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Energy Optimisation ENO 732
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An Optimal Design for Maximum Power Production from a Solar Field
installed with Stationary Solar Collectors
By
Ambrose Njepu
Department of Electrical, Electronics and Computer Engineering,
Date: 6th June, 2016
Energy Optimisation ENO 732
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An Optimal Design for Maximum Power Production from a Solar Field installed with
Stationary Solar Collectors
Ambrose Odinaka Njepu,
Abstract- The energy collected from a solar field is a function of the active collector cross-
sectional area, field dimensions, solar irradiation, inter-row spacing, row length and
mutual shading. This paper presents an optimal design for maximising the power output
of a constrained solar field installed with flat stationary solar collectors. The objective is
to maximise the number of solar collectors that can be installed in the solar field while
minimising mutual shading, inter-row spacing.
I. INTRODUCTION
Currently, the use of fossil fuel energy is the leading contributor of global warming. The threat
of global warming and the depleting fossil reserves in the face of the ever-rising energy
demand has led to explosion of research in sustainable and environmentally friendly renewable
energy sources. Solar energy has gained popularity in the last three decades thanks to its natural
abundance and environmental friendliness.
This paper presents a case study of a textile company that wants to use the energy generated
from a solar field to heat steam used for powering purpose. The dimension of the field is given
as length, L=500m and width, W=80m. Also, the dimension of the collector is given as length,
L=1.2m and width, W=0.6m. A model is required for the optimal distribution of collectors in
the solar field in order to maximise power output from the constrained field.
The authors of [1], developed an analytical shading model for rows of non-concentrating
collectors tilted towards the equator, showing than the effects of collector length is negligible
except at sunrise and sunset when the sunβs radiation is low. They also discussed beam
radiation and its shading effects. In [2], a model for total irradiation of shaded collector
assuming an infinite length of collector length in an isotropic model is developed. It discusses
the relationship between the diffused radiation and view factor of the sky as seen by the
collector.
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Similarly, a model for calculating the optimal tilt angle of a collector is developed in [3], it
shows that the tilt angle, π½, optimises the incidence angle, π, when π2πππ π ππ½2β < 0.
The power produced by a PV is proportional to the solar irradiance (I), the cross-sectional area
of the collector (π΄π) and the energy conversion efficiency (π) of the PV collector. The solar
irradiation is made up of beam, diffused and reflected radiation. Its magnitude varies at
different locations because of the relative angle between the sun and the earth. Maximum power
yield from the collector is reached when the incident sun ray is at right angle to the collector
plane. The solar tracking system is designed to track the solar radiations such that the incident
radiation is at right angle to the collector. It has been reported that the effective cross sectional
area has a direct relationship with the quantity of power produced. The lesser the active cross-
sectional area, the lesser the generation capacity of the PV collector [1] [2] [4].
For a large scale system, multiple rows of collectors are employed and this comes with its
advantages and disadvantages. Its major advantage is that it increases the capacity of the field
but it also reduces the active area of the active collectors due to an increase in mutual collector
shading. Mutual shading, inter-row spacing and tilt angle are the control variables for the
objective function [2].There is therefore a need for an optimal solution for the orientation of
the collectors in a given area for optimal energy collection and economic considerations.
The contribution of this paper is an optimal model for maximising the energy collected from
the solar field while minimising the inter-row spacing and mutual shading subject to
constraints.
The rest of this paper is laid out as follows: section II shows the problem formulation, the case
study analysis which includes the field dimensioning, solar angles and geometry, shading
effects and insolation are discussed in section III; modelling and optimisation is presented in
section IV and V respectively; while section V is the conclusion of the paper.
II. PROBLEM FORMULATION
The following assumptions are made for the optimal design of the placement of collectors in a
solar field for maximum power output collected from the solar field:
All panels are mounted parallel to each other on the ground.
All panels are tilted at an angle, π½, from the horizontal.
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The inclination/tilt angle π½, is the same for all collectors.
The collectors are mounted to a fixed position, no movement or rotation is allowed.
All panels must be installed facing the equator and the collector rows are inclined along
the east-west axis [2].
A clear sky of isotropic model is assumed for modelling the global irradiation [1] [2]
[4].
All collector panels have the same power capacity.
The energy conversion efficiency for all collectors is assumed to be the same.
A continuous row of collector is assumed, no spacing between row collectors.
No fencing around the field, so the first row of collectors is not shaded.
A walk-path of x m wide should go round the field for easy movement during
maintenance [4].
The collectors are mounted along the field length (i.e. south facing orientation).
An isotropic atmosphere and radiation is assumed
III. CASE STUDY
A. Solar Field Dimensioning
The textile has a field whose dimensions are given as length, L=500m and width, W=80m.
Also the dimension of a single panel is given as length, πΏπ=0.6m and height, H=1.2m. The
problem is the optimal placement or positioning of the collectors along the field to yield
maximum power.
A walk-path of x m wide is introduced around the field for easy movement during maintenance.
This reduces the active field length and width on both sides. The active field length becomes
β²πΏ1 = πΏ β 2π₯β² and width becomes β²π1 = π β 2π₯β². The number of collectors per row is
expressed as
ππ =πΏ β 2π₯
πΏπ=
500 β 2π₯
1.2 (1)
L1=500-2x
W1=80-2x
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Also, the number of rows (π π) in the field depends on the active field width (W-2x), collector
height (H), tilt angle (π½), the horizontal collector component (π) and the inter-row collector
spacing (D). The number of rows is expressed as:
π π =π β 2π₯
π + π·=
80 β 2π₯
π» sin π½ + π·=
80 β 2π₯
0.6 sin π½ + π· (2)
Where the value of D is defined in equation (11) below
B. Solar Geometry and angles
The relative angles of the sun and the earth determine the variations between the energy
delivered to the earth. Global insolation is a function of the solar angles. Azimuth (πΎπ ) and
altitude (πΌ)angles are used to determine the exact location of the sun in space [4]. The azimuth
angles are measured from true south positively in a clockwise direction to the horizontal
component of the sunβs radiation [4]. Other important solar angles are the tilt/inclination angle
(π½), incidence angle (π), collector azimuth angle(πΎπ), hour angle (π), latitude (β ) and the
declination angle (πΏ).
The equation (3) below shows the relationship between some solar angles [4]
sin β = sin β sin πΏ + cos β cos πΏ cos π (3)
β= sinβ1(sin β sin πΏ + cos β cos πΏ cos π) (4)
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Altitude angle Ξ± =49.6
Tilt angle Ξ² =49.6Due South
PV Module
SUN
Fig. 2: showing the relationship between the tilt and altitude angles.
Fig. 3: showing the solar angles
The relationship between the solar azimuth, declination, hour, latitude and altitude angle is
shown in equations (5) and (6) below:
sin πΎπ =cos πΏ π ππ π
cos πΌ (5)
cos πΎπ =sin β cos πΏ cos π β cos β sin πΏ
cos πΌ (6)
Therefore,
πΎπ = sinβ1 (cos πΏ π ππ π
cos πΌ) = cosβ1 (
sin β cos πΏ cos π β cos β sin πΏ
cos πΌ) (7)
Equation (8) shows the relationship between incidence, tilt, altitude and azimuth angles [4].
cos π = cos π½ sin πΌ + sin π½ cos πΌ cos πΎ (8)
cos π = sin(β β π½) sin πΏ + cos( β β π½) cos πΏ cos π (9)
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Fig. 4: showing the inter-row spacing and shading analysis.
The declination angle (πΏ) is the angle between the sunβs north or south-pole and the equator.
The value of declination angle is given as [5] [6] [7]
πΏ = 23.45 sin [360
365(284 + π)] (10)
Where π is the day of the year.
From figure 4, the inter-row spacing can be determined using the solar angles seen in [1]
π· =π1 β πππ» cos π½
π π β 1 (11)
π· =(80 β 2π§) β 0.6 ππcos π½
π π β 1 (12)
Where k is the number of rows, π π=1,2β¦.π π and π π is the maximum number of rows.
The vertical component of the collector (h) is important for shading analysis. It is given as
β = π»π πππ½ = π»πππ π½ π‘πππ½ (13)
Incidence angle is the angle between the collector normal axis and the sunβs radiation; it shows
the relative position of a collector to the point of maximum solar irradiation (i.e. normal axis).
It is expressed as [3]
cos π = sin πΏ sin β cos π½ β sin πΏ cos β sin π½ cos πΎ + cos πΎ cos β cos π½ cos π + cos πΏ sin β sin π½ cos πΎ cos π +
cos πΏ sin π½ sin πΎ sin π (14)
C. Shading analysis
Collectors cast shadows on the preceding collector which reduces the active area of the
collector and also the power production capacity of the collector. The shaded area is dependent
on tilt angle, inter-row distance, collector length, incidence and latitude angle [4].
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An inclined PV collector has lesser shading effect compared to the upright collector; this is
because some of the shadows are under the inclined collector.
The shadow height is defined interms of the collector height [4]
π»π = π» (1 βπ· + π» cos π½
ππ¦) (15)
ππ¦ = π» cos π½ +π» sin π½ cos πΎπ
tan πΌ (16)
Substituting ππ¦ into the π»π equation (15), the shadow height becomes:
π»π = π» (1 βπ· + π» cos π½
π» cos π½ +π» sin π½ cos πΎπ
tan πΌ
), (17)
where π»π is the shadow height and ππ¦ is the vertical component of the shadow.
From fig. 5, the length of the shading, πΏπ , is obtained by subtracting the length of the unshaded
portion from the entire length of the collector. This is expressed as [4]
πΏπ = πΏπ β πΏπ’ππ (18)
πΏπ = πΏπ β(π· + π» cos π½)ππ₯
ππ¦ (19)
ππ₯ is the horizontal component of the shadow, defined as
Fig. 5: showing the mutual shading effect of collectors in the field
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ππ₯ =π» sin π½ sin πΎπ
tan πΌ (20)
The length of the shadow is formulated by substituting the values of ππ₯ πππ ππ¦ from equations
(16) and (20) into equation (19) and it becomes:
πΏπ = πΏ β (π· + π» cos π½)sin π½ |sin πΎπ | tan πΌβ
cos π½ + sin π½ cos πΎπ tan πΌβ (21)
For πΎπ > 0, the shadow is eastward, and for πΎπ < 0 the shadow is westward [4].
For a more general analysis, the relative quantities are introduced. The area of the shaded
portion is defined by the product of equations (17) and (21). It is expressed as
π = πΏπ Γ π»π (22)
From figure 5, the collector height is given as
π»π = π» sin π½ (23)
The relative spacing between the rows of collectors is defined as [4]
π =π·
π»π (24)
The relative collector length
is
π =πΏπ
π»π (25)
the relative shadow height is defined as
βπ =π»π
π» (26)
The relative length of the shadow is
ππ =πΏπ
πΏπ (27)
The relative shadow height (βπ ) is obtained by substituting equations (15) and (19) into
equation (26) as seen below
βπ = 1 βπ sin π½ + cos π½
cos π½ + sin π½ cos πΎπ tan πΌβ (28)
And
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ππ = 1 β (|sin πΎπ |
π tan β) (
π sin π½ + cos π½
cos π½ + sin π½ cos πΎπ tan πΌβ) (29)
Therefore, the relative shadow area is
π =π»π πΏπ
π»πΏπ= βπ ππ (30)
D. Solar Irradiation
The power produced by a collector is proportional to the intensity of solar irradiation it receives.
The solar irradiation is composed of the beam, diffused and the reflected irradiation. Beam
irradiation is the direct solar radiations coming from the sun while diffused irradiation is the
scattered beam which reaches the earth after it has been scattered by the atmosphere.
1) Beam insolation
The beam irradiation on a tilted collector is expressed as [1] [4]
πΌπ΅ = πΌπ cos π (31)
The first row is unshaded, so it produces it produces the largest power in the field at any point.
However, it shades other subsequent collectors behind it, thereby reducing the active collector
areas. So the total beam irradiation on the shaded collector seen in [4] as
πΌπππ β = π»πΏπ(1 β π )πΌππ cos ππ (32)
Where πΌπππ β is the daily variation of the beam insolation on the shaded collector, H is the
collector height, L is the collector length and π is the shaded area of the collector at time j.
The total beam irradiation on a shaded collector is explicitly by substituting equation (9) into
(33)
πΌπππ β = π»πΏπ(1 β π )πΌππ sin(β β π½) sin πΏ + cos( β β π½) cos πΏ cos π (33)
2) Diffused insolation
The diffused irradiation on a tilted collector is given by [4]
πΌπ· = πΌπ cos2π½
2 , (34)
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where πΌπ is the diffused solar insolation on a horizontal surface and the minimum value for
cos2 π½
2 applies to an isotropic sky. The daily diffused insolation received by the shaded collector
is [4]
πΌππ β = πΌπ(cos2
π½
2+ cos2
πππ£
2β 1), (35)
where πππ£ is the screening angle.
3) Global Insolation
The effect of the reflected insolation on a tilted surface is negligible, so the global insolation
of an inclined collector is the sum of the beam and diffused insolation on the PV collector. This
is expressed as [1] [4]
πΌ = πΌπ cos π + πΌπ cos2π½
2 (36)
The global insolation on a shaded collector is defined by the sum of equations (32) and (35)
[1]:
πΌπ β = π»πΏπ(1 β π )πΌππ cos ππ + πΌπ(cos2π½
2+ cos2
πππ£
2β 1) (37)
The power output from a PV collector is dependent on the incident solar insolation upon it.
The total daily solar energy received by the collector, per unit area, in a month is defined as:
π = β πΌπβ
πππ
πππ
π = β(πΌππ cos ππ
πππ
πππ
+ πΌππ cos2π½
2)βπ , (38)
π = β(πΌππ cos ππ
πππ
πππ
βπ + ππ cos2π½
2) , (39)
where ππ is the energy received from the diffused insolation, πΌππ is the hourly variations of the
beam insolation and βπ is the sampling period, which is from sunrise to sunset.
The total energy from the beam insolation on the solar field is the sum of the beam insolation
on the unshaded and the shaded collectors [1] is given as
ππ,π = π»πΏπ [β πΌππ cos π ππ
π=1
π½
βπ + (π π β 1) β(1 β π )πΌππ cos ππ
π β1
π
βπ] , (40)
where π π=2,3,β¦. π π.
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Therefore, the total solar energy delivered to the PV solar collector is the sum of the beam and
diffused radiations on the unshaded and shaded rows of collectors as seen [1] as
ππ = π»πΏ [β πΌππ cos ππβπ +π πΌππ cos2 π½
2+ (π β 1) β (1 β π )πΌππ cos ππβππ + (π β 1) ππ (cos2 π½
2+ cos2 πππ£
2β 1)]
(41)
where π π=2,3,β¦ π π
IV. MODELLING
The total global irradiation on a tilted surface is the sum of the direct beam, diffuse and the
reflected radiation expressed as follows [8] [9]:
πΌπ = πΌπ΅ + πΌπ· + πΌπ , (42)
where πΌπ is the total global irradiation, πΌπ΅, πΌπ· πππ πΌπ are the beam, diffused and reflected
component of the solar irradiation on the tilted surface. Equation (42) can be expressed further
as [5]:
πΌπ = πΌπ π π + πΌπ π π + πΌπ π π , (43)
where πΌπ , πΌπ πππ πΌπ are the beam, diffused and the reflected component of solar insolation on a
horizontal surface. The daily beam irradiation on an inclined surface can be redefined as
πΌπ = (πΌ β πΌπ) π π (44)
Where πΌ and πΌπ are the global and diffused radiation on a horizontal surface, while π π is the
ratio between the beam radiation on a tilted surface to the horizontal surface. The daily reflected
ray can be redefined as
πΌπ =πΌπ(1 β cos π½)
2 (45)
The values of π π depends on the latitude of the collector. In the northern hemisphere, optimal
collector orientation is achieved by facing the equator (i.e. south facing), π π is given as [8]
π π,1 =cos(β β π½) cos πΏ sin ππ + ππ sin(β β π½) sin πΏ
cos β cos πΏ sin ππ + ππ sin β sin πΏ , (46)
while, the southern hemisphere, the collector orientation is facing the equation (i.e. north
facing), π π is given as [8]
π π,2 =cos(β + π½) cos πΏ sin ππ + ππ sin(β + π½) sin πΏ
cos β cos πΏ sin ππ + ππ sin β sin πΏ (47)
Where ππ is the sunset hour angle for the tilted surface for the mean day of the month.
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For an isotropic model, π π = π π expressed as:
π π = π π =1 + cos π½
2 (48)
The total irradiation on a tilted surface is re-expressed by substituting the equations (44) and
(45) into equation (42), given as:
πΌπ = (πΌ β πΌπ) π π + πΌππ π +πΌπ(1 β cos π½)
2 (49)
The effect of reflected radiation is significant on a horizontal surface but negligible on a tilted
surface, so the total insolation on an inclined surface is the sum of the direct beam insolation
and the diffused insolation.
πΌπ = (πΌ β πΌπ) π π + πΌππ π (50)
V. OPTIMISATION MODEL
Hourly power produced by the PV is a function of the collectorβs efficiency (π), area of the
collector (π΄π) and the intensity of the solar irradiation (πΌππ£). The hourly powered output of a
PV is given as:
π(π‘) = ππ΄ππΌππ£ (51)
The power output from an ideal solar field where there is no shading is given as:
π(π‘) = π π β ππ΄ππΌππ£
π π
π=1
, (52)
where π and π π are respectively, the number of solar collectors in a row and the total number
of rows in the solar field. Substituting πΌππ£ = πΌπ΅ + πΌπ· + πΌπ in equation (52) gives equation (53).
π(π‘) = π π β ππ΄π (πΌπ΅ + πΌπ· + πΌπ )
π
π=1
(53)
The value of πΌπ on a tilted surface is negligible, thus equation (53) reduces to equation (54):
π(π‘) = π π β ππ΄π (πΌπ΅ + πΌπ·)
π
π=1
(54)
Equation (54) is the expression for PV power output from a solar field assuming zero shading
effect. A scenario when there is no shading means that the spacing between the collector rows
is large, the panels are few and the energy produced from the field will be less compared to
when the collectors are more. For the optimal power production from the PV field, the number
Energy Optimisation ENO 732
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of collectors will increase and the inter-row spacing will be reduced. So the design for the
optimal performance of the solar field taking the inter-row spacing and the number of panels
into considerations.
For maximum power from a solar field constrained by the fixed field length πΏ and width π,
π π number of collector rows, distance, D, between rows, each collector length, π, collector
height π» and an tilted angle of π½ to the horizontal. The problem variables are π π, π½, π· and π».
The objective function of this problem is the yearly solar energy produced by the solar field
collector, which is given as follows [10]:
Maximise
π = ππ»πΏπ [ππ + ππ + (π π β 1)(πππ β + ππ
π β)] (55)
Where ππ is the yearly solar beam irradiation per unit area of an unshaded collector (which is
the first row), ππ is the yearly diffused irradiation per unit area of an unshaded collector, πππ β is
the average yearly beam irradiation per unit area of the shaded collectors and πππ β is the average
diffused solar irradiation per unit area of a shaded collector. ππ , ππ , πππ βπππ ππ
π β are defined
mathematically as:
ππ = β β πΌπ cos π Ξπ
ππ π
ππ π
365
π=1
(56)
ππ = πΉπ β β πΌπΞπ
ππ π
ππ π
365
π=1
(57)
πππ β = β β πΌπ cos π(1 β π ) Ξπ
ππ
ππ
365
π=1
(58)
πππ β = πΉπ
π β β β πΌπβΞπ
ππ π
ππ π
365
π=1
(59)
Where πΉπ πππ πΉππ β are the configuration factors for unshaded and shaded collectors
respectively
πΉπ = cos2 (π½
2) (60)
πΉππ β = cos2(π½/2) β
1
2[(π2 + 1)
12 β π] π πππ½ (61)
Energy Optimisation ENO 732
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Constraints
The objective function in constrained by these control variables are π π, π·, π», π½ [10].
The variation of the field and collector parameter is constrained by the width of the field W.
The equation below shows that the sum of the first row and the remaining rows must not greater
than the width of the field.
π π Γ π» Γ cos π½ + (π π β 1)π· β€ (π β 2π₯) (62)
The spacing between the rows is a control variable, which the minimum allowable space for
maintenance purposes. The spacing is constrained by the minimum allowable space for
maintenance and for shading reduction.
π· β₯ π·πππ (63)
This spacing should be at least the minimum space needed for maintenance purpose.
The collector height is maximum when it is standing at right angle to the horizontal(π» =
π΄πππ₯). However, for a tilted surface the height reduces as the angle decreases, so itβs height
must always be less than π΄πππ₯. It is given as
π» Γ sin π½ β€ π΄πππ₯ (64)
The collector height is limited by the manufacturerβs design, given as
π» β€ π»πππ₯ (65)
At any time, the tilted collector must be inclined at an angle between 0 and90Β°. This expressed
mathematically as
0Β° β€ π½ β€ 90Β° (66)
The more the rows, the more the shading effect and the greater the power produced by the solar
field. The number of the rows in the solar field must be greater than 2
π π β₯ 2 (67)
The PV is constrained by its capacity
0 β€ πππ£ β€ πππ£πππ₯ (68)
All the variables have non-negative values.
The optimisation problem is maximizing the annual solar energy yield from a solar field,
subject to constraints such as the inter-row spacing (D), tilt angle (π½), collector height (H),
solar irradiation (I), and the number of rows(π π).
Energy Optimisation ENO 732
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The optimisation model becomes
Maximize:
π = ππ»πΏπ [ππ + ππ + (π π β 1)(πππ β + ππ
π β)] (68)
Where ππ , ππ , πππ β πππ ππ
π β are defined in equations [56-59]
Subject to
π π Γ 1.2 Γ cos π½ + (π1 β 1)π· β€ (80 β 2π₯) (69)
π· β₯ π·πππ (70)
1.2 Γ sin π½ β€ 1.2 (71)
π» β€ π»πππ₯ (72)
0Β° β€ π½ β€ 90Β° (73)
π π β₯ 2 (74)
0 β€ πππ£ β€ πππ£πππ₯ (75)
VI. CONCLUSION
In this paper, it is seen that the optimal orientation for a solar panel should be facing the equator
and the angle should be its latitude angle. A sound knowledge of solar geometry proved to be
very important in determining the optimal position for receiving maximum solar irradiation
and in shadow control. This paper shows that in a fixed solar field, increasing the row spacing
will reduce the number of collector and reduce the power capacity of the field, And reducing
the row spacing will increase the number of collectors and also increase the power capacity of
the solar field even though the shading effect will rise. These quantities are inversely and this
paper presents the optimisation model that is the meeting point of both factors in order to
maximise the annual solar energy generated from the solar field.
Energy Optimisation ENO 732
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REFERENCES
[1] J. APPELBAUM and J. BANY, "SHADOW EFFECT OF ADJACENT SOLAR COLLECTORS IN
LARGE SCALE SYSTEMS," Solar Energy, vol. 23, pp. 497-507, 1979.
[2] R. E. JONES and J. F. BURKHART, "Shading effects of collector rows tilted toward the equator," Solar
Energy, vol. 26, pp. 563-565, 1981.
[3] E. A. Handoyo, D.Ichsani, and Prabowo, "The optimal tilt angle of a solar collector," International
Conference on Sustainable Energy Engineering and Application, pp. 166-175, 2013.
[4] J. Bany and J. Appelbaum, "THE EFFECT OF SHADING ON THE DESIGN OF A FIELD OF A FIELD
OF SOLAR COLLECTORS," Solar Ceils, no. 20, pp. 201 - 228, 1987.
[5] F. Mohsen,M. Radzi, M. Amran, F. Mohammad , Z. Mahdi, G. Zohreh, "Optimization and comparison
analysis for application of PV panels in three villages," Energy Science and Engineering, vol. III, no. 2, pp.
142-152, 2015.
[6] M.Kacira, M.Simsek, Y. Babur, and S. Demirkol, "Determining optimum tilt angles and orientations of
photovoltaic panels in Sanliurfa, Turkey," Renewable Energy, no. 29, pp. 1265-1275, 2004.
[7] A. Chandrakar and Y. Tiwari, "Optimization of Solar Power by varying Tilt Angle/Slope," International
Journal of Emerging Technology and Advanced Engineering, vol. III, no. 4, pp. 145-150, 2013.
[8] J. M. Ahmad and N. G. Tiwari, "Optimization of Tilt Angle for Solar Collector to Receive Maximum
radiation," The Open Renewable Energy Journal, no. 2, pp. 19-24, 2009.
[9] H. Danny , W. Li, and Lam N. T. Tony , "Determining the Optimum Tilt Angle and Orientation for Solar
Energy collection based on measured Solar radiance data," International Journal of Photoenergy, p. 9, 2007.
[10] D. Weinstock and J. Appelbaum, "Optimal Solar Field Design of Stationary Collectors," Journal of Solar
Energy Engineering, vol. 126, no. 905, pp. 1-8, 2004.