Report pv module performance

Susana Iglesias Puente, R. Kenny, T. Huld

RENEWABLE ENERGIES UNIT
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Table of contents

1 INTRODUCTION .............................................................................................1
1.1 The Joint Research Centre (JRC) .............................................................. 1
1.2 The Institute for Environment and Sustainability (IES) .................................... 4
1.3 The Solar Electricity Action ..................................................................... 4

2 OVERVIEW ON PHOTOVOLTAICS ........................................................................6
2.1 PV Technologies ................................................................................... 6
2.2 Operation Diagrams for PV Modules ........................................................... 8

3 INDOOR MEASUREMENTS .................................................................................9
3.1 Indoor measured matrix ......................................................................... 9
3.2 Empirical equation calculation ................................................................. 9
3.3 Nominal Operating Cell Temperature (NOCT) ............................................. 13

4 OUTDOOR MEASUREMENTS ............................................................................ 14

5 SOFTWARE DEVELOPMENT ............................................................................. 17
5.1 Solar_data_treatment.......................................................................... 18
5.2 Data_plotting .................................................................................... 22
5.3 Data_writing. .................................................................................... 23

6 NUMERICAL & GRAPHICAL RESULTS .................................................................. 24
6.1 AI01 (polycrystalline) .......................................................................... 24
6.2 DR01 (monocrystalline) ........................................................................ 31
6.3 LE02 (monocrystalline) ........................................................................ 37

7 ENERGY PREDICTION ON PV-GIS WEB SITE .......................................................... 44

8 CONCLUSIONS ............................................................................................. 47
8.1 Developed software ............................................................................ 47
8.2 Module performance predictions............................................................. 47
8.3 Personal experience ............................................................................ 48

9 SUGGESTED SOFTWARE IMPROVEMENTS ............................................................ 49

10 LIST OF FIGURES ......................................................................................... 50

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Table of contents

APPENDIX

A.1 Matlab program Solar_data_treatment………………….……………..……………………………………….52

A.2 Matlab function Eq_fit_params………………………….……………………………………….……………………70

A.3 Matlab funtion NOCT_estimation....…………………….…………………………………………….……………72

A.4 Matlab function Monthly_sum……………………………………………………………………………………………74

B.1 Matlab program Data_plotting …………………………………………………………………………………………83

B.2 Matlab function Month_teller..…….......…………………………………...……………………………………89

C.1 Matlab program Data_writing.….……………………………………………………………………….…………...91

C.2 Matlab function Matrix_converter……………………………………………………………….………………….94

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Nomenclature

Abbreviation Meaning

IES Institute for Environment and Sustainability
ESTI European Solar Test Installation
ENRA energy rating
MPP maximum power point
PV photovoltaic

Symbol Meaning Units

AM Air Mass []
FF Fill Factor []
Irr irradiance [W/m2]
I current [A]
IMPP current at MPP [A]
ISC short circuit current [A]
NOCT Nominal Operating Cell Temperature [oC]
P power [W]
Pmax maximum power output [W]
Tamb ambient temperature [oC]
Tmod module temperature [oC]
t time [h]
VMPP voltage at MPP [V]
VOC open circuit voltage [V]

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DEVELOPMENT OF MATLAB SOFTWARE TO ANALYSE AND PREDICT PV MODULE PERFORMANCE

1 INTRODUCTION

This report is based on work performed between 1st June and 30th November 2005, during
a training period on photovoltaics at the Renewable Energies Unit of the Joint Research Centre
of the European Commission in Ispra (Italy).

1.1 The Joint Research Centre (JRC)
The JRC is a research based policy support organization and an integral part of the
European Commission which mission is to provide the scientific advice and technical know-how
to support EU policies. As a service of the European Commission, the JRC functions as a
reference centre of science and technology for the Union. Close to the policy-making process, it
serves the common interest of the Member States. The JRC activities can be accessed on the
Internet by using the link: www.jrc.cec.eu.int

The JRC carries out extensive research of direct concern to European citizens and
industry. Over the years, the JRC has developed special skills and unique tools to provide
autonomous and Europe-wide expertise to improve understanding of the links between
technology, the economy and society. Eleven priorities have been identified to build on JRC
strengths under the EU Sixth Framework Programme (FP6) for research and technological
developments. Thematic concerns include:

Food safety - with a new food science and metrology pole to ensure quality systems
in the food chain.
Biotechnology - with a focus on genetically modified organism detection,
measurements and safety concerns.
Chemicals - particularly through the European Centre for Validation of Alternative
Methods and the European Chemical Bureau (ECB).
Health - with a focus on ensuring safety, quality and reliability of medical devices and
biological systems.
Environment - including climate change, sustainability and biodiversity.
Nuclear - including the safety of power plants, nuclear waste, nuclear safeguards and
non-proliferation control techniques.

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The structure of the JRC is based on seven specialised Institutes. The Directorate co-
ordinates the research performed by the seven institutes and helps to ensure its quality by
interacting with the international scientific community and industry. The seven JRC institutes
are located on five separate sites in Belgium, Germany, Italy, the Netherlands and Spain.

Figure 1. Map of the different institutes of the JRC.

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The main scientific institutes of the JRC are located in Ispra (Italy). Ispra is a small town
on the East side of Lago Maggiore (Regione Lombardia) in the Province of Varese. It has about
5000 inhabitants. The closest major city is Milan (approximately 60 km south-east), and the
region is best served by the Malpensa International Airport (located about 30 km south of the
JRC Ispra site). The Swiss border is just 30 kilometres away.

Figure 2. View of the JRC location in Ispra on the shore of Lago Maggiore.

The institutes situated in Ispra are:

The Institute for the Protection and the Security of the Citizen (IPSC).
The Institute for Environment and Sustainability (IES).
The Institute for Health and Consumer Protection (IHCP).

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1.2 The Institute for Environment and Sustainability (IES)
My training period took place in the Institute for Environment and Sustainability (Institute
home page: http://ies.jrc.cec.eu.int). In close co-operation with relevant partners in the
Member States and Applicant Countries, IES focus on:

Global Change: provides accurate information on changes in the chemical
composition of the atmosphere affecting climate change and in world’s
vegetation cover, and also their effect on the regional and global
environment.

Emissions, Air Quality and Health: focuses its activities in the areas of
emissions from mobile and stationary sources; air quality; exposure to
pollutants and health related studies; and radioactivity monitoring.

Water: provides scientific and technical support to the EU strategies for
the protection and sustainability of inland, coastal, marine and engineered
waters. Activities focus on ecological water quality; integrated river basin-
coastal zone management; chemical substances in surface and drinking
water, wastewater impacts; and molecular–based tools for chemical
responses and pathogen/microbe detection.

Terrestrial and Natural Resources: carries out research in support of EU
policies regulating: spatial characterization of the European territory, land
resources and bio-diversity, natural hazards, environmental impacts of
waste management strategies and protection of soil resources.

Renewable Energies: provides a Scientific and Technological reference
base on renewable energy sources and perform technology developments
where harmonisation is required, particularly in the field of Photovoltaic
Solar Electricity, end-use efficiency of electricity and electricity storage
problems for renewables.

The work of the Unit is carried out in two Research Actions:

Action 2312 – Scientific-Technical Reference System on Renewable energy and
Efficient Use of Electricity.
Action 2324 – Solar Electricity.

This work was carried out within the scope of the Solar Electricity Action, which is one of
the two principal research actions within the Renewable Energies Unit.

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1.3 The Solar Electricity Action
The Solar Electricity Action contributes to the implementation of renewable energy in
the European Union as a sustainable and long-term energy supply by undertaking new science
and technology developments in fields where harmonisation is required by customers,
developing standards and references to ensure the quality of 1st and 2nd generation
photovoltaic technology. The Action also acts as a catalyst for the development of the science
base of 3rd generation photovoltaic technology with particular attention to integrating the
scientific knowledge available in the new Member States of the EU.

The Unit is leading the efforts of IES in becoming a world-wide recognised centre of
reference for the intercalibration and accreditation of photovoltaic technologies, supporting
the Community goal of doubling the share of renewable electricity by 2010. In addition, the
vicinity of the JRC to the policy-making process has fostered activities on the efficient use of
electricity, underpinning Community policies to reduce the vulnerability of Europe’s energy
systems. A “Common Scientific-Technical Reference System on Renewable Energy and Energy
End-Use Efficiency” has been set up to support European policy makers in these tasks.

A team of 30 scientists, engineers and technicians, combined with the facilities and
workshops developed over the last 20 years ensure that the
European Solar Test Installation (ESTI), which is the main
research infrastructure of the Unit, remains as one of the
world’s leading laboratories for reference measurements.

ESTI is the first accredited test facility for the calibration of photovoltaic devices
worldwide based on the ISO/IEC standard 17025 “General requirements for the competence of
testing and calibration laboratories”, offering photovoltaic type approval tests and calibration
services to manufacturers, research partners and other users. The Renewable Energies Unit also
serves as reference centre for solar irradiance measurements.

More details about the activities of the Renewable Energies Unit can be accessed on the
website ies.jrc.cec.eu.int/Renewable_Energies.45.0.html .

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2 OVERVIEW ON PHOTOVOLTAICS

The word photovoltaic is a composition from the Greek word for "light" and the name of
the physicist Alessandro Volta. It designates the direct transformation of sunlight into
electricity by solar cells. The procedure is based on the photoelectric effect which was
discovered in 1839 by Alexander Becquerel. The photoelectric effect is the release of positive
and negative charge carriers from a solid body by incident light radiation.

A PV cell consists of two or more thin layers of semi-conducting material, most commonly
silicon. When the silicon is exposed to light, electrical charges are generated and they can be
conducted away by metal contacts as direct current (DC). The electrical output from a single
cell is small, so multiple cells are connected together and encapsulated to form a module
(sometimes referred to as ‘panel’).

2.1 PV Technologies
PV comes in many flavours, though the bulk of material in use nowadays is silicon-based.
The different technologies can be divided into 4 groups:

Crystalline silicon solar cells.

Amorphous silicon solar cells.

Other technologies (e.g. cadmium telluride and copper indium diselenide).

There are two main types of crystalline silicon cells: mono- and polycrystalline cells. The
structure of both is similar. They are called Thick Film Technologies because the wafer is
thicker than in Thin Film Technologies (amorphous silicon cells and other technologies). As this
work focuses on the performance of crystalline silicon cells, the main features of these will be
explained.

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2.1.1 Monocrystalline Silicone Solar Cells

This technology is the most efficient of the PV technologies;
its main advantage is its high efficiency (typically around 15%).

The manufacturing process is complicated, resulting in
slightly higher costs than other technologies. Monocrystalline
silicon cells are made using cells saw-cut from a single cylindrical
crystal of silicon.

Figure 3. Monocrystalline
silicon cell.

2.1.2 Polycrystalline Silicon Solar Cells

They tend to be slightly less efficient than the above
technology (with average efficiencies of around 12%).

Polycrystalline cells are cheaper to produce than
monocrystalline ones, due to the simpler manufacturing process.
They are made from cells cut from an ingot of melted and
recrystallised silicon. In the manufacturing process, molten silicon
is cast into ingots of polycrystalline silicon; these ingots are then
saw-cut into very thin wafers and assembled into complete cells. Figure 4. Polycrystalline
silicon cell.

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2.2 Operation Diagrams for PV Modules
The next diagram shows the typical I-V and P-V curve of a solar module for a given solar
irradiation and module temperature, reflecting the current-voltage behaviour of the module
and the typical values.

2.5 70
PMAX MPP
ISC 2 60
IMPP 50

power [W ]
1.5 40
current [A]

1 30
20
0.5
10
0 0
0 5 10 15 20 25 30 35 40 45 50
VMPP VOC
voltage [V]
Figure 5. Typical I-V curve and P-V curve.

The variables shown in Fig. 5 are the following:

Open Circuit Voltage (VOC) and Short Circuit Current ( ISC)

Maximum Power Point Voltage (VMPP) and Maximum Power Point Current (IMPP)

Additionally the corresponding power-voltage curve is shown, using the right-hand-side
scale, which is characterised by the Maximum Power Point (PMAX).

The power supplied to a load attached to a PV cell is determined by the product of
current and voltage. The maximum power output (MPP=Maximum Power Point) is equivalent to
the rectangle of maximum area that fits under an I-V curve.

PMAX = V MPP ⋅ I MPP (1)

Out of the I-V curve the Fill Factor, FF, can be determined, which is a measure of how
"square" an I-V curve is.

VMPP ⋅ I MPP
FF = (2)
VOC ⋅ I SC

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3 INDOOR MEASUREMENTS

The indoor measurements are carried out in two different adjoining Large Area Pulsed
Solar Simulator (LAPSS) laboratories, named SpectroLab LAPSS and PASAN LAPSS. Both
laboratories are completely dark rooms cloaked with black drapery. Although each laboratory
serves a different purpose in obtaining measurements, the basic superstructural parts of both
laboratories include an active electric load and a single flash solar simulator as a light source.
Such pieces of equipment are used for the ascertainment of the current-voltage behaviour of
photovoltaic modules. Furthermore, a crystalline silicon reference cell is necessary for the
measurements.

Three crystalline (two mono- and one poly-) modules have been analysed which ESTI
laboratory codes are LE02, DR01 and AI01, respectively. It is interesting to point out that these
names have been assigned by the JRC in order to protect the companies’ identity.

3.1 Indoor measured matrix
The measurements depending on temperature are done in PASAN LAPSS where the
module is characterised at each point on a matrix of maximum power point output values Pmax
[W] as a function of the module temperature and the incident irradiance. The Pmax under
Standard Test Conditions (STC) is labelled in red in Tables I through III. These conditions
correspond to an irradiance level of 1000 W/m2 at defined spectral irradiance distribution (AM
1.5) and a module temperature of 25 ºC.

3.2 Empirical equation calculation
Once we have the measured indoor matrix, the data are plotted and fitted to a surface
(using the program Table Curve 3D) to obtain an empirical equation to estimate Pmax. The
fitting equation, which in this case is the same for the three modules, is the following:

a + b ⋅ (ln Irr ) + c ⋅ Tmod
Pmax = (3)
1 + d ⋅ ln Irr + e ⋅ (ln Irr ) + f ⋅ Tmod
2

where the value of the parameters a, b, c, d, e, f is given by the fitting.

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Next the measured matrices and the fitted surfaces are shown for the analysed modules.

Irradiance [W/m2]
50 100 150 200 250 300 400 500 600 700 800 900 1000

25 2.00 4.49 7.10 9.77 12.52 15.26 20.78 26.44 31.68 37.07 42.22 47.77 53.09
Module Temperature [oC]

30 1.98 4.36 6.84 9.56 12.18 14.86 20.31 25.92 30.98 36.40 41.13 46.32 51.08
35 1.92 4.25 6.68 9.26 11.92 14.36 19.58 24.66 29.89 35.16 40.02 45.29 49.77
40 1.89 4.15 6.51 9.07 11.61 14.11 19.16 24.03 29.14 34.22 39.04 44.13 48.64
45 1.83 4.07 6.37 8.86 11.32 13.67 18.73 23.51 28.46 33.54 38.10 43.23 47.52
48 1.80 3.99 6.25 8.68 11.15 13.45 18.35 23.11 28.05 32.94 37.43 42.39 46.70
50 1.76 3.96 6.20 8.60 11.00 13.30 18.25 22.90 27.81 32.69 37.07 42.17 46.23
55 1.76 3.85 6.02 8.36 10.73 12.97 17.75 22.33 26.98 31.74 36.15 41.06 45.17
60 1.69 3.74 5.85 8.14 10.43 12.67 17.34 21.72 26.38 30.90 35.27 40.06 43.94

Table I. Matrix of indoor measured power [W] as a function of Irr and Tmod for AI01.

AI01 Indoor
Rank 196 Eqn 1132 z=(a+blnx+cy)/(1+dlnx+e(lnx)^2+fy)
r^2=0.99974319 DF Adj r^2=0.99972731 FitStdErr=0.2585647 Fstat=76302.371
a=-0.93125496 b=0.40257114 c=-0.0040224985
d=-0.26053276 e=0.017375655 f=0.00010847924

60 60
50 50
40 40
Pmax [W]

Pmax [W]

30 30
20 20
10 10
0 0
55 8 00
9
50 700 00
45 0 600
Te m 4 5
p [º 35 400 00
300 ²]
C] 30 2
1 00 00 W/ m
25 Irr [
20 0

Figure 6. 3-D visualisation of the indoor measured matrix & fitted performance surface, AI01.

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Irradiance [W/m2]
50 100 150 200 250 300 400 500 600 700 800 900 1000

25 3.17 7.49 12.04 16.83 21.72 26.38 36.35 46.34 55.97 65.62 75.99 85.32 94.95

30 3.12 7.32 11.80 16.43 21.11 25.87 35.55 45.36 55.49 64.77 74.82 83.97 93.21
35 3.07 7.19 11.60 16.18 20.88 25.50 34.90 44.67 54.32 63.72 73.35 82.27 91.39
40 3.01 7.05 11.34 15.83 20.45 25.01 34.23 43.76 53.37 62.48 71.75 80.63 89.27
45 2.97 6.88 11.12 1.00 19.98 24.46 33.40 42.67 52.09 61.02 70.22 79.00 87.34
48 2.91 6.84 10.96 15.28 19.61 24.09 33.10 42.00 51.30 60.04 68.75 76.94 85.91
50 2.90 6.80 10.89 15.14 19.59 23.77 32.62 41.65 50.92 59.22 68.21 76.59 85.31
55 2.80 6.54 10.59 14.69 18.98 23.17 31.81 40.62 49.29 57.50 66.46 74.55 83.07
60 2.73 6.39 10.34 14.32 18.48 22.70 31.01 39.71 48.50 56.66 65.15 72.84 80.96

Table II. Matrix of indoor measured power [W] as a function of Irr and Tmod for DR01.

DR01 Indoor
a=-1.5675042 b=0.61558713 c=-0.0043817042
d=-0.26677134 e=0.018194163 f=9.2588895e-05

100
90 100
80 90
70 80
60
Pmax [W]

70
50 60
Pmax [W]

40 50
30 40
20 30
10 20
0 10
55 0
50 90 100
Te 45 70 800 0 0
mp 0
[º C 4 3 5 50 600 0
] 30 400 0
30 10 200 0 / m²]
25 0 0 Irr [W

Figure 7. 3-D visualization of the indoor measured matrix & fitted performance surface, DR01.

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Irradiance [W/m2]
50 100 150 200 250 300 400 500 600 700 800 900 1000

25 1.60 3.79 6.02 8.30 10.66 12.99 17.06 22.40 27.14 32.09 36.28 40.95 45.59

30 1.61 3.69 5.84 8.08 10.38 12.60 16.63 21.56 26.33 30.99 35.15 40.26 44.30
35 1.56 3.63 5.70 7.92 10.12 12.27 16.23 21.04 25.59 30.05 34.19 39.31 43.20
40 1.53 3.51 5.55 7.69 9.89 12.00 15.80 20.57 25.01 29.42 33.35 38.38 42.21
45 1.50 3.44 5.40 7.51 9.64 11.69 15.45 20.03 24.38 28.68 32.58 37.41 41.30
48 1.47 3.39 5.34 7.42 9.53 11.55 15.27 19.88 24.08 28.26 32.12 36.83 40.62
50 1.45 3.34 5.24 7.30 9.36 11.34 15.09 19.54 23.82 28.00 31.85 36.53 40.25
55 1.41 3.26 5.11 7.16 9.14 11.13 14.69 19.11 23.18 27.35 31.00 35.59 39.25
60 1.36 3.16 4.98 6.92 8.89 10.76 14.22 18.49 22.47 26.37 30.20 34.71 38.17

Table III. Matrix of indoor measured power [W] as a function of Irr and Tmod for LE02.

LE02 Indoor
a=-0.88101569 b=0.36032919 c=-0.0033567692
d=-0.25694536 e=0.016878253 f=0.000113601

50
45 50
45
40
35 40
30 35
Pmax [W]

30
Pmax [W]

25
20 25
15 20
10 15
5 10
0 5
60 5 0
5 0 9
5 5 800 00
Te 4 600 700
mp 40 5 400 500
[º C 3 3
] 30 200 00 / m²]
25 100 Irr [W
20 0

Figure 8. 3-D visualization of the indoor measured matrix & fitted performance surface, LE02.

Under Standard Test Conditions (STC), the modules produce the highest power. Under
diminishing irradiance, and simultaneously increasing module temperature, the power
decreases.

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3.3 Nominal Operating Cell Temperature (NOCT)
The efficiency of PV cells varies with incident irradiance and cell temperature. The
module temperature is used thus for the empirical estimation of Pmax (with Eq. 3) instead of
the ambient temperature. Since for the open rack mounting case the difference between the
ambient and module temperature is proportional to irradiance, the module temperature can be
estimated using the following equation:

 NOCT − 20 
Tmod =   ⋅ Irr + Tamb (4)
 800 

The Nominal Operating Cell Temperature (NOCT) is by definition the module
temperature at an ambient temperature of 20 ºC and an irradiance of 800 W/m2. The
irradiance, Irr, is in W/m2 and the temperatures in ºC.

Generally, there is an historical record of the ambient temperature for most locations
around the globe; hence site-specific temperature data is readily available.

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4 OUTDOOR MEASUREMENTS

Long term outdoor measurements are essential for energy rating (ENRA) studies due to
three main reasons:

Predictions based on indoor laboratory measurements regarding energy performance
need to be validated with real field data.

Outdoor measurements may reveal interesting behaviour discrepancies between the
different material technologies that are not evident from indoor flash measurements.

They provide information about how module performance is affected by
environmental conditions such as cloudy skies resulting in a large portion of diffuse
light, a continuous change of the incident solar angle and gusts of wind and
precipitation.

The measurement site consists of a flat area with 9 module racks; one of those is used to
mount the energy rating modules. Next to the racks there is a cabin that contains the
measurement computer and the instrumentation for the ENRA investigations.

Figure 9. View of the outdoor measurement site at the JRC.

The modules are open-rack mounted and surrounded by black plates in order to provide
uniform conditions to all of them (see Fig. 10). The aluminium racks are adjustable as it is
necessary to keep the sun elevation angle within 90 ± 5o to the module surface at solar noon
(following the principles employed in the measurement of NOCT in IEC 61215).

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Figure 10. Outdoor measurements on the rack;
AI01 and DR01 (poly- and monocrystalline), respectively.

A KEPCO power supply is used as an active load for the module. During the measurements
it is programmed to set a range of voltages across the module terminals from slightly above the
VOC point to slightly below zero volts in order to cover VOC and ISC. Each of the tested modules is
connected to its own KEPCO.

In order to measure the temperature of the module, a
temperature sensor (PT100) is affixed to the back of each module as
shown in Fig. 11. As an aside, the cell temperature is not directly
measurable, and in fact in previous work the back of module
temperature has been found to be approximately two degrees lower
Figure 11. Temp.
than the cell temperature. sensor on the back of
the module.

The incident irradiance is measured by an ESTI sensor and a pyranometer, which are
mounted coplanar to the rack (Fig. 12). The pyranometer is the standard device for solar
irradiation measurements in meteorology. Unfortunately, they tend to be expensive and require
frequent recalibrations. Thus, there has been some strong research work to find a better
alternative solution, the ESTI sensor. The ESTI sensor is based on a monocrystalline silicon solar
cell and it shows similar behaviour to the crystalline modules. The cell is cut in half, one half

15


remains at short circuit current ISC to monitor irradiance and the other half remains at open
circuit voltage VOC to monitor cell temperature.

Pyranometer
ESTI sensor

Figure 12. Experimental setup for irradiance measurement.

The irradiances measured by the ESTI sensor and the pyranometer are not identical as
the devices operate on different principles and with different spectral ranges. For this reason
the data are analysed using both irradiance values in order to evaluate which one is most
appropriate.

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5 SOFTWARE DEVELOPMENT

The main task performed during the training period at the JRC consisted in the
development of specific software to treat systematically the outdoor experimental data of the
solar panels. This was carried out by programming in MATLAB, a high-
performance programming and visualization software designed for handling
large amount of data. The data obtained measuring the different parameters
involved in the module performance were stored in text files. The data files
are very large as they store data for several years; therefore the data
treatment using a spreadsheet is impractical.

Figure 13. Example of text file storing experimental data for several years.

As we can see in Fig. 13, the data are arranged in a fixed format inside the file. The
measurements are taken at fixed intervals, typically 4 minutes, from the morning until the
evening, when irradiance levels are above 50 W/m2.

The different parameters in the text files are separated by commas, the files show the
value of the following variables:

Date: day, month and year.
Time: hour, minutes and seconds.
ESTI: irradiance given by the ESTI sensor.
Pyran: irradiance given by the pyranometer.
Tamb: ambient temperature.
Tmod: module temperature.
Isc: short circuit current.
Voc: open circuit voltage.
Pmax: power output at MPP.

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Impp: current at MPP.
FF: Fill Factor.

The parameters that are used by the software are: date, time, ESTI, Pyran,Tamb, Tmod
and Pmax.

The software developed to analyse the data consists of three programs named
Solar_data_treatment, Data_writing and Data_plotting and several functions that are called by
the programs.

5.1 Solar_data_treatment
The main tasks carried out by this program are:

Obtain the values of the measured and estimated energy produced by the module.

Obtain the energy coming from the sun (irradiation).

Calculate these at different time intervals: day, month and year.

Compare measured and estimated energies, and other output results, numerically and
graphically.

This program is shown in Appendix A.1.

In order to make the structure of the program easier, some of the calculations are
performed by functions called by the program. Functions have a defined syntax in MATLAB:

function [output1, output2, …] = function_name (input1, input2, …)

Some values (input arguments) need to be passed to the function and it will calculate
other variables (output arguments) that are returned to the program that called the function. It
is important to point out that, in this case, the main calculated parameters are declared as
global variables, this means that those variables are shared by all the functions and programs.

These functions are:

Eq_fit_params. This function needs to know the name of the module which data are
going to be analysed. The output arguments are the different parameters of Eq. 3,
used to calculate Pmax. It also returns the module surface area.

NOCT_estimation. This function uses Eq. 4 to estimate Tmod.

Montly_sum. This is the most important and the longest of the functions. It integrates
Pmax over every day to get the total energy per day. The result of the function is an
array of 31 components containing the energy for each day.

Month_teller. This function tells the program Data_plotting the name of the month
that is going to be plotted.

Matrix_converter. This function converts 12-by-31 matrices into column arrays.

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Next, the actions carried out by the program, step by step, will be explained in detail.

1. Import the data from the text file.

The first action of the program is to import the data from the text file and store them in
different variables; this is achieved by using the function fscanf for the first row of the file
(made up of characters) and textread for the rest of the file. The latter stores every column of
the original file in an array.

2. Obtain the parameters of the empirical equation.

One of the main objectives of the program is to estimate the value of Pmax using different
methods and to compare it with the real value. The empirical equation for every module (Eq. 3,
obtained by fitting the outdoor data to a surface as described in Chapter 3) is usually the same
but the parameters in the equation are different. Therefore, it is necessary to tell the main
program these parameters and also the module surface area that will be used to calculate the
efficiency. This is obtained by using the function Eq_fit_params (shown in Appendix A.2) which
consists mainly of a switch structure; in this way, the function will return different values for
the parameters and the module surface area depending on the case, this is to say, the name of
the module.

3. Estimate Tmod from the ambient temperature and the irradiance.

In order to estimate the module temperature, it is necessary to plot Tmod-Tamb versus Irr
and to perform a least-squares fitting of the data (with the command polyval) to Eq. 4. The
function NOCT_estimation (shown in Appendix A.3) is in charge of performing these
calculations.

Once we get the slope of the fitting, Eq. 4 is used again with every single value of
irradiance and Tamb to obtain the Tmod estimated values. These estimates are also plotted in the
same graph as the measured values. The NOCT value is readily obtained from the equation’s
slope.

19


Figure 14. Experimental (points) and empirical (line) values of Tmod for AI01.

This process is carried out using both the ESTI and the pyranometer irradiance.

4. Estimate Pmax values with the empirical equation.

The next step is to calculate Pmax for every single measurement using the empirical
equation. As there are two values of irradiance, two different arrays containing values for Pmax
are obtained. Two further estimates are obtained by using the estimated Tmod instead of the
real one. This makes four different estimates in total.

5. Integrate Pmax over the day and store the results in 3-D arrays.

This is the most important and time-consuming part of the program, namely the
integration of the different parameters over individual days, and then by addition of the daily
values, months and years. In order to calculate this, twelve while loops (one for each month of
the year) are used inside a main for loop. Inside the while loops the function monthly_sum
(shown in Appendix A.4) is called once per every variable that is necessary to integrate. This
function works in the following way:

a. First of all, it calculates the time interval (in hours) between each measurement and
stores it in an array.

b. Then, most of the function consists of 31 while loops. Each of them integrates the
desired variable over the whole year for the year that is being evaluated.

20


c. Finally, the calculated value for each day is stored in an array that is returned to the
main program.

After the program goes through the main for loop once, 12 arrays of 31 components with
the total energy for every day are obtained (one for each month of the year). Then, these
arrays are concatenated to form a 12-by-31 matrix.

All the obtained matrices (one for every measured year) are
stored in the same variable to form a 3-D array (tensor). The structure
of this tensor is shown in Fig. 15 where the index k corresponds to the
number of years over which the performance of the module was
measured, this is to say, every ‘slice’ stores the total values of energy
for one year and there will be as many ‘slices’ as years during which
the measurements were taken. Figure 15. Structure
of a 3-D array.

Therefore, at this point of the program the main calculated variables (at three different
time intervals: per day, month and year) are:

The real energy produced by the module.

The estimated energy produced by the module using the empirical equation and the
irradiance values given by the ESTI sensor and the real module temperature.

irradiance values given by the pyranometer and the real module temperature.

irradiance values given by the ESTI sensor and the estimated module temperature
(using the NOCT).

irradiance values given by the pyranometer and the estimated module temperature
(using the NOCT).

6. Obtain the energy for every month and every year.

This is calculated by adding together the total energy for every day. The total energy for
every month is stored in a matrix whereas the energy for every year is stored in an array.

7. Calculate the BIAS error and the module efficiency.

An important parameter to evaluate the performance of the module is the efficiency
defined as:

Efficiency (%) =
Energy produced by the module (W ·h)
⋅ 100 (5)
Energy coming from the sun (W·h/m2 ) ⋅ module surface area (m2 )

21


The efficiency is also calculated for every measurement, day and month with regards to
the irradiance measured by the ESTI sensor and by the pyranometer.

Finally, the different energy estimates are compared to the measured energy using the
BIAS error (error in absolute terms).

All the values of efficiency and BIAS error are also stored in arrays.

5.2 Data_plotting
This program plots the different variables of interest to study the performance of the
module that is being analysed and to compare the estimated energy values with the real ones
at different time intervals (per day and per month). Bar graphs were chosen for most of the
plots instead of scatter graphs as in this way it is easier to visualise the results. The program
can be seen in Appendix B.1.

Since measurements are not available for every single day (due to, for example, system
crashes, temporary removal of modules for indoor measurements etc.), in order to compare the
energy for every month the total energy per month is divided by the number of days actually
measured each month. In this way, the daily average values for each month are obtained.

The function month_teller (shown in Appendix B.2) is called by the program inside the
for loops to obtain the month name (depending on the month number) that is being plotted;
making it possible to print the month name on each graph. This function consists of a switch
command that returns a different value of the month name depending on the case (the month
number). The month number needs to be converted into a string before passing it to the
function as the case must be a string; this is achieved by using the command int2str.

Several of the main graphs obtained are shown in Chapter 6. These graphs correspond to
the measurements performed with the modules AI01 and DR01 in 2003 and LE02 in 2002/3.

22


5.3 Data_writing.
This program creates several MATLAB text files and it stores the calculated variables in
them. Every file stores the same basic variables but for different time intervals, that is to say,
one of the files will contain the values of important variables for every single measurement,
then another one will contain the same parameters but for every day and another one for every
month.

The data for every day are stored in 12-by-31 matrices; therefore it is necessary to
convert these matrices into one-dimension arrays. This is carried out by the function
matrix_converter. The program and the function can be seen in Appendices C.1 and C.2,
respectively. The following figure shows, as an example, the results for the AI01 for every
month in 2003.

Figure 16. M-file containing the calculated monthly variables for AI01 in 2003.

It is important to point out that these data can be easily imported to a spreadsheet (e.g.
Excel) for further analysis.

23


6 NUMERICAL & GRAPHICAL RESULTS

In this chapter the measured energy and the estimates are compared to validate the
performance of the equation obtained by using the indoor measurements (Eq. 3).

6.1 AI01 (polycrystalline)
The AI01 is a polycrystalline module with a surface area of 0.491 m2. The energy
comparisons for this module are carried out for the year 2003 (excluding December).

Energy, 11 months [W·h] Relative error [%]

Measured value 66832 —

Estimate: ESTI 66860 0.04

Estimate: Pyran 67146 0.47

Estimate: ESTI & NOCT 66895 0.09

Estimate: Pyran & NOCT 67170 0.51

Table IV. Total measured energy and estimates for AI01 in 2003.

It is important to point out that for several days in December 2003 there was a problem
with the ambient temperature sensor as water leaked inside a junction box shorting the signal
cables, and consequently it was giving false readings. Because of this problem, the energy
values estimated for December 2003 using the estimated Tmod (which is calculated using the
Tamb) are wrong, and that is why Table IV doesn’t include this month (so that a comparison can
be made between the different estimates and the measured value). In order to obtain a good
value for the NOCT, December was not used when fitting the experimental data to Eq. 4 either.

Analysing the results in Table IV, it can be seen that the estimates using the irradiance
given by the ESTI sensor are the most accurate ones. In general, all the estimates are very
good.

Next we can see several graphs that show the module performance in 2003. Some of the
graphs show the energy and module efficiency for every month and others, for every day in two
chosen months: March and July. Due to the mentioned problem in December 2003, the estimate
using the NOCT was not plotted for this month in the following graphs.

24


Year 2003
9000

8000

7000

6000
Energy [W·h]

5000

4000

3000

2000 Measured energy
Empirical ESTI energy
Empirical ESTI & Tmod energy
1000

0
1 2 3 4 5 6 7 8 9 10 11 12 13
Months

Figure 17. Measured energy and estimates for AI01 in 2003.

The blue bars in the graph above represent the measured energy, the red bars the
estimate using the ESTI irradiance and the blue ones the estimate using the ESTI irradiance and
the NOCT (the estimated Tmod ). It can be seen that the total energy in November is very low.
This is because this was a month with exceptionally bad weather, and hence many low
irradiance days. In fact, there are no measurements for several days in that month, due to the
low irradiance since the system doesn’t take measurements when the irradiance is lower than
50 W/m2.

The graph shown in Fig. 17 has been normalised dividing the total energy for each month
by the number of days actually measured per month. The result is shown in Fig. 18.

25


DAILY AVERAGE 2003
400
Mean daily energy
Measured energy
350 Empirical ESTI energy

300

250
Energy [W·h]

200

150

100

50

0
2 4 6 8 10 12
Months

Figure 18. Average daily energy for AI01 in 2003.

In the graph above, the horizontal line shows the average energy per day produced by the
AI01 in 2003 that is about 210 W·h.

In the following graph (Fig. 19), we can see the predicted energy values taking into
account that there are some days missing, this is to say, without any measurements. These
values were calculated just by multiplying the average daily energy by the total number of days
in each month. This assumes that the missing days would have had the same average energy as
the average daily energy for the measured days, but allows us to estimate what the energy
prediction for the complete month would have been, and as long as the number of missing days
is small this is likely to cause only small errors. Note that it is important to distinguish between
days where data is missing due to lack of measurements rather than being due to exceptionally
low irradiance.

26


MONTHLY ESTIMATES 2003
9000

8000

7000

6000
Energy [W·h]

5000

4000

3000
Mean monthly energy
2000 Measured energy
1000 Empirical ESTI & Tmod energy

0
2 4 6 8 10 12
Months

Figure 19. Predicted energy for AI01 in 2003 taking into account the missing days.

The predicted value for the average monthly energy in 2003 is about 6375 W·h.

The following two graphs (Figs. 20 and 21) show the total energy per day for two
representative months of the year, March and July. It can be clearly seen that the energy
produced by the module is lower in March (a winter month) than in July (a summer month).

MARCH 2003
400

350

300

250
Energy [W·h]

200

150 Measured energy
100

50

0
5 10 15 20 25 30
Days

Figure 20. Measured energy and estimates for AI01 in March 2003.

27


JULY 2003
400

350

300

250
Energy [W·h]

200

150

100
Measured energy

0
5 10 15 20 25 30
Days

Figure 21. Measured energy and estimates for AI01 in July 2003.

The program Data_plotting also makes some graphs showing the module efficiency (using
the measured energy and the estimates) with regards to the ESTI irradiance as well as the
ambient and module temperature.

Year 2003
Mean efficiency ESTI
14 Measured energy <> ESTI irrad
Estimated ESTI energy <> ESTI irrad
Estimated ESTI & Tmod energy <> ESTI irrad
12

10
Efficiency [%]

8

6

4

2

0
2 4 6 8 10 12
Months

Figure 22. Monthly efficiency for AI01 in 2003.

28


AMBIENT AND MODULE TEMPERATURE FOR AI01 IN 2003
50

45

40

35
Temperature (ºC)

30

25

20

15

10 Ambient temperature
Measured module temperature
5 Estimated module temperature

0
1 2 3 4 5 6 7 8 9 10 11
Months

Figure 23. Ambient and module (AI01) temperature profiles in 2003.

The three differently coloured bars in Fig. 22 represent efficiency values with regards to
the ESTI irradiance calculated by using Eq. 5. The mean efficiency is also plotted and is around
10.1 %. Having a look at this graph, a tendency can be easily seen: in summer the efficiency is
lower than in winter. If we compare this graph with the one in Fig. 23, which shows the
monthly average values of daytime module and ambient temperatures, we can conclude that
the efficiency is lower in summer time when the module temperature is higher.

The comparison of the measured Tmod with the estimated values shows that the estimates
are accurate although it seems that Eq. 4 tends to underestimate in winter and to overestimate
in summer.

The following graphs (Figs. 24 and 25) show the daily efficiency for the AI01 module in
March and July 2003. When it comes to comparing the daily efficiency for a single month, no
tendencies can be observed; but as it has been pointed out in the previous discussion, the
efficiency is slightly higher in March (mean value: 10.4 %) than in July (mean value: 9.5 %).

29


MARCH 2003
Measured energy <> ESTI irrad
14 Estimated ESTI energy <> ESTI irrad
12

10
Efficiency [%]

8

6

4

2

0
5 10 15 20 25 30
Days

Figure 24. Daily efficiency for AI01 in March 2003.

JULY 2003
12

10
Efficiency [%]

8

6

4

2

0
5 10 15 20 25 30
Days

Figure 25. Daily efficiency for AI01 in July 2003.

30


6.2 DR01 (monocrystalline)
The DR01 is a monocrystalline module with a surface area of 0.826 m2. The following
table shows the total energy produced by this module during 10 months (excluding January and
December) in 2003.

Energy, 10 months [W·h] Relative error [%]


Estimate: ESTI 103038 -2.65

Estimate: Pyran 103432 -2.28

Estimate: ESTI & NOCT 103062 -2.63

Estimate: Pyran & NOCT 103447 -2.27

Table V. Total measured energy and estimates for DR01 in 2003.

As the measurements for this module are also from 2003, there was a problem with the
ambient temperature sensor in December (see the comments for the AI01 module
measurements in the previous section).

The estimations using the ESTI irradiance are slightly worse than the ones using the
pyranometer. The four predicted values underestimate the energy produced by the module,
contrary to what happens in the case of the AI01 (where all the estimates are higher than the
measured energy).

The monthly energy production is shown in Fig. 26 and we can see that the energy in
November 2003 is again very low in accordance with the results obtained for the AI01 (see Fig.
17).

Fig. 27 shows the average daily energy (normalised values) for every single month (bars)
and for the whole year (horizontal line); the latter is around 370 W·h.

31


Year 2003
16000

14000

12000

10000
Energy [W·h]

8000

6000

4000
Measured energy

0
1 2 3 4 5 6 7 8 9 10 11 12 13
Months

Figure 26. Measured energy and estimates for DR01 in 2003.

DAILY AVERAGE 2003
700

600

500
Energy [W·h]

400

300

200
Mean daily energy
Measured energy
100

0
2 4 6 8 10 12
Months

Figure 27. Average daily energy for DR01 in 2003.

32


The average monthly energy for the DR01 is 11266 W·h (as shown in Fig. 28), this is a
much higher value than for the AI01 but it is necessary to take into account that the surface
area for the DR01 is a 68% larger than for the AI01.

16000

14000

12000

10000
Energy [W·h]

8000

6000

4000 Mean monthly energy
Measured energy

0
2 4 6 8 10 12
Months

Figure 28. Predicted energy for DR01 in 2003 taking into account the missing days.

The following two graphs show the total energy per day in March and July, as it was done
for the AI01 module. If we compare these graphs with the corresponding ones for the AI01 (this
is to say, Fig. 29 with Fig. 20 and Fig. 30 with Fig. 21), it can be seen that the corresponding
graphs look very similar, with the main difference being the scaling of the y axis. This gives
confidence in the good performance of the measuring system: days with low produced energy
for the DR01 are also days with low energy for the AI01.

33


MARCH 2003
700

600

500
Energy [W·h]

400

300
Measured energy

100

0
5 10 15 20 25 30
Days

Figure 29. Measured energy and estimates for DR01 in March 2003.

JULY 2003
700

600

500
Energy [W·h]

400

300

200

Measured energy

0
5 10 15 20 25 30
Days

Figure 30. Measured energy and estimates for DR01 in July 2003.

The following three graphs (Figs. 31 to 33) show efficiency values for the DR01 in 2003;
the first one for the whole year and the next two for March and July. The average monthly

34


efficiency is around 10.4% as we can see in Fig. 31, although if there were measurements for
January this value would be slightly higher since the efficiency tends to be higher during the
colder winter months.

Year 2003
12

10
Efficiency [%]

8

6

4

2

0
2 4 6 8 10 12
Months

Figure 31. Monthly efficiency for DR01 in 2003.

Comparing Fig. 32 with Fig. 33, it can be observed that the efficiency is higher in March
(winter) than in July (summer) as expected.

35


MARCH 2003
12

10
Efficiency [%]

8

6

4

2

0
5 10 15 20 25 30
Days

Figure 32. Daily efficiency for DR01 in March 2003.

JULY 2003
12

10
Efficiency [%]

8

6

4

2

0
5 10 15 20 25 30
Days

Figure 33. Daily efficiency for DR01 in July 2003.

36


6.3 LE02 (monocrystalline)
The LE02 is a monocrystalline module with a surface area of 0.4508 m2. For this module
there are no measurements available for a whole year, and therefore the energy comparisons
are carried out from July 2002 to mid February 2003.

Energy, 7½ months [W·h] Relative error [%]


Estimate: ESTI 29401 -0.75

Estimate: Pyran 29219 -1.37

Estimate: ESTI & NOCT 29395 -0.77

Estimate: Pyran & NOCT 29213 -1.39

Table VI. Total measured energy and estimates for LE02 from Jul 2002 to mid Feb 2003.

The predictions for the LE02 show an underestimation in all the cases, with the estimates
using the ESTI irradiance being better than the ones using the pyranometer. In any case, the
error is small for the four estimates.

The following two graphs show the energy produced by the LE02 during the last six
months of 2002 (Fig. 34) and January and the first half of February of 2003 (Fig. 35). Observing
both graphs it can be seen that the energy in November and December 2002 is quite low in
comparison with January 2003. The reason is that in these two months there are quite a lot of
days missing (10 in November and 14 in December), whereas in January there is only one day
missing. These missing days seem to be due to the low irradiance levels (as the system doesn’t
take measurements if the irradiance is lower than 50 W/m2) when examining the recorded data
file for the LE02.

37


Year 2002
8000
Measured energy

6000

5000
Energy [W·h]

4000

3000

2000

1000

0
1 2 3 4 5 6 7 8 9 10 11 12 13
Months

Figure 34. Measured energy and estimates for LE02 in 2002.

Year 2003
8000
Measured energy

6000

5000
Energy [W·h]

4000

3000

2000

1000

0
1 2 3 4 5 6 7 8 9 10 11 12 13
Months

Figure 35. Measured energy and estimates for LE02 in 2003.

38


The daily average for the LE02 module is about 147 W·h as can be seen in the next two
graphs, Figs. 36 and 37.

DAILY AVERAGE 2002
400
Mean daily energy
Measured energy

300

250
Energy [W·h]

200

150

100

50

0
2 4 6 8 10 12
Months

Figure 36. Average daily energy for LE02 in 2002.

DAILY AVERAGE 2003
400
Mean daily energy
Measured energy

300

250
Energy [W·h]

200

150

100

50

0
2 4 6 8 10 12
Months

Figure 37. Average daily energy for LE02 in 2003.

39


The two following graphs, Figs 38 and 39, show the predicted energy taking into account
the missing days, i.e. assuming the daily average for the days which were not measured due to
system faults. This gives proof that November and December 2002 were months with very low
overall irradiation values.

8000

7000

6000

5000
Energy [W·h]

4000

3000

2000 Mean monthly energy
Measured energy
1000

0
2 4 6 8 10 12
Months

Figure 38. Predicted energy for LE02 in 2002 taking into account the missing days.

8000
Mean monthly energy
Measured energy

6000

5000
Energy [W·h]

4000

3000

2000

1000

0
2 4 6 8 10 12
Months

Figure 39. Predicted energy for LE02 in 2003 taking into account the missing days.

40


Figs. 40 and 41 show the daily values of measured and estimated energy production for
the months of July 2002 and January 2003 respectively.

JULY 2002
400
Measured energy

300

250
Energy [W·h]

200

150

100

50

0
5 10 15 20 25 30
Days

Figure 40. Measured energy and estimates for LE02 in July 2002.

JANUARY 2003
400
Measured energy

300

250
Energy [W·h]

200

150

100

50

0
5 10 15 20 25 30
Days

Figure 41. Measured energy and estimates for LE02 in January 2003.

41


Having a look at the efficiency values for the LE02 shown in Figs. 42 and 43, we can
observe that these values are less than 10% for all the measured months, with an average
efficiency of 9.1% for the final six months of 2002 and 9.6% in the first two months of 2003.

Year 2002
12

10
Efficiency [%]

8

6

4

2

0
2 4 6 8 10 12
Months

Figure 42. Monthly efficiency for LE02 in 2002.

Year 2003
12

10
Efficiency [%]

8

6

4

2

0
2 4 6 8 10 12
Months

Figure 43. Monthly efficiency for LE02 in 2003.

42

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