Proc. 29th IEEE PVSC, New Orleans, May 19-24, 2002 pp. 927-930.
USING A NATURAL AM1.5G SPECTRUM TO HELP DEFINE
AN AM1.5D SPECTRUM APPROPRIATE FOR CPV PURPOSES
1
1
1,2
1
David Faiman , Arnon Karnieli , Nurit Ninari , Vladimir Melnichak and Sareet Jacob
1
3
1,3
Department of Solar Energy and Environmental Physics
2
Wyler Department of Dryland Agriculture
The Jacob Blaustein Institute for Desert Research
Ben-Gurion University of the Negev
Sede Boqer Campus, 84990 Israel
Department of Chemistry, Brown University, Providence, RI 02912, USA
ABSTRACT
Spectral measurements were performed of direct
beam and global solar irradiance at normal incidence. The
measurements were taken at Sede Boqer, during
noontime, on a selection of cloudless days during the
period December 2001 – March 2002. For those days
having a low level of diffuse radiation, the ratios of direct
beam to global spectra were found to follow a previously
suggested, semi-empirical, 2-parameter formula based on
Rayleigh scattering. For one of the days, with an
unusually high level of diffuse radiation, this formula did
not provide an adequate fit to the data. In order to provide
an adequate fit it was found necessary to effect an ad hoc
modification to the algebraic form of the original formula.
INTRODUCTION
Because of their sensitivity to temperature, illumination
intensity and light spectrum, PV cells are characterized
under specified standard values of these external
parameters. So-called Standard Test Conditions (STC)
o
specify: a cell temperature of 25 C, an illumination
-2
intensity of 1000 W m , and a computer-generated
spectrum referred to as AM1.5 [1]. The latter was devised
so that it approximates the intensity of sunlight that would
be received on a tilted plane surface, on a clear day, with
the sun at a zenith angle of arcsec 1.5, and for a model
atmosphere containing specified concentrations of water
vapor, aerosol, etc. [2].
Recently, owing to increased interest in PV cells that
are designed to operate under high concentration levels of
solar energy (so-called CPV cells), it has been deemed
desirable to distinguish between global AM1.5G and direct
AM1.5D reference spectra. The motivation behind this
need is the realization that if the global clear sky intensity
-2
is, say, 1000 W m , the direct beam fraction would be
-2
substantially smaller, typically 800 W m . Hence, the use
-2
of a 1000 W m reference intensity for characterization
purposes would tend to under-rate a CPV cell relative to a
non-concentrator PV cell. Furthermore, given that it might
be desirable to adopt a lower level of illumination as a test
standard for CPV cells, it is natural to inquire what
spectrum should be used for this purpose.
It will be realized that this entire argument is mainly
cosmetic because the performance of a cell, whether PV
or CPV, under any set of standard operating conditions is
by no means a universal index of its relative excellence.
For example, if one cell has a higher efficiency than a
second cell under one set of external conditions, it is
entirely possible for the second cell to have a higher
efficiency than the first under a different set of conditions.
What one really needs to know, for comparison purposes,
is how the current-voltage characteristics of the two cells
depend on changes in temperature and light quality over
the entire range of their operating conditions.
Nevertheless, assuming it is agreed that a standard
AM1.5D reference spectrum is truly needed, an
immediate question arises as to how it should be
generated. One way might be to adopt the same AM1.5
spectrum for both types of cell characterization. Another
way, and one that has served as a basis for
recommendation as an international standard [3], is to use
a uniform set of assumptions concerning the atmospheric
constituents in order to computer-generate a pair of
standard AM1.5G and AM1.5D spectra.
In the present paper we examine a third possible
approach. It takes advantage of the known similarity [4] of
natural clear-sky, noontime spectra at Sede Boqer (Lat. =
o
o
30.9 N, Lon. = 34.8 E, Alt. = 470 m) to the international
standard AM1.5G spectrum [1].
METHODOLOGY
Our method is to measure pairs of clear-sky,
noontime, solar spectra, both normal global and direct
beam, and compare their relative shapes. This study was
started on the winter solstice day of the year 2001. At that
time we discovered that the ratio of the beam/global
spectra could be well approximated by a simple 2parameter formula based on a model in which Rayleigh
Proc. 29th IEEE PVSC, New Orleans, May 19-24, 2002 pp. 927-930.
4
B/G = 1 / [ a + (b/λ) ]
(1)
where a and b are constants.
The present paper extends our previous work by
studying additional pairs of spectra measured on sample
days during the first three months of 2002. We shall
examine the extent to which our previously proposed 2parameter formula remains valid, and the month-to-month
variation in parameter values observed for those
situations in which the simple model holds.
EXPERIMENTAL METHOD
Solar spectra were measured at Sede Boqer at
noontime on sample cloudless days. For this purpose a
Li-Cor L-1800 spectroradiometer, having a wavelength
range 300 - 1100 nm and a measurement interval of 2
nm, was employed. Global spectra were measured using
the Teflon dome that is attached to the body of the
instrument, with the latter tilted at normal incidence to the
incoming beam radiation. Direct beam spectra were
measured by adding a collimating pipe with a ratio of 10:1
for its length to internal diameter. For overall calibration
purposes, Eppley PSP and NIP full-spectrum radiometers
were employed, the calibration of which can be traced to
the IPC-IX international comparison. It should be
emphasized that although our spectroradiometer had
recently been re-calibrated by its manufacturer, its
absolute calibration is of little concern to us as our main
interest is in the ratio of pairs of measurements made with
this instrument.
Because each spectral scan lasts approximately 20 s
(when scanning the range 300 nm < λ < 1100 nm at 2 nm
intervals), there is an intrinsic degree of uncertainty in the
definition of the beam/global ratio. Our experimental
method therefore consisted of making, as rapidly as
possible, a series of alternate global and direct beam
spectral scans, during a half-hour time period starting
approximately 15 min before solar noon. In this manner, a
given direct beam scan could be compared with the global
scans that preceded and followed it, in order to test for
atmospheric stability.
Spectral scans were made on the dates: December
21, 2001; January 17, 2002; February 28, 2002 and
March 24, 2002.
RESULTS
All spectral scans were made on basically cloudless
days. Table 1 lists the average values of the normal global
and direct beam radiation measured while the spectral
scans were in progress. Also shown is the reading from a
nearby shadow band pyranometer (uncorrected for
shading ring losses), and some other relevant geometrical
parameters of interest.
Table 1: Solar irradiance and geometrical factors during
the spectral scans discussed here. [Horiz. Diffuse =
uncorrected shadow band reading, Air Mass = pressurecorrected value]
Date
Normal
Global
-2
[Wm ]
1083±9
1097±7
1095±9
1105±6
21.12.01
17.1.02
28.2.02
24.3.02
Direct
Beam
-2
[Wm ]
930±12
937±9
762±16
917±9
Horiz.
Diffuse
-2
[Wm ]
85±3
94±3
229±6
150±2
Zenith
Angle
[Deg.]
54.3
51.7
39.5
30.2
Air
Mass
1.62
1.52
1.22
1.09
One observes from Table 1 that 28.2.02 was an
unusually hazy day. For this reason its spectral scans will
be discussed separately from those taken on the other
dates.
If, for the purpose of this discussion, we label each
day’s scans, G1, B1, G2, B2, ….. Bn-1, Gn, then all pairs of
ratios B1/G1, B1/G2, B2/G2, … Bn-1/Gn, were first graphed
and examined visually. The graphs fell into two classes:
Class I graphs increased “almost” monotonically with
wavelength, whereas Class II graphs had varying
amounts of waviness superimposed on a monotonically
increasing shape similar to that of the Class I graphs.
More careful examination of the Class II graphs revealed
that, in addition to slight bumps and dips at fixed
wavelengths (which correlate with known water vapor
absorption bands in the atmosphere, and which can also
be discerned in the Class I graphs), there were other,
often much stronger, dips at arbitrary wavelengths. Fig.1
shows a typical Class II data set.
0.8
Ratio of spectral runs B3 and G4
Sede Boqer, 28.2.02
0.7
Beam/Global Ratio
scattering is the dominant factor. If B and G represent
simultaneously measured direct beam and normal global
solar spectra, respectively, and λ is the wavelength, then
the suggested relationship is [5]:
0.6
B3/G4
0.5
0.4
0.3
200
400
600
800
1000
1200
Wavelength [nm]
Figure 1: A typical set of Class II data (No attempt was
made to fit such sets)
The waviness that characterizes Class II data sets
was almost certainly brought about by intensity variations
in irradiance (probably caused by invisible passing clouds)
while a particular scan was in progress. For this reason all
Class II data were discarded as being of no physical
Proc. 29th IEEE PVSC, New Orleans, May 19-24, 2002 pp. 927-930.
interest. The Class I data sets were then earmarked for
more detailed study.
In the case of data from the December, January and
March scans, fits were made to eq.(1), using the method
of least squares. In all cases, extremely good fits were
2
obtained (i.e. low values of χ ). Fig. 2 shows a typical
example of a Class I data set and the corresponding fitted
curve.
Ratio of spectral runs B8 and G8
Sede Boqer,28.2.02
0.7
Beam/Global Ratio
Results for the days with low haze levels
0.75
B8/G8
0.65
Fit(1.40,266)
0.6
0.55
Model: y = 1/[a + (b/lambda)^4]
a = 1.403, b = 265.9 nm,
chi sq. = 0.00013
0.5
0.45
200
400
600
800
1000
1200
Wavelength [nm]
1
Ratio of spectral runs B5 and G5
Sede Boqer,17.1.02
Figure 3: A typical data set for the day 28.2.02,with
superimposed least-squares fit to eq.(1)
B5/G5
0.8
Fit(1.09,321)
For this reason, higher powers of the inverse
wavelength term were explored. The fifth power was
found to be an improvement but it was still too “round at
the elbow”. However, with higher powers, good fits could
be obtained. Specifically, by adopting a sixth-power
expression of the form:
0.7
0.6
Model: y = 1/[a + (b/lambda)^4]
a = 1.089, b = 320.7 nm,
chi sq.= 0.00002
0.5
0.4
6
B/G = 1 / [ a + (c/λ) ]
0.3
200
400
600
800
1000
Wavelength [nm]
Figure 2: A typical Class I data set with superimposed
least-squares fit to eq.(1)
Table 2 lists the resulting mean values of the
parameters a and b, together with their standard
deviations among all Class I data fits for each date in
question.
Table 2: Mean (and 1 σ) values of the parameters
resulting from fitting eq.(1) to all Class I data sets for
noontime spectral scans taken at Sede Boqer on clear
days during the period December 2001 – March 2002.
Date
21.12.01
17.01.02
24.03.02
Class I
data sets
4
5
3
Parameter a
1.082 ± 0.004
1.093 ± 0.003
1.132 ± 0.004
(2)
1200
Parameter b
[nm]
305.9 ± 1.1
321.5 ± 2.5
282.0 ± 1.2
Results for the day with high haze level
where a and c are constants, adequate fits could be
obtained. Fig.4 shows a typical sixth-power fit (using the
same data set shown in Fig.3).
0.75
0.7
Beam/Global Ratio
Beam/Global Ratio
0.9
Ratio of spectral runs B8 and G8
Sede Boqer, 28.2.02
B8/G8
0.65
Fit6(1.42,292)
0.6
0.55
Model: y = 1/[a + (c/lambda)^6]
a = 1.419, c = 291.9 nm,
chi sq. = 0.00002
0.5
0.45
0.4
200
400
600
800
1000
1200
Wavelength [nm]
Figure 4: Same data as Fig.3 but with superimposed
least-squares fit to eq.(2)
DISCUSSION AND CONCLUSIONS
For the Class I data sets taken on 28.2.02, it was
2
found that only poor fits (χ values were typically 5x higher
than those for the clear-day fits) were possible to the
algebraic form given in eq.(1). Fig.3 shows the best fit that
was obtained from among all data sets for this day.
4
Qualitatively one observes that the (b/λ) term does
not allow a steep enough initial rise with λ, which is a
characteristic of all data sets measured on this day.
If we compare the present results, obtained from a
study of selected days during 4 consecutive months, with
those from our published study [5] of a single day
(21.12.01), a number of clarifications become apparent.
First, for “clear” days, the originally suggested, semiempirical, formula, Eq(1), remains valid as a good
description of the ratio of direct-to-global spectra.
Furthermore, the month-to-month changes in the
parameters a and b are relatively small, as was to be
expected from our previous theoretical discussion [5].
Proc. 29th IEEE PVSC, New Orleans, May 19-24, 2002 pp. 927-930.
However, because the changes are relatively small,
and because, as we have seen here, the diffuse fraction
can have a qualitatively large effect, our data sample is
still too small to enable us to determine whether any
underlying seasonal trend exists in the variation of these
parameters. Because a seasonal trend was to be
expected for parameter a [5], this study will continue.
The interesting new result is the qualitatively different
shape that results when high haze levels are present. A
theoretical explanation for this observation is rendered
difficult by the fact that what we measure as “direct beam”
irradiance becomes less and less well-defined as the
haze level increases. On clear days, the length-toaperture ratio of 10:1 that characterizes the construction
of standard pyrheliometers represents approximately 10
solar diameters. In such situations the pyrheliometer
records essentially all of the direct beam radiation and a
negligibly small amount of spurious diffuse radiation.
However, as the haze level increases, so too does the
sun’s circumsolar halo. This results in an increasing
ambiguity as to how much of the pyrheliometer reading is
true direct beam radiation. For this reason, eq.(2) should
be regarded as a purely empirical formula, with no
theoretical basis at the present time. Its only value lies in
the fact that it provides a simple 2-parameter description
of the direct-beam spectrum (relative to the global
spectrum) on very hazy days. Such a description may be
useful for improving the understanding of CPV cells
operating under high levels of solar concentration on such
days. In any event, the possibility of characterizing
outdoor spectral conditions by two easily-measurable
parameters would lend further quantification to the testing
of CPV cells and modules.
ACKNOWLEDGMENTS
This research was performed with partial funding from
the Israel Ministry of National Infrastructures. One of the
authors [DF] is indebted to Tom Stoffel for operating our
cavity radiometer during the IPC-IX inter-comparison,
25.9-13.10.2000, Davos, Switzerland, to Daryl Myers for
some penetrating insights upon reading an early version
of this study, and to Indra Karki for assistance with data
processing.
REFERENCES
[1] International Standard: Photovoltaic devices, Part 3;
Measurement principles for terrestrial photovoltaic (PV)
solar devices with reference spectral irradiance data,
CEI/IEC 904-3, 1989.
[2] R.E. Bird and R.L. Hulstrom, Review, evaluation, and
improvement of direct irradiance models, ASME J. of
Solar Energy Eng. 1981; 103: 182-192.
[3] D. Myers, K. Emery and C. Gueymard. Proposed
reference spectral irradiation standards to improve
photovoltaic
concentrating
system
design
and
performance evaluation, (Poster 3 P1.8 at this
conference).
[4] D. Berman and
time-dependence of
with and without
environment, Solar
1997; 45: 401-412.
D. Faiman, EVA browning and the
I-V curve parameters on PV modules
mirror-enhancement in a desert
Energy Materials and Solar Cells
[5] D. Faiman, A. Karnieli and S. Jacob, Concerning the
relationship between clear-sky, global and direct beam,
solar spectra, Progress in Photovoltaics (accepted for
publication).