Solar Energy 74 (2003) 217–233
Partial shadowing of photovoltaic arrays with different system
configurations: literature review and field test results
Achim Woyte a , *, Johan Nijs a,b ,1 , Ronnie Belmans a
a
Katholieke Universiteit Leuven, Department of Electrical Engineering, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium
b
Photovoltech SA, c /o IMEC vzw, Kapeldreef 75, B-3001 Leuven, Belgium
Received 20 December 2002; received in revised form 4 April 2003; accepted 11 April 2003
Abstract
Partial shadowing has been identified as a main cause for reducing energy yield of grid-connected photovoltaic systems.
The impact of the applied system configuration on the energy yield of partially shadowed arrays has been widely discussed.
Nevertheless, there is still much confusion especially regarding the optimal grade of modularity for such systems. A 5-kWp
photovoltaic system was installed at K.U. Leuven. The system consists of three independent subsystems: central inverter,
string inverter, and a number of AC modules. Throughout the year, parts of the photovoltaic array are shadowed by
vegetation and other surrounding obstacles. The dimensions of shadowing obstacles were recorded and the expectable
shadowing losses were estimated by applying different approaches. Based on the results of almost 2 years of analytical
monitoring, the photovoltaic system is assessed with regard to shadowing losses and their dependence on the chosen system
configuration. The results indicate that with obstacles of irregular shape being close to the photovoltaic array, simulation
estimates the shadowing losses rather imprecise. At array positions mainly suffering from a reduction of the visible horizon
by obstacles far away from the photovoltaic array, a simulation returns good results. Significant differences regarding
shadow tolerance of different inverter types or overproportional losses with long module strings could not be confirmed for
the system under examination. The negative impact of partial shadowing on the array performance should not be
underestimated, but it affects modular systems as well as central inverter systems.
 2003 Elsevier Ltd. All rights reserved.
1. Introduction
In the industrialised countries, grid-connected photovoltaic (PV) systems are mainly installed on buildings.
The integration of these systems into the built environment
offers a large potential for cost reduction and can contribute to the overall value of urban architecture. A well
designed PV facade expresses the reconciliation of modern
technology and environmental concern, and thus is well
suited for application in contemporary urban design.
Wide experience with PV on buildings became available
in the early 1990s. In the German 1000-Roofs-PV-Programme that was started in 1990, partial shadowing of PV
arrays turned out to be one of the main reasons for
reductions in energy yield (Decker and Jahn, 1997; Erge et
al., 1998). The Japanese field test programme that was
initiated in 1992 returned similar results (Kurokawa et al.,
1997b; Otani et al., 2001). Up to then, partial shadowing
had mainly been considered a problem with regard to
thermal destruction of solar cells due to hot spots. Now,
overproportional losses due to partial shadowing of PV
arrays became an issue.
In the meantime, the impact of partial shadowing on the
energy yield of PV has been widely discussed. Nevertheless, there is still much confusion, especially regarding the
optimal grade of modularity of the system configuration.
2. Review and discussion of previous research
*Corresponding author. Tel.: 132-16-321-020; fax: 132-16321-985.
E-mail address: achim.woyte@esat.kuleuven.ac.be (A. Woyte).
1
ISES member.
2.1. Partial shadowing of photovoltaic devices
Shadowing of a single cell in a series string of solar
0038-092X / 03 / $ – see front matter  2003 Elsevier Ltd. All rights reserved.
doi:10.1016 / S0038-092X(03)00155-5
A. Woyte et al. / Solar Energy 74 (2003) 217–233
218
Nomenclature
STC
MPP
Wp, kWp
PAC,r
PDC,r
Yr
YrSh
YA
Yf
LC
LCSh
LCM
LS
PR
PR Sh
PRA
hEU
hS
Standard test conditions: irradiance 1000 W/ m 2 ; cell temperature 25 8C; spectrum air
mass 1.5
Maximum power point on the I–U curve of a PV device
Units for indication of rated PV power at STC (p: peak)
Rated AC power of a PV inverter
Rated DC power of a PV inverter
Reference yield: in-plane irradiation normalised on 1000 W/ m 2
Reference yield after shadowing: in-plane irradiation on the shadowed PV array
normalised on 1000 W/ m 2
Array yield: DC energy generation of the PV array normalised on rated PV power at
STC
Final yield: AC energy generation of the PV system normalised on rated PV power
at STC
Capture losses: LC 5Yr 2YA
Shadowing losses in irradiation: LCSh 5Yr 2YrSh
Miscellaneous capture losses: LCM 5YrSh 2YA
System losses: LS 5YA 2Yf
Performance ratio: PR5Yf /Yr
Performance ratio with reference yield after shadowing: PR Sh 5Yf /YrSh
Array performance ratio: PRA 5YA /Yr
European efficiency of a PV inverter: hEU 50.03h5 10.06h10 10.13h20 10.1h30 1
0.48h50 10.2h100 , the indexed h values indicate the inverter efficiency at the given
percentage of rated AC power
Long-term system efficiency in the field: hS 5Yf /YA
Subscripts
11, 12, 13, 14, 21, 31, 32, 34 Indication of PV subsystems and module strings
A, B, C, D
Indication of positions for in-plane irradiance measurements
cells leads to reverse bias of the shadowed cell. Reverse
bias and consecutive microplasma breakdown have been
physically described and modelled (Spirito and Albergamo, 1982; Bishop, 1988, 1989). Kovach (1995) performed a thorough analysis of the reverse-biased solar cell
and applied Bishop’s model in order to draw conclusions
on hot spot formation and yield reduction of PV arrays. For
commercially available crystalline and amorphous cells,
model parameters for both models were derived from
measurements by Alonso and Chenlo (1998). All the
authors observed that solar cell I–U characteristics in
reverse bias show more variation than in forward bias, a
¨
result that was statistically verified by Danner and Bucher
(1997) and Laukamp et al. (1999). Kovach (1995) also
found that under shadowing conditions a poor PV array
lay-out can lead to large energy losses and that even small
shadows can appreciably affect the energy yield.
In order to protect shadowed solar cells from breakdown, bypass diodes are applied. In the 1980s a number of
authors contributed to optimise the PV module design and
to determine the maximum number of solar cells per
bypass diode necessary in order to avoid the formation of
hot spots (Arnett and Gonzales, 1981; Bhattacharya and
Neogy, 1991; Gupta and Milnes, 1981; Shepard and
Sugimura, 1984). Based on these experiences, a hot-spot
endurance test became part of the type approval for
crystalline silicon modules according to IEC 61215 (1993).
As a rule of thumb, for a solar cell string of n cells being
equipped with one bypass diode, the absolute value of the
breakdown voltage of a reverse biased solar cell must be
greater than n up to n11 times 0.5 V. This value
approximately equals the MPP voltage of the n21 unshadowed crystalline silicon cells in series plus the transmission voltage of a silicon bypass diode, i.e., 0.5 to 1 V.
The weakest link in a cell string is the solar cell with the
highest breakdown voltage and thus the highest leakage
current (Gupta and Milnes, 1981; Hermann et al., 1997).
For today’s crystalline silicon modules, the breakdown
voltage of a solar cell usually is assumed to be less than
210 V. Therefore, mostly one bypass diode is applied per
18 cells in series. Multiple parallel interconnections between cell strings within one module, also discussed in the
literature, are usually not applied anymore today.
In measurements on commercially available reverse
biased solar cells, cases have been identified with a
breakdown voltage as high as 27.2 V, leading to a leakage
A. Woyte et al. / Solar Energy 74 (2003) 217–233
current of 1.4 A and associated maximum cell temperatures as high as 125 8C at 210 V reverse voltage. The
reverse bias behaviour in this study has been found to be
specific to the cell type (Hermann et al., 1998). More
recent measurements, carried out under the European
Commission’s Fifth Framework Programme (IMOTHEE
ERK5-CT1999-00005), returned similar results, leading to
the conclusion that cell sorting with regard to leakage
current should be included in the production process. That
way, less cells could be applied per bypass diode in
modules specifically made from cells with higher leakage
current and breakdown voltage (Hermann et al., 2001;
Alonso et al., 2001).
With the increasing architectural integration of PV into
roof structures and facades in the mid 1990s, again the
question was raised whether the bulky external bypass
diodes could be omitted or at least reduced in number.
Research was mainly carried out in the framework of the
German federal research and development (R&D) project
‘‘Qualifizierung von PV-Fassadenelementen’’ (BMBF-FKZ
032 9658). In that context, it was found that for glass /
glass modules, bypass diodes should not be omitted unless
the module design is modified by applying broader cell
connectors and a high-heat-conductivity foil in the module
back sheets (Knaupp, 1997). With these measures the peak
temperature could be reduced by about 16 K (Knaupp,
1997). PV modules were measured and simulated with
constructed cast shadows by Laukamp et al. (1998). It was
concluded that bypass diodes may only be omitted if the
irradiance distribution is virtually always homogeneous.
Furthermore, all cells applied must behave almost identically under reverse bias and their shunt resistance must not
be too high. This however presumes the availability of
solar cells with standardised reverse bias behaviour. Currently, cell manufacturers do not control the reverse bias
behaviour of their cells being the reason that in this study
even cells of the same type were found to behave
differently when biased in reverse direction (Laukamp et
al., 1999).
As a preliminary conclusion from the aforementioned
German R&D project, it was suggested that bypass diodes
should not be omitted (Stellbogen et al., 1998). In practice
one bypass diode per 18 to 20 cells should be applied. With
the application of more powerful solar cells Stellbogen et
al. (1998) suggest that even a smaller number of cells per
bypass diode might become necessary. The results from
the European IMOTHEE project generally confirm these
findings yet they more urgently suggest the need for a
smaller number of cells per bypass diode also for crystalline standard modules as long as manufacturers cannot
guarantee a continuously high quality with regard to
breakdown voltage and leakage current of the applied solar
cells (Hermann et al., 2001; Alonso et al., 2001).
While from an architectural point of view, it would be
desirable to omit the bypass diodes in the junction box,
from the shadowing point of view the more bypass diodes
219
are available, the better. A solution is offered to this
dilemma with directly integrating the bypass diode in the
semiconductor structure of each single cell (Suryanto
Hasyim et al., 1986). Another option for increased shadow
tolerance are cell-integrated converters (Meyer et al.,
1997). However, these are not likely to become commercially available in the near future (Quaschning et al.,
1996).
In the meantime, considerable effort has also been made
in simulating the electrical behaviour of shadowed PV
arrays. A mathematical description of shadowed PV arrays
was first derived by Rauschenbach (1968). Abete et al.
(1989) studied the behaviour of parallel and series connected solar cells under partial shadowing by applying
Bishop’s model. Quaschning and Hanitsch (1996a) developed a model for the photo current of partially
shadowed solar cells. Today, a large number of software
tools for the assessment of the electrical behaviour of PV
arrays is commercially available, however, not all of them
are suited for examinations down to the solar cell level
under reverse biased conditions (Zehner, 2001).
There are two fundamentally different approaches to
estimate the reduction in energy yield of partially
shadowed PV systems. One approach is to simulate the
shadows being cast on the PV array by surrounding
obstacles and their variation in time. For this purpose
Blewett et al. (1997) applied a heliodon as used by
architects to predict natural lighting effects. That way, it is
possible to predict the shadows cast on a PV array in the
built environment throughout the year based on an architectural model. Wilshaw et al. (1995) also determined
direct and diffuse irradiance, and PV module temperature
from the heliodon analysis, enabling conclusions on the
array yield of the PV system. In general, this type of
simulation can also be performed on a computer. If the
dimensions and arrangement of the shadowing objects are
known, the shape and size of the shadow, cast on the PV
array, can be determined at every moment of the year. By
further applying synthetic or empirical meteorological
data, the irradiance on the PV array can be calculated very
precisely for every moment in time, allowing for further
simulation of the electrical system behaviour. A detailed
description for the calculation of solar irradiance on
partially shadowed PV arrays is provided (Quaschning and
Hanitsch, 1995) as is a high-resolution electrical model for
PV arrays with inhomogeneously illuminated cells
(Quaschning and Hanitsch, 1996b). One obvious drawback
of such a model with high spatial and time resolution is the
necessary long computation time. Another one is the
necessity to know the precise dimensions and positions of
all shadowing objects.
Eleven out of 27 programs and tools, presented in a
market survey on commercially available PV simulation
software by Zehner (2001), feature possibilities for the
evaluation of partial shadowing. Four of them can calculate cast shadows as a function of time as described above.
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A. Woyte et al. / Solar Energy 74 (2003) 217–233
However, only one of them allows for detailed analysis
down to the level of the single solar cell (Laplace Systems,
2003). Another of these four programs is intended for
irradiance calculations only (Zehner, 2001), and the two
others have as the smallest spatial unit the PV module,
without applying Bishop’s model for single reverse-biased
PV cells (Viotto et al., 1997, 2000; Mermoud et al., 1998).
The second approach is based on describing the reduction in irradiation seen from a particular observer point on
the PV array. Most simulation programs in the aforementioned survey (Zehner, 2001) that feature shadowing,
apply such an approach where shadowing is considered by
a space angular description of the horizon reduction,
caused by the surrounding obstacles. Knowledge of the
dimensions of surrounding obstacles is not necessary here.
It is sufficient to record their two-dimensional space
angular map on the unit-sphere around the observer point.
The shadowing geometry can, e.g., be recorded by simple
optical measurements (Quaschning and Hanitsch, 1998b)
or by means of photography, either applying a spherical
lens (Grochowski et al., 1997; Woyte, 1997) or several
˜ and
photographs from a customary camera (Caamano
Lorenzo, 1997; Frei et al., 2000). After applying the
appropriate transformation of coordinates of the sky dome
for the specific lens, the reduction of the visible horizon by
surrounding obstacles can be read from the photographs.
As the space angular approach always is valid for one
particular position on the PV array only, it is mainly suited
for rough estimations of the reduction in solar irradiance
during a longer time interval. For the detailed analysis of
the electrical system behaviour, this approach is less
suited. Extensions of the space angular approach have been
proposed in order to make the method more convenient to
apply. Skiba et al. (2000) applied a digital camera and
image processing software in order to directly process the
geometry of surrounding obstacles for the yield simulation.
Tomori et al. (2000) proposed to take two or more fisheye
photographs in order to construct a three-dimensional
image of the surrounding obstacles that could then also be
used for calculating the time variation of cast shadows on
different positions of the PV array.
2.2. Partial shadowing with different system
configurations
Based on theoretical considerations, simulation, and also
laboratory and field tests, a number of guidelines for an
optimum arrangement of PV arrays have been determined.
Several authors have calculated the optimum spacing
between adjacent PV module rows in order to minimise the
losses due to mutual shading of one row by another
(Appelbaum and Bany, 1979; Bany and Appelbaum, 1987;
Quaschning and Hanitsch, 1998a; Versluis and Jongen,
2001).
The impact of the module orientation with snow-covered
modules has been determined (Quaschning and Hanitsch,
1997). In such a case when only a part of the PV module is
shadowed, the module orientation has a severe impact on
the energy yield. Since a partially shadowed 18-cell
substring is usually short-circuited by its bypass diode, it is
crucial to choose the module orientation in such a way that
the solar cells of as little different 18-cell substrings as
possible are shadowed at a time.
Decker et al. (1998) and Stellbogen and Pfisterer (1992)
extended this guideline to PV module strings. They recommended to wire the PV array in such a way that
shadowed and unshadowed modules are possibly not
connected in series but in parallel. This recommendation is
generally accepted as a rule of thumb in PV array design,
however, it only holds for certain model cases. The reason
is that the 18-cell substrings equipped with bypass diodes
form the largest significant unit of the PV array with regard
to string current limitation. Covering one entire module of
a module string leads to a lower string voltage. However, it
does not limit the total available string current. On the
other hand, covering one single cell of an 18-cell substring
limits the current of this particular substring to zero. At the
same time, the current of the entire module string bypasses
the 18-cell substring that includes the covered cell via the
bypass diodes. The power of the 17 unshadowed cells in
this substring is dissipated in the covered cell. Hence, the
situation of shadowed cells in an 18-cell substring cannot
be transferred to the case of shadowed modules in a
module string.
The impact of the module arrangement on the energy
yield of partially shadowed PV arrays in practice is not yet
clear. In practical situations a high number of factors needs
to be taken into account like MPP tracking voltage
window, DC bus voltage, number of parallel strings and
inverter type, and of course the particular shadowing
situation.
Another crucial and widely discussed question is the
grade of modularity of the system design. For the grid
connection of PV, generally three different classes of
system configuration are available: module inverters, string
inverters or central inverter. Recently, also a hybrid
concept has been presented (Meinhardt and Cramer, 2001).
The decision which configuration to choose, can have a
decisive impact on installation expense, balance-of-system
costs, and energy yield and must be made with regard to
the situation of the particular site and to the local climate
(Table 1).
In recent years, the advantages and drawbacks of these
different system configurations have been widely discussed. In general, module and string inverters are said to
be less sensitive to an inhomogeneous irradiance distribution and easier to install (de Graaf and van der
Weiden, 1994; de Haan et al., 1994; Kleinkauf et al., 1992;
Knaupp et al., 1996; Kurokawa et al., 1997a; Lindgren,
2000; Meinhardt et al., 1999). Central inverters are usually
less expensive, more efficient and more reliable on a
system base. From a survey on the German market, it
A. Woyte et al. / Solar Energy 74 (2003) 217–233
221
Table 1
Characteristic properties of different system configurations; ‘‘PV rated voltage’’ and ‘‘European efficiency’’ from a survey on the German
market (Hupach, 2002)
AC modules
String inverter
Central inverter
DC installation expense
No DC installation
No DC junction box
Complex DC installation
and protection
PV rated voltage
17–90 V
150–800 V
Maximum voltage limited by local codes
34–800 V
Ohmic DC-losses
(percentage of reference yield, estimated)
Negligible
|1% due to short DC lines
and high DC voltage
|1–5%, depending on
DC voltage and distances
European efficiency
87–93%
90–96%
88–96%
Monitoring
Difficult with large systems
Difficult with large systems
Central, thus easy
Maintenance and repair
Installed inverters are sometimes
difficult to reach
Installed inverters are sometimes
difficult to reach
Central, thus easy
appears that the specific prices of small module inverters
for AC modules are still more than twice as high as the
price of an inverter for a string or central configuration
(Fig. 1). Inverter reliability does very much depend on the
environment, and especially humidity and operating temperature (Wilk and Panhuber, 1995), and also on the
voltage quality of the grid. The criterion of shadow
tolerance that has so often been mentioned as an advantage
of modular systems is actually difficult to specify. A wider
MPP tracking voltage window might, e.g., contribute to
shadow tolerance. With several 18-cell substrings of a long
string of modules being shadowed, a wider MPP voltage
window can lead to higher yields, where another MPP
tracker might not succeed in setting a stable MPP. Such a
case has, e.g., been observed by Alonso et al. (1997).
The idea of modular system configurations being more
shadow tolerant than central configurations, is usually
derived from the current limiting effect that one shadowed
solar cell has on a string of cells. This however, does not
take into consideration the impact of the bypass diodes.
Again, the 18-cell substrings equipped with bypass diodes,
form the largest significant unit of the PV array with regard
to string current limitation. Another consequence of
inhomogeneous array illumination can be the mismatch of
parallel module strings. This may indeed lead to yield
reduction in central inverter systems.
Measurements and studies on existing PV systems with
inhomogeneuos irradiance distributions do not indicate
significantly better results for modular configurations. It
was confirmed by different authors from field experience
that in moderate climates mismatch losses of differently
oriented PV arrays connected to one single inverter, are
Fig. 1. Specific costs of PV inverters on the German market as a function of rated power (VAT excluded; source: Hupach, 2002).
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A. Woyte et al. / Solar Energy 74 (2003) 217–233
below 1% of the annual energy yield (Laukamp and
Wiemken, 1997; Maranda, 2001). Tegtmeyer et al. (1997)
concluded from laboratory measurements that when partial
shadowing occurs from time to time, with central inverters
additional losses are less than 5% of the optimum. A case
study by Beuth (1998) who simulated two existing PV
systems with partial shadowing for different configurations, did not show significant advantages of the module
inverter configuration. Based on costs for inverters and
installations, and reliability considerations, he recommends
the application of central or string inverters.
Conversely, Gross et al. (1997) conclude in another case
study based on heliodon analysis that replacing the present
central inverter by module inverters could reduce losses
due to shadowing from 25 to 19.5% of the annual energy
yield. From measurements in the field, Wheldon et al.
(2001) observed significant differences in performance
ratio between a central inverter PV system and a number of
AC modules at the same location. Partly these differences
are caused by the exceptionally low partial-load efficiency
of the central inverter. It is further suggested that the better
performance of the module inverter system would partly be
for the sake of reduced current limiting as it would occur
in series strings of modules and reduced string mismatch
under partial shadowing. For the analysis, the internal
monitoring functions of the inverters have been used
(Wheldon et al., 2001). For the module inverters, unfortunately this means that DC power is not available and
AC power has been calculated from voltage times current,
disregarding the non-unity power factor. In order to
analyse the impact of module inverters with partial
shadowing more in depth, knowledge of these quantities
would be key.
Similarly, Carlsson et al. (1998) recommend a modular
approach for increasing the yield of a partially shadowed
flat roof installation. Apparently, the extremely low yield
described there, mainly originates from mutual shading of
adjacent module rows, being comparable to the snow cover
of a few cells as examined by Quaschning and Hanitsch
(1997). If this is the case, module inverters would most
likely not bring much improvement for this installation. A
much more effective measure would be turning the module
frames by 908. In another case study of a heavily shadowed
PV system applying module inverters, Woyte et al. (2000)
clearly identified a positive impact of the modular design
regarding the avoidance of string mismatch. The question
whether a comparable yield could be received by applying
string inverters was not answered in this study.
The PV arrays described by Knaupp et al. (1996) and
Gross et al. (1997) are rather large facade installations of
10 kWp and 40 kWp, respectively. However, as a conclusion from experiences with AC modules in the Netherlands, Marsman et al. (1998) recommended that AC
modules should not be applied in systems with about more
than 10 modules. As a reason they gave relatively higher
inverter costs and rising problems with maintenance,
repair, and control of the plant. These conclusions are
supported by field test experiences with larger module
inverter systems where different inverters failed repeatedly
(Erge et al., 2001; Wheldon et al., 2001; Woyte et al.,
2000). Although inverter failures described there might be
due to infant diseases, a trend towards higher expenses for
monitoring and repair with module inverters may be
expected.
Although the opposite has often been stated, from the
literature there is no evidence neither on theoretical
grounds nor based on practical measurements that module
inverters are more shadow tolerant than string inverters.
This is because on the one hand, shadowing of single cells
can at most affect the current of the 18-cell substrings
equipped with a bypass diode, leading to increased capture
losses with module inverters as well as string inverters. On
the other hand, partial shadowing can lead to different
positions of the MPP in different strings of modules with
as a consequence mismatch of parallel strings on a central
inverter. Parallel mismatch can be avoided with string or
module inverters. With central inverters, the severity of
parallel mismatch depends very much on the particular
shadowing situation but also on the quality of the particular MPP tracker. Alonso et al. (1997) identified high
miscellaneous capture losses due to insufficient MPP
tracking with partially shadowed arrays. In the laboratory
the efficiency of MPP trackers with irregular I–U curves
can only be measured by means of rather complex and
¨
expensive equipment (Haberlin,
2001), being one of the
reasons why up to now there is relatively little experience
regarding the effectiveness of MPP trackers with partially
shadowed PV arrays.
Beside these theoretical considerations, there are virtually no field results that would allow to estimate the impact
of different system configurations on the energy yield of
partially shadowed PV arrays. This is why in the scientific
discussion, the impact of the system configuration on the
final yield of partially shadowed systems often does not
become clear. The monitoring campaigns on existing
installations usually suffer from a number of drawbacks.
Typical drawbacks are the lack of operational data as
irradiance on the PV array or on an unshadowed reference
location, or electrical DC power. However, the most
significant drawback is the lack of long-term performance
data from different alternative system configurations with
realistic and well known shadowing under identical operating conditions. Without such field test data from different
sites, it is almost impossible to make any firm statement on
the appropriateness of the different available system
configurations with regard to partial shadowing.
This is why at the electrical energy research group of
K.U. Leuven, a grid-connected photovoltaic system was
set up in 1999. The aim was to collect operational
experience with the different system approaches under
non-optimum operation conditions like partial shadowing
and also to assess the quality of photovoltaic system
A. Woyte et al. / Solar Energy 74 (2003) 217–233
components. The photovoltaic array with a peak power of
5.16 kW is situated on the roof of a university building in
Leuven–Heverlee in Belgium. Long-term analytical monitoring of the installation allows for a more detailed
analysis of the different system approaches, and conclusions on their appropriateness with regard to partial
shadowing can be drawn.
3. Photovoltaic system set-up
The PV array at K.U. Leuven is installed on a flat roof,
set up in three successive module rows. The site is situated
30 m above sea level at 4.78 eastern longitude and 50.98
northern latitude in a moderate maritime climate. The array
is shadowed by an air-conditioning system on the roof
(airco box) and by the front rows themselves. The visible
horizon is reduced by vegetation and a neighbouring
building, all leading to reduced array yields, in particular
during the winter.
Under these non-optimum but very typical conditions, a
PV system applying all of the three available design
approaches has been implemented (Woyte et al., 2001).
Looking at the designated site through a fish-eye lens (Fig.
2) gives a first impression of the reduction of the visible
horizon by surrounding obstacles as viewed from the PV
array location. The photographs in Fig. 2 had been taken
before the PV array was installed. The horizon reduction
by the PV array’s front row has been calculated afterwards
and added to the photographs as a hatched area limited by
a dashed line (Fig. 2).
By means of superposing coordinates of the sky dome,
one can determine the date and time of the day when a
certain point of the designated location for the PV array is
shadowed. The photographer’s position receives no direct
irradiance with solar elevation angles lower than approximately 108 during the whole day. Looking to the east, at
the very left of Fig. 2, one sees an alone-standing tree
covering the sun for azimuth angles east of 1108. This
223
position does not receive any direct radiation before
approximately 8:00 to 8:30 h true solar time, all over the
year. With some further photographs taken from other
positions, and recalling that the maximum height of the
sun from mid November to the end of January, in Belgium
does not exceed 208, an experienced PV system designer
can conclude that on the site shown in Fig. 2, roughly 8 to
15% average losses in annual irradiation have to be
expected. Having to accept these shadowing losses for the
given site, the designer can still optimise the array
arrangement in order to avoid increased miscellaneous
capture losses.
If geometric figures describing the surrounding obstacles
are unknown, the estimation based on experience and some
photographs can lead to good results. A design for the
K.U. Leuven system based on these estimations has been
drafted by applying the aforementioned rule of thumb. As
far as possible, only those modules, that receive homogeneous irradiance at a certain time and date have been
arranged to a common string. In order to recheck the
estimations derived from the fisheye photographs, the
losses in annual irradiation have been calculated by means
of computer simulation, applying the packages StaSol and
PVcad.
The program StaSol determines the annual irradiation
losses due to shadowing by a space angular approach,
comparable to the approach with the fish-eye photograph
(Grochowski et al., 1997; Woyte, 1997). Shadowing
objects are characterised by their two-dimensional map on
the unit-sphere as it is viewed from a specific observer
point. From the map of shadowing objects on the unitsphere, the reduction in direct and diffuse radiation for this
observer point is calculated, based on time series’ of global
and diffuse irradiance for one year. For the calculation of
diffuse radiation on the tilted surface, StaSol applies Hay’s
anisotropic model, taking into consideration a circumsolar
component but no horizon brightening (Iqbal, 1983). In the
present case, such a space angular computation with StaSol
has been carried out for a dense mesh of observer points in
Fig. 2. Fish-eye photograph of the site designated for the PV array, taken horizontally from 45 cm above the lower edge of the PV array,
superposed by coordinates of the sky dome; left: south-east direction, right: south direction.
A. Woyte et al. / Solar Energy 74 (2003) 217–233
224
Fig. 3. PV array site, array arrangement, and simulated annual reference yield on the PV array after shadowing (YrSh ) normalised on
reference yield without shadowing (Yr ), height level of the lower side of the PV array: 45 cm above the roof plane.
the PV array plane, with the two-dimensional map of the
shadowing objects calculated from their coordinates in the
three-dimensional space. The mesh density was one node
per 12 cm. Input data for the StaSol calculations were
hourly average values of global and diffuse irradiance,
recorded in Brussels–Uccle by the Royal Meteorological
Institute of Belgium in 1997. These data allow to determine the relative influence of shadowing on the annual
energy yield, and its distribution over the module arrays,
arranged as shown in Fig. 3.
PVcad calculates hourly irradiance values that can
further be processed in an electrical model of the PV
system. A ray tracing algorithm is applied in order to
calculate the shadows cast on the PV array by the
surrounding obstacle. The spatial resolution for PVcad is
the size of a PV module. The entire module is considered
to receive no direct radiation as long as a part of it is
struck by the cast shadow. The impact of horizon reduction
on diffuse radiation is also taken into consideration by
additionally applying a space angular approach to the
diffuse fraction (Viotto et al., 2000). For the calculation of
diffuse radiation on the tilted surface, PVcad applies Perez’
anisotropic model, taking into consideration a circumsolar
component and also horizon brightening (Perez et al.,
1987).
Based on these simulations, the 43 PV modules were
arranged in order to minimise losses due to shadowing by
nearby obstacles. The spacing between the module rows
has been chosen to be 5.60 m. The modules are southoriented and 308 tilted. According to Quaschning and
Hanitsch (1998a) the annual irradiation loss by mutual
shading of one row by another can then be estimated to be
about 7%. Larger spacing between the rows would lead to
intolerable shadowing of the middle array by the airco box
(Fig. 3).
Table 2 provides an overview on the configurations of
the different subsystems. For all subsystems the same type
of 120-Wp PV modules has been applied. The modules
consist of 72 polycrystalline solar cells either operating in
series connection, or as a parallel connection of two strings
of 36 cells each. A bypass diode is applied per 18 cells. In
practice, the module peak power under STC is lower than
120 Wp for most modules delivered. The peak power
values for the different subsystems in Table 2 are more
precise values, measured by the manufacturer before
delivery. The further analysis of yields and losses for the
different strings and subsystems is based on these measured values.
According to the simulation with StaSol, for the chosen
arrangement the annual reduction in reference yield due to
shadowing lies between 4 and 22% of the reference yield
from an unshadowed location (Fig. 3). Especially on the
outer east side of the middle row, shadowing is very
severe. In winter, especially the lower cells are shadowed
Table 2
Specifications of the different subsystems
Inverter class
Subsystem
PAC,r
(W)
PDC,r
(W)
MPP tracking
window (V)
No. of
modules
PV power
at STC (Wp)
MPP voltage
at STC (V)
Central inverter
String inverter
Module inverter
Module inverter
Module inverter
11
21
31
32
34
2280
1500
90
110
200
2500
1650
100
130
240
66 . . . 150
200 . . . 500
24 . . . 50
24 . . . 40
64 . . . 80
24
15
1
1
2
2835.0
1729.0
118.7
118.8
246.3
103
257
34
34
68
A. Woyte et al. / Solar Energy 74 (2003) 217–233
by the front module row and the airco box. In summer
during morning hours, these modules are shadowed by the
aforementioned tree in the south-east.
The low irradiation on the front array is mainly due to
the reduction of the visible horizon by vegetation and the
neighbouring building. Since neighbouring building and
vegetation are situated rather far from the PV array, the
solar irradiation is distributed relatively homogeneously
over this area.
On an annual basis the average shadowing loss in
reference yield amounts to 9.6%. A simulation with PVcad
based on synthetic irradiance values, also for the location
of Brussels–Uccle, leads to little higher values in reference
yield after shadowing with an average shadowing loss of
7%. These differences are discussed more in depth in the
following section.
The impact of the airco box and the front row of
modules on the eastern modules of the middle row can be
examined more in depth by means of Fig. 4. Viewed from
the photo position both, airco box and front row, are
approximately 108 high. For lower observer points on the
middle row, the visible horizon is mainly reduced by the
airco box, up to an elevation angle of 238 at the lower side
of the module frame. This means that during the winter
months, the lowest row of cells does virtually not receive
any direct radiation. Since the cell strings in the module
run in the vertical direction, this leads to current limiting in
all four 18-cell substrings of this module. At periods with
noteworthy direct irradiance with low solar elevation, all
four bypass diodes will conduct and the available power of
the unshadowed cells is dissipated in the few shadowed
cells, leading to extreme miscellaneous capture losses in
this module as a consequence of shadowing.
Conversely, the irradiance on the upper modules is
distributed much more homogeneously, even in winter.
Viewed from the photographer’s position of Fig. 2, the
horizon is reduced by vegetation and a neighbouring
building, up to 108 in the south east and up to approximately 58 in the south west. The neighbouring building and
vegetation are situated rather far from the PV array.
Therefore, this horizon reduction approximately also applies for the upper modules and unlike the one originating
from the airco box it is insensitive to small variations of
the observer position. Extreme miscellaneous capture
losses are not to be expected here.
225
The simulation with StaSol does not provide information
on the temporal variation in solar irradiance on the PV
array. Extreme shadowing situations as, e.g., the one
caused by the airco box are not detected. Even though, for
avoiding increased miscellaneous capture losses, only
neighbouring modules that on an annual basis receive
approximately equal irradiation were connected in series,
thus following the guidelines of Decker et al. (1998) and
Stellbogen and Pfisterer (1992). For the central inverter,
this issue has been realised as well as practically possible.
Since AC modules are generally considered to be more
shadow tolerant, the AC modules are placed to the local
minima of annual irradiation as shown in Fig. 3. Regarding
the string inverter, increased miscellaneous losses might
occur because of the local minimum in irradiation on the
outer east side. On the other hand, there are no parallelconnected module strings so that string mismatch is
disabled.
The system is monitored analytically according to the
guidelines of the European Commission. The quantities
monitored are shown in Table 3. The in-plane irradiance is
measured at four differently shadowed positions on the PV
array (Fig. 3) as well as on one unshadowed reference
position on another roof, about 80 m from the PV array.
Module temperatures are recorded for four modules close
to the different reference cells. DC string currents are
measured for all module strings, while DC system voltage
and AC energy yield are measured for each inverter. The
sampling period is set to 1 s and the measured data is
stored as 5-min average values.
4. Monitoring results
4.1. Comparison to simulation results
The values of reference yield after shadowing normalised on unshadowed reference yield measured during the
year 2001 are, at some positions considerably, lower than
the simulation results (Table 4). The values from the
simulation with PVcad are still little higher than those from
StaSol.
The approach of PVcad to consider the PV module for
not receiving any direct radiation when it is struck even
partly by a cast shadow, would suggest lower values for
Fig. 4. Front and middle module rows and air-conditioning system (airco box); cross section in north-south direction.
A. Woyte et al. / Solar Energy 74 (2003) 217–233
226
Table 3
Monitored quantities and applied sensors
Quantity
No.
Sensor
Meteorology
Irradiance, global horizontal (unshadowed)
Irradiance, diffuse horizontal (unshadowed)
Irradiance, global in-plane (unshadowed)
Irradiance, global in-plane (positions A–D on the PV array)
Ambient temperature
1
1
1
4
1
Pyranometer, WMO class II
Pyranometer, WMO class II with shadow ring
Reference cell, mono-Si, temperature compensated
Reference cell, mono-Si, temperature compensated
Pt 100 thermo resistance, radiation shielded
PV arrays
DC string current
DC system voltage
Module temperature
8
5
4
Hall effect current transducer
Hall effect voltage transducer
Pt 100 thermo resistance on the back of a PV cell
Inverter outputs
AC energy from inverter
5
Energy pulse counter
reference yield after shadowing from PVcad than from
StaSol. Also the consideration of horizon brightening in
PVcad might suggest slightly lower values for reference
yield after shadowing with PVcad since horizon reduction
by obstacles mainly affects the light incident from low
elevation angles. This light is underestimated in Hay’s
model in comparison to Perez’ model. Since the geometric
description of shadowing obstacles is identical for both
simulations, it must be concluded that the unexpectedly
higher annual irradiation from PVcad in comparison to
StaSol is due to the annual variation in the radiation input
data. Indeed, the diffuse fraction of measured global
radiation from 1997 that has been applied to the simulation
with StaSol amounts to 53% whereas the synthetic time
series of global radiation from PVcad contains 63% diffuse
radiation. Since diffuse radiation has no specific direction,
shadowing by obstacles does reduce the diffuse fraction
only by a small, relatively constant portion being roughly
proportional to the fraction of the sky dome covered by the
obstacles. On the other hand, the direct fraction of solar
radiation is limited to zero, when an observer point is
shadowed by an obstacle. Therefore, in general terms, the
shadowing losses in irradiation are the less severe, the
higher the diffuse fraction.
The variations in diffuse fractions of the different sets of
Table 4
Annual reference yield on the PV array after shadowing (YrSh )
normalised on reference yield without shadowing (Yr )
Reference cell
Normalised reference yield after shadowing
(YrSh /Yr ) (%)
position
PVcad
StaSol
Measurement
A
B
C
D
90
95
92
94
85
93
89
92
80
85
88
83
Average
93
90
86
input data can explain the variations between PVcad and
StaSol, however, they cannot explain the larger discrepancy between simulation results and measured values.
In 2001, the measured diffuse fraction of global radiation
was 57%. The inaccuracies introduced by the different
models for diffuse radiation on the tilted plane can not
satisfactorily explain this discrepancy either, even more
since the PVcad results, although calculated by the more
accurate Perez model, differ more from the measured
values than the StaSol results.
At position C where there are no obstacles close to the
PV array but only vegetation and a building on the horizon,
the results are rather accurate for both simulations. At the
other positions and especially position A, the aforementioned tree on the very left of Fig. 2 and the airco box
become significant. Especially the airco box but also the
tree are situated very close to the PV array. While the
dimensions of the airco box are comparably well known,
the dimensions of the tree could only be estimated from
optical measurements and they continuously vary with the
seasons. Even small inaccuracies in the geometric description of these two obstacles can lead to large errors in the
estimation of annual in-plane irradiation for positions close
to these obstacles.
It can be concluded that regardless of the applied
simulation model and the solar radiation input data,
simulation programs for partial shadowing are only as
good as is the description of the shadowing obstacles.
Especially with obstacles of irregular shape, situated close
to the PV array, considerable inaccuracies should be taken
into account.
4.2. Identification of losses on an annual basis
The performance analysis follows the terminology pro¨
posed by Haberlin
and Beutler (1995). Additionally, the
capture losses (LC ) are divided into shadowing losses
(LCSh ) and miscellaneous capture losses (LCM ).
A. Woyte et al. / Solar Energy 74 (2003) 217–233
In order to exactly determine LCSh , it would be necessary to measure solar irradiance on all significant positions
of the PV array, meaning at the very least one measurement per PV module. In practice, this is not feasible and
therefore, YrSh must be approximated for the different
subsystems from the available data. For the string inverter
and the AC module subsystems, the reference yield after
shadowing has been approximated by the measured value
from the respectively closest reference cell as indicated in
Fig. 3:
String inverter (subsystem 21): YrSh 5 YrShC
(1)
AC module (subsystem 31): YrSh 5 YrShA
(2)
AC module (subsystem 32): YrSh 5 YrShA
(3)
AC module (subsystem 34): YrSh 5 YrShD
(4)
Since the reference cells A, C, and D are all mounted at
the lower edge of a module row, the values from these
reference cells tend to underestimate the respective annual
reference yield after shadowing. Especially for AC module
subsystem 31 this might be critical due to the airco box
that affects reference cell position A much more than AC
module subsystem 31. This possible inaccuracy should be
kept in mind when analysing the capture losses in terms of
shadowing losses and miscellaneous capture losses.
For the central inverter (subsystem 11) that is spatially
extended over the two back module rows, the reference
yield after shadowing has been approximated by the
arithmetic average of the extreme values for these two
module rows. According to the results from StaSol (Fig.
3), the annual irradiation on the two rows of subsystem 11
is minimal at the reference cell positions A and D,
respectively, at the lower east of each module row. The
annual irradiation on subsystem 11 is maximal on the
upper west of each row. For the middle row, this value is
recorded at position B. For the back row, no reference cell
is available at the upper west. Since according to Fig. 3
this position is still shadowed significantly though considerably less than position B, the maximum reference
yield after shadowing for the back array is approximated
by the arithmetic average of reference yield at position B
and reference yield without shadowing. Under this assumption the arithmetic mean of these four extreme values
for the central inverter (subsystem 11) yields:
YrSh 5 f YrShA 1 YrShB 1 YrShD 1 (Yr 1 YrShB ) / 2 g / 4
5s2YrShA 1 3YrShB 1 2YrShD 1 Yrd / 8
(5)
The average YrSh for the entire PV system is then
calculated as the weighted average of YrSh for all
subsystems taking into account their particular surface
areas.
The performance ratio of the total system is 0.66. The
227
ratio between average YrSh and reference yield Yr is 0.86.
This means that approximately 14% of the available solar
irradiation is lost by shadowing instead of 7 to 10% as had
to be expected from the simulations. The performance ratio
based on reference yield after shadowing (PR Sh ) amounts
to 77% being a good value under normal operating
conditions and indicating that miscellaneous capture losses
are not higher than normal.
A look at the different subsystems shows that the losses
are distributed differently for each subsystem (Fig. 5).
Shadowing losses (LCSh ) are highest for the AC modules,
as they have intentionally been assigned to the positions
with lowest presumed annual irradiation.
The miscellaneous capture losses (LCM ), caused by
series and parallel mismatch, inefficient MPP tracking, and
high module temperatures are lower for the AC modules
than for the other configurations. The string inverter had an
outage of 10 days in June: its final yield and array yield
should be evaluated about 5% higher.
The system losses (LS ) that mainly occur in the inverter,
are the highest for module inverters. This can only be
partly explained by the generally lower efficiency of
smaller inverters as a function of scale. Table 5 compares
long-term system efficiency in the field (hS ) to the
European efficiency (hEU ) of the different inverters. Especially for the subsystems that are shadowed most severely,
the system losses are higher than the European efficiency
would suggest. These unexpected system losses can only
be explained by the fact that the subsystems in question
due to their comparably higher shadowing losses, operate
more time under partial load conditions associated to a
lower inverter efficiency. On the other hand, the string
inverter is generally shadowed little and it contains no
transformer, leading to a high efficiency even in comparison with inverters of similar size.
4.3. Array performance on a monthly basis
Fig. 6a shows the array performance ratio (PRA )
throughout the year. AC module subsystem 32 is suffering
considerably from shadowing in December and January.
Its upper neighbour, AC module subsystem 31, seems to
be much less affected. Based on Fig. 4 it can be concluded
that this is mainly a consequence of partial shadowing
being much more severe on the lower AC module
(subsystem 32) than on AC module subsystem 31. This has
also been confirmed by visual inspection. After light
snowfall in the early morning of 7 January 2003, the snow
on AC module subsystem 31 was melted very quickly by
the direct sunlight while AC module subsystem 32 partly
remained shadowed by the airco box and was still snowcovered for about half of its surface area around solar
noon. Closer analysis shows that also in winter the system
losses are equal for both module inverters. Therefore, it
must be concluded that the low performance of AC module
A. Woyte et al. / Solar Energy 74 (2003) 217–233
228
Fig. 5. Losses and yields for all subsystems, performance ratio (PR) and performance ratio with reference yield after shadowing (PR Sh );
LCSh : capture losses due to shadowing, LCM : miscellaneous capture losses, LS : system losses, Yf : final yield; monitoring from 1 January to 31
December 2001.
subsystem 32 in winter is a consequence of extreme
shadowing.
The array performance ratio of the separate strings of
the central inverter (Fig. 6b) does not indicate a serious
parallel mismatch. Throughout the year, slight differences
in array yield can be observed between the four strings.
These differences correspond to differences in reference
yield after shadowing. Increased miscellaneous capture
losses due to mismatch could not be verified.
4.4. Array performance on a winter day
Five-minute average values from a clear winter day
serve for a more detailed analysis of shadowing losses and
miscellaneous capture losses (Fig. 7). The in-plane irradiance at positions B and C is affected by shadowing
Table 5
Comparison of European efficiency to long-term system efficiency
in the field for the applied inverters
Inverter class
Subsystem
hS (%)
hEU (%)
hS /hEU
Central inverter
String inverter
Module inverter
Module inverter
Module inverter
11
21
31
32
34
88.7
91.8
83.8
81.8
87.6
90.0
94.4 a
90.3 a
90.0
90.6 a
0.986
0.972
0.928
0.909
0.967
a
¨
European efficiency from manufacturers, measured by Haberlin (2001).
only for a short time in the morning. The two positions on
the lower edges of the two back arrays, positions A and D,
are shadowed much more severely. Position A only
receives direct irradiance during 2 h in the late afternoon
which corresponds to the expectations derived on the basis
of Fig. 2 and Fig. 4.
The two AC modules subsystems 31 and 32 are situated
east of position A. Inspection of the output power of the
module strings (Fig. 8) shows that the DC power of
subsystem 32 during the whole day follows the diffuse
irradiance, without exhibiting the rise in direct irradiance
at position A although this AC module is situated less than
one metre east of position A. This indicates that part of the
AC module subsystem 32 indeed does not receive any
direct irradiance during these hours. Its low yield is
obviously due to shadowing. The losses are on the one
hand shadowing losses and on the other hand miscellaneous capture losses due to current limitation in its 18-cell
substrings caused by partial shadowing. The DC voltage at
AC module subsystem 32 from 9:00 to 15:00 h varied
between 28 and 33 V which is well inside the MPP
tracking range of the inverter. Hence, even with severe
shadowing of this AC module, the inverter’s MPP tracker
works well indicating that the system’s low performance
ratio is not caused by a low MPP tracking efficiency. Other
AC modules placed at this location would perform equally
badly.
String 12 of the central inverter array also is heavily
shadowed at this sample day. The string only has a 1–2-h
A. Woyte et al. / Solar Energy 74 (2003) 217–233
229
Fig. 6. Monthly array performance ratio (PRA ) in 2001.
maximum around noon when also the lowest row of cells
in this module string is free from shadowing by the front
rows or the airco box. This, however, has no significant
negative impact on the power generated by the other
strings of the central inverter generating high power as
soon as they receive sufficiently direct irradiance. Apparently the classical central inverter systems are less sensitive to shadowing than always assumed. A reduction of
string currents by series mismatch is mitigated thanks to
the bypass diodes, and also parallel string mismatch is
apparently not an issue for today’s MPP trackers.
5. Conclusions
Although considerable research on partial shadowing of
PV arrays has already been carried out, the impact of the
PV system configuration on the energy yield of partially
shadowed systems is not entirely clear. This is why a
partly shadowed PV system has been set up at K.U.
Leuven applying a central inverter as well as string and
module inverters. The installation has an overall performance ratio of 66%. Performance ratio after shadowing
amounts to 77% being a good value under normal oper-
230
A. Woyte et al. / Solar Energy 74 (2003) 217–233
Fig. 7. Solar irradiance, unshadowed and on the PV array on a clear winter day (20 December 2001).
ating conditions and indicating that additional mismatch
losses are low.
An estimation of irradiation losses due to shadowing has
been carried out. Measurements show that with obstacles
of irregular shape being close to the PV array, the
simulation estimates the shadowing losses up to 10% too
low. At array positions that mainly suffer from a reduction
of the visible horizon by obstacles being far from the PV
array, the simulation returns a rather good estimation of
shadowing losses.
For the system under examination, the monitoring
results show no evidence for a different behaviour with
regard to partial shadowing of central inverter, string
inverter, or module inverter configuration. Generally
speaking, AC modules are not more significantly shadow
tolerant than central inverter systems with long parallel
Fig. 8. DC power normalised on PV peak power for all strings on a clear winter day (20 December 2001).
A. Woyte et al. / Solar Energy 74 (2003) 217–233
strings. For string current limitation by shadowed cells, the
18-cell substring equipped with a bypass diode is the
largest significant unit causing similar capture losses in
module as in central inverter systems. With regard to
parallel mismatch, central inverter systems may suffer
increased miscellaneous capture losses as a consequence of
shadowing, but in the present case this effect could not be
found significant.
These results hold for situations with obstacles covering
the visible horizon or discrete obstacles that are considerably large, in order not only to shadow a few solar
cells per module during a longer period. For filigreeshaped obstacles that only shadow a few cells in several
modules, like, e.g., antennas or chimneys, this conclusion
does not necessarily apply. In such case however, AC
modules will suffer from increased miscellaneous capture
losses as non-modular PV systems do. Then amorphous
modules with cell-integrated bypass diodes or cell integrated inverters might provide a solution. Alternatively, the
most heavily shadowed positions should be equipped with
a dummy module.
In order to validate these results on a broader basis,
similar field test installations should be set up at different
locations and for diverse shadowing situations. The most
important data for such an evaluation are DC power down
to module level and solar irradiance on the PV array with
very high spatial resolution. A better understanding of
partially shadowed PV systems is crucial in order to
evaluate the different system configurations on an objective basis without being influenced by marketing argumentation.
Acknowledgements
The PV installation at K.U. Leuven has been supported
by the Belgian utility companies Electrabel and SPE within
¨
the project ‘‘Fotovoltaısche
zonnecelsystemen voor onderwijsinstellingen’’ and by the Flemish regional government.
Part of the work done was funded via the IWT-GBOU
project ‘‘Embedded generation: A global approach to
energy balance and grid power quality and security’’.
¨ Mencke & Tegtmeyer in Hameln, Germany
Ingenieurburo
is acknowledged for their practical assistance with the data
logging equipment.
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