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OPTIMIZATION OF SURFACE ORIENTATION
ANGLES TO RECEIVE MAXIMUM SOLAR
RADIATION AT SABHA CITY IN LIBYA
Thesis
By
HASAN M.S.ATIA
S951302505
MECHANICAL ENGINEERING DEPARTMENT
POSTGRADUATE PROGRAM
SEBELAS MARET UNIVERSITY
SURAKARTA
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CONTENT LIST
TITLE ... i
APPROVAL PAGE ... ii
SUPERVISOR ENDORSEMENT ... iii
CONTENT LIST ... iv
2.2.8 Extraterrestrial horizontal radiation ( ) ... 11
2.2.9 Average extraterrestrial horizontal radiation over the time step ... 12
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2.2.11 Monthly average daily for extraterrestrial
horizontal radiation, global horizontal
radiation and clearness index ... 12
2.2.12 Hourly clearness index ... 13
2.2.13 Solar radiation on the earth's surface... 13
2.2.14 Total radiation incident on tilted surface using Reindl et al. Model (1990) ... 14
2.3 Genetic Algorithm ... 17
2.3.1 Basic of Genetic Algorithm (GA) ... 17
2.3.2 The major steps algorithm of GA ... 17
CHAPTER III RESEARCH METHODOLOGY ... 21
3.1 Location selection ... 21
4.4 Monthly average daily Extraterrestrial (Ho), Global (H), Diffuse (Hd) and Beam (Hb) solar radiation on horizontal surface ... 27
4.5 Yearly Total Incident Solar Radiation versus Orientation Angles ... 28
4.6 Monthly Total Incident Solar Radiation versus Orientation Angles ... 29
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4.8 Yearly and Monthly Optimization for
South-Facing Surface (Azimuth Angle, ) ... 32
4.9 Comparison monthly and yearly total of solar radiation between horizontal surface, GA optimization, and south-facing optimization with the energy gain. ... 35
4.10 Comparison of monthly incident solar radiation and energy gain between horizontal surface, GA optimization, and facing south optimization ... 36
4.11 Proposed method evaluation ... 37
4.11.1 Evaluation method of Homer for present study using yearly orientation angles of GA optimization ... 39
4.11.2 Evaluation method of Homer for present study using monthly adjusted orientation angles of GA optimization ... 39
CHAPTER V CONCLUSION ... 41
5.1 Conclusion ... 41
5.2 Recommendation ... 41
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FIGURES LIST
Figure 1.1 Global horizontal irradiation of Libya ... 3
Figure 2.1 Angles of solar system panel (solar collector or PV panel). ... 7
Figure 2.2 Definition of latitude, hour angle, and solar declination angle ... 7
Figure 2.3 Yearly variation of solar declination. ... 8
Figure 2.4 Solar radiation components. ... 15
Figure 2.5 Flow chart of genetic algorithm ... 18
Figure 2.6 One-point crossover and mutation operators ... 20
Figure 3.1 Flow Chart of The Method ... 23
Figure 4.1 Comparison result of purposed method and previous study result for Fez city, Morocco ... 25
Figure 4.2 Monthly average daily solar radiations on horizontal surface .... 27
Figure 4.3 Monthly average daily global horizontal radiation and clearness index ... 28
Figure 4.4 3 dimensions surface of annual incident solar radiation versus orientation angles ... 29
Figure 4.5 Contour lines of annual incident solar radiation versus orientation angles ... 29
Figure 4.6 Monthly total incident radiations with tilt angle Optimization for South-Facing Surface ... 34
Figure 4.7 Tilt Angle of Yearly Optimization of South-Facing Surface ... 34
Figure 4.8 Comparison of yearly and monthly total of solar radiation and energy gain between horizontal surface, GA optimization, and south-facing optimization ... 35
Figure 4.9 Monthly solar radiations and energy gain of GA optimization and South-facing optimization ... 36
Figure 4.10 Yearly optimization orientation angles of GA comparing between proposed simulations with Homer software ... 39
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viii TABLES LIST
Table 4.1 Yearly optimum tilt angle of proposed method and previous
study result that conducted by Ihya et al (2014) for Fez city,
Morocco ... 24
Table 4.2 Monthly optimum tilt angle of proposed method and previous
study result that conducted by Ihya et al in 2014 for Fez city,
Morocco ... 24
Table 4.3 Annually total solar radiation on Horizontal Surface ... 27
Table 4.4 Description the objective function (fs_m) for monthly
simulation ... 30
Table 4.5 The best solution of yearly optimization using GA ... 31
Table 4.6 The second solution for monthly optimization using GA. ... 32
Table 4.7 Yearly and Monthly Optimum Tilt Angle for a South Facing
Solar Surface ... 33
Table 4.8 Total yearly and monthly solar radiation and energy gain of
horizontal surface, GA optimization, and south facing
optimization ... 36
Table 4.9 Monthly solar radiation and energy gain of GA optimization and
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NOMENCLATURE
is solar declination angle
n is the day of the year [a number 1 through 365]
is Solar Hour Angle (hr)
is the solar time (hr)
tc is the civil time in hours corresponding to the midpoint of the time step [hr]
is the longitude [°]
Zc is the time zone in hours east of GMT [hr] E is the equation of time [hr]
n is the day of the year, starting with 1 for January 1st.
is the angle of incidence [°]
is the slope of the surface [°]
is the azimuth of the surface [°]
is the latitude [°]
z is the zenith angle [°]
Gon is the extraterrestrial normal radiation [kW/m2] Gsc is the solar constant [1.367 kW/m2]
Go is the extraterrestrial horizontal radiation [kW/m2]
is the extraterrestrial horizontal radiation averaged over the time step [kW/m2]
1 is the hour angle at the beginning of the time step [°]
is the global horizontal radiation on the earth's surface averaged over the time
step [kW/m2]
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x is the diffuse radiation [kW/m2]
is hourly total radiation on a tilted surface (KW/ m2).
is hourly beam radiation on a tilted surface (KW/ m2).
is hourly ground-reflected solar radiation (KW/ m2).
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HASAN M. S.ATIA, NIM: S951302505, 2015. Optimization of Surface Orientation Angles to Receive Maximum Solar Radiation at Sabha City in
Libya: Supervisor I: Prof. Muhammad Nizam S.T., M.T., Ph.D. Supervisor II:
Dr. Miftahul Anwar, S.Si., M.Eng. Thesis, Postgraduate Program in Mechanical Engineering. Sebelas Maret University, Surakarta, Indonesia.
ABSTRACT
In this paper, the Genetic Algorithm (GA) is implemented to calculate the
optimum tilt and surface azimuth angle for solar system surfaces to receive
maximum solar radiation. Sabha city in Libya is selected to verify the results of
GA. The optimum surface orientation angles and the flat surface input solar
energies for these angles are calculated in monthly and yearly bases. Then, The
comparison of different optimizations of GA and South-Facing for an inclined
surface was compared with the horizontal surface in a year and the energy
gained was investigated. The total extra solar energy gained in one year for the
yearly optimized surface angles of GA and South-Facing compared to the
horizontal surface are 10.8% and 10.3%, respectively. The total extra solar
energy gained in one year for the monthly optimized surface angles of GA and
South-Facing compared to the horizontal surface are 18.72% and 18.03%,
respectively. The yearly optimum tilt angle of the generic algorithm was 30.4°
where the azimuth was at -19°. In another result, the yearly optimum tilt angle
of south-facing was 29°. It has been figured out that the yearly optimum tilt
angle of both was closed to the latitude of the location. Furthermore, the results
indicate that the monthly based optimization improved the energy gain higher
than the yearly based optimization. The genetic algorithm optimization
performed better results than the conventional south facing optimization
although the difference of the results was not significant for both yearly and
monthly total incident solar radiation.
