The geometry of collimators for devices or instruments dealing with terrestrial direct sunlight is discussed. Effects of the opening angle and slope angle of a collimator on the measurements are investigated with regard to variations of turbidity and air mass. Based on this investigation, geometric dimensions for collimators and certain realistic terrestrial reference conditions are recommended for the purpose of solar cell calibration in terrestrial applications

Chai, A. T.

English

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https://ntrs.nasa.gov/search.jsp?R=19770019678 2020-03-22T09:33:40+00:00Z
JUL 1977
^ Sn FEED
ERDA/NASA 1022/76/5
NASA CP-2010
Technical Report U-6
I
(NASA-CP-2010) SOME BASIC CONSIDERATIONS OF
MEASUREMENTS INVOLVING COLLIMATED DIRECT
SUNLIGHT (NASA) 17 p HC A02/MF AO1 CSCL 14A
U77-26622
Unclas
H1/44 35425
SOME BAS I C CONS I DERATION S OF MiASUREIVENTS
INVOLVING COLLIMATED DIRECT SUNLIGHT
An-Ti Chai
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Oh ®g
Prepared for
ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION
Office of the Assistant Administrator for
Solar, Geothermal, and Advanced Energy Systems
Division of Solar Energy
Under Interagency Agreement E(49-26)-1022
Presented at Second Annual Photovoltaic Measurements Workshop
Baton Rouge, Louisiana, November 10-12, 1976
SOME BASIC CONSIDERATIONS OF MEASUREMENTS
INVOLVING COLLIMATED DIRECT SUNLIGHT
by An-Ti Chai
Lewis Research Center
National Aeronautics and Space Administration
Cleveland, Ohio
ABSTRACT
The geometry of collimators for devices or instruments dealing with
terrestrial direct sunlight is discussed. Effects of the opening angle
and slope angle of a collimator on the measurements are investigated with
regard to variations of turbidity and air mass. Based on this investiga-
tion, geometric dimensions for collimators and certain realistic terres-
trial reference conditions are recommended for the purpose of solar cell
calibration in terrestrial applications.
SUMMARY
The geometry of collimators for devices or instruments dealing with
terrestrial direct sunlight is discussed. Effects of *re opening angle
and slope angle of a collimator on the measurements are investigated with
regard to variations of atmospheric turbidity and air mass. It is pointed
out that the slope angle should be specified after considering the colli-
mator size and the tracking capability of the instrument. The size of
opening angle affects the amount of circumsolar radiation and skylight
entering a collimator and the uniformity of illumination at the receiving
aperture. Based on this analysis, an opening angle in the range of 2.5-30,
which is equivalent to a 10 to 1 collimation ratio, with a slope angle
between 10 and 1.760 should be appropriate for the purpose of solar cell
-2-
calibration in terrestrial applications.
The reference conditions, specifically the air mass and atmospheric
turbidity for solar cell calibration are also discussed. It is recommended
'	 that the product of air mass and turbidity parameter be restricted to no
greater than 0.25 to avoid excessive nonuniformity of illumination at the
receiving aperture of a collimator.
INTRODUCTION
Owing to the technical difficulty in obtaining full knowledge of the
relationship between the global solar irradiance and general atmospheric
conditions, it has been a general consensus that solar cell calibration
under natural sunlight should be done under collimated direct sunlight
(ref. 1). In doing so, one is rid of the complication of the general sky
conditions, most prominently the cloud effects; however, one is confronted
with a new problem - how to construct a proper collimator.
The Joint International Radiation Conference at Davos in 1956 adopted
recommendations with regard to the construction of collimators used on
pyrheliometers (refs. 2 and 3). Unfortunately, these recommendations may
not be universally practiced. The solar cell community, for example, has
not strictly followed these recommendations. In a report entitled, "Interim
Solar Cell Test Procedures for Terrestrial Applications" (ISCTPTA), which
was issued in July 1975, (ref. 1) guidelines on the requirement of collima-
tion and reference conditions were presented for calibration of standard
cells. These guidelines do not appear to adequately cover the requirements
of collimators in certain realistic circumstances. This paper is intended
to clarify some of the confusions associated with these requirements and
EM
406-
-3-
to develop requirements for collimators for solar cell measurements.
BASIC CONSIDERATIONS IN COLLIMATOR DESIGN
There are three angles associated with the aperture conditions of
a collimator. If the radius of the limiting aperture is R, the radius
of the receiving aperture r, and the distance between them L, the angles
can be specified as (fig. 1)
the opening angle: 9 0 = tan-1 R
the slope angle: 8s = tan-1 R r
the limit angle: 8 R = tan-1 R ^+ r
According to a recommendation adopted at the Joint International Radiation
Conference at Davos in September 1956, (refs. 2 and 3), the slope angle
8s should be between 10 and 20 while the opening angle 8 0 must be less
than 40 . Many pyrheliometer manufacturers and instrument designers do not
follow the recommendations strictly, and they often specify only one angle -
the opening angle, or equivalently the full aperture angle, central angle,
acceptance angle, field of view, etc., which are two times the opening angle.
Frequently the ratio of a collimating tube length to its diameter (or
aperture diameter) is also used.
Specification of two of the three basic angles is necessary and suffici-
ent for complete design of a collimator. Opening angle and slope angle are
usually used for this purpose. In the following sections effects of these
two angles on measurements will be analyzed with respect to potential tracking
and radiation errors.
-4-
Slope Angle
The slope angle of a collimator is determined by several factors:
(angular) size of the light source, initial pointing error, and subse-
quent tracking error of the instrument during measurements. To show the
importance of having a proper slope angle, consider an extreme case, say
es = 0.
If the collimator is perfectly aimed at the center of the solar disk,
a point near the edge of the receiving area at the bottom of the tube views
only part of the solar disk (fig. 2). This leads to a nonuniformity of
intensity on the receiving area. Pointing error and tracking error make
the situation worse; the solar disk can be out of the view completely from
certain edge points. The nonuniformity of irradiance at the receiving area
could be large under these circumstances.
It is quite obvious that even if the collimator is perfectly aimed,
the slope angle has to be at least half the angular span of the solar disk
so that all parts at the receiving area can be illuminated by the entire
solar disk. Allowing imperfect aiming, it is necessary to have a slope
angle not less than the sum of: (a) one-half of the angular span of the
solar disk, frci., center to rim (0.26 0); (b) initial pointing error; and
(c) subsequent tracking error of the device.
In ISCTPTA the tracking accuracy was allowed to be ±2 0 . If the allowed
pointing error were as low as 0.25 0 , the slope angle of the collimator would
have to be 2.760 . If the full aperture angle (28 0) is 5.70 as specified in
ISCTPTA, and the radius of receiving area is 1.5 cm for a typical 2 cm x
2 cm size standard cell, then the length of the collimator must be over 837 cm.
I
I
doo
-5-
Collimators of such length are quite impractical for day-to-day calibra-
tion of solar cells.
In view of the fact that there are inexpensive solar trackers com-
mercially available with accuracy better than 10 , the tracking requirement
should be within ±(es - 0.76°) with 8 s , the slope angle, specified no
greater than 1.760 . With better tracking, smaller slope angles can be
used but should be no less than 10 .
Opening Angle
The size of the opening angle determines how much radiation passes
through the collimator. In addition to the direct solar radiation, cir-
cumsolar radiation and skylight also enter the collimator due to Mie
scattering by atmospheric aerosols and Rayleigh scattering by atmospheric
molecules. Ideally, one would like to use a collimator of very small open-
ing angle to eliminate the circumsolar radiation and skylight; however, it
is not practical to decrease the opening angle much below 5.7 0/2, which is
equivalent to the 10 to 1 collimation ratio found on many commercial pyre-
heliometers. For example, consider a collimator of 20 to 1 ratio (opening
angle of 1.43°). If the slope angle is 1.26° as discussed in the previous
section, a 1.5 cm radius receiving aperture would require a collimator
nearly 500 cm in length. Even with a slope angle of 1°, the length would
be close to 200 cm. Thus a 20 to 1 collimator is much too long for prac-
tical use. In the following discussion, the comparisons are made only
between collimators of 10 to 1 and 5 to 1 ratios in order to estimate the
circumsolar radiation and skylight received through the collimator, uni-
formity, and relative errors in measurement.
Ilk	 --	 r
	
i
-b-
Circumsolar radiation received through the collimator. - The circum-
solar radiation due to Mie scattering by atmospheric aerosols is higly
directional, with its major portion concentrated in the forward direction.
In actual measurement, it is difficult to separate the forward scattered
light from the direct sunlight. A certain amount of circumsolar radiation
must be included in the measurement.
Summarizing the data and analysis from a number of investigators,
Angstrom and Rodhe (ref. 4) presented in graphical form the dependence of
radiation from the solar aureole on turbidity p,:.:ameter ms and on full
aperture angle of a measuring instrument. The graph of this relationship
is reproduced here (fig. 3) for reference. The relative air mass is m and
B is the turbidity coefficient. The amount of circumsolar radiation is
measured in percentage of the direct radiation from the solar disk.
According to figure 3, for m$ - 0.2 the circumsolar radiation received
through the 10 to 1 (5.7 0) collimator is 4.7% of the direct radiation and
7.8% through the 5 to 1 (11.3 0) collimator. The difference in circumsolar
radiation receivea by these two collimators is then 3.1% of direct. For
ms - 0.1 this difference reduces to 1.5%. It has been proposed that use of
a collimator with large opening angle which allows all of the circumsolar
radiation to be included in the measurements could be advantageous. However,
there are other factors such as skylight and illumination errors at the test
l
plane to be considered.
Skylight radiation received through the collimator. - The amount of
skylight (diffused Rayleigh scattering) entering the instrument also increases
with the increase of the opening angle of its collimator. For a collimator
of 10 to 1 ratio, 280	5.70 , the solid angle subtended at the receiving
-7-
area is about 0.125% of the entire hemisphere. Excluding variations
in brightness across the sky, this opening angle allows approximately
0.25% of the total skylight, which is the total flux of diffuse light
received at a horizontal plane with the collimator removed, to enter
the instrument. For a collimator of 5 to 1 ratio (28 0 • 11.30), the
figure should be four times that much or about 1% of the total skylight.
Because of the strong wavelength scattering dependence	 4), the
Rayleigh scattering coefficient varies from 1 in the near IR to about 30
in the W. Thus, the skylight due to Rayleigh scattering has a spectral
composition significantly different from the direct sunlight; the result
is a combination of disproportionately enhanced short wavelengths and
much suppressed long wavelengths. Consequently, the skylight affects the
solar cell performance measurements much more than the comparable amount
of circumsolar light, which has a spectral distribution near to that of
direct sunlight.
Preliminary observations indicate that the ratio of short circuit
current output to irradiance for solar cells under skylight can be as
much as 15% lower than that under normal incident direct sunlight, depend-
ing upon general sky conditions. On the other hand, no significant differ-
ence in solar cell performance has been observed between measurements with
collimators of 10 to 1 ratio and those of 5 to 1 ratio. Thus, the apparent
'	 advantage of using larger opening angle to include more circumsolar light
may be outweighed by the disadvantage of introducing more spectrally differ-
=	 ent skylight.
Uniformity of illumination. - The opening angle can also affect the
r
a-
-8-
uniformity of illumination at the receiving aperture. With 280
 - 11.30.
the center of the receiving area gets additional radiation from the solar
aureole, which amounts to approximately 8% of the direct component for
m0 - 0.2 (fig. 3). For slope angle of 1-2°, the circumsolar radiation that
can reach the edge of the receiving area is approximately half of that re-
ceived at the center, that is, approximately 4% of the direct. If we ex-
tend the turbidity and air mass range to mO - 0.25 or more, the difference
can be over 5%. This difference, which is a direct measure of the nonuni-
fcrmity at the receiving plane, is significantly reduced for smaller open-
ing angles. In the case of 28 0 - 5.7°, the diffe 'nince should be about 2%
for m8 - 7.2.
Relative errors in measurement. - Relative errors in measurement due
to pointing and tracking inaccuracies are also different for collimators of
different opening angle. Referring to figure 4(a), let 69 be the sum of
pointing and tracking errors. The resultant error in the radiation fl.ux
which gets through the collimator can be expressed as
AF ti AQ - dI
	
(1)
where 60 is the solid angle error due to the 68 pointing error, dl/de
is the gradient of the intensity of the circumsolar radiation per unit solid
angle with respect to angular distance from the solar disk. The solid angle
AQ can be estimated from figure 4(b). When the axis of the collimator is
shifted by 68, a diameter at the limiting aperture perpendicular to the
shift sweeps an area (k68)2R. Therefore, the solid angle
t
w-9-
Ail W (Z68 )2R - 2R de
	 (2)
L 
hence
AF ti R • 
d8 
• de	 (3)
The quantity dI/de, in percent of the direct solar radiation per unit
solid angle, can be estimated from figure 3. For a collimator of 10 to
1 ratio 2RA - 1/10 and dI/de "5mO W/irr 2). Comparable values for a
collimator of 5 to 1 ratio are 1/5 and -m0(t2/nr2). Considering a high
turl-'_dity parameter case, say, m6 - 0.2, the uncertainties associated
with a pointing error of 0.5 0 would be around 0.2 and 0.02 percent for
collimators of 10 to 1 and 5 to 1 ratios, respectively. For a lower
turbidity parameter case such as and - 0.1, they are approximately 0.1
and 0.01 percent, both small quantities.
Sizes of Collimators in Different Confizurations
For given opening angle and slope angle, the size of a collimator is
dictated by the size of its receiving aperture. Typical reference solar
cells are 2 cm x 2 em squares. A collimator with a receiving aperture
radius of 1.5 cm is appropriate for the calibration of such cells under
terrestrial sunlight. For a quick comparison, dimensions for collimators
of 20 to 1, 10 to 1, and 5 to 1 ratios with different slope angles Are
given in Table 1. Lengths are measured in centimeters with r, the radius
of the receiving aperture, fixed at 1.5 cm.
-10-
Table 1. COMPARISON OF DIMENSIONS FOR COLLIW.TORS OF DIFFERENT OPENING
ANGLE AND SLOPE ANGLE
l
..--
Collimation Opening Slope Receiving Limiting Collimator
Ratios Angle Angle Aperture Aperture length
radius r cm radius R em R cm
1 0 4.91 198.81
20/1 1.430 1.26° 1.5 12.48 499.12
1.761-1 —
10 2.30 46.09
10/1 2.85" 1.26' 1.5 2.68 53.56
1.760 3.89 77.83
10 1.82 18.17
5/1 5.650 1.260 1.5 1.92 19.23
1.76 0 2.17 21.65
TERRESTRIAL REFERENCE CONDITIONS
In the ISCTPTA, solar cell calibration in natural sunlight requires
the following atmospheric conditions: (1) turbidity coefficient 8 must
be less than 0.2, and (2) air mass m must be between 1 and 2.5. Using
the worst combination of (1) and (2), the product of m8 can be as high
as 0.5, which according to a linear extrapolation of figure 3 could give
circumsolar radiation as much as 20% of the direct. Under this condition,
the nonuniformity of irradiance at the receiving area would be unacceptably
high even with 280 = 5.70 .
The compelling reason to allow m to be as large as 2.5 and 8 as
high as 0.2 is to accommodate the large air mass for winter months in the
northern states and the high turbidity for summer monthu in some populated
areas. However, the turbidity parameter which plays the essential rolB is
4
^.
1 I
f	 I	 ^	 1	 F	 !
-11-
the product m6. According to the survey presented by Flowers, et al.
(ref. 5), the turbidity conditions in the United States have values of
m6 less than about 0.25 most of the year. This occurs because in high
turbidit y summer months the air mass at solar noon is generally small,
while in winter months the turbidity is usuall y lower although the air
mass :s large. It is recommended, therefore, that the reference conditions
concerning turbidity and air mass specified in ISCTPTA be revised by
adding: the product of air mass and turbidity coefficient, mc, must be
no greater than 0.25.
It should be noted that the above recommendation is basea solely on
the consideration of accommodating the typ ical turbidity conditions with
acceptable nonuniformities discussed previously. Other factors may call
for even more stringent requirements on turbidity conditions.
Using collimators of large opening angle, most of the circumsolar
radiation can be included in the measurement. However, for the purpose
of solar cell calibration, this advantage can be outweighed by the draw-
backs of introducing more skylight and the increasing nonuniformity at the
receiving plane. Furthermore, a larger opening angle also makes the measure-
ments more vulnerable to the influence of gt.neral sky conditions.
Collimators with a small opening ongle such as a 20 to 1 collimation
ratio are impractical to use because of their physical sizes. Commercially
available pyrheliometers have 20 0 in the 5-6 0 range, which is equivalent
to a 10 to 1 collimation ratio, and there is no compelling reason to change
it. However, it is necessary to have the slope angle of the collimator
I'
r
FIG. 1, CROSS-SECTIONAL VIEW OF A COLLIMATOR
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400
FIG. 2. A VIEW FROM AN EDGE POINT NEAR THE RECEIVING APERTURE OF A
COLLIMATOR WITH ZERO SLOPE ANGLE. SHADED PART OF THE SOLAR
DISK IS OUT OF SIGHT.
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Some basic considerations of measurements involving collimated direct sunlight

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