Smart Grid and Renewable Energy, 2012, 3, 119-125
http://dx.doi.org/10.4236/sgre.2012.32017 Published Online May 2012 (http://www.SciRP.org/journal/sgre)
1
Optimum Tilt Angles for Photovoltaic Panels during
Winter Months in the Vaal Triangle, South Africa
Osamede Asowata*, James Swart, Christo Pienaar
Department of Electronic Engineering, Vaal University of Technology, Vanderbijlpark, South Africa.
Received January 31st, 2012; revised February 27th, 2012; accepted March 4th, 2012
ABSTRACT
Optimizing the output power of a photovoltaic panel improves the efficiency of a solar driven energy system. The
maximum output power of a photovoltaic panel depends on atmospheric conditions, such as (direct solar radiation, air
pollution and cloud movements), load profile and the tilt and orientation angles. This paper describes an experimental
analysis of maximizing output power of a photovoltaic panel, based on the use of existing equations of tilt angles de-
rived from mathematical models and simulation packages. Power regulation is achieved by the use of a DC-DC con-
verter, a fixed load resistance and a single photovoltaic panel. A data logger is used to make repeated measurements
which ensure reliability of the results. The results of the paper were taken over a four month period from April through
July. The photovoltaic panel was set to an orientation angle of 0˚ with tilt angles of 16˚, 26˚ and 36˚. Preliminary results
indicate that tilt angles between 26˚ and 36˚ provide optimum photovoltaic output power for winter months in South
Africa.
Keywords: Solar Energy; Optimum; Orientation Angle; Tilt Angle; Data Logger; Photovoltaic (PV) Panel
1. Introduction
Einstein said, ‘‘the release of energy has not created a
new problem, but has made more urgent the necessity of
solving an existing one’’ [1]. In the quest to harness clean
cheap energy from the sun, a phenomenon was discovered
in the early 19th century, where electrical energy is gener-
ated using the photovoltaic (PV) effect [2]. The sun is ap-
proximately 1.4 million km in diameter and 150 million
km from the earth. It has a surface temperature close to
5500˚C and it radiates energy at a rate of 3.8 × 1023 kW
per second on an average daily basis [3]. Solar energy is
supplied by nuclear fusion reactions near its core which
are estimated to continue for several billion years.
Solar energy can be converted directly into electricity
with modules consisting of PV cells. Electricity is usually
manufactured from fine film semiconductor devices capa-
ble of converting direct solar radiation into DC current.
The efficiency of PV cells varies from 3% to 31%, depend-
ing on the technology, the light spectrum, atmospheric con-
dition, temperature, design and the material used [4].
There are numerous isotropic and anisotropic mathe-
matical models, equations of latitude and simulation
packages that can estimate the optimum tilt and orienta-
tion angle of a PV panel for given latitude on earth. How-
ever, little real experimental data or no real consistency
exists with which to verify the suggested values for spe-
cific areas of latitude and longitude in South Africa. This
proves problematic for the successful installation of PV
panels for optimum output power.
The purpose of this study is to optimize the available
output power from a PV panel for a specific point of la-
titude in South Africa. Mathematical models and simu-
lation packages in combination with experimental data
were used to determine the optimum tilt and orientation
angles. This will enable a higher yield of solar energy,
thereby reducing dependence on traditional energy sources
such as fossil fuels. This study aims to identify ways of
improving the installation of PV panels for optimum an-
nual output power. A designed experimental approach
involving quantitative data and descriptive statistics is
used in this research. Figure 1 illustrates the tilt (y) and
orientation angles (α) of a single PV panel.
The paper firstly presents literature relating to the dif-
ferent PV panels that exist, and then introduces the em-
pirical test which was used with different tilt angles as
suggested by Heywood and Chinnery equations of lati-
tude. The research methodology is explained and initial
results are presented in a number of graphs and tables.
Statistical R2 values are obtained from the data derived
from the different tilt angles which are used to formulate
the conclusions.
*Corresponding author.

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa
120
Figure 1. Tilt and orientation angles of a PV panel.
2. Photovoltaic (PV) Panels
Three different types of PV panel modules basically exist,
namely the mono-crystalline, the poly-crystalline (or multi-
crystalline) and the amorphous silicon panels [5].
2.1. Mono-Crystalline
In mono-crystalline PV panels, cells are cut from a single
crystal of silicon [6]. It has a smooth texture which makes
the thickness of the slice visible. They are rigid and must
be mounted in a secure frame to protect them. The prin-
ciple advantage of mono-crystalline cells are their high
efficiencies, typically around 15%, although the manu-
facturing process required to produce mono-crystalline
silicon is complicated, resulting in slightly higher costs
than other technologies [7]. Figure 2 presents a photo-
graph of a mono-crystalline cell while Table 1 indicates
selected parameters for this type of PV panel.
Figure 2. A cell of a mono-crystalline PV panel.
Table 1. ZKX-160D-2 module/160Wp-180Wp mono-crystal-
line PV panel.
Specification Abbreviation Value
Maximum output power PMAX 160 W
Open circuit voltage VOC 42.8 V
Rated voltage VMPP 34.9 V
Short circuit current ISC 5.15 A
Rated current IMPP 5.03 A
2.2. Poly-Crystalline
Poly-crystalline (or multi-crystalline) cells are made from
a slice cut from a block of silicon consisting of a large
number of crystals [6]. They have a speckled reflective
appearance which makes the thickness of the slice visible.
In the manufacturing process, molten silicon is cast into
ingots of poly-crystalline silicon; these ingots are then
saw-cut into very thin wafers and assembled into com-
plete cells [7]. These cells are slightly less efficient, (av-
erage efficiencies of around 12%) and slightly less ex-
pensive than mono-crystalline cells, but also need to be
mounted in a secure frame. Figure 3 presents a photo-
graph of a poly-crystalline cell while Table 2 indicates
selected parameters for this type of PV panel.
2.3. Amorphous Silicon
These panels are also known as amorphous silicon (a-Si)
PV panels [8] (see Figure 4 for an example). Amorphous
silicon was first deposited from a silane discharge by
Figure 3. A cell of a poly-crystalline PV panel.
Table 2. Sun module SW220 poly-crystalline PV panel.
Specification Abbreviation Value
Maximum output power PMAX 220 W
Open circuit voltage VOC 36.6 V
Rated voltage VMPP 29.2 V
Short circuit current ISC 8.08 A
Rated current IMPP 7.54 A
Figure 4. A cell of an amorphous silicon PV panel.

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa 121
Chittik et al. in 1969. The progress in a-Si solar cell tech-
nology can be attributed to technological advances over
the last few decades [7]. The optoelectronic properties of
amorphous PV panels vary over a wide range and are
highly influenced by plasma deposition conditions [8].
Amorphous silicon PV panels are fabricated in a labora-
tory with a wide variety of different structures, but most
commercial products utilize p-i-n or n-i-p junctions. Mul-
ti-junction devices are also being designed to take ad-
vantage of a broader spectrum of the sun’s rays and to
maximize efficiency [9]. They are the least efficient and
least expensive to produce of the three different panels
discussed in this paper. Due to the amorphous nature of
the thin layer, it is flexible, and can be used to manufac-
ture flexible PV panels. A poor characteristic of amor-
phous solar cells is that their power output reduces over
time [7]. Table 3 indicates selected parameters for this
type of PV panel.
A Sun module SW220 poly-crystalline PV panel is
used in this research due to its lower cost and better per-
formance in areas of direct solar radiation.
3. Test System
Figure 5 shows a block diagram of the test system which
comprises a PV panel connected to a DC-DC converter
and a constant load resistance (Figure 6 shows a photo-
graph). Determining the optimum tilt angle involves
placing the PV panel at an orientation angle of 0˚ and
changing the angle of tilt to 16˚, 26˚ and 36˚ respectively.
These angles are derived from the Heywood and Chin-
nery equations of latitude for calculating tilt angles of PV
panels in South Africa. Vanderbijlpark lies on latitude of
26˚ south and longitude 27˚ east, giving the mathematical
results for tilt angles as shown in Table 4.
Table 3. Amorphous silicon thin film PV Panel (a-Si PV
module).
Specification Abbreviation Value
Maximum output power PMAX 41 W
Open circuit voltage VOC 58 V
Rated voltage VMPP 44 V
Short circuit current ISC 1.20 A
Rated current IMPP 0.94 A
Logging
Input power
Vi × Ii
Constant
Load
Resistor
PV Panel SW220
placed at different
tilt angles
DC-DC
Converter
12 V/24 V
For power
regulation
Logging
Output power
Vo × Io
Figure 5. Block diagram o f the p ractical set-up.
Load resistance DC-DC converter
Data logging interface circuit DAQ pro 5300 logger
Figure 6. Photograph of the practical set-up.
Table 4. Calculation of tilt angles.
Latitude of
VUT
Heywood and
Chinnery Equation
Calculation
For VUT
Tilt angles
Used at VUT
26˚ Ф – 10 26˚ – 10˚ 16˚
26˚ Ф 26˚ 26˚
26˚ Ф + 10 26˚ + 10˚ 36˚
A 12 V and 24 V DC-DC converter is used to regulate
the output power from the PV panel. A DAQ pro 5300
data logger is used to collect measurements (input voltage,
output voltage, input current and output current). The ex-
periment is repeated taking four samples each using the
16˚, 26˚ and 36˚ tilt angles. These samples ensure test-
retest reliability of the measuring instrument which must
be administered on at least two occasions [10].
Atmospheric conditions in terms of industrial pollution
[11] and cloud movement affect the performance of PV
panels, and therefore have a direct bearing on the total
number of complete samples which must be collected
[12]. This is seen in Figure 7 where cloud movement in-
terrupts the direct solar radiation from the sun for a par-
ticular day, these values are not averaged. It is difficult to
account accurately for these factors and may require ad-
ditional samples.
4. Initial Results
Regression analysis is modeling the relationship between
a scalar variable y and one or more variables denoted x
[13]. The polynomial regression is a form of linear re-
gression in which the relationship between the inde-
pendent variable x (time) and the dependent variable y

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa
122
Figure 7. Effect of cloud movement on direct solar radiation
received by a PV panel.
(voltage) is modeled. A regression analysis of the linear
equation is used to obtain the R2 value for the average
conversion-time per week. This enables one to establish a
relationship between the DC-DC converter voltage and
the conversion-time per week. A linear regression trend
analysis, using a polynomial 6, would be used to obtain
the R2 value for the average work-time per day. This en-
ables one to establish a relationship of the variability be-
tween the DC-DC converter voltage and the average
work-time per day. The R2 value in each case helps pre-
dict how well the value of the conversion-time predicts
the value of the DC-DC converter voltage.
True north is determined using a GARMIN Etrex GPS
handheld device. The PV panel is orientated parallel to
this direction resulting in an orientation angle of 0˚. Ex-
act longitude and latitude angles for the installation of the
single PV panel on the roof of the S-Block at Vaal Uni-
versity of Technology (VUT) are obtained with this de-
vice (Latitude: 26˚42'649"S and Longitude: 27˚51'809"E).
Preliminary results for open circuit voltages using tilt an-
gles of 6˚, 16˚ and 26˚ are presented in Figures 8-10 re-
spectively.
All three tilt angles provided an open circuit output vol-
tage of approximately 36 V from about 6 AM to around 7
PM. This coincides with the manufacturing specifications
shown in Table 2. These results further show that as the
Figure 8. Open circuit voltage for a tilt angle of 16˚.
Figure 9. Open circuit voltage for a tilt angle of 16˚.
Figure 10. Open circuit voltage for a tilt angle of 26˚.
day temperature increases, the output voltage of the PV
panel decreases. This phenomenon is known as tempera-
ture degradation.
Figure 11 presents the average conversion-time for the
22-29 April 2011, where a 24 V DC-DC converter was
used with the PV panel placed at a tilt angle of 26˚ and
an orientation angle of 0˚. The conversion-time of the sys-
tem (the time which power is being delivered to the load)
is derived with a normal probability plot using MS EX-
CEL in the Data Analysis Toolpak. Regression analysis
can be used for process optimization [13]. The point at
Figure 11. Regression analysis (linear) of the data obtained
for the 22-29 April 2011 (24 V DC-DC converter/PV panel
placed at a tilt angle of 26˚).

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa 123
which power is delivered to the load is indicated as point
A and represents the start of the conversion-time (being
19.68% for this given week). Point A on the Y-axis gives
a value of about 24 V which coincides with the output
voltage specification of the DC-DC converter.
A linear trend line specifies a statistical R2 value of
0.656 that indicates the relationship between the average
conversion-time of the system and the direct solar radia-
tion received from the sun. The average sun hours per
day for this specific week may be calculated as follows:
Sunhours per day24 hoursAveOnTime
24hours 19.68%
Sun hoursperday100


Sunhours per day4.72 hours
A regression analysis (Polynomial 6) is done in Figure
12 to obtain the average work-time per day for a set of
data taken over a week period, from the 22-29 April 2011.
A 24 V DC-DC converter was used. The R2 value is
0.845, which shows how well the resulting line matches
the original data points. It is also a statistical value that
indicates the strength of the relationship between the av-
erage work-time per day and the direct solar radiation re-
ceived from the sun. The wider the response (higher av-
erage work-time) the lower the R2 value.
Figure 13 shows the average conversion-time for the
Figure 12. Average work-time per day 22-29 April 2011 (24
V DC-DC converter/PV panel placed at a tilt angle of 26˚).
Figure 13. Regression analysis (linear) of the data obtained
for the 8-15 July 2011 (12 V DC-DC converter/PV panel placed
at a tilt angle of 16˚).
8-15 July 2011, where a 12 V DC-DC was used with the
PV panel placed at 16˚ and an orientation angle of 0˚. This
enables comparison with the 24 V DC-DC converter in
order to establish validity. Point A indicates the point
where the DC-DC converter starts delivering power to
the load, and is seen as an output voltage of 12 V on the
Y-axis which coincides with the specification of the DC-
DC converter. This analysis shows an average conver-
sion-time of 18.31%. This is derived from adding a data
label at point A, using MS EXCEL. This equates to the
percentage of available solar radiation for that specific
week. A linear trend line indicates a statistical R2 value
of 0.597. This value illustrates the strength of the rela-
tionship and the proportion of variability between the
average conversion-time and the available solar radiation
received. The DC-DC converter supplied power to the
load for about 18.31% of the week which equates to the
percentage of available solar radiation (sun hours) for
that specific week as follows:
Sunhours per day24 hoursAveOnTime


24hours 18.31%
Sunhours per day100


Sunhours per day4.39 hours

The regression analysis (polynomial 6) to obtain the
average work-time per day of a 12 V DC-DC converter
for the 8-15 July 2011 is presented in Figure 14.
The R2 value is 0.903, which indicates how well the
resulting line matches the original data points. It’s also a
statistical value that indicates the strength of the relation-
ship between the average work-time per day and the di-
rect solar radiation received. In this case, as compared to
Figure 12, it is seen that the narrower the response of the
curve (lower average work-time), the higher the R2 value.
These individual results were collated with the other re-
sults obtained for each week of data collected over a four
month period from April through July of 2011. The analy-
sis of this 12 week period is shown in Table 5, where the
data is ranked according to the regression trend value.
Figure 14. Average work-time per day 8-15 July 2011 (12 V
DC-DC converter/PV panel placed at a tilt angle of 16˚).

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa
124
Table 5. Set of data for the mont hs of April throug h July us-
ing 12 V and 24 V DC-DC converters.
Regression
trend value
Week
ending
DC-DC
converter
voltage
Tilt angle
Conversion-time/
wk as a
percentage
0.567 20-May 24 V 16˚ 2.84%
0.573 29-July 12 V 16˚ 11.53%
0.577 13-May 24 V 16˚ 2.52%
0.597 15-July 12 V 16˚ 18.31%
0.609 27-May 24 V 36˚ 10.07%
0.611 22-April 24 V 36˚ 8.76%
0.616 24-June 12 V 26˚ 20.2%
0.623 6-May 24 V 26˚ 16.19%
0.629 1-July 12 V 26˚ 19.81%
0.631 10-June 12 V 36˚ 14.94%
0.632 17-June 12 V 36˚ 19.74%
0.656 29-April 24 V 26˚ 19.68%
This regression trend line value (linear) indicates the rela-
tionship between the average conversion-time (actual di-
rect solar radiation received the PV panel for each week)
and the output voltage of the DC-DC converter.
5. Future Work
A new practical set-up comprising three identical PV
panels (each set to a different tilt angle of 16˚, 26˚ and
36˚) connected to identical solar chargers and load resis-
tances have been installed. This will expose the PV pan-
els to the same solar radiation and environmental factors
that influence their output power. This would enable an
accurate comparison of the data collected for each tilt
angle, thereby establishing validity. Figure 15 shows a
picture of the three identical PV panel set to different tilt
angles which have been installed on the roof of the S-
Block at VUT.
6. Conclusions
In review, the purpose of this research is to optimize the
Figure 15. Three identical solar panels set to tilt angles of
16˚, 26˚ and 36˚ degrees.
available output power from a PV panel, based on dif-
ferent tilt and orientation angles. The orientation angle is
initially fixed at 0˚, with only the tilt angle being varied.
Optimizing the output power will enable a higher yield of
solar energy, thereby reducing dependence on traditional
energy sources such as fossil fuels. The availability of
power was interpreted showing the average conversion-
time for the 22-29 April 2011 and for the 8-15 July 2011
(being 19.68% and 18.31% respectively, see Figures 11
and 13). The average conversion-time per week, for the
months of April through July with tilt angles of 16˚, 26˚
and 36˚ and a fixed orientation angle of 0˚ is presented in
Table 5. From the results gathered, doing a linear regres-
sion analysis reveals that generally the higher the average
conversion-time per week the higher the R2 value. A com-
parison between Figures 12 and 14 reveals that the values
of the linear trend value (polynomial 6) are not similar.
This is because Figure 12 represents a broader response
curve (higher average work-time per day giving an R2
value of 0.845) than Figure 14 (lower average work-time
per day giving an R2 value of 0.903).
The peak winter months in South Africa are June and
July, which indicated the highest regression trend value
(linear) for 26˚ and 36˚ tilt angles (see Table 5). This co-
incides with earlier endeavors to calculate the proper
choice of tilt angles using mathematical and simulation
models based on the research done by Chinnery [14]. These
initial experimental results therefore prove the validity
and reliability of these models for winter months in the
Vaal Triangle, South Africa.
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