“SOLAR RESOURCE”

By
Ir. Dr. Tunku Muhammad Nizar Tunku Mansur
Edited by:
Assoc. Prof. Ir. Dr. Muhammad Irwanto
THE EARTH’S SPINNING AXIS ORBITING THE SUN

Spring Equinox = 21 March Autumn Equinox = 21 Sept

Summer Solstice = 21 June Winter Solstice = 21 Dec

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 THE EARTH’S SPINNING AXIS ORBITING THE SUN
❑ The plane swept out by the earth in its orbit is called the
ecliptic plane. The earth’s spin axis is currently tilted 23.45o
with respect to the ecliptic plane.
❑ On March 21 and September 21, a line from the center of the
sun to the center of the earth passes through the equator
and everywhere on earth will have 12 hours of daytime and
12 hours of night, hence the term equinox (equal day and
night).
❑ On December 21, the winter solstice in the Northern
Hemisphere, the inclination of the North Pole reaches its
highest angle away from the sun (23.45o), while on June 21
the opposite occurs.

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SOLAR DECLINATION ANGLE

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SOLAR DECLINATION ANGLE

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 SOLAR DECLINATION ANGLE
❑ The angle formed between the plane of the equator and a
line drawn from the center of the sun to the center of the
earth is called the solar declination, δ.

Solar Declination Angle, δ for the 21st Day of Each Month (degrees)

Month Jan Feb Mac Apr May Jun Jul Aug Sept Oct Nov Dec

δ -20.1 -11.2 0.0 11.6 20.1 23.4 20.4 11.8 0.0 -11.8 -20.4 -23.4

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 EXAMPLE 1:
Example: Solar declination, δ on 21 May

For 21 May, n=141

360
𝛿 = 23.45 𝑠𝑖𝑛 𝑥 𝑛 − 81
365
360
𝛿 = 23.45 𝑠𝑖𝑛 𝑥 141 − 81
365
360
𝛿 = 23.45 𝑠𝑖𝑛 𝑥60
365
𝛿 = 23.45 𝑠𝑖𝑛 59.18o
𝛿 = 20.1o

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THE ALTITUDE ANGLE OF THE SUN AT SOLAR NOON

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 THE ALTITUDE ANGLE OF THE SUN AT SOLAR NOON
❑ The altitude angle is the angle between the sun and the local
horizon directly beneath the sun.
❑ From the given relationship, L is the latitude of the site and
βN is the solar altitude angle at solar noon.
❑ Zenith is referred to an axis drawn directly overhead at a site.
❑ On the average, facing a collector toward the equator (for
the Northern Hemisphere, which means facing south) and
tilting it up at an angle equal to the local latitude is a good
rule-of-thumb for annual performance.

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SOLAR POSITION AT ANY TIME OF DAY

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SOLAR POSITION IN RELATION WITH PV MODULE

𝛽 = 90𝑜 − 𝛽𝑁

90o
Tilt angle
of module b g Altitude of Sun

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 SOLAR POSITION AT ANY TIME OF DAY
❑ The location of the sun at any time of day can be described in
terms of its altitude angle βN and its azimuth angle φs as
shown in previous slide.
❑ By convention, the azimuth angle is positive in the morning
with the sun in the east and negative in the afternoon with
the sun in the west where true south as its reference.
❑ The solar altitude angle and azimuth angle is given by:

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 SOLAR POSITION AT ANY TIME OF DAY
❑ The hour angle, H is the number of degrees that the earth
must rotate before the sun will be directly over your local
meridian (line of longitude).
❑ The difference between the local meridian and the sun’s
meridian is the hour angle, with positive values occurring in
the morning before the sun crosses the local meridian.
❑ Considering the earth to rotate 360o in 24 h, or 15o/h, the
hour angle can be described as follows:

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 Example 2:
What is the titl angle should a south-facing solar PV
module at Shanghai, China (L = 31oN) on 21 March?
Answer:
For 21 March, δ = 0o
𝛽𝑁 = 90𝑜 − 𝐿 + 𝛿
𝛽𝑁 = 90𝑜 − 31 + 0
𝛽𝑁 = 59

𝛽 = 90𝑜 − 𝛽𝑁
𝛽 = 90𝑜 − 59𝑜
𝛽 = 31𝑜
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 Example 3:
Find the altitude and azimuth angles of the sun for
Perlis (L = 6.4oN) at 8.00 am on 21 August.
Answer:
For 21 October, δ = 11.8o
15
𝐻= x hour before solar noon
ℎ𝑜𝑢𝑟
15
𝐻= x 4 hour
ℎ𝑜𝑢𝑟
= 60o

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 Example 3:
𝑠𝑖𝑛𝛽𝑁 = 𝑐𝑜𝑠𝐿 𝑐𝑜𝑠𝛿 𝑐𝑜𝑠𝐻 + 𝑠𝑖𝑛𝐿 𝑠𝑖𝑛𝛿
𝛽𝑁 = 𝑠𝑖𝑛−1 (𝑐𝑜𝑠𝐿 𝑐𝑜𝑠𝛿 𝑐𝑜𝑠𝐻 + 𝑠𝑖𝑛𝐿 𝑠𝑖𝑛𝛿)
𝛽𝑁 = 𝑠𝑖𝑛−1 (𝑐𝑜𝑠6.4𝑜 𝑐𝑜𝑠11.8𝑜 𝑐𝑜𝑠60𝑜 + 𝑠𝑖𝑛6.4𝑜 𝑠𝑖𝑛11.8𝑜 )
𝛽𝑁 = 30.6𝑜

𝑐𝑜𝑠𝛿 𝑠𝑖𝑛𝐻
𝑠𝑖𝑛𝜙𝑠 =
𝑐𝑜𝑠𝛽𝑁
−1
𝑐𝑜𝑠𝛿 𝑠𝑖𝑛𝐻
𝜙𝑠 = 𝑠𝑖𝑛
𝑐𝑜𝑠𝛽𝑁
𝑐𝑜𝑠11.8 𝑜 𝑠𝑖𝑛60𝑜
𝜙𝑠 = 𝑠𝑖𝑛−1
𝑐𝑜𝑠30.6𝑜
𝜙𝑠 = 80 𝑜

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 Example 3:

b N = 30.6o
 s= 80o

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SUNPATH DIAGRAM FOR SHADING ANALYSIS

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SUNPATH DIAGRAM FOR SHADING ANALYSIS

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 SOLAR RADIATION
❑ Solar radiation may be discussed in terms of Irradiance,
Irradiation and Peak Sun Hour.
❑ Solar Irradiance (G) is defined as intensity of solar power at a
point of observation. Unit is Wm-2.
❑ Solar Irradiation (H) is defined as intensity of solar energy at
a point of observation . Unit is Whm-2.
❑ All measurement and design calculations related to solar-
based energy technologies use the integration of power
intensities over time to get solar energy intensity.
❑ The energy intensity (irradiation) may be reported as daily,
monthly or annually values.

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 SOLAR RADIATION
❑ In terms of irradiance, solar radiation reaching Earth surface
can be divided into following components:
Gglobal = Gdirect + Gdiffuse
❑ Solar irradiance that reaches the top of Earth’s atmospheric
is 1,367Wm-2 which is called solar constant (Gsc). This
radiation is largely reflected back into outer space which is
called Albedo.
❑ When it enters the atmosphere, the solar radiation will be a
combination of direct-beam radiation that passes in a
straight line to the receiver, diffuse radiation that has been
scattered by particles in the atmosphere, and reflected
radiation that has bounced off the ground or other surface in
front of the collector .
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 SOLAR RADIATION

The sun

Solar radiation at top of Reflected solar radiation

atmosphere (albedo) from
Go = 1,367 Wm-2 atmosphere

Diffuse solar
Reflected solar
radiation
radiation from
clouds ground

Solar radiation at sea level

G = 1,000 Wm-2

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SOLAR RADIATION

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 SOLAR RADIATION
The beam, Ib diffuse, I dt and reflected I rt solar radiation are given
by:
I b = Ae − km
 1 + cos  
I dt = CI b  
 2 
 1 − cos  
I rt =  I b (sin b + C ) 
 2 
I tt = I bt + I dt + I rt

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 Example 4:
Find the direct beam solar radiation normal to the
sun’s rays at solar noon on a clear day with latitude
angle of 𝟑𝟑. 𝟕𝒐 on May 21.

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Example 4:

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 SOLAR RADIATION
❑ The SI unit for energy is called joule (J). Since this unit is
relatively small quantity, large energy quantities such as solar
radiation data are often expressed in terms of Mega Joule
(MJ).
❑ Normally, energy unit that often used in solar engineering is
kilowatt hour (kWh).
❑ The conversion factor for MJ and kWh is

1kWh = 3.6 MJ
or
1MJ = 1/3.6 kWh

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 SOLAR RADIATION
❑ Often in PV system sizing, a more practical approach is using
Peak Sun Hour (PSH) approach.
❑ Technically, PSH is defined as the equivalent number of hours
in a day when the solar power intensity is 1000Wm-2, or
❑ The number of PSH for the day is the number of hours for
which energy at rate of 1kWm-2 would give an equivalent
amount of energy to the total energy for that day.

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 PEAK SUN HOUR (PSH)

Irradiance

1 kW / m2

Irradiance varies
during the day

Hour of
the day

7.00 am 10.00 am 2.00 pm 5.30

pm

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 SOLAR RADIATION
❑ Monthly Global Irradiation (kWhm-2) received by collector at
selected tilt angle facing South at Alor Setar (Azimuth = 0o)
TILT ANGLE
MONTH
0o 10o 20o 30o 40o
JANUARY 162.9 174.6 182.2 185.3 184.0
FEBRUARY 169.9 177.6 181.0 179.9 174.5
MAC 180.0 181.6 178.9 172.1 161.3
APRIL 169.5 164.9 156.5 144.7 129.7
MAY 156.6 148.4 137.1 123.0 106.6
JUNE 144.5 135.3 123.2 108.7 92.6
JULY 150.0 141.1 129.3 114.9 98.6
AUGUST 145.4 140.1 131.9 121.0 107.6
SEPTEMBER 139.4 138.4 134.4 127.6 118.1
OCTOBER 135.5 138.5 138.5 135.6 129.8
NOVEMBER 126.7 133.2 136.7 137.3 134.7
DECEMBER 136.9 146.6 153.0 155.9 155.1
YEAR 1817.4 1820.4 1782.8 1705.8 1592.7

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 SOLAR TIME
❑ The Sun’s apparent motion as seen by an observer on Earth is
called solar path and it can be traced based on Solar Time
(ST) and it does not necessarily coincide with Civil Time (CT)
which is local time shown by our watches.
❑ The relationship is given by:
ST = CT + [4 min/degreex (Lsite – Lsm) + E] where
ST = Solar Time (h)
CT = Civil Time (h)
Lsite = Longitude of the site (deg)
Lsm = Longitude of standard meridian of the site
E = Equation of Time (min)

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 SOLAR TIME

17

-14 304

46

Graph Equation of Time (EOT)

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 Example 5:
❑ Calculate the Solar Time for Kampung Wai at
latitude of 3.08 deg N and longitude of 101.00 deg E
if the standard meridian time is 120 deg E and Civil
Time are:
✓ 12.00PM on 15 Feb
✓ 1.00PM on 31 October

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 SOLAR TIME (EXAMPLE)
❑ From chart for E, on 15 February; E = -14min
ST = 12h +[4 x ( 101 – 120)min - 14min]
ST = 12h +[4 x (– 19)min - 14min]
ST = 12h – 76min - 14min
ST = 12h – 90min = 10h:30min
❑ From chart for E, on 31 Oct; E =+17min
ST = 13h +[4 x ( 101 – 120)min + 17min]
ST = 13h +[4 x (– 19)min + 17min]
ST = 13h – 76min + 17min
ST = 13h – 59min = 12h:1min
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 SOLAR TIME (Question)
❑ Pulau Ara has longitude 11.5 deg E and latitude f
22.2 deg S. Its longitude of standard meridian is 15
deg E. For solar time 11:40 am determine the Civil
Time during June solstice if E = -4min. ST=11h:40
min.
Answer:
CT = ST- {4min/degx(Lsite-Lst)+E}
= 11h:40min-{4min/degx(11.5 deg-15 deg)- 4 min}
= 11h:40min-{4min/degx(-3.5deg)- 4 min}
= 11h:40min+18min=11h:58min=11:58 am
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QUANTIFYING SOLAR ENERGY FOR PV APPLICATION

❑ For doing PV system sizing, one of the fundamental

quantities is the amount of solar energy available at
particular site.
❑ To obtain the value, the designer can use either
hardware equipment and / or software.
❑ Among the popular hardware equipments used are
pyranometer and solarimeter.
❑ Among the popular software used for analytical
method are such as PVSYST and HOMER.

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PYRANOMETER

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SOLARPATH FINDER

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SOLARPATH DIAGRAM

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SOLARPATH DIAGRAM

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 REFERENCES
❑ G.M. Masters, “Renewable and Efficient Electric Power
Systems”, John Wiley & Sons, 2004.
❑ Sulaiman Shaari, Ahmad Maliki Omar & Shahril Irwan
Sulaiman, “ Fundamentals of Solar Photovoltaic Technology”,
Sustainable Energy Development Authority of Malaysia,
2012.
❑ Shahril Irwan Sulaiman Sulaiman Shaari & Ahmad Maliki
Omar, “Solar Irradiation Data for Malaysia”, Sustainable
Energy Development Authority of Malaysia, 2012.
❑ www.solarpathfinder.com
❑ www.kippzonen.com

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