Solar energy is one of the renewable energies and it is designed for house is an important part of integration of solar panels to a house.

1. Solar Panel System Design
Zulfidin Khodzhaev
Istanbul Technical University
Istanbul, Turkey
khodzhaev@itu.edu.tr
Abstract —Solar energy is one of the renewable energies and
it is designed for house is an important part of integration of
solar panels to a house.
Keywords—solar energy, solar panel, sun angle, radiation.
I. INTRODUCTION
The energy consumption of the world is increasing with a
fast pace; since global population is forecasted to increase up
to 10 billion [1], global population will consume more energy
as standard of living increases. Current technology that is in
place for energy is not sustainable and it is estimated that fossil
fuels may run out by 2088; oil by 2052, with consumption rate
of 11 billion tonnes of oil per year; gas by 2060; coal by 2088,
if current trends in energy consumption is continued without
any change in governments policies [2].
It makes sense to develop new ways of obtaining energy,
and doing this with regard to sustainability of the methods
used. The technology of solar panels is one of the best ways to
integrate into solar energy, panels can be installed on the roof
or anywhere outside the house and it create a partial energy
need of the population, for now.
To design a system, we need to define what devices are
used in the house and how much energy they consume, and
based on energy consumption, batteries and panels can be
designed and installed.
The location where the analysis will be done is in
Dushanbe, Tajikistan. It is a city in Central Asia, with abun-
dance of sun at summer. 93% of the country consists of
mountains and most of those lands are not used in agriculture
which creates a great opportunity for using solar energy or any
other renewable energy.
II. SYSTEM DESIGN
To do analysis on the system, the typical daily used system
is designed. The report is intended to be realistic; therefore, the
number and components are chosen based on today’s world’s
needs. The loads chosen for this report is shown in Figure 1.
For the loads given Figure 1, the system design will be
based on what kind of load is being used i.e devices may
operate with AC (alternating current) or DC (direct current)
current which is shown in Figure 2.
For this paper, we will calculate formulas that needed to
understand and assess the performance of the panels. One of
Figure 1: Loads placed in our system
Figure 2: System design for Loads
them is declination angle which we need to understand sun’s
position on North and South Hemispheres:
δ = 23.45 × cos(
2π
365
× (n + 284)) (1)
where n is number of days.
Hours of the daylight, to understand how many hours the
sun shines at that place:
ω = (
24
π
) × arccos[(− tan(δ) × tan(ψ)] (2)
where ψ is latitude of the place. And ψ of Dushanbe is
38.53575o
N
The sun hour of Dushanbe is 4 hours and sun hour map is
shown in Figure 3.

2. Figure 3: Peak Sun Hour Map
Amount of Power required for PV Panel is given by:
P =
Total Energy demand
Equivalent Sun Hour
(3)
Sun angle is calculated; sun angle is the angle of incidence
at which sunlight strikes the earth at a particular time and
place. The angle controls the amount of heat energy received
at the place e.g. summer days are warmer than winter nights.
Sun angle can be calculated by:
α = [90 − (ψ − δ)] (4)
where signs of ψ and δ are based on Dushanbe location.
And, Daily extraterrestrial radiation which is the power of
the sun at the top of the Earth’s atmosphere, given by:
Io =
24.36
π
Iscf[cos(ψ) sin(δ) sin(ω) − ω sin(δ) sin(ψ)]10−6
(5)
Isc = σT4
∗ (
4 ∗ π ∗ R
4 ∗ π ∗ D
)2
= 1367(
W
m2
) (6)
f = 1 + 0.033 × cos(
2π
365
n) (7)
where n is number of days, Isc is solar constant, σ =
5.67 × 10 − 8W/m2 ∗ K4 is the Stefan Boltzmann constant,
R = 696 × 106m is the Sun radiuses, D = 150 × 109m is the
average distance between the Sun and the earth, ψ is latitude
of Dushanbe, δ is declination angle and f is correction factor
for solar constant.
Also, Hourly extraterrestrial radiation given by:
Io =
24.36
π
Iscf[cos(ψ) cos(δ)(sin(ω2) − sin(ω1)) + h]10−6
(8)
h = (ω2 − ω1) sin(ψ) sin(δ) (9)
w1 = (tss − 12) × 15o
(10)
w1 = (tsr − 12) × 15o
(11)
where tss is sunset time angle and tsr is sunrise time angle.
A. Analysis Results
There are some losses due to cables, charge controller and
battery bank. Loss due to cables, charge controller and battery
bank combined is nc=85 and loss due to inverter is ni=90. And
based on loss information, amount of Energy that PV Panels
should produce is:
PVarray =
289 + (289
0.9 )
0.85
= 718Wh (12)
The deviation angle from October 12 until December 30
of 2018 was calculated; this period comprises of 7 weeks and
it is shown in TableI.
Then, using deviation angle we can calculate hours of
daylight which is shown in TableII. We compare this result
with online daylight calculator and they seem to be similar:
Figure 4: Hours of Daylight [3]
Peak sun hour is 4 hours for Dushanbe and amount of
power required for PV is 179.5 W; this is the minimum value
required.

3. The panel was chosen from Alibaba website [4] with
charactersitics:
Panel Power = 100W
Voltage at Pmax(Vmp): 17.2 V
Current at Pmax(lmp): 5.89 A
To find number of panels is minimum of power required over
panel power output = 179.5/100 = 1.795= 2, so we need two
panels. And area of a panel is 0.6298 m2
, the total area of
panels will make: 1.2596 m2
which is suitable to install at
the roof or a any other part of the house i.e. garden.
To decide parallel or series panels:
Parallel Connection- Imax=2∗6.24 = 12.48 A (Imax=5.89 A)
Series Connection- Vmax=2 ∗ 20.4 = 40.8 V (Vmax=17.2 V )
Either way is compatible, then it can be parallel.
For charge controller, device for US 80.99$ was chosen
with specifications [5]:
Imax= 50 A and Vmax= 100 V . Since the current and voltage
is more than required, either connection of panels will work
without burning the charge controller.
Using sun angle formula sun angle on the surface and panel
angle relative to vertical position is calculated which is shown
in TableIII.
Lastly, the daily and hourly extraterrestrial radiation is
calculated by finding corresponding number of days for each
date, and calculating sunrise and sunset time angles; the results
are shown in TableIV .
III. CONCLUSION
The installation of the solar panels seems a reasonable
choice; the chosen load can be increased more, by including
other devices, since the total area that the panels will cover for
the system discussed is 1.2596 m**2 which is small and other
panels can be included too. In terms of cost: a panel that is
chosen costs US $ 0.98 per panel. Total cost of installation will
be: US $ 1.96. The cost of electricity in Dushanbe is 19.37
Diram per kW i.e. 2.1 US Cents per kW (based on conversion
between Diram and US Cent on 18.12.2018). The system uses
934 Watt per day or 347.448 kW per year which would cost
US $ 7.3 which would cover the cost of the panel. The Solar
panels are not efficient as much as people want; it may seem
costly at first, in long term usage, it proves to be efficient and
sustainable.
REFERENCES
[1] “World population projected to reach 9.7 billion by 2050,”
http://www.un.org/en/development/desa/news/population/2015-
report.html.
[2] “The end of fossil fuels,” https://www.ecotricity.co.uk/our-green-
energy/energy-independence/the-end-of-fossil-fuels.
[3] “Sunrise and sunset times in dushanbe,”
https://sunsetsunrisetime.com/tajikistan/dushanbe18858.html.
[4] “Sunrise and sunset times in dushanbe,”
https://www.alibaba.com/product-detail/A-100w-photovoltaic-solar-
panel-online60760029234.html.
[5] “Renogy rover 40 amp mppt solar charge controller,”
https://www.alibaba.com/product-detail/Renogy-Rover-40-Amp-MPPT-
Solar60647556764.html.

4. Table I: Deviation Angle in 7 Weeks.
Date - day.month.year Number of Days (n) Deviation Angle (δo
)
12.11.2018 314 -17.84789487
13.11.2018 315 -18.10707191
14.11.2018 316 -18.36088343
15.11.2018 317 -18.60925423
16.11.2018 318 -18.8521107
17.11.2018 319 -19.08938089
18.11.2018 320 -19.32099449
19.11.2018 321 -19.54688285
20.11.2018 322 -19.76697905
21.11.2018 323 -19.98121787
22.11.2018 324 -20.18953582
23.11.2018 325 -20.39187118
24.11.2018 326 -20.58816399
25.11.2018 327 -20.77835607
26.11.2018 328 -20.96239109
27.11.2018 329 -21.14021449
28.11.2018 330 -21.3117736
29.11.2018 331 -21.47701756
30.11.2018 332 -21.63589742
1.12.2018 333 -21.7883661
2.12.2018 334 -21.93437841
3.12.2018 335 -22.0738911
4.12.2018 336 -22.20686281
5.12.2018 337 -22.33325415
6.12.2018 338 -22.45302767
7.12.2018 339 -22.56614787
8.12.2018 340 -22.67258123
9.12.2018 341 -22.77229622
10.12.2018 342 -22.86526328
11.12.2018 343 -22.95145488
12.12.2018 344 -23.03084546
13.12.2018 345 -23.1034115
14.12.2018 346 -23.16913151
15.12.2018 347 -23.227986
16.12.2018 348 -23.27995754
17.12.2018 349 -23.32503073
18.12.2018 350 -23.3631922
19.12.2018 351 -23.39443066
20.12.2018 352 -23.41873684
21.12.2018 353 -23.43610355
22.12.2018 354 -23.44652563
23.12.2018 355 -23.45
24.12.2018 356 -23.44652563
25.12.2018 357 -23.43610355
26.12.2018 358 -23.41873684
27.12.2018 359 -23.39443066
28.12.2018 360 -23.3631922
29.12.2018 361 -23.32503073
30.12.2018 362 -23.27995754

5. Table II: Hours of Daylight.
Date - day.month.year Number of Days (n) Daylight (ω)
12.11.2018 314 10.01699678
13.11.2018 315 9.985476807
14.11.2018 316 9.954484662
15.11.2018 317 9.924034952
16.11.2018 318 9.894142345
17.11.2018 319 9.864821546
18.11.2018 320 9.836087282
19.11.2018 321 9.80795428
20.11.2018 322 9.780437249
21.11.2018 323 9.753550858
22.11.2018 324 9.727309714
23.11.2018 325 9.701728337
24.11.2018 326 9.676821142
25.11.2018 327 9.65260241
26.11.2018 328 9.629086267
27.11.2018 329 9.606286657
28.11.2018 330 9.584217315
29.11.2018 331 9.562891747
30.11.2018 332 9.542323199
1.12.2018 333 9.52252463
2.12.2018 334 9.503508691
3.12.2018 335 9.485287694
4.12.2018 336 9.467873589
5.12.2018 337 9.451277936
6.12.2018 338 9.435511882
7.12.2018 339 9.420586132
8.12.2018 340 9.406510929
9.12.2018 341 9.393296028
10.12.2018 342 9.380950673
11.12.2018 343 9.369483574
12.12.2018 344 9.358902888
13.12.2018 345 9.3492162
14.12.2018 346 9.340430499
15.12.2018 347 9.332552164
16.12.2018 348 9.325586951
17.12.2018 349 9.31953997
18.12.2018 350 9.31441568
19.12.2018 351 9.310217872
20.12.2018 352 9.306949664
21.12.2018 353 9.304613486
22.12.2018 354 9.303211081
23.12.2018 355 9.302743497
24.12.2018 356 9.303211081
25.12.2018 357 9.304613486
26.12.2018 358 9.306949664
27.12.2018 359 9.310217872
28.12.2018 360 9.31441568
29.12.2018 361 9.31953997
30.12.2018 362 9.325586951

6. Table III: Sun Angle.
Date - day.month.year Sun Angle (αo
) Panel Angle from Vertical (σo
)
12.11.2018 69.29 20.71
13.11.2018 69.55 20.45
14.11.2018 69.80 20.20
15.11.2018 70.05 19.95
16.11.2018 70.29 19.71
17.11.2018 70.53 19.47
18.11.2018 70.76 19.24
19.11.2018 70.99 19.01
20.11.2018 71.21 18.79
21.11.2018 71.42 18.58
22.11.2018 71.63 18.37
23.11.2018 71.83 18.17
24.11.2018 72.03 17.97
25.11.2018 72.22 17.78
26.11.2018 72.40 17.60
27.11.2018 72.58 17.42
28.11.2018 72.75 17.25
29.11.2018 72.92 17.08
30.11.2018 73.08 16.92
1.12.2018 73.23 16.77
2.12.2018 73.37 16.63
3.12.2018 73.51 16.49
4.12.2018 73.65 16.35
5.12.2018 73.77 16.23
6.12.2018 73.89 16.11
7.12.2018 74.01 15.99
8.12.2018 74.11 15.89
9.12.2018 74.21 15.79
10.12.2018 74.31 15.69
11.12.2018 74.39 15.61
12.12.2018 74.47 15.53
13.12.2018 74.54 15.46
14.12.2018 74.61 15.39
15.12.2018 74.67 15.33
16.12.2018 74.72 15.28
17.12.2018 74.77 15.23
18.12.2018 74.80 15.20
19.12.2018 74.83 15.17
20.12.2018 74.86 15.14
21.12.2018 74.88 15.12
22.12.2018 74.89 15.11
23.12.2018 74.89 15.11
24.12.2018 74.89 15.11
25.12.2018 74.88 15.12
26.12.2018 74.86 15.14
27.12.2018 74.83 15.17
28.12.2018 74.80 15.20
29.12.2018 74.77 15.23
30.12.2018 74.72 15.28

7. Table IV: Daily and Hourly Extraterrestrial Radiation
Date-day.month.year Days Sunrise Time Angle (Degree) Sunset Time Angle (Degree) Hourly E.R.(MJ/m2.hour) Daily E.R.(MJ/m2.day)
12.11.2018 314 112 248 4.233960909 0.02217001162
13.11.2018 315 112 247 4.264336288 0.02235510112
14.11.2018 316 113 247 4.29254207 0.02253055835
15.11.2018 317 113 247 4.35013611 0.02269666379
16.11.2018 318 113 246 4.373934255 0.02285370696
17.11.2018 319 114 246 4.395594818 0.02300198493
18.11.2018 320 114 246 4.448439155 0.02314180084
19.11.2018 321 114 245 4.465716885 0.02327346248
20.11.2018 322 115 245 4.480896693 0.02339728084
21.11.2018 323 115 245 4.528988253 0.02351356876
22.11.2018 324 115 245 4.575737369 0.02362263957
23.11.2018 325 116 244 4.548682311 0.02372480584
24.11.2018 326 116 244 4.59203566 0.02382037813
25.11.2018 327 116 244 4.634033822 0.02390966385
26.11.2018 328 116 243 4.636990023 0.02399296618
27.11.2018 329 117 243 4.637959517 0.02407058303
28.11.2018 330 117 243 4.675242331 0.02414280611
29.11.2018 331 117 243 4.711153056 0.02420992008
30.11.2018 332 117 243 4.745683176 0.02427220175
1.12.2018 333 118 242 4.699868795 0.02432991933
2.12.2018 334 118 242 4.73111208 0.02438333187
3.12.2018 335 118 242 4.760973677 0.02443268864
4.12.2018 336 118 242 4.789446674 0.02447822866
5.12.2018 337 118 242 4.816524511 0.02452018028
6.12.2018 338 119 241 4.760422446 0.02455876084
7.12.2018 339 119 241 4.784302342 0.02459417634
8.12.2018 340 119 241 4.806792116 0.02462662125
9.12.2018 341 119 241 4.827886643 0.02465627833
10.12.2018 342 119 241 4.847581118 0.02468331843
11.12.2018 343 119 241 4.865871053 0.02470790048
12.12.2018 344 119 241 4.882752268 0.02473017139
13.12.2018 345 119 241 4.898220892 0.02475026605
14.12.2018 346 119 240 4.870007355 0.02476830728
15.12.2018 347 120 240 4.840168352 0.02478440594
16.12.2018 348 120 240 4.851196091 0.02479866087
17.12.2018 349 120 240 4.860821933 0.02481115901
18.12.2018 350 120 240 4.869043524 0.02482197542
19.12.2018 351 120 240 4.875858791 0.02483117333
20.12.2018 352 120 240 4.881265945 0.02483880422
21.12.2018 353 120 240 4.885263477 0.02484490783
22.12.2018 354 120 240 4.887850158 0.02484951223
23.12.2018 355 120 240 4.889025037 0.02485263381
24.12.2018 356 120 240 4.888787442 0.02485427732
25.12.2018 357 120 240 4.887136983 0.02485443589
26.12.2018 358 120 240 4.884073545 0.02485309097
27.12.2018 359 120 240 4.879597299 0.02485021235
28.12.2018 360 120 240 4.873708696 0.02484575808
29.12.2018 361 120 240 4.866408473 0.02483967446
30.12.2018 362 119 241 4.942732375 0.02483189598