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THERMAL MODELS FOR PHOTOVOLTAIC MODULES IN THE BIPV APPLICATIONS
G.M. Tina
Department of Electric, Electronic and Systemistic Engineering – University of Catania
Viale A. Doria 6, 95125 Catania - Italy
G. Notton
‘Systèmes Physiques de l’Environnement’ Laboratory, University of Corsica,
UMR CNRS 6134, Route des Sanguinaires, F-20000 Ajaccio, France
ABSTRACT: The operation temperature of photovoltaic (PV) modules changes constantly with the ambient variables
(temperature, irradiance, wind speed and direction) as well as electrical operation point. In literature many papers
describe models which estimate PV module temperature as a static one and on hourly time base but, in this paper, in
order to establish a suitable model to monitor the temperature in a shorter time interval (i.e. a few minutes), a
comparison among three dynamic models have been carried out. In these models many parameters have to be fixed
starting from both manufacturer data and experimental tests. Numerical and experimental results, reported in this
paper, refer to a semi-transparent PV module, where some thermal sensors are installed. This type of PV module is
widely used as facades, roof or shading devices in office and commercial buildings.
Keywords: Photovoltaic module, thermal model, efficiency
1
INTRODUCTION
Photovoltaic (PV) systems are becoming larger and
more diffused. Nowadays different solutions are
technically and economically feasible such as building
integrated
photovoltaic
systems
(BIPVs)
and
concentrating PV systems. In these systems the PV cell
temperature can be a critical variable. Moreover, it is well
known that most of the solar radiation absorbed by a PV
module is not converted to electricity but contributes to
increasing the temperature of the module, thus reducing
its electrical efficiency. However, there are special
systems called hybrid Photovoltaic - Thermal (PV/T)
collectors where the thermal energy produced by the PV
cells is used to produce either hot water or hot air [1]. To
predict the energy production of PV modules, it is
necessary to evaluate the module temperature as a
function of environmental variables. Studies show that
there are many methods to calculate the module
temperature: in [2] the method is based on a simple
energy balance, where there is a parameter (empirically
determined) that depends on the wind speed, in [3]
starting from the temperature measured in the back of the
PV module, the method determines an expression to
calculate the cell temperature. The most well-known
method is based on the knowledge of NOCT (Normal
Operating Cell Temperature), that is provided by the PV
module manufacturers. But this simple method is the
most approximate, especially if the operating temperature
of free-standing PV arrays is predicted as it is a straight
proportion between the ∆T (cell temperature minus
ambient temperature) and G (irradiance) and it does not
take into account the real ventilation of the PV modules.
The simplifying hypothesis assumed in the NOCT
methodology, seems at first prohibitive for the use in the
BIPV modelling/design area. In other models ([4], [5],
[6], [7]) the panel is considered formed by a single layer,
so one equation to describe it is used, whereas in [8] and
[9], the PV panel is divided into horizontal sections and
an equation of the thermal balance is written for each
layer. When evaluating the efficiency of a PV system, the
temperature variations are often regarded as
instantaneous or use hourly steady state models.
However, the changes in temperature due to varying solar
radiation levels do not occur immediately. The PV
module heats up and cools down gradually from step
changes in solar radiation changes, following an
exponential response. If the power output from PV
module is modeled in short time periods, for example, on
a minute by minute basis, the temperature response
becomes considerably more important compared to the
period of interest. In this context, it is crucial to
determine the thermal time constant of a PV module (i.e.
the time taken for the panel temperature to reach 63% of
the total change in temperature in response to a step
change in the solar radiation). It ranges roughly from 5
min to 15 min, depending on the PV composition and
mounting arrangements.
In order to develop a suitable multi layer
thermal model of PV modules that can be used in BIPV
applications, and in particular to on-line applications (e.g.
monitoring or diagnostic), a comparison between three
models of the literature ([8]÷[10]) is reported.
2
THERMAL MODELS OF PV MODULES
Normally a PV module is encased in glass, the
entire ensemble consists of five mediums: glass, resin,
silicon, resin and glass. However, as the optical and
thermal properties of glass and resin are almost identical
and the thickness of the resin is very small, only three
mediums must be considered, glass, silicon and glass.
The following three isothermal regions are considered
(see Fig. 1): front (glass), central (silicon) and the rear
one (glass)
Back Glass (bg)
EVA
Glass Fibre
Cells (PV)
EVA
Front Glass (fg)
Figure 1 Layers of a PV module with the correspondent
subscripts.
Some common hypothesis are considered in the
following models:
- The exchanges heat from the sides of the
photovoltaic module are negligible (this assumption
may be less true in the case of modules with
aluminum frame, it is very realistic in the case of
panel without frame).
- All of the thermal materials properties considered
homogeneous, are independent of temperature.
- The part of solar radiation that is not converted
into electrical energy is absorbed by cells as heat.
- The thermal exchange among cells and EVA are
negligible.
- The ambient temperature is postulated as equal on
all sides of the module.
The models consider each layer as a homogenous
slab, thus in the layer which contains both PV cell and
glass fiber (see Fig. 1), calculation is carried out
assuming it as a layer of PV cell. However, it is clear that
PV cell and glass do not have the same thermal
behaviour. Thus, this difference is accounted for in the
models
by
adjustment
of
the
radiation
absorption/transmission factor of the layer according to
the percentage area of PV cell and fiber glass.
Verification with field measurement data proved it is a
sufficient representation of the actual thermal behaviour
of a semi-transparent PV panel [9].
The considered models are one-dimensional they are
made of a serial assembling of one-dimensional
elementary models, which explains the essential
thermal transfers. In fact, for each layer just one
temperature is
assigned, so distribution of the
temperature along the three dimensions of the module is
neglected. A more detailed model is reported in [9],
where the heat balance at the centre of each layer is
calculated.
The thermal mechanisms of a PV panel can be
considered in terms of their electrical equivalents by
correlating the electrical resistance and capacitance to the
thermal resistance qTh and thermal capacitance CTh. The
heat balance at each node is equivalent to a current
Kirchhoff law. The equivalent circuit is reported in Fig.
2, where both current and voltage ideal generators are
reported. The resistances determine the thermal steady
state answer of the PV module, whereas the capacitances,
together with resistances, intervene during the transients.
Using the electrical circuit, five equations can be
written at the corresponding nodes: T’fg (outside surface
of front glass), Tfg (internal temperature of front glass),
TPV (temperature of central layer, Tbg (internal
temperature of back glass), T’bg (external temperature of
back glass), whereas a circuit, made up of three nodes is
used in [8] and [10] (see Fig. 3).
Figure 2 five nodes equivalent electrical circuit of a PV
module
Tsky
Tgro
qr,fg,sky
qr,fg,gr
Tfg
qcd,fg
Ta
qconv,fg
Cfg
qcd,PV
TPV
1
2
CPV
qcd,bg
Cbg
Tbg
qr,bg,sky
qr,bg,gr
Tsky
Tgro
qconv,bg
Ta
Figure 3: three nodes equivalent electrical circuit of a
PV module
Actually the voltage generator “Tsky” (temperature of the
atmospheric filter) is complex and rarely available,
several expressions allows to calculate this temperature
depending on Ta and other atmospheric variables (air
pressure and humidity) [8].
It was made a comparison between three models in
literature [8 ], [9] and [10]. In particular the model
reported in [10], has been improved with the introduction
of the thermal capacities of the module. The symbols
used in the equations are different in the three references,
so they have be changed into the corresponding ones
used in [8]. So the set of equations is the following:
εg J
1+ cos β
1− cos β
1+ cos β
1− cos β
+εg Jg
≅ εg J
+ε g J
= εg J
2
2
2
2
(4)
Where
J g : ground-emitted longwave radiation,
(1)
(2)
Jg is assumed
as equal to J.
εg is the glass emissivity
The expression in the parenthesis accounts for correction
factor of outdoor long-wave radiation absorption in a
sloped panel. The first phrase
shows
absorption of the downwards longwave radiation while
the second phrase
(3)
Each equation has been normalized respect with the
Surface of layer that in this case, of course, are equal. On
the other hand, it is worth noticing that the current “Φ2”
has to be calculated considering that the global
photovoltaic surface is smaller than the surface of the
module. The studied models present many differences in
the expressions of the coefficients of the set of first order
differential equations; in particular the coefficients that
model the convective heat transfer from the PV panel
surface show the most important differences. Generally,
in the literature, we note a wide discrepancy in the value
taken for the convective coefficient [11].
In the following some other differences concerning the
radiative coefficients and the flux received per unit area
by the PV cells are described.
2.1 frontal layer
In the frontal layer, the main differences among the
studied models are about the radiative terms, the
correspondent terms are reported in Table 1.
Table 1 thermal balance of frontal layer: radiative
terms
shows absorption of the
ground-emitted longwave radiation, though essentially it
adds up to 1. It means that the radiative term between
front glass and ground is included in (4)
J, i.e. the atmospheric radiation, is a long wave radiation
emitted by the atmosphere with an almost constant
amount throughout the day. It does not contribute to PV
power generation but it heats up the panel, thus it is
included in the thermal equilibrium. Moreover, it is a
measured entity given in the weather data, thus we do not
need to calculate it from the sky temperature or other
weather data.
The amount of thermal radiation from the PV panel only
depends on its temperature and emissivity, but not on the
surrounding temperature so the sky temperature is not
included in the equation.
[10]: the radiative term between front glass and ground
does not appear because the experiments were ran with
the PV module in a horizontal position, but it was also
neglected because not only the difference of temperature
between front glass and ground normally is small but also
the optimal tilt angle of the modules in the regions where
the yearly solar radiation is high enough the tilt angle
ranges from 0 (equator) to 35-40 ° (mid latitude) so the
configuration factor between the front glass and cover
and the ground ranges from 0 to 0.3. Also the
configuration factors do not appear.
2.2 Central layer
In central layer the main difference is into the energy flux
Φ2 on the photovoltaic cells (i.e. the current generator in
figures 2 and 3). The correspondent terms are reported in
Table 2
[8]
Not
[9]
present
Table 2 Thermal balance of central layer
[8]
[9]
[10]
qr , fg , sky =
4
σ ⋅ ε g ⋅ (Tfg4 − Tsky
)
Tfg − Ta
Not
[10]
present
Some remarks about the expressions reported in Table 1
are reported:
[9]: Concerning the radiative component it is made of
two terms. The first one assumes the following
expression, where the two configuration factors appear:
2.3 Rear layer
In the rear layer, the main differences among the studied
models are about the radiative terms, the correspondent
terms are reported in Table 3
experimental ones. The model [9] underestimates the PV
module temperatures.
Table 3 Thermal balance of the rear layer
[8]
[9]
45
Not present
model [8]
model [9]
model [10]
measurements
40
Not present
[10]
Not present
35
T P V [ °C ]
30
3. VALIDATION OF THE MODELING
25
20
The photovoltaic module tested is a Photowatt PWX 500
using multi-crystalline technology with a thickness of 0.2
mm. The encapsulation of cells is made between two
sheets of tempered glass with high transmittance. The
dimension of the module is 1042 mm · 462 mm · 39 mm.
The peak power at a junction temperature equal to 25 °C
is 49 W at ±10% the electrical efficiency for this module
is equal to ηref = 0.13 at 25 °C and this reference for the
efficiency will be used to calculate the electrical
production of the PV module. Eight thermal sensors have
been integrated into the module during its manufacturing:
the first one measures the temperature on the back
surface of the glass cover, another one measures the
temperature on the back surface of the module and six
other sensors measure the temperature on six points on
the back surfaces of cells [8].
The evolution and of the other environmental parameters:
solar irradiance in the plane of the panel, ambient
temperature and wind speed are plotted in Fig. 5, whereas
the front and back glass temperatures, and the cells
temperature are in Fig. 6.
100
15
10
5
0
0.5
1
1.5
Time [sec]
2
2.5
3
4
x 10
Figure 7: Evolution of the central layer: mathematical
models and measurements
4. CONCLUSIONS AND PERSPECTIVES
This paper presented three thermal models available in
the literature to describe the behaviour of the PV cell
temperature. Two models [8] and [10] give similar results
in good accordance with experimental data although the
assumptions used in these models are different.
Such modelling is very useful to predict the productivity
of PV module specially when they are integrated in
building and compare it with the real production in same
meteorological conditions.
The final objective of ths work consists in developing a
prediction model easily usable in on-line applications
(e.g. monitoring or diagnostic).
90
5
80
REFERENCES
70
60
50
40
30
20
10
0
0
80
160
240
Time (min.)
320
400
480
Figure 5: Evolution of the environmental parameters
(percentage values): irradiance (Gmax=909 W/m2, blue
line), temperature (Tmax=15.17 °C, red line, dash-dot),
wind speed (vmax=5.2 m/s, green line, dash)
45
40
Temperature (°C)
35
30
25
20
15
10
5
0
0.5
1
1.5
Time (sec)
2
2.5
3
4
x 10
Figure 6: Evolution of the PV module temperatures:
front glass (blue line), central layer (red line), back glass
(green line)
We note that there is a good accordance between the
modeled temperatures from [8] and [10] and the
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[3] D.L. Field experience with a new performance
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59
Nomenclature of subscript
a = ambient
bg = back glass cover
PV = photovoltaic
cd = conduction
conv = convention
fg = front glass cover
gro = ground
g = glass
pv = photovoltaic
r = radiative
ref = reference conditions
sky = sky