MODELS AND RADIATION MEASUREMENTS FOR DELOCALIZED
PV MODULE PERFORMANCES ESTIMATION
S. Brofferio
Dipartimento. di Elettronica e Informazione, Politecnico di Milano
Piazza Leonardo da Vinci 32, 20133 Milano (Italy)
Tel. +39 02 23993577, Fax: +39 02 23993413, email: [email protected]
Abstract – Energy rating measurements of PV modules at their actual installation location are the
best assessment for reliable design and/or monitoring of PV plants. A methodology for the
estimation of maximum power for on-the-field conditions has been investigated and implemented.
It is based on a PV maximum power standard model and a power error correction model derived
from an adaptive artificial neural network. The on-the-field measurements of direct and diffused
radiations without shadowing ring, and the power correction model have been implemented in a
system for the estimation of the maximum power of any module in any place. The system consists
of two major parts: the local training and estimation station and the self powered remote
measurement system. The complete system can be upgraded for other applications in photovoltaic
plants and in remote monitoring stations.
Keywords: PV module modeling, PV energy rating
INTRODUCTION
Energy rating measurements of PV modules at their actual installation location are the best
assessment for reliable design and/or monitoring of PV plants. As this approach is too awkward due
to PV modules size and weight an alternative solution based on PV module performance models
and on-the-field environmental measurements is suggested. On the other side the current maximum
power models, based on data sheet or indoor laboratory measurements, are not satisfactory in most
operating conditions. In this paper a performance correction model using actual environmental
measurements is proposed. In the next section a simple maximum power model is reviewed and the
power correction model is introduced. In section three the basic simulation and experimental results
are discussed. In section four a new algorithm for the indirect measurement of diffused solar
radiation without shadow ring is presented. The last section presents the architecture of the system
implementing the proposed methodology.
THE MAXIMUM STANDARD AND CORRECTION POWER MODELS
The scientific and technical literature offers a large variety of maximum available power models
PM(G,Tm) as a function of global solar radiation G and module temperature Tm. We use the One
Diode Model (OMD) [1] as Maximum Power Standard Model (SMPM):
PM(G,Tm) = IscoG(Voco+VTolnG).FF(G,To).[1+(Tm-To)].
It needs only the Standard Test Conditions (STC) parameters: the short circuit current (Isco), the
open circuit voltage (Voco) and the maximum power temperature coefficient  the maximum power
Proceedings of the Solar Energy Tech 2010
ISBN 978-1-4467-3765-1
point current (IMo) and voltage (VMo) to determine the module thermal voltage (VTo).
From the I(V) curve of the ODM we have: VTo= (VMo-Voco)/ln(1-IMo/Isco).
Moreover: FF(G,To) ≈ [voco-ln(0,72+ voco)]/(1+ voco) where voco = Voco /VTo >10
The module temperature is Tm=Ta+ (NOCT-20)G/800 where NOCT is the Normal Operating Cell
Temperature, given by data sheets, and Ta the environment temperature. This model is a first
approximation; if the data sheets or laboratory measurements give more parameters better models
can be introduced [2], [3].
An experimental setup for the validation of the MPSM in operating conditions (Fig.1) consists of
the PV module under test, a Maximum Power Point Tracker (MPPT) for measuring its actual
maximum available power (PMm), G,, the diffused radiation Gd, Tm and Ta. The environmental
measurements allow the computation of PM(G,Tm), so that the power error PM of the MPSM under
test is:
PM = PMm - PM(G,Tm)
Ta
_
PM(G,Tm)
MPPT
Gd
PMe(G,Gd,Ta)
StandardMaximum
Power Model
(MPSM)
I,V
Tm
Training error
+
_
PMm
G
PV
PM
+
Power Correction
Model
(PCM)
G,Gd,Tm,Ta

PMm= PM(G;Tm)+PMe(G,Gd,Ta)
Figure 1. System for the validation of MPM, the definition and the training of the Power Correction Model (PCM)
T raining mode
 PM
M atching L ayer (M L )
IF(|P M - P S |/ P M > )  Pe H+1 = P M
E stim ation mode
 P M e (G ,G d,T a) =  P S
 PS
O utput Layer (O L ) P S =F(x, z ji; i= 0÷2) see 1) in Appendix
j,i
 Pe 1
C om petition L ayer (C L)
j 0 =argm in(|x-w h | h= 1÷H )
P e h
1
 Pe H
 PM
H
H +1
h
wh
x
Input layer (IL)
Input vector: x = (G , G d ,T a )
G
Gd
Ta
Figure 2. The PCM layered architecture
Different values of PM for the same (G,Ta) conditions have been found, this is due to the influence
of other factors as the diffused radiation, wind, etc; in this research we focus on fist one only.
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The error PM is used to train the Power Correction Model (PCM). It based on a supervised
adaptive artificial neural network (Fig.2) for optimal piecewise linear interpolation of PM whose
number of nodes depends on the desired precision; this is obtained by the adaptation threshold  (
=0,05÷0,9) [4]. The PCM input are the operating environmental conditions G, Gd, and Ta its output
is PMe(G,Gd,Ta), so that the estimated maximum available power at the actual operating
conditions is:
PMe(G,Ta) = PM(G,Tm)+PMe(G,Gd,Ta)
SIMULATIONS AND EXPERIMENTAL RESULTS
A specific thin film module technology was selected to validate its MPSM and to train the
corresponding PCM. As we are interested in the impact of the diffused radiation we experimented
with a micromorph module MCPH 105W of PRAMAC SWISS [5]. Its MPSM has been verified in
two conditions: the laboratory tests of the producer and at the Dipartimento di Elettronica e
Informazione (DEI).
First the maximum power PM of the producer tests has been compared with the MPSM with
parameters at STC with the well known result that the MPSM is valid with constant radiation in the
whole range of temperatures but is not valid at constant temperature with different values of
radiation.
Table Ia. Environmental conditions at DEI
G
Mean val.
St.dev.
Gd
Ta;
Tm
[W/m2]
[°C]
795,2 177,3 25,6 45,0
210,0 99,6 0,7
3,7
Then, in order to evaluate the impact of the actual operating conditions on the validity of the
MPSM we performed 34 measurements at different environmental conditions (Table Ia), in spring
2010 on the terrace of our Department, using the MPPT3K monitoring system of ISAAC [6] and a
shadowing ring for the measurement of Gd. The measured (PMmeas.) and the modelled performances
given by th MPSM (PMmodel) show the necessity of the PCM (Table.Ib).
Table Ib. PV module performances at DEI
Mean val.
St.dev
Voc
[V]
113,8
1
Isc
[A]
0,87
0,19
VM
[V]
83,7
1,7
PMmeas. PMmodel
IM
[W]
[A]
[W]
78,7
0,74
61,6
23,8
0,17
13
err%
27,8
83,1
Results of the experiments with PCM
The neural network has been trained using the MPSM with parameters at STC to estimate the
actual performances at DEI conditions. Table IIa shows that each PM is corrected by a PCM with
=0,2 and 12 hidden nodes which represent the vertex points of the piecewise linear interpolation.
Moreover Table IIb shows, for different values of the number of nodes and the corresponding
mean error.
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Table IIa. Benefits of the PCM implemented by the PCM with =0,2
Mean power
St. dev
PMmeas
78,7
23,8
PM
-17,5
11,2
PMest
61,2
12,9
%err
0,55
1,83
Table IIb. Effects of threshold  on the number of nodes and on estimation error

N.of nodes
%err
0,01
27
0,035
0,05
18
0,20
0,1
14
0,34
0,2
12
0,53
0,5
8
0,88
Modelling the diffused radiation
The previous experimental results confirm the necessity of using the diffuse radiation for a
satisfactory power estimation. We verified the model of the diffuse solar radiation (God) proposed
by Liu-Jordan [7], it assumes that Gdo is a function of the global radiation only. The daily diffuse
2
energy solar radiation (Wh/m .day) given by the Liu-Jordan model is:
Gdo=G(1,39-4,037 K+5,331 K2-3,018 K3 ) and K= G/Go.
2
where G (Wh/m .day) is the global energy radiation, Go= r.Io.H is the theoretical energy radiation
without atmospheric scattering attenuation; r and H account respectively for the current day EarthSun distance and sunlight hours [8]. We compared this model with the measurements of the
Osservatorio Meteorologico Duomo of July 2009 at their facility at Politecnico di Milano. The very
poor results (Table III) show that direct diffused radiation Gd measurements are always necessary.
Table III. Daily measured radiations G and Gd and estimated by Liu-JordanGdo
Radiations
Mean
St. dev..
Gd
Gdo
|Gd-Gdo|/Gdo
Wh/(m2d)
%
7319,59 2277,03
1106,07
51,24
854,27 576,10
414,66
16,25
G
AN ALGORITHM FOR SOLAR RADIATION COMPONENTS MEASUREMENT
The current methods for diffused radiation measurement require a shadowing ring that has to be
periodically tilted to track the sun; they are expensive, bulky and not suited for remote
measurements. We propose a method based on radiation measurements on a set of differently
oriented surfaces. The global radiation G is the sum of the direct radiation Gdir and the isotropic
diffused radiation Ghdif so that only two measurements of the global radiation on two differently
oriented planes are necessary for indirect measurement of Gdir and Ghdif (Fig.3). Using a vertical
plane southward oriented and an horizontal plane respectively capturing the global radiation GS and
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GZ we have (Fig.3):
Direct radiation: Gdir =(2GS –GZ)/(2nx-nz):
Diffused radiation on the horizontal plane: Ghdif = 2(nx GZ – nz GS)/(2nx-nz).
More complex estimations are based on up to five measurement planes [4]
Gdir.
nS
z
nm
y
x
Gm= nm.nSGdir.+ Gmdif.
Sun direction: nS=(nx,ny,nz); normal vector: nm
Figure 3. Relationships of solar radiations components: global (Gm), direct (Gdir) and diffuse (Gmdif)
THE SYSTEM
The PCM and the radiation measurement algorithm allow the definition of a system for the
estimations of the PV module performances (Fig.4) consisting of two parts:
a) the Local Training and Estimation Station (LTES): it includes the Maximum Power Point
Tracker (MPPT), the measurements equipment and the personal computer (PC).
b) the Remote Measurement System (RMS); it is handy and includes a photovoltaic power supply,
the environmental data sensors, GPS and GSM. The measurements of solar radiation
components without shadow ring and of temperatures are transmitted to PC which handles
also status and alarm communication.
Ta
Application
Sensors
G1
G2
C
GPS/
GSM
PV Charger
& Battery
Remote Measurement System (RMS)
Ta
PV
G
Telecom
Network
Gd
MPPT& Measurements
System
Training &
Estimation
PC
Local Training and Estimation Station (LTES)
Figure 4. The System architecture
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The system operates in two modes:
a) Training mode: evaluation of MPSM and training of the PCM;
b) Estimation mode: computation of the maximum module power by the LTES using the data
received from the RMS.
Suggested system expansions
The RMS can become the kernel of two applications in the sector of the photovoltaic industry:
1) An Antitheft System consisting of the RMS and a pulse transceiver located at the end of a
chain of PV modules. The pulses monitor the continuity of the PV modules cables and
immediately detect the theft of a module, of coarse during night;
2) A Handy Monitor System of the module efficiency in an operating PV plant. The system
measures the current and the voltage at the terminals of the module and computes its
efficiency using its MPSM and the trained PCM.
CONCLUSIONS
The paper has presented a model for upgrading maximum power standard models suited for actual
operating conditions using an adaptive algorithm for power error correction. The prototype of a
remote measurement device for direct and diffused radiations, based also on a new algorithm, is
being completed (Gallo fotovoltaico). Its precision and industrial costs have to be evaluated. A
system for delocalized PV module performances evaluation is also being implemented.
The remote solar radiation estimation system could be manufactured as a consumer product suited
also for applications beyond the photovoltaic sector as a general purpose monitoring system.
ACKNOWLEDGEMENTS
The author warmly thanks: PRAMAC SWISS for laboratory experimental data, ODM for the
radiations data, QSD for implementing a system prototype and Ing. Federico Mariotti for useful
discussions modules performances models.
REFERENCES
[1] M.A. Green: Solar Cells, Operating Principles, Technologies and System Applications Prentice
Hall (1982) and The University of South Wales Press (1998)
[2] W. Heydenreich et al.: Describing the World with Three Parameters: a New Approach to PV
Module Power Modelling, 23rd European Photovoltaic Solar Energy Conference, 1-5
September 2008, Valencia, Spain
[3] G. Friesen et al.: Energy Rating Measurements and Prediction at ISAAC, 22th European
Photovoltaic Solar Energy Conference, Sept. 2007, Milano (Italy)
[4] S. Brofferio, G. B Galimberti, L. Trollo, F. Mariotti: Models, Measurements and the “Gallo
Fotovoltaico: A System For The Estimation Of On-The-Field Pv Module Performances, 25th
European Photovoltaic Solar Energy Conf. / Wcpec-5, Valencia (Spain), September 6-10, 2010
[5] LUCEMCPH Technical Data Sheet: www.pramac.com
[6] MPPT3K: www.bipv.ch
[7] B.Y., R.C. Jordan: The Interrelationship and Characteristic Distribution of Direct, Diffuse and
Total Radiation, Solar Energy Vol. 4. 1960
[8] F.Groppi, C. Zuccaro: Impianti solari fotovoltaici a norme CEI, Editoriale Delfino (2007)
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