TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 80
1
5
~ 802
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.66
96
8015
Re
cei
v
ed
Jun
e
18, 2014; Revi
sed Septe
m
ber
16, 201
4; Acce
pted
Octob
e
r 15, 2
014
Emperical Computation of Solar Radiation and
Determination of Regression Coefficients for Khulna
City
Mohammad
Arif Sobha
n Bhuiy
a
n
1
, A
bdus Sobha
n Bhuiy
a
n
2
,
Muhammed Jamshed Alam
Pat
w
ary
3
*
,
Subrina Ak
ter
4
, Mohammad Monjur Ala
m
5
1
Electronic an
d Commu
nicati
on Eng
i
n
eeri
n
g
,
Sout
hern U
n
i
v
ersit
y
Ba
ng
la
desh, Ch
ittago
ng 40
00
2
Dept. of Appli
ed Ph
ysics, El
ectronics a
nd
Comm. Engi
ne
erin
g, Univers
i
ty of
Ch
ittago
ng
. Chittagon
g.
Ba
n
g
l
a
de
h
3,4,
5
Dept. of Computer Scie
nc
e and En
gi
neer
ing, Internat
i
o
n
a
l Islamic U
n
iv
ersit
y
C
h
ittag
o
ng, 154/A C
o
ll
ege
Roa
d
, Cha
w
k
b
azar, Chittag
o
n
g
, Bangl
ad
esh
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:jap
_cse@
iiuc.
ac.bd
A
b
st
r
a
ct
T
h
is study is
a
ccomplis
he
d to
calcu
l
ate
glo
b
a
l, di
ffuse
an
d
direct so
lar ra
d
i
atio
n e
m
p
i
rica
l
l
y on
a
hori
z
o
n
tal s
u
rface for the
di
vision
al
dist
rict
“Khuln
a
”
i
n
Bang
lad
e
sh (l
atitude
22
o47
΄
N and
lo
ngitu
d
e
89o
34
΄
E)
as w
e
ll
as to pr
ed
ict correl
a
tions
fo
r it by us
ing
se
veral
meteor
ol
ogic
a
l d
a
ta for
32 ye
ars b
e
tw
ee
n
198
0 an
d 20
1
2
. T
he glo
bal r
adi
ation
is fou
nd to be
maxi
mu
m i
n
the
month of Apri
l a
nd
min
i
mu
m in
the
mo
nth of D
e
c
e
mber
here. T
he esti
mated
valu
es of the
Angstro
m
’
s
r
e
gressi
on co
nstants a a
nd b
are
0.238
8 a
nd 0.
5
228 r
e
spectiv
e
l
y
. T
he other re
gressi
on co
nstants w
e
re als
o
compute
d
a
n
d
the corre
latio
n
s
prop
osed for K
hul
na ca
n b
e
u
s
ed i
n
future fo
r the esti
mati
o
n
of gl
oba
l, diffuse a
nd d
i
rect
solar ra
di
ation
if
the meteoro
l
o
g
i
cal p
a
ra
meter
s
rema
in av
ail
a
ble.
Ke
y
w
ords
: glo
bal ra
diati
on, di
ffuse radiati
on,
di
rect radi
atio
n, regressi
on c
onstant, sol
a
r
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The e
nergy i
ndee
d play
s
a vital rol
e
in
developm
ent
and
welfa
r
e o
f
human
bei
n
g
. The
r
e
exists a di
rect correlation b
e
twee
n the d
e
velopm
e
n
t of a country an
d it
s con
s
u
m
ption of energy.
Wo
rld re
se
rve of conventi
onal
en
ergy source
s are limited and
w
ill be use
d
up
once. Therefore
,
the wh
ole
wo
rld i
s
loo
k
in
g
for n
on-exh
austibl
e
en
ergy sou
r
ce
s f
o
r thei
r futu
re. Among th
e all
non-co
nventi
onal e
n
e
r
gie
s
, solar en
ergy is the
mo
st viable
opti
on if it can b
e
u
s
ed i
n
a
co
st
effective ma
n
ner. M
o
reove
r
sola
r e
n
e
r
g
y
conve
r
sion
tech
nolo
g
y i
s
e
n
viron
m
en
tally sou
nd.
As
the sola
r en
e
r
gy intercept
ed by the ea
rth in on
e
year is
ten times
more than the total fos
s
il
resou
r
ces i
n
cluding
undi
scovered
an
d u
nexplored n
o
n
-r
ecovera
b
le
re
serve
s
[1],
it is expe
cte
d
that the prese
n
t world
w
id
e resea
r
ch and
developm
ent
prog
ram o
n
solar en
ergy will help to solv
e
the future en
ergy crisi
s
of the worl
d.
The in
stallati
on of
sola
r
energy conv
ersi
on
syste
m
s ove
r
a
n
y pla
c
e
req
u
ires
cle
a
r
informatio
n a
bout the avail
ability of sunl
ight for
thei
r
optimal u
s
e.
Solar
radiatio
n is n
o
t unifo
rm
over all
pla
c
e
s
on
the e
a
rt
h whi
c
h
agai
n varie
s
from
time to time. Bangla
d
e
s
h,
being
situat
ed
betwe
en 2
0
o
3
4
΄
a
nd 26o3
4
΄
no
rth latitu
de, 88o
01
΄
a
nd 92
o41
΄
ea
st longitu
de, i
s
he
avenly gi
fted
with abundant sunshi
ne for
minimum of
8 months in
a year.
Th
eref
ore, the prospect
of utilization
of sola
r ene
rgy is very bri
ght. But sola
r radi
ation da
ta are not av
ailable in ma
ny location
s
of
Banglad
esh
due to a
b
sence o
r
ma
lfunction
of
mea
s
uri
n
g
instrument
s. However,
the
meteorologi
cal depa
rtmen
t
of Banglade
sh is
re
co
rd
in
g the climatol
ogical data such a
s
sun
s
h
i
ne
hour, temp
erature, humi
d
i
t
y etc. for most of the
di
stri
cts. The
s
e
data ca
n be
readily u
s
ed
in
empiri
cal
mo
dels to
com
p
ute the
glob
al
sol
a
r ra
diatio
n an
d its com
pone
nts
at a
n
y location.
We,
therefo
r
e, u
s
ed the
s
e
dat
a to
comp
ute
empi
rically
the gl
obal, dif
f
use
and
dire
ct solar radia
t
ion
over Khuln
a
as well as to
determi
ne the
values
of all the regress
i
on c
oeffic
i
ents
for it.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8015 – 80
21
8016
2. Estimatio
n
of Radia
t
io
n
Many resea
r
chers throu
g
h
out the world
have
estimat
ed the values of solar radi
a
t
ion and
its com
ponents for different areas of
the worl
d utilizing different formulas [2-12]. Here,
for
estimation
of
global
sol
a
r radiation
G, th
e form
ul
a p
r
o
posed
by H.P
.
Garg
an
d S.
N. Ga
rg [1
3] i
s
use
d
given b
y
Equation (1
).
(1)
)
W
0.0055
-
n/N
0.400
+
(0.414
G
G
at
o
Whe
r
e
Go i
s
the extraterrestrial
ra
diati
on,
n/N i
s
th
e ratio
of su
n shi
ne h
our and d
a
y
length and
Wat is the at
mosp
he
ric
water co
ntent per unit volu
me describe
d
in Eq (1d). From
geomet
rical
con
s
id
eratio
n
extraterre
strial daily
gl
o
bal
sola
r ra
diation
(Go
)
on a
ho
ri
zonta
l
surfa
c
e fo
r ea
ch statio
n is g
i
ven by Equation (1a
)
(1a
)
)
W
.
sin
sin
+
cos.W
cos
}(cos
4F)/
0.01163{(2
=
G
s
s
o
Whe
r
e F i
s
a
unit of conve
r
sion fa
ctor gi
ven in Equati
on (1
b),
φ
is the latitude in
radia
n
s,
δ
is the
solar de
clinatio
n g
i
ven in E
quat
ion
(1e
)
a
n
d
Ws is the
su
nset
angl
e gi
ven in E
quati
on
(1c
)
(1b)
/365)
d
×
360
cos
0.033
+
(1
60.0
×
1.95
=
F
(1c)
radians
)
tan
tan
(-
cos
=
Ws
-1
(1d)
)
T
0.0003
+
T
0.0055
+
T
0.3647
+
(4.7923
H
=
W
3
2
rel
at
And,
(1e)
d/365)
(360
sin
(27/60)]
+
[23
=
Whe
r
e
T is th
e ambi
ent te
mperature
in
oC fo
r the f
r
a
c
tional
su
nshi
ne du
ratio
n
n
/
N, Hrel
is the relative
humidity and
d being the n
u
mbe
r
of days after sprin
g
equin
o
x (21
s
t march).
For
estimatio
n
of diffuse radiation
(D), t
he
form
ula
propo
sed
by M. Hu
ssain [1
4] is u
s
e
d
given by Equation (2
).
,
(2)
}
W
0.0025
+
n/N)
x
(0.165
-
{0.306
G
=
D
at
o
For e
s
timatio
n
of direct or
beam ra
diatio
n (I),
the subt
ractio
n metho
d
[15] is used
given
by Equation (3).
(3)
D
-
G
=
I
Hen
c
e it sho
u
ld be noted
that all the radiati
on data a
r
e estim
a
ted in the unit of
Kwh/m
2
– day.
3. Dete
rmina
t
ion of Regr
ession Coefficient
Angstrom co
rrelation [16]
modi
fied by Prescott [17], given in Eq (4), for e
s
tim
a
tion of
global
radi
ation is
gene
rall
y employed a
ll over the
wo
rld. So, firstly the value
s
of the Re
gre
s
si
on
coeffici
ents (a and b) a
r
e
determi
ned fo
r Khulna
(4)
(n/N)
b
+
a
=
G/G
o
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Em
perical Co
m
putation of
Solar Radiati
on and
… (Mo
ham
m
ad Arif
Sobhan Bh
ui
yan
)
8017
Secon
d
ly, from Page co
rrelation [18], given in
Equ
a
tion (5
), for diffuse ra
dia
t
ion, the
values of the
correl
ation co
efficients
(c
a
nd d) for thi
s
station are de
termine
d
(5
)
)
(G/G
d
+
c
=
D/G
o
From An
gstrom like
co
rrelation [19],
giv
en in E
q
uation
(6),
for predi
ctin
g diffuse
radiatio
n over Khulna the va
lue
s
of the coefficient
s c
΄
and
d
΄
ar
e
dete
r
min
ed
(6)
(n/N)
d
+
c
=
D/G
o
Thirdly, from
both Pag
e
like and A
n
g
s
trom like
corre
l
ations [2
0], given in Eq
u
a
tion (7
and 8
)
, for e
s
timation of d
i
rect
sola
r ra
diation, t
he v
a
lue
s
of the
correl
ation
co
efficients
e, f, e
΄
and f
΄
are det
ermin
ed for K
hulna
(7)
)
(G/G
f
+
e
=
I/G
o
(8)
(n/N)
f
+
e
=
I/
G
o
To estimate
d
i
ffuse and
direct sol
a
r
radi
ation di
rectly from glob
al solar radiatio
n [21-22],
the values of
the coeffici
en
ts co, do, eo
and fo are d
e
t
ermine
d
(9)
(n/N)
d
+
c
=
D/G
o
o
(10)
(n/N
)
f
+
e
=
I/G
o
o
4. Results a
nd Discu
ssi
ons
The fluctu
atio
ns of mo
nthly averag
e Glo
bal,
Diffuse a
nd
Beam sol
a
r
ra
diation o
f
Khulna
throug
hout th
e year is
sho
w
n in Fig
u
re
1. It is
clear from the figure that the first pe
ak in t
h
e
global
sola
r radiation o
c
cu
rs in April/M
a
y (summe
r season). In this peri
o
d, bot
h
sun
s
hi
ne h
our
and
tem
p
e
r
at
ure are
hig
h
. But
the
seco
nd
p
e
a
k
o
c
cu
rs
i
n
Aug
u
st (autumn se
ason) whi
c
h
is no
t
so promin
ent
, due to short sun shi
n
ing
period al
th
o
ugh there is
high tempe
r
a
t
ure availabl
e.
Again, in
Nov
e
mbe
r
/De
c
e
m
ber (winte
r
sea
s
o
n
), tho
u
gh the
r
e i
s
e
noug
h
sun
sh
ining p
e
ri
od
s
but
the temperature is lo
w. Th
erefo
r
e, it
results in low gl
o
bal sol
a
r radi
ation.
The diffuse solar
radiatio
n
depe
nd
s on
relative humidi
ty and atmospheri
c
wate
r conte
n
t.
It increa
se
s
with the de
crease of sun
shini
ng ho
ur
and in
cre
a
se
of atmosph
e
r
ic
water
cont
ent.
Therefore, th
e diffuse
ra
d
i
ation is
ma
ximum in Ju
ne/July
(rai
n
y sea
s
on
) a
nd minim
u
m
in
De
cemb
er/
J
a
nuary (winte
r sea
s
o
n
).
The di
re
ct solar
radi
ation
is directly rela
ted to
su
nshi
ne d
u
rati
on an
d is, t
herefo
r
e,
maximum in March/April (summ
e
r
season)
an
d mini
mum in July (rainy se
ason
).
Figure 1. Monthly variation of Global, d
i
ffuse
and b
e
a
m sola
r ra
di
ation on a ho
rizontal
surfa
c
e
for Khulna
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8015 – 80
21
8018
The yea
r
to
year sea
s
on
al fluctuatio
n
s
of
Go
bal
solar
radi
ation
and the va
ri
ation of
annu
ally averaged gl
obal
sola
r radiatio
n is sho
w
n in
Figure 2 an
d 3 re
sp
ectiv
e
ly. There i
s
up
and
down of
global
sol
a
r radiation
in th
e graph
but
no cycli
c
patt
e
rn or
symm
etric va
riatio
n
of
radiatio
n is f
ound. F
r
om
Figure 2 it is cl
ear
th
at the monthly
averag
e Gl
obal radiatio
n is
maximum in the month of
April.
Figure 2. Year to year se
asonal variati
o
n
of Global sol
a
r ra
diation fo
r Khulna
Figure 3. Vari
ation of annu
ally averag
e
d
global solar
radiation for K
hulna
Usi
ng the
est
i
mated data i
n
the empi
ri
cal formul
a gi
ven in Equati
on (1 to
3),
several
correl
ation
s
are devel
ope
d Equation (4 to 10)
and
the corresp
ondin
g
reg
r
e
ssi
on co
effici
ents
(given i
n
T
abl
e 2
)
a
r
e
dete
r
mined fo
r th
e
station
Khul
n
a
. The
graphi
cal
rep
r
e
s
e
n
tations of the
s
e
correl
ation
s
a
r
e de
scrib
ed i
n
the followin
g
figure
s
(Fig
ure 4 to 10
):
Figure 4. Correlation b
e
tween n/N
a
nd
G/Go for coef
ficient a and
b
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Em
perical Co
m
putation of
Solar Radiati
on and
… (Mo
ham
m
ad Arif
Sobhan Bh
ui
yan
)
8019
Figure 5. Correlation b
e
tween G/Go a
n
d
D/G
for coeffi
cient
c and d
Figure 6. Correlation b
e
tween n/N an
d D/Go
for coeffi
cient
c' and d'
Figure 7. Correlation b
e
tween G/Go an
d I/G
for coeffi
cient
e and f
Figure 8. Correlation b
e
tween n/N a
nd I/Go for
coeffici
ent e'
and f'
Figure 9. Correlation b
e
tween n/N an
d D/G
for coeffi
cient
co and d
o
Figure 10. Co
rrel
a
tion bet
ween n/N an
d I/G
for coeffi
cient
eo and fo
Here, Figu
re
4 repre
s
e
n
ts the correlati
on betwe
e
n n
/
N and G/Go
(Equatio
n
4) and the
values of the
regre
s
sion
coefficient
s a and b ar
e d
e
t
ermine
d for the station Khulna. Simila
rly
Figure 5 to Figure 10 re
pre
s
ent the
correl
ation
s
given in Eq
uation (5) to
Equation (1
0)
respe
c
tively and th
e valu
es
of the
co
efficients c,
d, c
΄
, d
΄
, e, f
,
e
΄
, f
΄
, c
o
, do,
eo and
fo
are
determi
ned
from the
s
e
fig
u
re
s. Th
e va
lues of th
e
re
g
r
ess
i
o
n
c
o
e
ffic
i
e
n
ts ar
e r
e
p
r
es
en
te
d in
Table 2 an
d Table 3.
Table 2. The
comp
uted val
ues of r
egression
coeffici
e
n
ts for Khuln
a
a b
c
d
c
΄
d
΄
e
f
e
΄
f
΄
0.2388
0.5228
1.5288
-1.9024
0.3830
-0.2192
-0.4200
1.7102
-0.1440
0.7444
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8015 – 80
21
8020
The valu
e of
the sum of th
e re
gression
con
s
tant
s
(a +
b
)
whi
c
h re
pre
s
ent
th
e maximum
clea
rne
s
s ind
e
x (whe
n n/N = 1) is fou
nd
to be 0.7616.
Usi
ng the val
ues
of the co
efficients
a a
nd b for Kh
ul
na, a linea
r e
quation
re
co
mmend
ed
for the e
s
tima
tion of monthl
y average
glo
bal sola
r ra
di
ation over Kh
ulna i
s
given
by the Equati
on
(11
)
(11)
(n/N)
0.5228
+
0.2388
=
G/Go
Whi
c
h impli
e
s that ab
out 2
3
.88%
of extraterrest
rial ra
diat
ion ove
r
Khulna p
enet
rates the
atmosp
he
re o
n
a fully cloud
y day (n=0
) a
nd
abo
ut 76.1
6
% on a clea
r sky day re
sp
ectively.
Table 3 sho
w
s the values
of the correla
t
ion
coefficie
n
ts co, do, e
o
and fo Equation (9
-
10) for Khul
n
a
.
Table 3. The
values of ne
w correlatio
n coefficient
s for Khulna
Station c
o
d
o
e
o
f
o
Khulna 1.0829
-1.0095
-0.0751
1.0032
Usi
ng the
val
ues of the
co
efficients in E
quat
ion
(5
) –
Equation
(10
)
, the linea
r e
q
uation
s
recomme
nde
d for the e
s
timation of m
onthly avera
ge diffuse
a
nd direct sol
a
r ra
diation
over
Khulna a
r
e:
(12)
(G/Go)
1.9024
-
1.5288
=
D/G
(13)
(n/N)
0.2192
-
0.3834
=
D/Go
(14)
(n/N)
1.0095
-
1.0829
=
D/G
(15
)
(G/Go)
1.7102
+
0.4200
-
=
I/G
(16)
(n/N)
0.7444
+
0.1440
-
=
I/Go
(17)
(n/N)
1.0032
+
0.0751
-
=
I/G
5. Conclusio
n
Investment
s on sola
r ene
rgy systems i
n
any pl
ace require inform
ation of the availability
of sola
r en
ergy for its opti
m
um u
s
e. Bu
t the
measured ra
diation
data for a l
o
n
g
peri
od a
r
e
not
available all o
v
er Bangla
d
e
s
h. The
co
rrelations p
r
o
p
o
s
ed for Khul
na
in this study
can b
e
u
s
ed i
n
future for es
timation of s
o
lar radiations
if t
he data of
some
comm
o
n
meteorologi
cal pa
ram
e
te
rs
are
availabl
e. From the
stu
d
y it is cl
ea
r t
hat K
hul
na cit
y
is end
owed with sufficie
n
t
sol
a
r
radiatio
n
throug
hout
th
e yea
r
. The
r
e
f
ore,
sola
r e
n
e
rgy
system
s ca
n b
e
one
of the
best
o
p
tions of e
n
e
r
gy
supply in thi
s
city if it can be used in
a co
st effe
ctive mann
er.
The
co
rrel
a
tions propo
se
d for
Banglad
esh i
n
this
study
ca
n be
u
s
ed in futu
re
for e
s
timati
on of
sola
r
radiatio
ns if
the
meteorologi
cal data are
co
llected.
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TELKOM
NIKA
ISSN:
2302-4
046
Em
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