Pergamon
PII:
Solar Energy Vol. 72, No. 2, pp. 113–128, 2002
 2002 Elsevier Science Ltd
S 0 0 3 8 – 0 9 2 X ( 0 1 ) 0 0 0 9 4 – 9 All rights reserved. Printed in Great Britain
0038-092X / 02 / $ - see front matter
www.elsevier.com / locate / solener
THE THERMAL AND ELECTRICAL YIELD OF A PV-THERMAL
COLLECTOR
H. A. ZONDAG † , *, D. W. DE VRIES*, W. G. J. VAN HELDEN**, R. J. C. VAN ZOLINGEN***
and A. A. VAN STEENHOVEN*
*Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
**Energy research Centre of the Netherlands ECN, P.O. Box 1, 1755 ZG Petten, The Netherlands
***Shell Solar Energy B.V, P.O. Box 849, 5700 AV Helmond, The Netherlands
Received 9 May 2000; revised version accepted 28 August 2001
Communicated by BRIAN NORTON
Abstract—Four numerical models have been built for the simulation of the thermal yield of a combined
PV-thermal collector: a 3D dynamical model and three steady state models that are 3D, 2D and 1D. The
models are explained and the results are compared to experimental results. It is found that all models follow
the experiments within 5% accuracy. In addition, for the calculation of the daily yield, the simple 1D steady
state model performs almost as good as the much more time-consuming 3D dynamical model. On the other
hand, the 2D and 3D models are more easily adapted to other configurations and provide more detailed
information, as required for a further optimization of the collector. The time-dependent model is required for
an accurate prediction of the collector yield if the collector temperature at the end of a measurement differs
from its starting temperature.  2002 Elsevier Science Ltd. All rights reserved.
means of the Hottel–Whillier model, dating back
to 1958. Increasingly, the dynamical modelling of
thermal collectors has attracted attention. A comparison of three dynamical models has been made
by Klein et al. (1974). They identified a storage
effect – lowering the efficiency of the collector
during the period it is heating up to obtain its
working temperature – and a transient effect due
to the changing weather conditions. Smith (1986)
compared dynamical models with an increasing
number of nodes. From his results it can be
concluded that the modelling of the cover glass
does not have much impact on the thermal
efficiency, while the temperature difference between the fluid and the tube seems to be important.
The integration of PV and a thermal collector
into one design fundamentally changes the
characteristics of both. The electrical yield of the
PV-cells is influenced by the collector inflow
temperature and – for the case in which the panel
has an additional glass cover to reduce the heat
loss to the ambient – by the additional reflection
at this cover. The thermal yield of the collector is
changed by the increased heat transfer resistance
between the absorber and the fluid, the increased
specific heat – which approximately trebles due to
the presence of a PV-laminate – the lower light
absorption of the PV-laminate and the absence of
a spectrally selective coating.
1. INTRODUCTION
A combined PV-thermal collector – henceforth to
be called a combi-panel – consists of a photovoltaic laminate (a PV-laminate) that functions as
the absorber of a thermal collector. In this way, a
device is created that converts solar energy into
both electrical and thermal energy. The main
advantages of a combi-panel are:
1. An area covered with combi-panels produces
more electrical and thermal energy than a
corresponding area covered half with conventional PV-panels and half with conventional
thermal collectors. This is particularly useful
when the amount of space on a roof is limited.
2. Combi-panels provide architectural uniformity
on a roof, in contrast to a combination of
separate PV- and thermal systems.
3. Depending on the system configuration, the
average PV temperature in a PV-thermal collector might be lower than for a conventional
PV-laminate, thereby increasing its electrical
performance.
Much is known about the modelling of the
thermal efficiency of a conventional thermal
collector. A well-known way of modeling it is by
†
Author to whom correspondence should be addressed.
Tel.:
131-40-24-72140;
fax:
131-40-24-33445;
e-mail: h.a.zondag@wtb.tue.nl
113
114
H. A. Zondag et al.
In contrast to the situation for conventional
thermal systems, the literature on combined
photovoltaic-thermal collector design is not very
extensive. In order to optimise the overall design
of the collector, as well as to be able to predict the
effect of small improvements in the components
of the collector, an accurate numerical model is
required. However, the effort invested in modelling of PV-thermal collectors has been limited. A
model study was published in which the Hottel–
Whillier model was adapted to cover PV-thermal
collectors as well (Florschuetz, 1979) and several
researchers have made simulations in order to
determine the efficiency of a combi-panel system
(Cox and Raghuraman, 1985; Bergene and Løvvik, 1995). Nevertheless, as far as the present
authors are aware, a systematic comparison between various models for combi-panel efficiency
calculations has not been published yet. In order
to obtain more information on the design parameters of combi-panels, several models were built
and compared to experimental results.
2. EXPERIMENTAL SET-UP
In order to quantify the efficiency of a combipanel, an experimental prototype was built at the
Eindhoven University of Technology (de Vries,
1998; de Vries et al., 1999). This was a nonoptimised first prototype, which was built in order
to be able to validate the simulated values generated by the models under study. The prototype
was constructed by connecting a conventional
PV-laminate, containing multi-crystalline silicon
cells, to the absorber plate of a conventional
glass-covered sheet-and-tube collector, as shown
in Fig. 1. The panel was then integrated into a test
rig on the roof of the department of Mechanical
Engineering at the Eindhoven University of Technology.
The efficiency of the combi-panel has been
measured and has been compared to the efficiencies of a conventional sheet-and-tube thermal
collector and a multi-crystalline silicon PV-panel
of the same length and width, which were
positioned next to it in the test rig. A photograph
of the test rig is shown in Fig. 2. The original
thermal collector surface was somewhat larger
than the PV-laminate. In order to create similar
areas for the PV-laminate, the thermal collector
and the combi-panel, the absorbing surfaces of the
latter two were partly covered with insulation that
had a reflective aluminium top layer. In Fig. 2
these covered parts appear as the white areas
around the collector and the combi-panel. The
uncovered parts have an area of 0.94 m 2 each.
The water was drawn from the tank into the
thermal collector and the combi-panel by a NKF
Verder ND 300 KT 18 diaphragm pump. The
construction was such that the water heated by the
collector was discharged on the sewage system in
order to be able to keep the inlet water temperature at a constant value. The water flow through
the combi-panel and the conventional thermal
collector have been measured independently with
two rotary piston KENT PSM-LT PL 10 water
volume meters. The volume flow was measured
by dividing the counted amount of litres by the
measuring time. The wind speed has been measured with an EKOPOWER MAXIMUM cup
anemometer. The irradiation has been measured
with a Kipp & Zonen CM 11 pyranometer. The
temperatures of the PV-laminate, the combi-panel
laminate and the collector absorber as well as the
in- and outflow temperatures of the collector and
the combi-panel have been measured with thermocouples type K, which were calibrated to an
accuracy of 0.2 K. The thermocouples, the
pyranometer, the anemometer, the two water
meters and the electrical output of the combi-
Fig. 1. The combi-panel.
The thermal and electrical yield of a PV-thermal collector
115
Fig. 2. Left: the test rig. (Left to right: a conventional thermal collector, the combi-panel and a conventional PV-laminate). Right:
the insulation versus the location of the tubes.
Table 1. Characteristic system dimensions
A abs
A PV
B
D
Dinner
H
L
Lc
W
dabs
dPVglass
dcell
dtopglass
Absorber area
PV panel area
Bond width
Outer diameter tube
Inner diameter tube
Height insulating air layer
Length tube segment
Length of collector surface
Tube spacing
Thickness absorber
Thickness PV glass
Thickness silicon cell
Thickness cover glass
1.12 m 2
0.94 m 2
0.01 m
0.01 m
0.008 m
0.02 m
0.724 m
1.776 m
0.095 m
0.0002 m
0.003 m
0.00035 m
0.0032 m
panel and the PV-panel were read out by a
DORIC digitrend 220 datalogger. The time between two measurements was typically 11 s. The
PV-laminate was a standard Shell Solar PV-laminate consisting of 72 10 3 10 cm 2 EVA encapsulated multi-crystalline silicon cells with a low-iron
glass front and an PE /Al / tedlar film at the back.
The encapsulated cell efficiency under standard
conditions (1000 W/ m 2 , 258C) is typically 13%.
The laminate efficiency at 258C is 9.7%. The
thermal absorber is a standard ZEN thermal
collector: a sheet-and-tube absorber in which a
copper spiral is soldered to a copper sheet. The
distance between two neighbouring tubes is
10 cm, the tube diameter is 1 cm. Since the
absorber was covered with the PV-laminate, the
spectral selectivity of the collector surface was
destroyed. The length scales used in the calculations correspond to the experimental set-up and
are given in Table 1.
3. MODEL DESCRIPTION
3.1. Introduction
The heat flows through the combi-panel are
indicated in Fig. 3. Four numerical models have
Fig. 3. Cross section of the combi panel. The material layers in the combi-panel are indicated, as well as the temperatures and the
various heat fluxes. The dashed line shows the temperature distribution over the surface of the panel.
116
H. A. Zondag et al.
been developed that calculate these heat flows for
the determination of the daily yield of the combipanel. These models require a decreasing amount
of computation time at the cost of less detailed
information and an increased reliance on empirical correlations.
The results of the measurements and the calculations are the yield and the efficiency of the
collector. The yield of the collector is defined as
the amount of useful energy produced by it, while
the efficiency is defined as the yield divided by
the amount of solar energy received by the
collector. Both an electrical and a thermal efficiency are defined.
VMPP IMPP
hel ; ]]]
GA PV
(1)
~ psT out 2 T ind
mc
hth ; ]]]]]
GA PV
(2)
The four models have in common the way the
optical and electrical parts are calculated. The
electrical efficiency, which is a function of temperature, is given by
hel 5 h0s1 2 0.0045fT cell 2 258Cgd
(3)
The transmission–absorption factor ta of the
combi-panel has been calculated with an optical
model. The optical model calculated the coefficients of reflection at each material within the
PV-laminate, using the Fresnel equations. The
solar radiation was assumed to have no nett
polarisation, so the incoming light was split in
50% parallel and 50% transverse polarization.
Next, ta was determined for each mode separately
and the results were added. The calculation was
based on the assumption of specular reflection, so
diffuse reflection was not taken into account. A
further complication was presented by the fact
that a PV-laminate does not present a homogeneous surface but consists of different parts
(active PV-area, the top grid and the spacing
between the cells). For each part the value for ta
has been calculated separately and then ta of the
entire combi-panel has been determined by taking
the average of these values, weighed with the
respective surface areas. This method results in a
slight underestimation of ta due to the fact that no
exchange of light between the different material
surfaces is possible: light reflected by the top grid
area cannot be reflected back by the glass on the
PV area in our model. The average value of ta ,
which was found to be 0.74, was then inserted
into the thermal-yield models. In the models that
will be described in the following paragraphs, the
thermal efficiency is calculated from the effective
transmission–absorption factor by subtracting the
electrical efficiency from ta , according to ta ,eff 5
hta 2 thelj. Here, t represents the transmissivity
of the glass cover, which equals 92%. In this way
one obtains the amount of absorbed solar energy
that contributes to the thermal yield.
With respect to the thermal model, the modeling is simplified by regarding the serpentine-like
tube as a long straight tube, ignoring the effects
related to the bends, which are assumed to be of
secondary importance. In this way, two effects are
ignored:
1. Additional mixing in the tube due to the bends,
leading to a smaller heat resistance between
tube wall and fluid.
2. Variations in the area that supplies its heat to a
certain tube section.
In order to estimate these effects, simulations
were carried out. An increase of 20% in heat
transfer between tube and tube wall indicated lead
to an increase in thermal efficiency of less than
0.1%. Furthermore, the simulations showed that a
20% increase in fin area results in a reduction in
thermal efficiency of slightly less than 1%. In
addition, in the present experimental configuration, the width of the serpentine is approximately
the same as the width of the PV-laminate, as
shown in Fig. 2. This reduces these effects even
further. It is concluded that these 3D effects are
small.
The thermal resistances of the different layers
of material between the solar cells and the copper
absorber sheet have been lumped together into the
heat transfer coefficient h ca , which has been
measured to be 4563.3 W/ m 2 K for our experimental set-up. The value of h ca has been
determined by measuring the temperature difference between the glass surface of the PV and the
absorber and inserting the results into the formula
for h ca indicated below. It is assumed that the heat
loss to the ambient through the back of the
collector is negligible, as well as the temperature
difference between the glass and the cells.
~ sT out 2 T ind
cm
h ca 5 ]]]]]
A PVsT cell 2 T absd
(4)
3.2. Dynamical and steady state 3 D model
The first model that has been built is a fully
time-dependent quasi 3D model. It has been built
in order to be able to simulate the time-dependent
behaviour of the combi-panel. The model is quasi
3D since the absorber plate and the PV-laminate
are segmented in both the directions perpendicular
The thermal and electrical yield of a PV-thermal collector
to the flow (x-direction) and along the flow ( ydirection), but the top layer is only segmented in
the direction along the flow.
Since the heat stored in the combi-panel can
change over time, Eqs. (5) to (8) below describe
the time dependency of the heat flows through the
combi-panel (see Fig. 3):
D
1 k absdabs
S
qsky,rads yd 5 Fsky etopglass ssT 4topglasss yd 2 T 4skys ydd
qsky,convs yd 5 h windsT topglasss yd 2 T ad
Nu wind k
5 ]]]sT topglasss yd 2 T ad
Lc
(5)
etopglass elamv
4
5 ]]]]]]]]ssT lam
sx, yd
etopglass 1 elam 2 etopglass elam
2
2 T 4topglasss ydd
D
≠ T abssx, yd ≠ T abssx, yd
]]]]
1 ]]]]
A PV
≠x 2
≠y 2
in which rlamdlam c lam is defined as rcelldcell c cell 1
rglassdPVglass c glass . In the model, a slightly simplified set of equations is used since the second
order differentiations with respect to x are ignored, which is allowed since the change in the
x-direction (along the flow) is almost linear and
therefore substantially smaller than the differentiation with respect to y. In Eq. (6) the respective
areas are also indicated in order to account for the
absorber area that is covered by the insulation (see
photograph in Fig. 2). A abs is equal to A PV plus
the additional area covered by the insulation. The
changing temperatures of the glass cover and the
tube are calculated from
≠T topglasss yd
rglassdtopglass c glass ]]]]
≠t
5 q¯ air,rads yd 1 q¯ air,convs yd 2 qsky,rads yd 2 qsky,convs yd
(7)
D
≠T tube
1
1
]pD 2inner r Lc w 1 ]psD 2 2 D 2innerdLc tube ]]
4
4
≠t
~ wfT w ( y 2 1) 2 T w ( y)g
5 qtube LB 2 mc
(8)
in which L represents the length of a segment in
the y-direction and B represents the contact width
between the sheet and the tube. The seven heat
fluxes appearing in Eqs. (5) to (8) are determined
from the following relations (the tube is located at
segment x57):
(12)
qair,convsx, yd 5 h csT lamsx, yd 2 T topglasss ydd
Nu air k
5 ]]sT lamsx, yd 2 T topglasss ydd
H
(6)
S
(11)
qair,radsx, yd
≠T abs (x, y)
A abs rabsdabs c abs ]]]
≠t
5 qca (x, y)A PV 2 qbasx, yd A abs
2
(9)
(10)
2 qcasx, yd 1 k lamdlam
S
pDinner
qtubes yd 5 ]]h tubesT abss7, yd 2 T w ( y)d
B
pk
5 Nu tube ]sT abss7, yd 2 T ws ydd
B
4
4
1 Fearth etopglass ssT topglass
s yd 2 T a d
≠T lam (x, y)
rlamdlam c lam ]]]
≠t
5sta 2 theldG 2 qair,radsx, yd 2 qair,convsx, yd
≠ 2 T lam (x, y) ≠ 2 T lam (x, y)
3 ]]]]
1 ]]]]
≠x 2
≠y 2
117
(13)
qcasx, yd 5 h casT lamsx, yd 2 T abssx, ydd
(14)
qbasx, yd 5 h basT abssx, yd 2 T ad
(15)
For the Nusselt relations see Appendix A. The
vertical temperature gradient over the glass on top
of the PV-laminate is not calculated; the properties of the glass and the silicon are lumped
together within Eq. (6). The equations for qair,rad
and qair,conv (Eqs. (12) and (13)) are averaged in x
and the result is inserted into Eq. (7).
The steady state 3D model is exactly the same
as the dynamical model, except for the fact that in
Eqs. (5) to (8) the derivations with respect to time
have been set to zero. For example, Eq. (5)
changes into
05
sta 2theldG2qair,radsx, yd2qair,convsx, yd2qcasx, yd
S
≠ 2 T lam (x, y) ≠ 2 T lam (x, y)
1k lamdlam ]]]]
1]]]]
≠x 2
≠y 2
D
(16)
For the simulation of the equations presented
above, the derivations have been discretized as
shown below:
≠Q
]
≠t
U
t 5n
Q n11 2 Q n
5 ]]]
Dt
(17)
118
≠ 2Q
]]
≠y 2
H. A. Zondag et al.
U
x5n
Q n11 2 2Q n 1 Q n21
5 ]]]]]]
Dy 2
(18)
In Eqs. (5) to (8) the time step Dt is chosen to
be 0.108 s, which is equal to 1 / 100 of the time
step between two measurements in the experimental set-up. It was found that a larger step resulted
in an unstable calculation process while a smaller
time step did not change the results of the
calculation.
The PV-laminate and the absorber are subdivided into six segments in the y-direction (along
the flow). For the middle segments (2 to 5) the
temperature profile is assumed to be symmetric
with respect to the tube location in its center. The
segments are subdivided into seven elements in
the x-direction, perpendicular to the flow, as
shown in Fig. 4.
In order to obtain the proper temperature
gradients at both sides of the domain of the
calculation, a fake segment is introduced at each
side (for the case of the middle segments at m51
and 8; see Fig. 4) and a value is attributed to it
such that the boundary condition is satisfied. Both
for the absorber and the laminate, the boundary
conditions are provided by
≠T
]
≠x
≠T
]
≠x
U
U
x 50
5 0 ⇒ T m51 5 T m 52
(19)
x 50.5W
5 0 ⇒ T m 58 5 T m 56
The treatment of the begin- and end-segments
(segment numbers 1 and 6) differs somewhat
from the middle segments since the sides are
partially covered by the insulation material (as
shown in the photograph in Fig. 2). Zero heat flux
is assumed for the outer boundaries, while the
discretization is shown in Fig. 4. Since the PVlaminate is somewhat shorter than the copper
absorber, they do not end at the same segment
number. The boundary conditions are:
≠T
]
≠x
≠T
]
≠x
U
U
x 5end
x 5end
laminate
5 0 ⇒ T m519 5 T m 518
≠T
]
≠x
≠T
]
≠x
U
U
x 5end
5 0 ⇒ T m51 5 T m52
x 5end
5 0 ⇒ T m519 5 T m 518
5 0 ⇒ T m53 5 T m54
(20)
copper
For the calculation, an initial temperature dis-
Fig. 4. The discretisation in the x-direction for the 3D model; upper figure: the middle segments (2 to 5); lower figure: the outer
segments (1 and 6).
The thermal and electrical yield of a PV-thermal collector
119
tribution is assumed. The temperature distribution
on subsequent times is determined by integration
of Eqs. (5) to (8) with respect to time, using a
Runge–Kutta procedure. Using this model, the
time-dependent calculation of the yield over an
interval of 1 h roughly takes 2.5 h of calculation
time on a Pentium 3.
This set of equations contains nine heat fluxes.
Of these, seven are provided by the set of Eqs. (9)
to (15), although the quantities which in these
equations are functions of x should now be
replaced by their average value for each layer
segment in the collector. In particular, Eqs. (14)
and (15) now become
3.3. 2 D-model
qcas yd 5 h casT cell ( y) 2 T¯ abs ( y)d
(26)
qbas yd 5 h basT¯ abs ( y) 2 T ad
(27)
To reduce the calculation time required by the
model, it was decided to remove the time dependence of the model and to make a calculation
based on a layer-averaged basis. A new model has
been built, that solves the heat balance for all the
layers in the combi-panel. The model is 2D in the
sense that the collector is segmented in the ydirection (along the flow) and the heat balance is
assumed to hold for each segment independently.
The outflow temperature of the first segment is
the inflow temperature of the next. For each
segment, the set of equations below is solved by a
matrix-solving procedure.
A minor modification has been made by taking
into account the temperature drop over the glass
front of the PV-laminate and the glass cover. This
resulted in three additional equations. In the 3D
model these equations have been left out, since,
due to the discretisation, they would add another
50 equations to be solved, while it was found that
the effect of the temperature resistance of the
glass was less than 1% for reduced temperatures
less than 0.05. Another modification in the 2D
model was to ignore the effect of the edges of the
absorber that were underneath the insulation (see
Fig. 2). This made the area for loss to the rear of
the collector somewhat less, but the difference in
collector performance was not significant.
The fact that a temperature gradient now exists
over the glass layers means that the temperature
T topglass appearing in the 3D model now has to be
split up into T topglass↑ and T topglass↓ , while T lam is
split up into T cell and T PVglass . The heat balance is
represented in Fig. 3, which corresponds to the
following equations:
qwater ( y) 5 qca ( y) 2 qba ( y)
(21)
qca ( y) 5sta 2 theldG 2 qPVglass ( y)
(22)
qPVglass ( y) 5 qair,conv ( y) 1 qair,rad ( y)
(23)
qair,conv ( y) 1 qair,rad ( y) 5 qtopglass ( y)
(24)
qtopglass ( y) 5 qsky,conv ( y) 1 qsky,rad ( y)
(25)
The heat fluxes through the glass cover and the
PV glass are provided by two additional equations:
k glass
qPVglass ( y) 5 ]]sT cell ( y) 2 T PVglass ( y)d
dPVglass
(28)
k glass
qtopglass ( y) 5 ]]sT topglass↓ ( y) 2 T topglass↑ ( y)d
dtopglass
(29)
Finally, an equation is required for the average
absorber temperature T¯ abs . The temperature varies
along the surface as shown in Fig. 3, corresponding to the Hottel–Whillier equations for a
sheet-and-tube collector (Duffie and Beckman,
1991).
sta 2 theldG
Tsx, yd 5 T a 1 ]]]] 1 coshsmxd
h loss ( y)
T bond ( y) 2 T a 2sta 2 theldG /h loss ( y)
3 ]]]]]]]]]]
coshfmsW 2 Dd / 2g
(30)
in which the heat loss coefficient was approximated by:
qsky,rad ( y) 1 qsky,conv ( y) 1 qba ( y)
h loss ( y) 5 ]]]]]]]]]
T PVglass ( y) 2 T a
(31)
m 5sh loss /sk absdabs 1 k lamdlamdd 21 / 2
(32)
and the bond temperature is given by
T bond ( y) 5 T w ( y) 1 qw ( y) /h tube
5 T w ( y) 1 qw ( y)W/spNu tube k wd
(33)
with Nu tube given in Appendix A. Eq. (30) is
numerically integrated with respect to x in order
to provide the average absorber temperature.
The thermal efficiency has been calculated for
an increasing number of segments, as shown in
Fig. 5. This figure indicates that for the low flow
case, three segments are enough. For a high flow
case, the temperature increase within the collector
is less and a smaller number of segments is
sufficient.
120
H. A. Zondag et al.
Fig. 5. Calculated value of the efficiency at zero reduced temperature for an increasing number of segments (2D model) or
iterations (1D model).
The 2D model resulted in a very substantial
reduction in computation time, as it was 25 times
as fast as the 3D static model.
3.4. 1 D Model
For the computation of the annual yield, the 2D
model was still rather time consuming. To reduce
the calculation time even further, a 1D model has
been built. This 1D model is a Hottel–Whillier
model (Duffie and Beckman, 1991, pp. 253–281).
The thermal yield is given by
P 5 A PV FRssta 2 theldG 2 UlosssT in 2 T add
(34)
with FR representing the heat removal factor that
follows from the Hottel–Whillier equations:
absorber h ca the measured value of 45 W/ m 2 K
was used.
An iterative procedure is used. For the calculation, an initial value for the mean plate temperature is assumed and a value is calculated for the
thermal power P produced by the combi-panel.
For each subsequent iteration, a more accurate
value for the mean plate temperature is determined from
DT collector
T plate 5 T in 1 ]]] 1 DT ca
2
P
P
5 T in 1 ]] 1 ]]
~
2mc
A pv h ca
(39)
D
Ft 5s1 2 D/WdF 1 ]
W
(37)
This new value for the plate temperature is
inserted into the equation for Uloss in Appendix A
and into Eq. (1) for the electrical efficiency and
the calculation is repeated. The result converges
very fast (see Fig. 5). It was found that the 1D
model was roughly 30 times as fast as the 2D
model.
tanhfmsW 2 Dd / 2g
F 5 ]]]]]
msW 2 Dd / 2
(38)
4. RESULTS
~
mc
~ gd (35)
FR 5 ]]]s1 2 expf 2 A PVUloss F9 /mc
A PVUloss
F9 5h1 /Ft 1 Uloss /h ca 1 UlossW/spDh tubedj 21 (36)
In Eq. (38), m is again given by Eq. (32). The
equations are largely the same as for a conventional thermal collector, apart from the additional
term Uloss /h ca in Eq. (36), representing the heat
resistance between cells and absorber. In order to
calculate the thermal yield, equations are required
for the heat transfer coefficient through the cover
Uloss and the heat transfer coefficient from the
tube to the water h tube (both given in Appendix
A). For the heat transfer coefficient from cells to
4.1. Experimental verification of parameters
Measurements were carried out on the
prototype combi-panel to determine the experimental efficiency curves (de Vries, 1998; de
Vries et al., 1997; Zondag et al., 1999). The
measured efficiency curves for the prototype
combi-panel and the thermal collector are shown
in Fig. 6 and the corresponding efficiencies at
zero reduced temperature are summarized in
Table 2. The thermal efficiency is shown as a
The thermal and electrical yield of a PV-thermal collector
Table 2. Efficiencies at zero reduced temperature estimated
with the least square fits on two data sets for each panel
Panel
Number of
data in set
Eta zero
Thermal collector
Combi-panel without electricity
Combi-panel with electricity
22
8
12
0.8460.011
0.5960.015
0.5460.015
function of reduced temperature, which is defined
as
T red ; sT in 2 T ad /G
(40)
The assumption of a linear dependence of the
efficiency on the reduced temperature over the
range of reduced temperatures shown is in accordance with the results of the simulations for the
presented design.
Fig. 6 can be used to verify several experimental parameters. According to Eq. (34) the efficiency of a thermal collector can be written as
hth 5 P/GA 5 FRsta 2 theld 2 FRUloss T red
(41)
Fig. 6. Measured thermal efficiency (x) thermal collector,
(o, 1) combi-panel either without or with electricity production. The uncertainties (least square fits) in the measurements are presented by the bar lengths.
121
in which FR represents the heat removal factor
and h l the loss coefficient. FR is typically
0.8360.01, so the efficiency for zero reduced
temperature and zero electrical efficiency, 0.6,
automatically leads to a ta of 0.7260.02, which
corresponds to the calculated value of 0.74 that is
used in the models. The loss coefficient equals 5.2
W/ m 2 K, which resembles the value of 5.8 W/ m 2 K
calculated in the 1D model.
4.2. Dynamical influences
The dynamical performance of the 3D dynamical model has been tested by simulating the yield
of the combi-panel over a day. In order to do so,
the yield of the prototype combi-panel has been
measured together with the ambient conditions on
a day in October. Next, the data collected on the
irradiance and the ambient temperature were used
as the input data for the simulations. The results
for the 3D model together with the experimentally
measured data are presented in Fig. 7. According
to Fig. 7, the 3D model predicts the measured
outflow temperature of the combi-panel very well.
In the early hours the match is excellent. The fact
that the model slightly underpredicts the efficiency at the end of the day was attributed to the
tiles on the roof, which had been heated in the
course of the day and now increased the ambient
temperature in the direct vicinity of the combipanel.
Fig. 8 shows a close up of Fig. 7. The time lag
that appears in the figure corresponds to approximately 4 min between the increase in the irradiance and the increase in the outflow temperature, which is of the same order as the calculated
theoretical response time of the collector of
3.5 min for a mass flow of 60 l / h. It can be
concluded that the response time is small with
respect to the duration of a measurement, which
Fig. 7. Left: calculated (3D dynamical model) and measured outflow temperature for the case without production of electricity
~
(m561
l / h). The lower line presents the inflow temperature. Right: the corresponding irradiance.
122
H. A. Zondag et al.
Fig. 8. Close up of Fig. 7, illustrating the time lag between the irradiance (left curve) and the outflow temperature (right curve).
typically lasted several hours, but large with
respect to the sampling rate which was typically
10.8 s.
Since the calculation of the dynamical effects
took a lot of calculation time, it was decided to
establish the importance of the dynamical effects
for the calculation of the daily yield. Therefore,
the value of the daily yield determined from the
3D dynamical model has been compared to the
value of the daily yield determined from the 3D
steady state model. For a first try, the comparison
was performed with the data collected on a day in
August, a clear day without much fluctuation in
the irradiance. The data on the ambient conditions
were measured with an interval of 11 s. At the
end of the measurements, the data were averaged
over the hour and supplied to the model. The
results are shown in Fig. 9.
The yield determined from the dynamical 3D
Fig. 9. Output temperature of the combi-panel for a day with a
constant irradiance, calculated with the 3D dynamical model
(solid line) and the 3D steady model (dashed line).
model was found to be 11 046 kJ, corresponding
to 54.4% of the incoming solar energy, whereas
the steady model indicated a yield of 11 089 kJ,
corresponding to 54.2% of the solar energy. The
loss caused by ignoring the dynamical effects
over the day was therefore only 0.2%. It is
important to note, however, that the dynamical
model gives a lower yield at the beginning of the
day, due to the heating of the combi-panel,
whereas it predicts a higher efficiency at the end
of the day due to the cooling of the collector. This
effect is not calculated by the steady state models.
Therefore, if the yield is calculated over the first 5
h only, the difference between the models is
increased up to 0.8%. It should be concluded that
the dynamical effects largely cancel during the
day, since the reduced experimental efficiency in
the morning is compensated by the increased
experimental efficiency in the afternoon.
Next, the calculations were repeated for a day
in September with a strongly fluctuating irradiance. The results are shown in Fig. 10. For the
calculation of the yield over the entire day again
the dynamical and the steady state model produced exactly the same value of 45.4%. However,
if the calculation was confined to the first 3 h of
the day, the difference between the dynamical and
the steady state model was increased to 2.3%.
Even with the strongly fluctuating irradiation
observed on this day, the calculation of the
dynamical effects does not result in a more
accurate value for the yield over the entire day.
On the basis of these results it has been concluded
The thermal and electrical yield of a PV-thermal collector
Fig. 10. Output temperature of the combi-panel for a day with
a strongly fluctuating irradiance, calculated with the 3D
dynamical model (solid line) and the 3D steady model (dashed
line).
that for an accurate calculation of the annual
efficiency for our combi-panel collector, the dynamical effects do not have to be taken into
account, even though the specific heat is much
larger than for the case of a conventional thermal
collector, as indicated in Table 3. In addition, it
has been concluded that hourly data are sufficiently accurate for the calculation of the daily
yield, which strongly reduced the amount of data
to be processed.
4.3. Steady state performance of the combipanel
First, a comparison has been made between the
2D steady state model and the experiments. For
the calculations, the ambient conditions are presented in Table 4 while the system dimensions
were presented in Table 1. The results of the
simulation are shown in Fig. 11. The thermal
efficiency was determined as a function of reduced temperature for the 2D steady state model.
The agreement between the model and the experiTable 3. Specific heat of PV-thermal collector components
PV/ T
component
Specific heat
(J / kgK)
Copper tube 390
Copper sheet 390
Water
4180
Glass
840
EVA
2300
Silicon
760
Total
Component
mass (kg)
Heat storage
(J / K)
3.0
2.4
0.60
7.23
0.84
0.58
14.65
1170
936
2516
6080
1921
440
13 063
Table 4. Standard simulation conditions
Ta
G
Vwind
T sky
~
m
T in
w
208C
800 W/ m 2
1 m/s
48C
0.020 kg / s
20–608C
458
123
Fig. 11. Least squares fit of the measurements of the thermal
efficiency (solid) compared to the results obtained with the 2D
model (dashed). Upper line: conventional thermal collector,
middle line: combi-panel not producing electricity, lower line:
combi-panel producing electricity.
ments is well within the range of the experimental
data.
Next, the thermal efficiency calculated by the
1D, 2D, and 3D steady state models has been
compared. The simulations have been carried out
for the case in which no electricity is produced.
The result is given by Fig. 12. In order to allow a
good comparison between the models, curves are
shown for the 2D model without temperature
gradient over the glass (similar to the 3D model)
and the 3D model with the absorber area equal to
the PV area, (similar to the 1D and 2D models).
The figure shows that the results of the 1D and
the 2D model differ by roughly 1%. In comparison to the 2D thermal model, the 3D thermal
model predicts a 2% lower efficiency. However,
the figure shows that a large part of the 2%
difference between the 2D and the 3D model is
due to the absence of the heat resistance in the
glass in the 3D model. It should therefore be
concluded that a good correspondence exists
between the results of the models.
5. SIMULATION OF THE DAILY YIELD BY
THE 1D MODEL
As a final test, the thermal yield has been
simulated as a function of reduced temperature
with the 1D model. The ambient conditions
during the day were those presented in Fig. 13.
The inlet temperature was kept constant.
The results of the simulation are presented in
Figs. 14 and 15. Fig. 14 shows a good correspondence between the measurements and the
simulations, although the calculated values tend to
be slightly larger than the measured values,
124
H. A. Zondag et al.
Fig. 12. Comparison between the 1D, 2D and 3D thermal models for the case without production of electricity and h ca 5
45 W/ m 2 K.
corresponding to the small overprediction of the
efficiency observed in Fig. 11. In addition, it can
be observed that the simulations somewhat overpredict the measured thermal efficiency in the
morning and slightly underpredict the measured
thermal efficiency in the evening, as can be
expected from a steady state calculation, since the
heat storage effect (Klein et al., 1974) is not taken
into account.
Until now, all attention has been focussed on
the thermal efficiency of the system. However, for
a combi-panel also the electrical efficiency should
be determined. It turned out that the electrical
efficiency could be determined sufficiently accurately by the 1D model using Eq. (1).
Fig. 15 shows the measured electrical power of
the system and the temperature difference between the PV-panel and the PV-laminate that is
integrated into the combi-panel. The figure indicates that the electrical efficiency of the PV-panel
is slightly smaller than the electrical efficiency of
the combi-panel. This is due to the lower temperature of the cells in the combi-panel for the present
case in which the inlet temperature was kept
constant at approximately 188C. This implies that
the electrical gain due to cooling of the PV by the
Fig. 13. Ambient conditions as a function of time.
The thermal and electrical yield of a PV-thermal collector
125
Fig. 14. Calculated (dashed) and measured (solid) thermal power for the conventional thermal collector and the combi-panel as a
function of time.
water is even larger than the optical loss of the
combi-panel, that is due to the reflection at the
glass cover. This is expected, since additional
transmission losses of 8% correspond to a temperature difference of 168C, while a difference of
208C is observed.
6. ANNUAL YIELD OF A COMBI-PANEL IN A
DOMESTIC HOT WATER SYSTEM
Next, simulations have been performed to find
the thermal and electrical yield of the prototype
combi-panel for the Dutch meteorological KNMI
test reference year. The 1D steady model has been
used to model the case in which two similar
combi-panels with a joined area of 3.5 m 2 and a
mass flux of 50 kg /(m 2 / h) have been used to heat
a container of 175 l of water from 10 up to 608C.
A boiler unit was assumed to do the remainder of
the heating required if a temperature level of 608C
could not be reached by the combi-panel unit
alone. The pump was assumed to be operated by
an ideal control algorithm, switching it on whenever a positive yield would occur. The tapping
Fig. 15. Calculated (dashed) and measured (solid) DC electrical power for the PV-panel and for the combi-panel as a function of
time. In addition, the measured temperature of the PV panel and the PV combi laminate are indicated.
126
H. A. Zondag et al.
Table 5. ISSO warm water withdrawal schedule, (2) no withdrawal, (1) 175 / 8 l withdrawal
Hour
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Tapping
2
2
2
2
2
2
2
1
2
2
2
2
1
1
2
2
2
1
1
1
2
1
1
2
Table 6. Advantages of the four models
Model type
Characteristics
Calculation time
1D Steady model
Fast calculation of daily and annually averaged
yield for sheet-and-tube design
Like 1D steady model but easily adapted to
other configurations
Like 2D steady model but also detailed
information on temperature distribution
Like 3D steady model but also calculation of
instantaneous yield for non-steady conditions
Efficiency curve:
2D Steady model
3D Steady model
3D Dynamical model
pattern was modelled after the hot water withdrawal schedule of the ISSO (Institute for Study
and Stimulation of Research in the field of heating
and air conditioning), which is presented in Table
5. For the case in which heat and electrical energy
are produced simultaneously, the thermal efficiency has been found to be 33% for the
configuration used, as compared to 54% for the
conventional thermal collector. Taking into account low-irradiation loss, electrical loss due to
the angle of irradiation, losses due to the inverter
(typically 8%) and MPP-tracking losses of 2%,
the electrical efficiency of the panel was found to
be 6.7% as compared to 7.2% for the conventional PV-laminate under the same conditions. In this
case, therefore, in contrast to the situation in Fig.
15, the additional reflection losses in the PVcombi are not compensated by the cooling of the
PV. This is due to the higher average inlet
temperature of the water, which is heated during
the course of the day.
7. CONCLUSIONS
A dynamic 3D model and steady 3D, 2D and
1D models have been built, together with a first
non-optimised prototype of the combi-panel. The
efficiency curves determined from the models
correspond with the experimentally determined
curves well within the range of the experimental
data. It is concluded that for the determination of
the efficiency curves and the daily and annual
yield the simple steady 1D model performs satisfactorily, while the calculation time is substantially reduced in comparison to the more complicated
models, even for the case of a combi-panel with
its much larger specific heat in comparison to a
conventional thermal collector. In addition, for the
calculation of the daily yield, it is found that the
Hourly yield
0.27 s
0.05 s
8.35 s
1.67 s
229.31 s
45.86 s
–
2.5 h
error made by ignoring the dynamical effects is
very small.
The 1D steady model was subsequently used
for the calculation of the annual yield of a combipanel design. The thermal and electrical efficiencies have been found to be 33 and 6.7% for the
configuration used, as compared to 54% for the
conventional thermal collector and 7.2% for the
conventional PV-laminate under the same conditions. The advantage of the 1D model is that it
is roughly 30 times as fast as the 2D model,
which is about 25 times as fast as the 3D model.
Although the 1D model performs just as good
as the 2D model for the cases mentioned above,
the 2D and 3D models have some important
advantages over the 1D model since they are
more flexible and can easily be adapted to more
complicated combi-panel designs. Therefore, the
2D and 3D models are very important for further
optimization of the combi-panel, which is one of
the main targets in the ongoing research. By
variation of the model parameters information can
be obtained with respect to the effect of further
improvements. Table 6 summarizes the merits of
the four models.
NOMENCLATURE
A
B
c
D
F
FR
G
g
h
H
I
k
surface area (m 2 )
bond width (m)
specific heat (J / kgK)
tube diameter (m)
view factor
heat removal factor
irradiation (W/ m 2 )
gravitational acceleration (m / s 2 )
coefficient of heat transfer (W/ m 2 K)
height of insulating air layer (m)
current (A)
thermal conductivity (W/ mK)
The thermal and electrical yield of a PV-thermal collector
L
Lc
~
m
Nu
P
Pr
q
Ra
Re
T
T red
Uloss
V
W
x
y
b
d
e
h0
hel
r
s
t
ta
w
Subscripts
a
abs
b
ba
c
ca
conv
crit
el
in
lam
mpp
rad
th
w
127
length tube segment (m)
length collector surface (m)
mass flow (kg / s)
Nusselt number
thermal power generated (W)
Prandtl number
heat flux (W/ m 2 )
Rayleigh number
Reynolds number
temperature (K)
reduced temperature (Km 2 / W)
overall heat loss coefficient (W/ m 2 K)
voltage (V)
Tube spacing (m)
direction perpendicular to flow
direction of flow
coefficient of expansion of air
thickness of layer (m)
coefficient of emissivity
electrical efficiency at Standard Conditions
electrical efficiency
density (kg / m 3 )
constant of Stefan–Boltzmann
transmission of glass
transmission–absorption factor
collector angle
between PV and top cover by Hollands formula
(Duffie and Beckman, 1991, p. 160)
ambient
absorber
bond
from back to ambient
collector
from cells to absorber
convection
critical
electrical
inflow
laminate
maximum power point
radiation
thermal
water
Ra crit 5 10 8
F
1708ssin 1.8wd 1.6
Nu air 5 1 1 1.44 1 2 ]]]]]
Ra cos w
F
1708
3 1 2 ]]]
Ra cos w
1
Ra cos w
FS]]]
D
5830
G
G
1
0.333
21
G
1
(A.2)
In Eq. (A.2) the 1 indicates that the term only
has the value indicated between the brackets if the
latter is positive: it becomes zero if the quantity
between the brackets is negative.
Heat loss from cover glass to ambient due to
convection (Fujii and Imura, 1972):
Nu wind 5 0.56sRa crit cos wd 0.25
1 0.13sRa 0.333 2 Ra 0.333
crit d
(A.3)
gbsT topglass ( y) 2 T adL c3
Ra 5 Pr ]]]]]]]
n2
(A.4)
Heat loss at the upper surface (1 D model):.
Formula of Klein (Duffie and Beckman, 1991, p.
260):
N
1
Uloss 5 ]]]]]]
e 1 ]]
¯
h
C T lam 2 T a
wind
]] ]]]
T¯ lam sN 1 fd
5
F
G
21
6
ssT¯ 2lam 1T 2a dsT¯ lam 1T ad
1 ]]]]]]]]]]]]
2N1f2110.133elam
2N
selam 10.00591Nh windd 21 1 ]]]]]
etopglass
(A.5)
Acknowledgements—Part of the results presented on the 3D
dynamical model were obtained by Ben Ligtvoet, who was a
graduate student at the EUT at the time of this project.
where N5number of glass covers
f 5s1 1 0.089h w 2 0.1166h w epds1 1 0.07866Nd
C 5 520s1 2 0.000051w 2d for 08 , w , 708
APPENDIX A. THE HEAT TRANSFER
RELATIONS APPLIED
Heat
transfer
from
tube
to
water.
S
100
e 5 0.430 1 2 ]
T pm
D
h wind 5 wind heat transfer coefficient (W/ m 2 K)
5 2.8 1 3.0 Vwind
Re , 2300 ⇒ u tube 5 4.364
Re . 2300 ⇒ u tube 5 0.023Re Pr
(Bejan, 1993)
0.8
0.4
(A.1)
The Reynolds number is typically equal to 3200
throughout the measurements so the flow is in the
transition regime between laminar and turbulent.
Heat loss at the upper surface (3 D & 2 D
models):. Heat transport through the air layer
The temperatures in Kleins equation are in
Kelvin.
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