reflector materials for two-dimensional low-concentrating photovoltaic systems: the effect of...

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS

Prog. Photovolt: Res. Appl. 2005; 13:217–233

Published online 14 January 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/pip.588

Reflector Materials for Two-dimensional Low-concentratingPhotovoltaic Systems: the Effectof Specular versus DiffuseReflectance on the ModuleEfficiencyMaria Hall1*,y, Arne Roos2 and Bjorn Karlsson3

1Energy Technology Department, Swedish Energy Agency, P.O. Box 310, 631 04 Eskilstuna, Sweden2Division of Solid State Physics, Department of Engineering Sciences,Uppsala University, Box 534, 751 21 Uppsala, Sweden3Division of Energy and Building Design, Department of Construction and Architecture,Lund University, P.O. Box 118,221 00 Lund, Sweden, and Vattenfall Utveckling AB, 814 26 Alvkarleby, Sweden

Photovoltaic modules in two-dimensional low-concentrating systems with specular

parabolic reflectors often experience high local irradiance that causes high local cur-

rents and cell temperatures. This generally results in power losses. The use of low-

angle scattering reflectors gives a smoother irradiance distribution, which results in a

higher fill factor. In order to study how the choice of reflector material influences

system performance, two different reflector materials (anodised aluminium and lac-

quered rolled aluminium laminated on a plastic substrate) were compared. The total

and diffuse reflectance spectra of the reflector materials were measured, the inte-

grated hemispherical and specular solar reflectance values calculated, and the angu-

lar distributions of scattered light investigated. Two geometrically identical 3�concentrating photovoltaic systems with semi-parabolic over edge reflectors of the

different materials were tested outdoors. While the anodised aluminium reflector,

which had higher hemispherical and specular solar reflectance, resulted in a higher

short-circuit current, the low-angle scattering lacquered foil gave a higher fill factor,

due to a smoother image of the sun on the module surface, and an equally high cal-

culated annual electricity production. Given its low price, the latter reflector should

thus be more cost-effective in low-concentrating photovoltaic systems. Copyright #

2005 John Wiley & Sons, Ltd.

key words: photovoltaic systems; parabolic concentrators; reflector materials; optical proper-

ties; low-angle scattering; fill factor; anodised aluminium; reflector laminate

Received 5 March 2004

Copyright # 2005 John Wiley & Sons, Ltd. Revised 29 September 2004

*Correspondence to: Dr Maria Hall, Energy Technology Department, Swedish Energy Agency, P.O. Box 310, 631 04 Eskilstuna, Sweden.yE-mail: [email protected]

Contract/grant sponsor: Swedish Energy Agency.

Applications

1. INTRODUCTION

1.1. Motivation for low-concentrating photovoltaic systems

The high costs of photovoltaic (PV) modules and the limited space available for electricity production

units in urban areas motivate building integration of PV systems. When PV systems are integrated in

the buildings in the design phase, the cost of facade cladding, which is sometimes more expensive than

the PV modules, can be avoided, and this saving can be deducted from the investment cost of the PV system.

The high module costs also motivate the use of concentrators to increase the irradiance on the modules and

thereby increase the electricity production from a given module area. Building integration and concentration

can be combined, and this is less complicated if the concentrating systems are static. If a PV system is to be

integrated into a facade, it is almost always desirable to avoid moving parts. Since highly concentrating PV

systems have to track the sun in order to operate all year round and several hours per day, these kinds of systems

are not appropriate for building integration. In order not to waste a significant part of the annual irradiation,

static systems imply low concentration ratios. Furthermore, east–west aligned or vertical concentrators with

cylindrical geometries are often more easily integrated in facades, than concentrators with rotational

symmetry. Therefore, our work on building-integrated concentrating PV systems has been focussed on two-

dimensional systems with concentration ratios below 5� . Concentrating systems are also considered for solar

thermal applications and several papers have been published on the subject of non-imaging concentrators.1,2 An

overview of some design features can be found in the thesis by Ronnelid.3

Integration of PV systems into vertical facades is more appropriate at high latitudes, for example in

Sweden, where most of the annual irradiation is received at relatively low solar heights,4 than at lower

latitudes. Figure 1 shows the monthly total irradiation on the horizontal, Gh, and on a vertical wall that faces

south, Gv, at three different sites on the northern hemisphere: Stockholm (59�N, 18�E) in Sweden, Madrid

(40�N, 3�W) in Spain, and Accra (5�N, 0�) in Ghana. The figure shows that the difference between the annual

irradiation on a vertical wall (Gv¼ 960 kWh/m2) and on the horizontal (Gh¼ 980 kWh/m2) is negligible in

Stockholm, while it is significant in Madrid (Gv¼ 1260 kWh/m2, Gh¼ 1660 kWh/m2) and in Accra

(Gv¼ 800 kW h/m2, Gh¼ 1810 kWh/m2). Furthermore, in Stockholm, integration of a PV system in a ver-

tical wall facing southwards reduces the variation in electricity production between the summer and winter

seasons, compared with horizontal systems or systems that are inclined at low angles. In an optimised col-

lector system the tilt angle is somewhere in between vertical and horizontal, more vertical the further north

the system is situated. The solar irradiation is thus higher against an inclined surface than against the hor-

izontal surface shown in Figure 1 (except for Accra, which is close to the equator). However, the values for

the horizontal surface represent the total amount of solar energy available at the given location per square

metre of land area.

Figure 1. Monthly global irradiation on a horizontal plane and on a vertical wall that faces due southwards, for Stockholm,

Madrid, and Accra (data from Meteonorm)

218 M. HALL, A. ROOS AND B. KARLSSON

Copyright # 2005 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2005; 13:217–233

1.2. Previously developed concentrating systems with static parabolic reflectors

In 1999, a static, facade-integrated solar thermal collector with over edge parabolic reflectors having a geo-

metric concentration ratio of 3�was installed in Aneby (58�N, 14�E), Sweden.5 A similar prototype of a con-

centrating element for facade integration of thin-film modules has also been developed. The system is modular

and several concentrating modules can be put next to and on top of each other, like bricks in a wall. Each con-

centrating module includes a PV module in combination with an over edge semi-parabolic, east–west aligned

static reflector as well as thermal insulation in order to serve as an integrated multi-functional part of the

building envelope.6,7

1.3. Properties of reflector materials

Because of their low cost and their manufacturing flexibility, mirrors based on sheets of anodised aluminium

or thin-film-coated (reflectance-enhanced) aluminium are often used as concentrators in solar energy appli-

cations. Aluminium reflectors offer an initial total solar reflectance of about 90%, high specularity, and good

mechanical properties. However, for cost-effective solar heat or electricity production in concentrating sys-

tems it is also important that the optical properties of the chosen reflector material are long-term stable. The

high initial reflectance of aluminium-based reflectors is in general not preserved in an outdoor environment

and therefore studies of degradation of solar reflectors and other components of solar energy systems

have been initiated, for instance within the International Energy Agency’s, Solar Heating and Cooling

Programme’s Task 27.

It seems to be generally believed that reflectors for use in concentrating solar energy systems should

have as high specular part of the reflectance as possible.8,9 Indeed, a high specular reflectance is

important for highly concentrating solar thermal systems that produce water at high temperatures,10 and

for highly concentrating PV systems with sun-tracking, such as the EUCLIDES system.11 Accurate design

of the concentrator optics and tailoring of the resulting irradiance distribution on the cell surface is neces-

sary for highly concentrating systems, since an uneven irradiance distribution reduces the fill factor and the

open-circuit voltage.12,13 Photovoltaic modules in two-dimensional single or compound parabolic reflectors,

that focus radiation in a sharp line, experience large inherent local irradiance differences. This causes high

local currents and cell temperatures, which result in power losses, also in low-concentrating (<5� )

systems with two-dimensional parabolic reflectors, as has been shown earlier.6,7,14 Hence, in systems

of this type the use of reflector materials with a diffuse component of the reflectance, which is scattered

at low angles, may be favourable. A parabolic reflector with some low-angle scattering gives a smoother

irradiance distribution on the PV cells, which results in higher fill factor and higher power output.

Furthermore, the thin-film deposition processes used in the manufacturing of highly reflecting alumi-

nium-based mirrors are expensive, and possibly the use of low-cost materials with slightly lower specular,

and total, solar reflectance is more cost-effective for low-concentrating systems.

1.4. Objectives of this work

This work is part of a Swedish university–industry collaboration, aiming at decreasing the cost of solar elec-

tricity by designing modular static, low-concentrating PV systems for integration in a building envelope,

which includes standard modules designed for one-sun illumination, low-cost reflectors, and thermal insu-

lation. In order to keep costs down, the components should be off-the-shelf products and the system should

be easy to install, operate, and maintain. In the project reported in this article, the aim was to evaluate how

the performance of a concentrating PV system depends on the choice of reflector material and specifically to

investigate the differences in electricity production between low-concentrating systems with specular mir-

rors and systems with partly diffuse mirrors. The optical properties of two different reflector materials (one

specular and one partly diffuse) were investigated and parabolic over edge reflectors made of the materials

were tested in a prototype system in order to see how a significant diffuse component of the reflectance influ-

ences the module fill factor and the electric output.

SPECULAR/DIFFUSE REFLECTANCE AND PV EFFICIENCY 219


2. DESCRIPTION OF THE 3�CONCENTRATING TEST SYSTEM

2.1. Parabolic reflectors

The profile of a parabolic reflector can be described by15

r ¼ 2f

1þ cos’ð1Þ

where f is the focal length, r is the radius vector, and ’ is the angle between the z-axis (which will be called the

optical axis from here on) and the radius vector. The shape of the basic parabola is depicted in Figure 2.

The parabolic shape is utilised in various types of concentrating systems, which can be either two- or three-

dimensional. Three-dimensional parabolic concentrators have rotational symmetry around the optical axis,

while two-dimensional concentrators have translational symmetry. In a concentrating system that utilizes a

specular two-dimensional parabolic reflector, light that is incident parallel to the optical axis will be concen-

trated on a line at the focus of the system (into the paper at the focal point/line in Figure 2). In a three-

dimensional system, the focus will be point-like. If light is incident at an angle to the optical axis, it will be

focused between the vertex and the focal point, or rejected by the concentrator.

2.2. Geometry of the test system

Figure 3 shows a schematic of the concentrating system that was used for investigating the effect of specular

versus partly diffuse reflectors on the module efficiency. The system has an inclination � of the optical axis with

respect to the horizontal of 25�, which is the lower acceptance angle of the system. The module plane is tilted

forward at an angle of 20� with respect to the horizontal. This is close to the optimum angle, considering the

acceptance angles of the system and the geometrical design (height and thickness). The inclination of the mod-

ule also allows for radiation to reach the module directly, without first being reflected in the parabolic reflector.

The angle �, between the module plane and the optical axis, is thus 45�. At angles below the lower acceptance

angle, solar radiation will reach the module directly, without first being reflected in the parabolic reflector. The

same applies for solar altitude angles above about 70�. At the test site in Uppsala (latitude 60�N), the solar

altitude never exceeds 57�. However, the south-projected solar altitude, which is the projection of the solar alti-tude on the vertical plane extended from north to south, can be as high as 90�. The south-projected solar altitude

Figure 2. Cross-section of a parabolic reflector of length lwith a focal length f. The letter r denotes the radius vector, ’ is the

angle between the optical axis (denoted z) and the radius vector, and �a is the acceptance angle of the parabolic concentrator



is highest in the mornings and in the afternoons and equals 90� when the sun is due east or due west. The south-projected solar altitude is a useful tool for evaluating east–west aligned concentrators and can be utilised for

calculating the annual electrical output from a concentrating PV system.4 This implies that it is appropriate to

assess the optical efficiency of the system also for south-projected angles of incidence above 57�.For enabling tests of different reflector materials in the concentrating system, the two reflectors were fitted in

the same prefabricated structure of expanded polystyrene. It was thus possible to test the different reflector

materials without any difference in the geometry that could influence the results. Furthermore, the PV module

that was utilised in the measurements could be removed from the concentrating system and mounted elsewhere,

for example on a vertical wall, for reference measurements. The utilisation of the same PV module for all mea-

surements of current generation and electricity production enabled a direct comparison between the electrical

performance of the different concentrating systems and of the module without concentrators.

The geometric concentration ratio of the system Cg is defined as the ratio between the height of the entrance

aperture h and the module width a:

Cg ¼ h

a¼ cos2 �

2

� �cos2 �þ90

2

� � ¼ 2�96 ’ 3 ð2Þ

All symbols are given in Figure 3. With a module width, a¼ 143mm and with the angles � and � as stated

above, Equation (2) gives the height h of one concentrating element as 423mm. The minimum depth d of the

constructed system is equal to the focal length f which was calculated from Equation (1) and found to be

122mm. The ratio of the reflector area to the module area is denoted l, see Equation (3).

2.3. Photovoltaic module

The concentrating system was initially designed for thin-film copper–indium–gallium–diselenide (CIGS) mod-

ules. The work on the original system is further described elsewhere.6,16 In this project, a module of monocrys-

talline silicon was used instead of a CIGS module. The reason for using silicon cells in the string module is that

there are several module manufacturers in Sweden, which today assembly rectangular flat plate silicon modules,

that could easily transform parts of their assembly lines into string module manufacturing. Thus, the static low-

concentrating system could be of interest for the Swedish PV industry, provided that off-the-shelf silicon cells

are used. These cells are also significantly cheaper than cells especially designed for concentrating systems.

Figure 3. Schematic cross-section of the semi-parabolic concentrating system. The photovoltaic module plane has width a,

the focal length is f, and the reflector has length l. The acceptance angle of the system is denoted by �a and � is the angle

between the optical axis, z, and the module plane. The system height is h, while d indicates the minimum module depth



The string module which was used in the prototype was manufactured by the Swedish company Gallivare

PhotoVoltaics AB and consists of eight 11� 11 cm monocrystalline silicon cells, designed for operation under

one-sun illumination, connected in series and laminated on an aluminium fin. The total cell area is 0�13m2. The

width of the module is 143mm and the module length is 1�2m. There is no spacing between the PV cells, but

the aluminium fin as well as the reflector are extended 0�1m on both sides (the east and the west

during operation) of the string module. Photographs of the concentrating system and the PV module are shown

in Figure 4.

2.4. The evaluated reflector materials

The reflector materials that were evaluated in this work were a standard anodised aluminium sheet and a lac-

quered rolled aluminium foil laminated on a flexible plastic substrate. The latter material consists of a 9 mmrolled aluminium foil, which is glued on a substrate of 250 mm polyethylene terephthalate (PET) and covered

by a 2 mm layer of a combination of methyl methacrylate (MMA) and n-butylmethacrylate (BMA) lacquer. The

two reflector materials were chosen because of their mechanical properties that make it possible to bend them

into a parabolic shape, their relatively low price, and their different optical properties (one was specular and one

was partly diffuse, as will be shown later). The durability of the optical properties of these two and several other

reflector materials is being tested within the IEA Solar Heating and Cooling Programme’s Task 27. Tests are

ongoing and the results not yet available.17

Avisual inspection showed that the anodised aluminium reflector had an isotropic surface, while the lacquered

rolled aluminium foil on a flexible plastic substrate showed signs of the rolling process in the shape of visible

grooves. When the laminated rolled aluminium reflector was tested as an over edge reflector in the concentrating

system, the grooves were oriented perpendicular to the length of the photovoltaic string module.

2.5. System cost

The overall motivation for using concentrators in PV systems is to reduce the cost of the produced electricity. In

the system which is studied in this work, the reflector area needed is approximately three times the module area.

Figure 4. Concentrating photovoltaic system intended for facade integration. The system includes a photovoltaic string

module, a parabolic reflector with a geometric concentrationCg¼ 3, and polystyrene insulation (a). The photovoltaic module

consists of eight monocrystalline silicon cells which are connected in series and laminated on an aluminium profile (b)



In the general case, with a reflector area which is l times the module area it is cost-effective to use reflectors if

the following condition is satisfied:

Preflector lþ 1

�opt � Cg

PPV þ Pextra < PPV ð3Þ

In Equation (3) Preflector (s/m2) is the specific cost of the reflector, �opt is the optical efficiency of the con-

centrator,14 PPV (s/m2) is the specific cost of the PV module, and Cg is given by Equation (2). The cost of the

system is also influenced by other factors than just the cost of materials. Manufacturing, assembly, transport and

maintenance are also factors that must be considered. In Equation (3), these costs are indicated by introducing

the term Pextra (s/m2 module area). A simple example calculation using Preflector¼ 10, l¼ 3, �opt¼ 0�75, Cg¼ 3

and PPV¼ 500 show that the use of the concentrating system is justified as long as the extra cost does not exceed

247s/m2 module area. It is, however, beyond the scope of this optical study of reflector materials to go further

into the economy of this type of systems.

3. EXPERIMENTAL METHODS

3.1. Reflectance measurements

The total and diffuse spectral reflectance, Rtot(�) and Rdiff(�), of the reflector materials were measured at

near normal angle of incidence in a Lambda-900 spectrophotometer from Perkin Elmer, equipped with

an integrating sphere. The reason for measuring at near normal angles of incidence is that it is difficult to

measure diffuse reflectance accurately at grazing incidence angles18 and that it is the comparison between

the different materials that is of greatest importance. For a thorough investigation of the angular dependent

reflectance of the different reflector materials, the wide range of incidence angles on the reflector in the para-

bolic concentrator makes ray tracing analysis at all prevailing solar heights necessary in order to calculate

the weight of the different incidence angles and thereafter weighting the measured reflectance accordingly in

order to give an accurate figure of merit. However, this is beyond the scope of this work. Here, we have

chosen to compare the influence on system performance of the two reflector materials using full-scale out-

door experiments at different solar altitudes, see Section 3�3. Furthermore, the light scattering from the

materials has been analysed, see Section 3�2.The diffuse reflectance of the two materials was measured by letting the specularly reflected beam escape

through a 3�4� 3�4 cm port in the integrating sphere, while the total reflectance was measured with the port

closed. The specular reflectance was calculated as the difference between the measured spectral hemispherical

and diffuse reflectance:

Rspecð�Þ ¼ Rtotð�Þ � Rdiffð�Þ ð4Þ

The solar weighted total and specular reflectance values were calculated from measurement data using

Rsolartot;spec ¼

R10

Rtot;specð�ÞGbð�Þd�R10

Gbð�Þd�ð5Þ

where Gb(�) denotes the direct solar irradiance spectrum according to the ISO standard19 for air mass 1�5.In a concentrating photovoltaic system, the reflected light with wavelengths longer than the wavelength that

corresponds to the bandgap of the photovoltaic cell, does not contribute to current generation. Therefore, it is

sometimes useful to calculate and compare the solar photovoltaics weighted reflectance of the different reflector

materials. The calculation can be done by weighting the spectral reflectance by the solar spectrum and the spec-

tral response of the specific solar cell that is used in the system. However, in cases where the spectral response is

not known, the spectral reflectance can be weighted by the solar spectrum and a step function f(�), which is



unity for the useful wavelengths and zero outside this wavelength interval. This procedure is often convenient,

and makes the results more generally applicable. For example, the step function that applies for photoelectric

conversion in a typical silicon cell is thus given by

f ð�Þ ¼ 1 for 300 nm < � < 1200 nm

0 elsewhere

�ð6Þ

3.2. Measurements of light scattering

The spatial distribution of the scattered radiation from the anodised aluminium and the lacquered rolled alumi-

nium foil laminated on a PET substrate was measured in a scatterometer using light from a HeNe laser

(�¼ 633 nm) that was incident on the samples at an incidence angle of 45�. The detector was moved in the

hemisphere above the sample at a distance of 40 cm from the sample and with an angular resolution of 1� inthe azimuth � and zenith � directions (Figure 5). The lacquered rolled aluminium reflector was mounted with

the grooves from the rolling process in the plane of incidence.

3.3. Measurements of short-circuit currents and electrical power

The short-circuit current that is generated in a solar cell is proportional to the irradiance on the cell. Measure-

ments of the short-circuit current for different solar altitudes can therefore be used to obtain the optical effi-

ciency of a concentrating system as a function of solar altitude. This was done by dividing the measured

short-circuit current for the module in the concentrating systems by the short-circuit current for the vertically

mounted module and the concentration ratio of the parabolic reflector (3�). The short-circuit current as a func-

tion of solar altitude was measured outdoors, using the experimental set-up in Figure 6. In the figure, the con-

centrating system is rotated 90� and tilted 30� backwards in order to be able to measure system performance at

simulated solar altitude angles between �90� and 90�. This type of experiment can only be performed close to

the equinoxes, since only at these two times of the year, with the system inclined at an angle of 90� minus the

latitude (60�N in the case of Uppsala, where the experiments were performed), the sun moves in a plane that is

normal to the module and the reflector, and each hour corresponds to an angular movement of the sun of 15�. Itis thus possible to measure generated currents at all solar altitudes during a single day.

Current–voltage characteristics were measured outdoors for the vertically mounted module, for the module in

the concentrating system with the anodised aluminium reflector and for the module with the reflector of lac-

quered rolled aluminium on plastic. The measurements were performed at noon with the system in upright posi-

tion, as in Figure 4(a), at a solar altitude angle of 32� and solar azimuth angle of 0�. The results of the

measurements of short-circuit currents and current–voltage characteristics for the concentrating system with

different reflectors are presented in Section 4�2.

Figure 5. Schematic picture of the experimental set-up for measurement of light scattering from reflector surfaces. The

detector sweeps the � and � angles with a resolution of 1�. The incident HeNe laser beam is parallel to the table



All outdoor measurements on the two different systems were performed on two consecutive days around the

autumn equinox with clear sky conditions and an ambient temperature of 13–17�C. The total irradiance was

continuously measured in the south-facing vertical plane with a small calibrated solar cell and measurement

data were normalised to an irradiance of 1000W/m2. The measured total irradiance was 900–1050W/m2 during

all measurements. The module temperature was measured at two positions on the front and two positions on the

back of the module. The module mean temperature was calculated as the arithmetic mean of the measured tem-

perature at these four points.

3.4. Minsun calculations of annual output

Calculations, using the measured optical efficiency as a function of solar altitude angle, together with a refer-

ence year meteorological data and the incidence angle dependence of the cell efficiency, can give an estimated

annual output from the concentrating systems. In this work, the Minsun program was used to perform the cal-

culations. The Minsun program and the method for calculating the annual output is described elsewhere.16 In

this work, the method was modified to take into account the fact that the fill factor is different for the same

module in different types of concentrating systems, as will be shown in Section 4�2.

4. RESULTS

4.1. Optical properties of reflector materials

Figure 7 shows the measured total and specular reflectance spectra for the two different reflector materials in the

wavelength interval 200–2550 nm. While the total solar weighted reflectance of the two samples were similar,

the specular reflectance was significantly lower for the laminated reflector material than for the anodised alu-

minium reflector. The solar weighted and solar photovoltaic weighted total and specular reflectance values for

the two reflector materials are given in Table I. The solar photovoltaic weighted reflectance RPV was calculated

from Equation (5) and the step function given by Equation (6). The small difference between the solar and the

solar photovoltaic weighted reflectance values is explained by the fairly high reflectance of both reflector mate-

rials in the whole solar wavelength range (in particular the ultraviolet) and the fact that as much as 86% of the

solar energy is confined to the specified wavelength range. Weighting by a real spectral response curve would

probably have resulted in a larger difference between the solar and the solar photovoltaic weighted reflectance.

It would also have been possible to determine whether either of the two materials was proportionally better

Figure 6. The 3� concentrating system, rotated 90� and tilted 30� backwards (northwards) at the autumn equinox for

enabling simulation of different solar heights



suited for photovoltaic applications (as compared with solar thermal applications) than the other. Table I also

includes the retail prices per square metre reflector.

Figure 8 shows the angular distribution of scattered light from the lacquered rolled aluminium foil on plastic

and the anodised aluminium into the � and � directions, which are described in Figure 5. For the lacquered

rolled aluminium reflector, there is a significant difference between the scattering distributions in the two per-

pendicular directions. This reflector sample scatters more in the direction perpendicular to the groves from

the rolling process, than in the direction parallel to the grooves. However, the light scattering in the perpendi-

cular direction is confined to a rather narrow angular interval (0–9�). We therefore characterise this sample as

Figure 7. Measured total and specular reflectance of the anodised aluminium reflector and the lacquered rolled aluminium

foil laminated on plastic

Table I. Data for the two different reflector materials that were investigated in this project and the calculated solar and solar

photovoltaics weighted reflectance values. Retail prices depend on the purchased quantity

Material Mechanical properties Price per m2 Rsolartot Rsolar

spec RPVtot RPV

spec

s

Anodised aluminium Bendable, medium weight s 8�80 0�88 0�86 0�87 0�85Lacquered rolled aluminium, laminated Flexible, light weight s 2�20 0�85 0�58 0�83 0�55on a PET substrate

Figure 8. Scattered intensity in the � and� directions for the lacquered reflector and the anodised aluminium reflector. Note

that there are three almost perfectly overlapping curves in the narrower of the bell-shaped curves



low-angle scattering in the direction perpendicular to the direction of the grooves. In the direction parallel to the

grooves, the light scattering of this sample is as low as that of the anodised aluminium. The light scattering

distribution exhibited by the lacquered rolled aluminium reflector is typical for a material with a one-

dimensional surface structure, e.g., parallel grooves, in combination with a small isotropic surface roughness

caused by microscopic defects.20 Figure 9 shows the surfaces of the lacquered rolled aluminium reflector and

the anodised aluminium reflector, taken with an optical microscope connected to a CCD camera.

4.2. Generated short-circuit currents and power

Figure 10 shows the measured short-circuit current as a function of solar altitude for the string module in the

concentrating system with the two different reflector materials. The short-circuit current for the module when

mounted vertically without any reflector is also shown. The data for the concentrating systems were collected

Figure 9. Photographs of 320� 240mm of the surface of anodised aluminium (left) and lacquered rolled aluminium

reflector on PET (right)

Figure 10. Short-circuit current as a function of solar height for the photovoltaic module in the concentrating system with

different reflectors (anodised aluminium and lacquered rolled aluminium) and for the vertically mounted module



using the experimental set-up in Figure 6. The short-circuit currents were normalised to an irradiance of

1000W/m2. The lower acceptance angle of 25� for the parabolic concentrator is visible in Figure 10, as the

measured short-circuit current increases dramatically when the sun rises above this angle.

At a solar height of 5�, the short-circuit current generated by the module in the concentrating system perfectly

matches the short-circuit current obtained from the vertical module at a solar height of 65�. This is because themodule is inclined at an angle of 20� degrees to the horizontal and at solar heights below the lower acceptance

angle of 25�, only radiation that reaches the module directly contributes to the current generation. Thus, at solar

altitude angles below 25�, the current generated by the module in the concentrating systems would ideally be

equal to the current generated by the vertical module for the same angle of incidence. The reflector does not start

to work until over 25�, or somewhat lower for the low-angle scattering reflector. The increased acceptance angle

interval for the low-angle scattering reflector is explained by the fact that part of the radiation is scattered onto

the module plane. The broadening of the acceptance angle interval is clearly visible in Figures 11 and 12, which

show the image of a HeNe laser beam reflected in the parabolic reflector (made of lacquered rolled aluminium

foil on PET in Figure 11 and of anodised aluminium in Figure 12) onto the module plane. The dashed lines in

the figures indicate an imaginary module edge at a solar altitude of 24�, which is just below the lower accep-

tance angle of the parabolic concentrator. The inset in the figures shows the arrangement of the camera, reflector

and module plane. For parallel solar radiation, the observed pattern of the scattered beam radiation can be trans-

lated into a scattered band around the dashed line in Figure 12. As the solar altitude increases, this band moves

across the surface of the module, maintaining a smooth image of the sun on the module. The arc-like shape of

the radiation scattered from rolled metal sheet is utilised in booster reflectors for solar thermal collectors for

improving summer performance.21

Figure 13 shows the generated currents as function of voltage and the corresponding calculated power as a

function of voltage for the concentrating system with the two different types of reflectors and for the vertically

mounted module without reflector, at a solar height of 32�. The irradiance on the vertical plane facing due south,which varied between 900 and 1050W/m2 was measured continuously during the measurements and the gen-

erated currents were normalized to an irradiance of 1000W/m2 on the vertical plane. The measured maximum

power was 18W for the system with an anodised aluminium reflector, 20W for the system with a reflector of

lacquered rolled aluminium foil on plastic, and 12W for the vertical module. The fill factors for the different

Figure 11. Photograph of a beam from a HeNe laser, reflected and scattered from the anodised aluminium reflector. The

beam was incident on the parabolic concentrator with an angle of 24� over the horizontal. The dashed white line indicates thefront edge of the photovoltaic module. A schematic of the experimental set-up is shown as an inset in the top left corner of

the photograph



systems were calculated from the current–voltage characteristics in Figure 13. The fill factor was 0�50 for the

system with anodised aluminium reflector, 0�56 for the system with lacquered rolled aluminium reflector, and

0�66 without concentration.

At a solar altitude angle of 32�, the power generated in the system with a specular reflector as well as the fill

factor of this system were lower than the power and fill factor for the system with the laminated rolled alumi-

nium reflector. Thus, the somewhat lower total reflectance, and the significantly lower specular reflectance, of

Figure 12. Photograph of a beam from a HeNe laser, reflected and scattered from the lacquered rolled aluminium reflector.

The beam was incident on the parabolic concentrator with an angle of 24� over the horizontal. The dashed white line

indicates the front edge of the photovoltaic module. A schematic of the experimental set-up is shown in the top left corner of

the photograph

Figure 13. Measured current–voltage characteristics and calculated power as a function of voltage at a solar height of 32�

for the module in the concentrating system with reflectors of the two different materials and for the module mounted on a

vertical wall



the laminated rolled aluminium reflector is more than compensated for by the more favourable irradiance dis-

tribution on the module.

During the measurements that are displayed in Figure 13, the ambient temperature was constant at 17�C and

the photovoltaic module was allowed to cool for 15min between the three consecutive measurements. The

current–voltage characteristic of the module with a reflector of anodised aluminium was measured first, there-

after the current–voltage characteristic of the module with a reflector of lacquered rolled aluminium foil on PET

was measured, and finally, the current–voltage characteristic of the module without concentrator was measured.

The mean temperature of the module was measured before each of the three measurements. The mean tempera-

ture was found to be 40� 3�C in all three cases. However, the time between the temperature measurement

and the current–voltage measurement varied by a couple of minutes, and this delay may have caused a slight

difference in module mean temperature, although this was not observed in the measurements. An increased

module mean temperature may have caused the observed decrease in open-circuit voltage for the system with

a specular reflector. However, the decrease may also have been caused by high local temperature.

4.3. Estimation of annual electricity production

Calculations of the annual electricity production in Stockholm (59�2�N, 18�3�E), Sweden, of a vertical module

and of modules in the 3� concentrating systems with the different types of reflectors were performed using the

Minsun simulation program. Data for a meteorological reference year for Stockholm were used in the calcula-

tions. For the vertical module, calculations using the measured open-circuit voltage, the calculated fill factor,

and the measured short-circuit current as a function of solar altitude angle resulted in an estimated annual output

of 91 kWhperm2 cell area. For calculation of the annual output from the two concentrating systems, the mea-

sured short-circuit currents for the module in the respective system were used to obtain the optical efficiency, as

described in Section 3�3. The same open-circuit voltage as for the vertical module was used. The fill factors that

were used in the calculations of the output from the concentrating systems for solar altitude angles between 20�

and 70� were the measured fill factors at a solar altitude angle of 32� (0�50 for anodised aluminium and 0�56 forlacquered rolled aluminium). For solar altitude angles below 20� and above 70�, the measured fill factor for one-

sun illumination (0�66) was used, since no (or little in the case of the low-angle scattering reflector) concentra-

tion occurs at solar altitude angles below 20� and the irradiance on the modules is almost homogeneous above

70�, due to a large fraction of direct radiation on the module and only a small fraction of radiation that is

received after reflection in the parabolic reflector. Figure 14 shows the measured optical efficiencies of the sys-

tem, using the two different concentrators, as functions of solar altitude angle. The figure also shows the fill

Figure 14. Calculated optical efficiency for the photovoltaic module in the concentrating system using the two different

types of reflectors as a function of solar altitude. Also included in the graph is the fill factor weighted optical efficiency of the

module using the two different reflector materials



factor weighted optical efficiency (FFWOE). The FFWOE was calculated as the product of the measured opti-

cal efficiency of the reflector and the measured (or estimated) fill factor of the PV module at the different solar

altitude angles. The solar altitude dependent FFWOE for the PV module with the two types of reflectors were

used in some of the Minsun calculations of the annual electricity production. The effect on the calculated annual

electricity production of using the calculated fill factors is discussed in Section 5�2.The calculated annual output for a 3� concentrating system was 119 kWhperm2 cell area with a reflector of

lacquered rolled aluminium and 115 kWhperm2 cell area with a reflector of anodised aluminium. This corre-

sponds to an increase in annual production of 30% for a system with a reflector of lacquered rolled aluminium

and 26% with a reflector of anodised aluminium. Thus, in spite of the lower specular reflectance and slightly

lower total reflectance that results in a lower short-circuit current, a 3� concentrating system with a semi-

diffuse laminated rolled aluminium reflector will produce more electrical energy on an annual basis than a sys-

tem with a highly specular anodised aluminium reflector.

5. DISCUSSION

5.1. The cause of the large differences in fill-factor

The observed reduction of the open-circuit voltage in Figure 13 for the module in the concentrating system with

a specular reflector compared to the vertical module and the module with a low-angle scattering reflector cor-

responds to a decrease in maximum power of less than 0�5W. Hence, the reduction of the open-circuit voltage,

whether it is caused by an increase of the module mean temperature during the measurements or has other

causes, does not account for the significantly lower power at high irradiance for the module in the 3� concen-

trating system with specular reflectors than for the module with low-angle scattering reflectors. Instead, the

lower electrical power is caused by the decrease in module fill factor, which is believed to be due to the

large local irradiance that results in high local temperatures and current densities for the module with specular

reflectors.

5.2. Uncertainties in the calculation of annual electricity production

The calculated annual electricity production in the two concentrating systems investigated should not be

regarded as absolute values. They were performed to give an indication of the relative performance of the sys-

tems and for a comparison of the performance of the concentrating systems with the performance of the vertical

module. There are several factors that contribute to the uncertainty in the calculations of annual electricity pro-

duction from the module in the concentrating systems. First, the Minsun program uses input data for only every

tenth solar altitude angle in the interval 0–90�. This made it impossible to introduce the positive effect of

the broadening of the acceptance angle interval for the low-angle scattering reflector in the calculations. On

the other hand, the use of the measured fill factor for one-sun illumination (0�66) for solar altitude angles of

0–20� in the calculations of the annual electricity production biases the calculation somewhat in favour of the

low-angle scattering reflector, since this reflector material has the advantage of concentrating part of the radia-

tion already at solar altitude angles of 17� and above. However, the radiation incident in the angular interval

0–17� is below 5% of the total irradiation incident on the wall, and therefore the error in the calculation of

annual electricity that is caused by this approximation is considered small. Furthermore, the large differences

in fill factor will occur only when the irradiance on the wall is high. In practice, the irradiance at which the

measurements were performed can be considered as the worst case for the system with a specular reflector.

In total, the error in the calculations may be as high as 10–20%. Nevertheless, the comparison of the calculated

annual electricity production for the different systems points in favour of the low-angle scattering reflector.

5.3. Angular distribution of the scattered radiation

Our investigation has shown that, at high solar irradiation at incidence angles just above the acceptance angle, it

is favourable to use a partly diffuse reflector to smooth the image of the sun on the surface of the photovoltaic



module. However, the rolled aluminium reflector scatters light in an ordered fashion, at low angles in the direc-

tion perpendicular to the grooves from the rolling process. This fact must be considered when the results of this

work, implying that semi-diffuse reflectors can give an increase in power production compared to the use

of entirely specular reflectors, is interpreted. Isotropically scattering reflectors or rolled metal reflectors with

the grooves oriented parallel to the length of the module will give a different irradiance distribution on the mod-

ule and, at some solar heights, result in a significant loss of radiation as incident light will be reflected out of the

system and miss the module.

Geometrical mirror errors, such as dints or curvature errors, can also result in a more homogeneous irradiance

on the module. This was considered in this work when mounting the reflectors, and is not believed to have

influenced the results. It would, however, be interesting to see a development of reflector geometries for static

operation that are optimised to give a more homogeneous irradiance on the PV modules at those solar altitudes

at which the solar radiation, on average, is most intense, i.e., at noon in summer.

5.4. Long-term system performance

Aluminium reflectors offer a total solar reflectance of about 90% and good mechanical properties. Problems,

however, may occur due to their limited corrosion resistance. Lifetime tests, including outdoor and accelerated

ageing tests, are therefore necessary prior to application, in order to prove the optical durability of the reflector

materials. It is often desirable to be able to guarantee 10–20 year service lifetime. In many cases, ageing results

in a more diffuse reflectance. As we have seen, this may not be detrimental to system performance if the diffuse

radiation is scattered at low angles and in the direction parallel to the length of the module. When performing

ageing tests, it is therefore important not only to measure the total and specular reflectance before and after

ageing, but also to assess the spatial distribution of the diffuse reflectance.

The influence of dust accumulation on the string module and the reflector has not been considered in this

work, but ought to be analysed before putting the system into mass production. However, the overall close

to vertical orientation of the reflector and the 20� inclination of the PV module facilitates manual cleaning

and enables rain and snow to clean the module and reflector surfaces. If the system is used at locations where

the climatic conditions are more severe than in Sweden regarding soiling of the reflector and module surfaces it

may be appropriate to use an anti-reflectance treated glazing. This, however, will increase system cost and has

therefore not been considered in this work.

The long-term stability of the reflector materials used in the prototype system are not yet fully investigated,

even though recent, preliminary results from accelerated ageing tests in a climatic test chamber are promising

for both reflector materials investigated here.22 Furthermore, the environmental impact of manufacturing,

installing, and operating the facade-integrated photovoltaic systems with parabolic aluminium reflectors (of

whatever type chosen) should be analysed before widespread use is recommended.

6. CONCLUSIONS

The higher total and specular solar reflectance for the anodised aluminium than for the lacquered rolled alumi-

nium foil laminated on a plastic substrate resulted in a higher short-circuit current for the concentrating system

with a parabolic reflector of anodised aluminium. However, at high irradiance and a solar altitude angle just

above the acceptance angle, the module fill factor and electric output was higher for the system with the

low-angle scattering reflector, due to a smoother image of the sun on the module surface. The calculated annual

electricity production is approximately equal for both evaluated systems, and 25–30% higher than the output

from a vertically mounted module with the same cell area. The lacquered rolled aluminium foil on plastic costs

much less per square metre than the anodised aluminium reflector. Our conclusions are that the use of facade-

integrated low-concentrating photovoltaic systems with silicon string modules and static parabolic reflectors of

inexpensive laminated rolled aluminium has a potential to reduce the cost of solar electricity, and that the uti-

lization of reflectors with low-angle scattering instead of specular reflectors may increase system efficiency.



Acknowledgements

This work was carried out within the national Energy Systems Programme, which is financed by the Swedish Foun-

dation for Strategic Research, the Swedish Energy Agency, and Swedish industry. H. Gajbert at the Division of

Energy and Building Design at Lund University is acknowledged for the Minsun calculations. A. Werner, P.

Hansson, and J. Jonsson at the Department of Engineering Sciences at Uppsala University as well as the MSc

student D. Brogren are acknowledged for assistance in some of the measurements. A. Roos and B. Karlsson would

like to acknowledge the Swedish Energy Agency’s Solar Heating Programme (FUD) for financing.

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