report pv module performance

i

Susana Iglesias Puente, R. Kenny, T. Huld

RENEWABLE ENERGIES UNIT

ii

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

iii

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

iv

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]

DEVELOPMENT OF MATLAB SOFTWARE TO ANALYSE AND PREDICT PV MODULE PERFORMANCE

1

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.


2

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.


3

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).


4

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.


5

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 .


6

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.


7

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.


8

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.

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45 50

voltage [V]

curr

ent

[A]

0

10

20

30

40

50

60

70

po

wer

[W

]

ISC

VOC

IMPP

VMPP

MPPPMAX

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.

MPPMPPMAX I V P ⋅= (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.

SCOC

MPPMPP

IV

IVFF

⋅⋅= (2)


9

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:

( )( ) mod

2mod

maxlnln1

ln

TfIrreIrrd

TcIrrbaP

⋅+⋅+⋅+⋅+⋅+= (3)

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


10

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

Module

Tem

pera

ture

[oC

]

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

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.

0100

200300

400500

600700

800900

Irr [W/m²]

20253035

40455055

Temp [ºC]

0 0

10 10

20 20

30 30

40 40

50 50

60 60

Pm

ax

[W]

Pm

ax

[W]

AI01 IndoorRank 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=76302.371a=-0.93125496 b=0.40257114 c=-0.0040224985 d=-0.26053276 e=0.017375655 f=0.00010847924

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


11

Irradiance [W/m2]

50 100 150 200 250 300 400 500 600 700 800 900 1000

Module

Tem

pera

ture

[oC

]

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.

0 100200

300400

500600

700800

9001000

Irr [W/m²]

2530

3540

4550

55

Temp [ºC]

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

8080

9090

100100

Pm

ax [W

]

Pm

ax

[W]

DR01 IndoorRank 206 Eqn 1132 z=(a+blnx+cy)/(1+dlnx+e(lnx)^2+fy)

r^2=0.99847376 DF Adj r^2=0.99838974 FitStdErr=1.1141195 Fstat=14392.486a=-1.5675042 b=0.61558713 c=-0.0043817042

d=-0.26677134 e=0.018194163 f=9.2588895e-05

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


12

Irradiance [W/m2]

50 100 150 200 250 300 400 500 600 700 800 900 1000

Module

Tem

pera

ture

[oC

]

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.

0100

200300

400500

600700

800900

Irr [W/m²]

202530354045505560

Temp [ºC]

00

55

1010

1515

2020

2525

3030

3535

4040

4545

5050

Pm

ax [W

]

Pm

ax [W

]

LE02 IndoorRank 211 Eqn 1132 z=(a+blnx+cy)/(1+dlnx+e(lnx)^2+fy)

r^2=0.99975409 DF Adj r^2=0.99974068 FitStdErr=0.21054764 Fstat=90255.133a=-0.88101569 b=0.36032919 c=-0.0033567692 d=-0.25694536 e=0.016878253 f=0.000113601

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.


13

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:

ambTIrrNOCT

T +⋅

−=800

20mod (4)

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.


14

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).


15

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

than the cell temperature.

Figure 11. Temp. 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


16

remains at short circuit current ISC to monitor irradiance and the other half remains at open

circuit voltage VOC to monitor cell temperature.

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.

ESTI sensor Pyranometer


17

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.


18

� 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.


19

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.


20

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.


21

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.

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:

( ) 100·

% ⋅⋅

=)(mareasurfacemodule)(W·h/msunthefromcomingEnergy

h)(WmodulethebyproducedEnergyEfficiency 22

(5)

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.


22

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.


23

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.


24

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.


25

1 2 3 4 5 6 7 8 9 10 11 12 130

1000

2000

3000

4000

5000

6000

7000

8000

9000Year 2003

Months

Ene

rgy

[W·h

]

Measured energy Empirical ESTI energy Empirical ESTI & Tmod energy

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.


26

2 4 6 8 10 120

50

100

150

200

250

300

350

400DAILY AVERAGE 2003

Months

Ene

rgy

[W·h

]

Mean daily energy Measured energy Empirical ESTI energy Empirical ESTI & Tmod energy

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.


27

2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

7000

8000

9000MONTHLY ESTIMATES 2003

Months

Ene

rgy

[W·h

]

Mean monthly energy Measured energy Empirical ESTI energy Empirical ESTI & Tmod energy

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).

5 10 15 20 25 300

50

100

150

200

250

300

350

400MARCH 2003

Days

Ene

rgy

[W·h

]


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


28

5 10 15 20 25 300

50

100

150

200

250

300

350

400JULY 2003

Days

Ene

rgy

[W·h

]


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.

2 4 6 8 10 120

2

4

6

8

10

12

14

Year 2003

Months

Eff

icie

ncy

[%]

Mean efficiency ESTI Measured energy <> ESTI irrad Estimated ESTI energy <> ESTI irrad Estimated ESTI & Tmod energy <> ESTI irrad

Figure 22. Monthly efficiency for AI01 in 2003.


29

1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

40

45

50

Months

Tem

pera

ture

(ºC

)

AMBIENT AND MODULE TEMPERATURE FOR AI01 IN 2003

Ambient temperature Measured module temperature Estimated module temperature

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 %).


30

5 10 15 20 25 300

2

4

6

8

10

12

14

MARCH 2003

Days

Eff

icie

ncy

[%]

Measured energy <> ESTI irrad Estimated ESTI energy <> ESTI irrad Estimated ESTI & Tmod energy <> ESTI irrad

Figure 24. Daily efficiency for AI01 in March 2003.

5 10 15 20 25 300

2

4

6

8

10

12

14

JULY 2003

Days

Eff

icie

ncy

[%]


Figure 25. Daily efficiency for AI01 in July 2003.


31

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.


32

1 2 3 4 5 6 7 8 9 10 11 12 130

2000

4000

6000

8000

10000

12000

14000

16000Year 2003

Months

Ene

rgy

[W·h

]


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

2 4 6 8 10 120

100

200

300

400

500

600


Months

Ene

rgy

[W·h

]


Figure 27. Average daily energy for DR01 in 2003.


33

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.

2 4 6 8 10 120

2000

4000

6000

8000

10000

12000

14000


Months

Ene

rgy

[W·h

]


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.


34

5 10 15 20 25 300

100

200

300

400

500

600

700MARCH 2003

Days

Ene

rgy

[W·h

]


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

5 10 15 20 25 300

100

200

300

400

500

600

700JULY 2003

Days

Ene

rgy

[W·h

]


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


35

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.

2 4 6 8 10 120

2

4

6

8

10

12

14

Year 2003

Months

Eff

icie

ncy

[%]


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.


36

5 10 15 20 25 300

2

4

6

8

10

12

14

MARCH 2003

Days

Eff

icie

ncy

[%]


Figure 32. Daily efficiency for DR01 in March 2003.

5 10 15 20 25 300

2

4

6

8

10

12

14

JULY 2003

Days

Eff

icie

ncy

[%]


Figure 33. Daily efficiency for DR01 in July 2003.


37

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.


38

1 2 3 4 5 6 7 8 9 10 11 12 130

1000

2000

3000

4000

5000

6000

7000

8000Year 2002

Months

Ene

rgy

[W·h

]


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

1 2 3 4 5 6 7 8 9 10 11 12 130

1000

2000

3000

4000

5000

6000

7000

8000Year 2003

Months

Ene

rgy

[W·h

]


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


39

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.

2 4 6 8 10 120

50

100

150

200

250

300

350


Months

Ene

rgy

[W·h

]Mean daily energy Measured energy Empirical ESTI energy Empirical ESTI & Tmod energy

Figure 36. Average daily energy for LE02 in 2002.

2 4 6 8 10 120

50

100

150

200

250

300

350


Months

Ene

rgy

[W·h

]


Figure 37. Average daily energy for LE02 in 2003.


40

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.

2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

7000


Months

Ene

rgy

[W·h

]


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

2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

7000


Months

Ene

rgy

[W·h

]


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


41

Figs. 40 and 41 show the daily values of measured and estimated energy production for

the months of July 2002 and January 2003 respectively.

5 10 15 20 25 300

50

100

150

200

250

300

350

400JULY 2002

Days

Ene

rgy

[W·h

]


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

5 10 15 20 25 300

50

100

150

200

250

300

350

400JANUARY 2003

Days

Ene

rgy

[W·h

]


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


42

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.

2 4 6 8 10 120

2

4

6

8

10

12

14

Year 2002

Months

Eff

icie

ncy

[%]


Figure 42. Monthly efficiency for LE02 in 2002.

2 4 6 8 10 120

2

4

6

8

10

12

14

Year 2003

Months

Eff

icie

ncy

[%]


Figure 43. Monthly efficiency for LE02 in 2003.


43

The daily efficiency values for July 2002 and January 2003 are shown in Figs. 44 and 45.

For some days in July 2002, the efficiency is even lower than 9%.

5 10 15 20 25 300

2

4

6

8

10

12

14

JULY 2002

Days

Eff

icie

ncy

[%]


Figure 44. Daily efficiency for LE02 in July 2002.

5 10 15 20 25 300

2

4

6

8

10

12

14

JANUARY 2003

Days

Eff

icie

ncy

[%]


Figure 45. Daily efficiency for LE02 in January 2003.


44

7 ENERGY PREDICTION ON PV-GIS WEB SITE

Solar irradiation is a key factor determining electricity produced by PV systems. At

http://re.jrc.cec.eu.int/pvgis/pv/ we can find a solar radiation database of Europe developed

in the Geographical Information System (GIS) and three interactive web applications. The

database includes monthly and yearly average values for an assessment of the potential PV

electricity generation.

In the first web application, a user may browse radiation maps and query irradiation

incident on a PV module for different inclination angles. These maps are obtained by using the

data from weather stations all over the European subcontinent. The second application

simulates daily profiles of irradiance for a chosen month and module inclination and

orientation.

Figure 46. Solar irradiation map for the European subcontinent based on monthly averages.

The third web application estimates electricity generation for a chosen PV configuration.

To achieve this, geospatial data are combined with known correlations (similar to Eq. 3,

obtained also from the indoor measurements) for the estimation of the performance of

crystalline silicon modules under varying irradiance and temperature over large regions.

In Fig. 47 a graph of the estimated monthly production from a PV system, as calculated

by the PV estimation web application, is shown. The horizontal line in the graph represents the

average monthly production during the year.


45

Figure 47. Monthly energy prediction on PV-GIS web site.

Applying a GIS approach, the performance of crystalline silicon PV modules can be

estimated within a large geographical region. The results are made available for PV industry,

professionals and for the general public.

At this point, our aim is to establish if we can use monthly average data for the purposes

of energy rating. The reason for this is that the PV GIS system described above is based on

monthly averages of temperature and irradiation, while the outdoor experiments have

demonstrated the accuracy of the energy rating approach using real time data (sampled at 4 or

5 minute intervals). It is therefore necessary to find out the accuracy of the estimations of the

energy predictions using the same approach as used in the PV GIS system.

In order for a comparison to be made which identifies only the effect of the averaging

method it is necessary for data from the same time period and location to be used. The meteo

tower (situated at the JRC, Ispra) measures irradiance and ambient temperature data, sampling

once per minute. From this data monthly averages of in-plane irradiance and ambient

temperature are calculated. Then, assuming that for every day in a single month the values are

the same, daily variations at in-plane irradiance and ambient temperature are simulated.

These simulations use the movements of the sun to estimate the instantaneous irradiance at

any given time, while the instantaneous ambient temperature is simulated based on typical

cyclical daily temperature variations*. The energy production for the module AI01 in 2003 was

then calculated using these instantaneous values in Eq. 3.

_______________________________________________________

* Performed by Thomas Huld from the Renewable Energies Unit.


46

Estimates for the module AI01 for every month in 2003, as well as the measured and

predicted values using the irradiance given by the pyranometer, are shown in Table VII. In this

case, the estimate using the pyranometer irradiance was chosen instead of the one using ESTI

irradiance as the device that measures this variable in the meteo tower is also a pyranometer.

MMoonntthh Measured

energy [W·h]

Estimate

PV-GIS [W·h]

Relative error

[%]

Estimate

Pyran [W·h]

Relative error

[%]

Jan 4500 4518 0.4 4648 3.3

Feb 6007 5545 -7.7 6214 3.4

Mar 7831 6958 -11.1 8018 2.4

Apr 6751 5941 -12.0 6854 1.5

May 8659 7427 -14.2 8593 -0.8

Jun 7006 7750 10.6 6925 -1.2

Jul 8202 7671 -6.5 8136 -0.8

Aug 7471 7694 3.0 7354 -1.6

Sep 5554 6562 18.1 5513 -0.7

Oct 3546 4776 34.7 3553 0.2

Nov 1328 1429 7.7 1339 0.8

Dec 3513 3920 11.6 3594 2.3

TOTAL 70367 70195 -0.2 70740 0.5

Table VII. Comparison of measured energy values with estimates based on average monthly irradiance and Tamb data for AI01 in 2003.

The estimates given by the empirical equation using the pyranometer irradiance are quite

good at predicting the total monthly energy and the overall error is small (less than 1%).

When it comes to evaluate the closeness of the estimates using average irradiance and

ambient temperature values, this is to say, the estimates calculated in the same way the

predictions on the PV-GIS web site are carried out, we can see that the errors are really high

for some months although the total error for the whole year is acceptable. In this way, we can

conclude that the “PV-GIS type” prediction is good for a long period of time but not for single

months.


47

8 CONCLUSIONS

8.1 Developed software

The developed software makes possible to treat the data from the outdoor measurements

systematically, this is to say, in the same way (more objectively) for all the panels. Moreover,

different data sets of different lengths and from different modules can be easily analysed.

Nevertheless, the program is flexible as it can be modified to carry out the analysis in a

different way, expanded to perform new tasks by adding new functions or simply improved to

make it more user-friendly.

The use of this specific software allows the user to get the results in far less time than

employing a spreadsheet. At the same time, the results are more reliable as in a spreadsheet it

is easier to make some mistakes or get confused analysing a huge amount of data.

The program can function correctly with missing data: it doesn’t matter if there are no

measurements for several days in one month or even for some months, the program will not

crash or give wrong results. However, it is important for the user to clearly understand the

internal operation of the software in order to correctly interpret the output data.

8.2 Module performance predictions

Three crystalline (two mono and one poly) modules have been analysed. The following

table summarizes their main features, as well as the main parameters that show the module

performance.

AI01 DR01 LE02

Technology poly-Si mono-Si mono-Si

Surface area, [m2] 0.491 0.826 0.450

Average monthly energy, [W·h] 6375 11266 4482

Monthly energy/area [W·h/m2] 12984 13639 9960

Average efficiency, [%] 10.1 10.4 9.2

Table VIII. Module performance comparison for the 3 analysed modules.

From Table VIII it can be seen that the DR01 is more efficient and produces more energy

for unit of surface area compared to the LE02; despite the two of them being manufactured

with the same technology. This high performance for the DR01 is due to being a much newer

module than the LE02.

Regarding the estimates, the empirical equation from the solar simulator gives good

predictions compared with long term outdoor measurements. The relative error for the

estimates is always less than 3% as it can be seen in Table IX.


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Energy prediction using… AI01 DR01 LE02

ESTI irradiance 0.04 -2.65 -0.75

Pyran irradiance 0.47 -2.28 -1.37

ESTI irr & NOCT 0.09 -2.63 -0.77

Table IX. Relative error [%] for the energy estimates obtained using Eq.3 for the 3 analysed modules.

The predictions are better in the case of the polycrystalline module (AI01). Also, for the

polycrystalline module all the predictions overestimate the energy produced by the module

whereas in the case of the monocrystalline modules (DR01 and LE02) we have underestimations.

Comparisons with estimates based on average irradiance and temperature data (i.e. PV-

GIS) are very encouraging for long term energy predictions (relative error: -0.2%). This proves

the validity of using monthly averages for energy rating purposes.

8.3 Personal experience

During these six months of working experience I learned quite a lot about how PV

modules work. Helping with outdoor and indoor measurements was very useful for me to

understand the behaviour of solar panels. Moreover, this field experience was also important in

the development of the software to treat the outdoor data. On one hand, the outdoor

measurements were helpful to keep me in contact with the nature of the data and to

understand their importance for the module performance. On the other hand, the indoor

measurements showed me how to obtain experimentally the equation to estimate Pmax.

Obviously, I also improved a lot my programming skills.

As well as the scientific knowledge acquired, my stay at the JRC was a unique

opportunity to work in a multicultural environment as well as a good way to improve my English

noticeably.

Thanks to my supervisor Dr. Robert Kenny for his help and support in my daily work, to

Dr. Thomas Huld and to all my other colleagues of the Renewable Energy Unit for their help

during my stay in the unit.


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9 SUGGESTED SOFTWARE IMPROVEMENTS

The software presented in this report is awaiting some important improvements; the

outstanding ones that should be carried out are the following:

� Not all the measurements have been performed during the same number of hours per

day. Therefore, it is not accurate to compare the total energy per day without taking

this into account. It becomes necessary, then, to check the number of hours during

which the measurements were done for every day. On the other hand, if there is a big

interval of time during which the recording system was not working (e.g. ∆t > 6 min),

it is not precise realize the integration of Pmax to obtain the energy. The days for

which there are few measurements should be eliminated.

� When there are measurements for only a few hours or even any during a day, it is

difficult to know if it is because the irradiance was below 50 W/m2 (in which case the

system doesn’t take measurements) or if there was any other problem. To solve this,

it would be interesting to have a look at the record of irradiance values given by the

pyranometer in the meteo tower.

� Potentially, many graphs could be made to represent the data in different ways.

Some have already been made, some others that could be useful are: the irradiance

given by the two different kinds of irradiance meters, the BIAS error for the different

estimated values of energy in comparison to the real value, the mean value for the

month or for the year could be added to the already existing graphs (as a horizontal

line).

� The three different modules, for which the software was employed, were fitted to

the same empirical equation (Eq. 3) to estimate Pmax. So, the equation was

implemented in the main program (Solar_data_treatment). In order to make the

software more versatile there should be taken into account that this equation can

change depending on the module that is being analysed.

� The estimation of the Nominal Operating Cell Temperature (NOCT) is carried out with

all the Tmod, Tamb and irradiance values measured. A few of them are not good as can

be seen in the fitting graph (Fig. 14). It would be desirable to eliminate these bad

measurements and to perform the fitting again.

� The NOCT is, as already mentioned, the theoretical temperature of the module for an

ambient temperature of 20 ºC and an irradiance of 800 W/m2. Therefore, it would be

interesting to calculate the instantaneous values of Pmax using the NOCT and to

perform the integration over the whole year to compare the result with the real

annual value.


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10 LIST OF FIGURES

Figure 1. Map of the different institutes of the JRC. ..................................................... 2 Figure 2. View of the JRC location in Ispra on the shore of Lago Maggiore. ........................ 3 Figure 3. Monocrystalline silicon cell. ....................................................................... 7 Figure 4. Polycrystalline silicon cell. ........................................................................ 7 Figure 5. Typical I-V curve and P-V curve. ................................................................. 8 Figure 6. 3-D visualisation of the indoor measured matrix & fitted performance surface, AI01. 10 Figure 7. 3-D visualization of the indoor measured matrix & fitted performance surface, DR01.

..................................................................................................................... 11 Figure 8. 3-D visualization of the indoor measured matrix & fitted performance surface, LE02.12 Figure 9. View of the outdoor measurement site at the JRC. ......................................... 14 Figure 10. Outdoor measurements on the rack; .......................................................... 15 Figure 11. Temp. sensor on the back of the module. ................................................... 15 Figure 12. Experimental setup for irradiance measurement. .......................................... 16 Figure 13. Example of text file storing experimental data for several years. ...................... 17 Figure 14. Experimental (points) and empirical (line) values of Tmod for AI01. ..................... 20 Figure 15. Structure of a 3-D array. ........................................................................ 21 Figure 16. M-file containing the calculated monthly variables for AI01 in 2003. ................... 23 Figure 17. Measured energy and estimates for AI01 in 2003. .......................................... 25 Figure 18. Average daily energy for AI01 in 2003. ....................................................... 26 Figure 19. Predicted energy for AI01 in 2003 taking into account the missing days. ............. 27 Figure 20. Measured energy and estimates for AI01 in March 2003. .................................. 27 Figure 21. Measured energy and estimates for AI01 in July 2003. .................................... 28 Figure 22. Monthly efficiency for AI01 in 2003. ........................................................... 28 Figure 23. Ambient and module (AI01) temperature profiles in 2003. ................................ 29 Figure 24. Daily efficiency for AI01 in March 2003. ...................................................... 30 Figure 25. Daily efficiency for AI01 in July 2003. ........................................................ 30 Figure 26. Measured energy and estimates for DR01 in 2003. ......................................... 32 Figure 27. Average daily energy for DR01 in 2003. ...................................................... 32 Figure 28. Predicted energy for DR01 in 2003 taking into account the missing days. ............. 33 Figure 29. Measured energy and estimates for DR01 in March 2003. ................................. 34 Figure 30. Measured energy and estimates for DR01 in July 2003. ................................... 34 Figure 31. Monthly efficiency for DR01 in 2003. ......................................................... 35 Figure 32. Daily efficiency for DR01 in March 2003. ..................................................... 36 Figure 33. Daily efficiency for DR01 in July 2003. ....................................................... 36 Figure 34. Measured energy and estimates for LE02 in 2002. .......................................... 38 Figure 35. Measured energy and estimates for LE02 in 2003. .......................................... 38 Figure 36. Average daily energy for LE02 in 2002. ....................................................... 39 Figure 37. Average daily energy for LE02 in 2003. ....................................................... 39 Figure 38. Predicted energy for LE02 in 2002 taking into account the missing days. ............. 40 Figure 39. Predicted energy for LE02 in 2003 taking into account the missing days. ............. 40


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Figure 40. Measured energy and estimates for LE02 in July 2002. .................................... 41 Figure 41. Measured energy and estimates for LE02 in January 2003. ............................... 41 Figure 42. Monthly efficiency for LE02 in 2002. .......................................................... 42 Figure 43. Monthly efficiency for LE02 in 2003. .......................................................... 42 Figure 44. Daily efficiency for LE02 in July 2002. ........................................................ 43 Figure 45. Daily efficiency for LE02 in January 2003. ................................................... 43 Figure 46. Solar irradiation map for the European subcontinent based on monthly averages. .. 44 Figure 47. Monthly energy prediction on PV-GIS web site. ............................................. 45