P artial shadowing of photovoltaic arrays with different ... · MPP Maximum power point on the I–U curve of a PV device Wp, kWp Units for indication of rated PV power at STC (p:

Solar Energy 74 (2003) 217–233

P artial shadowing of photovoltaic arrays with different systemconfigurations: literature review and field test results

a , a,b ,1 a*Achim Woyte , Johan Nijs , Ronnie BelmansaKatholieke Universiteit Leuven, Department of Electrical Engineering, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium

bPhotovoltech 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-kWpphotovoltaic 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 byvegetation and other surrounding obstacles. The dimensions of shadowing obstacles were recorded and the expectableshadowing losses were estimated by applying different approaches. Based on the results of almost 2 years of analyticalmonitoring, the photovoltaic system is assessed with regard to shadowing losses and their dependence on the chosen systemconfiguration. The results indicate that with obstacles of irregular shape being close to the photovoltaic array, simulationestimates the shadowing losses rather imprecise. At array positions mainly suffering from a reduction of the visible horizonby obstacles far away from the photovoltaic array, a simulation returns good results. Significant differences regardingshadow tolerance of different inverter types or overproportional losses with long module strings could not be confirmed forthe system under examination. The negative impact of partial shadowing on the array performance should not beunderestimated, but it affects modular systems as well as central inverter systems. 2003 Elsevier Ltd. All rights reserved.

1 . Introduction reductions in energy yield (Decker and Jahn, 1997; Erge etal., 1998). The Japanese field test programme that was

In the industrialised countries, grid-connected photo- initiated in 1992 returned similar results (Kurokawa et al.,voltaic (PV) systems are mainly installed on buildings. 1997b; Otani et al., 2001). Up to then, partial shadowingThe integration of these systems into the built environment had mainly been considered a problem with regard tooffers a large potential for cost reduction and can contrib- thermal destruction of solar cells due to hot spots. Now,ute to the overall value of urban architecture. A well overproportional losses due to partial shadowing of PVdesigned PV facade expresses the reconciliation of modern arrays became an issue.technology and environmental concern, and thus is well In the meantime, the impact of partial shadowing on thesuited for application in contemporary urban design. energy yield of PV has been widely discussed. Neverthe-

Wide experience with PV on buildings became available less, there is still much confusion, especially regarding thein the early 1990s. In the German 1000-Roofs-PV-Pro- optimal grade of modularity of the system configuration.gramme that was started in 1990, partial shadowing of PVarrays turned out to be one of the main reasons for

2 . Review and discussion of previous research

*Corresponding author. Tel.:132-16-321-020; fax:132-16-2 .1. Partial shadowing of photovoltaic devices321-985.

E-mail address: [email protected](A. Woyte).1ISES member. 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

mailto:[email protected]

218 A. Woyte et al. / Solar Energy 74 (2003) 217–233

Nomenclature

2STC Standard test conditions: irradiance 1000 W/m ; cell temperature 258C; spectrum airmass 1.5

MPP Maximum power point on theI–U curve of a PV deviceWp, kWp Units for indication of rated PV power at STC (p: peak)P Rated AC power of a PV inverterAC,r

P Rated DC power of a PV inverterDC,r2Y Reference yield: in-plane irradiation normalised on 1000 W/mr

Y Reference yield after shadowing: in-plane irradiation on the shadowed PV arrayrSh2normalised on 1000 W/m

Y Array yield: DC energy generation of the PV array normalised on rated PV power atA

STCY Final yield: AC energy generation of the PV system normalised on rated PV powerf

at STCL Capture losses:L 5Y 2YC C r A

L Shadowing losses in irradiation:L 5Y 2YCSh CSh r rSh

L Miscellaneous capture losses:L 5Y 2YCM CM rSh A

L System losses:L 5Y 2YS S A f

PR Performance ratio: PR5Y /Yf r

PR Performance ratio with reference yield after shadowing: PR5Y /YSh Sh f rSh

PR Array performance ratio: PR5Y /YA A A r

h European efficiency of a PV inverter:h 50.03h 10.06h 10.13h 10.1h 1EU EU 5 10 20 30

0.48h 10.2h , the indexedh values indicate the inverter efficiency at the given50 100

percentage of rated AC powerh Long-term system efficiency in the field:h 5Y /YS S f A

Subscripts11, 12, 13, 14, 21, 31, 32, 34 Indication of PV subsystems and module stringsA, B, C, D Indication of positions for in-plane irradiance measurements

cells leads to reverse bias of the shadowed cell. ReverseNeogy, 1991; Gupta and Milnes, 1981; Shepard andbias and consecutive microplasma breakdown have beenSugimura, 1984). Based on these experiences, a hot-spotphysically described and modelled (Spirito and Alber- endurance test became part of the type approval forgamo, 1982; Bishop, 1988, 1989). Kovach (1995)per- crystalline silicon modules according toIEC 61215 (1993).formed a thorough analysis of the reverse-biased solar cell As a rule of thumb, for a solar cell string ofn cells beingand applied Bishop’s model in order to draw conclusions equipped with one bypass diode, the absolute value of theon hot spot formation and yield reduction of PV arrays. For breakdown voltage of a reverse biased solar cell must becommercially available crystalline and amorphous cells, greater thann up to n11 times 0.5 V. This valuemodel parameters for both models were derived from approximately equals the MPP voltage of then21 un-measurements byAlonso and Chenlo (1998).All the shadowed crystalline silicon cells in series plus the trans-authors observed that solar cellI–U characteristics in mission voltage of a silicon bypass diode, i.e., 0.5 to 1 V.reverse bias show more variation than in forward bias, a The weakest link in a cell string is the solar cell with the

¨result that was statistically verified byDanner and Bucher highest breakdown voltage and thus the highest leakage(1997) and Laukamp et al. (1999). Kovach (1995)also current (Gupta and Milnes, 1981; Hermann et al., 1997).found that under shadowing conditions a poor PV array For today’s crystalline silicon modules, the breakdownlay-out can lead to large energy losses and that even small voltage of a solar cell usually is assumed to be less thanshadows can appreciably affect the energy yield. 210 V. Therefore, mostly one bypass diode is applied per

In order to protect shadowed solar cells from break- 18 cells in series. Multiple parallel interconnections be-down, bypass diodes are applied. In the 1980s a number of tween cell strings within one module, also discussed in theauthors contributed to optimise the PV module design and literature, are usually not applied anymore today.to determine the maximum number of solar cells per In measurements on commercially available reversebypass diode necessary in order to avoid the formation of biased solar cells, cases have been identified with ahot spots (Arnett and Gonzales, 1981; Bhattacharya and breakdown voltage as high as27.2 V, leading to a leakage

A. Woyte et al. / Solar Energy 74 (2003) 217–233 219

current of 1.4 A and associated maximum cell tempera- are available, the better. A solution is offered to thistures as high as 1258C at 210 V reverse voltage. The dilemma with directly integrating the bypass diode in thereverse bias behaviour in this study has been found to be semiconductor structure of each single cell (Suryantospecific to the cell type (Hermann et al., 1998). More Hasyim et al., 1986). Another option for increased shadowrecent measurements, carried out under the European tolerance are cell-integrated converters (Meyer et al.,Commission’s Fifth Framework Programme (IMOTHEE 1997). However, these are not likely to become commer-ERK5-CT1999-00005), returned similar results, leading to cially available in the near future (Quaschning et al.,the conclusion that cell sorting with regard to leakage 1996).current should be included in the production process. That In the meantime, considerable effort has also been madeway, less cells could be applied per bypass diode in in simulating the electrical behaviour of shadowed PVmodules specifically made from cells with higher leakage arrays. A mathematical description of shadowed PV arrayscurrent and breakdown voltage (Hermann et al., 2001; was first derived byRauschenbach (1968). Abete et al.Alonso et al., 2001). (1989) studied the behaviour of parallel and series con-

With the increasing architectural integration of PV into nected solar cells under partial shadowing by applyingroof structures and facades in the mid 1990s, again the Bishop’s model.Quaschning and Hanitsch (1996a)de-question was raised whether the bulky external bypass veloped a model for the photo current of partiallydiodes could be omitted or at least reduced in number. shadowed solar cells. Today, a large number of softwareResearch was mainly carried out in the framework of the tools for the assessment of the electrical behaviour of PVGerman federal research and development (R&D) project arrays is commercially available, however, not all of them‘‘Qualifizierung von PV-Fassadenelementen’’ (BMBF-FKZ are suited for examinations down to the solar cell level032 9658). In that context, it was found that for glass/ under reverse biased conditions (Zehner, 2001).glass modules, bypass diodes should not be omitted unless There are two fundamentally different approaches tothe module design is modified by applying broader cell estimate the reduction in energy yield of partiallyconnectors and a high-heat-conductivity foil in the module shadowed PV systems. One approach is to simulate theback sheets (Knaupp, 1997). With these measures the peak shadows being cast on the PV array by surroundingtemperature could be reduced by about 16 K (Knaupp, obstacles and their variation in time. For this purpose1997). PV modules were measured and simulated with Blewett et al. (1997)applied a heliodon as used byconstructed cast shadows byLaukamp et al. (1998).It was architects to predict natural lighting effects. That way, it isconcluded that bypass diodes may only be omitted if the possible to predict the shadows cast on a PV array in theirradiance distribution is virtually always homogeneous. built environment throughout the year based on an ar-Furthermore, all cells applied must behave almost identi- chitectural model.Wilshaw et al. (1995)also determinedcally under reverse bias and their shunt resistance must not direct and diffuse irradiance, and PV module temperaturebe too high. This however presumes the availability of from the heliodon analysis, enabling conclusions on thesolar cells with standardised reverse bias behaviour. Cur- array yield of the PV system. In general, this type ofrently, cell manufacturers do not control the reverse bias simulation can also be performed on a computer. If thebehaviour of their cells being the reason that in this study dimensions and arrangement of the shadowing objects areeven cells of the same type were found to behave known, the shape and size of the shadow, cast on the PVdifferently when biased in reverse direction (Laukamp et array, can be determined at every moment of the year. Byal., 1999). further applying synthetic or empirical meteorological

As a preliminary conclusion from the aforementioned data, the irradiance on the PV array can be calculated veryGerman R&D project, it was suggested that bypass diodes precisely for every moment in time, allowing for furthershould not be omitted (Stellbogen et al., 1998). In practice simulation of the electrical system behaviour. A detailedone bypass diode per 18 to 20 cells should be applied. With description for the calculation of solar irradiance onthe application of more powerful solar cellsStellbogen et partially shadowed PV arrays is provided (Quaschning andal. (1998)suggest that even a smaller number of cells per Hanitsch, 1995) as is a high-resolution electrical model forbypass diode might become necessary. The results from PV arrays with inhomogeneously illuminated cellsthe European IMOTHEE project generally confirm these (Quaschning and Hanitsch, 1996b). One obvious drawbackfindings yet they more urgently suggest the need for a of such a model with high spatial and time resolution is thesmaller number of cells per bypass diode also for crys- necessary long computation time. Another one is thetalline standard modules as long as manufacturers cannot necessity to know the precise dimensions and positions ofguarantee a continuously high quality with regard to all shadowing objects.breakdown voltage and leakage current of the applied solar Eleven out of 27 programs and tools, presented in acells (Hermann et al., 2001; Alonso et al., 2001). market survey on commercially available PV simulation

While from an architectural point of view, it would be software byZehner (2001),feature possibilities for thedesirable to omit the bypass diodes in the junction box, evaluation of partial shadowing. Four of them can calcu-from the shadowing point of view the more bypass diodes late cast shadows as a function of time as described above.


However, only one of them allows for detailed analysis 1997). In such a case when only a part of the PV module isdown to the level of the single solar cell (Laplace Systems, shadowed, the module orientation has a severe impact on2003). Another of these four programs is intended for the energy yield. Since a partially shadowed 18-cellirradiance calculations only (Zehner, 2001), and the two substring is usually short-circuited by its bypass diode, it isothers have as the smallest spatial unit the PV module, crucial to choose the module orientation in such a way thatwithout applying Bishop’s model for single reverse-biased the solar cells of as little different 18-cell substrings asPV cells (Viotto et al., 1997, 2000; Mermoud et al., 1998). possible are shadowed at a time.

The second approach is based on describing the reduc- Decker et al. (1998)andStellbogen and Pfisterer (1992)tion in irradiation seen from a particular observer point on extended this guideline to PV module strings. They rec-the PV array. Most simulation programs in the afore- ommended to wire the PV array in such a way thatmentioned survey (Zehner, 2001) that feature shadowing, shadowed and unshadowed modules are possibly notapply such an approach where shadowing is considered by connected in series but in parallel. This recommendation isa space angular description of the horizon reduction, generally accepted as a rule of thumb in PV array design,caused by the surrounding obstacles. Knowledge of the however, it only holds for certain model cases. The reasondimensions of surrounding obstacles is not necessary here. is that the 18-cell substrings equipped with bypass diodesIt is sufficient to record their two-dimensional space form the largest significant unit of the PV array with regardangular map on the unit-sphere around the observer point. to string current limitation. Covering one entire module ofThe shadowing geometry can, e.g., be recorded by simple a module string leads to a lower string voltage. However, itoptical measurements (Quaschning and Hanitsch, 1998b) does not limit the total available string current. On theor by means of photography, either applying a spherical other hand, covering one single cell of an 18-cell substringlens (Grochowski et al., 1997; Woyte, 1997) or several limits the current of this particular substring to zero. At the

˜photographs from a customary camera (Caamano and same time, the current of the entire module string bypassesLorenzo, 1997; Frei et al., 2000). After applying the the 18-cell substring that includes the covered cell via theappropriate transformation of coordinates of the sky dome bypass diodes. The power of the 17 unshadowed cells infor the specific lens, the reduction of the visible horizon by this substring is dissipated in the covered cell. Hence, thesurrounding obstacles can be read from the photographs. situation of shadowed cells in an 18-cell substring cannotAs the space angular approach always is valid for one be transferred to the case of shadowed modules in aparticular position on the PV array only, it is mainly suited module string.for rough estimations of the reduction in solar irradiance The impact of the module arrangement on the energyduring a longer time interval. For the detailed analysis of yield of partially shadowed PV arrays in practice is not yetthe electrical system behaviour, this approach is less clear. In practical situations a high number of factors needssuited. Extensions of the space angular approach have been to be taken into account like MPP tracking voltageproposed in order to make the method more convenient to window, DC bus voltage, number of parallel strings andapply. Skiba et al. (2000)applied a digital camera and inverter type, and of course the particular shadowingimage processing software in order to directly process the situation.geometry of surrounding obstacles for the yield simulation. Another crucial and widely discussed question is theTomori et al. (2000)proposed to take two or more fisheye grade of modularity of the system design. For the gridphotographs in order to construct a three-dimensional connection of PV, generally three different classes ofimage of the surrounding obstacles that could then also be system configuration are available: module inverters, stringused for calculating the time variation of cast shadows on inverters or central inverter. Recently, also a hybriddifferent positions of the PV array. concept has been presented (Meinhardt and Cramer, 2001).

The decision which configuration to choose, can have a2 .2. Partial shadowing with different system decisive impact on installation expense, balance-of-systemconfigurations costs, and energy yield and must be made with regard to

the situation of the particular site and to the local climateBased on theoretical considerations, simulation, and also (Table 1).

laboratory and field tests, a number of guidelines for an In recent years, the advantages and drawbacks of theseoptimum arrangement of PV arrays have been determined. different system configurations have been widely dis-Several authors have calculated the optimum spacing cussed. In general, module and string inverters are said tobetween adjacent PV module rows in order to minimise the be less sensitive to an inhomogeneous irradiance dis-losses due to mutual shading of one row by another tribution and easier to install (de Graaf and van der(Appelbaum and Bany, 1979; Bany and Appelbaum, 1987; Weiden, 1994; de Haan et al., 1994; Kleinkauf et al., 1992;Quaschning and Hanitsch, 1998a; Versluis and Jongen, Knaupp et al., 1996; Kurokawa et al., 1997a; Lindgren,2001). 2000; Meinhardt et al., 1999). Central inverters are usually

The impact of the module orientation with snow-covered less expensive, more efficient and more reliable on amodules has been determined (Quaschning and Hanitsch, system base. From a survey on the German market, it


T able 1Characteristic properties of different system configurations; ‘‘PV rated voltage’’ and ‘‘European efficiency’’ from a survey on the Germanmarket (Hupach, 2002)

AC modules String inverter Central inverter

DC installation expense No DC installation No DC junction box Complex DC installationand protection

PV rated voltage 17–90 V 150–800 V 34–800 VMaximum voltage limited by local codes

Ohmic DC-losses Negligible |1% due to short DC lines |1–5%, depending on(percentage of reference yield, estimated) and high DC voltage 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 Installed inverters are sometimes Central, thus easydifficult to reach difficult to reach

appears that the specific prices of small module inverters shadow tolerant than central configurations, is usuallyfor AC modules are still more than twice as high as the derived from the current limiting effect that one shadowedprice of an inverter for a string or central configuration solar cell has on a string of cells. This however, does not(Fig. 1). Inverter reliability does very much depend on the take into consideration the impact of the bypass diodes.environment, and especially humidity and operating tem- Again, the 18-cell substrings equipped with bypass diodes,perature (Wilk and Panhuber, 1995), and also on the form the largest significant unit of the PV array with regardvoltage quality of the grid. The criterion of shadow to string current limitation. Another consequence oftolerance that has so often been mentioned as an advantage inhomogeneous array illumination can be the mismatch ofof modular systems is actually difficult to specify. A wider parallel module strings. This may indeed lead to yieldMPP tracking voltage window might, e.g., contribute to reduction in central inverter systems.shadow tolerance. With several 18-cell substrings of a long Measurements and studies on existing PV systems withstring of modules being shadowed, a wider MPP voltage inhomogeneuos irradiance distributions do not indicatewindow can lead to higher yields, where another MPP significantly better results for modular configurations. Ittracker might not succeed in setting a stable MPP. Such a was confirmed by different authors from field experiencecase has, e.g., been observed byAlonso et al. (1997). that in moderate climates mismatch losses of differently

The idea of modular system configurations being more 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).


below 1% of the annual energy yield (Laukamp and repair, and control of the plant. These conclusions areWiemken, 1997; Maranda, 2001). Tegtmeyer et al. (1997) supported by field test experiences with larger moduleconcluded from laboratory measurements that when partial inverter systems where different inverters failed repeatedlyshadowing occurs from time to time, with central inverters (Erge et al., 2001; Wheldon et al., 2001; Woyte et al.,additional losses are less than 5% of the optimum. A case 2000). Although inverter failures described there might bestudy by Beuth (1998)who simulated two existing PV due to infant diseases, a trend towards higher expenses forsystems with partial shadowing for different configura- monitoring and repair with module inverters may betions, did not show significant advantages of the module expected.inverter configuration. Based on costs for inverters and Although the opposite has often been stated, from theinstallations, and reliability considerations, he recommends literature there is no evidence neither on theoreticalthe application of central or string inverters. grounds nor based on practical measurements that module

Conversely,Gross et al. (1997)conclude in another case inverters are more shadow tolerant than string inverters.study based on heliodon analysis that replacing the present This is because on the one hand, shadowing of single cellscentral inverter by module inverters could reduce losses can at most affect the current of the 18-cell substringsdue to shadowing from 25 to 19.5% of the annual energy equipped with a bypass diode, leading to increased captureyield. From measurements in the field,Wheldon et al. losses with module inverters as well as string inverters. On(2001) observed significant differences in performance the other hand, partial shadowing can lead to differentratio between a central inverter PV system and a number of positions of the MPP in different strings of modules withAC modules at the same location. Partly these differences as a consequence mismatch of parallel strings on a centralare caused by the exceptionally low partial-load efficiency inverter. Parallel mismatch can be avoided with string orof the central inverter. It is further suggested that the better module inverters. With central inverters, the severity ofperformance of the module inverter system would partly be parallel mismatch depends very much on the particularfor the sake of reduced current limiting as it would occur shadowing situation but also on the quality of the par-in series strings of modules and reduced string mismatch ticular MPP tracker.Alonso et al. (1997)identified highunder partial shadowing. For the analysis, the internal miscellaneous capture losses due to insufficient MPPmonitoring functions of the inverters have been used tracking with partially shadowed arrays. In the laboratory(Wheldon et al., 2001). For the module inverters, un- the efficiency of MPP trackers with irregularI–U curvesfortunately this means that DC power is not available and can only be measured by means of rather complex and

ÄC power has been calculated from voltage times current, expensive equipment (Haberlin, 2001), being one of thedisregarding the non-unity power factor. In order to reasons why up to now there is relatively little experienceanalyse the impact of module inverters with partial regarding the effectiveness of MPP trackers with partiallyshadowing more in depth, knowledge of these quantities shadowed PV arrays.would be key. Beside these theoretical considerations, there are virtual-

Similarly, Carlsson et al. (1998)recommend a modular ly no field results that would allow to estimate the impactapproach for increasing the yield of a partially shadowed of different system configurations on the energy yield offlat roof installation. Apparently, the extremely low yield partially shadowed PV arrays. This is why in the scientificdescribed there, mainly originates from mutual shading of discussion, the impact of the system configuration on theadjacent module rows, being comparable to the snow cover final yield of partially shadowed systems often does notof a few cells as examined byQuaschning and Hanitsch become clear. The monitoring campaigns on existing(1997). If this is the case, module inverters would most installations usually suffer from a number of drawbacks.likely not bring much improvement for this installation. A Typical drawbacks are the lack of operational data asmuch more effective measure would be turning the module irradiance on the PV array or on an unshadowed referenceframes by 908. In another case study of a heavily shadowed location, or electrical DC power. However, the mostPV system applying module inverters,Woyte et al. (2000) significant drawback is the lack of long-term performanceclearly identified a positive impact of the modular design data from different alternative system configurations withregarding the avoidance of string mismatch. The question realistic and well known shadowing under identical oper-whether a comparable yield could be received by applying ating conditions. Without such field test data from differentstring inverters was not answered in this study. sites, it is almost impossible to make any firm statement on

The PV arrays described byKnaupp et al. (1996)and the appropriateness of the different available systemGross et al. (1997)are rather large facade installations of configurations with regard to partial shadowing.10 kWp and 40 kWp, respectively. However, as a conclu- This is why at the electrical energy research group ofsion from experiences with AC modules in the Nether- K.U. Leuven, a grid-connected photovoltaic system waslands, Marsman et al. (1998)recommended that AC set up in 1999. The aim was to collect operationalmodules should not be applied in systems with about more experience with the different system approaches underthan 10 modules. As a reason they gave relatively higher non-optimum operation conditions like partial shadowinginverter costs and rising problems with maintenance, and also to assess the quality of photovoltaic system


components. The photovoltaic array with a peak power of position does not receive any direct radiation before5.16 kW is situated on the roof of a university building in approximately 8:00 to 8:30 h true solar time, all over theLeuven–Heverlee in Belgium. Long-term analytical moni- year. With some further photographs taken from othertoring of the installation allows for a more detailed positions, and recalling that the maximum height of theanalysis of the different system approaches, and conclu- sun from mid November to the end of January, in Belgiumsions on their appropriateness with regard to partial does not exceed 208, an experienced PV system designershadowing can be drawn. can conclude that on the site shown inFig. 2, roughly 8 to

15% average losses in annual irradiation have to beexpected. Having to accept these shadowing losses for the

3 . Photovoltaic system set-up given site, the designer can still optimise the arrayarrangement in order to avoid increased miscellaneous

The PV array at K.U. Leuven is installed on a flat roof, capture losses.set up in three successive module rows. The site is situated If geometric figures describing the surrounding obstacles30 m above sea level at 4.78 eastern longitude and 50.98 are unknown, the estimation based on experience and somenorthern latitude in a moderate maritime climate. The array photographs can lead to good results. A design for theis shadowed by an air-conditioning system on the roof K.U. Leuven system based on these estimations has been(airco box) and by the front rows themselves. The visible drafted by applying the aforementioned rule of thumb. Ashorizon is reduced by vegetation and a neighbouring far as possible, only those modules, that receive homoge-building, all leading to reduced array yields, in particular neous irradiance at a certain time and date have beenduring the winter. arranged to a common string. In order to recheck the

Under these non-optimum but very typical conditions, a estimations derived from the fisheye photographs, thePV system applying all of the three available design losses in annual irradiation have been calculated by meansapproaches has been implemented (Woyte et al., 2001). of computer simulation, applying the packages StaSol andLooking at the designated site through a fish-eye lens (Fig. PVcad.2) gives a first impression of the reduction of the visible The program StaSol determines the annual irradiationhorizon by surrounding obstacles as viewed from the PV losses due to shadowing by a space angular approach,array location. The photographs inFig. 2 had been taken comparable to the approach with the fish-eye photographbefore the PV array was installed. The horizon reduction (Grochowski et al., 1997; Woyte, 1997). Shadowingby the PV array’s front row has been calculated afterwards objects are characterised by their two-dimensional map onand added to the photographs as a hatched area limited by the unit-sphere as it is viewed from a specific observera dashed line (Fig. 2). point. From the map of shadowing objects on the unit-

By means of superposing coordinates of the sky dome, sphere, the reduction in direct and diffuse radiation for thisone can determine the date and time of the day when a observer point is calculated, based on time series’ of globalcertain point of the designated location for the PV array is and diffuse irradiance for one year. For the calculation ofshadowed. The photographer’s position receives no direct diffuse radiation on the tilted surface, StaSol applies Hay’sirradiance with solar elevation angles lower than approxi- anisotropic model, taking into consideration a circumsolarmately 108 during the whole day. Looking to the east, at component but no horizon brightening (Iqbal, 1983). In thethe very left of Fig. 2, one sees an alone-standing tree present case, such a space angular computation with StaSolcovering the sun for azimuth angles east of 1108. This 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.


Fig. 3. PV array site, array arrangement, and simulated annual reference yield on the PV array after shadowing (Y ) normalised onrSh

reference yield without shadowing (Y ), height level of the lower side of the PV array: 45 cm above the roof plane.r

the PV array plane, with the two-dimensional map of the nearby obstacles. The spacing between the module rowsshadowing objects calculated from their coordinates in the has been chosen to be 5.60 m. The modules are south-three-dimensional space. The mesh density was one node oriented and 308 tilted. According to Quaschning andper 12 cm. Input data for the StaSol calculations were Hanitsch (1998a)the annual irradiation loss by mutualhourly average values of global and diffuse irradiance, shading of one row by another can then be estimated to berecorded in Brussels–Uccle by the Royal Meteorological about 7%. Larger spacing between the rows would lead toInstitute of Belgium in 1997. These data allow to de- intolerable shadowing of the middle array by the airco boxtermine the relative influence of shadowing on the annual (Fig. 3).energy yield, and its distribution over the module arrays, Table 2provides an overview on the configurations ofarranged as shown inFig. 3. the different subsystems. For all subsystems the same type

PVcad calculates hourly irradiance values that can of 120-Wp PV modules has been applied. The modulesfurther be processed in an electrical model of the PV consist of 72 polycrystalline solar cells either operating insystem. A ray tracing algorithm is applied in order to series connection, or as a parallel connection of two stringscalculate the shadows cast on the PV array by the of 36 cells each. A bypass diode is applied per 18 cells. Insurrounding obstacle. The spatial resolution for PVcad is practice, the module peak power under STC is lower thanthe size of a PV module. The entire module is considered 120 Wp for most modules delivered. The peak powerto receive no direct radiation as long as a part of it is values for the different subsystems inTable 2 are morestruck by the cast shadow. The impact of horizon reduction precise values, measured by the manufacturer beforeon diffuse radiation is also taken into consideration by delivery. The further analysis of yields and losses for theadditionally applying a space angular approach to the different strings and subsystems is based on these mea-diffuse fraction (Viotto et al., 2000). For the calculation of sured values.diffuse radiation on the tilted surface, PVcad applies Perez’ According to the simulation with StaSol, for the chosenanisotropic model, taking into consideration a circumsolar arrangement the annual reduction in reference yield due tocomponent and also horizon brightening (Perez et al., shadowing lies between 4 and 22% of the reference yield1987). from an unshadowed location (Fig. 3). Especially on the

Based on these simulations, the 43 PV modules were outer east side of the middle row, shadowing is veryarranged in order to minimise losses due to shadowing by severe. In winter, especially the lower cells are shadowed

T able 2Specifications of the different subsystems

Inverter class Subsystem P P MPP tracking No. of PV power MPP voltageAC,r DC,r

(W) (W) window (V) modules at STC (Wp) at STC (V)

Central inverter 11 2280 2500 66 . . . 150 24 2835.0 103String inverter 21 1500 1650 200 . . . 500 15 1729.0 257Module inverter 31 90 100 24 . . . 50 1 118.7 34Module inverter 32 110 130 24 . . . 40 1 118.8 34Module inverter 34 200 240 64 . . . 80 2 246.3 68


by the front module row and the airco box. In summer The simulation with StaSol does not provide informationduring morning hours, these modules are shadowed by the on the temporal variation in solar irradiance on the PVaforementioned tree in the south-east. array. Extreme shadowing situations as, e.g., the one

The low irradiation on the front array is mainly due to caused by the airco box are not detected. Even though, forthe reduction of the visible horizon by vegetation and the avoiding increased miscellaneous capture losses, onlyneighbouring building. Since neighbouring building and neighbouring modules that on an annual basis receivevegetation are situated rather far from the PV array, the approximately equal irradiation were connected in series,solar irradiation is distributed relatively homogeneously thus following the guidelines ofDecker et al. (1998)andover this area. Stellbogen and Pfisterer (1992).For the central inverter,

On an annual basis the average shadowing loss in this issue has been realised as well as practically possible.reference yield amounts to 9.6%. A simulation with PVcad Since AC modules are generally considered to be morebased on synthetic irradiance values, also for the location shadow tolerant, the AC modules are placed to the localof Brussels–Uccle, leads to little higher values in reference minima of annual irradiation as shown inFig. 3.Regardingyield after shadowing with an average shadowing loss of the string inverter, increased miscellaneous losses might7%. These differences are discussed more in depth in the occur because of the local minimum in irradiation on thefollowing section. outer east side. On the other hand, there are no parallel-

The impact of the airco box and the front row of connected module strings so that string mismatch ismodules on the eastern modules of the middle row can be disabled.examined more in depth by means ofFig. 4.Viewed from The system is monitored analytically according to thethe photo position both, airco box and front row, are guidelines of the European Commission. The quantitiesapproximately 108 high. For lower observer points on the monitored are shown inTable 3.The in-plane irradiance ismiddle row, the visible horizon is mainly reduced by the measured at four differently shadowed positions on the PVairco box, up to an elevation angle of 238 at the lower side array (Fig. 3) as well as on one unshadowed referenceof the module frame. This means that during the winter position on another roof, about 80 m from the PV array.months, the lowest row of cells does virtually not receive Module temperatures are recorded for four modules closeany direct radiation. Since the cell strings in the module to the different reference cells. DC string currents arerun in the vertical direction, this leads to current limiting in measured for all module strings, while DC system voltageall four 18-cell substrings of this module. At periods with and AC energy yield are measured for each inverter. Thenoteworthy direct irradiance with low solar elevation, all sampling period is set to 1 s and the measured data isfour bypass diodes will conduct and the available power of stored as 5-min average values.the unshadowed cells is dissipated in the few shadowedcells, leading to extreme miscellaneous capture losses inthis module as a consequence of shadowing. 4 . Monitoring results

Conversely, the irradiance on the upper modules isdistributed much more homogeneously, even in winter. 4 .1. Comparison to simulation resultsViewed from the photographer’s position ofFig. 2, thehorizon is reduced by vegetation and a neighbouring The values of reference yield after shadowing normal-building, up to 108 in the south east and up to approximate- ised on unshadowed reference yield measured during thely 58 in the south west. The neighbouring building and year 2001 are, at some positions considerably, lower thanvegetation are situated rather far from the PV array. the simulation results (Table 4). The values from theTherefore, this horizon reduction approximately also ap- simulation with PVcad are still little higher than those fromplies for the upper modules and unlike the one originating StaSol.from the airco box it is insensitive to small variations of The approach of PVcad to consider the PV module forthe observer position. Extreme miscellaneous capture not receiving any direct radiation when it is struck evenlosses are not to be expected here. 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.


T able 3Monitored quantities and applied sensors

Quantity No. Sensor

MeteorologyIrradiance, global horizontal (unshadowed) 1 Pyranometer, WMO class IIIrradiance, diffuse horizontal (unshadowed) 1 Pyranometer, WMO class II with shadow ringIrradiance, global in-plane (unshadowed) 1 Reference cell, mono-Si, temperature compensatedIrradiance, global in-plane (positions A–D on the PV array) 4 Reference cell, mono-Si, temperature compensatedAmbient temperature 1 Pt 100 thermo resistance, radiation shielded

PV arraysDC string current 8 Hall effect current transducerDC system voltage 5 Hall effect voltage transducerModule temperature 4 Pt 100 thermo resistance on the back of a PV cell

Inverter outputsAC energy from inverter 5 Energy pulse counter

reference yield after shadowing from PVcad than from input data can explain the variations between PVcad andStaSol. Also the consideration of horizon brightening in StaSol, however, they cannot explain the larger dis-PVcad might suggest slightly lower values for reference crepancy between simulation results and measured values.yield after shadowing with PVcad since horizon reduction In 2001, the measured diffuse fraction of global radiationby obstacles mainly affects the light incident from low was 57%. The inaccuracies introduced by the differentelevation angles. This light is underestimated in Hay’s models for diffuse radiation on the tilted plane can notmodel in comparison to Perez’ model. Since the geometric satisfactorily explain this discrepancy either, even moredescription of shadowing obstacles is identical for both since the PVcad results, although calculated by the moresimulations, it must be concluded that the unexpectedly accurate Perez model, differ more from the measuredhigher annual irradiation from PVcad in comparison to values than the StaSol results.StaSol is due to the annual variation in the radiation input At position C where there are no obstacles close to thedata. Indeed, the diffuse fraction of measured global PV array but only vegetation and a building on the horizon,radiation from 1997 that has been applied to the simulation the results are rather accurate for both simulations. At thewith StaSol amounts to 53% whereas the synthetic time other positions and especially position A, the aforemen-series of global radiation from PVcad contains 63% diffuse tioned tree on the very left ofFig. 2 and the airco boxradiation. Since diffuse radiation has no specific direction, become significant. Especially the airco box but also theshadowing by obstacles does reduce the diffuse fraction tree are situated very close to the PV array. While theonly by a small, relatively constant portion being roughly dimensions of the airco box are comparably well known,proportional to the fraction of the sky dome covered by the the dimensions of the tree could only be estimated fromobstacles. On the other hand, the direct fraction of solar optical measurements and they continuously vary with theradiation is limited to zero, when an observer point is seasons. Even small inaccuracies in the geometric descrip-shadowed by an obstacle. Therefore, in general terms, the tion of these two obstacles can lead to large errors in theshadowing losses in irradiation are the less severe, the estimation of annual in-plane irradiation for positions closehigher the diffuse fraction. to these obstacles.

The variations in diffuse fractions of the different sets of It can be concluded that regardless of the appliedsimulation model and the solar radiation input data,simulation programs for partial shadowing are only asT able 4

Annual reference yield on the PV array after shadowing (Y ) good as is the description of the shadowing obstacles.rSh

normalised on reference yield without shadowing (Y ) Especially with obstacles of irregular shape, situated closer

to the PV array, considerable inaccuracies should be takenReference cell Normalised reference yield after shadowinginto account.(Y /Y ) (%)rSh r

position PVcad StaSol Measurement 4 .2. Identification of losses on an annual basisA 90 85 80B 95 93 85 The performance analysis follows the terminology pro-C 92 89 88 ¨posed byHaberlin and Beutler (1995).Additionally, theD 94 92 83 capture losses (L ) are divided into shadowing lossesC

(L ) and miscellaneous capture losses (L ).CSh CMAverage 93 90 86


In order to exactly determineL , it would be neces- ratio between averageY and reference yieldY is 0.86.CSh rSh r

sary to measure solar irradiance on all significant positions This means that approximately 14% of the available solarof the PV array, meaning at the very least one measure- irradiation is lost by shadowing instead of 7 to 10% as hadment per PV module. In practice, this is not feasible and to be expected from the simulations. The performance ratiotherefore, Y must be approximated for the different based on reference yield after shadowing (PR ) amountsrSh Sh

subsystems from the available data. For the string inverter to 77% being a good value under normal operatingand the AC module subsystems, the reference yield after conditions and indicating that miscellaneous capture lossesshadowing has been approximated by the measured value are not higher than normal.from the respectively closest reference cell as indicated in A look at the different subsystems shows that the lossesFig. 3: are distributed differently for each subsystem (Fig. 5).

Shadowing losses (L ) are highest for the AC modules,CShString inverter (subsystem 21):Y 5 Y (1)rSh rShC as they have intentionally been assigned to the positions

with lowest presumed annual irradiation.AC module (subsystem 31):Y 5Y (2)rSh rShA The miscellaneous capture losses (L ), caused byCM

series and parallel mismatch, inefficient MPP tracking, andAC module (subsystem 32):Y 5Y (3) high module temperatures are lower for the AC modulesrSh rShA

than for the other configurations. The string inverter had anAC module (subsystem 34):Y 5Y (4) outage of 10 days in June: its final yield and array yieldrSh rShD

should be evaluated about 5% higher.Since the reference cells A, C, and D are all mounted at The system losses (L ) that mainly occur in the inverter,S

the lower edge of a module row, the values from these are the highest for module inverters. This can only bereference cells tend to underestimate the respective annualpartly explained by the generally lower efficiency ofreference yield after shadowing. Especially for AC module smaller inverters as a function of scale.Table 5comparessubsystem 31 this might be critical due to the airco box long-term system efficiency in the field (h ) to theS

that affects reference cell position A much more than AC European efficiency (h ) of the different inverters. Espe-EU

module subsystem 31. This possible inaccuracy should be cially for the subsystems that are shadowed most severely,kept in mind when analysing the capture losses in terms of the system losses are higher than the European efficiencyshadowing losses and miscellaneous capture losses. would suggest. These unexpected system losses can only

For the central inverter (subsystem 11) that is spatially be explained by the fact that the subsystems in questionextended over the two back module rows, the reference due to their comparably higher shadowing losses, operateyield after shadowing has been approximated by the more time under partial load conditions associated to aarithmetic average of the extreme values for these two lower inverter efficiency. On the other hand, the stringmodule rows. According to the results from StaSol (Fig. inverter is generally shadowed little and it contains no3), the annual irradiation on the two rows of subsystem 11 transformer, leading to a high efficiency even in com-is minimal at the reference cell positions A and D, parison with inverters of similar size.respectively, at the lower east of each module row. Theannual irradiation on subsystem 11 is maximal on theupper west of each row. For the middle row, this value is 4 .3. Array performance on a monthly basisrecorded at position B. For the back row, no reference cellis available at the upper west. Since according toFig. 3 Fig. 6a shows the array performance ratio (PR )A

this position is still shadowed significantly though con- throughout the year. AC module subsystem 32 is sufferingsiderably less than position B, the maximum reference considerably from shadowing in December and January.yield after shadowing for the back array is approximated Its upper neighbour, AC module subsystem 31, seems toby the arithmetic average of reference yield at position B be much less affected. Based onFig. 4 it can be concludedand reference yield without shadowing. Under this as- that this is mainly a consequence of partial shadowingsumption the arithmetic mean of these four extreme values being much more severe on the lower AC modulefor the central inverter (subsystem 11) yields: (subsystem 32) than on AC module subsystem 31. This has

also been confirmed by visual inspection. After lightY 5 Y 1 Y 1 Y 1 (Y 1 Y ) /2 /4f grSh rShA rShB rShD r rShB snowfall in the early morning of 7 January 2003, the snow

5 2Y 1 3Y 1 2Y 1 Y /8 (5) on AC module subsystem 31 was melted very quickly bys drShA rShB rShD r

the direct sunlight while AC module subsystem 32 partlyremained shadowed by the airco box and was still snow-The averageY for the entire PV system is thenrSh

covered for about half of its surface area around solarcalculated as the weighted average ofY for allrSh

noon. Closer analysis shows that also in winter the systemsubsystems taking into account their particular surfacelosses are equal for both module inverters. Therefore, itareas.must be concluded that the low performance of AC moduleThe performance ratio of the total system is 0.66. The


Fig. 5. Losses and yields for all subsystems, performance ratio (PR) and performance ratio with reference yield after shadowing (PR );Sh

L : capture losses due to shadowing,L : miscellaneous capture losses,L : system losses,Y : final yield; monitoring from 1 January to 31CSh CM S f

December 2001.

subsystem 32 in winter is a consequence of extreme only for a short time in the morning. The two positions onshadowing. the lower edges of the two back arrays, positions A and D,

The array performance ratio of the separate strings of are shadowed much more severely. Position A onlythe central inverter (Fig. 6b) does not indicate a serious receives direct irradiance during 2 h in the late afternoonparallel mismatch. Throughout the year, slight differences which corresponds to the expectations derived on the basisin array yield can be observed between the four strings. ofFig. 2 and Fig. 4.These differences correspond to differences in reference The two AC modules subsystems 31 and 32 are situatedyield after shadowing. Increased miscellaneous capture east of position A. Inspection of the output power of thelosses due to mismatch could not be verified. module strings (Fig. 8) shows that the DC power of

subsystem 32 during the whole day follows the diffuse4 .4. Array performance on a winter day irradiance, without exhibiting the rise in direct irradiance

at position A although this AC module is situated less thanFive-minute average values from a clear winter day one metre east of position A. This indicates that part of the

serve for a more detailed analysis of shadowing losses and AC module subsystem 32 indeed does not receive anymiscellaneous capture losses (Fig. 7). The in-plane ir- direct irradiance during these hours. Its low yield isradiance at positions B and C is affected by shadowing obviously due to shadowing. The losses are on the one

hand shadowing losses and on the other hand miscella-neous capture losses due to current limitation in its 18-cell

T able 5 substrings caused by partial shadowing. The DC voltage atComparison of European efficiency to long-term system efficiency

AC module subsystem 32 from 9:00 to 15:00 h variedin the field for the applied invertersbetween 28 and 33 V which is well inside the MPP

Inverter class Subsystem h (%) h (%) h /hS EU S EU tracking range of the inverter. Hence, even with severeshadowing of this AC module, the inverter’s MPP trackerCentral inverter 11 88.7 90.0 0.986

aString inverter 21 91.8 94.4 0.972 works well indicating that the system’s low performanceaModule inverter 31 83.8 90.3 0.928 ratio is not caused by a low MPP tracking efficiency. Other

Module inverter 32 81.8 90.0 0.909 AC modules placed at this location would perform equallyaModule inverter 34 87.6 90.6 0.967 badly.

a String 12 of the central inverter array also is heavilyËuropean efficiency from manufacturers, measured byHaber-lin (2001). shadowed at this sample day. The string only has a 1–2-h


Fig. 6. Monthly array performance ratio (PR ) in 2001.A

maximum around noon when also the lowest row of cells 5 . Conclusionsin this module string is free from shadowing by the frontrows or the airco box. This, however, has no significant Although considerable research on partial shadowing ofnegative impact on the power generated by the other PV arrays has already been carried out, the impact of thestrings of the central inverter generating high power as PV system configuration on the energy yield of partiallysoon as they receive sufficiently direct irradiance. Appar- shadowed systems is not entirely clear. This is why aently the classical central inverter systems are less sensi- partly shadowed PV system has been set up at K.U.tive to shadowing than always assumed. A reduction of Leuven applying a central inverter as well as string andstring currents by series mismatch is mitigated thanks to module inverters. The installation has an overall per-the bypass diodes, and also parallel string mismatch is formance ratio of 66%. Performance ratio after shadowingapparently not an issue for today’s MPP trackers. amounts to 77% being a good value under normal oper-


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 array, the simulation returns a rather good estimation oflosses are low. shadowing losses.

An estimation of irradiation losses due to shadowing has For the system under examination, the monitoringbeen carried out. Measurements show that with obstacles results show no evidence for a different behaviour withof irregular shape being close to the PV array, the regard to partial shadowing of central inverter, stringsimulation estimates the shadowing losses up to 10% too inverter, or module inverter configuration. Generallylow. At array positions that mainly suffer from a reduction speaking, AC modules are not more significantly shadowof the visible horizon by obstacles being far from the PV 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).


biased silicon solar cells. In: Proceedings of the 2nd Worldstrings. For string current limitation by shadowed cells, theConference on PVSEC, Vienna, pp. 2376–2379.18-cell substring equipped with a bypass diode is the

A lonso, M.C., Herrmann, W., German, R., Boehmer, W., Wam-largest significant unit causing similar capture losses inbach, K., 2001. Outdoor hot-spot investigation in crystallinemodule as in central inverter systems. With regard tosilicon solar modules. In: Proceedings of the 17th EC PV Solarparallel mismatch, central inverter systems may sufferEnergy Conference, Munich, pp. 638–641.increased miscellaneous capture losses as a consequence of

A ppelbaum, J., Bany, J., 1979. Shadow effect of adjacent solarshadowing, but in the present case this effect could not becollectors in large scale systems. Solar Energy 23, 497–507.

found significant.A rnett, J.C., Gonzales, C.C., 1981. Photovoltaic module hot spot

These results hold for situations with obstacles coveringdurability design and test methods. In: Proceedings of the 15th

the visible horizon or discrete obstacles that are con- IEEE Photovoltaic Specialists Conference, Kissimmee, pp.siderably large, in order not only to shadow a few solar 1099–1105.cells per module during a longer period. For filigree- B any, J., Appelbaum, J., 1987. The effect of shading on the designshaped obstacles that only shadow a few cells in several of a field of solar collectors. Solar Cells 20, 201–228.modules, like, e.g., antennas or chimneys, this conclusion B hattacharya, G., Neogy, C., 1991. Removal of the hot-spotdoes not necessarily apply. In such case however, AC problem in photovoltaic modules and arrays. Solar Cells 31,modules will suffer from increased miscellaneous capture 1–12.losses as non-modular PV systems do. Then amorphousB euth, O., 1998. Vergleichende Systemanalyse netzgekoppelter

¨Photovoltaikanlagen. Universitat Hannover, Fachbereich Elek-modules with cell-integrated bypass diodes or cell inte-¨trotechnik and Institut fur Solarenergieforschung, Hannover.grated inverters might provide a solution. Alternatively, the

B ishop, J.W., 1988. Computer simulation of the effects of electri-most heavily shadowed positions should be equipped withcal mismatches in photovoltaic cell interconnection circuits.a dummy module.Solar Cells 25, 73–89.In order to validate these results on a broader basis,

B ishop, J.W., 1989. Microplasma breakdown and hot-spots insimilar field test installations should be set up at different

silicon solar cells. Solar Cells 26, 335–349.locations and for diverse shadowing situations. The most B lewett, T., Horne, M., Hill, R., 1997. Heliodon prediction ofimportant data for such an evaluation are DC power down shading on building integrated photovoltaic systems. In:to module level and solar irradiance on the PV array with Proceedings of the 26th IEEE Photovoltaic Specialists Confer-very high spatial resolution. A better understanding of ence, Anaheim, CA, pp. 1393–1396.

˜partially shadowed PV systems is crucial in order to C aamano, E., Lorenzo, E., 1997. On-site characterisation of grid-connected PV systems. In: Proceedings of the 14th EC PV Solarevaluate the different system configurations on an objec-Energy Conference, Barcelona, pp. 1536–1539.tive basis without being influenced by marketing ar-

C arlsson, P., Cider, L., Lindgren, B., 1998. Yield losses due togumentation.shading in a building integrated PV installation; evaluation,simulation and suggestions for improvements. In: Proceedingsof the 2nd World Conference on PVSEC, Vienna, pp. 2666–

A cknowledgements2670.

¨D anner, M., Bucher, K., 1997. Reverse characteristics of commer-The PV installation at K.U. Leuven has been supported cial silicon solar cells—impact on hot spot temperatures and

by the Belgian utility companies Electrabel and SPE within module integrity. In: Proceedings of the 26th IEEE Photovoltaic¨the project ‘‘Fotovoltaısche zonnecelsystemen voor onder- Specialists Conference, Anaheim, CA, pp. 1137–1140.

wijsinstellingen’’ and by the Flemish regional government. D ecker, B., Jahn, U., 1997. Performance of 170 grid connected PVplants in northern Germany—analysis of yields and optimi-Part of the work done was funded via the IWT-GBOUzation potentials. Solar Energy 59, 127–133.project ‘‘Embedded generation: A global approach to

D ecker, B., Grimmig, B., Stellbogen, D., 1998. Projektierung vonenergy balance and grid power quality and security’’.Photovoltaik-Fassadenanlagen. In: Proceedings of the 13thÏngenieurburo Mencke & Tegtmeyer in Hameln, GermanySymposium Photovoltaische Solarenergie, Staffelstein, pp. 197–is acknowledged for their practical assistance with the data204.

logging equipment. Ë rge, Th., Hoffmann, V.U., Kiefer, K., Rossler, E., Rindelhardt,U., Teichmann, G., Decker, B., Grochowski, J., Heilscher, G.,

¨Schneider, M., Blasser, G., Ossenbrink, H., Becker, H.,Vaassen,R eferences W., Genennig, B., Riess, H., Sprau, P., 1998. The German

´ ´1000-roofs-PV-programme—a resume of the 5 years pioneerproject for small grid-connected PV systems. In: Proceedings ofA bete, A., Barbisio, E., Cane, F., 1989. A study of shading effectsthe 2nd World Conference on PVSEC, Vienna, pp. 2648–2651.in photovoltaic generators. In: Proceedings of the 9th EC PV

Ë rge, Th., Beuschel, A., Kiefer, K., Rossler, E., Schmitz, W.,Solar Energy Conference, Freiburg, pp. 240–244.2001. Operation experience of the 120 kWp PV system ‘‘But-A lonso, M.C., Arribas, L.M., Chenlo, F., Cruz, I., 1997. Shadingzweilerhof’’. In: Proceedings of the 17th EC PV Solar Energyeffect on a roof integrated grid-connected PV plant. In: Proceed-Conference, Munich, pp. 2375–2378.ings of the 14th EC PV Solar Energy Conference, Barcelona,

pp. 1891–1894. F rei, R., Meier, C., Eichenberger, P., 2000. A fast, efficient andA lonso, M.C., Chenlo, F., 1998. Experimental study of reverse reliable way to determine the PV-shading horizon. In: Proceed-


ings of the 16th EC PV Solar Energy Conference, Glasgow, p. K ovach, A.M., 1995. Effect of Partial Shading on the Energy2678. Performance of Photovoltaic Arrays Integrated onto Buildings.

¨d e Graaf, L.E., van der Weiden, T.C.J., 1994. Characteristics and VDI-Verlag, Dusseldorf.performance of a PV-system consisting of 20 AC-modules. In: K urokawa, K., Kamisako, K., Shimizu, T., 1997a. ConceptualProceedings of the 1st World Conference on PVSEC, Hawaii, considerations on PV systems composed of AC modules. Solarpp. 921–924. Energy Mater. Solar Cells 47, 243–250.

G rochowski, J., Fuge, U., Niehage, M., 1997. STASOL Ein K urokawa, K., Sugiyama, H., Uchida, D., 1997b. Extended¨Programm zur Simulation der Solarstrahlung unter Berucksich- performance analysis of 70 PV systems in Japanese field test

tigung von Teilabschattungen der Diffus- end Direktstrahlung. program. In: Proceedings of the 26th IEEE PhotovoltaicIn: Proceedings of the 12th Symposium Photovoltaische Specialists Conference, Anaheim, CA, pp. 1249–1252.Solarenergie, Staffelstein, pp. 106–110. L aplace Systems (2003). Photovoltaic system simulation software

G ross, M.A., Martin, S.O., Pearsall, N.M., 1997. Estimation of Solar Pro.http: / /www.lapsys.co.jp /,accessed 31 March 2003.output enhancement of a partially shaded BIPV array by the use L aukamp, H., Wiemken, E., 1997. Mismatch effects and inverterof AC modules. In: Proceedings of the 26th IEEE Photovoltaic sizing in PV generators with different sections. In: ProceedingsSpecialists Conference, Anaheim, CA, pp. 1381–1384. of the 14th EC PV Solar Energy Conference, Barcelona, pp.

G upta, A., Milnes, A.G., 1981. Effects of shading and defects in 1101–1105.solar cell arrays: a simple approach. In: Proceedings of the 15th L aukamp, H., Kresse, A., Leithold, W., 1998. PV-Module ohneIEEE Photovoltaic Specialists Conference, Kissimmee, pp. Bypass-Dioden? In: Proceedings of the 13th Symposium Photo-1111–1116. voltaische Solarenergie, Staffelstein, pp. 437–442.

¨d e Haan, S.W.H., Oldenkamp, H., Frumau, C.F.A., Bonin, W., L aukamp, H., Danner, M., Bucher, K., 1999. Sperrkennlinien von1994. Development of a 100 W resonant inverter for AC- Solarzellen und ihr Einfluss auf Hot-Spots. In: Proceedings ofmodules. In: Proceedings of the 12th EC PV Solar Energy the 14th Symposium Photovoltaische Solarenergie, Staffelstein,Conference, Amsterdam, pp. 395–398. pp. 414–419.¨H aberlin, H., Beutler, Ch., 1995. Normalized representation of L indgren, B., 2000. A PV-module oriented inverter, feeding a lowenergy and power for analysis of performance and on-line error voltage AC bus. In: Proceedings of the 16th EC PV Solardetection in PV systems. In: Proceedings of the 13th EC PV Energy Conference, Glasgow, pp. 2531–2534.Solar Energy Conference, Nice, pp. 934–937. M aranda, W., 2001. Parallel operation of non-uniformly oriented¨H aberlin, H., 2001. Evolution of inverters for grid connected PV-arrays. In: Proceedings of the 17th EC PV Solar EnergyPV-systems from 1989 to 2000. In: Proceedings of the 17th EC Conference, Munich, pp. 2665–2668.PV Solar Energy Conference, Munich, pp. 426–430. M arsman, H., Kil, A.J., Hoekstra, K.J., Burges, K., Hommerson,

H ermann, W., Wiesner, W., Vaassen, W., 1997. Hot spot inves- J.R., Oldenkamp, H., 1998. Design and operational experiencetigations on PV modules—new concepts for a test standard and with small and medium sized inverters in The Netherlands. In:consequences for module design with respect to bypass diodes. Proceedings of the 2nd World Conference on PVSEC, Vienna,In: Proceedings of the 26th IEEE Photovoltaic Specialists pp. 1987–1993.

´ Ćonference, Anaheim, CA, pp. 1129–1132. M einhardt, M., Leonavivius, V., Flannery, J., O Mathuna, S.C.,H ermann, W., Adrian, M., Wiesner, W., 1998. Operational be- 1999. Impact of power electronics packaging on the reliability

haviour of commercial solar cells under reverse biased con- of grid connected photovoltaic converters for outdoor applica-ditions. In: Proceedings of the 2nd World Conference on tions. Microelectron. Reliability 39, 1461–1472.PVSEC, Vienna, pp. 2357–2359. M einhardt, M., Cramer, G., 2001. Multi-string-converter: the next

H ermann, W., Alonso, M.C., Boehmer, W., Wambach, K., 2001. step in evolution of string-converter technology. In: Proceed-Effective hot-spot protection of PV modules—characteristics of ings of the European Power Electronics Conference, Graz,crystalline silicon cells and consequences for cell production. Proceedings on CD-ROM.

Ïn: Proceedings of the 17th EC PV Solar Energy Conference, M ermoud, A., Roecker, C., Bonvin, J., Muller, A., 1998. PVSYSTMunich, pp. 1646–1649. 3.0 software: ergonomics & accessibility. In: Proceedings of the

¨H upach U. (2002). Kriterien fur gute Wechselrichter, Photon 2nd World Conference on PVSEC, Vienna, pp. 2632–2635.Special, pp. 46–56. M eyer, T., Schmidt, H., Toggweiler, P., Riatsch, J., Weng, M.,

I EC 61215 (1993). Crystalline silicon terrestrial photovoltaic (PV) Guillardeau, D., 1997. Single cell module integrated convertermodules—design qualification and type approval. system (SCMIC) preliminary results. In: Proceedings of the

I qbal, M., 1983. In: An Introduction to Solar Radiation. Academic 14th EC PV Solar Energy Conference, Barcelona, pp. 2214–Press Canada, Don Mills, pp. 315–316. 2217.

K leinkauf, W., Sachau, J., Hempel, H., 1992. Developments in O tani, K., Sakuta, K., Sugiura, T., Kurokawa, K., 2001. Per-inverters for photovoltaic systems. In: 11th EC PV Solar formance analysis and simulation on 100 Japanese residentialEnergy Conference, Montreux, pp. 1029–1033. grid-connected PV systems based on four year experience. In:

¨K naupp, W., Schekulin, D., Voigtlander, I., Bleil, A., Binder, C., Proceedings of the 17th EC PV Solar Energy Conference,1996. Operation of a 10 kW PV facade with 100 W AC Munich, pp. 2403–2406.photovoltaic modules. In: Proceedings of the 25th IEEE Photo- P erez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987.voltaic Specialists Conference, Washington, DC, pp. 1235– A new simplified version of the Perez diffuse irradiance model1238. for tilted surfaces. Solar Energy 39, 221–231.

K naupp, W., 1997. Evaluation of PV module designs at irregular Q uaschning V., Hanitsch R. (1995). Shade calculations in photo-operation conditions. In: Proceedings of the 26th IEEE Photo- voltaic systems. Paper presented to ISES World Congress,voltaic Specialists Conference, Anaheim, CA, pp. 1235–1238. Harare.

http://www.lapsys.co.jp/






Q uaschning, V., Piske, R., Hanitsch, R., 1996. Cost effectiveness Photovoltaik-Anlagen. In: Proceedings of the 12th Symposiumof shadow tolerant photovoltaic systems. In: Proceedings of the Photovoltaische Solarenergie, Staffelstein, pp. 241–245.EuroSun ‘96, Freiburg, pp. 819–824. T omori, T., Otani, K., Sakuta, K., Kurokawa, K., 2000. On-site

BIPV array shading evaluation tool using stereo-fisheye photo-Q uaschning, V., Hanitsch, R., 1996a. Influence of shading ongraphs. In: Proceedings of the 28th IEEE Photovoltaic Special-electrical parameters of solar cells. In: Proceedings of the 25thists Conference, Anchorage, AK, pp. 1599–1602.IEEE Photovoltaic Specialists Conference, Washington, DC, pp.

1287–1290. V ersluis, R., Jongen, S., 2001. Optimisation of PV array geometry.In: Proceedings of the 17th EC PV Solar Energy Conference,Q uaschning, V., Hanitsch, R., 1996b. Numerical simulation ofMunich, pp. 451–453.current–voltage characteristics of photovoltaic systems with

shaded solar cells. Solar Energy 56, 513–520. V iotto, M., Esser, M., Pukrop, D., Stellbogen, D., 1997. PVcad—¨ an integrated tool for the design of PV facades. In: ProceedingsQ uaschning, V., Hanitsch, R., 1997. Erhohung des Energieertrages

¨ of the 14th EC PV Solar Energy Conference, Barcelona, pp.von Photovoltaikanlagen durch Anderung der Modulbefes-1902–1905.tigung. In: Proceedings of the 12th Symposium Photovoltaische

Solarenergie, Staffelstein, pp. 231–235. V iotto M., Giese H., Hertenstein A., Hait E., Kunz E., Funtan P.,Pukrop D., Esser M., Langer C., Stellbogen D., Geyer D.Q uaschning, V., Hanitsch, R., 1998a. Increased energy yield of(2000). Hilfe zu PVcad. PVcad 1.2.1, Help file,http: /50% at flat roof and field installations without optimized/www.iset.uni-kassel.de/pvcad/,accessed 31 March 2003.module structures. In: Proceedings of the 2nd World Confer-

ence on PVSEC, Vienna, pp. 1993–1996. W heldon, A.E., Cherruault, J.-Y., Wheeler, S.J., Doptidis, G.,2001. Comparative performance of a central inverter andQ uaschning, V., Hanitsch, R., 1998b. Irradiance calculation onindividual module inverters on a building-integrated-photovol-shaded surfaces. Solar Energy 62, 369–375.taic roof. In: Proceedings of the 17th EC PV Solar EnergyR auschenbach, H.S., 1968. Electrical output of shaded solarConference, Munich, pp. 396–400.arrays. In: Proceedings of the 7th IEEE Photovoltaic Specialists

W ilshaw, A.R., Gonzalez, N.J., Blewett, T., Pearsall, N.M., 1995.Conference, Pasadena, CA, pp. 243–252.Temperature and shading effects on the performance of aS hepard, Jr. N.F., Sugimura, R.S., 1984. The integration of bypassbuilding integrated photovoltaic array in Newcastle upon Tyne.diodes with terrestrial photovoltaic modules and arrays. In:In: Proceedings of the 13th EC PV Solar Energy Conference,Proceedings of the 17th IEEE Photovoltaic Specialists Confer-Nice, pp. 664–667.ence, Orlando, FL, pp. 676–681.

W ilk, H., Panhuber, C., 1995. Power conditioners for gridS kiba, M., Faller, F.R., Eikmeier, B., Ziolek, A., Unger, H., 2000.interactive PV systems, what is the optimal size: 50 W or 500Skiameter shading analysis. In: Proceedings of the 16th EC PVkW. In: Proceedings of the 13th EC PV Solar Energy Confer-Solar Energy Conference, Glasgow, pp. 2402–2405.ence, Nice, pp. 1867–1870.S pirito, P., Albergamo,V., 1982. Reverse bias power dissipation of

W oyte, A., 1997. Charakterisierung von Abschattenden Objektenshadowed or faulty cells in different array configurations. In:und ihr Einfluss auf den Energieertrag von Photovoltaik-An-Proceedings of the 4th EC PV Solar Energy Conference, Stresa,

¨lagen. Universitat Hannover, Fachbereich Elektrotechnik andpp. 296–300.Ïnstitut fur Solarenergieforschung, Hannover.S tellbogen, D., Pfisterer, F., 1992. Ausgangsleistung von PV-

W oyte, A., Belmans, R., Neyens, J., Nijs, J., Coppye, W., DeGeneratoren mit unterschiedlicher Orientierung und beiGheselle, L., 2000. Case study of a building-integrated photo-Teilabschattungen. In: Proceedings of the 8th Internationalesvoltaic system with modular electrical design. In: ProceedingsSonnenforum, Berlin, pp. 707–712.of the Conference UIE Electricity for a Sustainable UrbanS tellbogen, D., Knaupp, W., Laukamp, H., Herrmann, W., 1998.Development, Lisbon, pp. 307–314.Schutz von PV-Fassadenelementen bei Teilabschattungen. In:

W oyte, A., Belmans, R., Nijs, J., Verbeeck, L., Lemmens, J.P.,Proceedings of the 13th Symposium Photovoltaische Solarener-2001. Optimised application of grid-connected photovoltaics.gie, Staffelstein, pp. 443–447.In: Power-Gen Europe 2001, Brussels, Proceedings on CD-S uryanto Hasyim, E., Wenham, S.R., Green, M.A., 1986. ShadowROM.tolerance of modules incorporating integral bypass diode solar

Z ehner, M., 2001. Virtual assistants—market survey of PV designcells. Solar Cells 19, 109–123.and simulation software. Photon Int. 4 (1), 31–40.T egtmeyer, D., Nasse, W., Grochowski, J., 1997. Untersuchung

des Betriebsverhaltens von Wechselrichtern in netzgekoppelten

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