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IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014 647
Optimal Orientation and Tilt Angle for
Maximizing in-Plane Solar Irradiation
for PV Applications in Singapore
Yong Sheng Khoo, Andr
´
e Nobre, Raghav Malhotra, Dazhi Yang, Member, IEEE, Ricardo R
¨
uther,
Thomas Reindl, and Armin G. Aberle, Senior Member, IEEE
Abstract—The performance of photovoltaic (PV) modules and
systems is affected by the orientation and tilt angle, as these pa-
rameters determine the amount of solar radiation received by the
surface of a PV module in a specific region. In this study, three
sky models (Liu and Jordan, Klucher, and Perez et al.) are used
to estimate the tilted irradiance, which would be received by a PV
module at different orientations and tilt angles from the measured
global horizontal irradiance (GHI) and diffuse horizontal irradi-
ance (DHI) in Singapore (1.37
◦
N, 103.75
◦
E). Modeled results are
compared with measured values from irradiance sensors facing
60
◦
NE, tilted at 10
◦
,20
◦
,30
◦
,40
◦
, and vertically tilted irradiance
sensors facing north, south, east, and west in Singapore. Using the
Perez et al. model, it is found that a module facing east gives the
maximum annual tilted irradiation for Singapore’s climatic con-
ditions. These findings are further validated by one-year compre-
hensive monitoring of four PV systems (tilted at 10
◦
facing north,
south, east, and west) deployed in Singapore. The PV system tilted
10
◦
facing east demonstrated the highest specific yield, with the
performance ratio close to those of other orientations.
Index Terms—Irradiation maximization, optimal tilt angle, ori-
entation, PV modules, solar irradiance.
I. INTRODUCTION
A
MONG the most important parameters that affect the per-
formance of a photovoltaic (PV) system are the orien-
Manuscript received August 29, 2013; revised November 4, 2013; accepted
November 18, 2013. Date of publication December 12, 2013; date of current
version February 17, 2014. The Solar Energy Research Institute of Singapore is
sponsored by the National University of Singapore (NUS) and Singapore’s Na-
tional Research Foundation (NRF) through the Singapore Economic Develop-
ment Board. This work was supported by the NRF under Grant NRF2008EWT-
CERP02-031 “High Performance Photovoltaic Systems for Tropical Regions–
Optimization of PV Systems Performance.” The work of Y. S. Khoo was sup-
ported by a Ph.D. scholarship from the NUS Graduate School for Integrative
Sciences and Engineering.
Y. S. Khoo and A. G. Aberle are with the National University of Singapore,
NUS Graduate School for Integrative Sciences and Engineering, Singapore, and
also with the Solar Energy Research Institute of Singapore, Singapore 117574
(e-mail: yongshengkhoo@nus.edu.sg; armin.aberle@nus.edu.sg).
A. Nobre is with the Universidade Federal de Santa Catarina, Campus Uni-
versit
´
ario Trindade, Florian
´
opolis, SC 88040-900, Brazil, and also with the So-
lar Energy Research Institute of Singapore, Singapore 117574 (e-mail: andre.
nobre@posgrad.ufsc.br).
R. R
¨
uther is with the Universidade Federal de Santa Catarina, Campus
Universit
´
ario Trindade, Florian
´
opolis, SC 88040-900, Brazil (e-mail: ricardo.
ruther@ufsc.br).
R. Malhotra, D. Yang, and T. Reindl are with the Solar Energy Research
Institute of Singapore, Singapore 117574 (e-mail: raghav0211@gmail.com;
seryangd@nus.edu.sg; thomas.reindl@nus.edu.sg).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JPHOTOV.2013.2292743
tation and tilt angle selected for the array installation, which
determines the amount of solar radiation received by the sur-
face of the PV modules. For Singapore (1.37
◦
N, 103.75
◦
E),
with very limited land area (country size ∼720 km
2
), it is de-
sirable that modules are oriented in such a way as to harness
the maximum solar energy possible. In this paper, we study the
optimal orientation and tilt angle for fixed-tilt PV systems in
Singapore to maximize solar energy resource harvesting, using
both modeling and experimental approaches.
In the past, many authors presented models to predict so-
lar radiation on inclined surfaces from the typically measured
global horizontal irradiance (GHI) and diffuse horizontal irradi-
ance (DHI) [1]–[8]. While the direct beam radiation on a tilted
surface can be calculated using geometric relations, the con-
version for the diffuse radiation is more complex and has been
approached using different models. The first-generation model
converts the horizontal diffuse radiation to the tilted plane by
assuming that the total sky diffuse radiation content is isotrop-
ically distributed [1]. However, this assumption is not strictly
true. Newer models treat the diffuse radiation component as
anisotropically distributed, where the irradiance is treated as
the sum of circumsolar and background sky diffuse compo-
nents [2]–[8].
For this study, three transposition models (Liu and Jordan [1],
Klucher [4], and Perez et al. [8]) are investigated to find the best
model for Singapore’s climatic conditions. The accuracies of
the models are determined by comparing the estimated results
with measured values in the field. Comparisons are made for
surfaces oriented at 60
◦
NE with tilt angles of 10
◦
,20
◦
,30
◦
,
40
◦
, and vertically mounted surfaces facing north, south, east,
and west. The normalized root mean square error (NRMSE)
statistical method is used to quantify the accuracy of each model
compared with the measured results.
Using hourly GHI and DHI data measured over a period
of three years, we observe the annual irradiation variability in
Singapore. We additionally use the data to calculate the hourly
tilted irradiance for all possible tilt angles and orientations. The
hourly tilted irradiances are then summed up in order to obtain
annual tilted irradiances. The tilt angle and orientation that yield
the highest annual tilted irradiance is considered to be the op-
timal tilt angle and orientation for the observed year. Finally,
with the availability of data from a PV site, during the third
year of assessment, the estimated optimal orientation is vali-
dated with a one-year evaluation of the PV systems’ monitored
data.
2156-3381 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications
standards/publications/rights/index.html for more information.
648 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014
Fig. 1. Photograph of the irradiance measurement station located on the roof
of the Solar Energy Research Institute of Singapore.
II. IRRADIANCE MEASUREMENT STATION FOR
MODEL EVA L UAT I O N
The irradiance measuring station (see Fig. 1) is located on
the roof of the Solar Energy Research Institute of Singapore
(SERIS) building at the National University of Singapore (NUS)
campus (1.30
◦
N, 103.77
◦
E). It commenced operations in June
2010.
At its final configuration, 12 irradiance measurement sensors
are installed: one silicon sensor tilted at 0
◦
measuring GHI, four
silicon sensors facing 60
◦
NE tilted at 10
◦
,20
◦
,30
◦
, and 40
◦
,
four silicon sensors vertically tilted facing north, south, east,
and west, a pyranometer (CMP11 from Kipp and Zonen) mea-
suring GHI, and a sunshine pyranometer (SPN1 from Delta-T)
measuring both GHI and DHI.
All silicon sensors are calibrated every 2 years at Fraunhofer
ISE’s CalLab with ±2% accuracy, while all other sensors are cal-
ibrated at the same time interval at the respective manufacturers.
The silicon sensors are crystalline silicon PV devices with tem-
perature correction. After the station completed a 1-year period
of data collection in May 2011, annual average for GHI and DHI
for the following 2 years (June 2011 to May 2013) was created,
by plotting a moving 12-month average of these two irradiation
parameters for comparison against the long-term typical meteo-
rological year (TMY) for Singapore as per Meteonorm 7.1 (see
Fig. 2).
Although climatic conditions do vary on a yearly basis, they
usually stay within a range of ±16% [9], as also shown in Fig. 2.
All sensors are installed on the rooftop without obstructions
from nearby buildings, hence free from any shading throughout
the year. The sensors are cleaned every week, to prevent soil-
ing accumulation. Data sampling for all parameters takes place
every 1 s, with logging at 1 min intervals.
For an initial analysis of the weather conditions in Singapore,
data from the first full 12-month period (June 2010 to May
2011) for GHI and DHI are analyzed. For in depth analysis,
tilted silicon sensors were installed during the second year. We
average data to hourly intervals for calculation and comparison
with the modeled results (second full 12-month period, from
June 2011 to May 2012). Finally, with the availability of data
Fig. 2. Average annual GHI and DHI shown as a moving 12-month average.
The TMY for Singapore as per Meteonorm 7.1 is 1 632 kWh/m
2
/yr for GHI
and 934 kWh/m
2
/yr for DHI.
from a real-world PV system, the third year (June 2012 to May
2013) is used for the validation of our findings.
III. C
OMPUTATION METHODOLOGY
Three transposition models are used to convert the hourly
measured GHI and DHI into hourly tilted irradiance. The models
are Liu and Jordan’s isotropic diffuse sky model [1], Klucher’s
model [4], and Perez et al.’s model [8]. The Liu and Jordan
model is one of the earliest and simplest models. Because of
its simplicity, it is most widely used in estimating the tilted
irradiance. The models from Klucher and Perez et al. offer
better accuracy, but increase the computational intensity. The
idea behind this study is to investigate models with different
complexity and to benchmark their accuracy in modeling tilted
irradiance for Singapore’s climatic conditions.
A. Liu and Jordan Model
The Liu and Jordan model is one of the earliest and simplest
irradiance models [1]. It assumes an isotropic diffuse sky model
and can be computed in the following way:
I
T
= I
b
R
b
+ I
d
1+cosβ
2
+ Iρ
g
1 − cosβ
2
(1)
where I
T
is the tilted irradiance, I
b
the beam irradiance on a
horizontal surface, R
b
the ratio of beam radiation on the tilted
surface to that on a horizontal surface at any time, I
d
the diffuse
horizontal irradiance, β the tilt angle, I the global horizontal
irradiance, and ρ
g
the ground reflectance. An in-depth under-
standing of this model is available in the literature [1], [10], [11].
While this is the most trivial method, the assumption of an
isotropic diffuse sky is not strictly true.
B. Klucher Model
The diffuse content of the sky is anisotropic in nature. There
is an increase in radiation intensity around the circumsolar re-
gion of the sky and at the horizon. Temps and Coulson [3]
developed an anisotropic sky model for a clear sky by modify-
ing the isotropic model, to take into account the horizontal and
KHOO et al.: OPTIMAL ORIENTATION AND TILT ANGLE FOR MAXIMIZING IN-PLANE SOLAR IRRADIATION 649
circumsolar brightening
I
T
= I
b
R
b
+ I
d
1+cosβ
2
1+sin
3
β
2
× (1 + cos
2
θ sin
3
θ
z
)+Iρ
g
1 − cosβ
2
(2)
where θ is the angle of incidence and θ
z
the zenith angle.
(1 + sin
3
β
2
) accounts for the increase in sky light near the hori-
zon during clear days, and (1 + cos
2
θ sin
3
θ
z
) accounts for sky
brightening near the sun.
In further studies, Klucher showed that the Temps and
Coulson model provides an excellent prediction for clear-sky
conditions, but overestimates for overcast skies. He also found
the opposite to be true for the Liu and Jordan model. He then
further modified the Temp and Coulson model to [4]
I
T
= I
b
R
b
+ I
d
1+cosβ
2
1+F sin
3
β
2
× (1 + F cos
2
θ sin
3
θ
z
)+Iρ
g
1 − cosβ
2
(3)
where F =1−
I
d
I
2
is the modulating function to correct the
Temps and Coulson clear-sky anisotropic model. Under an over-
cast sky, F becomes zero, reducing the Klucher model to the Liu
and Jordan model. Under a clear sky, F approaches 1, reducing
the Klucher model to the Temp and Coulson model.
C. Perez et al. Model
The Perez et al. model [8] is based on a detailed statistical
analysis of the sky’s diffuse components. The model breaks
the diffuse irradiance into three components of isotropic back-
ground, circumsolar, and horizon zone
I
d,tilt
= I
d
1+cosβ
2
(1 − F
1
)+F
1
cosθ
cosθ
z
+ F
2
sinβ (4)
where I
d,tilt
is the total tilted diffuse irradiance, F
1
the cir-
cumsolar brightness coefficient, and F
2
the horizon brightness
coefficient. F
1
and F
2
are related to sky irradiance conditions,
which are described using three variables: 1) sun position (zenith
angle θ
z
); 2) sky clearness index ε; and 3) brightness index Δ.
The sky clearness index ε is defined as
ε =
(I
d
+ I
b,n
)/I
d
+1.041θ
3
z
1+1.041θ
3
z
(5)
where I
b,n
is the direct normal irradiance. The sky brightness
index Δ is defined as
Δ=m
I
d
I
E
(6)
where m is the air mass and I
E
the extraterrestrial irradiance. For
the model, ε is separated into eight bins. For different bins, the
brightness coefficients F
1
and F
2
are considered linear functions
of θ
z
and Δ
F
1
= f
11
(ε)+Δf
12
(ε)+θ
z
f
13
(ε) (7)
F
2
= f
21
(ε)+Δf
22
(ε)+θ
z
f
23
(ε) (8)
TABLE I
P
EREZ MODEL COEFFICIENTS TO DESCRIBE DIFFERENT SKY CONDITIONS [8]
where the six coefficients f
ij
for each category of ε are found
by the least square fit to the experimental data. A recommended
set of these coefficients (using experimental data from different
locations and climatic conditions [8]) is given in Table I.
To find the total tilted irradiance, the beam irradiance and the
ground reflectance must be added
I
T
= I
b
R
b
+ I
d,tilt
+ Iρ
g
1 − cosβ
2
. (9)
IV. R
ESULTS
Using the three models discussed earlier, hourly measured
GHI and DHI are converted into hourly tilted irradiance for
different orientations and tilt angles of interest. The modeled
results are then compared with the experimental results.
A. Measurement Results
Readings from calibrated silicon irradiance sensors at vari-
ous orientations and tilt angles were analyzed (over a period of
one year) to provide a validation of the modeling results; they
also serve as an initial indication of the optimal orientation and
tilt angle for maximum energy harvesting. The annual irradi-
ance (from the chosen 12-month period from June 2011 to May
2012) received by each silicon sensor is summarized in Table II.
As can be seen, the horizontal sensor and the sensor oriented at
60
◦
NE with a tilt angle of 10
◦
received the highest annual
irradiance. Among all the vertically tilted sensors, the east-
facing sensor received the highest annual irradiation. However,
since the uncertainty of the measurement (±2%) is higher than
the gain/loss verified for silicon sensors from 0
◦
to 20
◦
tilt, it is
not possible to determine the best tilt angle.
From the yearly measurements, a typical day is calculated. A
typical day is obtained by averaging the yearly measurements
(1-h data) into a single day. A typical day for irradiance sensors
at different orientations are shown in Fig. 3. From Fig. 3, among
the group of sensors oriented at 60
◦
NE, the maximum irradi-
ance is observed at a tilt angle of 10
◦
. Further increasing the tilt
angle leads to a decrease in irradiance capture. Also noticeable
is that the east fac¸ade irradiance sensor has a much higher ir-
radiance reception compared with the west fac¸ade sensor. This
650 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014
TABLE II
A
NNUAL IRRADIATION (kWh/m
2
)RECEIVED BY SILICON SENSORS AT
DIFFERENT ORIENTATIONS AND TILT ANGLES IN SINGAPORE FROM
JUNE 2011 TO MAY 2012
can be explained by the fact that Singapore is usually sunnier in
the morning compared with the afternoon, because of cumulus
clouds building up in the afternoon, which is typical for tropical
locations. The sensor facing north has a slightly higher irradi-
ance reception than the sensor facing south, even though the sun
path in Singapore is equally long in the south as in the north,
due to the close proximity to the equator. This might be due to
yearly seasonal variations.
Table II and Fig. 3 provide an early indication that PV mod-
ules/systems facing east would receive a higher amount of solar
irradiance in Singapore.
B. Irradiance Model Comparison
Using the hourly measured GHI and DHI over the 1-year
period, tilted irradiance values for the different orientations and
tilt angles of interest are calculated. The derived irradiances
using the Perez et al. model are compared with the measured
readings and shown in Fig. 4 for 10
◦
,20
◦
,30
◦
, and 40
◦
, and in
Fig. 5 for the fac¸ade sensors.
At lower tilt angles, the modeled results are very accurate; at
higher tilt angles, the modeled values show a stronger deviation.
This is due to the error of assuming a constant ground reflectance
ρ
g
of 0.2. At higher tilt angles, both the diffuse component
and the ground reflected component of sunlight become more
dominant in determining the total tilted irradiance; the small
error in ρ
g
is exacerbated at higher tilt angles.
For comparison of the three different models, we use the sta-
tistical NRMSE method to calculate the deviation of the mod-
eled results from the measured results. The NRSME results for
the three models are shown in Table III, for all different orien-
tations and tilt angles.
From Table III, it can be seen that all models offer very
accurate results at low tilt angles. As the angle increases, the
NRMSEs also increase. Among all three models, the model
from Perez et al. offers the most accurate results (i.e., lowest
NRMSE). This is not surprising because this model consists of
coefficients that are obtained empirically and statistically based
Fig. 3. Irradiance distributions for a typical day in Singapore based on em-
pirical data from June 2011 to May 2012 for irradiance sensors facing 60
◦
NE,
tilted at 0
◦
,10
◦
,20
◦
,30
◦
, and 40
◦
and vertically mounted irradiance sensors
facing north, south, east, and west (1-h data; the lines are guides to the eye).
Fig. 4. Measured versus modeled irradiance using the Perez et al. model for
irradiance sensors oriented at 60
◦
NE with tilt angles of 10
◦
,20
◦
,30
◦
, and 40
◦
in Singapore. The comparison is done for the full 12-month period from June
2011 to May 2012.
Fig. 5. Measured versus modeled irradiance using the Perez et al. model
for vertically tilted irradiance sensors facing north, south, east, and west in
Singapore. The comparison is done for the full 12-month period from June
2011 to May 2012.
KHOO et al.: OPTIMAL ORIENTATION AND TILT ANGLE FOR MAXIMIZING IN-PLANE SOLAR IRRADIATION 651
TABLE III
C
OMPARISON OF THE NORMALIZED ROOT MEAN SQUARE ERRORS (NRMSE)
FOR ALL DIFFERENT ORIENTATIONS AND TILT ANGLES AVA I L A B L E AT SERIS’
M
ETEOROLOGICAL STATION IN SINGAPORE FOR THE THREE TRANSPOSITION
MODELS:LIU AND JORDAN,KLUCHER,PEREZ et al.
on different sky conditions. Since the Perez et al. model offers
the most accurate predictions, it is used in the following to
find the optimal orientation and tilt angles for PV modules in
Singapore’s climatic conditions.
C. Optimal Orientation and Tilt Angle for Maximum Annual
Tilted Irradiation Harvesting
Using the Perez et al. model, the annual tilted irradiation for
all possible orientations and tilt angles were calculated. Fig. 6
summarizes the results in a polar contour plot for the first year
of data acquired by our station (June 2010 to May 2011). As can
be seen, a surface oriented slightly south of due east and with
a tilt angle of 26
◦
would yield the maximum annual irradiation
of 1 562 kWh/m
2
recorded for the evaluated year. This can be
explained by the fact that Singapore is usually sunnier in the
morning than in the afternoon, as mentioned earlier.
Initial findings (see Fig. 6) showed that a module tilted fac-
ing east will receive highest annual solar irradiation. However,
this observation might be due to the seasonal variation for that
particular year. The GHI and DHI data were measured for two
more years from June 2011 to May 2012, and then from June
2012 to May 2013. The polar contour plots of the annual tilted
irradiation for different tilts and orientations are shown in Figs. 7
and 8.
Both Figs. 7 and 8 show that a module facing east would have
received highest annual irradiation for the two aforementioned
years under evaluation. The optimal tilt angles shown in Figs. 7
and 8 are lower than the one showed in Fig. 6. While there is
some seasonal variations effect, Figs. 6–8 confirm that a mod-
ule facing east will receive the highest annual irradiation. In
practice, PV installers might want to have more flexibility when
mounting PV modules at a site, for instance, to avoid the extra
cost of more complex mounting structures. For this purpose, the
orientation and tilt angles which represent values that are less
than the optimal point to a maximum of 5% are shown within
the dotted circle lines in Figs. 6 through 8.
D. System Results
To further validate the findings in Section IV-C, several PV
systems were evaluated with identical monitoring equipment.
At the site under study in Singapore, four identical PV sub-
systems with the same installed capacity, same module, and
Fig. 6. Polar contour plot of annual tilted irradiation for different tilts and
orientations in Singapore. The radius indicates the tilt angle, while the polar
angle refers to the orientation. A surface facing 97
◦
SE with tilt angle of around
26
◦
receives the highest annual irradiation of 1 562 kWh/m
2
, shown as the
“x” in the polar contour plot, based on empirical GHI and DHI data of one-
year period of June 2010 to May 2011. The orientation and tilt angles, which
represent values that are less than the optimal point to a maximum of 5%, are
shown within the dotted circle.
Fig. 7. Polar contour plot of annual tilted irradiation for different tilts and
orientations in Singapore. The radius indicates the tilt angle, while the polar
angle refers to the orientation. A surface facing 78
◦
NE with tilt angle of around
7
◦
receives the highest annual irradiation of 1 531 kWh/m
2
, shown as the “x”in
the polar contour plot, based on empirical GHI and DHI data of one-year period
of June 2011 to May 2012. The orientation and tilt angles, which represent
values that are less than the optimal point to a maximum of 5%, are shown
within the dotted circle.
Fig. 8. Polar contour plot of annual tilted irradiation for different tilts and
orientations in Singapore. The radius indicates the tilt angle, while the polar
angle refers to the orientation. A surface facing 88
◦
NE with tilt angle of around
9
◦
receives the highest annual irradiation of 1 523 kWh/m
2
, shown as the “x”in
the polar contour plot, based on empirical GHI and DHI data of one-year period
of June 2012 to May 2013. The orientation and tilt angles, which represent
values that are less than the optimal point to a maximum of 5%, are shown
within the dotted circle.
652 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014
same inverter brands and specifications were analytically mon-
itored for a period of 12 months (June 2012 to May 2013).
The systems are all tilted at 10
◦
and oriented in the four cardi-
nal directions (one subsystem for each orientation): north (0
◦
),
south (180
◦
), east (90
◦
), and west (270
◦
). In order to assess the
electrical performance of each PV system, both the dc and ac
outputs were monitored. For the dc output, precision shunts and
transducers with small uncertainties (±0.2%), and for the ac
output, class-0.5% energy meters were installed after each sub-
system’s inverter outputs. The calculation of the performance
ratio (PR) of each PV system is based on the readings of four
in-plane silicon sensors (one per subsystem). Similar to the
SERIS meteorological station (see Fig. 1), these silicon sen-
sors were also calibrated at Fraunhofer ISE’s CalLab with ±2%
accuracy.
Fig. 9 shows the monthly irradiation variations for each of the
orientations. The east-oriented silicon sensor (1 457 kWh/m
2
to-
tal annual irradiation for the measured period) received +4.1%
more irradiation than the west-oriented sensor (1 399 kWh/m
2
).
The difference between the north facing and south facing sen-
sors was negligible. Overall, the highest annual irradiation oc-
curred for the east orientation, which was 1.0% higher than the
second-best orientation (south) and 4.1% higher than the worst
orientation (west). While the 1% difference between east and
south sensors fall within the 2% uncertainty of the measure-
ments, it is clear that the east facing sensor has an advantage
over the west facing sensor.
For each PV system, the data are only collected when the
site’s global irradiance (GHI) is above 50 W/m
2
. This threshold
was set to arbitrarily create a filter level which would guarantee
that all four PV systems are concurrently operational at any
given point-in-time, as well as filtering out nonmeaningful data
around the inverter cut-off point. The overall availability of the
monitoring system was very high, with only about 0.1% of
data points lost in over half a million points for the analyzed
period.
As shown in Table IV, and as expected from Section IV-A, an
east-oriented PV system will have a higher yield in Singapore
compared with other azimuths. In the investigated 12-month
period, the east-facing system generated 2% more electricity
than the west-facing system. Relating the annual yield to the in-
plane irradiation, which is expressed in the performance ratio,
there was no statistically significant variation between the four
investigated systems (note that the measurement error is in the
order of ±3% [12], [13]). However, the west-facing system
might have a slightly better PR value; this could be due to
the slightly lower module temperatures (∼0.6
◦
C) recorded for
this system as compared with the east-facing system. As module
temperatures account for 45%–60% of all losses associated with
PV systems in the tropics [12], even variations in the order of a
few
◦
C can significantly affect a system’s PR.
Climatic conditions do vary on a yearly basis, but these are
usually constrained to ranges within ±16% from TMYs. While
the results shown in Figs. 7–9 are empirically drawn from differ-
ent calendar years at the SERIS meteorological station, it could
be demonstrated that similar patterns of higher irradiation on
east-oriented surfaces are present.
Fig. 9. Monthly irradiation variations (shown as daily averages). The two
y-axes have been offset to facilitate viewing. The lines are guides to the eye.
TABLE IV
P
ERFORMANCE PARAMETERS OF THE FOUR INVESTIGATED PV SYSTEMS
V. C ONCLUSION
Using hourly measured global horizontal irradiance (GHI)
and diffuse horizontal irradiance (DHI) data, modeling was per-
formed to calculate the hourly tilted irradiance for different
orientations and tilt angles in Singapore. The optimal orienta-
tion and tilt angles were then determined by finding the value
for which the total radiation on a particular PV surface was the
highest for the three-year period under investigation (June 2010
to May 2013). For this study, the sensors at the meteorological
station were cleaned every week, to prevent soiling. For a future
study, the investigation of the soiling effect on the PV perfor-
mance of different module orientations will also be taken into
consideration. The modeling results were validated by irradi-
ance sensors and measurements on a real-world PV system.
Using the Perez et al. model, it was found that surfaces tilted
eastward yield maximum annual in-plane irradiation in Singa-
pore climatic conditions. PV systems at different orientation, but
identical tilt and system configurations, were evaluated, with an
east-oriented system showing the highest yield. These findings
provide useful information for PV system integrators, both in
Singapore and in equatorial countries with similar climatic con-
ditions, on how to best design PV systems for maximized energy
yield.
R
EFERENCES
[1] B. Liu and R. Jordan, “Daily insolation on surfaces tilted towards equator,”
ASHRAE J., vol. 10, pp. 53–59, 1961.
KHOO et al.: OPTIMAL ORIENTATION AND TILT ANGLE FOR MAXIMIZING IN-PLANE SOLAR IRRADIATION 653
[2] C. Gueymard, “An anisotropic solar irradiance model for tilted surfaces
and its comparison with selected engineering algorithms,” Solar Energy,
vol. 38, no. 5, pp. 367–386, 1987.
[3] R. C. Temps and K. L. Coulson, “Solar radiation incident upon slopes of
different orientations,” Solar Energy, vol. 19, no. 2, pp. 179–184, 1977.
[4] T. M. Klucher, “Evaluation of models to predict insolation on tilted sur-
faces,” Solar Energy, vol. 23, no. 2, pp. 111–114, 1979.
[5] J. E. Hay and J. A. Davies, “Calculation of the solar radiation incident on
an inclined surface,” in Proc. First Can. Solar Radiation Workshop, 1980,
pp. 59–72.
[6] R. Perez, R. Stewart, C. Arbogast, R. Seals, and J. Scott, “An anisotropic
hourly diffuse radiation model for sloping surfaces: Description, perfor-
mance validation, site dependency evaluation,” Solar Energy, vol. 36,
no. 6, pp. 481–497, 1986.
[7] R. Perez, R. Seals, P. Ineichen, R. Stewart, and D. Menicucci, “A new
simplified version of the Perez diffuse irradiance model for tilted surfaces,”
Solar Energy, vol. 39, no. 3, pp. 221–231, 1987.
[8] R. Perez, P. Ineichen, R. Seals, J. Michalsky, and R. Stewart, “Modeling
daylight availability and irradiance components from direct and global
irradiance,” Solar Energy, vol. 44, no. 5, pp. 271–289, 1990.
[9] M. Schnitzer, C. Thuman, and P. Johnson. (2013). Understanding
the variation in estimated long-term solar resource estimates: Which
data set accurately represents your project site? [Online]. Avail-
able: http://www.awstruepower.com/wp-content/uploads/2012/05/Paper_
ASES_2012_P50_Variation.pdf.
[10] J. A. Duffie, W. A. Beckman, and W. M. Worek, Solar Engineering of
Thermal Processes. New York, NY, USA: Wiley, 1991, vol. 2.
[11] T. Muneer, Solar Radiation and Daylight Models. Evanston, IL, USA:
Routledge, 2012.
[12] A. Nobre, Z. Ye, H. Cheetamun, T. Reindl, J. Luther, and C. Reise, “High
performing PV systems for tropical regions—Optimization of system per-
formance,” presented at the 27th Eur. Photovoltaic Solar Energy Conf.
Exhib., Frankfurt, Germany, 2012, pp. 3763–3769.
[13] N. H. Reich, B. Mueller, A. Armbruster, W. G. J. H. M. van Sark,
K. Kiefer, and C. Reise, “Performance ratio revisited: Is PR > 90% re-
alistic?” Progress Photovoltaics: Res. Appl., vol. 20, no. 6, pp. 717–726,
2012.
Yong Sheng Khoo received the B.S. and M.Eng. de-
grees in mechanical and aerospace engineering, both
from Cornell University, Ithaca, NY, USA, in 2008
and 2009, respectively. He is currently working to-
ward the Ph.D. degree with the Graduate School for
Integrative Science and Engineering, National Uni-
versity of Singapore.
His current research interests include characteri-
zation and optimization of photovoltaic modules for
enhanced outdoor performance.
Andr
´
eNobrereceived the B.Eng. degree in mechan-
ical engineering from Universidade Federal de Minas
Gerais, Belo Horizonte, Brazil, and the M.Eng. de-
gree in technology management from the University
of South Australia, Adelaide, Australia. He is cur-
rently working toward the Dr.Eng. degree with Uni-
versidade Federal de Santa Catarina, Florian
´
opolis,
Brazil, under the topic short-term irradiance forecast-
ing for photovoltaic applications in tropical regions.
Raghav Malhotra received the B.Eng. degree
from the National University of Singapore (NUS),
Singapore, specializing in energy systems.
He has worked on characterizing the performance
of photovoltaic (PV) modules in the tropics, with the
Solar Energy Research Institute of Singapore. He is
also the NUS PV Design Team Leader for the Solar
Decathlon China 2013 competition in which 36 uni-
versities from 13 different countries are taking part.
Dazhi Yang (M’13) received the B.Eng. and M.Sc.
degrees from Department of Electrical and Com-
puter Engineering, National University of Singapore,
Singapore, in 2009 and 2012, respectively, where he
is currently working toward the Ph.D. degree.
He is employed full-time by the Solar Energy
Research Institute, Singapore. His research inter-
ests include statistical modeling for solar irradiance,
forecasting methodologies, and environmental data
mining.
Ricardo R
¨
uther received the M.Sc. degree in metal-
lurgical engineering and materials science from Uni-
versidade Federal do Rio Grande do Sul, Porto Ale-
gre, Brazil, in 1991 and the Ph.D. degree from The
University of Western Australia, Crawley, Australia,
in 1995.
He is currently an Associate Professor with
the Universidade Federal de Santa Catarina, Flo-
rian
´
opolis, Brazil. He was a Postdoctoral Research
Fellow with The Fraunhofer Institute for Solar En-
ergy Systems, Germany, in 1996, and the Department
of Electrical and Electronic Engineering, The University of Western Australia,
in 2011. He has also been a tenured academic with Universidade Federal de
Santa Catarina since 2000. His main interests include the area of photovoltaic
solar energy conversion, thin-film solar cell performance in warm climates, so-
lar radiometry, and, more recently, smart-grids and electric vehicles.
Thomas Reindl received the Master’s degree in
chemistry, the Ph.D. degree in natural sciences,
and an MBA degree from INSEAD, Fontainebleau,
France, all awarded with highest honors. He received
the Ph.D. degree from the University of Regensburg,
Regensburg, Germany, in 1996.
He began his career in 1992, focusing on photo-
voltaics (PV) with SIEMENS Corporate R&D Labs.
He was then selected for a German government schol-
arship, working in China as a foreign expert in the PV
industry. Afterward, he held several management po-
sitions at SIEMENS Solar Asia, SIEMENS HQ, and with ILIOTEC as Chief
Operating Officer in charge of PV technology and engineering. He is currently
the Deputy CEO and the Director of “Solar Energy Systems” with the Solar
Energy Research Institute of Singapore. His research interests include high-
efficiency solar photovoltaic systems and components, solar potential analysis,
irradiance forecasting, and PV grid integration.
Armin G. Aberle (SM’02) received the physicist and
the Ph.D. degrees in physics from the University of
Freiburg, Freiburg, Germany, in 1988 and 1992, re-
spectively. In 1999, he received the Dr.rer.nat.habil.
degree in physics from the University of Hanover,
Hanover, Germany.
He is currently the Chief Executive Officer with
the Solar Energy Research Institute of Singapore
(SERIS), National University of Singapore (NUS),
Singapore. His research interest includes reducing the
cost of electricity generated with silicon solar cells
(wafer-based and thin-film-based). He has published over 300 papers, and his
work has a high impact, with over 4000 citations. He is an Editor of several
scientific journals. In the 1990s, he established the Silicon Photovoltaics (PV)
Department, ISFH, Hamelin, Germany. He then worked for ten years in Aus-
tralia as a Professor of PV with the University of New South Wales, Sydney. In
2008, he joined NUS to establish SERIS, with particular responsibility for the
creation of a Silicon PV Department.
