On the effect of the PV array inclination to its performance &
efficiency
S. Kaplanis1 E. Kaplani1, P. Wolf2
1. Mech. Engineering dep., TEI Patra, Greece, kaplanis@teipat.gr
2. Technical University of Prague, Czech Republic, petr.wolf@post.cz
Abstract
The paper outlines the experimental set up as developed in order to obtain measurements and determine the power
performance of a PV array, its efficiency and the temperature on its surface. The investigation covers a PV array
system placed in a free environment, outdoors. The experiments were carried out for different inclinations of the PV
panels and various levels of solar radiation on them. The paper provides an analysis of the results and argues about
the coefficient which relates the PV panel surface temperature with the solar radiation intensity on it, with the angle
of inclination, α, as a parameter.
Additionally, there are presented the results of the rate of change of the PV power output and its efficiency with
respect to the solar radiation intensity for various angles of inclination, related to the air flow type and pattern at the
back surface of the PV panels.
Keywords: PV efficiency, Performance, Angle of inclination
Those cases above are very important for
investigation, either for the design of buildings
with solar technology elements integrated into
their structure,[17-20], or for a more accurate
estimation of the energy to be delivered by a PV
generator in a period of time.
On the other hand, the wind strongly affects the
PV module temperature,[4]. Therefore, it is
necessary to distinguish between natural
convection of heat, where air flow is caused by
the difference in temperatures, between the PV
cell
temperature
and
its
environment
temperature, or forced air flow, due to wind.
Also, the wind direction matters.
1. INTRODUCTION
The temperature developed in a PV cell working
in field conditions, or integrated into a building
shell, strongly affects the PV cell efficiency and
plays a significant role in the PV cell
performance and the overall annual yield, [1-16].
The temperature of the PV cell depends on the
solar radiation intensity on the cell, IT (W/m2),
the ambient air temperature, Ta (°C), the cell
technology and structure, the geometry of the PV
array in the field, that is the tilt angle and the
orientation, as well as its surrounding.
+hpv,b *Apv*(Tpv,b –Ta )
As the irradiated PV module can use only a
small part of the radiation for power generation,
the rest of the radiation, minus the reflected part,
is dissipated, finally, into heat. This causes the
PV cell temperature to raise above the ambient
air temperature. Provided the conditions of the
PV system and its surrounding do not change
fast, then, steady state prevails and the thermal
capacities of the PV system can be neglected.
This heat is then passed into the environment.
The expression which may hold for the energy
balance for steady state conditions takes the
form:
(1)
(τα) is the transmission-absorption coefficient as
analysed in [21].
ηpv is the PV efficiency, hpv,f and hpv,b are the
surface heat transfer coefficients in W/m2K for
the front and back surface of the PV panel,
which differ according to the Heat Transfer
theory,[22,23].
Giving values to ηpv and to hpv one comes to a
formula like the one below for laminar flow:
Tpv= Ta + 0.0425* IT
(τα)*ΙΤ = ηpv*IT + hpv,f * Apv *(Tpv,f –Ta )
1
(2)
Tpv= Ta + λ* IT
(5)
where λ can be a function dependent on many
parameters, like:
a. the solar radiation spectrum, or
correspondingly the clearness index, Kt,
[15,24,25]
b. the inclination angle, α, as hpv generally
depends on this angle,
c. the type of flow, natural or forced flow,
and
d. the pattern of air flow past the PV panel,
ie laminar or turbulent, which determine
the value of hpv, [22,23] .
It is, therefore, important to design experiments
to determine the PV panel performance, its
maximum power, Pm and ηpv, associated to the
IT and the α value, as parameters.
According to the analysis above, as the cases
b,c,d are inter-related, the coefficient λ (Km2/W)
might well be assumed as a function of the
inclination of the module, α, where λ=f(α.) or
more accurately from the Heat Transfer theory,
is a function of cos(α), [26,27].
All these lead to the conclusion that even with
the same solar radiation intensity on two PV
cells, which have different inclination angles,
one may get different results for Pm, ηpv and
Tpv.
Figure 1. A PV array positioned with a
changing inclination in a free space outdoors.
The measurements were done in Patras, Greece
in June 2007 with PV modules, SM 55, in
outdoor conditions. The wind velocity was less
than 1m/s. PV cooling was mostly due to natural
air convection and infrared radiation from the
PV modules..
The experimental set up is shown by the
schematic diagram in fig. 2. The system built to
collect and manage data and measure PV module
performance, consists of:
1. A data logger, Campbell Scientific
CR1000
2. An i-V characteristic portable system ,
developed and built for this project
3. A Pyranometer Kipp & Zonen, type
CMP3 and temperature sensors:
thermocouple “T” ( Copper-Constantan)
and a portable infra-red thermometer,
type Mikron M90 series. The sensors
were placed on the back side of the PV
module directly on the Tedlar foil. A
second thermocouple in a cage was used
to measure the ambient air temperature,
Ta.
Simultaneously,
the
i-V
characteristic of the PV panels were
obtained for all cases examined.
4. Software to analyze the i-V data
DESCRIPTION OF THE PV SYSTEM
DESIGN AND THE EXPERIMENTAL SETUP
To determine the function f(α) and draw
conclusions on the effect of α on the PV
performance, field measurements were taken for
different IT and α values. PV cell temperatures,
as well as ambient temperatures, were measured
in an attempt to fit the data, finally obtained, on a
curve with cos(α), as variable. The i-V
characteristic curves and therefore, the max.
power Pm were both measured and determined
for different inclinations and irradiation levels,
outdoors.
A PV generator in a free space outdoors.
PV panels are placed in a free space with an
inclination angle, manually fixed, see fig.1.
In this mode of experiments, the air flow is
rather free depending on the angle of inclination.
The differences in the results, as to be presented
and discussed, may be attributed to the changes
of the air flow pattern, developed in each set, due
to the geometry of the PV and its surrounding
environment.
2
Figure 1. Schematic diagram of the experimental set up
Figure3. Temperature increase, Tdif, vs IT for
various inclination angles of the PV array
placed on a free environment, outdoors.
RESULTS
Eq (3) provides that Tdif / IT = λ. Fitting the
Tdif / IT measured data onto a curve:
The experiments were conducted so that Tpv,
Ta, and IT were measured, for various α values
from 160 to 750. This inclination is measured
from the horizontal position. Pm and ηpv were
determined vs IT for predetermined values of the
angle of inclination, α. Each measurement lasted
for a period of time, as to reach at steady state
and get a whole performance profile of a range
of IT values under such conditions. The
monitoring system showed when steady state
conditions were reached.
During such periods, the i-V curves were
obtained, so that Pm be determined. Then, the
relative efficiency, Pm/IT, was calculated.
In this set of experiments, the results are
rationally interpreted.
Tdif increases with IT and takes larger values for
small α, as shown in fig. 3; .
However, as air flow at the back side of the PV
surface changes to turbulent, [15, 22, 26, 27],
due to increase in the Grashof number, at about
40-450, we observe a larger drop in Tdif ; see fig.
6, the curve for inclination angle at 460.
On the contrary, in high α values, the flow of the
air passed by the PV panel turns again laminar or
the layers glide over the back PV surface.
k0 +k1*cos(α) + k2*cos(α)2
(6)
we obtain good results as shown in fig. 4, where
the coefficients of the quadratic function take
values: k1 = 1.66E-1 k2 = -2.37E-1 k3 =
1.02E-1
and the norm of residuals = 2E-3
Figure 4. Tdiff /IT= λ, the solar radiation coefficient for
the PV panel temperature vs cos(α) fitted on a quadratic
polynomial fitting. The PV array is positioned in a free
space outdoors.
Analysis of the data, taken from fig. 3 show that
λ coefficient which appears in eq.(3) takes values
in the range:
[ 0.05 for inclination 650 , 0.035 for 47 0 , 0.04
for 26 0 and 0.045 for 160 ]
3
In the case of the PV array in a free environment,
λ values get higher at low and high α angles, as
again the flow turns to be laminar, due to low
Tpv and low IT.
with two different α angles, or the expression
was estimated from the data of any curve in fig.
6, which holds for a specific α angle, for a range
of IT values.
Finally, the rate of change of the PV power
output and its relative efficiency vs IT with
parameter the angle of inclination, α, are given in
figs. 5 and 6, respectively.
In addition, the same analysis was followed to
obtain values of , (dηpv/dΤ)/ηpv using data
between the curve for 470 and 160 This analysis
gave a higher value for (dηpv/dΤ)/ηpv. The
relative change was estimated to about 1.0%/0C, which verifies the effect that the
inclination angle has in the PV performance.
The integrated relative change of (dη/dIT)/η over
a range of IT that is [(dηpv/dIT)/ηpv]δΙΤ
for the same angle of inclination, α, is obtained
from fig. 6, through the analysis:
[(dηpv/dI)/ ηpv]*δΙ = [V-1oc *(dVoc/dT)*(dT/dI) +
I1sc*(disc/dT)*(dT/dI)+FF-1*(dFF/dT)*(dT/dI)]*δΙ
The estimation of the expression
(dηpv/dI)/ ηpv using the known values of the rate
of change of Voc , isc , FF and the rate Tpv
changes with IT , taken from fig. 6, provides a
theoretical value of -3.7 – 3.8 % for the range of
measurements from 800 to 1000 W/m2
On the other hand the analysis of the
experimental data in fig. 6 provides a value of 7% at 470 and – 5.56 % at 160 for the same range
800 to 1000 W/m2
Figure 2. PV power increase vs IT for various
inclination angles. The figure stands for
a PV array positioned in a free space, outdoors.
2. CONCLUSIONS
This paper describes the performance
measurements and results as obtained by various
lay outs of a PV array. The target was to find the
dependence of PV output on the inclination and
the temperature developed in it. As seen from the
fitting results, the coefficient which relates the
Tpv with IT was found to fit well on a quadratic
polynomial with cos (α).
If the temperature had no effect, the PV
efficiency would increase by the irradiation
increase. As seen in figs. 3,5 and 6 the
temperature increase has a strong effect on the
PV efficiency and thus in real conditions the
efficiency decreases as irradiation increases.
The paper succeeded to provide a detailed
analysis of the PV performance, as determined
by the i-V curves, the relative efficiency and the
temperature profiles developed at the back
surface of the PV panels.
For a PV array positioned in a free space the
values of the coefficient which relates Tpv with
IT lie within the range:
Figure 3. Relative efficiency, Pm/IT vs IT for various
inclination angles. The figure holds for a PV array
placed in a free space, outdoors.
An analysis of the data provided in figs. 3,5 and
6 was attempted. The curve values representing
the inclination angles 470 and 260, in fig 3 interrelated with the ones of fig. 6, are chosen for IT
values: 700, 800, 900 W/m2.
The relative change of the efficiency over the Tdif
for both the inclination angles of the PV panel,
(dηpv/dΤ)/ηpv, was estimated to take values from
about – 0.40%/0C to -0.5%/0C.
It is important to argue about the above
expression, which was calculated either for the
same solar irradiation, IT, on the PV panel and
4
[ 0.05 for inclination 650 , 0.35 for 47 0 , 0.04 for
26 0 and 0.45 for 160 ].
These results were interpreted as influence of the
heat transfer coefficient, hpv, which changes with
Tpv and with the flow rate which in turn depends
on the inclination α, [22, 23, 26, 27].
The change of air flow from laminar to turbulent
at about 400-450 is evident in fig. 6. This change
is mentioned in [22].
However, at high α values the flow gets laminar,
as it was the case for low α values. The reason
now is that the IT for high inclinations is low and
therefore the Tpv gets low values with a
subsequent decrease of the Grashof number. It is
essential that the effect of inclination is complex
due to changes in air flow and further extended
studies are required about the air flow pattern
developed.
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ACKNOWLEDGEMENTS
The authors thank the Greek Ministry of
Education EPEAEK III Programme and the
project ARCHIMIDES for funding this study, as
well as the ERASMUS Program of the European
Commission for the grant to one of the authors,
Mr P. Wolf.
[15]
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