Energy Conversion. Vol. 14, pp. 61-71. Pergamon Pres.?, 1975. Printed in Great Britain
Effect of Shading on CdS/Cu,S Solar Cells
and Optimal Solar Array Design*
MOHAMED SAYEDj-§ and LARRY PARTAINS
(Received July
1973)
Abstract-The effects of shading on solar arrays in general has been analyzed using the specific Z-V characteristics of a CdS/Cu,S
solar cell. The major differences in the amount of power lost with various array configurations subjected to identical shading
conditions has been determined. The conditions under which localized heating or ‘hot spots’ occur has been treated and the criteria
for their avoidance has been precisely defined. The effects of protective diodes in reducing power loss and in preventing ‘hot spots’
has been included. Genera1 design rules to assist in obtaining optimal solar structures have been formulated and presented.
1.
rntroduction
Loss of
output
power from an array of solar cells is
unavoidable if a portion of the array is shaded from
incident light. However, the amount of power lost
depends on the configuration used to connect the cells
[l-71. Some connection schemes with particular portions
shaded result in reverse voltage across individual cells.
These cells then absorb rather than deliver power and
severe localized heating can result [7, 81. Such ‘hot
spots’ can cause individual cel1 failure [9] and can
result in power loss from large sections of an array [7].
The addition of shunt diodes shorts out these reverse
voltages preventing ‘hot spots’ [2-71. Instead of reverse
voltages, recent studies have shown that other combina-
tions of 41s and shading produce reverse currents
through individual cells
[
101. The resulting power
absorption is avoided by plating diodes in series with
the cells to black the reverse current. These reverse
current levels are low and no significant heating or
‘hot spot’ formation has been attributed to them.
In the references cited above, power loss studies have
been largely confined to particular cases. Few attempts
have been made to define rules for optimal arrays in
general. This previous work has dealt specifically with
silicon solar 41s intended for space applications where
considerations of weight, size, efficiency, but not tost,
are strong constraints. When tost becomes a major
concern, as in large scale terrestrial solar energy con-
version, materials other than silicon become attractive
alternatives. In particular, thin film CdS/&S hetero-
junction cells have the potential for reducing power
conversion costs by several orders of magnitude
[l
1,
121
even though their efficiency is somewhat less than
that of silicon (5-8 per cent
[l
1-131
compared to 11 per
cent [3]).
* Supported by a grant from the National Science Foundation.
t Present address: Microwave Division, Hewlett-Packard
Company, Palo Alto, California 94304, U.S.A.
$ Correspondence should be directed to this author. Electrical
Engineering Department, University of Delaware, Newark,
Delaware 19711, U.S.A.
5 Institute of Energy Conversion, University of Delaware,
Newark, Delaware 19722, U.S.A.
This paper investigates the effects of shading various
configurations in genera1 using CdS/Cu,S cel1 charac-
teristics. Since the I-V properties of al1 solar 41s are
similar, implications for al1 cel1 types are obtained.
In particular, we have studied the precise shading
conditions under which reverse voltage and current
occur. Confìgurations less susceptible to ‘hot spots’
and excessive power loss have been found. We have
quantified the shading effects for the various array
contìgurations so that direct comparisons can be made
for series and parallel connections with and without
protective diodes. Finally, we have formulated genera1
design guidelines to aid in obtaining optimal solar array
structures.
2.
Analysis of Shading
The effects of shading depend on the I-V charac-
teristics of the solar cells, the type of biasing (e.g. maxi-
mum power, minimum load current fluctuation or
minimum load voltage fluctuation) and load used
(resistive, inductive, constant or variable) and the
connection scheme.
A.
Measurement of cel1 characteristics
The I-V curves of a 3 x 3 in., CdS/Cu,S solar cel1
(No. 1-1: 6-5) manufactured by Clevite-Gould, were
measured under three conditions. First the cel1 was
exposed to a light intensity equivalent to the mean maxi-
mum solar value of 100 mW/cms. Next an opaque
cover was placed over one half the cel1 surface so that
only the uncovered portion was exposed to light. Finally
the I-V characteristics were measured in the dark. The
light source was a calibrated solar simulator of intensity
air mass one. Air mass one is the mean maximum
solar intensity at sea leve1 in contrast to air mass zero
which is the mean value in space. This simulator ap-
proximated the spectra1 distribution of sunlight and
was calibrated (& 2 per cent) with a standard cel1
flown from NASA’s Lewis Research Center. The resulting
reverse voltage characteristics are shown in Fig. 1.
Figure 2 gives the forward characteristics. Only in the
fourth quadrant is the I-Y product negative indicating
61