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ANALYSIS OF FLAT PLATE PHOTOVOLTAIC-THERMAL (PVT) MODELS
J. Bilbao and A. B. Sproul
School of Photovoltaic and Renewable Energy Engineering
University of New South Wales
Kensington, NSW 2052, Australia
ABSTRACT
In this work the performance of four PVT water models
were compared: the default TRNSYS PVT model Type50, a
modified version of the same model (Type50-C), a new
model (Type850) developed using analytical solutions and
the empirical relation presented by Akhtar and Mullick [11]
to calculate the cover temperature in flat plate collectors,
and a double iteration numerical model. A detailed analysis
and comparison between all four models was carried out to
identify specific errors, and Type50 and Type850 were also
compared based on the annual thermal and electrical yields
of a PVT residential system using TMY2 data. Results show
that errors from some models can be as high as 60% under
specific conditions, and close to 10% for annual yield
figures.
Key words: Photovoltaic-Thermal, PVT, Modeling,
1. INTRODUCTION
Within TRNSYS 16, the default model for PVT systems
simulations is Type50, which is based on the Florschuetz
[1] model to simulate the performance of PVT water
systems. In essence, it is an extension of the Hottel-Whillier
[2] model for flat plate collectors. Type50 also incorporates
the empirical expression for heat losses developed by Klein
[3] in conjunction with the convection loss coefficient
suggested by McAdams [4]. This is more or less the
standard Duffie and Beckman approach [5] which has been
widely used for the last 30 years. Today, more accurate
models and empirical expressions exist. Charalambous et al
[6] was the first to present a review of the literature
available for PVT systems, covering existing analytical and
numerical models, simulations and experimental work.
Later, Zondag presented a complete review [7] of PVT
technology, including models developed. In summary, most
of the early work on PVTs developed analytical models
based on the Hottel-Whillier [2] model for flat plate
collectors. According to Charalambous “Florschuetz
modified the Hottel–Willier analytical model for flat plate
collectors so… all existing expressions and information
available in the literature (such as the collector efficiency
factor, F’ and the heat removal factor, Fr) still apply”.
Bergene and Løvvik [8] found that their model (a more
detailed version of the Hottel-Willier model) was able to
predict PVT system efficiencies well, but they could not
compare their results to experimental data as system
parameters were missing in the available literature. Sandnes
and Rekstad [9] found a good level of agreement with their
experimental results. Zondag et al [10] developed and
compared four numerical models, a 3D dynamical model,
and 3D, 2D and 1D static models. He found that all the
models simulate the PVT system efficiency within 5% error
of the experimental data, and that the 1D model, based on
Hottel–Whillier and Klein equations, was well suited for
annual yield studies, mainly for its computational speed.
Although, annual yield figures for a domestic PVT system
were reported, they were obtained by using the 1D model,
and no comparison with the more accurate numerical
models was carried out.
It could be concluded from the literature that Klein’s
equation gives a reasonable approximation for steady state
models, with an adequate agreement with experimental
2
data. However, Klein’s equation has not been tested against
annual yield results using experimental data or other
models. Moreover, according to Akhtar and Mullick [11],
Klein’s equation can produce errors of up to 10% in the
estimation of the top losses of a flat plate collector for high
plate temperatures, and around 5% for low plate
temperatures. In the same publication, Akhtar and Mullick
propose a new experimental relation to estimate the cover
temperature of a flat plate hot water system, in replacement
of Klein’s equation.
The objective of this work was to check the results of
different PVT models for collectors with and without a
cover. The analysis is focused on heat transfer from the top
surfaces of the collector, and therefore is relevant not just
for PVT water models but also PVT air. Particular attention
was paid to the performance of the standard model included
in TRNSYS, Type50 (and therefore Florschuetz and Klein
approach), against more accurate models, like the developed
Type850. Section two of this paper will describe in detail all
the models used in the work. In section three, the results of
several simulations between the models are presented,
including in-depth comparisons. Finally, in section four,
several conclusions and recommendations are provided. The
nomenclature is presented in section five.
2. DESCRIPTION OF PVT MODELS USED
A total of four PVT models were used in this work:
1) a numerical model using a double iteration solving
method of the heat transfer equations;
2) a numerical model, with a single iteration process,
where the cover temperature is calculated using the
relations developed by Akhtar and Mullick (Type850);
3) Type50 model (part of the standard TRNSYS software
package);
4) a modified version of Type50, in which F’ is calculated
for each simulation (called Type50-C).
All of the above models were implemented in Excel. These
models can generate quick steady state results under
particular conditions, and are used for detailed comparison
between the models, but are not suited for year long
simulations.
In order to study the effects of the approximations made in
Type50 on an annual yield basis, model number 2, called
Type850 from now onwards (work of the authors), was also
implemented in TRNSYS, due to its simplicity and good
accuracy when compared to the double iteration numerical
model (model number 1).
In the following sections all the models will be described in
more detail.
2.1 Double iteration numerical model (implemented in
Excel)
As its name implies, in this numerical model a double
iteration is required to calculate all the heat transfer
equations for the case of the PVT collector with cover. First,
the initial cover and absorber plate temperatures are set: for
the cover temperature the ambient temperature plus one
degree is used, and 100°C is used for the plate temperature,
which is close to the stagnation temperature.
With Tp and Tc, the Nusselt number of the air in the cavity is
estimated using Buchberg [12] relation, in order to calculate
the convection losses between both surfaces. Also, from
Cooper [13] the relations from the Tables of Thermal
Properties of Gases, U.S. Department of Commerce, were
used to model the property of the air in the cavity between
the plate and cover, according to the average temperature of
both surfaces. Then all the convective and radiative losses
are calculated and combined as per equation 1, in order to
estimate the total losses of the PVT module.
(1) [( )
( ) ]
where Urpc and Ucpc are the radiative and convective losses
between the plate and the cover, Urcs and Uw are the
radiative and convection losses of the top cover, and UBE is
the back and edge losses, constant during the simulation.
Then, the thermal efficiency factors are calculated, starting
by F’, using the equation for collectors with square
channels:
(2)
⁄
where hf is the total thermal conductance between the plate
and the fluid. Fr is calculated using the standard equation in
[5]. Then the electrical and thermal useful energy rates per
unit of area are calculated using:
(3) [ ( )]
(4) ( ( ))
Notice that for the thermal energy output, the absorbed solar
energy is corrected using the electrical energy produced by
the PV cells. The mean plate temperature and the cover
temperature are calculated using an energy balance
approach:
(5)
(6) ( ) ( )
( )
3
From this point onwards, the new values of Tp or Tc can be
used to recalculate all the equations until the chosen
variables converge. Then the same process can be used with
the other variable until it converges. This double iteration
process will have to be repeated until the error in both
variables is small. If done manually it can be a lengthy
process, but in excel the solver routine can be used, and
solutions are found automatically.
For the case of the PVT collector without a cover, there is
no need to estimate the cover temperature and a single
iteration approach is enough to accurately calculate all the
heat losses. The simulation starts with an initial estimation
of the plate temperature. Then, the total losses (UL) are
calculated by adding the radiation (Urcs) and convection
(Uw) losses from the top of the panel, plus the back and
edge losses (UBE).
Once the losses are calculated, the same equations used for
the collector with a cover (Eqs. 2, 3, 4, and 5) are used to
calculate F’, Fr, Qe, Qu, and Tp, but the cover temperature is
replaced by the plate temperature when required.
2.2 Single iteration model, TYPE850 (implemented in
Excel and TRNSYS)
In this model, the empirical relations developed by Akhtar
and Mullick [11] to estimate the cover temperature of Flat
Plate Solar Collectors were used. One of the strengths of
these empirical relations is that they allow for the use of the
Sky Temperature, and therefore, the correct calculation of
the radiation losses.
The algorithm and equations used in this model are exactly
the same as in the double iteration model, except for the use
of the cover temperature equations. This allows having one
less unknown variable and therefore, only a single iteration
process can be used. This iteration allows for the self-
correction of the thermal energy output (eq. 4) and UL, so
there is no need to use Florschuetz’s proposed adjustment
for PVT panels. This also allows the use of Akhtar and
Mullick equations without the need of any modifications.
For the case of the PVT collector without a cover, the
algorithm and equations are the same as for the first model.
2.3 Standard PVT model, Type50 (implemented in Excel,
existing in TRNSYS)
As explained above, Type50 is a very close implementation
of Florschuetz [1] work. Type50 has four modes of
operation for flat plate collectors, and other modes for
concentrating collectors not reviewed in this paper. In this
work, MODE 2 will be used because it proved to be more
stable than the others. However, in MODE 2 the angular
dependence of the cover transmisivity is considered
constant (unlike MODE4 which includes the incident angle
modifiers, but was unable to converge), so adjustments were
introduced to the solar irradiance data to take into account
the angle of incidence to make a fair comparison with the
rest of the models.
Type 50 also uses a single iteration approach to solve the
heat transfer equations, thanks to the use of Klein’s equation
to estimate the top cover losses.
Some key Type50 model details and differences with the
original Florschuetz work are:
- The algorithm runs for three iterations (controlled by an
internal counter) for each time step, after which the
program exits the simulation with whatever values are
achieved.
- Equations for the calculation of F’ were not implemented
in Type50, as F’ is a given parameter to the model and
remains constant through the whole simulation.
- The mean fluid temperature is approximated as the
average of the inlet and outlet temperature, which is
different to the true analytical value.
- The cell temperature is calculated at the end of each time
step and is used only for output purposes and not as part
of the internal calculations.
- The thermal losses are calculated using the empirical
equation developed by Klein [3], which does not take into
account the sky temperature
- In the implementation of Klein’s equation in Type50, the
mean water temperature is used instead of the mean plate
temperature.
In the Excel implementation of this model, the three
iterations limit was not used, and the algorithm runs until
the values converge.
2.4 Modified Standard PVT model, Type50-C
(implemented in Excel)
This type uses the same equations as Type50, but F’ is
calculated using equation 2 for each simulation. This allows
an accurate value of the efficiency factor to be calculated
depending on the calculated heat losses. Although this is
certainly an improvement over Type50, it also makes the
model more susceptive to the possible errors introduced in
the calculation of the top losses by Klein’s equation.
3. RESULTS
In the first three parts of this section, all the models using
empirical equations (models 2 to 4) are compared in detail
against the double iteration numerical model (model 1),
studying for example the impact of the simplifications made
4
in Type50, particularly, the use of the constant F’
coefficient. For the purpose of these comparisons, the Excel
implementations of the models were used, with the
parameters at design conditions, shown in Table 1.
TABLE 1: PARAMETERS AT DESIGN CONDITIONS
FOR THE CALCULATION OF F’
Parameter Value
No Cover
Value
Cover Description
H 800 800 Solar Radiation (W/m2)
Vw 2 2 Wind velocity (m/s)
Tin 20 20 Inlet Temperature (°C)
Tamb 20 20 Amb. Temperature (°C)
B 30 30 Panel Tilt (degrees)
εp 0.850 0.850 Collector Plate Emissivity
εg - 0.850 Glass cover Emissivity
α 0.900 0.900 Effective Absorptance
τ 0.920 0.846 Total Transmittance
ηr 0.144 0.144 Cell Eff. at Ref. Temp.
βr 0.0048 0.0048 Cell Temp. Coef. (1/K)
ů 0.020 0.011 Mass Flowrate (Kg/s.m2)
hf 56.923 43.258 Plate to Fluid (W/m2.C)
UL 18.596 4.622 Total Losses (W/m2.C)
F’ 0.754 0.903 Collector Eff. Factor
In part 3.4 of this section, Type50 and Type850 are
compared on an annual basis, using a simulation of a
residential hot water system in TRNSYS.
3.1 Effects of F’ simplification
F’ was calculated at the design conditions (see Table 1) and
kept constant in Type50, but it was calculated for each
simulation in Type50-C. The value of Fr was compared for
both models to quantify the errors of the simplification,
because is directly proportional to the useful thermal energy
Qu. Results for different combinations of ambient
temperature, inlet temperature and wind velocity are shown
in Figure 1 and Figure 2 respectively, for both type of
collectors (with and without a cover).
For the panel without a cover, changes in the wind speed
have an important impact in the calculation of Fr, so the
changes in the inlet and ambient temperatures are dwarfed
in comparison. This is a logical result, because convection
losses are dominant in a coverless panel. When the panel
operates close to the “design conditions”, the errors are
small and less than 5%, but at high wind speeds errors can
escalate up to 30%. The problem of Klein’s equation for
coverless panels as implemented in Type50, is the use of the
mean fluid temperature instead of the correct mean plate
temperature. The effects of a constant F’ are less
pronounced in PVT modules with a cover, as the maximum
Fig. 1: Fr percentage error for fixed ambient temperature
Fig. 2: Fr percentage error for fixed inlet temperature.
14
16
18
20
22
24
26
28
30
0 1 2 3 4 5 6 7 8 9 10
Tin
( C
)
Wind Velocity (m/s)
a) Fr percentage error (Tamb = Tsky = 20 C, N = 0)
5%-10%
0%-5%
-5%-0%
-10%--5%
-15%--10%
-20%--15%
-25%--20%
-30%--25%
-35%--30%
15
20
25
30
35
40
45
50
55
0 2 4 6 8 10
Tin
( C
)
Wind Velocity (m/s)
b) Fr percentage error (Tamb = Tsky = 20 C, N = 1)
2%-3%
1%-2%
0%-1%
-1%-0%
-2%--1%
-3%--2%
-4%--3%
-5%--4%
-6%--5%
14
16
18
20
22
24
26
28
30
0 1 2 3 4 5 6 7 8 9 10
Ta
mb
( C
)
Wind Velocity (m/s)
a) Fr percentage error (Tin = 20 C, N = 0)
5%-10%
0%-5%
-5%-0%
-10%--5%
-15%--10%
-20%--15%
-25%--20%
-30%--25%
-35%--30%
14
16
18
20
22
24
0 2 4 6 8 10
Ta
mb
( C
)
Wind Velocity (m/s)
b) Fr percentage error (Tin = 20 C, N = 1)
1.5%-2.0%
1.0%-1.5%
0.5%-1.0%
0.0%-0.5%
-0.5%-0.0%
-1.0%--0.5%
-1.5%--1.0%
-2.0%--1.5%
-2.5%--2.0%
-3.0%--2.5%
5
error is kept below 6%. In this case, the inlet temperature is
shown to have an equally important effect to the wind
velocity. The results suggest that the effects of using a fixed
F’ are reasonable for a PVT system with a cover.
3.2 Comparison of Type50, 50-C, and 850 against Model 1
Klein’s equation is close to the correct calculation of top
losses when ambient temperature is similar to sky
temperature (cloudy sky), so Type50 should perform well
under these conditions. However, PVT panels have high
emissivity –unlike solar hot water collectors that usually
have selective surfaces– so it’s expected that changes in the
sky temperature will produce noticeable effects in the
performance of the models even for panels with covers. The
model using Akhtar and Mullick equations was also
included. Figure 3 shows the errors for qu and Figure 4 for
UL, for PVT panels with (N=1) and without (N=0) cover.
For this set of simulations all the parameters were kept at
the design conditions (best case scenario for Type50),
except for the inlet temperature. From Figure 3 and Figure 4
we can conclude that:
- The levels of error for Type50-C are close to zero for
cloudy sky conditions, and independent of wind velocity
and inlet temperature. In clear sky conditions, the errors
are limited to 50 W/m2.
- Type50 does not perform well in the calculation of qu,
resulting in errors above 150 W/m2, for clear and cloudy
skies. The use of a fixed F’ has an undesirable large
impact in this case.
- In the calculation of UL, both models, Type50 and
Type50-C, have considerable errors except for the panel
without a cover and cloudy skies. In all other cases, the
errors are significant
- Because the thermal losses are underestimated, the useful
thermal energy for both models, Type50 and Type50-C,
were overestimated, although the corrected model has
consistently smaller errors.
- The model using Akhtar and Mullick equations does
remarkably well, with errors well below 5% for UL and
under 1 to 2 W/m2 for qu, which is a big improvement
over Type50.
The correction factor proposed by Florschuetz [1] can
account for up to 5% of difference in the calculation of UL.
When using iterative methods, the extra correction leads to
a under prediction of UL and over prediction of the useful
thermal output. The results show that the biggest limitation
of Type50 is the implementation of Klein’s equation, as
even Type50-C, using correct F’ values can produce errors
as high as 7% at the design conditions, and up to 17% in the
worst cases.
3.3 Performance under stagnation
It’s important to study no flow conditions in a PVT system,
more than in a normal flat plate collector, because the
temperatures reached in the plate affect the electric
performance. Therefore, it is imperative for a PVT model to
estimate as accurately as possible the stagnation
temperatures.
Fig. 3: qu absolute error compared to numerical model.
Fig. 4: UL percentage error compared to numerical model.
0
20
40
60
80
100
120
140
160
180
200
15 20 25 30 35 40
(W/m
2)
Tin ( C)
a) qu absolute error (Wv=2m/s, Ta=20 C, N=0)
Type50-C, Ts=Ta Type50, Ts=Ta Type50-C, Ts=Ta-18 Type50, Ts=Ta-18
0
20
40
60
80
100
120
140
160
180
200
15 20 25 30 35 40 45 50 55
(W/m
2)
Tin ( C)
b) qu absolute error (Wv=2m/s, Ta=20 C, N=1)
A&M, Ts=Ta Type50-C, Ts=Ta Type50, Ts=Ta
A&M, Ts=Ta-18 Type50-C, Ts=Ta-18 Type50, Ts=Ta-18
-60%
-55%
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
15 20 25 30 35 40 45 50 55
Tin ( C)
a) UL percentage error (Wv=2m/s, Ta=20 C, N=0)
Type50-C, Ts=Ta Type50, Ts=Ta Type50-C, Ts=Ta-18 Type50, Ts=Ta-18
-60%
-55%
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
15 20 25 30 35 40 45 50 55
Tin ( C)
b) UL percentage error (Wv=2m/s, Ta=20 C, N=1)
A&M, Ts=Ta Type50-C, Ts=Ta Type50, Ts=Ta
A&M, Ts=Ta-18 Type50-C, Ts=Ta-18 Type50, Ts=Ta-18
6
Fig. 5: qe absolute error compared to numerical model in
stagnation conditions.
Depending on the size of the system, and its operation and
controls, it is probable that a PVT system will spend several
hours in stagnation during summer. Figure 5 shows the
results for the error in the calculation of the electric output
per unit of area, for different wind, inlet temperature
(needed for the calculation Tmf and of UL in Klein’s
equation), and sky temperature under stagnation. As can be
seen, Type50 tends to underestimate the electrical output
under stagnation conditions; which will suggest an
overestimation in the plate temperatures. This agrees with
the results reported by the ECN [14]. Errors in the collector
without a cover are generally small. For the collector with a
cover, errors are more important and close to 10% under
design conditions or around 7 (W/m2). The model using
Akhtar and Mullick equations again performs well.
3.4 Annual Yields Comparison in TRNSYS
In this section, the thermal and electrical annual yield of a
residential PVT system located in Sydney, Australia, are
presented. The system was simulated using TRNSYS, with
two different PVT models: Type50, and Type 850. The
simulation models the energy requirements of a standard
four person residence in the Sydney climate. The annual hot
water energy consumption is estimated to be 2,709 kWh, or
7.4 kWh/day, and the annual electric energy usage is
estimated as 8,249 kWh, or 22.6 kWh/day (total daily
energy consumption of 30kWh); figures derived from
DEWHA and IPART reports [15-16]. The PVT system is
connected to a 300 liter electric boosted hot water tank, with
a set point of 60°C. The electric output of the PV array is
assumed to be always at the maximum power point, and no
losses in the inverter or cables have been incorporated. For
both models a PVT panel of 1.28m2 was used, with an
electrical efficiency of 14% at STC. The size and the
electrical efficiency of the PVT panel are similar to
commercially available PV panels.
Fig. 6: annual yield percentage error for different
parameters and climates, Type50 against Type850.
A system of 3,240Wp comprised of 18 panels was chosen to
simulate a typical system, similar to what would be installed
on a house rooftop. Two scenarios were used, systems with
and without a cover. All the parameters are kept equal
between both models and scenarios. Results of the errors
between Type 50 and Type 850 are presented in Figure 6:
auxiliary energy (Qaux), the electrical energy (Qpv), pump
energy (Qpump), and the net energy (Qnet) defined as Qnet =
(Qload - Qaux) + Qpv - Qpump.
-8
-7
-6
-5
-4
-3
-2
-1
0
1
15 20 25 30 35 40 45 50 55
(W/m
2)
Tin ( C)
a) qe absolut error (Wv=2m/s, Ta=20 C, N=0)
Type50, Ts=Ta Type50, Ts=Ta-18
-8
-7
-6
-5
-4
-3
-2
-1
0
1
15 20 25 30 35 40 45 50 55
(W/m
2)
Tin ( C)
b) qe absolute error (Wv=2m/s, Ta=20 C, N=1)
A&M, Ts=Ta Type50, Ts=Ta A&M, Ts=Ta-18 Type50, Ts=Ta-18
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Flow Rate (Kg/s.m2)
a) Qaux percentage error (18 panels)
Sydney - No Cover Melbourne - No Cover
Sydney - With Cover Melbourne - With Cover
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Flow Rate (Kg/s.m2)
b) Qpv percentage error (18 panels)
Sydney - No Cover Melbourne - No Cover
Sydney - With Cover Melbourne - With Cover
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Flow Rate (Kg/s.m2)
c) Qnet percenatge error (18 panels)
Sydney - No Cover Melbourne - No Cover
Sydney - With Cover Melbourne - With Cover
7
The results show that Type50 is consistently over predicting
the thermal output, and therefore, the auxiliary energy
required is under predicted with respect to Type 850. Errors
for the annual amount of required auxiliary energy are
around 15% for panels with cover and 6% for panels
without a cover. On the electrical output, Type50 with a
cover under predicts the annual yield by 7% and over
predicts the panel without a cover by 3%, i.e., Type50 with
cover runs “hotter” than Type850, and Type50 without a
cover runs “cooler”. The energy required by the pump is in
direct relation of the amount of hours that the thermal
system was working. In this scenario, Type50 with and
without a cover runs the pump 7% and 20% longer time
frames, respectively. Some findings might seem
contradictory, but in reality, they reflect how a PVT system
performance changes depending on the size of the system,
its operation, and in particular, if it was carried out as an
individual unit or as part of a system. This reaffirms the
point that PVT systems performance and design should be
always analyzed in the context of an application.
4. CONCLUSIONS
From the specific analysis of Type50, we can summarize
the shortcomings of the model as:
- The value of F’ is assumed as a constant parameter,
independent of the changes in the total losses UL which
depends on ambient conditions (wind speed, ambient
temperature) and fluid temperature. Errors of up to 10%
are expected when maintaining F’ constant.
- Sky temperature is not used for the calculation of
radiation losses. This is particularly important in PVT
systems, compared to hot water collectors, because PV
panels have high emissivity.
- The model implements the original equation of Klein [3]
using Tmf instead of Tp. This leads to more errors and
instabilities when Tmf < Tamb. For PVT systems with small
areas, this is not an uncommon scenario (Akhtar and
Mullick equation has the same problem when Tp < Tamb,
less often).
- The model uses Florschuetz’s correction factor for UL to
account for the electrical output of the system. However,
it is considered that this correction factor should not be
used.
- As a result, Type50 calculation of UL can produce errors
of up to 60% in the worst cases.
- Although 3 iterations should be enough for the model to
converge most of the times, there is no guarantee that
moderate errors could not be happening in some time
steps.
From the annual yield analysis we can conclude that:
- Even though the errors are in general smaller than in the
specific analysis, some serious differences are still
present, specifically regarding the thermal output and its
effect in the auxiliary power, with maximum errors of
16% for Sydney climate and 32% for Melbourne climate.
- Type50 underestimates the thermal losses of the panel and
therefore the model overestimates the thermal output. This
results in the controller running the pump more hours
during the year, which leads to large errors in the
calculations of the annual energy required by the pump
system.
- PV electric energy output errors are of the order of ±5%,
which can be considered acceptable.
- As for any summary of data, the annual yield gives an
average of the errors, possibly masking large differences
in the operation of the system in a day to day basis.
In conclusion, it appears clear that Type50 offers several
limitations where high levels of accuracy are required.
Although the electrical output accuracy is worrying at a
model level, the errors in the annual yield case are
acceptable. The errors on the thermal output can be above
10%, which introduces a higher level of uncertainty in the
design of a system. On the other hand, the work proposed
by Akhtar and Mullick [7] proved to be exceptionally
accurate when compared to the complete numerical
solution. Finally, it is recommended that system analyses
with whole year simulations (using TMY2 data or similar)
should be used to study the performance of PVT systems
and to compare different models.
5. NOMENCLATURE
B tilt angle of panel
F’ collector efficiency factor
Fr collector heat removal factor
H total solar radiation incident on collector
N number of covers
qu useful thermal energy collection rate per unit area
qe useful electrical energy collection rate per unit area
S absorbed solar radiation per unit area
Ta ambient temperature
Tc cover temperature
Tin inlet temperature
Tp mean plate temperature
Tr PV reference temperature
Ts sky temperature
hf thermal conductance between absorber and fluid
UBE bottom and edges heat loss coefficient
UL overall heat loss coefficient
Ucpc convection heat loss coefficient among plate and cover
Urcs radiation heat loss coefficient between cover and sky
Urpc radiation heat loss coefficient between plate and cover
Uw convection heat loss coefficient due to wind speed
ů mass flow rate
Vw wind velocity
α effective absorptance of collector absorber
8
βr temperature coefficient of solar cell
σ Stefan–Boltzmann constant
εg glass emissivity
εp absorber plate emissivity
ηr cell efficiency at reference temperature
τ transmittance of collector glass cover
6. REFERENCES
(1) Florschuetz, L. W., Extension of the Hottel-Whillier
model to the analysis of combined photovoltaic/thermal flat
plate collectors, Solar Energy 22(4): 361-6, 1979
(2) Hottel, H. C., Whillier, W., Evaluation of flat-plate solar
collector performance, Proceedings Of the Conference on
the use of Solar Energy, University of Arizona, Vol II: 74-
104, 1958
(3) Klein, S.A., Calculation of flat-plate collector loss
coefficients, Solar Energy 17: 79-80, 1975
(4) McAdams, W.C., Heat Transmission (3rd
Edn),
McGraw-Hill, 1954
(5) Duffie, J.A. and Beckman W.A., Solar Engineering of
Thermal Processes (3rd
Edn), Wiley, 2006
(6) Charalambous, et al., Photovoltaic thermal (PV/T)
collectors: A review, Applied Thermal Engineering 27(2-3):
275-286, 2007
(7) Zondag, H. A., Flat-plate PV-Thermal collectors and
systems: A review, Renewable and Sustainable Energy
Reviews 12(4): 891-959, 2008
(8) Bergene, T. and O. M. Løvvik., Model calculations on a
flat-plate solar heat collector with integrated solar cells,
Solar Energy 55(6): 453-462, 1995
(9) Sandnes, B. and J. Rekstad., A photovoltaic/thermal
(PV/T) collector with a polymer absorber plate.
Experimental study and analytical model, Solar Energy
72(1): 63-73, 2002
(10) Zondag, H. A., de Vries, D. W., et al., The thermal and
electrical yield of a PV-thermal collector, Solar Energy
72(2): 113-128, 2002
(11) Akhtar, N. and Mullick, S. C., Approximate Method
For Computation of Glass Cover Temperature and Top
Heat-Loss Coefficient of Solar Collectors with Single
Glazing, Solar Energy 66(5):349–354, 1999
(12) Buchberg, H., Catton, I., Edwards, D.K., Natural
Convection in Enclosed Spaces - A Review of Application
to Solar Energy Collection, Journal of Heat Transfer 98(2):
182-189, 1976
(13) Cooper, P.I., The Effect of Inclination on the Heat Loss
From Flat-Plate Solar Collectors, Solar Energy 27(5):413-
420, 1981
(14) PVT performance measurement guidelines, PV
Catapult, ECN and ISFH, 2005
(15) DEWHA, Energy Use in the Australian Residential
Sector 1986 – 2020, Department of the Environment,
Water, Heritage and the Arts, 2009
(16) IPART, Residential energy and water use in Sydney,
the Blue Mountains and Illawarra Results from the 2006
household survey, Independent Pricing and Regulatory
Tribunal of New South Wales, 2007