site-dependent system performance and optimal inverter sizing of ...

SITE-DEPENDENT SYSTEM PERFORMANCE AND OPTIMAL INVERTER SIZING OF
GRID-CONNECTED PV SYSTEMS
Bruno Burger' & Ricardo Riithe
'Fraunhofer Institute for Solar Energy Systems SE, Deparfment of Electrical Energy Systems
Heidenhofstr, 2,791 IO Freiburg - GERMANY
Tel.: *49 761 4588 5237 FAX: +49 761 4588 9237 Email: bruno.burger@ise.fraunhofer.de
'LABSOLAR - Laboratorio de Energia Solar & LabEEE - Laboratbrio de Eficigncia Energetica em Edificaq6es
Universidade Federaf de Santa CatarindUFSC, Caixa Postal 476, Florianopolis - SC, 88040-9QO. BWlL
Tel.: +55 48 331 5174 FAX: +55 48 331 7615 Email: ruther@mboxl.ufsc.br
ABSTRACT
The sizing of gridconnected PV systems does not
usually take into account the site-dependent peculiarities
of the solar irradiation distribution characteristics. Because
of the perceived notion that PV systems will hardly ever
have a DC output equal to or above their STCrated
nominal power, inverters are usually sized with a nominal
AC output power some 30% (sometimes even more)
below the PV array nominal power. This practice might
lead to considerable energy losses, especially in the case
of PV technologies with low temperature coefficients of
power and at sites with warm climates and an energy
distribution of sunlight shifted to higher irradiation levels.
We discuss the consequences of the time resolution of the
irradiation data set used to determine a particular site
irradiation distribution on inverter siring. Most of the
available irradiation data measured at individual sites are
hourly averages, which read to fiftering of irradiation
peaks, which might result in inaccurate performance
estimations. When calculating inverter yearly efficiencies
using both hourly averages and one-minute averages of
the solar irradiation, we can show that the actuaf losses
due to inverter undersizing increase with increased time
resolution, revealing that hourly averages hide important
irradiation peaks.
INTRODUCTION
Grid-connected applications are the fastest growing
segment of the photovoltaic (PV) market. with premium
feed-in tariffs available in many countries [I]. In many
situations, optimizing the PV amy energy yield will justify
the extra cost that might be incurred by this optimization,
and inverter sizing might be an interesting design aspsct
to look into. System design recommendations for gridconnected
PV installations usually lead to inverters with a
nominal power considerably smaller than the PV array's
nominal power. Because of the perceived notion that PV
systems will hardly ever have a DC output equal to or
above their STC-rated (STC = 1000 W/m2; AM 1.5
spectrum, operating cell temperature 25%) nominal
power, inverters are usually sized with a nominal power
some 30% (sometimes even more) below the W array
nominal power [2-7]. Furthermore, inverter technology has
evolved considerably in recent years, with improved
efficiency curves especially at partial loads, and PV
module nominal power tolerances, which used to be +or-
10% (in practice more often -10% than +IO% [S.9]) are
today evolving to + or - 2.5% [IO]. In practice, recent
measurements on 100 new PV modules made at the
Fraunhofer ISE [I 11 have resulted in a mean-3.4% power
deviation from STC, with a considerable amount of
modules with deviations close to -10%.
Especially for the market-dominant crystalline silicon
(c-Si) PV technology. which presents a strong negative
coefficient of power, the high irradiation levels that lead to
maximum output are associated with high cell operating
temperatures, which usually prevent the PVarray to reach
its nominal DC power. This rationale has led to a rule of
thumb, by which inverter nominal AC power can be
designed lower than the PV array nominal DC power. This
'practice might lead to considerable energy losses,
especially in the case of PV technologies with IOW
temperature coefficients of power like thin film amorphous
silicon (a-Si) and Cadmium Telluride (CdTe). at sites with
warm climates, high incidence of clear skies, and an
energy distribution of sunlight shifted to higher irradiation
levels [IZ]. It has been shown that +Si output
performance stabilizes at different levels depending on the
particular site prevailing temperature conditions, with
higher stabilized performance levels at sites with a year-
round higher temperature [I 31.
State-of-the-art inverters reach peak efkiencies in
the 95% - 97% range, with efficiency curves which differ
in shape due to basically two different optimization
approaches: (i) a low self-consumption strategy leads to
high efficiency at small partial loads (at 0 to 10% of
nominal power range). at the expense of performance at
the higher end of the curve (at nominal power) and peak
efficiency at partial loads usually below 50% of nominal
load; and (ii) a small input power level dependency
strategy (for loads above - 30% of nominal) leads to good
performance at the higher end of the curve, at the
expense of performance at small partial loads (at 0 to 10%
of nominal power range) [2].
0-7803-87074/05/$20.00 02005 IEEE.
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The first strategy is more commonly used by inverter
manufacturers and typically, inverter efficiencies peak at
30 to 40% of nominal power, with somewhat reduced
effkiencies at full load. Undersized inverters might
therefore operate closer to full capacity (and therefore
below maximum performance levels) more often,
depending on the site distribution of irradiation levels.
Because undersized inverters will operate at full load more
often, they will reach operating temperatures that might
trigger temperature-reducing features of their algorithms,
leading to further energy losses. Figure 1 shows a typical
inverter efficiency vs. % of nominal capacity curve,
including power limitation losses due to overloading [ 141.
65 I I
-_
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Pk I L,
Fig. 1: Typical inverter efficiency curve as a function of loading (X
of nomiiral AC power), including power limitation lases for input
power levels above the inverter nominal p e r 1141.
Radiation levels above 900Wlm' occur some 10% of
the time, and the coriesponding energy fraction is
above 31%. Figure 4 shows, also for the Freiburg site, but
for mean hourly values; the energy distribution of the
incoming solar radiation. with the same format presented
in figures 2 and 3, The figure shows how the hourly
averages tend to smooth out maxima, resulting in a
distribution profile which is quite different from the ones
resulting from figures 2 and 3. and a shift of the energy
content to lower irradiation levels. While still over 63% of
daytime hours present radlation levels 1.300W/m2, with
a corresponding energy content of some 20% of the total
incident energy, less than 3% of daytime hours present
radiation levels 1 1000Wlm2, corresponding to some 9%
of the incident energy. These results differ considerably
from what is seen for IGseconds or oneminute
resolutions, demonstrating that the use of hourly averages
hides important information and is not representative of
the real solar resource distribution profiles. Radiation
levels above 900Wlm' occur - 7% of the time, and the
corresponding energy fraction Is just above 23%. It is
thus clear that the real energy content at these higher
irradiation levels is underestimated when using hourly
averages.
r51i I .
I 2f2tL7
I I I L
IRRADIATION DATA SAMPLING RATE
Based on global horizontal irradiation data measured
by pyranometers located at the Fraunhofer ISE in Freiburg
(48' N. Germany, with typical yearly global horizontal
radiation - 1150kWh/mz) at 10-second intervals, and at
the Solar Energy Research Laboratory - LABSOLAR in
Florianopolis (27' S, Brazil, with typical yearly global
horizontal radiation - 1 550kWh/m2) at one-minute
intervals, we have studied the distribution of the incoming
solar radiation at these sites as instant values (Freiburg),
and as oneminute and hourly averages (Freiburg and
Florianopolis) at 30 degrees tilted surfaces.
Figures 2 and 3 show, for the Freiburg site and
respectively for 10-second instant values and for oneminute
averages, the energy distribution of the incoming
solar radiation, distributed at 50W/m2 bins, with bars
representing the percentage of the energy content at the
respective radiation level interval, and solid lines
representing the percentage of daytime hours (i.e.,
irradiation > 2Wlm ) when radiation levels occur at the
particular interval considered. The results for these two
different time resolution sampling rates are very similar,
and both figures demonstrate that while over 63% of the
daytime hours present radlation levels 5 300W/m2, the
corresponding energy content represents only some 20%
of the total incident energy. Looking at the high end of
the radiation level distribution shows that onty some 5% of
the daytime hours present radlation levels 2 1 OOOW/mz,
but the corresponding energy content is over 16%.
I
I
Fig. 2: Distribution of instant dues (90 sac. resolution =
3.153.600 instant values) of solar radiation d 30' tilt at the
Freiburg site. sorted at 50W/m2 bins, with bars representing the %
of the solar energy content ai the paticular interval, and the did
line representing the % of daytime hours at the respecthm
irradiation level.
0 2W 400 Bw 800 1COO 12W Wr"
Fig. 3: Distribution of tho, one-minute averages (525.600 mean
values) of the solar radiation at 30" I at the Freiburg site, sorted
at 50Wlm' bins, with bars representlng the % of the solar energy
content at the particular interval, and the solid line presenting
the % of daytime hours at the respective iadiation level.
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Fig. 4: Distribution of the hourly alverages (8760 mean dues) of
the solar radiation at 30' tilt at the Freiburg site, sorted at 50W/m2
bins. with bars representing the % of the solar energy content at
the particular interval, and the solid line representing the 96 of
daytime hours at the respective irradiation level.
looking at the solar energy resource distribution at
the Florianopolis site, respectively at oneminute and
hourly averages, figures 5 and 6 show that while over 50%
of the daytime hours present radiation levels
300Wlm2, the corresponding energy content is less than
15% of the total incident energy. At these low-light
levels there is not much difference between the two
different time resolutions. Considerable differences
emerge when looking at the high end of the radiation level
distribution. which shows for the oneminute averages that
some 9% of the daytime hours present radiation levels
- s t000W/m2, with a corresponding energy content of
some 23%; hourly averages for the same range
correspond to around 6% of daytime hours, and below
11% of the total energy content. Radiation levels above
900W/m2 occur some 16% of the time when looking at
one-minute averages, and below 3% of daytime hours
when using hourly averages, with corresponding energy
fractions respectively above 38% and 25%.
Fig. 6: Distributim of the hourly averages (8760 mean values) of
the solar radiation at 30' tilt at the Fforianopolis site, sorted at
50W/m2 bins, with bars representing the % of the solar energy
content a1 the particular interval, and the solid line rqressnting
the % of dayl" hours at the respective irradiation level.
INVERTER YEARLY EFFICIENCY AND LOSSES
Figure 7 shows inverter yearly efficiency curves.
including power limitation losses, for the Freiburg site as it
function of the relation between the solar generator DC
power rating and the inverter AC nominal rating.(ratio PSG
I PinvAc-nom), calculated for the three different solar
radiation data time resolutions studied. The solid line
corresponds to instant (10-second) data, the dashed line
corresponds to mean minute values, and the dotted line
corresponds to mean hourly values. It can be noticed that
hourly averages lead to undersized inverters with respect
to the PV generator DC nominal power. Figure 8 shows
the inverter yearly losses due to power limitation for the
same irradiation data, again demonstrating that hourly
averages of solar radiation lead to underestimating the
real losses that. will occur with increasing the solar
generator size with respect to the inverters nominal power.
Figures 9 and 10 show respectively for the Florianopolis
site, the inverter yearly efficiency curves. including power
limitation losses, and the inverter yearly losses due to
power limitation. Solid lines correspond to mean minute
values, and dashed lines correspond to mean hourly
values. It can be seen that if PSG I Pinv.~~-nom is set above
1.1, hourly averages tend to overestimate efficiency and
underestimate losses, demonstrating the experimental
artifact induced by the use of the lower time resolution
radiation data.
I
Fig. 5: Distribution of the oneminute averages (525.600 mean
values) of the solar radiation at 30' tiit at the Florianopdis site,
sorted at 50W/m2 bins. with bars representing the % of the solar
energy content at the particular interval, and the solid line
representing the % of daytime hours at Re respective inadiation
level.
I
CONCLUSIONS
Using instant (10-seconds), one-minute and hourly
averages of solar radiation data for Freiburg - Germany,
and one-minute and hourly averages of solar radiation
data for Florianopolis - Brazil. we have shown the effects
of data sampling on the optimum inverter sizing of gridconnected
PV systems. When calculating inverter yearly
efficiency values, and yearly losses due to inverter power
limitation, using both hourly averages and onwninute
averages of solar irradiation, we have demonstrated that
the estimation of the actual losses due to inverter
e
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~~ -
undersizing increases with increased time resolution of the
radiation measurements, revealing that hourly averages
hide important irradiation peaks. In fact, results with hourly
averages are an experimental artifact, and lead to an
estimation of the solar energy resource distribution that
does not correspond to reality. Hourly averages of
irradiation values lead to inverter undersizing and the
associated energy losses.
Fig. IO: Inverter yearly losses due to power limitation af the
Flohnopolis siie vs. inverter sizing. Solid line = mean minute
values; dotted line = mean hourly values of the solar radiation.
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Fig. 7: Inverter yearly Efficiency, including power limitation losses,
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Fig. 8 Inverter yealy losses due to power limitation at the
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