ensure anti-corrosion protection. This is
also applicable to doors, trays, bolts, nuts, washers and fixation elements in
general.
19) All the parts of the supporting structure must be correctly assembled, must fit
with each other and must be compatible to avoid galvanic corrosion.
20) Supporting structures must allow every single module to be accessible for
periodic inspections.
21) PV modules must be rigidly fixed to the supporting structure with appropriate
clams and/or bolts and nuts according to the PV modules manufacturer
specifications.
22) All the PV modules must be elevated at a height of 1 meter (to avoid shade
from vegetation) to 4 meters (to facilitate clean-up tasks) above the floor level
and have a free separation space between adjacent modules at least of 1 cm.
23) Supporting structures must allow quick drainage in the case of heavy showers.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
24) Mounting systems of supporting structures must allow acceptable thermal
expansion of all the system components.
25) Moorings and tensioners of the supporting structures should be clearly marked
for easy maintenance.
4.4.3
Inverters.
26) Nominal power of the PV inverter should be equal or larger than 80% of the
STC nominal power of their corresponding PV array:
N
PInv
 0.80 PN*
27) The so-called “European efficiency” of the inverters must be at least 0.95. This
efficiency is given by the formula:
 EUR  0.03 5  0.06 10  0.13 20  0.130  0.48 50  0.2 100
where  5 , 10 ,  20 , 30 , 50 , 100 are the instantaneous power efficiency
values at 5%, 10%, 20%, 30%, 50% and 100% load.
28) The inverters should properly operate at their nominal power and with an
ambient temperature TA = 50ºC.
29) In order to preserve the quality of the general electricity service, the inverters
should comply with IEC 61000-6-2 and IEC 61000-6-4 (EMI), with EN 50178
(Grid quality requirements) and also with particular national codes.
NOTE. Concrete project specifications should pay particular attention to clarify the following
aspects: response to abnormal conditions of voltage or frequency, response face voltage sags,
power factor and regulation of active and reactive power.
30) The inverters should include anti-islanding protection with automatic shut
down once sags requirements are fulfilled, in accordance with standard IEC
62116.
31) Inverter-on after grid voltage and frequency restoring should be delayed
between 1 to 3 minutes.
32) The inverters should include protection against inverse polarization in its DC
input, short-circuits in its AC output, over-voltages (operative surge arrestors)
in both input DC and output AC, insulation failure with output to relay.
33) The inverters should include detection and protection in case of lack of
insulation in accordance with the requirements of standard IEC 60364-7-712.
34) The inverter should include and emergency stop device (software or hardware)
and it should be easily accessible.
25
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
35) In order to facilitate the acceptance tests, the inverter must include means
(shunt, toroid, etc.) for measuring DC input current with accuracy of, at least,
0.5%. Such means must be duly certified and fully accessible during reception
test.
NOTE. This specification applies only if acceptance tests consider not only a PR or a PRSTC
measurement, but also additional equipment characterization.
36) Own consumption of inverters can be powered by the same line which
connects the inverter or line of auxiliary services.
37) When using central inverters, they should be located inside a specific building
(electrical room) with adequate fans or air circulation systems to avoid
overheating. The building door should have a blocking system (or alternative
option) for when it is open to avoid damage due to wind gusts.
38) When using distributed inverters, they can be located inside a building or
outdoors. In the latter case, inverters should be in the shade and enclosures
must have a minimum level of protection IP54. Anyway, they have to be
installed on supporting structures which are adequate to carry its weight over
their entire lifetime and in well ventilated areas with at least minimal clearance
to walls, other objects and other inverters as specified by the manufacturer.
39) The inverter should record data about the main electrical operation variables
(DC and AC currents, DC and AC voltages; DC and AC power; power factor,
alarms status) with good accuracy and at least each 15 minutes.
4.4.4
LV/MV transformer, protection and measurement cells.
40) LV/MV transformers and MV protection and measurement cells must comply
with the national regulations.
41) Preferably, inverters, transformers and protection and measurement cells
should be hosted together in prefabricated concrete buildings, steel containers,
etc. in such a way that in-field cabling and installation works are minimized.
4.4.5
Measurement, monitoring and data acquisition.
4.4.5.1 Effective incident irradiance and cell temperature sensors.
42) The sensors to measure the effective incident irradiance over the PV arrays,
Gef, and their cell temperature in operation, TC, will be reference PV modules
of the same manufacturer, type and model than the ones installed in the PV
arrays.
26
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
43) The PV reference modules for measuring Gef will be equipped with class 0.5
shunt resistors in such a way that the corresponding voltage for the STC
irradiance G* = 1000 W/m2 ranges from 100 mV to 200 mV. These resistors
shall be installed with similar IP protection degree than the PV module box.
44) Measurement procedures will be in accordance with IEC 60891, IEC 60904-2
and IEC 60904-5. Stabilization and calibration of reference modules must be
done by a well-recognized independent laboratory.
NOTE. Round-robins among independent laboratories have shown calibration accuracy better
than 2% for crystalline silicon modules. Nevertheless, specification can assign priority to a
particular laboratory.
45) Pairs of reference PV modules (one for Gef and another for TC) will be
distributed along the PV plant, in order to get Gef and TC average
representative values, to estimate the dust energy impact (by cleaning just a
group) and to provide redundancy for increasing monitoring reliability. The
following rules apply:
a) At least, two pairs of reference modules.
b) The distance between any points of a PV array and a pair of reference
modules must be less than 300 m.
46) Additionally, a pair of PV reference modules will be supplied and keep on
dark conditions, to allow for future recalibrations of the installed ones.
47) All the reference PV modules will be installed and fixed to the support
structure in the same way than the PV array ones and must remain out of any
shadow.
4.4.5.2 Meteorological station.
48) The meteorological station must include:
a) A pyranometer class I/II, in accordance with ISO 9060, to measure the
horizontal global irradiation, G(0), installed at such a height that can be
easily cleaned and is free of shade (not lower than 2 m)..
b) A thermometer to measure the absolute room temperature (PT100,
PT1000 or equivalent), protected from direct sunlight and direct wind
gusts, with accuracy better than 0.5ºC.
c) An anemometer and a vane for measuring wind speed and direction at 4
meters high. The tower supporting the wind speed sensor must be
securely anchored to the ground.
d) A Data Acquisition System (hereafter DAS) with additional channels
enough to record the signal of the reference PV modules.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
49) The meteorological station will be close to the general services building, in
such a way that the pyranometer can be easily cleaned.
4.4.5.3 SCADA.
50) The SCADA has to be able to communicate with and receive relevant
information from:
a) All the inverters of the PV installation, in order to monitor the relevant
variables of energy flux (DC and AC currents, DC and AC voltages; DC
and AC power; power factor, alarms status).
b) All the connection boxes of the PV arrays, in order to monitor the status
of string fuses and switches.
c) All the tracker control units, in order to monitor the status of tracking
routine.
d) The meteorological station, in order to monitor all the measured variables.
e) All the reference PV modules that are not connected to the meteorological
station DAS or to the inverter inputs.
f) All the energy meters.
g) All the MV protection cells, in order to monitor the status of switches and
protections.
51) To avoid problems with lightning, the communication between the SCADA
and all these devices should be done via optical fibers or wi-fi network.
52) The SCADA must include transmission facilities though GSM and also via
Internet.
53) The SCADA system should not include remote control of the PV installation.
The remote operation is not recommended. The PV installation must be
continuously connected to the grid. In case of disconnection is recommended
that a person check in which was the direct cause.
4.4.6
Buildings and auxiliary services.
54) The low voltage electricity line for supplying auxiliary services shall have a
LV/LV isolating transformer to avoid earth derivations through the parasitic
capacity of PV array.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
NOTE. The need of this specification depends on the inverter internal configuration. In case of
the so called “transformerless“, TL, inverters this isolating transformer is not required.
55) Preferably, central inverters, LV/MV transformers, associated protections and
panels must be located inside prefabricated buildings to allow mount, connect
and test the equipment in the factory, so that work in the field is minimized.
56) The project must include a general service building to house the spare parts,
tools, computers, visitor reception, etc.
57) The buildings doors should have a blocking system (or alternative option) for
when they are open to avoid damage due to wind gusts.
58) All the buildings of the installation must be watertight.
4.4.7
Grounding and lightning protection.
59) MV and LV groundings must be independents to avoid that a fault in the MV
line impacts negatively on the LV connected devices.
60) All the metallic structures and devices connected on the LV line must be
grounded. This connection must be equipotential.
61) The PV arrays:
a) They do not require an external system of lightning protection.
b) Positive and negative DC cables of the PV arrays should be installed in
such a way as to reduce as much as possible the area of the loop of the
array wiring.
62) The protection against lightning of building must fulfil the standards IEC
61173 and 60364-7-712 (besides the national requirements).
4.4.8
Safety and fire protection.
63) All the PV installation must be protected by a metallic fence of, at least, 2.5 m.
high, with a suitable gap at the bottom to allow small wild animals to enter the
PV plant but not people.
64) Around the perimeter of the PV installation should have a system of
surveillance and automatic intrusion detection.
65) Extinguishing fire means should be provided in accordance with
corresponding national rules.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
4.4.9
Civil works.
66) The civil works must include, but not limited to, the following works:
a) Soil improvement and consolidation, if necessary.
b) Preparation of roads for proper access to all the PV arrays, connection
boxes, inverters, etc.
c) PV arrays structure foundations if this solution was selected against
rammed piles.
d) Construction of the building if not delivered as standard complete
product.
e) Construction of underground cable ducts and trenches below freezing
depth inside the PV installation.
f) Drainage system for storm water for proper infiltration to the subsoil.
g) Fence foundations.
67) General state-of art, site information and existing national rules must be
considered to derive particular civil works specifications. For example:
a) Foundation design must be consistent with the “Soil Geotechnical
Analysis”.
b) The MV cable will be laid in a minimum depth of 0.9 m on a sand bed of
0.1 m thick and protected with flexible corrugated tube of an adequate
section to leave 50% of its space for future needs. Refilling will be done
with appropriate material in layers of 15 cm thickness, each properly
compacted. Up to 20 cm above crest level of the cables a signal band for
each of the cables will be laid; and the routing of the cables within the
installation will be marked by upright post (guide marks) with plates at
least every 200 m and where required for reasons for change of direction.
c) The LV cable will be laid in a minimum depth of 0.8 m on a sand bed of
0.1 m thick and protected with flexible corrugated tube of an adequate
section to leave 50% of its space for future needs. Refilling will be done
in layers of 15 cm thickness, each properly compacted. About 15 cm
above crest level of the cables a signal band for each of the cables will be
laid.
d) The crossings of roads will be made through appropriate cement cable
ducts or polyethylene heavy duty (PEH) pipes, with a wall thickness of
not less than 5 mm.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
e) Chests or manholes must be installed every 90 m and in any change of
direction.
68) Based on the climatic data and specially the rainfall data, and the Site’s
configuration and topography, the Contractor will design and build a drainage
system in order to protect the installation infrastructures against erosion and
flash floods.
69) Location of fence, meteorological station, posts, walls, buildings, trees, etc.
must avoid cast shadows over PV arrays and, if existing, must allow normal
movement of trackers.
70) Especial efforts should be made to properly integrate PV installations in their
surrounding environment and ecosystem.
4.5 Quality control procedures.
Table 5 describe the key features of the testing programme
PHASE
Prior to the installation
Laboratory measurements
Commissioning
In-field measurements
After one year
of routine operation
TESTS
Module tests:
 I-V curves before and
after Sun exposition.
 Temperature and low
light coefficients.
Module tests:
 Visual and thermal
inspection.
 STC power.
System test:
 PRSTC.
 PV arrays and inverter
characterization.
Module tests
 Visual and thermal
inspection.
System test
 PR and PRSTC.
OBJECTIVE
 To identify possible
anomalies.
 To prepare reference
modules as irradiance
and temperature sensors.

To identify possible
defects.
 To assure system
performance satisfies
specifications.
 To tune PV system
efficiency models.

To analyze real system
performance.
 To advise on handover of
ownership.
Table 5. Key features of the testing programme.
4.5.1
Prior to installation.
71) Prior to the shipphing to the installation, a sample of PV modules will be
tested at a recognized laboratory. The minimum number of specimens is the
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
number of reference modules defined at 4.4.5.1 plus four. These modules must
be accompanied by corresponding electric characteristics obtained at the
manufacturer flash.
72) Module power output at STC will be measured, first, as received and, second,
after a minimum Sun exposition period equivalent to 60 kWh/m2. A warning
will be issue if:
a) In average, the STC power measured at “as received” modules differs
more than 2% of the flash value.
b) Any PV module degrades more than 2%.
73) Temperature and low light efficiency coefficients will be measured after the
minimum Sun exposition period. Energy Yield Assessment (already done at
the design phase, using datasheet performance information) will be repeated
using the average measured coefficients as input for PV array performance
modelling. A warning will be issued if corresponding yearly energy yields
differs more than 2%.
74) The modules will be calibrated to serve as reference devices for measuring
effective irradiance and module temperature at actual PV arrays. For that, half
the modules will be equipped with shunt resistors. Final calibration values will
be issue after a comparison process among all the modules, to assure that
corresponding irradiance and temperature measurements differ less than 1%.
4.5.2
Commissioning.
75) After an initial period of Sun exposure long enough for the total irradiation on
the PV arrays reaches at least 200 kWh/m2 and, in any case, not less than one
month the following tests will be carried out:
a) Visual and thermal (IR) inspection of the PV arrays.
b) STC power of individual PV modules.
c) Performance Ratio of the generator units at STC, PRSTC.
d) Characterization of generators units: inverter efficiency versus load and
STC power of PV generator referred at inverter input and performance
index referred at energy meter input.
NOTE. Independent characterization of PV arrays and inverters is not strictly required
to assure the whole system performs as expected. However, derived information can be
useful for fine tuning of PV performance models which, in turns, can be useful for
further failure detection and degradation estimation.
76) Any PV module showing the “important visual faults” specified at the norm
IEC 61215 will be rejected.
32
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
77) Thermal (IR) images must be obtained with the PV system in normal operation
and must respect the following conditions:
a) On-plane irradiance higher than 700 W/m2.
b) Irradiance variations during the previous 10 minutes less than 20%
78) Observed hot-spots are characterized by means of the difference between the
temperature of the coldest solar cell, TCC, and the temperature of the hottest
solar cell, THC, of the affected PV module, normalized at STC irradiance. That
is:
∗
∆𝑇𝐻𝑆
= (𝑇𝐻𝐶 − 𝑇𝐶𝐶 )
𝐺
𝐺∗
79) Hot-spots acceptance/rejection criteria are:
∗
a) ∆𝑇𝐻𝑆
≥ 100ºC leads to automatic rejection, even when the hot-spot is
caused by any shadow affecting the PV array.
∗
b) ∆𝑇𝐻𝑆
> 20ºC in absence of shades leads to automatic rejected.
∗
c) 10𝑜 C ≤ ∆𝑇𝐻𝑆
≤ 20𝑜 C in absence of shades will lead to measure the
effective power loss, understood as the decrease of the PV module
operation voltage in relation to a non-defective module of the same string.
The PV module will be rejected if such effective power loss excess 20%.
∗
d) ∆𝑇𝐻𝑆
< 10ºC is always acceptable.
80) A representative number of PV modules (at least, 10 modules per MW) will be
selected for I-V curve testing. Corresponding STC power values will be
derived from I-V curves measured outdoors. Actual irradiance and temperature
values, required for translation to STC, must be given by a reference module
located very close to the measured module.
81) Resulting average STC power must be at least 96% of the average flash
values, provided by the PV module manufacturer. Moreover, resulting STC
power for every individual module must be at least 94% of the corresponding
flash value.
82) The PRSTC test principle consists on the simultaneous observation of the
operating conditions: on-plane effective irradiance, Gef, and cell temperature,
TC; and on comparing the estimated energy, calculated from the operating
conditions, with the actual produced energy, calculated as the difference in the
energy-meter readings at the beginning and at the end of the tests, EAC,REAL.
83) The minimum period for the PRSTC test must be five consecutive days.
Measurements must be registered from sunrise until sunset. The test duration
33
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
must be long enough to fulfil the condition of at least 24 hours of on-plane
irradiance higher than 700W/m2.
84) PV arrays and irradiance sensors must have the same soiling degree during the
entire PRSTC test.
NOTE: That can be achieved by cleaning both (array and sensors) just before the beginning of
the test or, which is simpler, not cleaning during the previous 15 days. Whichever the case,
any action affecting the degree of dirtiness of the PV arrays and sensors must be avoided.
85) The operating conditions Gef and TC will be recorded at least once per minute.
86) The value of PRSTC is given by:
E AC , REAL
PR STC 
P*
t
G*
 G 1   T
ef ,i
i
C ,i
Gef ,i
Gef ,i 

 TC* a  b *  c ln * 
G
G 


where P* is the array nominal power, G* = 1.000W/m2, T*C = 25ºC, t is the data
time resolution (1 minute or less), “i” is the time index for all the test period,  is
the power temperature coefficient, whose value is negative and it is provided by
the PV modules manufacturer and a, b and c are the parameter describing the
dependence of the modules efficiency on irradiance. All these parameters must
have the same values that supposed at the Energy Yield Assessment carried out
at the project design phase.
NOTE: In any case, the PV performance model at the Energy Yield Assessment and at the PR STC
test should be consistent.
87) Resulting PRSTC value must be equal or higher than 0.85.
NOTE: This acceptance threshold value must be put into relation with allowed loses scenario
at the Energy Yield Assessment. For example: Lumped PV array and inverter technical loses:
7%; DC/AC loses: 3%; LV/MV loses: 2%; technical availability and tolerance: 3%, lead to
allow up to 15% of total energy loses, which is in coherence with 0.85 (0.85+0.15 = 1)
88) The PV system characterization test principle consist on the simultaneous
observation of the operating conditions –on plane effective irradiance (Gef) and
cell temperature (TC)–, and of the power system response –inverter DC input
power (PDC) and inverter AC output power (PAC).
NOTE: Security related reasons usually recommend restricting P AC measurements to the low
voltage inverter output. Nevertheless, the concept can be easily extended to LV/MV or even
MV/HV transformers, providing accurate enough power measurements are available .
89) PDC and PAC must be measured with a high quality wattmeter.
NOTE: Particular attention should be paid to DC current measurements. Clamp meters are
adequate for highly accurate AC current measurement but not for DC current ones .
34
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
90) The minimum period for the characterization test must be 24 hours.
Measurements must be registered from the sunrise until the sunset (or from
midday of the first day to the midday of the next one). The test duration must
be long enough to fulfil the condition of at least 4 hours of irradiance level
higher than 700 W/m2.
91) Operation conditions and power values must be recorded at least once per
minute.
92) For every set of values (Gef, TC, PDC) not affected by anomalous effects
(shadows, inverter shut down, etc.) and fulfilling the condition Gef > 800
W/m2, the DC PV array power at the standard temperature, PDC,25, must be
calculated with the following equation:
PDC , 25 
PDC
1   TC ,i  TC* 


Then, the STC power result at the inverter input, P*G,INV, is the value providing
the best fit to the line given by the equation:
PDC , 25  PG*, INV
Gef
G*
The set of points (PDC,25, Gef) are the obtained in the test.
NOTE 1. Previous equations implicitly assume that PV array performance is almost constant
for irradiances over 800 W/m2, which is typically the case for crystalline silicon modules. The
characterization test concept can be extended to Thin Film materials, providing careful
consideration of efficiency versus irradiance particularities.
Note 2: An alternative option for obtaining the array STC is to measure the I-V curve with an
electronic load as defined in IEC 60904-1 and extrapolate it to STC as defined in IEC 60891.
This alternative procedure could be more difficult for large PV arrays (electronic loads used
to be limited in its input current) and its uncertainty could be higher, as it is based on only a
few measurements of the I-V curve at midday.
93) For every set of values (Gef, TC, PDC) not affected by anomalous effects
(shadows, inverter shut down, etc.) and irrespective of the irradiance, the DC
PV array power at the standard temperature, PDC,25, must be calculated with
the following equation:
PDC , 25 
PDC
1   TC ,i  TC* 


Then, the irradiance coefficients a, b and c are the values providing the best fit
to the equation:
∗
𝑃𝐷𝐶,25 = 𝑃𝐺,𝐼𝑁𝑉
𝐺𝑒𝑓
𝐺𝑒𝑓
𝐺𝑒𝑓
(𝑎
+
𝑏
+
𝑐
𝑙𝑛
)
𝐺∗
𝐺∗
𝐺∗
35
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
94) In order to characterize the inverter, every set of values (PDC, PAC) will be
translated to the corresponding set of values ( inv, p):
inv 
PAC
p
PAC
N
PINV
PDC
N
where PINV
is the inverter nominal power. The so-called inverter efficiency
coefficients, k0, k1 and k2, are obtained as the best fit of all the points ( inv, p)
in the next equation:
 inv  p  
p
p  k 0  k1 p  k 2 p 2
The same equation can be used to obtain the values 5, 10, 20, 30, 50, 100
corresponding respectively to p = 0.05, p = 0.1, p = 0.2, p = 0.3, p = 0.5 and p
= 1, involved in calculating the energy efficiency of the inverter.
4.5.3
After one year of operation.
95) The supplier will operate the PV installation, under its exclusive responsibility,
during the first year after commissioning.
96) Provisions must be taken to clean the PV arrays each time the dirtiness degree
reaches 5%.
NOTE 1: Specific dirtiness threshold for cleaning must reflect a compromise between the cost
of cleaning and the cost of energy. Practical values range from 3 to 6%.
NOTE 2: Daily cleaning one of the reference modules devoted to measure irradiance while
keeping the others un-cleaned provides a practical method for estimating the dirtiness degree,
just by comparing corresponding irradiance readings.
97) The visual and thermal inspections of the PV arrays, and the measurement of
STC power of individual modules already specified for Commissioning tests
–76) to 81)– must be repeated at the end of this year.
98) The yearly value of PR is given by:
PRYEAR 
where “i” extends to all the year.
36
E AC , REAL
t
P* *  Gef ,i
G i
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
99) Resulting PRYEAR value must be equal or higher than 0.77.
NOTE: This acceptance threshold value must be put into relation with allowed loses scenario
at the Energy Yield Assessment. Following with the example given at specification 87),
unavoidable yearly losses at the PV array (thermal, irradiance, shading and inverter
saturation), as estimated in this Yield Assessment, must be added to the already considered
15% of energy losses. Assuming that such unavoidable loses are estimated at 8%, allowable
total energy loses stand up to 23%, which is consistent with the here prescribed PRyear value.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
REFERENCES
1. Muñoz J., Lorenzo E. Capacitive load based on IGBTs for on-site characterization
of PV arrays. Solar Energy 80, 11. 1489-1497, (2006).
2. Muñoz J., Lorenzo E., Martínez-Moreno F., Marroyo L., García M. An investigation
into hot-spots in two large grid connected PV plants. Progress in Photovoltaics:
Research and Applications 16, 8. 693-701. (2008).
3. Narvarte L., Lorenzo E. Tracking and Ground Cover Ratio. Progress in
Photovoltaics: Research and Applications 16, 8. 703-714. (2008).
4. Martínez-Moreno F., Muñoz J., Lorenzo E. Experimental model to estimate shading
losses on PV arrays. Solar Energy Materials and Solar Cells 94, 12. 2298-2303
(2010).
5. Muñoz J., Martínez-Moreno F., Lorenzo E. On-site characterisation and energy
efficiency of grid-connected PV inverters. Progress in Photovoltaics: Research and
Applications 19, 2. 192-201. (2011).
6. Lorenzo E., Narvarte L., Muñoz J. Tracking and back-tracking. Progress in
Photovoltaics: Research and Applications 19, 6. 747-753. (2011).
7. Martínez-Moreno F., Lorenzo E., Muñoz J., Moreton R. On the testing of large PV
arrays. Progress in Photovoltaics: Research and Applications 20, 1. 100-105. (2012).
8. Leloux J., Narvarte L., Trebosc D. Review of the performance of residential PV
systems in Belgium. Renewable and sustainable energy reviews 16, 1. 178-184
(2012).
9. Leloux J., Narvarte L., Trebosc D. Review of the performance of residential PV
systems in France. Renewable and sustainable energy reviews 16, 2. 1369-1376
(2012).
10. Lorenzo E., Zilles R., Moretón R., Gómez T., Martínez de Olcoz A. Performance
analysis of a 7-kW crystalline silicon generator after 17 years of operation in
Madrid. Progress in Photovoltaics: Research and Applications.
DOI.10.1002/pip.2379 (2013).
11. Moretón R., Lorenzo E., Muñoz J. A 500-kW PV generator I-V curve. Progress in
Photovoltaics: Research and Applications. DOI.10.1002/pip.2401 (2013).
12. Muñoz J., Lorenzo E., Carrillo J.M., Moretón R. Design of a twin capacitive load
and its application to the outdoor rating of photovoltaic modules. Progress in
Photovoltaics: Research and Applications. DOI.10.1002/pip.2425 (2013).
13. Leloux J., Lorenzo E., García-Domingo B., Aguilera J., Gueymard C.A. A bankable
method of assessing the performance of a CPV plant. Applied Energy 118, 1-11.
(2014).
14. Lorenzo E., Moretón R., Luque I. Dust effects on PV array performance: in-field
observations with non-uniform patterns. Progress in Photovoltaics: Research and
Applications 22, 6. 666-670. (2014).
15. Allet N., Baunmgartner F., Sutterlueti J., Shreier L., Pezzotti M., Haller J.
Evaluation of PV System Performance of Five Different PV Module Technologies.
26th European Photovoltaic Solar Energy Conference. 3239-3247 (2011).
16. Stein J., Suttrelueti J., Ransome S., Hansen C.W., King BH. Outdoor Performance
Evaluation of Three Different Models: single-diode, SAPM and Loss Factor Model.
SAND Report 2013-7913C. 2013
17. Klise G.T., Stein J.S. Models used to assess the performance of photovoltaic
systems. Sandia National Laboratories 2009, Report SAND 2009-8258.
38
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
18. Mermoud A., Lejeune T. Performance Assessment of a Simulation Model for PV
Modules of Any Available Technology. 25th European Photovoltaic Solar Energy
Conference. 4786-4791. (2010).
19. King D.L., Boyson W.E., Kratochvil J.A. Photovoltaic array performance model.
Sandia National Laboratories, Report SAND2004-3535 (2004).
20. Fabero F., Vela N., Alonso-Abella M., Chenlo F. Characterization of recent
commercial technologies of PV modules based on outdoor and indoor I-V
measurements. 20th European Photovoltaic Solar Energy Conference. 2059- 2062.
(2005).
21. Montgareuil A.G, Martin J.L., Mezzasalma F and Merten J. Main results of the first
intercomparison campaing of European irradiance sensors at INES Cadarache. 22nd
European Photovoltaic Solar Energy Conference. 2601- 2607. (2007).
22. Friesen G, Gottschalg R, Beyer H, Willinas S, Guerin de Montgareuil A, van der
Borg N, van Sark WGJM, Huld T, Müller B, de Keizer AC, Niu Y. Intercomparison
of different energy prediction methods within the European project
"PERFORMANCE". 22nd European Photovoltaic Solar Energy Conference. 26592663. (2007).
23. Reich NH, Mueller B, Armbruster A, van Sark WGJHM, Kiefer K, Reise C.
Performance ratio revisitred: is PR>90% realistic? Progress in photovoltaics:
Research and applications. 20, 6. 717-726. (2012).
24. Düpont R. Cada uno mide como puede. Photon. La revista de fotovoltaica. 42-60.
(2009).
25. Hermmann W., Man S., Fabero F., Betss T., Van der Borg N., Friesen G., Zaaiman
W. Advanced intercomparison testing of PV modules in European test laboratories.
22nd European Photovoltaic Solar Energy Conference. 2506- 2510. (2007).
26. Gueymard C. Direct and indirect uncertainties in the prediction of tilted irradiance
for solar engineering applications. Solar Energy 83, 3. 432-444 (2009).
39
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
ANNEX 1. PV ENERGY PERFORMANCE MODELLING
INTO THE FRAME OF QUALITY ASSURANCE OF PV
POWER SYSTEMS CONNECTED TO THE GRID
INTRODUCTION
Technical quality assurance procedures look for tightening expectations and realities. When a
PV plant connected to the grid is concerned, prior to its construction, expectation is
established by means of a forecast simulation exercise describing the expected site evolution
of the operation conditions, namely, in-plane irradiance, G, and PV module temperature, TC,
and the corresponding power response of the PV system. That allows estimating the yearly
energy production, of paramount importance for the economic balance and for the bankability
of the PV plant. Solar radiation databases and technical specifications of the PV plant
components provide input data for this exercise.
It must be noted that predicting operation conditions unavoidable rely on available
meteorological data that are far from being an exact science, as revealed by significant
discrepancies between the many popular meteorological data sources (Lorenzo, 2011) and by
dedicated studies (Martinez J, 2009) (D Thevenard, 2013). Because of that no one can holds
responsible neither for future weather nor for operation conditions evolution. However, the
power response of PV generators is mainly a matter of technical quality and strict
responsibilities use to be endorsed to PV equipment suppliers, who obviously must agree on
the corresponding technical specifications they are requested to guarantee. In other words, at
the lights of market applicability, the models describing the energy performance of the PV
plant must not only be accurate but also based on features specifically guaranteed by
manufactures.
Later, once the PV plant is in operation, its technical quality is assessed through some
performance indexes derived from observed energy productions. Typically, this is done at the
Commissioning, during a relatively short period of few weeks, and also at the routine
operation, considering full year periods. Contractual rules for responsibilities endorsement
(acceptance/rejection, penalties, etc.) are associated to these indexes. Again, the calculation of
such indexes requires modelling the performance of the PV plant components and, again, such
modelling must be accurate and based on technical information previously agreed with
corresponding manufactures.
The efficiency of other than PV generator components (DC/AC inverters, transformers, wires,
etc.) is usually known with high accuracy (let us say, better than 1%). Hence, the problem of
modelling the PV plant performance reduces in practice to describe the DC maximum power,
PDC, response of the PV arrays, i.e., to give a solution for the function PDC = PDC(G, TC). This
response is often named “performance surface”. It is worth nothing that the particular point of
this surface corresponding to the so called Standard Test Conditions, STC (irradiance = 1000
W/m2; spectrum AM1.5; cell temperature = 25oC) is just the rated power of the PV generator.
In the following we will use an asterisk* to refer to parameters measured under these
40
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
conditions. Hence, P* = PDC (G*, TC*). Note that this point is, in fact, an input for the
performance surface, i.e., PDC = PDC (P*, G, TC).
Reviewing models for performance surface construction at the lights of, both, accuracy and
market applicability is the main objective of this paper. Besides reviewing today quality
assurance practices and PV modelling possibilities, this paper presents the results of a careful
measuring campaign with four different today commercial PV technologies: c-Si, CdTe, CIGS
and amorphous silicon, a-Si. Six PV arrays (three are a-Si, from different manufactures), each
with P*between 2 and 2,4 kW, have been connected to the grid at the South of Navarra (Spain)
and keep in routine operation along two years, from March 2011 to February 2013. Measured
power and energy production values are compared with modeled ones from different sets of
equations. It is anticipated that a simple model considering just the maximum power point, but
not the full I-V curve, and requiring coefficients which are already considered at standard tests
leads to daily energy errors about 2%, below the uncertainties associated to in-field
measurements.
COMMON QUALITY ASSURANCE PRACTISES
Today widespread quality control practices somewhat related with PV performance modelling
are:
PV module data sources and guarantees
Manufactures provide data sheets for each PV module type. According with the standard EN
50380 (“Data sheet and nameplate information for photovoltaic modules”) they must contain
characteristic values for three points of the I-V curve (PDC, ISC, VOC and VMPP) for two different
(G, TC) conditions: STC (G*, TC*), NOCT (800 W/m2, ≈45o C), the efficiency reduction from STC
to (200W/m2, TC*), the NOCT and the temperature coefficients for open circuit voltage, β, and
for short-circuit current, γ. However, this norm is nowadays far of being generally respected. In
contrast, despite not required at EN 50380, all the data sheets we know include the value of
the temperature coefficient for power, γ. Our experience with today data sheets suggests two
main drawbacks.
On the one hand, data sheets content is often not fully coherent. For example, there are two
ways of deriving P* values from I-V curves measured at other than STC conditions. The one is
to extrapolate to STC the full I-V curve in accordance with IEC-6081, using α and β. The other
consist on, first, obtain the maximum power of the measured curve and, second, to
extrapolate to STC only this value, using γ. Ideally, both results should fully coincide. However,
they usually differ about 2-3%, and our experience includes differences up to 5%. This can be a
consequence of differences on the characteristics of different specimens belonging to the
same PV module type. In fact, module to module parameter variations has been signaled as a
significant source of uncertainty (Allet N, 2011) (Stein J, 2013). Another possible reason is
certain carelessness in data sheet content, foster by the scarce use on rigorous quality control
process.
41
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
In fact, today standard guarantees are restricted to the value of P*while the rest of the data
sheet content is given by way of general information, but not particularly intended to support
efficiency quality controls. Because of that, guarantees on other than P*values must be agreed
with the PV modules manufacturer, prior to the PV modules supply. The IES-UPM experience
on the quality control of large PV plants, now spanning PV plants up to about 300 MW and
mainly performed on the frame of “due diligences” associated to large (multimegawatt) PV
plant bank financing, includes several cases of PV manufactures providing guarantees also on γ
values. This is important because thermal loses (due to TC≠TC*) use to be the particularly
relevant at the energy balance of a PV plant.
On the other hand, data sheets content do not allow to easily fitting the PV performance
models on the back of energy yield forecast. For example, the well-known 5 parameters one
diode model requires the value of the parallel resistance, given by the slope around ISC, which
cannot be derived from today data sheets. Attempting to overcome these lacks of information,
additional data can be obtained from, other than manufacturers, organizations allowing the
access to I-V curve databases they compile with own measurements performed on particular
specimens they acquire at the market. Obviously, PV manufactures deny contractual liability
for this information.
Both, datasheet limitations and doubtful representativeness of data from particular
specimens, represent uncertainty sources for energy yield forecasts performed at the project
design. Uncertainty can be further reduced by fitting the performance model with data directly
measured at the concerned PV array. However, that can only be made once the PV generator
installation. Hence, after the responsibility guarantees chain has been established. In practice,
that often leads the involved EPC (Engineering, Procurement and Construction) company to a
rather unfair position: To assume responsibilities on the full energy behavior of the PV array
having the only formal support of PV manufacturer guarantees on P* values. That demands to
enlarge the PV manufacturers’ commitment to also give guarantees on other than P* values.
This is likely easier when such values are directly obtained from datasheets (for example, the
NOCT and temperature coefficients) that when they are extracted from other than PV
manufacturers information (for example, the value of the parallel resistance obtained from a IV curve database form an independent organization).
Finally, it is opportune to remember than PV modules are usually marketed with power
tolerances around 3% and that the variability of other characteristics is even larger. As a
representative example, observed width ranges at a flash-list of 126 crystalline silicon PV
modules recently received at our laboratory are 3% for P*(which corresponds to a common
market tolerance), 6.4 % for ISC*, 1.2% for VOC*, 5.2% for IM* and 5.4% for VM*.
Energy yield forecast
Energy yield forecast is more often performed by means of commercially available software
packages (www.pvresources.com). Most of them describe the PV behavior by means of the so
called 5 parameters one diode model equation. Required input data (series and shunt
resistance, photocurrent, saturation current and diode quality factor) are mainly obtained
42
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
from I-V curves databases which are not linked to the PV manufactures but to independent
testing organizations. That entails the breaking-off of the responsibility chain. For example,
PVsyst relies on databases from TISO (Swiss test center for PV modules) and from PHOTON
(German PV journal) and warn the user about the lack of PV manufactures commitment “..for
definitive simulations, the user is advised to carefully verify the library data with the last
manufacturer’s specifications…We drop out any responsibility about the integrity and the
exactness of the data and performance including in the library..” (Disclaimer at the PVSYST
User’s Guide). The same is found at the concerned databases: “The database was compiled to
the best of our knowledge and with the greatest possible accuracy. At the same time, PHOTON
cannot be held responsible from any damage that results from the use of this database.”
(Disclaimer at Photon database). The PVsyst authors have even express their wishes of further
PV manufactures commitment: “..These data are key parameters of the model, and should be
part of the module’s specifications in the future..” (Mermoud A., 2010). However, these data
remain absent from the PV module manufacturer’s engagement.
On-site measurement campaigns
Technical performance of grid connected PV plant is usually assessed by means of the
Performance Ratio, PR, observed along a given operation period. This index , defined in IEC
61724 (“Photovoltaic system performance monitoring: guidelines for measurement, data
exchange and analysis”), is calculated as
𝑃𝑅 =
𝐸𝐴𝐶
(1)
∗ 𝐺𝑌
𝑃𝑁
∗
𝐺
Where EAC is the energy effectively delivered to the grid, 𝑃𝑁∗ in the nominal power of the PV
generator, understood as the product of the number of PV modules multiplied by the
corresponding in-plate STC power, and GY is the in-plane yearly irradiation during that period.
The PR value can be directly calculated without any kind of modelling, because EAC, 𝑃𝑁∗ and GY
values are directly given by the billing energy meter of the PV plant, the PV manufacturer data
sheet (or the flash-list) and the integration of a solar irradiance signal.
This mere PR is adequate when full year periods are considered, because, for given PV plant
and site, this value tends to be constant along the years, as much as the climatic conditions
tend to repeat. This way, contractual management of the PR only requires of an agreement on
the solar radiation measuring device and on the correction to account for long-term
degradation effects. However, quality assurance procedures also include the consideration of
other than full year periods. Reception testing when the PV plant is put into commissioning,
and monthly production reporting are two relevant examples.
When sub-year periods are considered, the PR dependence on unavoidable and time
dependent loses, requires corresponding correction in order to properly qualify the technical
quality of a PV plant. Otherwise, the qualification result of a same PV plant varies with the
climatic conditions of the qualification period, which seems contrary to the common sense.
These loses are the ones derived from the efficiency variation with temperature and
irradiance, from intrinsic to PV design phenomena: shades and inverter saturation, and from
43
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
possible angular and spectral response differences between the PV generator and the
irradiance sensor. A convenient way of doing such correction is to consider the so called
Performance Ratio at Standard Test Conditions, PRSTC, which can be properly understood as the
PR of the same PV plant but corresponding to an hypothetic period with the PV generator is
permanently keep at STC (G = 1000 W/m2; TC= 25oC) up to receive the same amount of onplane irradiation that corresponding to the qualification period. The PRSTC for a given period,
∆T, is given by:
𝑃𝑅
∆𝑇
𝑃𝑅𝑆𝑇𝐶,∆𝑇 = ∏ (1−∆𝐸
)
𝑖
(2)
𝑖
Where ∆E represents energy losses during the considered period and the subscript “i” extends
to all the unavoidable energy losses phenomena. All these losses must be calculated from
measured G and TC values, which require some kind of modelling. The coherence of the full
quality assurance process requires using the same PV performance model that at the energy
yield forecast. Otherwise, energy forecast underlying assumptions are not properly verified.
Thermal losses are typically the most significant at the global energetic balance of a PV plant.
In energy terms, ∆ETC≠TC*, they result from weighting the power thermal losses, ∆PTC≠TC*, by the
incident irradiance. That is:
∆𝐸𝑇𝐶≠𝑇𝐶 ∗ =
∫∆𝑡 ∆𝑃𝑇𝐶≠𝑇𝐶∗ .𝐺.𝑑𝑡
∫∆𝑡 𝐺.𝑑𝑡
(3)
where ∆PTC≠TC* derives from the performance surface:
∆𝑃 𝑇𝐶≠𝑇𝐶 ∗ =
𝑃𝐷𝐶 (𝑃∗ ,𝐺,𝑇𝐶 )−𝑃𝐷𝐶 (𝑃∗ ,𝐺,𝑇𝐶∗ )
𝑃𝐷𝐶 (𝑃∗ ,𝐺,𝑇𝐶∗ )
(4)
Broadband irradiance and effective irradiance
Solar radiation databases provide input data for energy yield forecast in terms of broadband
(as seen by piranometers) horizontal radiation. Then, PV performance modelling requires
transposition from horizontal to the plane of array and also correction for angular, spectral and
soiling loses. This way the so called effective (as seen by PV generators) radiation is obtained.
However, when on-site testing of PR or PRSTC values, effective irradiance can be directly
measured by using a reference module of the same type of that the concerned PV generator.
This way, such correction and corresponding uncertainties (typically about 2-3%) are fully
avoided. Hence, reference modules are particularly suitable for assessing the technical quality
of PV plants. Nevertheless and despite this is unanimously recognized at specialized
laboratories (King DL, 2004) (Fabero F., 2005) (Montgareuil A.G, 2007) (Friesen G G. R., 2007)
(Martinez MF, 2011) (Reich NH M. B., 2012) such modules are seldom used at today
commercial PV plants. A possible explanation is that reference modules are understood as
similar to reference cells. This is theoretically correct, because their angular and spectral
responses are the same. However, their practical use significantly differs. A large variety of
reference cells is found at the market, and some are non-standardized and bad quality
44
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
products (poorly encapsulated, suspicious calibrations, etc.) often leading to unacceptable
measurement errors (Düpont R., 2009). That is in detriment of the general reputation of
reference devices and favour to opt for pyranometers, which are well standardized and good
quality products. To make matter worse, reference modules are not the object of routine
market activities. Instead, they must be specifically prepared which means stabilization
followed by calibration. The stabilization requirements are given at international standards IEC
61215 and IEC 61640. In any case, this makes a minimum Sun exposition of 60 kWh/m2. It is
worth mentioning that round-robin tests performed in European laboratories have shown
calibration accuracy better than 2% for crystalline silicon modules (Hermmann W., 2007). It is
also worth mentioning that reference modules and PV generators response to dirt
accumulation is the same: neither the irradiance measured by the reference modules or the
efficiency of the PV generators are affected by isolated dirtiness as, for example, caused by
depositions of birds. Hence, reference Si-x modules are very good quality products (design
approved by IEC 61215) allowing in-field measurements of PV generator characteristics with
the lowest possible uncertainty.
In that follows we will adhere to this practice, dealing with performance surfaces defined as
PDC = PDC (P*, Geff, TC), where Geff means effective irradiance. This way, energy yield forecast
has to deal with problem of deriving this value from the corresponding broadband irradiance,
Gbb. This problem is left here for future work.
PERFORMANCE SURFACE MODELLING ALTERNATIVES
MPP models
The simplest PV performance surface model describes just the maximum power point of the
PV generator and is given by the linear relation:
𝑃𝐷𝐶 = 𝑃∗
𝐺𝑒𝑓𝑓
(5)
𝐺∗
This formula implicitly assumes that PV module efficiency is constant, which is scarcely
realistic. A first refinement consists on considering that efficiency is affected by temperature,
decreasing at a constant rate. That leads to:
𝑃𝐷𝐶 = 𝑃∗
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛾(𝑇𝐶 − 𝑇𝐶∗)]
(6)
where γ is considered a constant value. This formula goes a long way back (Evans D, 1981)
(Osterwald, 1986), handling with this equation requires just information from today standard
measurements: P* is the PV array rated power, which can be estimated as the product of the
number of PV modules constituting the PV array multiplied by their nameplate STC power, and
γ is routinely measured into the frame of worldwide extended accreditation procedures: IEC
61215 and IEC 61646 for crystalline silicon and thin film devices, respectively. P*and γ values
are always included in PV manufacturer’s data sheets or in more specific information as flashreports. This allows for straightforward responsibility assignments. As mentioned above, P* is
precisely the object of standard PV manufacturers guarantees, and our experience on due
diligences includes several cases of PV manufactures also assuming responsibilities for γ
values.
45
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Equation (6) can be slightly complicated to also consider the efficiency dependence on
irradiance. That was initially attempted by adding a base 10 logarithm (Evans D, 1981)but it is
better implemented by an empirical model proposed about ten years ago (Randall JF, 2003)
(Willians SR, 2003) and already used by several authors (Beyer H.G., 2004) (Reich NH v. S.,
2009). This way:
𝑃𝐷𝐶 = 𝑃∗
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛾(𝑇𝐶 − 𝑇𝐶∗ )](𝑎1 + 𝑎2
𝐺𝑒𝑓𝑓
𝐺∗
+ 𝑎3 𝑙𝑛
𝐺𝑒𝑓𝑓
𝐺∗
)
(7)
Where a1, a2 and a3 are empirical parameters that can be directly determined from two
measured values of the relation between the efficiency at a given G divided by the efficiency at
G*, keeping TC = TC*. The particularization of this equation for STC leads to the condition
𝑎1 + 𝑎2 = 1
(8)
Efficiency increases with decreasing irradiance, due to series resistance effects, are
represented by the term a2.Geff/G*, providing a2≤0, while efficiency decreases with decreasing
irradiance, due to parallel resistance effects, are represented by the term a3.ln(Geff/G*),
providing a3 ≥0.
Looking for yield estimations based on only information originally disclosed by PV
manufactures, the possibilities to fit the model with data sheet information deserves particular
comment: As mentioned above, some data sheets give efficiency values for three different
operation conditions: STC (G*, TC*), NOCT (800 W/m2, ≈45o C) and low irradiance (200W/m2;
25oC) and also give the value of the temperature coefficient for power, γ. That allows
correcting the NOCT efficiency to (800W/m2, 25oC). Then, these three efficiency values at 1000
W/m2, 800 W/m2 and 200W/m2 theoretically allow fitting a model with three parameters.
However, errors in the efficiency of 800 W/m2 propagate nearly 1 to 1 to the results of yearly
energy calculations, and the uncertainty of this value is in the 2% range with current data
sheets (Heydenreich W., 2008). Efficiency value at 600 W/m2 would be better than at 800
W/m2, but it will likely be a long way until such value appears on standard data sheets.
A practical possibility for setting a1, a2 and a3 values rely on standard tests. The sequence test
prescribed in IEC 61215 and IEC 61646 includes the measurement of the efficiency at G= 200
W/m2, or G/G* = 0.2. A possible approximation from only this value is:
𝑎1 = 1; 𝑎2 = 0; 𝑎3 =
𝜂200
−1
𝜂1000
𝑙𝑛0.2
(9)
Because a2=0, this approximation neglects the positive effect of decreasing irradiance due to
the series resistance. However, when c-Si and sunny places are concerned, it can be even more
important than the negative effect of decreasing irradiance due to the parallel resistance.
Because of that, we generally disregard this possibility. Another practical possibility,
overcoming this difficulty, consists on granting generality to already published values for
particular specimens. For example, the JRC of ISPRA has published efficiency values at different
irradiances for several technologies (Kenny RP, 2013).
Finally, efficiency measurements can be performed for specific PV module or array. This
cannot be applied for energy yield forecast, but it provides a further interesting reference.
46
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Table A1.1 present the results of adjusting the model parameters for the Yingly YL 160
polycrystalline silicon PV module with these three possibilities. In all the cases, the value of γ
has been the same that at the data sheet. Models are denoted with a sequence of letters:
First, the model type (“MPP”); second, the addressed efficiency dependence (“C” means
constant efficiency, “T” means efficiency dependence on only TC, “TG” means dependence on
TC and Geff) and, third, the source of information (“D”, “P” and “OM” means, respectively,
datasheet, published and own measurements). Figure 1 shows the corresponding relative
efficiency, ηG/η*, versus irradiance curves. Later on, we will see that the large difference on
model parameters, despite corresponding visible differences on these curves, has rather little
impact on energy calculations.
Model
Information
source
Input data
parameters
notation
o
γ (%/ C)
a1
a2
a3
None
None
MPPC
0
1
0
0
Data sheet
P*=160W
MPPTD
-0.45
1
0
0
MPPTGD
-0.45
1.10
-0.1
0.08
MPPTGP
-0.45
1.184
-0.184
0.118
MPPTGA
-0.45
1.266
-0.266
0.166
PNOCT= 116.2 W
η200/ η1000≥0.95
o
γ = -0.45 %/ C
(Kenny RP,
2013) for a
Pc_Si PV
module
Oper Cond
PDC(W)
STC
53.3
0.6G , TC*
*
32.4
*
10.2
0.2G , TC*
Own
η.6G*/ η* = 1.03
Measure.
η.2G*/ η*= 0.95
Table A1.1. Parameters of different MPP model versions for the YL 160 silicon PV module
Table A1.2 contains a chronological list of different formulations of MPP models. They have
been proposed mainly to improve the accuracy of TF modules at very low irradiance and also
to cope with the logarithm in case G =0. However, associated differences in terms of yearly
energy yields are scarcely significant; typically well below the uncertainty of in-field
measurements. A round-robin of different energy prediction methods, some based on such
different formulations, within the European project “Performance” has concluded that “All
47
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
energy prediction methods showed similar results, which does not allow for any preferred
selection at this stage” (Friesen G G. R., 2007).
Equation
Reference
𝐺𝑒𝑓𝑓
𝜂(𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) = 𝜂 ∗ [1 + 𝛾(𝑇𝐶 − 𝑇𝐶∗ ) + 𝑎𝑙𝑜𝑔10 ( ∗ )]
𝐺
(Evans D,
1981)
𝑃𝐷𝐶 (𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) = 𝐴 + 𝐵𝐺𝑒𝑓𝑓 + 𝐶𝐺𝑒𝑓𝑓 𝑇𝐶
(Taylor RW.,
1986)
𝜂(𝐺𝑒𝑓𝑓 ) = 𝑃0 + 𝑃1 𝐺𝑒𝑓𝑓 + 𝑃2 𝑙𝑛𝐺𝑒𝑓𝑓
(Willians SR,
2003)
𝜂(𝐺𝑒𝑓𝑓 ) = 𝑎. 𝑙𝑛𝐺𝑒𝑓𝑓 + 𝑏
(Randall JF,
2003)
𝜂(𝐺𝑒𝑓𝑓 ) = 𝜂 ∗ [𝑎1 + 𝑎2 𝐺𝑒𝑓𝑓 + 𝑎3 𝑙𝑛(𝐺𝑒𝑓𝑓 . 𝑊 −1 𝑚2 )]
(Beyer H.G.,
2004)
𝜂(𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) = 𝜂 ∗ [1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝑐0 𝑙𝑛 (
+ 𝛽(𝑇𝐶 − 𝑇𝐶∗ )]
𝐺𝑒𝑓𝑓
𝐺𝑒𝑓𝑓
2
)
+
𝑐
𝑙𝑛
(
)
1
𝐺∗
𝐺∗
𝑃𝐷𝐶 (𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) = 𝐷1 𝐺𝑒𝑓𝑓 + 𝐷2 𝑇𝐶 + 𝐷3 (𝑙𝑛𝐺𝑒𝑓𝑓 )𝑑5 + 𝐷4 𝑇𝐶 (𝑙𝑛𝐺𝑒𝑓𝑓 )𝑑5
𝜂(𝐺𝑒𝑓𝑓 ) = 𝑎𝐺𝑒𝑓𝑓 + 𝑏𝑙𝑛(𝐺𝑒𝑓𝑓 + 1) + 𝑐[𝑙𝑛2
𝐺𝑒𝑓𝑓 + 𝑒
− 1]
𝐺𝑒𝑓𝑓 + 1
(Willians S B.
T., 2005)
(Rosell JI,
2006)
(Heydenreich
W., 2008)
𝜂(𝐺𝑒𝑓𝑓 ) = 1 + 𝑎(𝐺𝑒𝑓𝑓 − 1) + 𝑏𝑙𝑛𝐺𝑒𝑓𝑓 + 𝑐(𝐺𝑒𝑓𝑓 − 1)2 + 𝑑𝑙𝑛2 𝐺𝑒𝑓𝑓
(Montgareuil
AG, 2009)
𝜂(𝐺𝑒𝑓𝑓 ) = 𝑎1 + 𝑎2 𝐺𝑒𝑓𝑓 + 𝑎3 𝑙𝑛(𝐺𝑒𝑓𝑓 + 𝑎4 )
(Reich NH v.
S., 2009)
𝑃𝐷𝐶
𝐺𝑒𝑓𝑓
𝐺𝑒𝑓𝑓
𝐺𝑒𝑓𝑓
1 + 𝑘1 𝑙𝑛 ∗ 𝐺𝑒𝑓𝑓 + 𝑘2 𝑙𝑛( ∗ )2 + 𝑘3 (𝑇𝐶 − 𝑇𝐶∗ ) + 𝑘4 (𝑇𝐶 − 𝑇𝐶∗ )𝑙𝑛 ∗
𝐺
𝑒𝑓𝑓
𝐺
𝐺
𝐺 ]
= 𝑃∗ ∗ [
𝐺𝑒𝑓𝑓 2
𝐺
∗
∗
2
+𝑘5 (𝑇𝐶 − 𝑇𝐶 )𝑙𝑛( ∗ ) + 𝐾6 (𝑇𝐶 − 𝑇𝐶 )
𝐺
(Huld T F. G.,
2011)
Table A1.2. MPP models equations. The notation (𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) means the whole power surface is
described by only this equation, dealing together with irradiance and temperature effects. The
notation (𝐺𝑒𝑓𝑓 ) means that both effects are treated as independent of each other. The given
equation describes the dependence on irradiance, while the temperature dependence is given
by the additional factor [1 + 𝛾(𝑇𝐶 − 𝑇𝐶∗ )].
48
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
It is also worth comment that equation (7) associate easy calculations. For example, thermal
losses calculation from Geff and TC records is straightforward
∆𝑃 𝑇𝐶≠𝑇𝐶 ∗ = −𝛾(𝑇𝐶 − 𝑇𝐶∗ )
(10)
and
∆𝐸𝑇𝐶≠𝑇𝐶 ∗ = −
∫∆𝑡 .𝛾(𝑇𝐶 −𝑇𝐶∗ ).𝐺𝑒𝑓𝑓 .𝑑𝑡
∫∆𝑡 𝐺𝑒𝑓𝑓 .𝑑𝑡
(11)
Moreover, it can be corrected to estimate shading losses (Quaschning V., 1998) (Martinez F M.
J., 2010) and it has an inherent facility for solving the inverse to the performance surface. The
value of P* can be directly deduced from PDC measurements by the inverse of equation (9),
which provides a way of accurate measuring of the real STC power of large PV arrays (Martinez
MF, 2011)
The on-going attempt of the IEC (International Electrotechnical Commission) to develop an
“energy rating” standard for PV devices includes an empirical MPP model, allowing the
adjusting parameters to vary with Geff and TC, if necessary. Described in IEC 618532, parts 1 to
4, this attempt looks for rating the PV modules by the energy they produce along five standard
days which are intended to be representative of different climates types around the world (for
example, the so called NICE day attempts to represent climates characterized by Normal
Irradiance and Cold Environment conditions). These reference days are tabulated with
irradiance, ambient temperature, wind speed, angle of incidence and spectral distribution over
each day. The PV module performance surface is obtained by measuring 21 power values at
corresponding pairs of irradiance (from 100 to 1100 W/m2) and temperature (from 15 to
75oC). Additional measurements are also required to asses spectral and angle of incidence
effects. In practice, all these measurement entail significant complexity (Kenny RP, 2013) at the
only reach of few specialized laboratories. Both, complexity and laboratory constraints are
heavy prices that must be justified by significant accuracy gains, which does not seem to be
the case. In fact, a detailed validation of the complete IEC 618532 methodology for c-Si
modules has conclude that errors in daily terms are generally within +/- 10% for the daily
calculations, and remember that similar accuracies can be already reached for c-Si modules by
neglecting all spectral and angel of incidence effects (Friesen G G. R., 2007).This is noticeable
because it suggest that benefits than can be expected from increasing modeling complexity are
rather modest. In fact, the paper includes the following sentence: “The authors feeling is that
the complexity of the standard is actually not beneficial for an accurate energy prediction, as it
requires data which is actually normally not know and the generation of this… seems to affect
the overall agreement more than it would be without this complicated step” (Jyotirmoy Roy,
2008). Moreover, the representativeness of the standard days is also put into question. : “…for
a relevant energy rating, a longer and more representative time scale than the reference days
would need to be chosen” (Jyotirmoy Roy, 2008). Similar conclusions got the authors of a
comparison between this model and the much simpler one given by equation (7) with real data
recorded at Canada. “While the median absolute errors for the more complex IEC 61853
method were generally lower (2% as opposed to 2.8% for the other method) it is not clear
49
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
whether the gain in accuracy would justify the added cost in complexity..” (Poissant Y P. S.,
2008)
Also based on large sets of empirical measurements made on modules in other than STC, is the
effort been made at Sandia National Laboratories from mid-1990 (King DL, 2004) to develop a
PV array performance model, capable of modelling the performance of concentrators as well
as flat-modules. The original version of this model uses broadband irradiance as input and
includes several equations and many coefficients to cope with spectral and angular responses.
However, that is not necessary when using effective irradiance as input and the model can be
substantially simplified. This model determines the performance surface by means of empirical
equations for, both, the current and voltage at the maximum power point. Combining both,
expressions of the relative efficiency can be derived. A rather simple possibility, originally
developed at TISO, a Swiss test centre for photovoltaic modules, is given by (Willians S B. T.,
2005):
𝐺𝑒𝑓𝑓
𝐺𝑒𝑓𝑓
𝜂(𝐺𝑒𝑓𝑓 , 𝑇𝐶 ) = 𝜂 ∗ [1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝑐0 𝑙𝑛 ( ∗ ) + 𝑐1 𝑙𝑛2 ( ∗ ) + 𝛽(𝑇𝐶 − 𝑇𝐶∗ )]
𝐺
𝐺
This equation was implemented in the PVGIS interactive web applications for the estimation of
PV production, using empirical values obtained from measurements of a single c-Si module: α
=1.2x10-3 oC-1 ; β = -4.6x10-3 oC-1 ; c0=0.033 and c2=-0.0092 (Huld T S. M., 2008). Later, it has
been substituted by a slightly more complex possibility (Huld T F. G., 2011):
𝑃𝐷𝐶 =
𝐺𝑒𝑓𝑓
𝑃∗ 𝐺 ∗ [
1 + 𝑘1 𝑙𝑛
𝐺𝑒𝑓𝑓
𝐺∗
𝐺𝑒𝑓𝑓 2
) + 𝑘3 (𝑇𝐶 − 𝑇𝐶∗ ) + 𝑘4 (𝑇𝐶
𝐺∗
𝐺
𝑇𝐶∗ )𝑙𝑛( 𝑒𝑓𝑓
)2 + 𝐾6 (𝑇𝐶 − 𝑇𝐶∗ )2
𝐺∗
𝐺𝑒𝑓𝑓 + 𝑘2 𝑙𝑛(
+𝑘5 (𝑇𝐶 −
− 𝑇𝐶∗ )𝑙𝑛
𝐺𝑒𝑓𝑓
𝐺∗
] (12)
Coefficients for 18 crystalline PV modules has been obtained by means of an extensive
measurement campaign (at least 24 power values at corresponding (Geff, TC) pairs have been
measured for each module), and the results have been combined to generate a model for a
generic crystalline silicon module that has been included in the online PV estimator in PVGIS. It
is given by k1= -0.01724; k2= -0.04047; k3= -0.0047 oC-1; k4=1.49x10-4 oC-1 ; k5= 1.47x10-4 oC-1 and
k6=5x10-6 oC-2.
FF models
The performance surface can also be described through the Fill Factor, FF.
𝑃𝐷𝐶 = 𝐼𝑆𝐶 𝑉𝑂𝐶 𝐹𝐹
(13)
The relation with the operation conditions is given by:
∗
𝐼𝑆𝐶 = 𝐼𝑆𝐶
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )]
∗
𝑉𝑂𝐶 = 𝑉𝑂𝐶
[1 + 𝛽(𝑇𝐶 − 𝑇𝐶∗ )]
50
(14)
(15)
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
It can be postulated that the FF is independent of irradiance and linearly related with
temperature, so that:
𝐹𝐹 = 𝐹𝐹 ∗ [1 + 𝜉(𝑇𝐶 − 𝑇𝐶∗ )]
(16)
where ξ is the temperature coefficient for fill factor. The derivative of equation (13) with
respect to temperature leads to
1 𝑑𝑃𝐷𝐶
𝑃𝐷𝐶 𝑑𝑇𝐶
=
1 𝑑𝐼𝑆𝐶
𝐼𝑆𝐶 𝑑𝑇𝐶
+
1 𝑑𝑉𝑂𝐶
𝑉𝑂𝐶 𝑑𝑇𝐶
+
1 𝑑𝐹𝐹
(17)
𝐹𝐹 𝑑𝑇𝐶
or
𝛾 =𝛼+𝛽+𝜉
(18)
Combining these equations leads to:
𝑃𝐷𝐶 = 𝑃∗
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝛽(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝜉(𝑇𝐶 − 𝑇𝐶∗ )]
(19)
Which allows directly solving the performance surface using the temperature coefficients
given at manufactures datasheet. Because the FF is in practice much less temperature
sensitive than VOC, some authors have suggested to consider it as constant, or ξ = 0 (Fuentes
M, 2007).
This formula disregards the efficiency dependence on irradiance. However, that can be
considered by adding a semi-empirical corrective term to the calculation of VOC. This way,
equation (15) is replaced by:
∗ [1
𝑉𝑂𝐶 = 𝑉𝑂𝐶
+ 𝛽(𝑇𝐶 − 𝑇𝐶∗ )] + 𝑉𝑡 𝑙𝑛
𝐺𝑒𝑓𝑓
(20)
𝐺∗
and
𝑃𝐷𝐶 = 𝑃∗
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝛽(𝑇𝐶 − 𝑇𝐶∗ )][1 + 𝜉(𝑇𝐶 − 𝑇𝐶∗ )][1 +
𝑉𝑡
∗ [1+𝛽(𝑇 𝑇 ∗ )]
𝑉𝑂𝐶
𝐶− 𝐶
𝑙𝑛
𝐺𝑒𝑓𝑓
𝐺∗
]
(21)
Vt is the sometimes called thermal voltage, which is given by:
𝑉𝑡 = 𝑚𝑁𝐶𝑆
𝑘𝑇𝐶
𝑞
(22)
where m is the usual ideality factor, NCS the number of solar cells associated in series, k is the
Boltzmann’s constant – 1.381x10-23J/oK- and q is the absolute value of the charge on an
electron - -1.602x10-19C -. TC is expressed in absolute temperature (K). 1.1 ≤ m ≤1.3 is a
reasonable choice range for crystalline silicon.
Table A1.3 describes different based on FF modelling possibilities for the Yingly 160 YL PV
module. The notation letter sequence is now: First, the model type (“FF”) and second, the
51
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
addressed FF dependence (“C” , “T” and “G” respectively means constancy, dependence on
temperature and dependence on irradiance).
Model
Source of
information
Input data
Notation
P*=160W
Datasheet
Parameters
FFC
FF* = 0.717, ξ = 0
FFTD
FF* = 0.717, ξ = -0.02%/oC
ISC*= 7.8 A
VOC*= 29 V
o
α= 0.1 %/ C
o
β = -0.37%/ C
FFTGD
FF* = 0.717, ξ = -0.02%/oC, m=1.3
o
γ = -0.45 %/ C
Table A1.3. Parameters of different FF model versions for the YL 160 silicon PV module.
Full I-V curve models
A PV generator is traditionally represented by an equivalent circuit referred as the 5parameter one diode model. It is composed by a current source, an anti-parallel diode, an
internal series resistance and a shunt/parallel resistance. Based on the Shockley and Queisser
diode equation, the corresponding mathematical model is given by
𝑉+𝐼𝑅𝑆
)−
𝑉𝑡
𝐼 = 𝐼𝐿 − 𝐼0 [exp (
1] −
𝑉+𝐼𝑅𝑆
𝑅𝑃
(23)
where the 5-parameters are: the photocurrent, IL, the diode saturation current, I0, the thermal
voltage, Vt, the series resistance, RS, and the parallel resistance, RP. Good descriptions of this
model are available from the early photovoltaic days (Loferski J., 1993) and are easily found at
basic text books (Backus C.E., 1976) (Green M., 1982) (Duffie& Beckman, 1991) (Lorenzo E,
1994). Dealing in practice with this model requires solving three different problems:
-
To extract the parameters at STC from available information
To extend the parameters to other than STC
To solve the equation to find the MPP value.
Extraction of parameters at STC
The literature is rich in variations around methods to solve the problem of extracting these I-V
model parameters from measured I-V curves. (Charles JP, 1981) (Phang JCH, 1984) (Jia QX,
1995) (Chan D.S.H, 1987) (de Blas M, 2002) (Haouari-Merbah M, 2005) (Bashahu M N. P., 2007)
(Bouzidi K, 2007) (Tsuno Y., 2007) (Zhou W, 2007) (Kim W, 2010) (Ghani F, 2012) (Dongue SB,
2013) (Stein J, 2013) (Hernandez J, 2013) (Singh NS, 2013) (Venkateswarlu G, 2013) (Ortiz-
52
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Conde A, 2014) (Ma T Y. H., 2014). However, for our present purposes, fitting the model with
PV manufacturer’s datasheet is more relevant.
In principle, to determine 5 parameters requires 5 independent information sources:
equations, datasheet values or assumptions. Two are easily obtained from writing the
equation (23) for ISC* and VOC*. Respectively:
∗
𝐼𝑆𝐶
= 𝐼𝐿∗ − 𝐼0∗ (𝑒𝑥𝑝
∗
𝐼𝑆𝐶
𝑅𝑆∗
𝑉𝑡∗
− 1) −
∗
𝐼𝑆𝐶
𝑅𝑆∗
∗
𝑅𝑃
(24)
and
0 = 𝐼𝐿∗ − 𝐼0∗ 𝑒𝑥𝑝
∗
𝑉𝑂𝐶
𝑉𝑡∗
−
∗
𝑉𝑂𝐶
∗
𝑅𝑃
(25)
There are many possible approaches for the other three. A simple one consist on imposing the
P* value and making reasonable assumptions for m and RP*. Note this approach assures P* but
do not requires the I-V curve passing for any particular point, apart ISC*and VOC*. Then, the
corresponding FF*is compared with the fill factor of an ideal cell (a cell with RS*null and RP*
infinite), FF0, using available semi empirical expressions for the MPP (Green M., 1982). The
following equations apply:
∗
𝑣𝑂𝐶
=
∗
𝑉𝑂𝐶
𝑉𝑡∗
𝑟𝑃∗ = 𝑅𝑃∗
𝐹𝐹0∗ =
∗
𝐼𝑆𝐶
∗
𝑉𝑂𝐶
𝑟𝑆∗ = 𝑅𝑆∗
∗
𝐼𝑆𝐶
∗
𝑉𝑂𝐶
∗
∗
𝑣𝑂𝐶
−ln(𝑣𝑂𝐶
−0.72)
∗
𝑣𝑂𝐶 +1
(26)
(27)
∗
𝑣𝑂𝐶
+0.7 𝐹𝐹0∗ (1−𝑟𝑆∗ )
)[ 𝑟 ∗ ]}
∗
𝑣𝑂𝐶
𝑃
𝐹𝐹 ∗ = 𝐹𝐹0∗ (1 − 𝑟𝑆∗ ) {1 − (
(28)
Again, 1.1 ≤ m ≤1.3 is a reasonable choice range for crystalline silicon. Obviously, RP*must be
larger than VM*/(ISC*-IM*). Therefore, a possibility consists on using a multiple of this quantity
as a default value for each technology (PVsyst). For example, 5 times can be a reasonable
approach for crystalline silicon modules. The calculation sequence is: obtain vOC* and rP* from
m, RP and equation (26), rS*from equation (28), RS*from equation (26) and solve the system
formed by equations (24) and (25). A further simplification of this approach is considering
RP*as infinite. Then:
𝐹𝐹 ∗ 𝑉 ∗
𝑅𝑆∗ = (1 − 𝐹𝐹∗ ) 𝐼𝑂𝐶
∗
0
𝑆𝐶
∗
∗
𝐼𝐿∗ ≈ 𝐼𝑆𝐶
and 𝐼0∗ = 𝐼𝑆𝐶
exp (−
∗
𝑉𝑂𝐶
)
𝑉𝑡∗
(29)
Assuming RP*as infinite simplify the equivalent circuit of the PV generator, resulting the so
called “4-parameters model”, which is extensively used for crystalline silicon modules
operating in sunny places (Jia Q, 1988) (Lorenzo E, 1994) (Xiao W, 2004) (Bellini A, 2009)
(Hernandez J, 2013) (Massi Pavan A M. A., 2014), because it represents a good compromise
between accuracy and complexity. On the same lines, even the “3-parameters model”
resulting from the ideal cell, where effects of series and parallel resistances are neglected,
leads to reasonable good results, showing PDC errors below 4% for a large range of Geff and TC
(Mahmoud Y, 2010) (Saloux E, 2011) (Vajpai J, 2013).
53
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Coming back to the 5-parameters model, several equations can serve as additional pieces of
information. For example, a third equation results from imposing the I-V curve passing for the
point (IM*, VM*). Writing equation (23) for this point leads to:
1
𝐼∗
𝑀
𝑆𝐶
∗
(1−𝑅𝑆∗ /𝑅𝑃
)
)]
∗
∗
𝑂𝐶 /(𝑅𝑃 𝐼𝑆𝐶 ))
∗
𝑅𝑆∗ = 𝐼∗ [𝑉𝑂𝐶
− 𝑉𝑀∗ + 𝑉𝑡∗ ln (1 − 𝐼∗𝑀 (1−𝑉 ∗
(30)
A four equation derives from imposing the derivative of power in this point is null. Then
𝑑𝑃
𝑑𝑉
=
𝑑(𝐼𝑉)
𝑑𝑉
𝑑𝐼
= 𝐼 + 𝑉 𝑑𝑉
(31)
dI/dV can be obtained by observing that the mathematical model (equation (23))is of the
shape I = f(I,V).
𝜕𝑓(𝐼,𝑉)
𝜕𝐼
𝑑𝐼 = 𝑑𝐼
+ 𝑑𝑉
𝜕 𝑓(𝐼,𝑉)
𝜕𝑉
(32)
or
𝑑𝐼
𝑑𝑉
=
𝜕 𝑓(𝐼,𝑉)
𝜕𝑉
𝜕 𝑓(𝐼,𝑉)
1−
𝜕𝐼
(33)
partial derivatives are
𝜕 𝑓(𝐼,𝑉)
𝜕𝑉
𝐼
= − 𝑉0 𝑒𝑥𝑝
𝑡
𝑉+𝐼𝑅𝑆
𝑉𝑡
1
−𝑅
𝑃
and
𝜕 𝑓(𝐼,𝑉)
𝜕𝐼
=−
𝐼0 𝑅𝑆
𝑉+𝐼𝑅
𝑒𝑥𝑝 𝑉 𝑆
𝑉𝑡
𝑡
𝑅
− 𝑅𝑆
(34)
𝑃
and writing the condition (dP/dV)MPP=0 for STC leads to
∗
𝐼𝑀
+ 𝑉𝑀∗
𝑉∗ +𝐼∗ 𝑅∗
𝐼∗
1
− 0∗ 𝑒𝑥𝑝 𝑀 ∗𝑀 𝑆 − ∗
𝑉𝑡
𝑉𝑡
𝑅𝑃
∗
∗ 𝑅∗
𝐼∗0 𝑅𝑆
𝑉∗𝑀 +𝐼∗𝑀 𝑅𝑆
1+ ∗ 𝑒𝑥𝑝
− ∗𝑆
𝑉𝑡
𝑉𝑡∗
𝑅𝑃
=0
(35)
The fifth equation can be derived from the open circuit temperature coefficient data, writing
∗
𝑉𝑂𝐶 (𝑇𝐶 ) = 𝑉𝑂𝐶
[1 + 𝛽(𝑇𝐶 − 𝑇𝐶∗ )]
(36)
for a TC value close to TC*. The particular temperature value is not critical, since any TC ranging
from 1 to 10 K above or below TC*leads to the same result. VOC(TC) is found from equation (25)
–written without asterisks- once the temperature dependence of I0, IL, Vt and RP is now. This
dependence is considered in the following section. Now, the system formed by equations (24),
(25), (30), (35) and (36) is complete. This particular approach (De Soto W, 2006) has been
widely used in USA and it was adopted as a standard for energy calculations at the solar
initiative promoted by the California Energy Commission, CEC. However, solving this implicit
and non-lineal equation system requires numerical methods demanding extensive
computation and also good initial guesses for the iterations to converge. Powerful
mathematical tools such as the equation solver EES from F-Chart (De Soto W, 2006), the
Newton-Raphson (Villalva MG G. J., 2009), the bisection (Sera D, 2007) and the Levenberg-
54
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Marquardt algorithms (Celik AN, 2007) has been employed. The inherent difficulties of this
process have stimulated the research of alternatives.
Other equations have been derived from recognizing the slope of the I-V curve at ISC can be
assimilated to the RP (Chan D, 1986) (Sera D, 2007) (Ma T Y. H., 2014)
𝑑𝐼
|
𝑑𝑉 𝐼𝑆𝐶
=−
1
𝑅𝑃
(37)
, the slope of the I-V curve at MPP is immediately deduced from equation (31) (Xiao W, 2004)
(Saloux E, 2011)
𝑑𝐼
|
𝑑𝑉 𝑀𝑃𝑃
𝐼
= − 𝑉𝑀
(38)
𝑀
or from establishing a relation between m and RP (Jia QX, 1995).
𝑉𝑡=
𝑉𝑀 +𝐼𝑀 𝑅𝑆 −𝑉𝑂𝐶
𝑅
𝑉 −𝑉𝑀
(𝐼𝑆𝐶 −𝐼𝑀 )(1+𝑅 𝑆 )+ 𝑂𝐶
𝑅𝑃
𝑃
𝑙𝑛[
]
𝑅
𝑉
𝐼𝑆𝐶 (1+ 𝑆 )− 𝑂𝐶
𝑅𝑃
𝑅𝑃
(39)
Assuming a value for m, simplifying (24)
𝑅∗
∗
𝐼𝐿∗ = 𝐼𝑆𝐶
(1 + 𝑅𝑆∗ )
(40)
𝑃
and iterating on RS and RP until finding the only pair (RS,RP) that warranties P*has been
proposed as a way of facilitating the extraction of parameters (Villalva MG G. J., 2009). Fixing
the values of m and also RS and RP and deriving IL and I0 from solving the system formed by (24)
and (25) is another easy possibility. The following equations have been proposed for that
(Carrero C, 2010).
𝑅𝑆∗ =
1
∗
∗ (𝑉𝑂𝐶
𝐼𝑀
− 𝑉𝑀∗ − 𝑉𝑡∗ 𝑙𝑛
∗
∗ ∗
𝑉𝑀
+𝑉𝑡∗ −𝐼𝑀
𝑅𝑆
)
𝑉𝑡∗
(41)
and
𝑅𝑃∗ =
∗
∗
∗ ∗
(𝑉𝑀
−𝑉𝑡∗ )(𝑉𝑀
−𝐼𝑀
𝑅𝑆 )
∗ −𝐼 ∗ )(𝑉 ∗ −𝐼 ∗ 𝑅 ∗ )−𝐼 ∗ 𝑉 ∗
(𝐼𝑆𝐶
𝑀
𝑀 𝑀 𝑆
𝑀 𝑡
(42)
Reviews of loses resistance estimation methods can be found (Bashahu M H. A., 1995) (Coftas
D, 2008). There is also a trickle of mathematical innovation propositions: Lambert functions
(Jakhrani A, 2014) (Ghani F, 2012), Genetic algorithms (Venkateswarlu G, 2013), Special Trans
Function Theory (Singh NS, 2013), Generalized Reduced Gradient (Lo Brano V C. G., 2013)
Extension of parameters to arbitrary conditions
Most typically, IL is assumed to be almost linearly related with Geff
𝐼𝐿 = 𝐼𝐿∗
𝐺𝑒𝑓𝑓
𝐺∗
[1 + 𝛼(𝑇𝐶 − 𝑇𝐶∗ )]
55
(43)
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
The diode saturation current is given by the equation (Messenger RA, 2004)
𝐸
𝑇
1
1
𝐼0 = 𝐼0∗ ( 𝑇𝐶∗ )3 exp[ 𝑘𝑔 (𝑇 ∗ − 𝑇 )]
𝐶
(44)
𝐶
𝐶
where Eg is the material energy band gap (1.121 eV for crystalline silicon). Eg exhibits a small
temperature dependence that can be described by (De Soto W, 2006)
𝐸𝑔
= 1 − 0.0002677(𝑇𝐶 − 𝑇𝐶∗ )
𝐸𝑔∗
m is assumed to be constant, so that:
𝑇
𝑉𝑡 = 𝑉𝑡∗ 𝑇𝐶∗
(45)
𝐶
TC at equations (15) and (16) is expressed in absolute temperature (K). RS is generally assumed
to be constant, while an empirical equation is used to describe the observed relation between
RP and G (De Soto W, 2006)
𝐺∗
𝑅𝑃 = 𝑅𝑃∗ 𝐺
(46)
𝑒𝑓𝑓
Mainly looking for improving the reproducibility of the model at low irradiance conditions,
alternatives to this typical procedure have been proposed: PVsyst assume that that RP
increases quasi-exponentially when G diminishes:
𝑅𝑃 = 𝑅𝑃∗ + (𝑅𝑃0 − 𝑅𝑃∗ )𝑒𝑥𝑝 (−𝑐𝑅𝑃
𝐺𝑒𝑓𝑓
𝐺∗
)
(47)
where the parallel resistance at no irradiance, RPO, and the exponential coefficient cRP are
empirically adjusted. The observed ratio RP* /RPO ranges from 4 for crystalline silicon to 12 for
triple junction amorphous. cRP ranges from 2 (CdTe) to 5.5 for Si (Mermoud A., 2010).
Dependences of I0 on Geff and of RS on TC can be considered by introducing an empirical
equation for RS
𝑅𝑆 = 𝑅𝑆∗ 𝑒𝑥𝑝[𝛿(𝑇𝐶 − 𝑇𝐶∗ )]
(48)
and replacing (I0) with:
𝐺∗
𝐼0 = 𝐼0∗ (𝐺
𝑒𝑓𝑓
𝑇
𝐸
1
1
)𝜏 ( 𝑇𝐶∗ )3 exp[ 𝑘𝑔 (𝑇 ∗ − 𝑇 )]
𝐶
𝐶
𝐶
(49)
where δ and τ are empirical values that have to be adjusted with other than STC information,
given raise to the so called seven-parameters models (Boyd T, 2011) (Siddiqui M, 2013). In fact,
CEC require PV manufactures providing the maximum current and voltage at 200W/m2 and
25oC (CEC).
An alternative equation for I0, based on the temperature coefficient of voltage data, is
obtained deriving I0 from (25)
𝐼0 = (𝐼𝐿 −
𝑉𝑂𝐶
𝑉
) 𝑒𝑥𝑝 (− 𝑉𝑂𝐶 )
𝑅𝑃
𝑡
56
(50)
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
and
∗ [1
𝑉𝑂𝐶 = 𝑉𝑂𝐶
− 𝛽(𝑇𝐶 − 𝑇𝐶∗ )] + 𝑉𝑡 𝑙𝑛
𝐺𝑒𝑓𝑓
𝐺∗
(51)
Solving the model to find the MPP value
Equation (23) is an implicit and non-linear one, which is typically solved by iterative methods
(Newton-Raphson, etc.). Ruiz has developed an analytical procedure, based on the Taylor
series of the first Newton-Raphson step, which is easy of apply. It is given by the following
equations:
𝐷𝑀0 =
𝑣𝑂𝐶 −1
𝑣𝑂𝐶 −𝑙𝑛 𝑣𝑂𝐶
𝑖𝑠 =
2
𝐷𝑀 = 𝐷𝑀0 + 2𝑟𝑆 𝐷𝑀0
1−𝑔𝑝 (1−𝑟𝑠 )
(53)
1−exp(−𝑣𝑜𝑐 (1−𝑟𝑠 ))
𝑖𝑠′ = 1 + 𝑖𝑠 𝑒𝑥𝑝[−𝑣𝑜𝑐 (1 − 𝑟𝑠 )]
𝐷
′
𝑖𝑀
= 𝑖𝑠′ − 𝑣 𝑀
𝑜𝑐
𝐼𝑀
𝐼𝑆𝐶
𝑣𝑠′ = 1 −
1
ln(𝑣𝑜𝑐 𝑖𝑠 )
𝑣𝑜𝑐
1
′
𝑣𝑀
= 𝑣𝑠′ + 𝑣 𝑙𝑛𝐷𝑀
′
′
= 𝑖𝑀
− 𝑔𝑝 (𝑣𝑀
− 𝑟𝑠 )
(52)
𝑜𝑐
𝑉𝑀
𝑉𝑂𝐶
𝐼
′
= 𝑣𝑀
− 𝐼 𝑀 𝑟𝑠
𝑆𝐶
(54)
(55)
(56)
where the normalized conductance is gp = 1/rP and vOC, rS and rP are given by (26) written
without asterisks. This set of equations avoids the calculation of IL and I0.
Combining models (3, 4 or 5 parameters) and methods for extracting parameters, translating
to other than STC conditions and solving the MPP point, give rise to a multiplicity of based on IV curve modelling approaches. Looking for exploring the usefulness in practice of this
multiplicity, we have selected:
-
4 parameters model, m=1, RS as given by (30).
5 parameters, m=1.2, RS as given by (41); RP as derived from (28).
5 parameters as given at the PVsyst database, RP dependence as (47)
5 parameters as given at the PVsyst database, RP dependence as (46). This case is
referred as IVPVsystN-2.
5 parameters as given at the PVsyst database, RP dependence as (47) and solving MPP
by (52) to (56)
5 parameters as adjusted to measured I-V curves at different operation conditions, RP
dependence as (46) and solving MPP by (52) to (56)
The first and second approaches entail low and medium complexity, respectively. The third is
the standard approach of PVsyst, which is a widely reputed software that can somewhat serve
as reference. PVsyst considers the RP dependence as (47) and solves the MPP using a NewtonRaphson algorithm. Hence, the two following cases are variations around this reference and
have been notated, respectively as V1 and A. Finally, the last case requires additional I-V
57
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
measurements and can be understood as representing large complexity. Table A1.4 describes
these modelling possibilities for the Yingly 160 YL PV module. The notation letter sequence is
now: First, the model type (“IV”); second, the number of parameters (3, 4 or 5); third the
assumption for m (“12” means m=1.2, “A” means adjusted) and, fourth, the solving method for
MPP (“N” and “A” means Numeric and Analytic).
Model
Source of
information
Datasheet
Input data
P*=160W
Notation
Parameters
IV410N
m= 1,
ISC*= 7,8 A
RP = ∞,
VOC*= 29 V
RS = 0,505 Ω
o
α= 0.1 %/ C
IL*=ISC*
o
β = -0.37%/ C
I0*= 0.48 nA
IM*= 7 A
IV512N
0.292 Ω, RP =
80.6 Ω , IL*=7.83
A, I0*= 22.8 nA
VM*= 23 V
PVSyst
databases
m= 1.2, RS =
m= 1.17, I0*= 13.8 nA,
IVPVsystN
Ídem data
RP = 160 Ω, RS = 0,34
Ω
IVPVsystN-2
IL*=7.83 A
IVPVsystA
m= 1.28, ISC*= 8,045 A
Own
o
measurements α= 0.019 %/ C
IV5AA
o
β = -0.385%/ C
RP = 85 Ω, RS = 0,35 Ω
Table A1.4. Parameters of different I-V curve model versions for the YL 160 silicon PV module
Other models
PDC variations with Geff and TC are implicit at the STC values of the 5 parameters and
corresponding extrapolation equations of the one diode model. As mentioned above,
58
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
difficulties for extracting parameters from only manufactures datasheets usually leads to rely
on different approximations (or on additional independent measurements at particular
specimens, not necessarily representative of the same module type and bin average) leading
to also different STC parameters values (See Table 4). Together with different extrapolation
techniques, that has led to model accuracy suspicions, mainly when low irradiances and TF are
concerned. In fact, significant differences on thermal power coefficients and low irradiance
efficiency between the values predicted with commercial simulation software and the
experimental values have been reported (Ransome S S. J., 2012). That has provided the
motivation for other modelling proposals. In fact, this is the common motivation in the back of
all the here referenced as MPP and FF models, all based on adjust thermal and irradiance
coefficients for power to empirical values, and also on the back of using some empirical
equations for translating STC parameters to other conditions. Hence, distinguishing between
MPP, Full I-V curve and other models entail some confusion. Nevertheless, this section groups
together some proposals having in common to be formulated by other than direct PDC
equations or other than equation (23) formulations.
The so called “Loss Factor Model” has born on amorphous silicon ambiences. The efficiency
variations with irradiance are described by means of the product of five lose factors,
respectively, accounting for the variations of ISC, VOC, the two I-V curve tilts at ISC and VOC, and a
kind of FF, relating the maximum power not with the usual product ISCxVOC but with the
product of the I and V coordinates of the crossing point of these two tilts. Each of these factor
are empirically fitted to the following functional form
𝑓(𝐺) = 𝑐1 + 𝑐2 log 𝐺 − 𝑐3 𝐺 2
(57)
So that 15 parameters (additional to α and β, required for describing the variation of ISC and
VOC with temperature, and even an extra fill factor temperature coefficient added in the last
versions of this model ) and, therefore, an extensive dedicated measurement campaign are
required. Based on these lose factors have physical meaning since they relate directly to the
behavior of the key points of the I-V curve, this model can likely provide diagnostic information
about the relative “health” condition of the modules. As far as we know, this model has never
been published at journals submitted to peers review. Instead, it has been often presented on
conferences (Ransome S, A Review of kWh/kWp measurements, analysis ans modelling, 2008)
(Ransome S S. J., 2011) (Sellner S S. J., 2012) (Ransome S S. J., 2012).
Explicit formulations of the I-V curve, looking for easy analytical manipulations and closed form
solutions of the performance when operating with load, can be found at (Akbaba M, 1995)
(Ortiz-Rivera E, 2005) and (Massi Pavan A M. A., 2014). They are not further described here,
because they do not affect to the prediction of the maximum power. The last has been used to
analyze mismatch effects in large-scale solar parks (Massi Pavan A M. A., 2014). A modified
formulation of equation (23) implicitly making both series and parallel resistances sensitive to
irradiance according with equation (46) has also been proposed (Lo Brano V O. A., 2010).
The case of a-Si
a-Si modules are subject to the Staebler-Wronski effect, where there is a decrease in
performance upon exposure to light typically reducing the efficiency by 15-20% compared with
59
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
its initial value. Additionally, after reaching the stabilization (about 6 months of outdoor
exposure), the efficiency of this material exhibits seasonal variations that have been attributed
to mainly two effects: spectral effects, and thermal annealing. These seasonal changes can be
described very closely with the sinusoidal function (Nikolaeva-Dimitrova M, 2010):
𝜂(𝑡)
𝜂∗
𝑡
= 𝐴𝑠𝑖𝑛 (2𝜋 𝑇 + φ) + 𝜂𝐴𝑉
(58)
Where A is the amplitude, t is the time (month) at which we wish to predict the efficiency, T is
the total time period (12 months), φ is the phase and 𝜂𝐴𝑉 is the average efficiency.
PV performance models comparison
Roughly speaking, the PV performance modelling panorama can be understood as mainly
originated at ambiences, having different means, skills and mandates. On the none hand, big
specialized laboratories, like JRC in Europa or SANDIA in USA, that are particularly well
prepared for systematic and highly accurate measurements on commercial PV modules and
use to be deeply involved in national PV promotion initiatives, have been the main cradle of
MPP models, which are essentially empirical and require easy calculations, like adjusting
polynomials . On the other hand, universities, typically dealing with research and fundamental
studies and being particularly interested on publishable innovations, have been the main
cradle of full I-V models, which are essentially physical and require relatively complex
calculations, like solving implicit and non-linear equations system.
Not surprisingly, most today available model comparisons have been made inside each one of
these two ambiences. In fact, among the vast literature disclosed by PV performance
modelling reviews (Balasubramanian B, 2014) (Ma T Y. H., 2014) (Rus-Casas C, 2014), we only
have found 2 papers simultaneously dealing with energy yields predicted by MPP and IV curve
models and, even those in a rather restricted manner:
The first (Cameron CP, 2008) compares the energy yield observed at three c-Si PV arrays
located at Alburquerque (USA) with the predictions of three performance modelling
alternatives available within the so called Solar Advisor Model, SAM, a free software
developed by the NREL: the Sandia model, a 5-parameter one-diode model and the simplest
MPP that considers only the efficiency dependence on temperature, above referred as MPPTD.
The coefficients for implementing the SANDIA and 5-parameters models are taken from the
database distributed with SAM (derived from particular specimens measured at SANDIA and
NREL) while the temperature coefficient for the MPPTD was taken from the manufactures
datasheet. The PV arrays are of different power (1.1, 1.11 and 2.3 kW) and composed by the
same module type but from two different bins (210 and 220 STC rating nameplate). The
interesting results is not only that “..all the modules agree within about 2%”, but also that the
differences of a same model for the three PV arrays are slightly larger than that. Than can be
properly understood as that the differences due to module to module variations supersede the
differences due to model to model variations. Module to module variations have also been
signaled as the main responsible of energy yield prediction errors for other authors (Willians S
B. T., 2006).
60
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
The second (Reich NH v. S., 2009) analyses the low light performance of 41 commercially
produced c-Si cells. Because the work is made on the context of Product Integrated PV, that
are likely to be operated most often indoors that outdoors, this work pays particular attention
to the range of very low irradiances (< 100 W/m2). Despite this range is scarcely relevant for
standard PV generators, the conclusions of the paper are still useful: the accuracy of diode
models in this range can be very high but is very dependent on the used parameters (this is
because RP is of paramount importance in this range, which is not the case at normal
irradiances); the MPP model given by:
𝜂(𝐺𝑒𝑓𝑓 ) = 𝜂 ∗ [𝑎1 + 𝑎2
𝐺𝑒𝑓𝑓
𝐺∗
𝐺𝑒𝑓𝑓
+ 𝑎3 𝑙𝑛 (
𝐺∗
+ 𝑎4 )]
(59)
performs very well. Note this equation is an adaptation of equation (7) by including an
additional parameter in the logarithmic part, just to avoid negative efficiencies and to improve
fitting accuracy at very low light, below 1W/m2. Again, this is scarcely important for normal
irradiances); and that cells from one and the same manufactures show large differences in cell
efficiencies at low irradiance. That helps to understand that module to module variations use
also to be large.
On the other hand, MPP models have been extensively compared within the European
Commission funded projects PV-Catapult and PV-Performance. Participated by relevant
research institutions, the declared goal of these initiatives was investigating energy rating
procedures and supporting the development of IEC 61833. To these aims, round robins
between the models used at these institutes, all of them MPP models, have been performed.
At the first round-robin, most the models listed at table 2 were investigated for four different
module technologies (sc-Si, mc-Si, CIS, 3j-aSi) and four different sites: Cadarache in France
(Latitude, φ = 44º; Yearly global irradiation at a latitude tilted surface, Ga(φ) = 1591 kWh/m2
and Diffuse/global ration, D/G = 0.35, according with PVGIS), Wroclaw in Poland (φ =51º; Ga(φ)
= 1100 kWh/m2; D/G = 0.53), Petten in Holland (φ =53º; Ga(φ) = 1128 kWh/m2; D/G = 0.49) and
Loughborough in England (φ =53º; Ga(φ) = 1043 kWh/m2; D/G = 0.57). They conclude that “..all
the prediction methods showed similar results..” (Friesen G, 2007). Uncertainties on monthly
energy yields using broadband irradiance as input has been or the order of 5%. They also
conclude that “…the use of module sort-circuit current as self-reference for the irradiance
determination instead of the pyranometers values leads to a significant improvement”,
reducing uncertainty to about 2% (Friesen G D. S., 2009). It is opportune to remember than 2%
is below the PV module standard tolerance (3% in P* and more than 5% in ISC*, IM* and VM*).
Similar conclusions have follow MPP and FF models comparisons performed at the university
of Jaen in Spain (φ =38º; Ga(φ) = 1854 kWh/m2; D/G = 0.31). Concerning the c-Si, the
conclusion has been that “..taking an overall view both, FFK and Osterwalds models –here
referred as FFC and MPPTD- combine simplicity and accuracy best, so they are definitively
recommended for PV engineering in Mediterranean climates “ (Fuentes M, 2007). And this
conclusion has been later extended to thin films, following a testing campaing with four
different technologies a-Si, CIGS, CdTe and a-Si:H/μSi:H) in Jaen, Madrid (φ =41º; Ga(φ) = 1763
kWh/m2; D/G = 0.31) and Barcelona (φ =41º; Ga(φ) = 1675 kWh/m2; D/G = 0.33) (TorresRamírez M, 2014).
61
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
All these above mentioned comparisons have been performed taking into account just energy
prediction accuracy. The question of model complexity and accuracy benefits is on the roots of
possible model justification and deserves particular attention. Obviously, the greater the
complexity of a particular model is the largest must be the accuracy of the corresponding
energy predictions. Otherwise, the model is not justified. Regrettably, papers on the back of
model proposals use to restrict their arguments to present the corresponding accuracy when
describing the performance surfaces observed at their own experiments. However, and
somewhat surprisingly, the comparison with other description possibilities associated to
classical knowledge use to be disregarded, so that the relation between complexity increase
and accuracy benefits is not addressed in these papers. For the surprise of many, further
independent studies and round robin comparisons are showing that grounds for possible
accuracy gains are rather limited and, therefore, that large complexity is scarcely justified.
“Surprisingly, there doesn´t seem to be a need for overly complicated modelling to achieve this
accuracy for most technologies”. That can be read at the final brochure of the Integrated
Project Performance, an European initiative dealing with setting standards for the PV industry
(EPIA, 2009), following a round robin test comparing 8 energy prediction methods from well
know European PV laboratories (Friesen G., 2007).
On the other hand, it is opportune to remember that quality control at large PV plants includes
also reception tests where the inverse problem, i.e. derive PV system characteristics like P* or
PRSTC is also relevant. A word of caution is necessary here regarding current commercial
software: as far as we know, none includes facilities for affording such inverse problem.
Finally, generality, understood as the model capability to deal with all PV technologies: c-Si, TF
and concentrators, has often been signaled as a relevant advantage. However, we think this is
a reminiscence of past decades, when many believed that c-Si technologies were inherently
expensive and that the global PV market will mainly develop by means of other than c-Si
alternatives. Far from that, c-Si predominance is being consolidated at current markets. Hence,
a PV performance model can be very useful if it performs accurately for this material.
EXPERIMENTAL SET-UP
In order to provide an empirical base for evaluating PV performance models, six PV arrays of
different technologies (crystalline silicon Si-x, CdTe, CIGS, amorphous silicon a-Si and two
double junction a-Si/µSi from different manufacturers), each with P* between 1890 W and
2400 W, have been connected to the grid by means of 2.5 KW inverters, at Navarra (Spain). All
the PV generators are static, tilted 30°, due South oriented and fully free of shades. Because
PV power is always lower than the inverter capacity, it never goes to saturation, so that PV
arrays are permanently keep at the maximum power point, MPP. PDC at the inverter entry, GEFF
and TC are measured at 1 second rate and recorded as 10 minutes averages. Moreover, once
per month and profiting of clear days, the systems are disconnected during few minutes and
PV arrays I-V curves are measured Table A1.5 shows the main features of the involved
instrumentation.
62
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Parameter
Manufacturer
Maximum uncertainty
DC Voltage
Yokogawa
±(0.2% of reading + 0.2% of range)
DC Current
Yokogawa
±(0.2% of reading + 0.2% of range)
DC Active Power
Yokogawa
±(0.3% of reading + 0.2% of range)
IV Characteristic
Photovoltaik Engineering
<1%
Pt100 Temperature
Omega
B Class = ± 0.3˚C at nominal resistance (0˚C)
B Class = ± 0.8˚C at nominal resistance (100˚C)
Global Radiation 30º
mc-Si reference modules
±2% (Calibrated by CIEMAT*)
Yingli Solar
Table A1.5: Installed data acquisition equipment, sensors, and their uncertainties.
Ideally, Geff is directly given by PV reference devices of the same technology and equally soiled
than corresponding PV arrays. In fact, when PV arrays produce electricity, heat dissipation is
somewhat lower than at reference modules. But derived temperature differences are very
low, typically less than 2oC, so that Geff measurements are not affected. On the other hand,
due to doubts about the stability of TF materials, c-Si reference modules entail less uncertainty
and are today much better accepted by the market actors than TF ones. Because of that, we
decided to measure Geff with only two c-Si reference PV modules, located at the PV arrays
surface extremes. Other authors adhere to the same practice (Kenny R, 2003) (Friesen G C. D.,
2007) (Sellner S S. J., 2012) (Stein J, 2013). Derived consequences for TF modeling are
discussed later on this paper. Now, it is worth mentioning that differences between irradiance
measurements of these two reference modules are always lower than 1%, suggesting that dust
cover is homogeneous over the full PV arrays surface, so that it can be properly disregarded in
the analysis. TC is measured by means of thermocouples placed in the center of the rear side of
two modules of each PV array (approximately, 10% of the total modules). Temperature
differences from these two thermocouples are always lower than 2oC, suggesting that
averages are very representative of the whole PV array operation temperature.
63
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Figure A1.1. General view of the PV arrays
In addition, it was mounted a meteorological station with a horizontal pyranometer, a
pyranometer with shadowing and a thermocouple, which are able to register the following
variables: global radiation, diffuse radiation and air temperature.
Because thermal losses are particularly relevant, power temperature coefficients of the same
PV modules where the thermocouples are placed were measured at the beginning of the
experiment. That has been made outdoors, by exposing the PV modules to the Sun, after being
keep at ambient temperature, and recording several I-V curves meanwhile TC increase.
Uncertainty is minimized by placing the PV modules nearly perpendicular to Sun, so that Geff ≈
G*, and with wind speed below 1m/s. Then, α, β and γ values are given by the slope of
ISC(G*,TC), VOC(G*,TC) and PDC(G*,TC) versus TC (Figure A1.2), respectively. Table A1.6 presents
the results, together with other features of the PV arrays.
Finally, one must mention that the experiment started in Mars 2011 and is still on-going but
that the a-Si PV array from manufacturer M2 has been dismantled in January 2012, due to
reasons quite foreign to the experiment.
Alfa = 0.086 (%/ºC)
R2 = 0.978
Beta = -0.308 (%/ºC)
3.565
R2 = 0.998
Gamma = -0.272 (%/ºC)
62.5
156
62
155
61.5
154
R2 = 0.992
3.56
Voc (G=1000) (V)
Isc (G=1000) (A)
3.55
3.545
3.54
3.535
P (G=1000) (W)
3.555
61
153
60.5
152
60
151
3.53
3.525
3.52
18
20
22
24
26
T (ºC)
28
30
32
59.5
18
20
22
24
26
28
30
32
150
18
20
22
T (ºC)
Figure A1.2: Coefficient temperature measurements at the CIGS module.
64
24
26
T (ºC)
28
30
32
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Manufacturer
Generator
PNameplate/
module
M1
Si
160
M2
a-Si
M3
Total
Total
Nameplate γ(%/˚C)
modules
Power
14
2240
-0,45
60
40
2400
-0,23
a-Si/µSi
130
18
2340
-0,28
M4
a-Si/µSi
135
14
1890
-0,24
M5
CIGS
107
18
1926
-0,446
M6
CdTe
175
30
2250
-0,25
Table A1.6. Main features of the PV arrays
WHEATHER AND OPERATION CONDITIONS
Table A1.7 summarizes the main characteristics of the solar radiation at the site, long the two
years considered in this work. Yearly radiations have been 1922 kWh.m-2 for the first year and
1882 kWh.m-2 for the second year. Monthly averages of the daily irradiation vary from 2.6
kWh.m-2 in November 2011 to 7.6 kWh.m-2 in July 2012. Table A1.8 shows the equivalent PV
module temperature, TCEQ, observed at these months. TCEQ is defined as the average of TC
weighted by the irradiance, corresponding just to these months. It is worth noting that PV
module equivalents temperatures differences are below 3.5ºC. As expected, the greater the PV
module efficiency, the lower the module equivalent temperature. Finally, the distribution of
both irradiance (horizontal and in the plane of the array) and temperature (ambient and cell
temperatures) are shown in Figure A1.3.
In-plane global total (daily) irradiation
Period
Year
Worst month
Best month
1922 (5.3)
77 (2.6)
214 (6.9)
1882 (5.2)
92 (3)
236 (7.6)
First year:
March 2011-February 2012
Second year:
March 2012-February 2013
Table A1.7: Yearly and monthly in-plane irradiations for the two years of operation.
65
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Teq. (ºC)
G30º
Month
(kWh.m-2)
M1
M2
M3
M4
M5
M6
November 2011
77
26
26
26
25
29
25
July 2012
236
39
-
42
40
41
41
Table A1.8: Equivalent module temperature corresponding to the best and the worst months.
0.25
0.25
0.2
0.2
0.15
F(Ta)
F(G0)
First Year
Second Year
First Year
Second Year
0.1
0.05
0
0
0.15
0.1
0.05
500
1000
0
-10
1500
0
10
20
30
50
0.25
0.25
First Year
Second Year
0.2
0.15
0.15
F(G)
F(Tc)
0.2
0.1
0.05
0
0
40
Ta (ºC)
G0 (W)
First Year
Second Year
0.1
0.05
500
1000
0
-20
1500
G (W)
0
20
40
60
Tc (ºC)
Figure A1.3. Observed distribution of operation conditions
RESULTS
Figure A1.3 suggest that any one-year period is statistically representative. Hence, in order to
have the maximum available data for all the PV arrays, we have generally selected the period
March 2011 – February 2012 for presentation purposes.
Looking for assessing the model usefulness for quality assurance purposes, we have compared
the MPP and the full I-V curve fitting alternatives described above. The P* values have been
the nominal ones, referred as nameplate values at table 4.
Comparison is performed in terms of the daily energy errors, which is relevant for energy yield
forecast, and also in terms of the weekly PR and PRSTC constancy along the year, which is
66
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
relevant for on-site measurements campaigns. In order to consider their real impact on energy
yield calculations, the errors are weighted by the respective daily irradiation (Hoff TE, 2012).
This way, the Error and the Weighted Error at day “i” are, respectively, given by:
𝐸𝑀𝑂𝐷,𝑖 −𝐸𝐸𝑋𝑃,𝑖
𝐸𝑖 = (
𝐸𝐸𝑋𝑃,𝑖
𝑊𝐸𝑖 = 𝐸𝑖 (∑𝑁
)
(60)
𝐺𝑒𝑓𝑓𝑑,𝑖
(61)
𝑖=1 𝐺𝑒𝑓𝑓𝑑,𝑖 )/𝑁
Where EMOD and EEXP represent the daily modelled and experimental PV array energy values,
Geffd the daily effective irradiation and N extends to the number of days of the considered
period (year or week, in our case). It worth nothing that the Mean Beas Weighted Error is
equal to the error on the energy calculated for the considered period.
Crystalline silicon
Energy yield
Figure A1.4 shows the frequency distribution of the daily energy errors, E and also WE, and its
relation with the clearness index of the day, KTd, for the MPPTGA model. Corresponding MBWE
and RMSWE values are -0.08 % and 1.18 %. The following comments apply:
-
The MBWE error obviously depends on the difference between the nominal and the
actual peak power value. In fact, P* values deduced from our I-V measurements
suggest the actual STC power is 2% larger than the nominal value, which is likely a
consequence of the positive tolerance (0-+3%) at PV manufacturing process. Hence,
looking for disclosing the errors associated to the model itself, regardless of the
manufacturer tolerance, we have used P*=1.02xP*NOM as the reference for energy
calculations. Obviously, using P*=P*NOM will increase the errors by 2%.
-
Apart of the P*value, the main source of error is the limited model ability of a model
with only three parameters (a1, a2 and a3) to reproduce the observed efficiency at low
irradiances. Because of that, the lower KTd the higher absolute E. However, the low
overall impact on energy, observable on the WE versus KTd figure, does not motivate
for model complexity increases, requiring additional parameters and experimental
PDC(Geff, TC*) values for fitting.
-
Thermal loses accounts for 4% (∆ETC≠TC* is equal to the MBWE difference between
MPPC and MPPTD models). Irradiance losses, accounts for only 0.4% (∆EG≠G* is given by
the MBWE difference between MPPTD and MPPTGA models). Obviously, this result is
local and PV module dependent. Hence, it is worth remembering that Navarra is a
rather sunny place.
67
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Errors
Weighted Errors
(a)
(b)
Figure A1.4. (a) Observed frequency distribution of the daily energy errors and weighted
errors for the MPPTGA model. (b) Its relation with the clearness index of the day.
Table A1.9 gives the errors for all the considered models. Comments are:
-
Rather simple MPP and FF models perform as well as the more complex IV ones.
-
The use of published values for polycrystalline modules (MPPTGP) performs better
than the use of a generic c-Si model (MPPTGPVGIS).
-
IV models are rather sensitive to RP assumptions, as disclosed by the differences
between IV410N (RP* = ∞) and IV512 (RP* = 60 Ω), and also between 5PVsystN (RP
versus G as per equation (47)) and 5PVsystN-2 (RP versus G as per equation (46)).
-
The analytical procedure proposed by Ruiz for solving the MPP point of an I-V curve is
very convenient. It is very easy of implement and associated errors are insignificant, as
revealed by the similarity of 5PVsystN and 5PVsystA results.
68
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
-
Somewhat surprising, the MPPTD, considering just the variation of the efficiency with
TC but neglecting the effects of G performs very well. In order to further explain this
result, which is consistent with the energy loses balance mentioned above, figure A1.5
plots the ratio ∆ERP/∆ERS versus KTd, as given by MPPTGA, where ∆ERP and ∆ERS,
respectively, represents the daily energy loses and gains due to RP and RS effects. They
mutually cancel for KTd ≈ 0.45 and they asymmetrically behave respect to KTd: RS gains
for KTd > 0.45 are lower than RP loses for KTd < 0.45. The figure also helps to understand
that this result is local and PV module dependent.
MPP models
C
TD
TGD
TGP
TGPVGIS
TGA
ME
3.25
0.99
-1.04
-0.55
- 2.8
-0.83
RMSE
5.68
3.2
1.37
1.58
3.16
-2.77
MWE
4.4
0.36
-0.69
-0.03
- 1.73
-0.08
RMSWE
6.98
1.21
1.1
1.1
0.85
1.18
FF models
C
TD
TGD
ME
1.81
1.9
1.77
RMSE
3.33
3.43
3.17
MWE
1.88
2.05
-1.24
RMSWE
3.21
3.46
2.58
IV models
410N
512N 5PVsystN
5PVsystN-2
5PVsystA 5AA
ME
-0.05
-10.93
-5.56
-0.95
-7.53
0.05
RMSE
7.07
12.79
11.01
3.59
17.22
0.85
MWE
1.8
-6.87
- 2.39
-0.22
-2.48
0.04
RMSWE
2.59
1.14
1.38
1.03
2.64
0.84
Table A1.9. Mean and RMS values, expressed in %, of the daily energy errors and weighted
errors associated to 15 different PV performance modelling alternatives.
69
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Losses Rp/Gains Rs
2,5
2
1,5
1
0,5
0
0
0,2
0,4
KT
0,6
0,8
1
Figure A1.5. Daily ratio between energy loses due to RP and energy gains due to RS versus
clearness index
Performance indexes
Figure A1.6 shows the observed evolution of the weekly PR and PRSTC, again from March 2011
to February 2012. Thermal and irradiance loses at the last have been calculated with the
MPPTGA model. As expected, the PRSTC performs significantly more constant, allowing for a
much sound technical quality evaluation on the basis of the energy production observed in
relatively short periods. Table A1.10 presents the corresponding mean, maximum and
minimum values for this year and also for the year from March 2012 to February 2013. As
expected, PRSTC performs significantly more stable than PR. We have notices on some technical
quality evaluations done on the basis of observed PR values, by considering a different
reference value for each month. The 12 reference PR values are established by a simulation
exercise on the basis of solar radiation and ambient temperature databases. However, the
validity of this PR monthly correction procedure is likely not general by restricted to particular
climatic regions. In fact, our results show weekly PR variations up to 5 % on the same month,
which seem not adequate for large scale PV plants qualification
70
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Figure A1.6. Observed evolution of the weekly PRW and PRSTCW, from March 2011 to February
2012
PRW
PRSTCW
March 2011 – February 2012
Mean
Maximum
Minimum
1.06
0.85
0.93
(+12.8 %)
(-8.9 %)
0.97
0.94
0.95
(+2.3 %)
(-1 %)
March 2012 – February 2013
Mean
Maximum
Minimum
1.040
0.752
0.936
(+10.5 %)
(-18.7 %)
0.987
0.934
0.953
(+3.3 %)
(-1.9 %)
Table A1.10. Mean, maximum and minimum values of PRW and PRSTCW values observed along
two years. PRSTCW is significantly more stable than PRW
Modelling possibilities for other than c-Si modules are still under review
CONCLUSIONS
-
MPP and FF models are very simple and perform as well as the more complex I-V
models.
-
For the here considered site and polycrystalline silicon module, considering just the
efficiency dependence on temperature, by means of the corresponding coefficient
given at datasheet is enough.
-
The PRSTC performs much more constant along the year that the mere PR. Hence, it
should be preferred to assess the technical quality of PV plants on the basis of
relatively short period (few weeks) energy productions.
71
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
References
(2006). Standard IEC 60904-3.Measurement principles for terrestrial photovoltaic solar devices
with reference spectral irradiance data. International Electrotechnical Commission.
Geneva, Switzerland.
Akbaba M, A. M. (1995). A new model for I-V characteristic of solar cell generators ans its
applications. Solar Energy Materials and Solar Cells, 123-132.
Allet N, B. F. (2011). Evaluation of PV System Performance of Five Different PV Module
Technologies. 26th European Photovoltaic Solar Energy Conference. Hamburg.
Backus C.E. (1976). Solar Cells. IEEE Press.
Balasubramanian B, A. A. (2014). Performance Evaluation of Solar Photovoltaic (PV) Array
Based on Mathematical and Simulation Modelling: A Review. Australian Journal of
Basic and Applied Sciences, 469-477.
Bashahu M, H. A. (1995). Review and Test of Methods for Determination of the Solar Cell
Series Resistance. Renewable Energy, 129-138.
Bashahu M, N. P. (2007). Review and tests of methods for the determination of the solar cell
junction ideality factors. Solar Energy, 81, 856-863.
Bellini A, B. S. (2009). Simplified Model of a Photovoltaic Module. Applied Electronics, (pp. 4751). Pilsen.
Beyer H.G., B. J. (2004). Identification of a general model for the MPP performance of PVmodules for the application in a procedure for the performance check of grid
connected systems. 19th European Photovoltaic Solar Energy Conference, (pp. 443447). Paris.
Bouzidi K, C. M. (2007). Solar cells parameters evaluation considerin the series and shunt
resistance. Solar Energy Materials & Solar Cells, 1647-1651.
Boyd T, K. S. (2011). Evaluation and Validation of Equivalent Circuit Photovoltaic Solar Cell
Performance Models. Journal of Sola Energy Engineering, doi:10.1115/1.4003584.
Brano, L. (2010). An improved five-parameters model for photovoltaic modules. Sol. Energy
Mat. Sol. Cells, 1358-1370.
Cameron CP, B. W. (2008). Comparison of PV System Performance-Model Predictions with
Measured PV System Performance. 33rd IEEE PVSC. San Diego, CA.
Carrero C, R. J. (2010). Simple estimation of PV modules loss resistances for low error
modelling. Renewable Energy, 1103-1108.
CEC. (n.d.). Guidelines for Califonnia's Solar Electric Incentive. Retrieved 7 22, 2014, from
www.energy.ca.gov.
72
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Celik AN, A. N. (2007). Modelling and experimental verification of the operating current of
mono-crystalline photovoltaic modules using four and five parameter models. Applied
Energy, 1-15.
Chan D, P. J. (1986). A comparative study of extraction methods for sollar cell model
parameters. Solid-state Electronics, 329-337.
Chan D.S.H, P. J. (1987). Analytical methods for the extraction of solar-cell single and doublediode model parameters from I-V characteristics. IEEE Transactions on Electron
Devices, 34, 286-293.
Charles JP, A. M. (1981). OJO. Solar Cells, 169-OJO.
Chine W, M. A. (2013). Models of Photovoltaic Modules with Graphical User Interface. First
International Conference on Nanoelectronics, Communicaations and Renewable
Energy. Jijel (Algeria).
Coftas D, C. P. (2008). Results on series and shunt resistances in a c-Si PV cell. Comparisons
using existing methods and a new one. Journal of Optoelectronics and Advanceed
Materials, 3124-3130.
D Thevenard, S. P. (2013). Estimating the uncertainty in long-term photovoltaic yield
predictions. Solar Energy, 432-445.
de Blas M, T. J. (2002). Selecting a suitable model for characterizing photovoltaic devices.
Renewable Energy, 371-380.
de Blas MA, T. J. (2002). Selecting a suitable model for characteizing photovoltaic devices.
Renewable Energy, vol 20, 371-380.
De Soto W, K. S. (2006). Improvement and validation of a model for photovoltaic array
performance. Solar Energy, 78-88; doi:10.1016/j.solener.2005.06.010.
Dongue SB, N. D. (2013). An Improved Nonlinear Five-Point Model for Photovoltaic Modules.
International Journal of Photoenergy, doi.org/10.1155/2013/680213.
Duffie& Beckman. (1991). Solar Engineering of Thermal Process. New York: John Wiley and
Sons.
Düpont R. (2009). Cada uno mide como puede. Photon. La revista de fotovoltaica, 42-60.
EPIA. (2009). IP-Performance. Setting the standards for the PV industry. Free available at
www.pv-performance.org.
Evans D. (1981). Simplified Method for Predicting Photovoltaic Array Ouput. Solar Energy, 555560.
Evans DL. (1981). Simplyfied method for predicting photovoltaic array output. Solar Energy,
555-560.
73
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Fabero F., V. N.-A. (2005). Characterization of recent commercial technologies of PV modules
based on outdoor and indoor I-V measurements. 20th PVSEC, (pp. 2059-2062).
Barcelona.
Friesen G. (2007). Intercomparison of different energy predictions methods within the
European project "Performance" - results of the 1st Round Robin. 22nd EUPVSEC.
Milano.
Friesen G, C. D. (2007). Energy Rating Measurements and Preddictions at Issac. 22th European
PVSEC. Milan.
Friesen G, D. S. (2009). Intercomparison of different energy prediction methods within the
European project "Performance"-results of the 2nd Round-robin. 24th European
PVSEC, (pp. 3189-3197). Hamburg.
Friesen G, G. R. (2007). Intercomparison of different energy prediction methods within the
European project "PERFORMANCE". 22nd European Photovoltaic Solar Energy
Conference, (pp. 2659-2663). Milan.
Friesen G., G. R. (2007). Intercomparison of different energy prediction methods within the
European project "PERFORMANCE". 22nd European Photovoltaic Solar Energy
Conference, (pp. 2659-2663). Milan.
Fuentes M, N. G. (2007). Application and validation of algebraic methods to predict the
behaviour of crystalline silicon PV modules in Mediterranean climates. Solar Energy,
1396-1408.
Ghani F, D. M. (2012). Extration of solar cell modelling parameters using the Lambert Wfunction. 50th Annual Conference, Australian Solar Energy Society. Melbourne.
Gow JA, M. C. (1999). Development of a photovoltaic array model for use in power-electronics
simulation studies. IEE Pocd Electr Power Appl, 193-200.
Green M. (1982). Solar Cells: operating principles, technology and system applications. Prentice
Hall.
Guide, P. U. (2013). Available at www.pvsyst.com.
Hansen CW, L.-H. A. (2013). Sensitivity of single diode models for photovoltaic modules to
method used for parameter estimation. 28th European PVSEC. Paris.
Hansen CW, R. D. (2012). Calibration of the Sandia Array Perormance Model Using Indoor
Measurements. IEEE 38th PVSC.
Haouari-Merbah M, B. M. (2005). Extraction and analysis of solar cells parameters from the
illuminated current-voltage . Sol Energy Mster Sol Cells, 225-33.
Hermmann W., M. S. (2007). Advanced intercomparison testing of PV modules in European
test laboratories. 22nd PVSEC, (pp. 2506-2510). Milan.
74
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Hernandez J, V. W. (2013). Practical method for estimating the power and energy delivered by
photovoltaic modules operating under non-standar conditions. Progress in
Photovoltaics:Research and Applications, 867-875. DOI:10.1002/pip.2168.
Heydenreich W., M. B. (2008). Describing the world with three parameters: a New approach to
PV module power modelling. 23 rd EUPVSEC, (pp. 2786-2789). Valencia.
Hoff TE, P. R. (2012). Reporting of irradiance modeling relative prediction errors. Progress in
Photovoltaics: Research and Applications, OJO/DOI: 10.1002/pip.2225.
Huld T, F. G. (2011). A power-rating model for crystalline silicon PV modules. Solar Energy
Materials & Solar Cells, 3359-3369.
Huld T, S. M. (2008). Greographical Variation of the Conversion Efficiency of Crystalline Silicon
Photovoltaic Modules in Europe. Progress in Photovoltaics: Research and Applications,
595-607 / DOI: 10.1002/pip.846.
Jakhrani A, S. S. (2014). An Improved Mathematical Model for Computing Power Output of
Solar Photovoltaic Modules. International Journal of Photoenergy,
doi.org/10.1155/2014/346704.
Jia Q, A. W. (1988). A novel approach for evaluating the series resistance of solar cells. Sola
Cells, 311-318.
Jia QX, E. K. (1995). Analytical solution for solar cell model parameters from illuminated
current-voltage characteristics. Philisophical Magazine B, 375-382.
Jyotirmoy Roy, .. (2008). Validatuon of proposed Photovoltaci Energy Rating Standard and
Sensitivity to Environmental Parameters. 23rd European Photovoltaic Solar Energy
Conference, (pp. 2728-2734). Valencia.
Kenny R, F. G. (2003). Energy Rating of PV modules: Comparison of Methods and Approach.
3rd World Conference on Photovoltaic Energy Conversion. Osaka.
Kenny RP, V. D. (2013). Power rating of photovoltaic modules including validation of
procedures to implement IEC61853-1 on solar simulators and under natural sunlight.
Progress in Photovoltaics / DOI:10.1002/pip.2365.
Kim W, C. W. (2010). A novel parameter extraction method for the one-diode solar cell model.
Solar Energy, 1008-1019.
King DL, B. W. (2004). Photovoltaic array performance model, Sandia report SAND2004-3535.
Kurobe K-i, M. H. (2005). New two-diode model for detailed analysis of multicrystalline silicon
solar cells. Jpn J Appl Phys.
Lo Brano V, C. G. (2013). An efficient analytical approach for obtaining a five parameters model
of photovoltaic modules using only refeerence data. Applied Energy, 849-903.
75
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Lo Brano V, O. A. (2010). An improved five-parameters model for photovoltaic modules. Solar
Energy Materials & Sola Cells, 1358-1370.
Loferski J. (1993). The first forty years: A brief history of the modern photovoltaic age. Prog.
Photovolt: Res.Appl. doi:10.1002/pip 4670010109, 1:67-68.
Lorenzo E. (1994). Solar Electricity: Enineering of Photovoltaic Systems. Sevilla: Progensa.
Lorenzo, E. (2011). Energy Collected and Delivered by PV Modules. In A. L. Hedeus, Hansbook
of Photovoltaic Science and Engineering-2nd edition (pp. 993-997). Wiley.
Ma T, Y. H. (2014). Development of a model to simulate the performance characteristics of
crystalline silicon photovoltaic modules/strings/arrays. Solar energy, 31-41.
Ma T, Y. H. (2014). Solar photovoltaic system modelling and performance prediction.
Renewable and Sustainable Energy Reviews, 304-315.
Mahmoud Y, X. W. (2010). A Simple Approach to Modelling and Simulation of Photovoltaic
Modules. IEEE Transactions on Sustainable Energy, 185-186.
Martinez F, L. E. (n.d.). On the testing of large scale PV arrays. Progress in Photovoltaics.
Martinez F, M. J. (2010). Experimental model to estimate shading losses on PV arrays. Solar
Energy Materials & Solar Cells, 2298-2303.
Martinez J, L. E. (2009). Direct and indirect uncertainties in the prediction of tilted irradiance
for solar engineering applications. Solar Energy, 432-444.
Martinez MF, L. E. (2011). On the testing of large PV arrays. Progress in Photovoltaics, 222-223.
Massi Pavan A, M. A. (2014). A study on the mismatch effect due to the use of different
photovoltaic modules classes in large-scale solar parks. Progress in Photovoltaics:
Research and applications, 332-345.
Massi Pavan A, M. A. (2014). Explicit empirical model for the general photovoltaic devices:
Experimental validation at maximun power point. Solar Energy, 105-116.
Mermoud A., L. T. (2010). Performance Assessment of a Simulaion Model for PV Modules of
Any Available Technology. 25th European Photovoltaic Solar Energy Conference.
Valencia.
Messenger RA, V. S. (2004). Photovoltaics System Engineering, 2º Ed. Boca Ratón (FL): CRC
Press LLC.
Montgareuil A.G, M. J. (2007). Main results of the first intercomparison campaing of European
irradiance sensors at INES Cadarache. 22nd PVSEC, (pp. 2601-2607). Milan.
Montgareuil AG, S. L. (2009). A new tool for the MotherPV method: Modelling of the irradiance
coefficientn of photovoltaic modules. 24th EUPVSEC, (pp. 3305-3309). Hamburgo.
76
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Nikolaeva-Dimitrova M, K. R. (2010). Seasonal variations on energy yield of a.Si, hybrid, and
crystalline Si PV modules. Progress in photovoltaics: Research and Applications, vol 18,
311-320.
Nishioka K, S. N. (2007). Analysis of multicrystalline silicon solar cells by modified 3-diode
equivalente circuit moelling taking leakage current through periphery into
consideration. Sol Energy Mater Sol Cells.
Ortiz-Conde A, G. S.-G. (2014). A review of diode and solar cell equivaalent circuit model
lumped parameter extraction procedures. Facta Universitatis. Electronics and
Energetics, 57-102 / DOI: 10.2298/FUEE1401057O.
Ortiz-Rivera E, P. F. (2005). Analytical Model for a Photovoltaic Module using the Electrical
Characteristics provided by thee Manufacturer Data Sheet. IEEE Power Electronics
Spacialist Conference, (pp. 2087-2091). Recife.
Osterwald. (1986). Translation of device performance measurements to reference conditions.
Solar Cells, 269-279.
Phang JCH, C. D. (1984). OJO. Electronic Letters, 406-OJO.
Poissant Y, P. S. (2008). A Comparison of Energy Rating Methodologies using Field Test
Measurements. 23rd European PVSEC, (pp. 2657-2662). Valencia.
Poissant Y, P. S. (2008). A Comparison of Energy Rating Methodologies using Field Test
Measurements. 23 rd European PVSEC, (pp. 2657-2662). Valencia.
pvpmc.org/modeling. (2013). steps. Accessed on 11thNov2013.
PVsyst. (n.d.). User`s Guide PVsyst Contextual Help. Available at www.pvsyst.com.
Quaschning V., H. R. (1998). Irradiacne calculations on shaded surfaces. Solar Energy, 369-375.
Randall JF, J. J. (2003). Is AM1.5 applicable in practice? Modelling eight photovoltaic materials
with respect to light intensity and two spectra. Renewable Energy, 1851-1864.
Ransome S. (2008). A Review of kWh/kWp measurements, analysis ans modelling. 23 th
European PVSEC. Valencia.
Ransome S. (2010). A detailed comparison of measured outdoor performance versus
simulation program predictions for different PV technologies. PVSAT. Souhampton.
Ransome S. (2012). a. PVSAT. Suhampton.
Ransome S, S. J. (2011). Improving and Understanding kWh/kWp simulations. 26 th European
PVSEC . Hamburg.
Ransome S, S. J. (2012). PV technology differences and discrepancies in modelling between
simulation programs and measurements. 38 IEEE PVSC . Austin (Texas).
77
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Reich NH, M. B. (2012). Performance ratio revisitred: is PR>90% realistic? Progress in
photovoltaics: Research and applications, DOI:10.1002/pip.1219.
Reich NH, v. S. (2009). Crystalline silicon cell performance al low intensities. Solar Energy
Materials & Solar Cells, 1471-1481.
Rosell JI, I. M. (2006). Modelling power output in photovoltaic modules for outdoor operating
conditions. Energy Conversion and Mangement, 2424-2430.
Rus-Casas C, A. J.-H. (2014). Classification of methods for annual energy harvesting calculations
of photovoltaic generators. Energy Conversion and Management, 527-536.
Saloux E, T. A. (2011). Explicit model of photovoltaic panels to determine voltages and currents
at the maximun power point. Solar Energy, 713-722.
Sauer K.J., R. T. (2013). Systematic Approaches to Ensure Correct Representation of Measured
Multi-Irradiance Module Performance in PV System Energy Production Forecasting
Software Programs. PV Performance Modelling Workshop. Santa Clara.
Sellner S, S. J. (2012). Advanced PV module performacne characterization and validation using
the novel Loss Factors Model. 38th IEEE PVSC, (pp. 2938-2943). Austin (Texas).
Sellner S, S. J. (2012). Advanced PV module performance characterization and validation using
the novel Loss Factors Model. 38th PVSEC. Austin.
Sera D, T. R. (2007). PV panel model based on datasheets values. IEEE Transactions on Power
Electronics, 2392-2396.
Siddiqui M, A. M. (2013). Parameter estimation for five- and seven-parameter photovoltaic
electrical models using evolutionary algoritms. Applied Soft Computing, 4608-4621.
Singh NS, J. A. (2013). An Exact Analytical Method for Calculating the Parameters of aa Real
Solar Cell Using Special Trans Function Theory (STFT). International Journal of
Renewable Energy Research, 201-206.
Stein J, S. J. (2013). Outdoor Performance Evaluation of Three Different Models:single-diode,
SAPM and Loss Factor Model. SAND Report 2013-7913C.
Taylor RW. (1986). System and module rating: advertised versus actual capability. Solar Cells,
335-44.
Torres-Ramírez M, N. G. (2014). Study on analytical modelling approaches to the performance
of thin film PV modules in sunny inland climates. Energy, 1-10.
Tsuno Y., H. Y. (2007). Modelling I-V Curves of PV Modules Using Linear
Interpolation/Extrapolation. 17 International PVSEC. Fukuoka.
Vajpai J, K. H. (2013). Mathematical Modelling and Experimental Validation of Performance
Characteristics of Solar Photovoltaic Modules. International Journal of Applicaation or
Innovation in Engineering & Management, 295-301.
78
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Venkateswarlu G, S. R. (2013). Modeling and Parameter Extraction of PV modules Using
Genetic Algorithms and Differential Evaluation. IOSR Journal of Electrical and
Electronics Engineering, 37-44.
Villalva MG, G. J. (2009). Comprehensive Approach to Modelling aand Simulation of
Photovoltaic Arrays. IEEE Transactions on Power Electronics, 1198-1208.
Villalva MG, G. J. (2009). Comprehensive approach to modelling and simulation of photovoltaic
arrays. IEE Trans Power Electron, 1198-208.
Willians S, B. T. (2005). Evaluating the State of the Art of Photovoltaic Performance Modelling
in Europa. 20th Europen PVSEC. Barcelona.
Willians S, B. T. (2006). Accuracy of Energy Prediction Methodologies. 4th IEEE World
Conference on Photovoltaics, (pp. 2206-2209). Hawai.
Willians SR, B. T. (2003). Modelling Lomg-term Module Performance Based on Realistic
Reporting Conditions with Consideration to Spectral Effects. 3rd World Conference on
Photovoltaic Energy Conversion, (pp. 1908-1911). Osaka (Japan).
Xiao W, D. W. (2004). A Novel Modelling Method for Photovoltaic Cells. 35 th Annual IEEE
Power Electronics Specialist Conference, (pp. 1950-1956). Aachen.
Zhou W, Y. H. (2007). A novel model for photovoltaic performance prediction. Applied Energy,
1187-1198.
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ANNEX 2. DEALING IN PRACTICE WITH HOT-SPOTS
R. Moretón1, E. Lorenzo1, L. Narvarte1
1
PV Systems Research Group, Solar Energy Institute, Polytechnic University of Madrid, Spain
ABSTRACT
The hot-spot phenomenon is a relatively frequent problem in current photovoltaic
generators. It entails both a risk for the photovoltaic module’s lifetime and a
decrease in its operational efficiency. Nevertheless, there is still a lack of widely
accepted procedures for dealing with them in practice. This paper presents the
IES-UPM observations on 200 affected modules. Visual and infrared inspection,
electroluminescence, peak power and operating voltage tests have been
accomplished. Hot-spot observation procedures and well defined acceptance and
rejection criteria are proposed, addressing both the lifetime and the operational
efficiency of the modules. This procedure is oriented to its possible application in
contractual frameworks.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
1
INTRODUCTION
A hot-spot consists of a localized overheating in a photovoltaic (PV) module. It
appears when, due to some anomaly, the short circuit current of the affected cell
becomes lower than the operating current of the whole and giving rise to reverse
biasing, thus dissipating the power generated by other cells as heat. Figure A2.1
shows two infrared (IR) images of hot-spots. The anomalies that cause hot-spots
can be external to the PV module: shading [1-3] or dust [4]; or internal: microcracks [5-8], defective soldering [5-6,9-11], PID [12-13]... In general, when a hotspot persists over time, it entails both a risk for the PV module’s lifetime and a
decrease in its operational efficiency [5-6,14-17].
(a)
(b)
Figure A2.1. Hot-spots in two modules. (a) General view of a tracker with hot-spots caused by PID.
(b) Hot-spot caused by micro-cracks. The operating temperature of the hot-spot is 87 ºC while the
mean temperature of the rest of the module is 53 ºC.
Hot-spots are relatively frequent in current PV generators and this situation will
likely persist as the PV technology is evolving to thinner wafers, which are prone to
developing micro-cracks during the manipulation processes (manufacturing,
transport, installation, etc.)[7,10-11,18-19]. Fortunately, they can be easily
detected through IR inspection, which has become a common practice in current
PV installations[6,16,20-22]. However, there is a lack of widely accepted
procedures for dealing with hot-spots in practice as well as specific criteria
referring to the acceptance or rejection of affected PV modules in commercial
frameworks. For example, the hot-spot resistance test included in IEC-61215
(Crystalline silicon terrestrial photovoltaic modules. Design qualification and type
approval) is successfully passed if the module resists the hot-spot condition for a
period of 5 hours, which suggests that this standard addresses transitory hotspots, as those caused by also transitory shading, but not permanent ones, caused
by internal module defects [23]. Along the same lines, the IEC-62446 (Grid
connected photovoltaic systems. Minimum requirements for system
documentation, commissioning tests and inspection) only states: “A hot-spot
elsewhere in a module usually indicates an electric problem […] In any case
investigate the performance of all modules that show significant hot-spots” [24].
Furthermore, a draft of the IES-60904-12 (Photovoltaic devices: infrared
thermography of photovoltaic modules) clearly establishes how to capture,
process and analyse the IR images, but still does not set out any PV module
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
acceptance/rejection criteria [25]. The IES-UPM experience includes many cases of
actors in the PV sector, mainly module manufacturers and engineering,
procurement and construction companies (EPC), requesting advice on how to
proceed with collections of IR images of affected modules, and which
corresponding contracts lacked the previsions to ask a relevant question: which
affected PV modules should be changed under the PV manufacturer’s
responsibility?
This paper addresses both the lifetime and the operational efficiency of PV
modules with hot-spots. Starting from the observations of 200 affected modules as
experimental support, hot-spot observation procedures and well defined
acceptance/rejection criteria are proposed, looking for its possible application in
contractual frameworks.
2
FUNDAMENTALS OF HOT-SPOTS
For explanation purposes, we first consider the case of a group of n identical solar
cells, associated in series and protected by a by-pass diode (Figure A2.2-a). The
operating conditions: incident irradiance, G, operating temperature, TC, and
polarization voltage, V, are such that a certain current, IC, is circulating through
these cells. A hot-spot appears in a cell (Figure A2.2-b) when some defect (microcrack, shade, etc.) reduces its corresponding short circuit current, ISC,D, so that
𝐼𝑆𝐶,𝐷 < 𝐼𝐶
(1)
which forces the cell to operate at a negative voltage,
𝑉𝐷 = −(𝑛 − 1)𝑉𝑁𝐷 + 𝑉
(2)
where subscripts “D” and “ND” refer, respectively, to defective and non-defective
cells. Consequent power dissipation heats the defective cell, giving rise to a hotspot, characterized by the temperature increase of this cell in relation to the
non-defective ones, ∆𝑇𝐻𝑆 . The by-pass diode assures V ≥ 0, thus limiting the
negative biasing and the power dissipation in this cell. Obviously, the maximum
hot-spot temperature is attained when the group is short-circuited or, which is
nearly the same, when the bypass-diode is ON. Note that ∆𝑇𝐻𝑆 is directly related to
the product 𝐼𝐶 × 𝑉𝐷 . In other words, hot-spot temperature mainly depends on the
operating voltage and incident irradiance (which modulates 𝐼𝐶 ), on the defect
gravity (which determines 𝐼𝑆𝐶,𝐷 ) and on the second quadrant I-V characteristic of
the defective cell (which modulates 𝑉𝐷 ). As this characteristic can substantially
differ from one cell to another, even within the same PV module [REF/JM], the hotspot temperature also depends on the particular defective cell. As a representative
example, Figure A2.3 shows the second quadrant I-V curves of 7 solar cells of a
same PV module [26]. It can be observed that power dissipation at a hot-spot can
vary an order of magnitude depending on the defective cell [1-2,16,26-27].
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
(a)
(b)
Figure A2.2. (a) Electrical connection of n originally identical cells protected by a by-pass diode.
One of the cells is affected by a shade or an internal defect that limits its short-circuit current. (b)
I-V curve of both the affected cell and the non-affected ones.
Figure A2.3. Second quadrant I-V characteristics of 7 cells of a same PV module. The great
dispersion is notorious. Voltages for a same current vary about one order of magnitude.
Now, let us consider the case of a PV module made up of three series associated
groups, each made up of n cells and a bypass diode (Figure A2.4-a). Note that many
currently commercial PV modules respond to this configuration, with n ranging
typically from 20 to 24. A defective cell like the one described above does not
reduce now the PV module sort-circuit current but becomes an anomalous step in
the first quadrant of the I-V and P-V curves (Figure A2.4-b).
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
(a)
(b)
Figure A2.4. (a)Electrical scheme of a PV module with 3 groups, each made up of n cells and a
by-pass diode. (b) I-V and P-V curves of a defective and a non-defective module. Observe the
difference in the current at the maximum power point.
Again, ∆𝑇𝐻𝑆 depends on the operating voltage of the concerned group, which, in
turn, depends on the operating voltage of the PV module. The voltage at the step
marks the bypass diode turning ON, and ∆𝑇𝐻𝑆 reaches its maximum for the voltage
range below this step. Figure A2.5 shows examples of I-V curves of real modules
affected by hot-spots. It is worth noting that current at the maximum power point
of the defective module, 𝐼𝑀,𝐷 , is always lower than that corresponding to the
non-defective ones, 𝐼𝑀,𝑁𝐷 :
𝐼𝑀,𝐷 < 𝐼𝑀,𝑁𝐷
(a)
(3)
(b)
Figure A2.5. (a) I-V curve of a defective module affected by a fill-factor loss (b) I-V curve of a
defective module with a step anomaly.
Furthermore, if a module like these is connected in series with many other
modules (often between 20 and 30 modules) and the resulting string is connected
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
to an inverter able to impose the MPP, the operating current of the group must
range from between 𝐼𝑀,𝑁𝐷 and 𝐼𝑀,𝐷 . Then, the larger the number of modules in the
series, the closer the operating current will be to 𝐼𝑀,𝑁𝐷 . In this situation, the
operating voltage of the defective module is well below that corresponding to its
MPP. The important thing to remember is that the power loss of a defective PV
module is much larger when it works associated to other non-defective modules
than when it works alone. A practical consequence of the latter is that this module
could pass the standard warranty conditions (referring to the maximum power of
the module alone) while failing to deliver the power in practice.
Figure A2.6. I-V curves of a defective and a non-defective module connected in series. Sinusoidal
signals represent the oscillations due to the MPP tracking. Voltage excursions are clearly greater in
the defective module, leading to variations in the operating voltage and differences between both
modules.
On the other hand, figure A2.6 helps us to understand two hot-spot related
phenomena derived from the typical slight current excursion caused by the
inverter MPP tracking algorithm. On the one hand, the associated voltage
excursion of the defective module is much larger than that corresponding to the
non-defective ones. On the other hand, the operating voltage differences between
defective and non-defective modules, ∆𝑉𝐻𝑆 , can vary following the MPP search. In
turn, these voltage fluctuations become ∆𝑇𝐻𝑆 fluctuations. This is clearly visible in
figure A2.7, which shows the records, every 5 seconds, of ∆𝑉𝐻𝑆 versus ∆𝑇𝐻𝑆 in a
particular defective module (measurement details are explained later) over a
period of a day. Large instability is observed in the low ∆𝑇𝐻𝑆 region (below 20 °C),
which is obviously also associated with low irradiances (characteristic of the early
morning, the late afternoon and passing clouds), when the MPP algorithms are
prone to instability. However, the relationship between ∆𝑉𝐻𝑆 and ∆𝑇𝐻𝑆 becomes
essentially stable in the high ∆𝑇𝐻𝑆 region, where most energy is generated.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Figure A2.7. Operating voltage losses, ∆𝑉𝐻𝑆 versus hot-spot temperature, ∆𝑇𝐻𝑆 . The MPP tracking
algorithm makes∆𝑉𝐻𝑆 fluctuate at low irradiance
These phenomena can also be observed in figure A2.8, which shows the
simultaneous records of the in-plane irradiance (black line) and the operation
voltages of 3 modules of the same string (one non-defective, blue dots; and two
defective, yellow and red dots). Large voltage excursions in the defective module
become evident.
Figure A2.8. Evolution of the operating voltage of 4 modules in the same string.
Finally, not only defective cells but also defective by-pass diodes can bring about
hot-spots. In the latter case, short-circuited diodes give rise to an easily
recognizable thermal pattern, consisting of an anomalous hotter band, somewhat
like a brushstroke extended over the cells protected by the affected diode, with
several cells exhibiting temperature differences of about 5 °C. Figure A2.9 shows
an example of a PV module with a conducting by-pass diode.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
(a)
(b)
Figure A2.9. (a) PV module with one conducting by-pass diode. The cells protected by the diode are
4 °C hotter than the rest of the cells. (b) Close view of the connection box. The affected diode is at
110 °C while the others are working at 70 °C.
This is because the solar cells that make up real PV modules are not completely
identical, but have a certain electrical characteristic mismatch that becomes a
dispersion of voltage. At the short-circuit condition imposed by the defective diode,
the sum of the voltage of all the cells protected by it is null, leading some cells
becoming positive biased and others becoming negative biased. In this situation,
the latter are slightly hotter than the former. Obviously, despite the temperature
difference remaining low, such a module loses effective power, at a ratio equal to
the number of defective diodes divided by the total number of diodes.
2.1 Hot-spot characterization
Because of the aforementioned dependence on ∆𝑇𝐻𝑆 with irradiance, it is
appropriate to characterize hot-spots through a value normalized to the standard
irradiance, 𝐺 ∗ =1000 W/m2.
∆𝑇𝐻𝑆 ∗ = ∆𝑇𝐻𝑆
𝐺∗
𝐺
where * stands for the Standard Test Conditions (STC). Up to now, there has not
been a widely accepted correlation for considering this effect on the heating of
modules [25]. Nevertheless, we think that there is a certain advantage of assuming
that the temperature difference is proportional to the incident irradiance.
Non-linearities in the ∆𝑇𝐻𝑆 − 𝐺 relationship are likely to be small for the relatively
narrow irradiance range defined by 𝐺 > 700 𝑊/𝑚2 , which is the condition that
we have imposed on our IR images.
Finally, it should be mentioned that slight temperature differences also appear in
non-defective modules, mainly due to differences in heat dissipation. For example,
the cells near the frame tend to be cooler while the cells around the connection box
tend to be hotter. In our case, we propose ∆𝑇𝐻𝑆 ∗ = 10 °𝐶 (4 °C due to the variation
in the cell efficiency in the first quadrant and 6 °C due to dissipation differences) as
a minimum threshold to consider the PV module as possibly defective.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
3 EXPERIMENTAL OBSERVATIONS
In this work, we have analysed a sample of 200 PV defective modules from two PV
plants located at Cuenca and Cáceres (Spain), respectively, 122 poly-crystalline
silicon modules from one single manufacturer (p-Si1) and 78 mono and polycrystalline silicon modules from two manufacturers (m-Si and p-Si2). These
defective modules were selected on the basis of a previous IR report made by the
maintenance personnel of the PV plants. Then, we carried out the following tests:
visual inspection, IR inspection, electroluminescence (EL), peak power and
operating voltage. The Cuenca PV plant (12 MW) has been in operation since
September 2011. Hot-spots soon appeared, but the module manufacturer agreed
to substitute all the modules exhibiting ∆𝑇𝐻𝑆 ∗ > 30 °𝐶 on March 2013. The IR
inspection that led to the selecting of the sample of defective modules was carried
out on June 2013 and the IES-UPM tests on January 2014. The process was similar
for the Cáceres PV plant (8 MW). The operation start-up was in September 2008,
the modules with hot-spots larger than 30 °C were substituted on June 2010, the IR
inspection leading to the detection of the 78 defective modules took place in July
2012 and, finally, the IES-UPM tests were carried out in May 2013. It is worth
noting that, in the case of the Cuenca PV plant, the initial IR inspection was made in
the summer while the tests were carried out the following winter, while in the case
of the Cáceres PV plant both inspections took place near the summer months. We
will later discuss the consequences of these differences.
3.1 Visual inspection
Figure A2.10 show examples of visible defects, where micro-cracks cause a current
drift and a corresponding heat that leads to the burning of the metallization fingers
and in bubbles at the rear of the modules. However, we found observable defects in
only a 19% of the concerned PV modules, which is too weak a correlation for
considering visual defects as a basis for dealing with hot-spots.
(a)
(b)
Figure A2.10. (a) Burnt metallization fingers caused by micro-cracks (b) Bubbles at the rear part of
the PV modules affected by hot-spots.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
3.2 Infrared inspection
We obtained the IR images by means of an infrared camera (FLIR-E60). As the
relevant parameter in this test is more the temperature difference than the
absolute temperature value, imaging can be done at either the front or the back of
the module. Just for convenience, we did all of them at the rear. Figure A2.11 shows
the frequency distribution of ∆𝑇𝐻𝑆 . This does not reflect the total hot-spot
occurrence, but only the hot-spots observed some months after the substitution of
all the modules with ∆𝑇𝐻𝑆 ∗ > 30 °𝐶. Hence, the distribution tail beyond this value
is a clear symptom of hot-spot time evolution. We did not observe any PID
phenomena (which, as observed in figure A2.1(a), typically lead to a recognizable
spatial pattern), thus most hot-spots are likely to be due to micro-cracks and
depend on the temperature of the module, as the thermal stress affects the contact
resistance between the two sides of the crack. Hence, an evolution of ∆𝑇𝐻𝑆 ∗ is to be
expected over the year, being larger in summer than in winter. On the other hand,
daily thermal cycling typically entails degeneration, leading to a probable
worsening of hot-spots over time. However, these are not absolute rules. Each
micro-crack is somewhat unique and even an improvement with thermal cycling
can be observed [18].
Figure A2.11. Frequency distribution of the temperature difference in the PV modules with hotspots. The values with ∆𝑇𝐻𝑆 ∗ > 30 °𝐶 reflect the hot-spot evolution.
Figure A2.12 shows the combined result of these effects. Each point in the graph
describes the observed ∆𝑇𝐻𝑆 ∗ at two different moments. Figure A2.12(a) shows the
evolution at the Cáceres PV plant between July 2012 (average ambient
temperature, TA = 34 °C) and May 2013 (TA = 25 °C). All the modules showing
∆𝑇𝐻𝑆 ∗ > 5 °C in July have been considered. Despite the dispersion being high, on
average, ∆𝑇𝐻𝑆 ∗ has increased 11%. Figure A2.12(b) shows the case at the Cuenca
PV plant between June 2013 (TA = 28 °C) and January 2014 (TA = 10 °C). Only those
modules with ∆𝑇𝐻𝑆 ∗ > 15 °C in June have been considered on this occasion. Here,
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
the average ∆𝑇𝐻𝑆 ∗ has decreased by 22%, in an example of seasonal effects
overcoming the degradation over time.
(a)
(b)
Figure A2.12. Hot-spot temperature evolution. Each point corresponds to a particular module and
describes ∆𝑇𝐻𝑆 ∗ at two different moments. At the Cáceres PV plant (a), both moments were during
hot months. A general ∆𝑇𝐻𝑆 ∗ increase over time is noticeable (slope coefficient > 1). On the other
hand, at the Cuenca PV plant (b), the latter moment was during a colder month than the former. In
this case, an average ∆𝑇𝐻𝑆 ∗ decrease can be observed (slope coefficient < 1).
3.3 Electroluminescence
The objective of this test was to analyse the correlation between the portion of
isolated area of a cell affected by micro-cracks and the magnitude of hot-spots. The
analyses were carried out directly in the field during night using an EL camera
(pco.1300 solar) and a power source. Each module was polarized in the fourth
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
quadrant at 25% of the STC rated short circuit current. The experiment was
carried out in January 2014 and applied only to a smaller sample of 35 PV modules
in the Cuenca PV plant, due to the difficulties of implementing this test on site. We
have followed the crack type classification proposed by Köntges et alt. [18],
dividing the affected cells into C-type (those exhibiting only background noise for
the inactive cell part) and B-type (those exhibiting a reduced intensity but higher
than the background noise). Figure A2.13 shows an example of an EL image
obtained in the field and figure A2.14 shows the relationship between the fraction
of cell that is isolated and the temperature difference.
Figure A2.13. Electroluminescence image of a hot-spot affected PV module obtained in the field.
Two cells with appreciable isolated areas can be observed (nearly a 40% for the left side cell – 20%
B-type and 20% C-type crack – and almost 20% for the upper side cell – B type crack).
∗
Figure A2.14. Relationship between ∆𝑇𝐻𝑆 and the fraction of cell isolated by a crack. Squares and
circles represent B-type and C-type cracks respectively, in accordance with the Köntges et alt
classification.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
We observed that all the modules showing a hot-spot in the summer IR inspections
had some micro-crack in the affected cell but none of the cells with B-type cracks
generated a hot-spot in winter. A proportional but very weak trend between the
isolated area and ∆𝑇𝐻𝑆 ∗ (R2=0.03) was found. The relationship between the
isolated fraction area and the power loss of the module, which remained very weak
(R2=0.05) was also analysed. A possible explanation is that the contact resistance
between the two sides of the micro-crack varies with module temperature and can
be much larger during the day (when hot-spots are observed) than during the
night (when EL are obtained). Then, some areas can be miss-classified, leading to
an incorrect estimation of the hot-spot problem. Whichever the case, EL images,
despite being a very useful tool for quality control during the PV manufacturing
processes, is not appealing for dealing with hot-spots in the field.
3.4 Electrical inspections: power and operating voltage
Individual I-V curves of all the affected PV modules were obtained with a
commercial I-V tracer (Tritec Tri-ka) and extrapolated to STC in accordance with
the IEC-60891 (procedure 1), using the current and voltage temperature
coefficients given by the manufacturer. 53% of the modules presented some
anomalies in the I-V curve, as steps or an abnormally low fill factor. Figure
A2.15(a) shows the relationship between ∆𝑇𝐻𝑆 ∗ and the power loss in respect to
the manufacturer’s flash value, for 50 PV modules of the Cuenca PV plant. The high
spread can be observed as can the fact that most of the modules satisfied the usual
power warranty condition (typically, 90% of the minimal rated power output after
10 years). However, this is scarcely representative of their in-field behaviour,
which is better appreciated through the operating voltage of the module, when
working within the PV array. The latter was measured by simply inserting “T”
connectors into the module output wires. Then, the voltage losses as regards the
non-defective modules can be understood directly as power losses, as the current
is common for all the modules connected in series. Figure A2.15(b) shows the
relationship between the power loss and the operating voltage loss for the same 50
modules. As can be observed, the effective losses are a 55% higher than the power
losses when considering the module alone.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
(a)
(b)
Figure A2.15. (a) Relationship between the temperature difference and the power loss for 50 PV
modules. 8 of them are out of warranty conditions. (b) Relationship between the power loss and the
operating voltage loss (effective power loss). In this case, 19 modules do not comply with warranty
requirements.
Two key observations can be outlined. First, the standard peak power is not a good
indicator of the energy production capacity of defective modules, so that it must be
disregarded for dealing with hot-spots. Second, the correlation between ∆𝑇𝐻𝑆 ∗ and
∆𝑉𝐻𝑆 ∗ and thus, power losses during operation, is positive, but the large dispersion
does not allow the correlation at individual levels to be applied. In other words, the
power loss of a defective module must be deduced from direct voltage
measurements not from thermal observations. Apart of that, figure A2.16 shows
the relationship between the temperature difference and the operating voltage loss
for a more complete ensemble of the 113 PV modules of the three different
manufacturers.
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Figure A2.16. Relationship between the temperature difference and the operating voltage loss for
113 modules from 3 different manufacturers.
It can be observed that the behaviour is not the same for every manufacturer
(neither in the correlation slope nor in the spread around it). The correlation
between operating voltage loss and temperature difference is stronger in the case
of module p-Si1 (R2=0.63) and weaker for the cases of modules m-Si and p-Si2.
These divergences likely reflect differences in the original material as well as
non-uniform degradation affection due to different operation times (3 years in the
case of module p-Si1 and 5 years for modules m-Si and p-Si2). Whichever the case,
this behaviour spread is not relevant here.
4 DISCUSSION
Hot-spots threaten the PV module lifetime, as degradation processes are generally
accelerated by temperature. In particular, encapsulate discoloration and browning,
and delamination [28-29]. Previous experiences do not allow a clear relation
between module temperature and lifetime [14] to be established. Therefore, in
order to set a maximum acceptable value, ∆𝑇𝐻𝑆,𝑀𝐴𝑋 ∗ , we must rely on intuitive but
reasonable approaches. We propose to consider 85°C, which is the maximum
temperature of the thermal cycling tests described in the IEC-61215 as the
maximum absolute PV module temperature for acceptance/rejection purposes.
This limit has been also proposed by other authors [14]. Then, ∆𝑇𝐻𝑆,𝑀𝐴𝑋 ∗ should be
thus so as to guarantee that the hot-spot absolute temperature remains below that
limit. Figure A2.17 shows the annual frequency distribution of the day-time
operating temperature in the Cuenca PV plant, which can be considered as
representative of a Mediterranean climate (characteristic of southern Europe and
some parts of USA, Australia or South America). The maximum cell temperature is
70 C and the 99-percentile temperature is 65°C. As these high temperatures are
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
also associated to high irradiances, setting ∆𝑇𝐻𝑆,𝑀𝐴𝑋 ∗ = 20°𝐶 limits the time above
85 °C to around 40 hours a year (1% of the time) for these climate conditions,
which seems a reasonable commitment. Moreover, it avoids reaching 100°C, which
has been sometimes suggested as an absolute maximum for preventing early
degradation [31].
Figure A2.17. Annual frequency distribution of the operating temperature at the Cuenca PV plant
As regards energy losses, it seems logical to just extend the application of usual
warranties to defective modules. Hence, it is proposed to reject any module
exhibiting hot-spots whose corresponding voltage losses (in relation to a nondefective module being part of the same series association) within the PV system
in normal operation, exceeds the allowable peak power losses fixed at standard
warranties. This is also applicable to PV modules with defective by-pass diodes,
regardless the temperature of the derived hot-spot.
5 CONCLUSIONS
There is still not a widely accepted reference on how to face the hot-spot problem
within commercial frameworks. Supported by experimental observations on 200
PV modules exhibiting hot-spots, the following procedure is proposed as a
practical in-field approach to accomplish IR imaging inspection:
1) Assure G > 700 W/m2
2) Perform the analyses in summer, preferably on the hottest days
3) Extrapolate the temperature difference, ∆𝑇𝐻𝑆 ∗ , considering a lineal
relationship with the irradiance.
Then, for every PV module with a hot-spot, the following is proposed:
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PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
4) If ∆𝑇𝐻𝑆 ∗ < 10°𝐶, to consider the module non-defective, except in the case
that one or more by-pass diodes are defective.
5) If ∆𝑇𝐻𝑆 ∗ > 20°𝐶, to consider the module defective.
6) If 10°𝐶 < ∆𝑇𝐻𝑆 ∗ < 20°𝐶, to consider all the modules with an effective
power loss (measured as a decrease in the operating voltage in relation to a
non-defective module of the same string) that exceeds the allowable peak
power losses fixed at standard warranties defective.
Finally, it is worth mentioning that this procedure and acceptance/rejection
criteria have already been applied by the IES-UPM when mediating in hot-spot
conflicts between module manufacturers and EPC during the last years.
REFERENCES
[1] Alonso-Garcia, M. C., Ruiz, J. M., & Chenlo, F.. Experimental study of mismatch and shading
effects in the I-V characteristic of a photovoltaic module. Solar Energy Materials and Solar
Cells, 2003; 90(3), 329-340 .
[2] Herrmann W., Wiesner W., Vaassen W. Hot spot investigations on PV modules – New concepts
for a test standard and consequences for module design with respect to by-pass diodes. 26th
Photovoltaic Specialists Conference, 1997; 1129 – 1132, Anaheim, CA, USA.. DOI:
10.1109/PVSC.1997.654287
[3] Molenbroek, E., Waddington, D. W., & Emery, K. A.. Hot spot susceptibility and testing of PV
modules. In Photovoltaic Specialists Conference, 1991. Conference Record of the Twenty
Second IEEE (pp. 547-552).
[4] Lorenzo, E., Moretón, R., & Luque, I.. Dust effects on PV array performance: in‐field
observations with non‐uniform patterns. Progress in Photovoltaics: Research and Applications,
2014; 22(6), 666-670.
[5] García M., Marroyo L., Lorenzo E., Marcos J., Pérez M. Observed degradation in PV plants
affected by hot-spots. Progress in Photovoltaics: Research and applications, 2013. DOI:
10.1002/pip.2393
[6] Bluerhop Cl., Schegel D., Niess M., Vodemayer C., Weissmann R., Brabec C.J. Reliablity of IRimaging of PV-plants under operating conditions Solar Energy Materials & Solar Cells, 2012;
107: 154-164. DOI: 10.1016/j.solmat.2012.07.011
[7] Grunow, P., Clemens, P., Hoffmann, V., Litzenburger, B., & Podlowski, L. Influence of micro
cracks in multi-crystalline silicon solar cells on the reliability of PV modules. Proceedings of the
20th EUPVSEC, 2005, Barcelona, Spain, 2042-2047.
[8] Brun, X. F., & Melkote, S. N. (2009). Analysis of stresses and breakage of crystalline silicon
wafers during handling and transport. Solar energy materials and solar cells; 2009, 93(8),
1238-1247.
[9] Muñoz J., Lorenzo E., Martínez-Moreno F., Marroyo L., García M. An investigation into hot-spots
in two large scale PV plants. Progress in Photovoltaics: Research and applications, 2008; 16:
693-701. DOI: 10.1002/pip.844
[10] Chaturvedi, P., Hoex, B., & Walsh, T. M. Broken metal fingers in silicon wafer solar cells and PV
modules. Solar Energy Materials and Solar Cells, 2013; 108, 78-81.
[11] Gabor, A. M., Ralli, M., Montminy, S., Alegria, L., Bordonaro, C., Woods, J., ... & Williams, T.
Soldering induced damage to thin Si solar cells and detection of cracked cells in modules.
In Proceedings of the 21st European Photovoltaic Solar Energy Conference (pp. 2042-2047),
2006.
96
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
[12] Berghold J., Koch S., Böttcher A., Ukar A., Leers M., Grunow P. Potential-induced degradation
(PID) and its correlation with experience in the field. Photovoltaics International. 19th edition.
85-92.
[13] Hacke, P., Terwilliger, K., Glick, S., Trudell, D., Bosco, N., Johnston, S., & Kurtz, S. Test-to-failure
of crystalline silicon modules. In 35th IEEE Photovoltaic Specialists Conference, 2010 244-250.
[14] Osterwald, C. R., & McMahon, T. J. History of accelerated and qualification testing of terrestrial
photovoltaic modules: A literature review. Progress in Photovoltaics: Research and
Applications, 2009; 17(1), 11-33.
[15] Munoz, M. A., Alonso-García, M. C., Vela, N., & Chenlo, F. Early degradation of silicon PV
modules and guaranty conditions. Solar energy, 2011; 85(9), 2264-2274.
[16] Simon, M., & Meyer, E. L. Detection and analysis of hot-spot formation in solar cells. Solar
Energy Materials and Solar Cells, 2010; 94(2), 106-113.
[17] Radziemska, E. The effect of temperature on the power drop in crystalline silicon solar cells.
Renewable Energy, 2003; 28(1), 1-12.
[18] Köntges M., Kunze I., Kajari-Schröder S., Breitenmoser, X., Bjorneklett. The risk of power loss in
crystalline silicon based PV modules due to micro-cracks. Solar Energy Materials & Solar Cells,
2011, 95: 1131-1137. DOI: 10.1016/j.solmat.2010.10.034
[19] Kajari-Schröder S., Kunze I., Eitner U., Köntges M. Spatial and orientational distribution of
cracks in crystalline PV modules generated by mechanical load tests. Solar Energy Materials &
Solar Cells, 2011, 95: 3054-3059. DOI: 10.1016/j.solmat.2011.06.032
[20] King, D.L., Kratochvil, J.A., Quintana, M.A., McMahon, T.J. Applications for infrared imaging
equipment in photovoltaic cell, module, and system testing. 28th Photovoltaic Specialists
Conference, 1487 – 1490. Anchorage, AK, USA.(2000) DOI: 10.1109/PVSC.2000.916175
[21] Auer R., Jahn U., Buerhop-Lutz C. Infrared analysis of PV modules for improving quality.
Proceedings of the 22nd EUPVSEC, Milan, Italy (2007)
[22] Botsaris, P. N., & Tsanakas, J. A. Infrared thermography as an estimator technique of a
photovoltaic module performance via operating temperature measurements. In Proceedings
of the 10th ECNDT Conference, 2010.
[23] IEC Standard 61215: Crystalline silicon terrestrial photovoltaic (PV) modules - Design
qualification and type approval. International Electrotechnical Comission, 1995.
[24] IEC Standard 62446: Grid connected photovoltaic systems. Minimum requirements for system
documentation, commissioning tests and inspection. International Electrotechnical Comission,
2009.
[25] IEC Standard 60904-12: Infrared thermography of photovoltaic modules. International
Electrotechnical Comission, 2014. Draft version.
[26] Alonso-Garcia, M. C., & Ruiz, J. M. Analysis and modelling the reverse characteristic of
photovoltaic cells. Solar Energy Materials and Solar Cells, 2006; 90(7), 1105-1120.
[27] Herrmann, W., Adrian, M., & Wiesner, W. Operational behaviour of commercial solar cells
under reverse biased conditions. In Proceedings of the Second World Conference on
Photovoltaic Solar Energy Conversion, 1998, 2357-2359.
[28] Jordan, D., Wohlgemuth, J., & Kurtz, S. Technology and Climate Trends in PV Module
Degradation. Proceedings of the 27th EUPVSEC, 2012, Frankfurt, Germany
[29] Schlothauer, J., Jungwirth, S., Köhl, M., & Röder, B. Degradation of the encapsulant polymer in
outdoor weathered photovoltaic modules: Spatially resolved inspection of EVA ageing by
fluorescence and correlation to electroluminescence. Solar Energy Materials and Solar Cells,
2012; 102, 75-85.
[30] Pern, F. J., & Glick, S. H. Photothermal stability of encapsulated Si solar cells and encapsulation
materials upon accelerated exposures. Solar energy materials and solar cells, 2000 61(2), 153188.
[31] Lathrop JW, Davis CW, Royal E. An accelerated stress testing program for determining the
reliability sensitivity of silicon solar cells to encapsulation and metallization systems.
97
PhotoVoltaic Cost Reduction, Reliability, Operational performance, Prediction and Simulation
Proceedings of the 16th IEEE PV Specialists Conference, San Diego, California, USA, 1982; 1262–
1267.
98