POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER
De e mining he Le el o Global Sola Radia ion
on he Ea h’s Su ace
Zdenek DOSTAL, Mi osla DULIK
Ins i u e o Au el S odola, Facul y o Elec ical Enginee ing, Uni e si y o Zilina in Lip o sky Mikulas,
kp . J. Nalepku 1390, 031 01 Lip o sky Mikulas, Slo ak Republic
[email p o ec ed], [email p o ec ed]
DOI: 10.15598/aeee. 13i5.1391
Abs ac . The a icle analyzes he Ea h’s su ace in-
sola ion. Fo he analysis, wo me hods a e desc ibed
- he me hod o app oxima e calcula ion and u bidi y
me hod using Linke u bidi y index. The me hods con-
side he la i ude o cu en loca ion on he Ea h’s su -
ace, a mosphe e a enua ion and o he majo ac o s.
To ob ain mo e accu a e alues, long- e m measu e-
men s a he cu en loca ion should be ob ained.
Keywo ds
Insola ion o he Ea h’s su ace, me hod o
app oxima e calcula ion, enewable ene gy e-
sou ces, u bidi y me hod.
1. In oduc ion
E iciency o enewable ene gy sou ces (RES) is based
on he deg ee o global sola adia ion. The mos im-
po an ac o is an insola ion, i.e. he inciden sola
adia ion. The emaining componen s o sola adia-
ion - di use and e lec ed adia ion is al eady a ec ed
by he en i onmen and has less impac on o e all e -
iciency. RES a e equen ly deployed as sou ces o
ene gy ha a e based on he use o di ec , indi ec o
media ed sun adia ion [13], [14], [15].
Di ec and indi ec sola adia ion is used by sola
pho o ol aic (PV) cells, he concen a ion sola pho-
o ol aic cells, sola collec o s and concen a ion sola
collec o s. Sunligh , s o ed in o he o ms o ene gy, is
used in biomass sys ems, hea pumps, wind u bines,
e c. [6], [7], [8], [9], [11]. Geo he mal sys ems ha e spe-
cial posi ion - hey p ocess he hea gene a ed by he
Ea h’s co e. In addi ion, o ming he Ea h’s co e and
man le was also signi ican ly a ec ed by sunligh . This
p ocess would ha e de eloped qui e di e en ly wi h-
ou he sunligh . In addi ion o RES sys ems, ene gy
is usually con e ed and s o ed du ing sho and long-
e m pe iods [1], [2]. Di e en ypes o s o age sys ems
a e a key elemen o RES. This pape deals wi h he
me hod o app oxima e calcula ion o sola adia ion
and u bidi y me hod, analyzing di ec sun adia ion
a selec ed loca ion [5].
2. Me hod o App oxima e
Calcula ion
The me hod o app oxima e calcula ion o di ec sola
adia ion (insola ion) is based p ima ily on an analysis
o he posi ion on he Ea h’s g ound, including seas
and oceans. C ucial a e he geog aphical coo dina es -
la i ude and longi ude o he selec ed loca ion [3].
2.1. E ec o he Cu en Loca ion
La i ude
The insola ion o he ac i e su ace is in luenced by
i s posi ion, depending on he la i ude. The angle o
ele a ion is c ucial o de e mining he insola ion o
he ac i e su ace [3]:
= 90 −a c an DSZ
RZsin κ+κ, (1)
whe e is he angle o ele a ion be ween he sun’s ays
and he su ace no mal (◦), DSZ is he dis ance Sun
- Ea h (150 ·109m), RZis he adius o he Ea h
(6378000 m), κis he angle be ween he la i ude o he
sun and he la i ude o he ac i e su ace (◦) and ϕis
he la i ude o he ac i e su ace (◦).
To de e mine he a e age ele a ion angle κ, we can
calcula e wi h he la i ude o he cu en si e. As he
sun mo es om he T opic o Cance o he T opic o
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Sun
T opic o Cap iho n
T opic o
Cance
Equa o
A ic ci cle
D
SZ
φ
OR
φ
κ
R
Z
κ
ε
θ
μ
b
Fig. 1: The cu en loca ion on he Ea h’s su ace, exp essed
using he la i ude.
Cap ico n (and back), pola days and nigh s a e also
impo an phenomenons o loca ions behind he no h
and sou h ci cle. We can de e mine κusing he ollow-
ing able (see Tab. 1):
Tab. 1: De e mina ion o κacco ding o he la i ude.
T opics Tempe a e F igid
zone zone
Sun o e
he T opic κ=ϕOR −ϕ κ =ϕ−ϕOR κ=ϕ−ϕOR
o Cance
Sun o e κ=ϕ κ =ϕ κ =ϕ
he Equa o
Sun o e
he T opic κ=ϕ−ϕOR κ=ϕ−ϕOR κ=ϕ+ϕOR
o Cap ico n
The exposu e o he ac i e su ace is a iable - when
he angle γinc eases, he ac i e su ace dec eases. The
insola ion can be e en ze o when he inciden adia ion
is pa allel o he ac i e su ace (see Fig. 2).
0 10 20 30 40 50 60 70 80 90
0
200
400
600
800
1000
1200
1400
La i ude (°)
Inciden powe (W ⋅ m−2)
Fig. 2: Insola ion a ec ed by he la i ude.
2.2. The In luence o he
A mosphe e Laye ’s Thickness
o e he Cu en Loca ion
Wi h inc easing la i ude, he hickness o he a mo-
sphe e, h ough which sun’s ays each he Ea h’s su -
ace, inc eases. Also, he heigh o he sun abo e he
ho izon dec eases. The e o e, sun’s ays ha e o pen-
e a e he Ea h’s a mosphe e unde highe angle and
he a mosphe e laye appea s o be hicke (see Fig. 3).
φ
h
m
n
HA
RA
RZ
φ
KH
Ψ
Fig. 3: E ec o la i ude on he pene a ion o sunligh h ough
a laye o he a mosphe e.
We assume ha he inciden ays om he sun a e
pa allel so we can igno e calcula ion e o . A he same
ime we assume he hickness o he a mosphe e o he
Ea h o be 100 km (Ka man line KH= 100 km).
Then he adius o he Ea h’s a mosphe e is RA=
R+ 100 km, i.e. RA= 6478 km [3]. The in luence o
he hickness o he a mosphe e HAis also dependen
on he loca ion acco ding o he alue o he la i ude
ϕ. F om he calcula ed alue HA, we can consequen ly
calcula e he a io kP:
HA=qR2
A−(RZsin ϕ)2
−RZcos ϕ, (2)
kP=HA
KH
,(3)
whe e HAis he hickness o he a mosphe e in he
di ec ion o sola adia ion (m) and ϕis he la i ude
(◦). The pa ame e kPexp esses a enua ion by a -
mosphe e depending on de ined la i ude (see Fig. 4).
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0 10 20 30 40 50 60 70 80 90
0
200
400
600
800
1000
1200
1400
La i ude (°)
Inciden powe (W ⋅ m−2)
Fig. 4: A enua ion by a mosphe e.
2.3. The In luence o Bo h Fac o s
The e ec o bo h ac o s is shown in Fig. 5.
0 10 20 30 40 50 60 70 80 90
0
200
400
600
800
1000
1200
1400
La i ude (°)
Inciden powe (W ⋅ m−2)
E ec o la i ude
E ec o a mosphe e
Fig. 5: E ec o bo h ac o s - la i ude and a mosphe e.
2.4. Inclina ion o he Ac i e Su ace
o he Sola Panel
Since ac i e su ace o sola panel is no always exac ly
o ien ed a he sun, i is necessa y o conside i s az-
imu h and ele a ion (see Fig. 6) [4].
The o e all e iciency o he sola panel, aking in o
accoun ele a ion, is exp essed by:
PVYR =PDOP ·cos Θ,(4)
whe e PVYR is he p oduced powe (W·m−2), PDOP is
an inciden powe (W·m−2) and Θis an angle be ween
he no mal o ac i e su ace and he ele a ion angle o
he sun.
Sun T opic o
Cance
Equa o
A ic ci cle
φ
κ
ε
θ
Su ace
no mal
Sun
ω
λ
α
Su ace
no mal
Sou h
Fig. 6: Ac i e su ace o sola panel - ele a ion and azimu h.
The o e all e iciency o he sola panel, aking in o
accoun azimu h, is exp essed by:
PVYR =PDOP ·cos λ, (5)
whe e PVYR is he p oduced powe (W·m−2), PDOP is
an inciden powe and λis an azimu h angle be ween
he no mal o he ac i e su ace and he azimu h angle
o he sun.
The in luence o bo h ac o s (angle Θand angle λ)
is in Fig. 7.
−50 050
−50
0
50
0
0.2
0.4
0.6
0.8
1
La i ude (°)
Ele a ion (°)
Ra io o inciden and p oduced powe
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 7: The in luence o azimu h and ele a ion on p oduced
powe .
Angles o ele a ion (Θ) and azimu h (λ) span om
nega i e o posi i e alues, depending on he o ien a-
ion o he sola panel in ela ion o he sun.
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2.5. Assessmen
The e ec o la i ude on he insola ion can be calcu-
la ed. This e ec , howe e , can be success ully elim-
ina ed by o a ing he ac i e su ace di ec ly owa ds
he sun. Un o una ely, inc easing o he a mosphe e
laye ’s hickness wi h inc easing la i ude canno be
elimina ed. Nea he A c ic Ci cle, he hickness o he
a mosphe e a ec s he insola ion wi h a g ea deal. To
ob ain maximum amoun o p oduced ene gy, sola and
PV elemen s a e mainly placed on he walls and oo s o
buildings, o ien ed on sou h. When an op imal o ien a-
ion is no possible, insola ion is a ec ed by he angle
be ween he sun and no mal o ac i e su ace. This
e ec can be elimina ed using acke sys em, which
op imizes posi ion o ac i e su ace bo h in ele a ion
and azimu h. On he o he hand, hese p esump ions
ake in o accoun only ideal wea he condi ions, no
he eal e ec s o wea he .
3. Tu bidi y Me hod
3.1. How o Calcula e Posi ion o
he Sun
To calcula e amoun o sun ene gy deli e ed on he
Ea h’s su ace, i is necessa y o exp ess he angle o
incidence o sunligh on he Ea h’s su ace. To de-
e mine he cu en loca ion, he la i ude is a key pa-
ame e . The angle o incidence is no cons an - i
a ies depending on he season as he ele a ion angle
a ies. Ne e heless, we can calcula e exac ele a ion
and azimu h wi h ega d o sun posi ion wi h su i-
cien accu acy [5]. Declina ion δis an angle be ween
he Ea h and he di ec ion o he sun’s ays exp essed
by:
δ= 23.45 ·sin(29.7·M+ 0.89 ·D−109),(6)
whe e δis declina ion angle (◦), Mis a numbe o
mon h, Dis a numbe o a day in a mon h. To calcula e
he heigh o he sun abo e he ho izon, we employ
ollowing o mula:
h= a csin(sin ϕ·sin δ−cos ϕ·cos δ·cos ω),(7)
whe e his he heigh o he sun abo e he ho izon (◦),
ϕis he la i ude (◦) and ωis he hou angle o he a c
in deg ees (◦) exp essed by:
ω= 15 ·T, (8)
whe e Tis an hou .
Azimu h o he sun can be calcula ed o ei he
no he n o sou he n hemisphe e. We p esen equa-
ions o no he n hemisphe e, depending on he ime
o he day. Fo hou s be o e noon ollowing equa ion
applies:
γS= a ccos sin ϕ·cos δ·cos ω+ cos ϕ·sin δ
cos h,(9)
whe e γSis he azimu h o he sun calcula ed om
he no h (◦), δis he declina ion angle (◦), ϕis he
la i ude (◦), ωis he hou angle (◦) and his he heigh
o he sun abo e he ho izon (◦).
Fo hou s a e noon ollowing equa ion applies:
γS= 360 −a ccos sin ϕ·cos δ·cos ω+ cos ϕ·sin δ
cos h.
(10)
3.2. Di ec Radia ion
To calcula e di ec adia ion IB, i is necessa y o
know some a iables men ioned abo e and Linke u -
bidi y index [5], exp essing ai pollu ion a he cu -
en loca ion. Linke u bidi y index o ai is calcula ed
by long- e m me eo ological measu emen s, conside -
ing al i ude, pollu ion and ype o se lemen . How-
e e , Linke u bidi y index a ies h oughou he yea .
In he win e mon hs i ’s lowe and in he summe
highe . Following equa ion exp esses di ec adia ion:
IB =
PSK sin h−0.1·TL(TL−1)
30 ·cos Θ
sin h−0.106 ·TL
,(11)
cos Θ = cos ·sin h+ sin ·cos h·cos(α−ω),(12)
whe e IB is di ec adia ion (W·m−2), PSK is a sola
cons an (W·m−2), Θis an angle be ween su ace no -
mal and sun ays (◦), his he heigh o he sun abo e
he ho izon (◦), is an angle be ween e ical and sun
ays (◦), ωis an azimu h o he sun (measu ed om
he no h) (◦), αis an azimu h o no mal (measu ed
om he no h) (◦) and TLis Linke u bidi y index.
3.3. Di use Radia ion
Di use adia ion ID is de ined as a dispe sion o sun-
ligh on he a oms and molecules o he a mosphe e
and ae osols, suspended in he ai [3]. Di use adia ion
IDH (W·m−2) adia ing ho izon al su ace is exp essed
by:
IDH=PSK ·sin h−
IB ·sin h
cos Θ ·
·(0.25 + 0.025TL).
(13)
To calcula e di use adia ion on inclined su ace ID
(W·m−2):
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ID =IDH
21 + cos +0.94 ·ecos Θ +1.84
TL
−1.44·cos ,(14)
whe e IDHis di use adia ion on ho izon al su ace
(W·m−2), ID is di use adia ion on inclined su ace
(W·m−2), IB is di ec adia ion (W·m−2), PSK is a
sola cons an (W·m−2), Θis an angle be ween su ace
no mal and sun ays (◦) and is an angle be ween
e ical and sun ays (◦).
3.4. Re lec ed Radia ion
The e ain su ounding he i adia ed su ace is cha -
ac e ized by he e lec ance o inciden adia ion. This
alue a ies om ρ= 0.90 ( o esh snow) o ρ= 0.15
( o g assy ege a ion in summe ). Re lec ed adia ion
IR (W·m−2) can be exp essed by ollowing app oxi-
ma e ela ion [3]:
IR = 0.5·ρ·(1 −cos )·PSK sin h
cos Θ +IDH.(15)
3.5. To al Radia ion
The o al adia ion e e s o as global sola adia ion.
Global sola adia ion IG (W·m−2) is he sum o di ec
and di use adia ions [3]:
IG =IB +ID, (16)
and some imes i is exp essed as:
IG =IB +ID +IR. (17)
The in ensi y o o al sola adia ion de e mines he
ene gy gain o he ac i e su ace [3].
3.6. Conclusion
This me hod deals wi h he impac o la i ude, a mo-
sphe e and angle o inclined su ace. The in luence o
he a mosphe e is no aken in o accoun - his pa ame-
e is eplaced by Linke u bidi y index. In addi ion o
he calcula ion o di ec adia ion, his me hod also de-
e mines he di use adia ion (di use in a mosphe e)
and e lec ed adia ion (on Ea h’s su ace).
4. Real Si ua ion
Each au ho uses o his analyses all he a ailable
da a and alues. Fo example, Halahya had had a ail-
able da a alues o P ague, B no, B a isla a, Kosice,
Snezka and Lomnicky s i [3]. Ob iously, in hese loca-
ions Czechoslo ak hyd ome eo ological ins i u e had
i s own measu ing s a ions. Howe e , how could we
e alua e he si ua ion a o he loca ions? Fo example,
he e a e special maps c ea ed by PVGIS [12], showing
a e age alues o sola adia ion a selec ed loca ion
o coun y. This kind o map de e mines he amoun
o sola adia ion, analyzing and showing i on a map
in app op ia e scale. Acco ding o he colo scale, i ’s
possible o de e mine qui e quickly a e age amoun o
sola ene gy (kWh·m−2) a di e en loca ions. How-
e e , hese alues a e jus app oxima e because o wo
easons:
•These alues we e measu ed du ing a pe iod om
4/2004 o 3/2010. This ime pe iod is qui e sho ,
so some co ec ions would be equi ed. Mo e ex-
ac alues could be a ailable a e measu emen s
du ing longe pe iods o ime, as yea seasons ha e
been sligh ly changing.
•Howe e , i he s a is ical e alua ions a e ca ied
ou o e a numbe o yea s, i would no ensu e
he e inemen o he esul s. Clima ologis s no e
ha me eo ological si ua ion has been dynami-
cally changing du ing las yea s. We can see sig-
ni ican changes in he in e als o weeks. Du ing
las 50 yea s win e s we e cold and almos cons an
- oughly om he beginning Decembe un il he
end o Ma ch and summe s om June o Augus .
In he las ew yea s, he e a e almos pe iodic
luc ua ions, when in July snows, and Decembe
and Janua y a e wa ms ( empe a u es a e e y
o en abo e ze o). Wi nesses ha e ce ainly no-
iced ha win e u ns o summe in a ew weeks
and a pe iod o g adual wa ming has almos dis-
appea ed. In summe , s o ms we e mild, las ing
o 2–3 hou s. Usually, when he s o m passed,
he empe a u e g adually inc eased. Nowadays,
s o ms a e accompanied by hail, al e na i ely by
o nadoes. In he pas , he e had been no o na-
does in Eu ope - now hey a e e y equen du ing
summe seasons.
The mos accu a e measu emen o he amoun o a-
dia ion (kWh·m−2) can be ob ained du ing long- e m
pe iods. Fo his eason he RES sys ems also include
senso s o measu ing a ious pa ame e s [10]. The e-
sul s p o ide in o ma ion and an o e iew o ei he
yea pe iod o consecu i e yea s. This kind o anal-
ysis p o ides a e age esul s o he cu en loca ion.
This kind o analyse also elimina es he numbe o ac-
o s no p o ided by special kind o map, men ioned
abo e [12]. Fo compa ison, insula ion analysis o e
h ee days in July 2007 is p esen ed in Fig. 8.
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4 6 8 10 12 14 16 18
0
200
400
600
800
1000
1200
Hou o day (h)
Insola ion (W ⋅ m−2)
15/7/2007
21/7/2007
22/7/2007
Fig. 8: Insola ion du ing h ee day pe iod.
On 15 h o July 2007, he wea he was a o able, and
insola ion eached ela i ely high alues, wi hou any
in e up ions. Opposi e o his day was 21s o July
2007 - his day was qui e mis y and pa ially cloudy.
Insola ion was qui e low. On 22nd o July 2007, mea-
su ed alues we e also e y in e es ing. The wea he
was a o able, excep o highe humidi y, sligh ly de-
c easing insola ion. F om abou 1 PM un il 2 PM,
he e was a s o m, causing signi ican ly dec eased inso-
la ion. A e inishing his s o m, he insola ion pa ly
inc eased. To demons a e basic calcula ions o inso-
la ion, he e is a Tab. 2 p o iding basic amoun s o
insola ion and p oduced ene gy o hese days.
Tab. 2: Insola ion du ing selec ed days.
Da e Insola ion
(kWh·m−2)
15/7/2007 12.305
21/7/2007 6.375
22/7/2007 8.870
Du ing a sunny day insola ion can each a alue o
12.305 kWh·m−2. In case o mis o clouds, insola ion
d ops signi ican ly, pe haps by hal o mo e. Howe e ,
he e a e some days wi h dynamic wea he changes,
like 22nd o July 2007 - almos all day was sunny, bu
when s o m came, insola ion was educed o a e y
small alue.
Sola panels can be ins alled in wo ways. Fi s ly,
hey a e ixed o di e en su aces ha ing cons an o i-
en a ion in ela ion o he sun. Cons uc ions can be
deployed on Ea h’s su ace, o ixed o he walls o
oo s. Ano he op ion is using o a acke sys em, p o-
iding highe e iciency. Acco ding some da a p o ided
by he p oduce s, o e all e iciency can by inc eased
e en by 30 %. In his case, he angles be ween su ace
no mal and he sun (Θand λ) a e cons an ly e alua ed
and minimized. Howe e , his ype o implemen a ion
is a he cos ly.
5. Conclusion
Calcula ion o global sola adia ion, i.e. insola ion o
he Ea h’s su ace, seas and oceans was analyzed by
wo me hods:
•Me hod o app oxima e calcula ion, based on la i-
ude and longi ude o cu en loca ion, in luencing
o e all insola ion.
•Tu bidi y me hod, aking in o accoun Linke u -
bidi y ac o .
To ob ain mo e accu a e esul s, i is be e o e-
place app oxima ed alues o insola ion wi h he esul s
o long- e m measu emen s a selec ed loca ion. I all
ac o s a e aken in o accoun , p edic ions o insola ion
o selec ed loca ion will be mo e accu a e and eliable.
Acknowledgmen
This wo k was suppo ed by VaV p ojec s o he ope -
a ional p og am "Cen e o excellence o powe elec-
onic sys ems and ma e ials o he componen s",
p ojec code 2008/2.1/01-SORO, ITMS 26220120003,
"Cen e o excellence o powe elec onic sys ems and
ma e ials o he componen s II.", ITMS 26220120046.
P ojec is co- unded om EU unds. This wo k was
suppo ed by he Slo ak Resea ch and De elopmen
Agency unde con ac no. APVV-0888-11. This
wo k was suppo ed by p ojec ITMS: 26210120021,
co- unded om EU sou ces and Eu opean Regional De-
elopmen Fund.
Re e ences
[1] BACA, P. and R. BILKO. Elec ochemical sys-
ems (ba e ies) used in pho o ol aic applica ion.
In: 4 h In e na ional wo kshop on eaching in
pho o ol aic. P ague: IET Czech Ne wo k, 2008,
pp. 75–76. ISBN 978-80-01-04047-8.
[2] BACA, P. P ehled moznos i akumulace elek icke
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Abou Au ho s
Zdenek DOSTAL g adua ed in 1981 as an elec ical
enginee a he Mili a y Academy in Lip o sky Miku-
las. In 1994 he inished his pos -g adua e s udies. In
2000, he was awa ded wi h an academic i le Associa e
p o esso , specialized in ada da a p ocessing. A e
inishing he uni e si y he has been ocusing on enew-
able ene gy sou ces. Since 2003 he has been in e es ed
in o - he-g id elec ici y sys ems and emo e a ea
powe supply (RAPS) sys ems mo e in ensi ely. A
he Ins i u e o Au el S odola in Lip o sky Mikulas he
has cons uc ed se e al expe imen al de ices.
Mi osla DULIK g adua ed in 2000 as an elec ical
enginee a he Academy o A med Fo ces in Lip o sky
Mikulas. In 2005 he inished his Ph.D. s udies. He
has specialized in mic op ocesso p og amming and
compu e ne wo ks. Since 2008 he has also in e es ed
in con olling sys ems o enewable ene gy sou ces,
ying o de elop new concep s and solu ions, op imiz-
ing o e all pe o mance.
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