Determination of the working temperature of photovoltaic (PV) modules is an essential task in research and engineering projects. It acquires more relevance in the current environment, characterized by increasing figures of installed PV power, module efficiency, solar applications, and operational configurations. However, most of the current procedures for temperature determination of PV modules are simply based on empirical correlations, carried out at conditions defined by some specific standards, with the corresponding lack of accuracy when modules work under real conditions. Thus, the present work looks into a formal procedure for temperature determination by conducting a power balance between the dynamic incoming and outgoing power fluxes. Some additional parameters are included when compared with classic expressions. In particular, the spectral reflectance of the tandem glass-semiconductor is measured to determine the reflected fraction of solar irradiance. The relationship between reflectance and equilibrium temperature is determined for a representative group of PV modules, and the influence that the working point exerts on the module temperature has also been taken into account. Finally, the influence of spectral distribution on module temperature has been quantified by simulations carried out by using a spectral model. In this way, determination of absolute temperature is achieved within a ±2°C range, regardless of module characteristics and climatic or operational conditions. In addition, temperature differences between PV modules that work under the same external conditions can be predicted within ±0.5°C. To summarize, a thermal model suitable for different PV modules and working configurations is presented. Some new parameters are introduced in the calculus process, and the influence of the most relevant ones has been quantified. In this way, the present work is aimed at making a contribution to the study of PV module temperature.

1.
Fuentes
,
M. K.
, 1984, “
Thermal Modelling of Residential Photovoltaic Arrays
,”
Proceedings of the 17th IEEE PVSC
, pp.
1341
1346
.
2.
Chenlo
,
F.
, 2002,
Cálculo de la Temperatura de Operación de Células Solares en un Panel Fotovoltaico Plano
,
Ciemat
,
Madrid
.
3.
Servant
,
J. M.
, 1985, “
Calculation of the Cell Temperature for Photovoltaic Modules From Climatic Data
,”
E.
Bilgen
and
K. G. T.
Hollands
, eds.,
Proceedings of the Ninth Biennial Congress of the ISES—Intersol 85
, Montreal, Canada, extended abstracts, p.
370
.
4.
Jones
,
A. D.
, and
Underwood
,
C. P.
, 2001, “
A Thermal Model for Photovoltaic Systems
,”
Sol. Energy
0038-092X,
70
(
4
), pp.
349
359
.
5.
Prorok
,
M.
,
Kołodenny
,
W.
,
Zdanowicz
,
T.
,
Gottschalg
,
R.
, and
Stellbogen
,
D.
, 2008, “
Reducing Uncertainty of PV Module Temperature Determination Based on Analysis Using Data Gained During Outdoor Monitoring
,”
Proceedings of the 23rd EU-PVSEC
, Valencia, pp.
2865
2871
.
6.
de la Breteque
,
E. A.
, 2009, “
Thermal Aspects of c-Si Photovoltaic Module Energy Rating
,”
Sol. Energy
0038-092X,
83
, pp.
1425
1433
.
7.
Skoplaki
,
E.
, and
Palyvos
,
J. A.
, 2009, “
Operating Temperature of Photovoltaic Modules: A Survey of Pertinent Correlations
,”
Renewable Energy
0960-1481,
34
, pp.
23
29
.
8.
International Electrotechnical Commission
, 2005, “
Crystalline Silicon Terrestrial Photovoltaic (PV) Modules—Design Qualification and Type Approval
,” International Standard IEC 61215, Ed. 2.
9.
Duffie
,
J. A.
, and
Beckman
,
W. A.
, 2006,
Solar Engineering of Thermal Processes
,
3rd ed.
,
Wiley
,
Hoboken, NJ
.
10.
Gee
,
J. M.
, and
Schubert
,
W. K.
,
Tardy
,
H. L.
,
Hund
,
T. D.
, and
Robison
,
G.
, 1994,
The Effect of Encapsulation on the Reflectance of Photovoltaic Modules Using Textured Multicrystalline-Silicon Solar Cells
,
First WC-PEC
.
11.
ASTM Standard G173-03, 2003, “
Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface
,” ASTM International, West Conshohocken, PA.
12.
Lienhard
,
J.
, IV
, and
Lienhard
,
J.
, V
, 2004,
A Heat Transfer Textbook
,
3rd ed.
,
Phlogiston
,
Cambridge, MA
.
13.
Bejan
,
A.
, and
Krauss
,
A.
, 2003,
Heat Transfer Handbook
,
Wiley
,
New York
.
14.
Martín
,
N.
, and
Ruiz
,
J. M.
, 2001, “
Calculation of the PV Modules Angular Losses Under Field Conditions by Means of an Analytical Model
,”
Sol. Energy Mater. Sol. Cells
0927-0248,
70
, pp.
25
38
.
15.
Martín
,
N.
, and
Ruiz
,
J. M.
, 2005, “
Annual Angular Reflection Losses in PV Modules
,”
Prog. Photovoltaics.
,
13
, pp.
75
84
.
16.
Rohsenow
,
M.
,
Hartnett
,
P.
, and
Cho
,
I.
, 1998,
Handbook of Heat Transfer
,
3rd ed.
,
McGraw-Hill
,
New York
, pp.
25
27
, Table 1.10.
17.
Colburn
,
A. P.
, 1933, “
Method of Correlating Forced Convection Heat Transfer Data and Comparison With Fluid Friction
,”
Trans. Am. Inst. Chem. Eng.
0096-7408,
29
, pp.
174
210
.
18.
Churchill
,
S. W.
, and
Ozoe
,
H.
, 1973, “
Correlations for laminar forced convection in flow over an Isothermal flat plate and in developing and fully developed flow in an isothermal tube
,”
ASME J. Heat Transfer
0022-1481,
95
, pp.
416
419
.
19.
Churchill
,
S. W.
, and
Chu
,
H. H. S.
, 1975, “
Correlating Equations for Laminar and Turbulent Free Convection From a Vertical Plate
,”
Int. J. Heat Mass Transfer
0017-9310,
18
, pp.
1323
1329
.
20.
Fujii
,
T.
, and
Imura
,
H.
, 1972, “
Natural Convection Heat Transfer From a Plate With Arbitrary Inclination
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
755
764
.
21.
Schott
,
T.
, 1985, “
Operational Temperatures of PV Modules
,”
Proceedings of the Sixth PV Solar Energy Conference
, pp.
392
396
.
22.
Swinbank
,
W. C.
, 1963, “
Long Wave Radiation From Clear Skies
,”
Q. J. R. Meteorol. Soc.
0035-9009,
89
, pp.
339
348
.
23.
Daguenet
,
M.
, 1985, “
Les séchoirs solaires, théorie et pratique
,” UNESCO.
24.
Aubinet
,
M.
, 1994, “
Long Wave Sky Radiation Parametrization
,”
Sol. Energy
0038-092X,
53
(
2
), pp
147
154
.
25.
Adelard
,
L.
,
Pignolet-Tardan
,
F.
,
Mara
,
T.
,
Lauret
,
P.
,
Garde
,
F.
, and
Boyer
,
H.
, 1998, “
Sky Temperature Modelisation and Applications in Building Simulation
,”
Renewable Energy
0960-1481,
15
, pp.
418
430
.
26.
NIST ITS-90 Thermocouple Database 60, 2000, based on NIST Monograph 175, Web Version 2.0, July, National Institute of Standards and Technology, U.S. Commerce Department.
27.
Osterwald
,
C. R.
,
et al.
, 2006, “
Resistive Loading of Photovoltaic Modules and Arrays for Long-Term Exposure Testing
,”
Prog. Photovoltaics
1062-7995,
14
, pp.
567
575
.
28.
International Standard IEC 60904-3, 2008, “
Photovoltaic Devices. Part 3: Measurement Principles for Terrestrial Photovoltaic (PV) Solar Devices With Reference Spectral Irradiance Data
,” Ed. 2.0, International Electrotechnical Commission.
29.
Bird
,
R. E.
, and
Riordan
,
C. J.
, 1986, “
Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres
,”
J. Clim. Appl. Meteorol.
0733-3021,
25
(
1
), pp.
87
97
.
You do not currently have access to this content.