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JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 15, No. 5- 6, May – June 2013, p. 550 - 554
Weighted efficiency measurement of PV inverters: introducing ηİZMİR
İLKER ONGUN*, ENGIN ÖZDEMIRa Ege University Ege Meslek Yuksekokulu, 35100 Bornova İzmir, Turkey a Kocaeli University, Faculty of Technology, Department of Energy Systems Engineering, 41380 Umuttepe Kocaeli.
Conversion efficiency of DC/AC inverters depends on some parameters and fluctuates over the input power of the inverter. Since the PV inverters operate under a fluctuating input power supplied by the PV modules, conversion efficiency must be measured against the weights of the probable power ranges which represent the various irradiation values. This approach of having different weights for different irradiation ranges resulted in two basic weighted conversion efficiency models of ηEURO and ηCEC. These two models consider the irradiation distribution over the whole annual sunny time and prioritize the ranges with various weight factors. Since the irradiation profiles vary around the planet, inverter efficiencies must be evaluated against local irradiation profiles to get more precise annual energy yield estimation. This paper presents ηİZMİR, a weighted conversion efficiency evaluation model, derived from the İzmir irradiation profile. This model has been developed in a way that it should be simple and accurate so it has been matched with other models for its estimation capabilities. The results are discussed here and suggestions being made. (Received December 18, 2012; accepted June 12, 2013) Keywords: PV inverters, conversion efficiency, weighted efficiency, ηEURO, ηCEC, ηİZMİR
1. Introduction Penetration of grid connected photovoltaic power
systems (PVPS) is rapidly increasing for two decades. As they are being an embedded part of the electric networks, their electricity generations have started to be studied more intensively. The incentives given by the governments for those systems due to the paradigm change in the energy field has triggered a further acceleration in those studies.
Electricity generation of a PV power system depends on the solar irradiation received by the PV modules and the efficiency of the system. The efficiency of a PVPS on the other hand, is a multifold concept covering conversion efficiency of the PV modules along with the conversion efficiency, MPPT performance and some other properties of PV inverter used.
PV inverters are evaluated with their overall efficiency. Overall efficiency is described as the ratio of the energy delivered by the PV inverter at the AC terminals to the energy provided by the PV array [1]. The two efficiencies involved in the inverters are conversion efficiency (ηconv) and MPPT efficiency (ηMPPT) described as,
(1) and
(2) respectively, where,
· is instantaneous value of the delivered power at the AC terminal,
· is instantaneous value of the power drawn by the inverter, p t · dt is instantaneous value of the MPP power provided by the PV array (or PV simulator). Thus, the overall efficiency including both efficiencies becomes;
(3)
Besides the straightforward mathematics here,
especially with the grid connected power plants, annual yield estimation needs further effects to be studied accurately for realistic revenue projections. One these would be the input power fluctuations resulting from climatic conditions, since the value of PV array power explicitly affects both conversion and MPP tracking efficiencies of the PV inverter.
The first weighted efficiency calculation concerning the effect of irradiation profile on the inverter efficiency has been introduced with north-western Germany climate data (Trier) in 1991 [2], [3]. The formula given in a footnote of a magazine article then became a well-known comparison tool among PV inverters Although the weather data used for calculating the weighting factors do not represent whole Europe – especially the South – the formula know is now known as the “European Efficiency – [4]. European Efficiency formula is given as;
4 1 1 2 2 3 3
4 4 5 5 6 6
EURO EU MPP EU MPP EU MPP
EU MPP EU MPP EU MPP
a a aa a a
η η η ηη η η
= ⋅ + ⋅ + ⋅
+ ⋅ + ⋅ + ⋅
0
0
( )
( )
M
M
T
AC
conv T
DC
p t dt
p t dtη
⋅=
⋅
∫
∫
0
0
( )
( )
M
M
T
DC
MPPT T
MPP
p t dt
p t dtη
⋅=
⋅
∫
∫
0
0
( )
( )
M
M
T
AC
T
MPP
p t dtt conv MPPT
p t dtη η η
⋅= ⋅ =
⋅
∫
∫
wMt
hfWicC
eeaii
ts
elrapmIIBims
where isMPPT efficienthese values ar
The variahighly emphasfor the geograpWith the incnstallations ha
comparison toCommission u
Weig
Pa
PM
Weig
Pa
PM
The quickevaluates highemphasizes machieve more nverter, than nverter.
Evaluationthat, local clstrategies affec
2. ETA İz Since the
effective on ocations coul
represent Turkalmost in the process, the measurementsIn some assInstitute’s meBasic measuren DMİ Men
minute resolushown in Fig 1
W
s the weightinncy at partialre listed in Taations in thesized in this fphical locatio
creasing peneave been mad
ool has been inutilizing the Sa
ghting Factor
artial MPP power
MPP, PVS/PDC,r
ghting Factor
artial MPP power
MPP, PVS/PDC,r
k comparisonher irradiation
more on the loprecise annua maximum
n of weightelimatic condicts inverters’
zmir
effect of climefficiency,
ld be done. Hkey (lat. E42ºmiddle (lat. EState Meteo
s database wasessments, Eeasurement daement set is tanemen Obserution. Annual1.
Weighted effici
ng factor and l MPP power
able:1. e lower irradformula, makins with highe
etration of Pde in southern ntroduced by acramento clim
Table
0,03
0,05
Table
0,04
0,1
n of two tablen region in mower part. Boual yield esti
m conversion
ed efficiency itions (latitudenergy efficie
matic conditiofurther resea
Here, İzmir haº-E36º), for it E38º30’). Duriorology Direas used as primEge Universiata base has aken during 2rvation Statiol distribution
iency measurem
is the sr. The indices
diation levelsing it less suiter solar irradiaVPSs, and mlocations, anoCalifornia Enmatic data [5]
1. Weighted eff
0,06
0,1
2: Weighted eff
0,05
0,2
es show that Cmore detail and
th can be useimation for aefficiency of
approach shde) and tracencies [6].
ns is known tarch for varas been chose
geographicaling the evalua
ectorate’s climmary data souiy Solar En
also been u2009 through 2on no. 1778
of these dat
ment of PV inve
static s for
s are table
ation. more other nergy ].
ηCECwas
who
fficiency formula
0,13
0,2
fficiency formula
0,12
0,3
CEC d EE ed to a PV f that
hows cking
to be rious en to lly is ation mate urce.
nergy used. 2012 9 at ta is
accotempmod
andcurr
wheTPV
Cη
OCV
SCI
erters: introduci
Using same C formula cons suggested as
ose coefficient
a coefficients fo
0,1
0,3
a coefficients fo
0,21
0,50
Fig. 1. 2009 irrM
Energy calcuording to EN
mperature depdule has been
irradiance anrent of a cSi m
ere,
1
4
CEC CEC
CEC
aa
ηη
= ⋅
+ ⋅
(, 1OC STCV β= ⋅ +
,SC STCSTC
GIG
= ⋅
ing ηİZMİR
structure witnsidering the h;
ts are shown i
or ηEuro.
0,4
0,5
or ηCEC.
1 0,5
0 0,7
radiation and tMenemen observ
ulations have 50530. In th
endent open calculated as,
nd temperatumodule has bee
is PV modu
1 2
4 5
MPP CEC
MPP CEC
aa
ηη
+ ⋅
+
( ))PV STCT Tβ ⋅ − ⋅
(1 ( PVC
Tα⋅ + ⋅ −
th the Europehigher irradia
in Table 2.
8 0,
5 1
3 0,0
5 1
temperature datvation station.
been made fohis document,
circuit volt,
ure dependent en calculated
ule temperatur
2
5
MPP CEC
MPP CE
aa
ηη⋅ +
⋅ +
ln 1G
G CC
⎛ ⎛ ⎞+ ⋅⎜ ⎜ ⎟⎜ ⎝ ⎠⎝
))STCT−
55
ean Efficiencytion condition
(5
,2
1
05
1
ta from DMİ
or cSi moduleirradiance an
tage of a cS
6
t closed circuas,
7
re ºC;
3 3
6 6
C MPP
EC MPP
ηη⋅
⋅
V RC C G⎞
− ⋅ ⎟⎟⎠
51
y, ns
5)
es nd Si
6
uit
7
552 İlker Ongun, Engin Özdemir
TSTC is standard test condition temperature 25 C°; G is solar irradiation W/m2; α is temperature coefficient of current 0,25%/ ºC; β is temperature coefficient of voltage 0,4%/ ºC; and technology depending correction factors CR, is 2,514 · 10 W/m2 CV, is 8,593 · 10 CG is 1,088 · 10 m2/W.
For simplification reasons, a 1 000 W PV array with Uoc,STC=100 V and Isc,STC=10 A has been considered.
The irradiation data has first been evaluated for annual energy distribution against irradiation classes. Results are presented in Fig:2. A quick inspection of the graph reveals
that, one third of annual energy yield would be harvested at and below 500 W/m2 irradiation levels. The other one thirds would be harvested between 500-750 W/m2 and above 750 W/m2 irradiation classes respectively.
This clearly shows that yield estimations made based on European efficiency wouldn’t be valid for İzmir irradiation since it assumes 79% of annual yield would be harvested at and below 500 W/m2 irradiation levels (referring Table:1).
CEC efficiency on the other hand, shows a closer match with İzmir irradiation profile at lower levels since it assumes 42% energy yield for that range (referring Table:1). However, this model still don’t show a proper match for medium and high irradiation levels for it assumes 95% of annual yield would be harvested below 750 W/m2 irradiation levels, which is not the case with İzmir data.
Fig. 2. 2009 irradiation profile evaluation for annual energy yield distribution.
The reason for European efficiency formula is not grasping İzmir energy yield can be its being based on hourly irradiation averages [4] instead of a high resolution irradiation measurement data set.
The failure of CEC efficiency may be resulted from its lack of considering temperature effect significant enough.
Further inspection of İzmir irradiation data and the energy yield calculations gives the weights in the Table:3 for 10% irradiation classes, values in the PMPP/PSTC row is representing the midpoints of these bins.
Table 3. Weighted efficiency formula coefficients for ηEuro.
PMPP/PSTC
(%) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
IZM (ALL) (%) 1,31 2,83 4,02 4,90 5,72 6,80 8,24 9,12 9,49 11,45 14,41 13,35 7,11 1,03 0,18 0,03 0,01
Cumulative energy yield 1,31 4,14 8,16 13,06 18,78 25,58 33,82 42,94 52,43 63,88 78,29 91,64 98,78 98,78 99,96 99,99 100
0,00
1,00
2,00
3,00
4,00
5,00
6,00
7,00
8,00
9,00
10,00
0,00
0,00
0,01
0,10
1,00
10,00
50 100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
1250
1300
Energy (%
)
Irradiation Time (%
)
Irradiation Classes (W/m2)
Annual Energy Distribution by Irradiation Classes (2009 ‐Menemen)
Energy %
cPm1
dSw
manTİa
a
bnmtb
One of th
calculations hPMPP/PSTC ratimodule tempe1 000 Wp cS
The valuedistribution ofSacramento. Iwould have hi
Since themuch of the yand CEC effnecessary for Thus, a reducİzmir efficiencand their respe
Table 5: Re
PMPP/PST
IZM (5) IZM (4)
These val
and
These sug
been tested agnumber of commeasures at ththese evaluatibelow.
(5)IZMη =
(4)IZMη =
W
he most impohere is, thereio, due to terature. This i PV array c
PM
EURCEIZMIZM
es in the tablef a PVPS in İzInverter efficiigher weights e lower generyield, the resofficiencies at r hot climateced number ocy formula. Fective weights
educed number efficien
TC 10% 302,3% 13,4% 12
ues in the tabl
ggested evalugainst Europemmercially avhe AIT Inveron graphs are
10%
70%
0,02
0,28
η
η
= ⋅ +
+ ⋅ +
10%
70%
0,04
0,53
η
η
= ⋅ +
+ ⋅
Weighted effici
ortant result e is no instathe diminishimeans that th
could produce
Table 4: We
MPP/PSTC 5RO 3C
M (EURO) M (CEC)
e reveal that, zmir is differeiency values fin İzmir cond
ration classes lution shown lower parts
s with high of weightings
Five and four s are shown in
of evaluation cncy formula.
0% 50% ,1% 21,8% 2% 21%
le yields,
uation formulean and CEC vailable PV invrter Test Labe shown Fig.
30%
90%
0,13
0,35
η
η
+ ⋅ +
+ ⋅
30%0,12 η+ ⋅ +
iency measurem
derived fromance above ng effect ofhere is no w
e 1 000 W po
eights for İzmir
5% 10% 153% 6%
4% 1% 6%
2%
energy generaent than in Trifor higher po
ditions. do not repreboth in Euro does not ssolar irradia
s are proposeevaluation cla
n Table 5.
classes for İzmir
70% 90%27,6 35,2%53% -
las have togeefficiencies f
verters’ efficiboratory. Thre
3 through Fi
50%0,22 η+ ⋅
50%0,21 η+ ⋅
ment of PV inve
m the 90%
f the way a
ower
throman
EuroTab
data calculated
5% 20% 2513% 5%
10% 7%
ation er or wers
esent pean seem ation. ed as asses
r
8
9
ether for a ency
ee of ig. 5
erters: introduci
oughout the ynners.
A comparisoopean and C
ble 4.
d for Euro and
5% 30% 5010% 412% 216% 212% 1
Fig. 3. Comp
Fig. 4. Compa
ing ηİZMİR
ear in İzmir,
on of İzmir CEC efficien
CEC classes.
0% 75% 108% 1% 53%9% 9% 26%
arison for a wid
rison for a rela
unless it is c
data based cncies are pre
00% 20% 5%
39% 34%
de voltage rang
atively low volta
55
ooled by som
alculations foesented in th
ge inverter.
age inverter.
53
me
or he
5
s
ciTd
ensTfd
crac
554
Fig. 5. Com 3. Concl The rem
summarized bThere is
climatic condinstalled in İz
This brings in data set to ach
Although evaluation of Pnot suitable fsince it is baThis inadequformula whicdifferent weig
Here withcould be madreliability. Besalso simpler consider.
mparison for a r
usion
markable conelow: a distinctive
itions, MPP pzmir would no
a need for furhieve a more re
it provides PV inverters, for yield esti
ased on a noruacy has beech makes usehting pattern.
h the İzmir effde with localsides the increthan the oth
relatively high v
nclusions of
e indication power generatot exceed 85%rther researcheliable result. a good basisEuropean eff
imations in srthern climateen fixed by e of the sam
ficiency formulized data seteased reliabilithers with 33
İlker
voltage inverter
this study
that, due toted by a PV a% of STC po
h using a multi
s for performficiency formusouthern locate data evalua
CEC efficime approach
ula, the evaluat in an enhaty, new formu
3% less term
r Ongun, Engin
r.
are
o the array ower. iyear
mance ula is tions
ation. ency with
ation anced ula is
ms to
Inst“DiEU
doctConInveInst
[1] T
[2] R
[3] A
[4] B
[5] F
[6] V
____*Co
n Özdemir
Acknowledg The authors
titute of Techstributed EneProject no. 22The content
torate thesis nversion Efficerters”, studititute, İzmir, T
References
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____________rresponding a
gements
of this papehnology suppoergy Resource28449”. ts of this p“Determinati
ciency for Tied in Ege
Turkey.
s
0, 2010, Overahotovoltaic InvPrivate Photovungsanlagen im
WE Energie AGen von „Euro-
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n Efficiency”, ess 2007 (Vol4
____________author: ilker.on
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