Pergamon
PII: S0038 – 092X( 01 )00091 – 3
Solar Energy Vol. 72, No. 1, pp. 63–73, 2002
 2002 Elsevier Science Ltd
All rights reserved. Printed in Great Britain
0038-092X / 02 / $ - see front matter
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A PHOTOVOLTAIC / THERMAL (PV/ T) COLLECTOR WITH A POLYMER
ABSORBER PLATE. EXPERIMENTAL STUDY AND ANALYTICAL MODEL †
BJØRNAR SANDNES ‡ and JOHN REKSTAD
Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
Received 20 June 2000; revised version accepted 20 July 2001
Communicated by BRIAN NORTON
Abstract—A polymer solar heat collector was combined with single-crystal silicon PV cells in a hybrid
energy-generating unit that simultaneously produced low temperature heat and electricity. The PV/ T unit was
tested experimentally to determine its thermal and photovoltaic performance, in addition to the interaction
mechanisms between the PV and thermal energy systems. Thermal efficiency measurements for different
collector configurations are compared, and PV performance and temperature readings are presented and
discussed. An analytical model for the PV/ T system simulated the temperature development and the
performance of both the thermal and photovoltaic units.  2002 Elsevier Science Ltd. All rights reserved.
shared (Loferski et al., 1982). The total area
devoted to solar collectors is also reduced.
PV/ T systems have not seen the intensive
research and development activity documented for
thermal and photovoltaic collectors separately
(Duffie and Beckman, 1991; de Winter, 1990;
Fahrenbruch and Bube, 1983; Zweibel, 1990).
Work has however included some experimental
studies (Fujisawa and Tani, 1997; Garg et al.,
1994; Lalovic´ et al., 1986) and also theoretical
modeling of PV/ T systems (Bergene and Løvvik,
1995; Florschuetz, 1979; Sopian et al., 1996),
giving performance results and predictions for
different collector designs and model parameters.
The aims of the present study were threefold:
firstly to design and build a PV/ T test collector
using single-crystal silicon cells in combination
with a solar heat absorber in polymer plastics.
Secondly to conduct experimental trials on the
test collector to establish its thermal and photovoltaic performance, and also to investigate the
interaction mechanisms between the two energy
systems. And thirdly to employ an analytical
model for the combined system by modifying
well-known models for flat-plate collectors to
include effects of the additional solar cells and the
geometry of the particular absorber that was used.
1. INTRODUCTION
Solar heat collectors can be combined with photovoltaic cells to form hybrid energy generating
units that simultaneously produce low temperature
heat and electricity. The radiant energy from the
sun is partly converted to electricity by photovoltaic cells in thermal contact with a solar heat
absorber, and excess heat generated in the photovoltaic cells serves as input for the thermal
system. During operation a heat carrier fluid
removes heat from absorber and cells. These solar
cells, cooled by the heat carrier, operate at a low
and stable temperature that gives increased solar
cell power output since photovoltaic conversion
efficiency is a linearly decreasing function of
temperature (Wysocki and Rappaport, 1960;
Saidov et al., 1995). The collected heat can be
utilized in, for example, domestic hot water
systems or as space heating.
The photovoltaic / thermal (PV/ T) collector also
offers economical advantages compared to a
combination of separate thermal and photovoltaic
panels. The transparent cover and supporting
frame are components the two panels have in
common, and in a combined system these are
2. THE PV/ T COLLECTOR
†
This article was originally intended to be published as part of
the Special Issue ‘Selected Proceedings of EuroSun 2000’
[Solar Energy 69 (Suppl.) (1–6), 2000]
‡
Author to whom correspondence should be addressed.
Tel.:
147-2285-6459;
fax:
147-2285-6422;
e-mail: bsand@fys.uio.no
A combined photovoltaic / thermal (PV/ T) collector was constructed by pasting single-crystal
silicon cells onto a black plastic solar heat absorber. The PV cells are extremely brittle, and
63
64
B. Sandnes and J. Rekstad
have a considerably lower thermal expansion
coefficient than the polymer material. A silicon
adhesive was therefore used that was sufficiently
elastic to absorb the difference in thermal expansion between the cells and the plastic absorber,
and a thin adhesive layer ( | 0.5 mm) ensured
acceptable thermal contact.
Thirty PV cells (1.5 Wp each) were arranged in
six rows of five cells, as illustrated in Fig. 1,
giving a total PV unit area of 0.32 m 2 . The six
rows were separated into two equal units of 15
series-connected cells, allowing the two units to
be connected in series (30 cells in series), or
alternatively used in parallel. The absorber surface
temperature increases in the direction of flow, that
is from top to bottom for this system (see
description below). The cells with highest measured short-circuit current, Isc , were therefore
placed at the top of the panel, followed by cells of
decreasing Isc towards the bottom. Since increased
temperature gives slightly higher current output
from the cells, this placing minimizes the difference in current output, thus increasing the overall
efficiency when the cells are connected in series
(Reiche et al., 1994).
The solar heat collector used for the PV/ T
system was developed as a joint venture by
Fig. 1. Interconnected PV cells pasted on the absorber plate in
six rows of five cells. The three top rows can be disconnected
from the three bottom rows to form two submodules. Also
shown are measurement points for PV cell temperatures T 1 and
T 2 and absorber plate temperature T 3 .
SolarNor AS, the University of Oslo and General
Electric Plastics. The absorber plate of modified
polyphenylenoxid (PPO) plastics contains internal, wall-to-wall channels filled with ceramic
granulates (Fig. 2) (Henden et al., 2000). The
heat carrier fluid (water) is pumped up to an
internal distribution channel at the top of the
collector, and, by force of gravity, flows down
through the parallel absorber channels. Water fills
the vacant space between the ceramic particles
and is brought in contact with the top absorber
sheet, enabling good heat transport from absorbing surface to heat carrier fluid. The fluid flow in
the square wall-to-wall channels covers the entire
back of the absorber surface, resulting in a
uniform temperature distribution across the width
of the absorber.
The absorber plate of the PV/ T collector was of
width 0.59 m and length 0.82 m. The radiation
absorptance for the PPO material is a 5 0.94 at
incidence angle normal to the surface (Henden et
al., 2000). A glass cover was used instead of the
polycarbonate cover sheet normally installed with
this collector type due to the superior optical
properties of glass. The thickness of the glass
plate was 4 mm, and the transmittance at incidence angle normal to the surface | t 5 0.9. The
distance between the absorber and the glass plate
was |1.2 cm.
The SolarNor heat collector is a component of
an overall energy system that aims at minimizing
exergy loss by keeping the system temperature as
close to the application temperature as possible
(Rekstad et al., 2000). A low system temperature
is also favorable for the PV/ T collector since the
photovoltaic conversion efficiency decreases with
temperature.
Fig. 2. The SolarNor collector. The absorber of PPO plastic
contains internal, wall-to-wall channels filled with ceramic
granulates (source: SolarNor, 1996).
A photovoltaic / thermal (PV/ T) collector with a polymer absorber plate
3. EXPERIMENTAL METHOD
The combined PV/ T collector was tested experimentally in a series of field trials to determine
its thermal and photovoltaic performance, in
addition to the coupling between the two energy
systems. The experimental system consisted of
collector, storage tank (30 l), tubing and circulation pump. Measured parameters included irradiation I, storage tank temperature T i , ambient air
temperature T a , PV cell temperatures T 1 and T 2 ,
and absorber plate temperature T 3 (Fig. 1). Irradiation and temperature readings were logged at
intervals of 2 min 22 s during the experiments.
The data sets were smoothed (5 point averaging)
before calculations in order to reduce fluctuations,
and the efficiency analysis was based on clear sky
periods with reasonably constant irradiation. PV/ T
thermal efficiency, hT , was calculated from energy
balance analysis of the system, where the wellinsulated storage tank acts as a calorimeter. The
photovoltaic conversion efficiency, hPV , was determined from measured current–voltage (IV )
characteristics at different temperatures, with irradiance and cell temperature recorded.
Three collector configurations were tested to
investigate how the thermal performance is affected by converting a solar heat collector to a
combined PV/ T system. The absorber plate has
two identical sides of which one was covered with
PV cells and hence constituted the combined
photovoltaic / thermal absorber (PV/ T). The other
side, the black absorber plate, was tested for
comparison to a ‘pure’ thermal system (T). A
cover glass was later mounted on the PV/ T
absorber in a configuration referred to as the
glazed PV/ T absorber (PV/ Tg). The back-side of
the collector was insulated with 5-cm-thick mineral wool for all configurations. The PV cells were
not operated during thermal performance experiments. The relative effect of PV electrical output
on thermal efficiency was investigated by running
the PV/ T thermal system with the PV module in
an alternating on / off cycle.
Maximum power point PV efficiencies were
found from IV-characteristics taken for both series
connection of all 30 cells, and for parallel connection of the two submodules. Characteristics
were taken when the PV/ T absorber had reached
stagnation temperature (no circulation of fluid, no
cooling), and also after the start of thermal
operation at low temperature, thus determining the
effect of cooling on the temperature-dependent
PV efficiency under the prevailing conditions. PV
cell temperatures were also logged during the
65
thermal performance experiments to investigate
correlations between cell temperature and ambient / system parameters.
Thermistors (Dale 9M1002-C3 (10 K)) with an
accuracy of 60.28C from 230 to 908C and a
SolData photoelectric pyranometer (no. 289HD)
were used in conjunction with a data logger
(SolDat Tattle Tale Lite) for the temperature and
irradiation measurements. A set of nine power
resistors (Series HS50, ELFA), with resistances
ranging from 0.68 to 15.0 V, were used to
measure the current–voltage characteristics of the
solar cells. The total experimental error was
estimated to 10% for both thermal and photovoltaic efficiency data based on an analysis of
combined error from all measured parameters.
4. DATA ANALYSES
Standard test procedure is to report collector
thermal efficiency based on measurements of inlet
and outlet temperature and flow-rate. Constant
inlet fluid temperature and incidence radiation
nearly normal to the collector plane eliminates
effects of heat capacity, system components and
angle of incidence dependencies. The small temperature difference between inlet and outlet is
however difficult to measure with desired accuracy in small (and low-efficient) systems, and this
motivates the calorimetric experimental set-up
that measures total system energy uptake based on
storage tank temperature readings (Henden et al.,
2000). The collector thermal efficiency, hT , including stored specific heat, is obtained from
energy flow analysis of the system (Fig. 3), giving
QU 1 QS QT 1 QL 2 QP 1 QS
hT 5 ]]] 5 ]]]]]].
AI
AI
(1)
The total heat collected in the storage tank Q T is
determined from the derivative of the measured
storage tank temperature T i . The amount of
energy stored as specific heat in the collector
plate, Q S , can similarly be calculated from the
derivative of the collector plate temperature which
can be approximated by the derivative of the
storage tank temperature. The heat loss from the
tank is determined as
E
Q L 5 (UA) tank (T i 2 T a ) dt
(2)
where (UA) tank is the heat transfer coefficient for
the storage tank (measured independently). Q P is
the constant heat input from a circulation pump
submerged in the storage tank.
The collector absorbs less energy at higher
66
B. Sandnes and J. Rekstad
Fig. 4. Thermal efficiency data and average efficiency curves
for the three collector configurations: thermal absorber (T)
(circles, solid line), photovoltaic / thermal absorber (PV/ T)
(triangles, dashed line) and photovoltaic / thermal absorber
with additional cover glass (PV/ Tg) (squares, dotted line).
Fig. 3. The energy flow in the experimental system. The
collected energy results in useful energy gain, Q U , and energy
stored in the collector as specific heat, Q S . The total energy
collected in the storage tank, Q T , is the sum of the useful
energy gain, the input from the pump, Q P , and the storage tank
heat loss, Q L .
radiation incidence angle as the reflection from
the surface increases. One way to compensate for
this, is to equally reduce the measured irradiation
by a modifying factor, Kta (u ), which is a function
of the angle of incidence, u (Duffie and Beckman,
1991). Corrections must only be performed when
the angle dependency of the pyranometer and the
collector surface is significantly different. The
following assumptions were made: no corrections
necessary for the black absorber and the PV/ T
absorber since the angle of incidence behavior of
the absorber and pyranometer is not significantly
different, and the absorbing surface of the
pyranometer is a silicon PV cell, as are the
collector cells. When the cover glass was added to
the system (glazed PV/ T absorber), additional
reflection from the glass was introduced which
was corrected for. u was determined as a function
of time of day and subsequently used to calculate
the incidence angle modifier, Kta (u ), with the
incident angle modifier coefficient b 0 5 2 0.1 for
glass (Duffie and Beckman, 1991).
5. RESULTS
The collector instantaneous thermal efficiency
was calculated according to Eq. (1) for each
experiment, with corrections as described in the
previous section. Experimental data for the ther-
mal absorber, T, the PV/ T collector and the
glazed PV/ Tg collector are plotted against (T i 2
T a ) /I in Fig. 4. The Hottel–Whillier equation
expresses the collector thermal efficiency as a
linearly decreasing function of the parameter
(T i 2 T a ) /I:
Ti 2 Ta
hT 5 FR (ta ) 2 FRUL ]]
I
(3)
(Duffie and Beckman, 1991; Hottel and Whillier,
1958). A linear curve fit to the experimental data
points for each individual day gave the intersection with the y-axis, FR (ta ), and the slope of the
curve, FRUL , which are listed in Table 1. The date
for the experiments and the collector configurations T, PV/ T and PV/ Tg are indicated. The
linear efficiency curves plotted in Fig. 4 illustrate
the average values of the thermal efficiency
parameters FR (ta ) and FRUL from Table 1 for the
different collector configurations.
The following observations are made based on
the efficiency plots in Fig. 4. The black absorber
Table 1. Thermal efficiency parameters (intersection FR (ta ),
and slope FRUL ) for all days of experiment
Date (d.m.y)
Collector
FR (ta )
FR U L
R
19.09.97
15.10.97
16.10.97
20.10.97
27.10.97
29.10.97
03.11.97
T
PV/ T
T
PV/ T
PV/ T
PV/ Tg
PV/ Tg
0.87
0.77
0.84
0.79
0.72
0.70
0.72
18.2
16.2
14.7
17.4
11.0
8.1
8.5
0.99
0.95
0.95
0.97
0.97
0.95
0.88
The collector configurations are indicated in the table:
thermal absorber (T), photovoltaic / thermal absorber (PV/ T)
and photovoltaic / thermal absorber with additional cover glass
(PV/ Tg). R is variance explained by linear dependency
A photovoltaic / thermal (PV/ T) collector with a polymer absorber plate
plate (T) absorbs radiation most efficiently. Covering the absorber with photovoltaic cells (PV/ T)
reduces the energy absorptance of the collector,
and the heat loss coefficient is slightly lower
compared to the absorber only situation. The
effect of adding a glass cover plate (PV/ Tg) to
the collector, is to reduce the heat loss to the
surroundings, but the energy absorptance of the
system is also reduced by reflection from the glass
surface.
Scattering of the data points are mainly due to a
rather long sampling interval (2 min 22 s) for the
irradiation readings and also the higher order
temperature effects on the collector parameters.
Irregular irradiation on the 03.11.97 produced the
large scattering in the PV/ Tg data. The effect of
wind on heat loss is particularly important for
unglazed collectors, which may partly explain
observed differences in heat loss as wind speed
was not recorded during the experiments.
The thermal system was logged with the PV
cells both on and off, and the resulting thermal
efficiency is plotted in Fig. 5. (The ‘smooth’
transition between PV on or off is an artifact of
the data averaging procedure.) Extracting electrical power from the PV module reduces the
available solar energy and thus thermal efficiency
for the heat collector. The efficiency reduction is
|10% as seen from the graph. The electrical
power output was calculated from the measured
voltage over a power resistor of 6.8 V. The
average electrical power output from the PV
]
module was P 5 32.3 W. The experiment was
stopped during the second round of PV output
because of shading from clouds.
The I–V characteristics plotted in Fig. 6 show
the effect of cooling on the photovoltaic output
67
Fig. 6. IV-characteristics for series (square symbol) and parallel (circle) combination of the submodules at cell temperatures
of 188C (dashed lines) and 528C (solid lines).
for both series and parallel connection of submodules. The average cell temperature was re]
]
duced from T c 5528C to T c 5188C, a temperature
difference of DT c 5348C, by operating the heat
collector with cold water (T water ¯10–128C). The
average insolation was during this experiment
]
I 5 749 W/ m 2 , and the ambient air temperature
8–98C. Fig. 6 illustrates the most pronounced
temperature effect as a decrease in the open
circuit voltage, Voc , which is due to the diode
reverse saturation current which increases exponentially with temperature (Fahrenbruch and
Bube, 1983; Wysocki and Rappaport, 1960;
Saidov et al., 1995).
The photovoltaic efficiency, hPV , of the collector is calculated from the maximum power points
found visually from the I–V curves:
ImpVmp
hPV 5 ]].
A cI
(4)
Table 2 lists Vmp , Imp and hPV for the series (S)
and parallel (P) arrangements with corresponding
]
average cell temperature T c (with and without
cooling). The results show a relative decrease in
hPV of 0.07% / K and 0.1% / K for the series and
parallel combinations, respectively. Note that PV
efficiency results are based on total cell area, not
the area of the collector.
Table 2. Maximum power point voltage Vmp , current Imp and
photovoltaic efficiency hPV for series (S) and parallel (P)
combination of cells. T c is average cell temperature
Fig. 5. PV/ T collector thermal efficiency, with and without
PV power output.
S/P
T c (8C)
Vmp (V)
Imp (A)
hPV (%)
S
P
S
P
18
18
52
52
14.69
6.93
11.19
5.28
2.16
4.62
2.39
4.59
13.3
13.4
10.9
9.9
68
B. Sandnes and J. Rekstad
Hottel–Whillier model a fin efficiency F 5 1,
which simplifies the expression for the collector
efficiency factor F9:
1
F9 5 ]]].
UL
11]
h
(7)
For the combined system with PV cells pasted on
part of the absorber surface, the heat transfer
coefficient, h, can be calculated as a weighted
mean of the absorber and the PV cell heat transfer.
The amount of solar energy available for the
thermal system is reduced since electrical energy
is extracted from the solar cells:
Fig. 7. Fluid inlet temperature (solid line), average measured
cell temperature (dotted line) and theoretical cell temperature
(thin solid line) for the PV/ Tg system, 03.11.97.
]
The average measured PV cell temperature, T c
is in Fig. 7 plotted against time, together with
storage tank temperature T i for one of the experiments (03.11.97). Also plotted in the figure is
theoretical cell temperature T c , calculated as a
function of T i , the thermal efficiency of the
collector, hT , and irradiation I:
T c 5 T i 1 khT I
(5)
S
D
Ac
S 5 (ta ) eff I 5 (ta ) 2 hPV ] I.
A
(8)
The transmittance–absorptance product, (ta ), is
assumed equal for the absorber plate and PV cells.
The photovoltaic conversion efficiency, hPV , is
temperature dependent, but because this temperature effect on S is small, and the time dependency
leads to a differential equation not easily solved,
hPV is assumed constant in the model. The solar
irradiation was represented by a second order
polynomial that was fitted to experimental data
for each individual day
I(t) 5 g0 1 g1 t 1 g2 t 2 .
where
1 2 FR
k 5 ]]
FR U L
(6)
in terms of the model parameters. The constant k
was in Eq. (5) used to fit the curve manually to
the experimental data for each day. hT was
calculated according to Eq. (3) with the characteristics from Table 1 inserted for each day
separately. The expression for the cell temperature
in Eq. (5) is a reformulation of the mean absorber
plate temperature as calculated by Duffie and
Beckman (1991).
6. ANALYTICAL MODEL
A PV/ T system analytical model was developed based on the equations for the fin-tube
collector configuration outlined in Duffie and
Beckman (1991) and Hottel and Whillier (1958),
but modified to include the effects of integrated
solar cells and also a different absorber plate
design (Bergene and Løvvik, 1995).
The square, ‘wall-to-wall’, fluid channels of the
absorber plate used in this study ensures (ideally)
that the fluid flow covers the entire back side of
the absorber surface. This gives in terms of the
(9)
The solar energy collector delivers its useful
energy gain, Q U , to the storage tank, with additional heat input from the pump, Q P 5 K. Limited
by the heat loss to the surroundings, Q L , the total
thermal energy stored in the fluid becomes:
QT 5 QU 2 QL 1 QP.
(10)
With expressions inserted:
dT i
mCp ] 5 AFRf(ta ) eff I(t) 2 UL (T i 2 T a )g
dt
2 (UA) tank (T i 2 T a ) 1 K.
(11)
This linear first-order differential equation has the
solution
S
D
vg2 2
vg1 2vg2
T i (t) 5 ]t 1 ] 2 ]]
t
u
u
u2
vg0 vg1 2vg2 w
1 ]2]
1 ]]
1]
u
u
u2
u3
S
F S
D
vg0 vg1 2vg2
1 T i,0 2 ] 2 ]
1 ]]
u
u2
u3
w
1 ] exp(2ut)
u
DG
where
(12)
A photovoltaic / thermal (PV/ T) collector with a polymer absorber plate
AFRUL 1 (UA) tank
u 5 ]]]]]
mCp
(13)
AFR (ta ) eff
v 5 ]]]
mCp
(14)
(AFRUL 1 (UA) tank )T a 1 K
w 5 ]]]]]]]]
mCp
(15)
69
thus, the time development of T i is determined
using known system properties and ambient conditions, and from this expression other system
characteristics can be found.
With the solar cell temperature calculated as
described in the previous section,
T c (t) 5 T i (t) 1 khT I(t)
(16)
the photovoltaic conversion efficiency can be
modeled as a linearly decreasing function of
temperature:
hPV (t) 5 href 2 m (T c (t) 2 T ref ).
(17)
When the thermal system is switched off (no
circulation of fluid, no cooling of PV cells), the
solar cells operate at the collector stagnation
temperature
(ta ) eff I(t)
T s (t) 5 T a 1 ]]].
UL
(18)
The effect of cell cooling on PV performance is
investigated by substituting T s for T c as cell
temperature in the model.
The PV/ T system was also compared to a
‘pure’ PV module without thermal insulation. An
energy balance on a PV module cooled by losses
to the surroundings can be written as (Duffie and
Beckman, 1991)
(ta ) PV I(t) 5 hPV (t)I(t) 1 UPV (T PV (t) 2 T a ).
(19)
A nominal operating cell temperature of
T PV,NOCT 5458C (Siemens Solar, 2000) at I 5 800
W/ m 2 , T a 5208C and hPV 5 0 gives UPV 5 28.8
W/(m 2 K) with (ta ) PV assumed equal to 0.9.
(Open-rack mounted module. Heat loss coefficient
expected lower for building mounted modules
with covered back surfaces which would result in
higher operating temperatures.) The time-dependent PV module temperature T PV (t) can be found
with the expression for hPV from Eq. (17) inserted
into Eq. (19):
T aUPV 1 I(t)((ta ) PV 2 href 2 m T ref )
T PV (t) 5 ]]]]]]]]]].
UPV 2 m I(t)
(20)
Fig. 8. Simulated time development of inlet fluid temperature
T i and solar cell temperature T c (solid lines) superimposed on
the experimental data (dashed lines). PV/ Tg system, 03.11.97.
The PV module efficiency is found by substituting
T PV for T c as cell temperature in Eq. (17).
Fig. 8 shows the inlet fluid temperature T i and
solar cell temperature T c of the glazed photovoltaic / thermal system plotted against time. The
simulated curves (solid lines) are superimposed on
the experimental data (dashed lines). The good
agreement between the theoretical curves and the
experimental data confirms the validity of the
model equations. The simulations are however
‘fine-tuned’ for each day separately, since the
input parameters are calculated from the corresponding experimental data. Fig. 8 and the following figures display simulations based on results obtained with the glazed collector (PV/ Tg),
on the 03.11.97.
In Fig. 9, the simulated inlet fluid temperature
T i and collector thermal efficiency hT are plotted
both with PV power output from the cells (solid
lines), and without PV power output (dashed
lines). The thermal efficiency is higher when no
electrical power is extracted from the cells since
more solar energy becomes available for the
thermal system. The gain in thermal efficiency
without PV output gives a faster increasing storage tank temperature T i . The increased heat loss
resulting from the higher operating temperature
achieved, subsequently reduces the thermal efficiency later in the day as seen from the figure.
When no heat is removed from the collector
(thermal system off), the cell temperature is
assumed equal to the collector stagnation temperature (Eq. (18)). In Fig. 10, the simulated
photovoltaic power output is plotted against time
both with cooling of the cells (solid line) and
without cooling (dashed line). Also illustrated in
70
B. Sandnes and J. Rekstad
Fig. 9. Calculated inlet fluid temperature and thermal efficiency with PV power output (solid lines) and without PV power output
(dashed lines). The higher thermal efficiency without PV output gives a faster increasing storage tank temperature. PV/ Tg system,
03.11.97.
the figure is the gain in accumulated PV energy
that is achieved by cooling the cells. This results
from integrating the difference in power output
between ‘cooling’ and ‘no cooling’ of the PV cells
over time. The graph shows a net gain of 8.9 W h
at the end of the day for the simulation. This
represents an 8.8% increase in PV energy output
compared to the ‘no cooling’ situation.
Fig. 11 shows a general comparison of simulated cell temperatures and photovoltaic power
output from the PV/ T system, the PV/ Tg system
and a PV module without thermal insulation. A
clear summer day was simulated, with peak
irradiation of 1 kW/ m 2 and constant ambient
temperature of 208C. The PV module temperature
follows the irradiation, with a maximum temperature of 46.68C, while the PV/ T and PV/ Tg cell
temperatures are governed by the increasing temperature of the heat storages, with maximum
temperatures of 49.8 and 59.68C, respectively.
The integrated PV energy output over the day is
for the PV module 306.9 W h, for the PV/ T
system 339.3 W h and for the PV/ Tg system
296.2 W h. Note however that the superior energy
output of the PV/ T system (|10% more than the
PV module) is mainly due to the fact that the
system is unglazed while the PV module is
Fig. 10. Simulated PV power output with and without cooling
of the solar cells, solid and dashed line, respectively. Also
plotted is the accumulated difference in energy output between
the two cases. PV/ Tg system, 03.11.97.
Fig. 11. Simulated cell temperature and photovoltaic power
output for the PV/ T system (solid lines), the PV/ Tg system
(dashed lines) and a PV module without thermal insulation
(dotted lines).
A photovoltaic / thermal (PV/ T) collector with a polymer absorber plate
modeled with a transmittance–absorptance product of 0.9. The simulations so far reflect a system
with continuous accumulation and increasing
temperature in the heat store. If however the
PV/ T collectors are implemented in a system with
draw-off of thermal energy, the PV cell temperature would be kept at a lower and more stable
level. By assuming a constant system (storage)
temperature of 308C, the same simulation as
above gives a total PV energy of 349.1 W h for
the PV/ T system and 307.1 W h for the PV/ Tg
system.
7. DISCUSSION
The average collector thermal efficiency curves
displayed in Fig. 4 for the different collector
configurations illustrate how the thermal properties of the collector are modified when it is
converted from a thermal to a PV/ T collector.
Pasting solar cells onto the absorbing surface
reduces the solar energy absorbed by the panel
( | 10% of incident energy). This can be attributed
to lower optical absorption in the solar cells
compared to the black absorber plate (reduced
(ta ) for the collector). In addition, there is an
increased heat transfer resistance between the
absorbing surface and the heat carrier fluid introduced in the cell / absorber-plate interface which
reduces the collector heat removal factor, FR .
The efficiency curves of Fig. 4 also suggest a
lower heat loss coefficient for the photovoltaic /
thermal absorber (PV/ T) compared to the thermal
absorber (T), although there is a relatively large
uncertainty associated with the data. Reduced heat
loss for the PV/ T collector can be explained by
the selective absorbing properties of the solar
cells. The semiconductor material absorbs the
solar part of the spectrum, but is transparent to
long-wave radiation below the cut-off wavelength
(1.15 mm). High reflectivity metallic contacts on
the back of the solar cells gives low emissivity in
the long wavelength region. Heat loss is further
reduced by the added cover glass (PV/ Tg), but is
still quite high compared to other glazed collectors, which indicates heat loss at the edges of the
collector. The edges of the absorber were in direct
contact with an uninsulated aluminum frame, and
since the collector area is small, edge effects are
relatively significant. The reduction in optical
efficiency (|5%) is caused by the additional
reflection from the cover glass surface, but would
be expected to be higher since reflection from
glass surfaces is generally |10%.
The effect of extracting electrical power from
71
the solar cells is a corresponding reduction in the
solar energy available for the thermal system. A
decrease in the thermal efficiency of |10% as
seen from Fig. 5, is equivalent to |36 W (750
W/ m 2 irradiation), which is in reasonable agreement with the measured 32–33 W PV output.
The photovoltaic output of the collector is |41 W
when the measurements are converted to reference conditions (I 5 1 kW/ m 2 , T c 5258C). This is
comparable to small PV modules commercially
available. The efficiency temperature coefficient
( m 50.07% / K for series and m 50.1% / K for
parallel connection of cells) is higher than the
reported m 50.05% / K for single-crystal silicon
cells (Saidov et al., 1995), but within the range of
the experimental error which was large for these
readings.
The solar cell efficiency is, because of its
temperature dependence, governed to some extent
by the thermal system. Eq. (5) relates the cell
temperature to the thermal system, with the inlet
fluid temperature as the single most important
parameter. The difference between cell and inlet
temperature is proportional to the thermal efficiency of the collector and the irradiation. The
constant k is inversely proportional to the collectors cooling effectiveness, and is determined by
the heat removal factor FR and the overall heat
loss UL .
The cooling effect achieved by a combined
PV/ T collector is thus determined mainly by the
inlet fluid temperature, and to a lesser degree by
the thermal characteristics of the collector.
Siemens Solar reports a nominal operating cell
temperature of 458C for some of their PV modules
(Siemens Solar, 2000). Given similar conditions
(I 5 800 W/ m 2 , T a 5208C, wind speed51 m / s)
the cell temperature can be calculated for the
PV/ T collector. The results show that the cell
temperature is kept below 458C (and net cooling
achieved) provided that the inlet fluid temperature
does not exceed 408C for the PV/ T collector
without cover glass, and 308C with cover glass
under these conditions.
The PV/ T collector is partly motivated by the
cooling effect that can be achieved for the solar
cells. This puts an upper limit on the system
temperature, which must be considerably lower
than the desired cell temperature (depending on
the thermal characteristics of the collector). The
PV/ T concept can be successful when integrated
into a system that covers energy demands of
temperatures that are sufficiently low to give the
desired cooling effect (e.g. floor heating systems
(25–408C)).
72
B. Sandnes and J. Rekstad
8. CONCLUSION
A combined thermal and photovoltaic solar
energy collector was successfully constructed by
pasting single-crystal silicon cells onto a black,
plastic, heat absorber. The adhesive was sufficiently elastic to absorb the difference in thermal
expansion between the cells and the absorber.
A comparison of the PV/ T absorber to a pure
thermal absorber showed reduced thermal efficiency for the PV/ T system which was attributed
to:
• available solar energy for the thermal system
reduced by the fraction of the incident energy
converted to electricity by the PV cells;
• a lower optical absorption in the photovoltaic
cells compared to the black absorber plate;
• increased heat transfer resistance introduced in
the cell / absorber interface.
The PV/ T system can on the other hand reduce
heat loss from the collector as the solar cells act
as selective absorbers. Heat loss was further
reduced by an additional cover glass while at the
same time increasing reflective losses.
Cooling of the PV cells was achieved by lowtemperature operation of the heat collector which
resulted in improved PV efficiency. The solar cell
temperature correlated strongly to the system
(inlet fluid) temperature and also to the collectors’
heat transport characteristics. The combined PV/ T
concept must therefore be associated with applications of sufficiently low temperature to give the
desired cooling effect.
An analytical model of the PV/ T system simulated the temperature development of the system,
and photovoltaic and thermal performance. The
simulation results were in agreement with the
experimental data.
NOMENCLATURE
A
Ac
b0
Cp
F
F9
FR
g0,1,2
h
I
Imp
K
Kta (u )
k
m
2
collector area (m )
total PV cell area (m 2 )
incidence angle modifier coefficient
heat capacity of fluid (J kg 21 K 21 )
fin efficiency
collector efficiency factor
collector heat removal factor
irradiation curve fitting constants
heat transfer coefficient between absorber and
fluid (W m 22 K 21 )
22
irradiation (W m )
current at maximum power point (A)
pump power (W)
incidence angle modifier
system thermal property (K m 2 W 21 )
total mass of fluid in system (kg)
]
P
QL
QP
QS
QT
QU
S
T 1,2
T3
Ta
Tc
]
Tc
Ti
T i,0
T PV
T PV,NOCT
T ref
Ts
t
UL
UPV
(UA) tank
Vmp
Voc
a
hPV
hT
href
u
m
(ta )
(ta ) eff
(ta ) PV
average PV power output (W)
heat loss from storage (J)
heat input from submerged pump (J)
specific heat stored in collector (J)
total energy collected in storage tank (J)
useful energy output from collector (J)
available solar energy (W m 22 )
measured PV cell temperatures (K)
measured absorber plate temperature (K)
ambient air temperature (K)
calculated PV cell temperature (K)
average measured cell temperature (K)
storage tank temperature (K)
initial storage tank temperature (K)
PV module temperature (K)
nominal operating cell temperature (K)
PV temperature at reference conditions (K)
collector stagnation temperature (K)
time (s)
collector overall heat loss coefficient (W m 22
K 21 )
PV module heat loss coefficient (W m 22 K 21 )
storage tank heat transfer (W K 21 )
voltage at maximum power point (V)
open circuit voltage (V)
absorber plate absorptance
photovoltaic conversion efficiency
collector thermal efficiency
PV efficiency at reference conditions
angle of incidence
PV efficiency temperature coefficient (K 21 )
transmittance–absorptance product without PV
power output
effective transmittance–absorptance product with
PV power output
transmittance–absorptance product for ‘pure’ PV
module
Acknowledgements—The authors wish to thank Dr. Ole Martin
Løvvik and Dr. Joanna Maloney Sandnes for helpful discussions and for proof-reading this manuscript.
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