Int. Journal of Renewable Energy Development 7 (2) 2018: 123-130
P a g e | 123

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Int. Journal of Renewable Energy Development (IJRED)
Journal homepage: http://ejournal.undip.ac.id/index.php/ijred
Research Article

Determining the Optimum Tilt Angles to Maximize the
Incident Solar Radiation - Case of Study Pristina
Xhevat Berishaa*, Arianit Zeqiria and Drilon Mehaa
Department of Thermoenergetics and Renewable Energy, Faculty of Mechanical Engineering, Pristina, Str. Sunny Hill n.n. 10000
Kosovo
ABSTRACT. Solar energy is derived from photons of light coming from the sun in a form called radiation. Solar energy finds
extensive application in air and water heating, solar cooking, as well as electrical power generation, depending on the way of
capturing, converting and distribution. To enable such application, it is necessary to analyze the horizontal tilt angle of horizontal
surfaces – in order that when the solar energy reaches the earth surface to be completely absorbed. This paper tends to describe the
availability of solar radiation for south-facing flat surfaces. The optimal monthly, seasonal, and annual tilt angles have been
estimated for Pristina. The solar radiation received by the incident plane is estimated based on isotropic sky analysis models, namely
Liu and Jordan model. The annual optimum tilt angle for Pristina was found to be 34.7°. The determination of annual solar energy
gains is done by applying the optimal monthly, seasonal and annual tilt angles for an inclined surface compared to a horizontal
surface. Monthly, seasonal and annual percentages of solar energy gains have been estimated to be 21.35%, 19.98%, and 14.43%.
Losses of solar energy were estimated by 1.13 % when a surface was fixed at a seasonal optimum tilt angle, and when it was fixed at
an annual optimum tilt angle, those losses were 5.7%.
Keywords: solar energy; gains; estimation; tilt angle; South-facing.
Article History: Received February 15th 2018; Received in revised form May 12th 2018; Accepted June 2nd 2018; Available online
How to Cite This Article: Berisha, Xh., Zeqiri, A. and Meha, D. (2018) Determining the Optimum Tilt Angles to Maximize the Incident Solar
Radiation - Case of Study Pristina. Int. Journal of Renewable Energy Development, 7(2), 123-130.
https://doi.org/10.14710/ijred.7.2.123-130

1.

Introduction

Because of a significant increase in energy demands,
conventional energy sources are being violently
consumed, leading to an increase of pollutants released
from the burning of fossil fuels. Knowing that solar
equipment’s do not have moving parts, they are
considered to have a greater lifetime and do not cause
pollution compared to other energy sources. Therefore,
solar energy is considered amongst the most common
solutions production thermal energy, for heat water and
district heating, and electricity energy.
Because of a significant increase in energy demands,
conventional energy sources are being violently
consumed, leading to an increase of pollutants, which are
released from the burning of fossil fuels. Knowing that
solar equipment’s do not have moving parts, they are
considered to have a greater lifetime and do not cause
pollution compared to other energy sources. Therefore,
solar energy is considered as one of the best solutions.
In most cities of Kosovo, the maximum global solar
radiation is reached during July, whereas the minimum
during December.
The performance of solar equipment’s (i.e. solar
collectors for water and air heating, power generation,
photovoltaic systems, etc.), is closely related to the

inclined angle from the surface that absorbs the light of
the sunshine (i.e. with their placement plane).
Sun tracking systems are used to increase the
acceptance of solar radiation. The usage of these systems
has a significant cost to the normal operation of an entire
system, due to the consumption of a considerable energy
generated.
Hence, the estimation of the optimal tilt angle has a
crucial effect on the solar technology. Additionally, as
stated by Eldin et al. (2016), trackers need periodic
maintenance and calibration and require input energy
for their operation which is in the range of 5–10% of the
energy produced. Further, as explained by Sinha and
Chandel (2016), trackers are made up of sophisticated
mechanical parts which add to capital cost and an
increase in cost of absolute power produced from solar PV
panels. Other method suggested by Yakup et al. (2001) is
to optimize the orientation of flat surfaces at optimum
tilt inclination (βopt). Vieira et al. (2016) performed an
experimental study which suggested that the sun
tracking panel exhibited a low average gain in power
generated, relative to the fixed panel. In another study
conducted by Sinha and Chandel (2016), it was reported
that the horizontal axis weekly adjustment tracking
systems and vertical axis continuous adjustment

* Corresponding author: xhevat.berisha@uni-pr.edu

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Citation: Berisha Xh., Zeqiri A. and Meha D. (2018) Determining the Optimum Tilt Angles to Maximize the Incident Solar Radiation - Case of Study Pristina.
Int. Journal of Renewable Energy Development, 7(2), 123-130, doi.org/10.14710/ijred.7.2.123-130

P a g e | 124
tracking systems, produced less energy annually than
the existing PV systems at fixed tilt. As suggested by
Ahmad and Tiwari (2009), optimum tilt inclination can
be adjusted daily, monthly, seasonally, bi-annually or
annually for maximizing the performance of the device in
use. In the city of Shterpca, the annual solar radiation is
estimated to be 1333.7 kWh/m2/year, while in the city of
Gjakova 1495.1 kWh/m2/year. Furthermore, as suggested
by Naumann and Pireci (2012), knowing the geographical
position of the aforementioned cities, we can accept an
average value of solar radiation of 1400 kWh/m2/year for
the climate conditions of Kosovo.
This solar radiation potential can be utilized in
desalination, solar-thermal collectors, building heating,
day-lighting, and Photovoltaic (PV) Cells etc.
Researchers are therefore concerned to maximize the
amount of useful energy that can be extracted through
the incoming solar radiations. Yakup and Malik (2001)
implied that it is believed that proper installation of
these devices can make a remarkable change in the
observed performance. Hence, climatology, latitude,
orientation, tilt angle, azimuth angles and the usage over
a period in a specific geographical region affect the
performance of the abovementioned devices.
The tilt of a surface (β) is one of the significant factors
that considerably affect the availability of solar radiation
on a flat surface. As suggested by Ahmad et al. (2016)
and Okoye et al. (2016) optimization of the performance
of solar-based devices requires option-like solar tracking
equipment, which follow trajectories of Sun’s motion to
enhance incident radiation. However, these options are
not always economical.
The Optimization of the tilt angle has been conducted
by numerous researchers including Bakirci (2012);
Ertekin et al. (2008); Stanciu et al. (2016); Hartner
(2015); Calabr (2013) and Mehleri (2010) for different
countries in Europe, Soulayman and Sabbagh (2015);
Jafari et al. (2012); Jafarkazemi (2012); Moghadam et al.
(2011); Jafarkazemi (2013); Tamimi and Sowayan (2012);
Benghanem (2011); Elminir et al. (2006); Alatarawneh et
al. (2016); Shariah et al. (2002) and Skeiker (2009) for
Middle East and lastly Khahro et al. (2015); Krishna et
al. (2015); Handoyo et al. (2013); Li and Lam (2007);
Tang and Wu (2004); Eke (2011) and Siraki and Pillay
(2012) for Asia.

Table 1
Division of Kosovo municipalities according to climate sub-zones
Nr
Zone 1
Zone 2
Zone 3
Zone 4
1

Peje

Prizren

Podujeve

Gjilan

2

Decan

Dragash

Kamenice

Viti

3

Gjakove

Mitrovice

Istog

Kacanik

4

Kline

Skenderaj

Zubin Potok

Shterpce

5

Rahovec

Lipjan

Leposavic

6

Suhareke

Pristine

Zvecan

7

Malisheve

Ferizaj

Vushtrri

Source: Naumann and Pireci (2012).

2. Methodology of analysis concepts – Data on
solar radiation
For the purposes of this paper, we used
meteorological data for daily mean global radiation
and diffuse radiation on a horizontal plane,
extracted from the information provided by the
Meteorological Institute of Kosovo and are
presented in Fig. 1.

Fig. 1 Monthly means daily global radiation Gm and diffuse
radiation Dm on horizontal plane of Pristina

Location of study
Pristina – the capital city – (42.65˚ N, 21.15˚ E and
573 m a.s.l.) is situated in the north-east of Kosovo
characterized by a humid continental climate with
maritime influences. Summers are warm and winters are
relatively cold and snowy.
According to a study conducted by by Naumann and
Pireci (2012) for zones with solar radiation potential,
Kosovo has been divided into four zones of rough solar
radiation.
Population density in Kosovo is greater in the central
and western parts compared to the eastern parts. The
highest values of solar radiation are shown in Zone 1
while the lowest appear in Zone 4. The division of
municipalities by area of solar radiation intensity is
presented in Table 1 provided by Naumann and Pireci
(2012).

Fig. 2 Global horizontal radiation in Kosovo
Source: http://globalsolaratlas.info/downloads/kosovo

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Int. Journal of Renewable Energy Development 7 (2) 2018: 123-130
P a g e | 125
æ
H ö
H æ 1 + cos b ö
æ 1 - cos b ö (4)
R = ç1 - D ÷ Rb + D ç
÷+ rç
÷
H
H
2
2
è
ø
è
ø
è
ø

and
are are the monthly average daily global and
diffuse radiations on a horizontal surface;
is the ratio
of the mean daily direct radiation on an inclined surface
to that on a horizontal surface, and the parameters
correlated by ground reflection coefficient (albedo ρ=0.2);
β represents the tilt angle. Radiation beam falling on an
inclined surface is given by Liu and Jordan (1962):

H B = ( H - H d ) × Rb

As defined by Jakhrani et al. (2013), the reflected
radiation is “the part of the total solar radiation that is
reflected by the surface of the earth, and by any other
surface intercepting object such as trees, terrain or
buildings on to a surface exposed to the sky is termed as
ground reflected radiation”. Reflected radiation on an
inclined surface is given by:

Fig. 3 Direct normal radiation in Kosovo
Source: http://globalsolaratlas.info/downloads/kosovo

In Fig. 2 presents the yearly average of global
radiation, horizontal plane, in Kosovo. As per Fig. 1, the
highest value of average global solar radiation in Kosovo
is in the city of Gjakova. In Fig. 3 is presented the annual
average direct normal radiation, horizontal plane, for
Kosovo cities.
3. Estimation of solar radiation on the inclined
surface
Global solar radiation monthly mean data for an
inclined surface are necessary for the designing of solar
energy systems. These data are often not available.
Therefore, we need tend to estimate the data by
considering the monthly average of the global solar
radiation on the horizontal plane (presented in Fig. 3.),
which is the most important parameter for estimating
the optimum tilt angle.
The study presents a simple and universal method of
determining the mean monthly global radiation based on
the existing methodology given by Paul et al. (2016).
As defined by Liu and Jordan (1962), Jakhrani et al.
(2013), and Muneer (2004), the total solar energy
received on an inclined surface is “the sum of the beam,
diffuse, and reflected radiation”.
Thus, the total solar radiation monthly average (in
kWh/m2/day) for an inclined surface is calculated as
follows:

HT = H B + H D + H R

(5)

(1)

Mathematically, the optimal value of the tilt angle
(βopt) is determined by differencing Eq. 1 depending on
the angle of inclination (β).

d
( HT ) = 0
db

(2)

HT = R × H

(3)

R presents the ratio between the global radiation

monthly mean on an inclined surface than for the
horizontal one. Below is presented the R ratio as defined
by Liu and Jordan (1962) and Bakirci (2012):

H R = H × Rr

(6)

is the reflected conversion factor:

æ 1 - cos b ö
Rr = r ç
÷
2
è
ø

(7)

Where ρ is the constant that depends on the type of
ground surrounding tilted surfaces and is called the
ground reflectance or albedo. According to Kondratev
(1969), the value of albedo most commonly used is ρ= 0.2
for hot and humid tropical locations, ρ= 0.5 for dry
tropical locations, and ρ= 0.9 for snow covered ground.
The ground reflection coefficient is assumed ρ= 0.2 for
the climate conditions in Pristina.
Widen (2009) defines the diffused radiation ( H D ) as
the fraction of total solar radiation, received from the sun
when its direction has been changed by atmospheric
scattering. The diffused radiation direction o is highly
variable and difficult to determine. It is a function of the
condition of cloudiness and atmospheric clearness which
is extremely unpredictable. Diffused radiation fraction is
the sum of isotropic, circumsolar, and horizon
brightening components. The isotropic diffuse radiation
component is “received evenly from the entire sky dome”
as defined by Robinson and Stone (2004). The
circumsolar diffuse part is received from the onward
solar radiation dispersion and focused around the sun
sky section. The horizon brightening component is
concentrated near the horizon and it is most visible
during clear skies as presented by Liu and Jordan (1960).
In general, isotropic, circumsolar, and horizon
brightening factors compose the diffuse fraction of
radiation on an inclined surface. In Liu and Jordan
(1960) model, the diffuse radiation was assumed isotropic
only while circumsolar and horizon brightening were
taken as zero.
Diffuse radiation falling on an inclined surface is
calculated as follows:
H D = H d × Rd

(8)

Where
is the diffuse conversion factor presenting the
ratio of diffuse solar radiation on an inclined surface to
diffuse solar radiation on a horizontal surface, given as:

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Berisha Xh., Zeqiri A. and Meha D. (2018) Determining the Optimum Tilt Angles to Maximize the Incident Solar Radiation - Case of Study Pristina.
Int. Journal of Renewable Energy Development, 7(2), 123-130, doi.org/10.14710/ijred.7.2.123-130

P a g e | 126
æ 1 + cos b ö
Rd = ç
÷
2
è
ø

(9)

The monthly average data of the daily global
radiation, taken from Fig. 3., are used in the following
expressions for determination of other parameters.
According to Paul et al. (2016), the following expression
determines the monthly average of daily diffuse
radiation:
Hd
= 0.96268 - (1.45200 × KT ) + 0.27365 × KT2
H

(

+

(

0.04279 × KT3

)

) + ( 0.000246 × ( SSHA) )

(10)

+ ( 0.001189 × ( NHSA ) )

Where SSHA is the sunset hour angle in degrees on the
“monthly average day (n)”, which can be calculated from
the following equation:

SSHA = ws' = cos-1 ( - tan (f - d ) tan d )

(11)

NHSA is the noon solar angle from the horizon in
degrees on the “monthly average day (n)” and can be
estimated as follows:
(12)

NHSA = 90 - f - d

The monthly average clearness index K T is the ratio of
monthly average daily radiation on a horizontal surface
to the monthly average daily extraterrestrial radiation
and can be obtained from:
(13)

KT = H / H 0

Where,
is the monthly mean daily extraterrestrial
radiation on a horizontal surface, and it is calculated
using Albotenau et al. (2015) formula:

æ
æ 360n ö ö
I 0 ç1 + 0.033cos ç
÷÷
è 365 ø ø
è
2pws
æ
ö
ç cos f cos d sin ws + 360 sin f sin d ÷
è
ø
H0 =

24 ´ 3600

p

According to Cooper Cooper (1969), declination angle
is calculated using the following relation:

é ( 284 + n ) ù
d = 23.45sin ê360
ú
365 û
ë

where n is the day of the year.
Various researchers have proposed numerous models
which are classified as isotropic including Liu and Jordan
(1960), Tian (2001), Koronakis (1986) and Badescu (2002)
and anisotropic Hay (1979), Reindl et al. (1990), Klucher
(1979) models, Skartveit and Olseth (1986), and Steven
and Unsworth (1980) to estimate solar radiation on
inclined surfaces. However, according to Tang and Wu
(2004), measured diffuse solar radiation data gives better
estimates of the optimum tilt angle. In this study,
measured data of global and diffuse solar radiation has
been utilized to calculate the optimum tilt angles. Liu
and Jordan (1960) (isotropic) model has been used to
estimate total solar radiation on inclined flat surfaces
facing south.
The angle of incidence for a surface oriented in any
direction can be mathematically expressed by the
following relation given by Duffie and Beckman (2006):

cos q = sin d sin j cos b - sin d cos j sin b cos g
+ cos d cos j cos b cos w + cos d sin j sin b cos g cos w (16)
+ cos d sin b sin g sin w
For a surface in northern hemisphere facing south
(i.e. γ = 0̊) Eq. (16) can be simplified as:
cosq = sin (f - b )sin d + cos(f - b )cos d cos w

Where I0 represents the solar constant (1367 W/m2); n
shows the number of daily readings in a given month,
counted from 1 January (1–365); f is location geographic
latitude; ωs is sunrise/sunset angle on a horizontal
surface; δ is sun declination. As defined by Cooper
(1969), the “monthly average day” is the day of the
month, whose solar declination is closest to the average
declination for that month. The maximum value of the
declination angle (δ) is +23.45˚ during June 21st–22nd,
while its minimum value is -23.45˚ during December
20th–21st. The declination value is zero on March 22nd
and September 22nd of the year, see Table 2.
Table 2
Monthly representative day and its corresponding declination (δ
in degrees)
Month
Jan.
Feb.
Mar.
Apr.
May
Jun.
Day (n)
17
47
75
105
135
162
Declination (δ) -20.92 -12.05 -2.43
9.41 18.79 23.09
Month
July
Aug.
Sep.
Oct.
Nov.
Dec.
Day (n)
198
228
258
288
318
344
Declination (δ) 21.18 13.46
2.22
-9.60 -18.91 -23.05

(17)

For a horizontal surface (β=0̊), the angle of incidence
(θ) becomes equal to zenith angle (θz). Substituting this
value in Eq. (17), zenith angle can be written as:

cos q z = sin j sin d + cos j cos d cos w
(14)

(15)

(18)

The total solar energy received on an inclined surface
is the sum of beam and diffuse radiations directly
incident on a surface and reflected radiations (reflected
by the surroundings).
According to Liu and Jordan (1960), the beam
conversion factor is given as:
Rb =

cos (f - b ) cos d sin w + (p / 180 ) w sin (f - b ) sin d
cos f cos d sin ws + (p / 180 ) ws sin f sin d

(19)

Where ω is the sunrise (or sunset) hour angle for the
inclined surface.

w = min{ws , ws' }

(20)

The hour angles at sunrise and sunset ωsare very
useful parameters. Since, numerically these two angles
have the same value the sunrise angle is negative, and
the sunset angle is positive. Both can be calculated from
the following expression:

ws = cos-1 ( - tan f tan d )

(21)

If a surface is inclined from the horizontal, the Sun
may rise over its edge after it has risen over the horizon.
Therefore, the surface may shade itself for some days.
The sunrise and sunset angles for an inclined surface ( )

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Int. Journal of Renewable Energy Development 7 (2) 2018: 123-130
P a g e | 127
facing the equator (i.e. facing south for the northern
hemisphere) are given by:

ws' = cos -1 ( tan (f - b ) tan d )

(22)

4. Results and Discussions
Equations (1-22) are used to determine the monthly
mean daily global solar radiation on the south-facing
inclined surface for the location under study, Pristina. By
changing the tilt angle from 0° to 90° in values of 0.1°,
the optimal tilt angle is defined by the corresponding
value of maximum solar radiation for a certain period.
Based on the methodology used in Section 3 and on
the Liu and Jordan model (1960), estimations have been
made to obtain the optimum monthly, seasonal, and
yearly/annual tilt angles by corresponding to global solar
radiation on an inclined surface – results are given in
Table 3.
Table 3
The optimum monthly, seasonal, and annual tilt angles βopt (O)
for Pristina
Month
Station
Period
Jan. Feb. Mar. Apr. May Jun.
Monthly 64.8 56.5
43
25
9.2
0.3
Pristina
Seasonal 62.1 62.1 25.7 25.7 25.7 8.9
f=42° 39’ N
Annual 34.7 34.7 34.7 34.7 34.7 34.7
Month
Station
Period
July Aug. Sep. Oct. Nov. Dec.
Monthly 4.8 19.2 37.3 54.3 63.8 66.4
Pristina
Seasonal 8.9
8.9 50.9 50.9 50.9 62.1
f=42° 39’ N
Annual 34.7 34.7 34.7 34.7 34.7 34.7

To continue with, the daily extraterrestrial radiation on a
horizontal surface H 0 , clearness index KT , diffuse solar
radiation on a horizontal plane H d , optimal tilt angle βopt,
monthly average daily global radiation in optimal tilt
angle H T , and the comparison H with H T in percentage,
has also been estimated and are presented in Table 4, –
which shows the minimum and maximum value of H T ,
that correspond to December and July respectively.

Fig. 4 Monthly mean solar radiation data for Pristina when the
tilt angle variates from 0o to 90o: a) January-June and b) JulyDecember

For all the months and different tilt angles, monthly
average total solar radiation was calculated using Eq. (1).
The findings have been plotted and are shown in Fig. 4
for Pristina, where the tilt angle has been varied in the
range of 0–90˚ (in steps of 10˚). Fig. 4.a) and 4.b) show
the total solar radiation versus tilt angle from January to
June and from July to December respectively. It is
apparent from the Fig. 4 that the solar radiation is an
intensive function of tilt angle. The calculated solar
energy radiation incident on the flat surface is increased,
with the increasing of horizontal position from 0˚ to an
angle of inclination, but a further increase of the tilt
angle of the flat surface will result in the decreasing of
solar radiation received.

Table 4

Ho (kWh / m 2 / day), K T , H d (kWh / m 2 / day), bopt ( o ), H T (kWh / m 2 / day)
and comparison with H in location Pristina city
Month

Ho

KT

Hd

β opt (o )

HT

H o / H T (%)

January
February
March
April
May
June
July
August
September
October
November
December
Average
% Gain

3.60
5.04
7.24
9.17
11.34
11.62
11.98
10.32
7.84
5.86
4.14
3.38
7.63
-

0.45
0.49
0.52
0.54
0.53
0.56
0.56
0.58
0.58
0.57
0.50
0.42
0.53
-

0.69
0.96
1.36
1.76
2.29
2.30
2.36
1.90
1.36
1.00
0.77
0.65
1.45
-

64.8
56.5
43
25
9.2
0.3
4.8
19.2
37.3
54.3
63.8
66.4
-

3.14
3.89
4.81
5.33
6.07
6.52
6.70
6.23
5.46
5.12
3.97
2.90
5.01
21.35

95.03
58.13
26.58
7.24
0.83
0.00
0.15
4.01
19.21
53.75
92.72
104.23
21.34
-

Fig. 5 Average maximum total solar optimum annual for
Pristina

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Berisha Xh., Zeqiri A. and Meha D. (2018) Determining the Optimum Tilt Angles to Maximize the Incident Solar Radiation - Case of Study Pristina.
Int. Journal of Renewable Energy Development, 7(2), 123-130, doi.org/10.14710/ijred.7.2.123-130

P a g e | 128
radiation is achieved for every month with unique
optimum tilt angle – which increases in winter months
and decreases to the minimum value in summer &
autumn months, (see Fig. 5). Fig. 6 compares the average
annual solar radiation on a tilted surface fixed at
monthly, seasonal, and yearly optimum tilt angles for
Pristina. As observed from the Fig. 6, the annual average
total solar radiation estimated at monthly optimum tilt
angle is found to be the highest, followed by average
annual solar radiation estimated at seasonal and annual
optimum tilt angles value.
The aforementioned optimal tilt angles are also
plotted in Fig. 5.

Fig. 6 Variations of monthly, seasonal & annual optimum tilt
angles for south-facing surface in Pristina

Gains of solar radiation available on an inclined
surface are defined as follows:

æ H T ( b = b opt ,i ) ö
Gains (%) = ç
- 1÷ ´ 100
ç H T ( b = 0)
÷
è
ø

(23)

where i= monthly, seasonal and annual.

Fig. 7 Seasonal mean solar radiation in Pristina for: Spring,
Summer, Autumn, Winter, when the tilt angle charges from 0o
to 90o. (Considering the azimuth angle=0o for maximum solar
radiation).

Therefore, four seasonal optimum tilt angles were
obtained (corresponding to each season) 62.1˚ in winter,
25.7˚ in spring, 8.9˚ in summer, and 50.9˚ in autumn.
Thus, winters have a higher value of optimum tilt angle,
while summers observe a lower tilt angle value. Annual
optimum tilt angle was calculated by using expressions
from Section 3 and has resulted to be 34.7˚ for Pristina.
Annual average total gains of solar radiation on an
optimally tilted angle of a surface in comparison to a
horizontal surface are 21.35% (monthly optimum tilt
angle), 19.98% (seasonal optimum tilt angle) and 14.43%
(annual optimum tilt angle).
Results for the diffuse radiation on a horizontal plane;
the yearly (annual) and seasonal optimal tilt angles for
each season; the monthly average daily global radiation
for optimal tilt angle; and the comparison between H
with HT in percentage are presented in Table 5.

The result also indicated that the optimum angle
differs with the yearly months. The maximum solar
Table 5
H d (kWh/m2/day), βopt (O), H T (kWh/m2/day) and the comparison with H of Pristina for seasonal and annual tilt angles
Month
January
February
March
April
May
June
July
August
September
October
November
December
Average
% Gain

Seasons
Winter
Spring

Summer

Autumn
Winter

Hd
0.69
0.96
1.36
1.76
2.26
2.29
2.35
1.90
1.36
1.01
0.76
0.65
1.45
-

Seasonal Annual Seasonal
HT
βopt
βopt
62.1
62.1
25.7
25.7
25.7
8.9
8.9
8.9
50.9
50.9
50.9
62.1
-

34.7
34.7
34.7
34.7
34.7
34.7
34.7
34.7
34.7
34.7
34.7
34.7
-

3.14
3.88
4.64
5.33
5.91
6.48
6.69
6.16
5.34
5.11
3.88
2.90
4.95
19.98

Annual
HT

HT / H

HT / H

Seasonal

Annual

2.78
3.66
4.77
5.27
5.70
5.88
6.17
6.07
5.46
4.87
3.54
2.54
4.73
14.43

95.03
57.72
22.11
7.24
-1.83
-0.61
0.00
2.84
16.59
53.45
88.35
104.23
19.98
-

72.67
48.78
25.53
6.04
-5.32
-9.82
-7.77
1.34
19.21
46.25
71.84
78.87
14.43
-

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Int. Journal of Renewable Energy Development 7 (2) 2018: 123-130
P a g e | 129
For all the months and different tilt angles, monthly
average total solar radiations for the city of Pristina,
were calculated using the procedure described in the
previous section, based on the Liu & Jordan model,
estimates have been made to obtain optimum tilt angles
and corresponding total solar radiation on inclined
surfaces.
Figure 8 describes the variation of beam conversion
factor with days of the year at various tilt angles for the
city of Pristina. Also, Figure 9 shows the variation of
diffuse and reflected conversion factors at different tilt
angles.

Fig. 8 Beam conversion factor at different tilt angles for Pristina

Fig. 9 Diffuse and reflected conversion factors for Pristina

5. Conclusion
By making adjustments in the surface inclination,
energy falling on a surface can be significantly improved.
Different months have different values for optimum tilt
angles due to the change of the Sun's position. The
following conclusions are drawn:
- Seasonal optimum tilt angles are 62.1˚ (winter),
25.7˚ (spring), 8.9˚ (summer), and 50.9˚ (autumn).
Tilt angles are higher in winter rather than in
summer.
- The Annual optimum tilt angle (
) is 34.7˚.
- Maximum and minimum values of total solar
radiation at annual optimum tilt angle are 6.17
kWh/m2/day (July) and 2.54 kWh/m2/day
(December).
It is recommended that where possible the surface
must be inclined at monthly or seasonal optimum tilt
angles to reach the highest possible values of solar

radiation. The annual optimum tilt angle can be used for
surfaces with fixed inclination where the changing of tilt
angle is not often possible.
By doing so, the system optimization is achieved to
enable the highest absorption of solar radiation from an
inclined surface.
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Citation: Berisha Xh., Zeqiri A. and Meha D. (2018) Determining the Optimum Tilt Angles to Maximize the Incident Solar Radiation - Case of Study Pristina.
Int. Journal of Renewable Energy Development, 7(2), 123-130, doi.org/10.14710/ijred.7.2.123-130

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