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Ex eme P oduc ion Condi ions o Pho o ol aic
Powe Plan Ope a ed in Dis ibu ion G id
Ma in SMOCEK, Zdenek HRADILEK
Depa men o Elec ical Powe Enginee ing, Facul y o Elec ical Enginee ing and Compu e Science,
VSB-Technical Uni e si y o Os a a, 17.lis opadu 15/2172, 708 33 Os a a-Po uba, Czech Republic
ma in.smo[email p o ec ed], [email p o ec ed]
Abs ac . Pho o ol aic powe plan s a e sou ces o
elec ical ene gy ha a e e y dependen on wea he
condi ions. This pape in e es s in desc ip ion o
s ochas ic p oduc ion o powe in pho o ol aic powe
plan s and subsequen ly i s impac on he dis ibu ion
powe g id. S ochas ic p oduc ion o powe om hese
sou ces is conside able and ha dly p edic able. The aim
o his su ey is o assess he in luence o pho o ol aic
powe plan s ope a ion on he daily load diag am wi h
ega d o ou pu change di e ence o ac i e powe a
he ele an subs a ion. E alua ion is based on eal-
ime synch onous da a measu ing bo h on-si e pho o-
ol aic powe plan ope a ion and on-si e elec ic powe
line ou pu om he subs a ion. This measu emen is
used o sugges ion o a gene al calcula ion me hodol-
ogy o he assessmen o he di e ence o ac i e powe
a a pa icula node o he g id unde a ious powe
changes om he pho o ol aic powe plan . S a is i-
cal me hods ha e been employed o p ocess a me hodol-
ogy in o de es ablish ex eme condi ions o p oduc ion
powe o pho o ol aic powe plan .
Keywo ds
Calcula ion me hodology, pho o ol aic powe
plan , eal measu emen , s a is ical me hods,
s ochas ic e ec .
1. In oduc ion
Dependence ope a ion o bo h pho o ol aic powe and
wind powe plan is conside able on me eo ological con-
di ions [3], [4]. This pape con ains a desc ip ion o he
assessmen ocused on he issues o calcula ion me hod-
ology. Mos s udies deal wi h he p edic ion o powe
as [6], bu he pu pose o his me hodology is o de-
e mine di e ences in ac i e powe induced by ope a-
ion o pho o ol aic powe plan s (PVP). The su ey
is based on ac ual long- e m moni o ing o a speci ic
powe plan . The da a a ailable has been ob ained by
measu emen a he PVP ope a ion si e as well as he
poin o elec ic powe ou pu om subs a ion plan ,
whe e he PVP is connec ed. Bo h measu emen s we e
conduc ed on synch onised basis.
The e alua ion o PVP p oduc ion is conduc ed by
means o se e al indi idual asks ha can be spli in o
wo s ages. The i s s age de e mines me hodology
o se -up o ex eme h esholds o p oduc ion gene -
a ed by he PVP and he second s age conce ns ana-
lysis o he impac o hese ex eme h eshold alues
on he magni ude o ac i e powe lows a he place
o measu emen wi hin subs a ion plan . The eached
esul s om he analysis o PVP a e use o es ablish
a me hodical calcula ion model o conside he impac
o s ochas ic p oduc ion o ac i e powe in he PVP
on he dis ibu ion g id a a ious nominal alues o
peak powe wi hin a ious ime in e als h oughou
he yea .
The ope a o s o such g ids conside he s ochas ic
na u e o he powe supplied undesi able. Such con-
di ions esul in highe demand o ese e capaci y in
e ms o Ancilla y Se ices o ensu e he equi ed bal-
ance be ween immedia e p oduc ion and consump ion
o elec ic powe . Po en ial changes o powe low ep-
esen jus ano he nega i e consequence. Tha a ec s
he p ope unc ioning o means o g id p o ec ion.
The e a e also p oblems wi h keeping he equi ed s a-
ble ope a ing g id pa ame e s. This calcula ion model
is es ablished wi h espec o he po en ial impac on
p ese ing he magni ude o capaci y Ancilla y Se -
ices [5].
2. A ea o a Measu ed G id
The da a was ob ained by measu emen bo h a PVP
ope a ion and on he ele an powe line ou pu o he
subs a ion plan , whe e his PVP is connec ed [1].
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2.1. Da abase o Measu ed Da a
1) Pho o ol aic Powe Plan
The peak ou pu o his PVP is 1.1 MWp. The mea-
su emen was conduc ed on he low ol age side on
a con inuous basis o one yea . Accu a ely ha was
om 30.6.2010 ill 29.6.2011. The da a was eco ded
wi h ime s ep se a one-minu e inc emen s.
2) Ou pu Subs a ion Plan
The measu emen a he powe line ou pu was con-
duc ed on he high ol age end and an wi hin a ious
ime pe iods om 26.7.2010 ill 23.6.2011. Same as o
PVP, he measu emen was pe o med a one-minu e
inc emen s. The measu emen p ocess p oduced many
ope a ing alues and pa ame e s. This su ey deals
wi h he analysis o he ac i e powe Po e ime pa h
. Pe cen age e alua ion and mu ual compa ison o
da a measu ed on PVP and a he subs a ion poin
ha e been illus a ed in Fig. 1. Columns in cha s ep-
esen indi idual mon hs. The las column shows an
a e age o all mon hs moni o ed. In o al, he e a e
98 % o he da a om PVE and 64 % o he da a om
he subs a ion, whe e:
•p - pe cen a ailabilily,
•x-axis - indi idual mon hs,
•su - a e age sum o indi idual mon hs.
Fig. 1: Pe cen age compa ison o da a measu ed [1].
2.2. Ne wo k Topology
The ne wo k opology has a loop sys em, ye i is ope-
a ed in he adial sys em. When his measu emen
was conduc ed, he PVP was he only elec ic powe
sou ce wi h signi ican ou pu on a gi en powe line,
whe e:
•PVP - pho o ol aic powe plan ,
•SS - sec ion swi ch (disconnec ed),
•110/22 kV - subs a ion plan 110/22 kV.
Fig. 2: Measu e g id opology [1].
The i s measu emen was pe o med a he ou going
eede om he subs a ion 110/22 kV using he side o
lowe ol age le el o 22 kV. The second measu emen
was done a he connec ion poin o he pho o ol aic
plan o he g id a he ol age le el o 0.4 kV. Bo h
measu emen s we e conduc ed in a synch onous man-
ne . Poin s o measu emen a e lagged ed in Fig. 2.
3. Ancilla y Se ices
The T ansmission G id Code (GC), pa II, as amended
by e ision 14 duly app o ed by he Ene gy Regula-
o y O ice on 1.1.2014 in Czech Republic, de ines he
ma e s ele an o he u ilisa ion o GC wi h espec
o Ancilla y Se ices. The documen con ains me ho-
dology o de e mina ion o summa y con ol backups
o SS o he powe g id in Czech Republic. One o
he p e equisi es o de e mina ion o summa y con-
ol backups o SS is he so-called de ia ion ODOZE( ).
This is a pa ame e o es ablish he inc emen o bal-
ancing de ia ion caused by p oduc ion om newly in-
s alled enewable esou ces o elec ic powe . As s a ed
he e (1), his inc emen is de ined by he sum o he
inc ease gene a ed by ope a ion o wind ODV E( )and
pho o ol aic ODF V E( )powe plan s. The de ia ion
ODOZE( )is hen used o de e mine olumes o SS e-
qui ed o he subsequen pe iod, based on exis ing in-
o ma ion om p epa a ions o he ope a ion, e.g.:
ODOZE( )=ODV E( )+ODF V E( ).(1)
This s a emen , desc ibed equa ion (1), implies ha
he e ec o ins alled capaci y o pho o ol aic powe
plan s has a ce ain impac on he calcula ion o SS.
Aim o his su ey is o assess i and how much he PVP
p oduc ion has in luence o o al calcula ion o SS wi h
espec o indi idual mon hs. The simila app oach o
e alua ion is also desc ibed in [7].
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4. Ex eme Condi ions
The consis ency and comp ehensibili y o his a icle
a e suppo ed by he esul s om own su ey o de-
ine a me hodology o de e mina ion o ex eme p o-
duc ion condi ions o pho o ol aic powe plan . These
ma e s we e p esen ed in de ail a he con e ence [2].
Essen ial esul s will be desc ibed.
4.1. Pho o ol aic Powe Plan
Figu e 3 shows h ee cu es as a sample o analyzed
da a in his pape . Indi idual cu es co espond as
ollows:
•p oducend powe om PVP (g een),
•powe lowing h ough he subs a ion (blue),
•loads (black).
Fig. 3: Sample o examined da a.
The powe di e ence o PVP has a nega i e impac on
immedia e powe balance be ween p oduc ion and con-
sump ion wi hin he powe g id. Fo his eason, he
analysis o ex eme h esholds is necessa y. Based on
ac o s desc ibed in [2], one-minu e ou pu se ies was
con e ed in o i e-minu e inc emen s. De o ma ion o
he da a in o ma ion wi h espec o u he p ocess-
ing and e alua ion a ge is negligible. As an example,
u he s eps desc ibed in his a icle analyse da a in
Ap il 2011.
Figu e 4 shows ex eme a eas o PVP p oduc ion
( he g een cu e om Fig. 3. The h esholds o hese
ex eme condi ions a e de ined by wo eg ession poly-
nomial Eq. (2) and Eq. (3), which o m he op and
bo om en elope cu es o s ochas ic changes in he
p oduced powe . The equa ions a e as ollows:
PF V Emax =−5700,51 + 63525,7·T ime
−246642 ·T ime2+ 400745 ·T ime3(2)
−279206 ·T ime4+ 66861,7·T ime5,
PF V Emin = 4554,05 −68932,4·T ime
+414328 ·T ime2−1,25591 ·106·T ime3(3)
+2,0145 ·106·T ime4−1,62904 ·106·T ime5
+523013 ·T ime6.
De e mina ion o hese ex eme condi ions was con-
duc ed based on s a is ical me hods ha u ilize he el-
e an equency ca ego ies using he so-called S u ges
ule. This is a ule o op imal de e mina ion o e-
quency ca ego ies. Nex s ep is o e alua e daily load
Fig. 4: Ex eme condi ions o PVP.
diag am. Co ela ion ields o daily load diag am ( he
black cu e om Fig. 3) can be subjec o eg ession
analysis applied o enable de e mina ion o di e en ial
powe h esholds o loads. I is desc ibed in Fig. 5. Ex-
eme h eshold condi ions, Eq. (4) and Eq. (5), ha e
been de e mined using 95 % p edic ion le els. Fo mo e
in o ma ion on his issue e e o [2]. The equa ions a e
as ollows:
Fig. 5: Ex eme condi ions o daily diag am.
P e ious analyses ha e p oduced he ex eme di e -
ence o ou pu gene a ed by PVP and de e mina ion o
h esholds o daily load diag am. Ex eme condi ions
ha migh occu a he subs a ion plan ou le co e-
spond wi h he sum o ex eme condi ions bo h PVP
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POBDmax(M W ) = 2,13445 + 0,000174187 ·T ime −4,6908 ·10−8·T ime2+ 4,32657 ·10−12 ·T ime3
−1,78877 ·10−16 ·T ime4+ 3,85326 ·10−21 ·T ime5−4,49778 ·10−26 ·T ime6(4)
+2,69318 ·10−31 ·T ime7−6,46948 ·10−37 ·T ime8,
POBDmin(M W )=1,45615 + 0.000176551 ·T ime −4,72509 ·10−8·T ime2+ 4,35116 ·10−12 ·T ime3
−1,79852 ·10−16 ·T ime4+ 3,87564 ·10−21 ·T ime5−4,52732 ·10−26 ·T ime6(5)
+2,71398 ·10−31 ·T ime7−6,52996 ·10−37 ·T ime8.
and he daily load diag am. They ha e been de ined
as ollows:
1) Maximum Ex eme Condi ions:
ma ching he maximum ex eme condi ion ha may
occu . I is equal o he di e ence be ween he max-
imum ex eme o DLD (uppe p edic ion le el 95 %)
and he minimum ex eme o PVP:
PROZ(max)=POBD(max)−PF V E(min)(MW ).(6)
2) Minimum Ex eme Condi ions:
ma ching he minimum ex eme condi ions ha may
occu . I is equal o he di e ence be ween he min-
imum ex eme o DLD (lowe p edic ion le el 95 %)
and he maximum ex eme o PVP:
PROZ(min)=POBD(min)−PF V E(max)(MW ).(7)
These cu es Eq. (6) and Eq. (7) a e po ayed in
Fig. 6. They demons a e he maximum ex eme con-
di ions ha may occu o a ele an ou le o he g id
a he ou going eede om he subs a ion. In o de o
Fig. 6: Subs a ion ou le ex eme condi ions.
con ol o de eloped me hodology, he measu ed da a
o lowing powe a he poin o he subs a ion ( he blue
cu e om Fig. 3) a e plo ed in calcula ed compe en
h esholds o cu es desc ibing he minimum and max-
imum ex eme powe (desc ibed in Fig. 5) which could
occu a he ou le om he subs a ion plan . This
si ua ion shows Fig. 7. All he da a and e alua ion
me hodology we e conside ed wi h he eliabili y le el
o 95 %. This pa icula case conce ns 95.54 % o alues
si ua ed wi hin he de ined ou pu ex eme condi ions.
This ac jus i ies he co ec ness o he p ocess.
Fig. 7: Con ol o adjus men o powe ou pu di e ence esh-
olds.
5. Sugges ed Me hodical
Models
5.1. Assessmen Me hodology
The p ocess o assessmen me hodology is desc ibed by
he block diag am in Fig. 8. The diag am is di ided
in o h ee e ical and h ee ho izon al sec ions. Ve -
ical columns a e sepa a ed by a dashed ec o , and
ho izon al lines a e highligh ed by blue backg ound.
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1) Ve ical Sec ions
The i s column ep esen s measu ed da a undamen-
al o he es ablishmen o his me hodology.
The second column p o ides a desc ip ion o sug-
ges ed calcula ion me hodology. The i s s ep equi ed
p ocessing o da a, o he so-called Pos -P ocessing
(block P.-P ocess.). The nex s ep was o enume a e
ex eme condi ions o powe ou pu o pho o ol aic
powe plan s (block Ex . PVP), ex eme condi ions
o he daily load diag am (Ex . DLD) and ex eme
condi ions a he ou going eede om he subs a ion
(Ex . SUB). De e mina ion o Ex . SUB i s ly e-
qui ed ob aining he da a wi hou impac o p oduc-
ion om he PVP. This da a ep esen s so-called he
ow da a (only loads) o daily load diag am (block
DLD). The ow da a was de e mined by sub ac ion o
he immedia e ou pu da a du ing ope a ion o PVP
om he immedia e ou pu da a measu ed a he sub-
s a ion. This sub ac ion is subjec o accu a e syn-
ch onising (block Synch.) o bo h se s o da a mea-
su ed. Subsequen ly, ex eme condi ions o DLD we e
e alua ed. Sui able sum o Ex . DLD and Ex . PVP
can help wi h assessmen o ex eme condi ions occu -
ing a he subs a ion (block SUM Ex .).
The las column con ains di e ences o ac i e powe
o he PVP (block P di . P P) and he da a measu ed
a ou going eede om he subs a ion (block P di .
SUB and P di . DLD).
2) Ho izon al Sec ions
As p e iously men ioned, he diag am is also di ided
in o h ee ho izon al lines.
The i s line comp ises blocks linked by means o
ed a ows. These desc ibe he s eps o assessmen o
powe di e ences on he PVP i sel only. This indica-
o does no include he impac o daily load diag am.
This assessmen is hen used o de e mine he model
si ua ions o indi idual mon hs wi h u he po en ial
o lexible al e a ions acco ding o he panel ype al-
eady known and i s nominal peak powe . This s ep is
he mos impo an and di icul o all e alua ion.
The las ho izon al line con ains blocks linked wi h
g een a ows. The da a measu ed a subs a ion in-
cludes he impac o PVP ope a ion oo. De e mina-
ion o he di e ence o ac i e powe in his manne
is co ec , al hough dedica ed only. I canno be ap-
plied o ano he model si ua ion in a b oade sense,
being limi ed o hese speci ic da a measu ed a his
pa icula subs a ion and he ele an PVP.
These issues do no also deal wi h a case, when he
di e ence o ac i e powe would change wi h he con-
s uc ion o a new PVP wi hin he pa icula loca ion.
The second line p o es i sel as an op imal solu ion,
and i is linked o blocks using blue a ows. We need
o ealize ha ex eme condi ions o powe a he sub-
s a ion occu due o ex eme condi ions on bo h he
PVP as well as a daily load diag am. As men ioned
p e iously, he da a measu ed a ou going eede om
he subs a ion mus be educed by sub ac ing he da a
pe aining o powe p oduced by he PVP. This s age
al eady enables o de e mine he ex eme condi ions
o daily load diag am as well as PVP o any ypes o
panels wi h a ying peak powe igu es.
Model si ua ions o ex eme condi ions o PVP may
also be use ul o a ious model o simula ion p ocesses,
whe e he change o load diag am is al eady an ici-
pa ed.
5.2. Calcula ion Model
The sugges ed assessmen me hodology can be used
o se up a calcula ion model. The calcula ion model
con ains blocks linked wi h ed a ows.
The main ad an age o he e y assessmen o ex-
eme s a es o PVP and DLD has been desc ibed
abo e. This idea has been also ans e ed in o he cal-
cula ion model. Ano he i e u able ad an age b ough
by analysis o such sepa a ed da a is a mo e accu a e
ma hema ical desc ip ion. I has o be ealized ha
he DLD and PVP p oduc ion cu es di e g ea ly in
na u e ha is also one o he easons, why examin-
ing ei he ex eme sepa a ely is mo e con enien be-
o e calcula ion o model si ua ion o ex eme condi-
ions o PVP (block PVP) equi es knowledge o he
panel ype and hei nominal peak powe igu es. Fu -
he equi emen s o be me include he p econdi ion
assuming s a ic posi ion o he panel in o de o maxi-
mize p o i (inclina ion a app ox. 38◦wi h espec o
he ho izon al plane and sou hwa ds o ien a ion). The
ed a ow in Fig. 8 ep esen s he in eg a ion o model
ex eme condi ions o PVP in o he calcula ion p ocess
and he poin o assessmen . The poin o assessmen
(block 110/22), which is o be used o assessmen o
he powe di e ence, mus be iden i ied wi h he na-
u e o powe load - he daily load diag am. These load
cu es a e usually moni o ed by dis ibu o s a ce ain
i al poin s. Da a o igina ing om a ious model o
simula ion p ocesses can be also used.
5.3. Annual Ex eme Condi ions o
PVP
Maximum ex eme condi ions o p oduc ion a e de-
sc ibed in Fig. 9 and Fig. 10. Figu e 9 co e s mon hs
wi hin he pe iod om Decembe ill June, i.e. he
pe iods o win e and summe sols ice. One can no-
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Fig. 8: Block diag am o assessmen me hodology.
ice ha he dispe sion o p oduc ion ime is ex ended
p opo ionally o he inc easing du a ion o sunshine
wi hin pa icula mon hs, and he ampli ude is ising
wi h inc easing in ensi y o sola adia ion. The maxi-
mum occu s in May a he ha du ing he summe sol-
s ice, as migh be expec ed. This case he e o e leads
o he es ablishmen o an op imal a io be ween he
in ensi y o sola adia ion and a e age empe a u e
du ing he pa icula mon h (p e ious mon hs indica e
lack o sola adia ion and he subsequen mon hs b ing
highe ambien empe a u e wi h a nega i e impac on
panel e iciency). Figu e 10 shows maximum cu es
Fig. 9: Ex eme condi ions o PVP, Decembe o June.
om July ill Decembe , i.e. be ween he summe and
win e sols ice.
Fig. 10: Ex eme condi ions o PVP, July o Decembe .
6. Conclusion
B ie ly speaking, his measu emen is used o sugges-
ion o a gene al calcula ion me hodology o assess-
men o di e ence o ac i e powe a a pa icula node
o he g id unde a ious ic ional changes o powe
om he pho o ol aic powe plan o he whole sola
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a m, o e en in case o expec ed changes o p edic ions
in he daily load diag am. Compa ing maximum ex-
emes o each mon h indica es signi ican di e ences.
I is clea ha di e en pe iods du ing he yea ha e
in luence o he assessmen o Ancilla y Se ices. Nex
S eps o his s udy will ocus on he applica ion o his
me hodology on a ull da abase and e alua ion he e-
la ionship o each mon h o Ancilla y Se ices.
Acknowledgmen
This wo k was suppo ed by he Minis y o Educa-
ion, You h and Spo s o he Czech Republic (No.
SP2014/187) and by he p ojec ENET (Resea ch and
De elopmen o Inno a ions Ope a ional P og ammes
No. CZ.1.05/2.1.00/03.0069).
Re e ences
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Abou Au ho s
Ma in SMOCEK was bo n in H anice. In 2011
he g adua ed VSB-Technical Uni e si y o Os a a,
Facul y o Elec ical Enginee ing and Compu e Sci-
ence, elec ical powe enginee ing. Today he is Ph.D.
s uden in he Depa men o Elec ical Powe Engi-
nee ing, VSB-Technical Uni e si y o Os a a and he
applies himsel o he issue o pho o ol aic powe plan .
Zdenek HRADILEK was bo n in B no. A e
g adua ion o college educa ion a Facul y o Elec ical
Enginee ing and Compu e Science B no Uni e si y
o Technology in 1962 he wo ked as a echnician in
company Sou he n Mo a ian powe plan s in B no,
han he wo ked as a majo powe -supply di ec o in
Hea -supply Os a a and om 1966 un il now he is a
he VSB-Technical Uni e si y Os a a. His scien i ic
p epa a ion g adua ed by his candida e disse a ion
de ending a he B no Uni e si y o Technology in
1972. He de ended his doc o al hesis a he Czech
Technical Uni e si y in P ague in 1988 and was
appoin ed as p o esso .
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