Photovoltaic System Performance Enhancement With Non-Tracking
Planar Concentrators: Experimental Results and Bi-Directional
Reflectance Function (BDRF) Based Modelling
Rob W. Andrews ∗ , Andrew Pollard∗ and Joshua M. Pearce †
∗
Department of Mechanical and Materials Engineering
Queen’s University, Kingston, Ontario, Canada
† Department of Materials Science and Engineering and the Department of Electrical and Computer Engineering
Michigan Technological University, Houghton, MI, USA
Abstract—Non-tracking planar concentrators are a low-cost
method of increasing the performance of traditional solar photovoltaic (PV) systems. This paper presents new methodologies for
properly modeling this type of system design and experimental
results using a bi-directional reflectance function (BDRF) of
non-ideal surfaces rather than traditional geometric optics. This
methodology allows for the evaluation and optimization of specular and non-specular reflectors in planar concentration systems.
In addition, an outdoor system has been shown to improve energy
yield by 45% for a traditional flat glass module and by 40% for
a prismatic glass crystalline silicon module when compared to
a control module at the same orientation. When compared to a
control module set at the optimal tilt angle for this region, the
energy improvement is 18% for both system. Simulations show
that a maximum increase of 30% is achievable for an optimized
system located in Kingston, ON using a reflector with specular
reflection and an integrated hemispherical reflectance of 80%.
This validated model can be used to optimize reflector topology
to identify the potential for increased energy harvest from both
existing PV and new-build PV assets.
Index Terms—planar concentrator, low concentration, crystal
silicon,optics, BDRF, reflectors, booster mirrors, photovoltaic,
photovoltaic system
N OMENCLATURE
Gdif f
GDN I
Gp
Gim
Eri
Ero
i
Em
Ta
Am
AR
Frm
x
y
y
r
wref l
Diffuse irradiation (W/m2 )
Direct normal irradiation (W/m2 )
DNI projected onto the vertical plane
(W/m2 )
Irradiance on the surface of the module due
to reflection (W/m2 )
Energy incident on the reflector surface (W )
Energy leaving the reflector surface, per
degree (W/θ)
Energy incident on the surface of the module (W )
Ambient temperature (C)
Module
Area assuming a unit depth
∫
( dz = 1) (m2 )
Area ratio of illuminated to non-illuminated
module area
View factor between module and reflector
Dimension along the module (m)
Dimension along the reflector (m)
Dimension orthogonal to x and y (m)
Direct distance between dx and dy (m)
Reflector length (m)
wmod
L′
Lm
Waz
θ
θ′
β
γarray
γsun
αp
αp
ω
ωincl
ϕ
ϵ
m
ρ
module length (m)
Distance of reflector image along x axis (m)
height of the point of intersection of the
reflector image to the module edge (m)
Distance from reflector edge to top of the
reflector image in the z plane
Angle between outgoing ray and reflector
surface normal
Angle between incoming ray and reflector
surface normal
Angle between reflected ray and module
surface normal
Surface azimuth, 0o south
Sun azimuth, 0o south
Solar Elevation angle
Solar Profile angle
Module angle
Included angle between module and reflector
Reflector angle
Half angle between θ and θ ′
Beckmann surface roughness
Hemispherical reflectance
I. I NTRODUCTION
Solar photovoltaic (PV) systems are a rapidly expanding
sustainable renewable energy market, and will play a large role
in the future sustainable energy mix [1], [2]. Currently, commercial and utility scale PV installations are predominately
arranged in multiple parallel rows of flat modules, which are
aligned towards the mean maximum solar intensity [3].
Modules must be installed with a setback from the row in
front of it, to reduce inter-row shading losses and allow maintenance access. The spacing of these rows is highly dependent on
the latitude of the solar array, land availability, and economic
constraints which determine the economic performance of a
system [4]. Typically, the row spacing is designed to reduce
inter-row shading losses that occur in the early morning and
late afternoon; however, this arrangement leaves the spaces
between rows illuminated during the periods of highest solar
resource which is around solar noon [5].
Previous work has investigated the application of planar
reflectors for both solar thermal and photovoltaic applications. Much of the early work on planar concentration was
focused on the improvement of winter time yields for solar
thermal systems [6]–[9]. Some studies found that the optimal
orientation for this at high latitudes was a vertical collector
with a horizontal reflector [8]. A large body of literature has
Unfortunately, though the technical feasibility of these
systems has been shown, at the time of publication only
one entity has commercialized a comparable system for PV
applications [21], and because of assumptions made in the
design of the system, specialized parallel modules must be
utilized with this system, which tend to increase the costs of
the system.
In order to investigate the potential implementation of nontracking planar concentration PV systems for conventional
low-cost PV modules, this study: 1) develops and validates
a model using the concept of the BDRF of non ideal surfaces
rather than geometric optics and 2) experimentally investigates
systems in an outdoor test site in Kingston, Ontario utilizing
commercially available crystalline silicon PV modules. The
proposed model integrates previous work which analytically
investigated the module temperature increases, diode loading,
and angle of incidence effects. The outputs of this model
are used to perform a sensitivity analysis which identifies
important factors in the design of low-level concentration
systems.
This chapter is derived from a technical paper submitted
to the IEEE Photovoltaics Specialists Conference (PVSC) of
the same name [22] study expands on this work through: 1)
refining and further validating a model using the concept of the
BDRF of non ideal surfaces rather than geometric optics, 2)
undertaking laboratory scatterometry and solar simulator testing to compliment experimental data collected at an outdoor
test site in Kingston, Ontario 3) utilizing the validated model
to perform a sensitivity analysis which identifies important
factors in the design of low-level concentration systems. It
should be noted that the original reported boost of 35 % for
a prismatic glass module was erroneous, and upon further
analysis it was found that the boost is in-fact 40 %
1.68m
1.35 m 1.65 m
2.0m
There are limited examples of experimental studies that
address the specific effects of low-level concentration on PV
system losses, and recently a study was undertaken to identify
these additional loss mechanisms [20].
II. E XPERIMENTAL A PPARATUS
A. Outdoors testing
A 6m × 2.5m planar concentrator was installed at the Open
Solar Outdoors Test Field (OSOTF) in Kingston, Ontario (44◦
14 0 N, 76◦ 30 0 W) in the fall of 2011 [23]. Two stacks of
landscape crystalline silicon (c-Si) PV modules were arranged
in front of the wide planar reflector, and their actual locations
with respect to the reflector are shown in Figure 1. One stack
had modules with a prismatic glass front sheet, and the other
stack had traditional flat glass modules. Each module had a
length of 1m in the plane shown in Figure 2 and the reflector
had a length of 2.5m in the same plane. Figure 2 shows the
two dimensional domain used for the analysis and modeling
of the system, and is described in detail in section III-A.
1.32 m
Flat Glass Prismatic
Flat Glass Prismatic
2.5m
also looked at various ray tracing models for estimating the
increase in irradiation from a given reflector geometry [8]–
[18]. Of these models, there are some that account for diffuse
reflectors that utilize a combined view factor and specular
reflectance model [11], [13], [14], some that analyze a two
dimensional specular reflectance model [18], and some that
include experimental results [7], [10], [18], [19]
Currently, planar reflectors are utilized in district heating
solar thermal plants in Sweden and Denmark [5], and have
been shown experimentally to increase the thermal energy
collection at sites of 60◦ N latitudes by around 30% [18]
compared to a module at the same tilt angle of 45◦ . It has
been proposed that the introduction of non-specular corrugated
booster reflectors may further increase the outputs of these
fields by up to 8% [5] and the Bi Directional Reflectance
Function (BDRF) of these corrugated materials also have been
characterized [12].
Reflector
cL
6.0 m
Fig. 1: Plan view of installed system
The tilt angles of the surfaces from horizontal were initially
ϕ = 20◦ and ω = 57◦ , see Figure 2. After July, 2013 the
reflector angle, ϕ was changed to 15o to test the sensitivity
of the proposed model to changes in input conditions. These
values were chosen based on an initial optimization of the
system using the methodology outlined in [20].
A set of control modules with no reflectors were installed at
the same module tilt angle, and at a tilt angle of 30o to closely
match the optimal tilt angle for the region. This is slightly
different than the overall optimal angle for the Kingston region
of 35o due to mechanical limitations of the racks used in the
study. Based on analysis using the PVSYST modeling tool, the
difference in irradiance on a surface at 30o in the Kingston
region is less than 0.4%.
Meteorological measurements were made with two CMP 22
pyranometers, which measured global horizontal and diffuse
horizontal irradiation, and temperature and wind speed measurements were taken at the site. The modules were monitored
for short-circuit current (Isc ) and for temperature at the top
and bottom of the module.
N''
e
ul
od
M
dx
ω
β
x
N'
θ
y
φ
θ'
dy
75°
60°
Specular
Semi-Diffuse
Incident/scatter
Angle
45°
30°
r
cto
fle
Re
Fig. 2: Schematic of the modeled domain, all dimensions are
in the plane normal to the surface which they are measuring.
B. Scatterometry
A J.A Wollam variable angle spectroscopic ellipsometer
(VASE) was utilized to performed scatterometry on both
reflector materials. The reflector samples were adhered to a
standard glass slide, which was placed on the rotating sample
mount of the VASE. Scattered irradiation was measured using
the collimated receiver from angles of -10◦ to 10◦ degrees
from specular, and at wavelengths of 300nm-1000nm in increments of 100nm. The sample was rotated with respect to
the light source, and scatterometry was measured at angles
of incidence relative to the reflector surface of 75◦ , 60◦ ,30◦ ,
and 15◦ . The reflectivity at each wavelength was weighted by
the quantum efficincy of a c-Si module, in order to derive
a spectrally integrated reflectivity. The experimental results
are shown normalized by the maximum reflectivity at each
incidence angle in Fig 3.
The data is presented in a normalized fashion, as the
primary purpose of this dataset is the validation of the
use of the normalized Beckmann distribution introduced in
section ??, and the derivation of physically representative
scattering coefficients. Because the ellipsometer used is highly
0.8
0.2 0.4 0.6
Normalized Reflectance
1.0
Fig. 3: Polar Co-ordinate view of normalized measured scatterometry data for the semi-diffuse and specular reflector.
Irradiance
Irradiance
Sensor
15
cm
1c
m
m
m 3c
1c
The concentration system was installed in November 2011,
and had two forms of reflector installed: i) semi-diffuse,
flexible reflector made of an alumized PET laminate, (Foylon),
and used until July, 2012, and ii) a specular aluminzed PET
reflector (mylar), which was installed for the remainder of the
test period. The Mylar and Foylon reflectors had a hemispherical reflectivity of approximately 73% and 84%, respectively
on installation. After 2 years of exposure, the hemispherical
reflectivity of the Mylar and Foylon decreased to 60% and
65%, respectively. It should be noted that both these films
do not display good long-term weathering characteristics and
should not be used for long term system analysis or PV
system augmentation. The modules and reflector were cleaned
of any major soiling and organic depositions when they were
observed.
15°
10cm
θincluded
θsensor
Reflector
material
Fig. 4: Schematic depicting the apparatus utilized to simulate
a reflector system under a solar simulator.
collimating, and scattering measurements were taken only in
a two dimensional plane, the intensity measurements are not
physically representative.
C. Solar simulator testing
A small-scale model of a large scale reflector system was
constructed to produce validation data for the proposed reflector model under controlled laboratory conditions. A schematic
of the test system utilized is shown in Figure 4.
Irradiance was provided by a class AA solar simulator. The
illuminated area projected onto the test apparatus had a visible
diameter of 14 cm, however there was significant attenuation
at the edges of this projected area. Thus, it was ensured that
at all times the sensor and the majority of the reflector were
within an area described by a 9cm diameter which maintained
a uniform intensity within 3% of the peak area mean, as shown
in Figure 5
Tests were performed by setting an included angle between
the reflector and sensor, (θincluded ), and subsequently varying
the sensor angle, (θsensor ) from 0o to 90o from the horizontal.
This process was repeated for multiple reflector samples, and
a summary of the experimental results is shown in Figure 6
20 cm
10cm 10cm
and Spizzichino [27]. Recently, BDRF modelling and research
has been a focus in the field of computer graphics [24],
[28]–[30]. A modified version of the Cook-Torrance model is
used in this paper, which is a commonly implemented model
capable of simulating nearly specular to highly diffuse and
anisotropic surfaces [24], [25]. Here, this BRDF formulation
has been modified to ensure energy conservation.
The BDRF defines irradiance that reaches a module as a
function of both the angle of incidence (θ’) and the angle
of viewing (θ) of the light. In the case of a perfectly specular
reflector, the BDRF resembles the Dirac function, with a value
of 1 when the incident angle equals the outgoing angle (θ=θ’),
and 0 at any other viewing angle. This is the assumption of a
ray-tracing concentrator model. However, real surfaces are not
perfect specular reflectors and thus reflect light in a distribution
as defined by the BDRF of the material, and is a combination
of both diffuse and specular reflections.
⌀9cm
%Intensity
⌀14cm
Distance from center (cm)
Fig. 5: Illustration of the illuminated area projected onto the
surface of the test apparatus
120
Foylon
Mylar
Aged Mylar
Aged Foylon
Vertical Al
Horizontal Al
White Paint
Sensor Voltage(V)
100
80
60
40
20
0
20
0
10
20
30
40
50
Sensor angle(o )
60
70
80
90
Fig. 6: Summary of reflector characteristics for a variety of
materials, with an included angle (θincluded ) of 100o . The
sudden rise in output around 15o is due to the top edge of the
reflector image reaching the bottom edge of the sensor. The
gradual decline in intensity after the peak is due to the dilution
of the reflector image as is extends beyond the top of the sensor
element, and is also dominated by angle of incidence effects.
III. M ODELLING
A reflectance model based on a Bi-Directional Reflectance
Function, BDRF, for an isotropic roughened surface is developed here to predict the performance of the reflector system.
The model methodology presented in this paper uses the concepts of the BDRF of non-ideal surfaces rather than traditional
geometric optics [24], [25]. This methodology allows for the
evaluation of non-specular reflectors in planar concentration
systems, which has been shown to increase the energy yields
from these systems compared to purely specular reflectors. [5],
[26]
The BDRF classifies the three dimensional scattering of
light from a surface, and is described theoretically by Beckman
A. Model Domain
The domain being considered in this model is shown as a
function of the representative angles in Fig 2. An integrative
approach is taken in the analysis, where the contribution of
irradiation to a differential point on the PV module (dx) from
each differential scattering element on the reflector (dy) is
computed. Thus, an integration is performed along the two
principle directions of the array, x and y as shown in Figure 2.
In order to account for the diode topology of a PV module,
the model divides each module domain into four distinct
sections along the x-coordinate. The minimum irradiance from
any of the four domains is taken as the limiting energy incident
on the module, and is used to predict the overall energy
production of the module.
B. Model Derivation
A set of simplifying assumptions are used:
1) The reflector is assumed to be infinite and homogeneous
along its length. Therefore reflection is only considered
in a two dimensional plane normal to the infinite dimension. NOTE: For the experimental validation of the
model, azimuthal effects of the finite reflector were taken
into account as described in section III-C.
2) The reflector is a broadband reflector, and spectral
attenuation is not taken into account.
The major implication of simplifying the domain of the
reflector onto two-dimensional geometry is to properly account
for the projection of the three-dimensional incident light ray
onto the two dimensional domain. This is done using a
modified version of the profile angle, αp equation introduced
in [31] and recommended in [32]:
αs
tan(αp )
Gp
= π/2 − Zenith
(1)
tan(αs )
= cos(γsun
−γArray )
sin(αs )
= GDN I sin(α
p)
(2)
(3)
Where Zenith is the solar zenith angle, αs is the three
dimensional solar elevation angle, γsun and γarray are the
Eri
′
Eref l
=
=
Ep cos(θ )dydz[W ]
Eri BDRF (θ, θ′ )ρ[W/θ)]
(4)
(5)
Em
=
(6)
dθ
=
BDRF (θ, θ′ )
=
Eref l dθ[W ]
dycos(β)
r
D(θ, θ′ )
∫ π2
D(θ, θ′ )dθ
−π
(7)
(8)
Mylar Experimental
Foylon Experimental
1.2
1.0
0.8
0.6
0.4
0.2
0.00
10
20 30 40 50 60 70
Angle of incidence/scatter angle ( ◦ )
Gim =
Gp ρ
Am
∫
0
Lsect
∫
Lm,max
BDRF (θ, θ ′ )cos(θ′ )
Lm,min
cos(β)
dxdy (9)
r
where Gim is the irradiance (W/m2 ) on the surface of the
module, ρ is the specularly constant surface reflectivity, θ’ is
constant for a given time step, and θ, β, and r are a function
of the linear distances along reflector and module, x and y:
√
(x2 + y 2 − 2xy cos(ϕ + ω − π/2)
]
[
2
2
2
−1 r + y − x
π − sin
2ry
r
=
θ
=
β
= (π − ϕ − ω) − θ
(10)
(11)
(12)
and D(θ,θ’) is given by the Beckmann distribution [27].
cos2 (ϵ)−1
1
m2 cos2 (ϵ)
exp
(13)
m2 cos4 (ϵ)
θ + θ′
ϵ = θ−
(14)
2
where m is a physical parameter that represents the rms
slope of surface roughness on the reflecting surface and
generally m ∈ [0 0.5]. ϵ is the angle from the surface normal
of the vector bisecting θ and θ′ .
The BDRF of the two surfaces used in this study were
measured using the scatterometry techniques described in
section II-B. The theoretical approximations for the BDRF
using Equation 13 were also calculated for values of m=0.03
for the specular reflector and m=0.07 for the semi-diffuse
reflector, which were found to be the closest match to the
D(θ, θ′ )
=
80
90
Fig. 7: Comparison of measured scatterometry results from
both reflector materials to modelled BDRF distributions for
two values of the roughness coefficient (m).
2
Equations 4-8 can be combined and integrated along the
characteristic dimensions, and divided by the area of the
module being analyzed (Amodule ) to obtain the irradiance on
the module surface.
m=0.03 Beckmann
m=0.07 Beckmann
Normalized scattering
solar and array azimuth angles, respectively, and αp is the
two-dimensional solar profile angle.
Recalling the model domain that is depicted in Fig 2,
Equation 4 shows the radiant intensity [W] that impacts the
plane reflector at point dy and to a depth dz. Equation 5
represents the value of reflected radiant intensity per unit depth
through a differential ∫angle [W/θ]. Note that the BDRF is
π
normalized such that 0 BDRF dθ = 1. Equation 6 shows
the radiant intensity per unit depth that strikes the surface of
the module. Note that θ is defined in Equation 7 in terms of
the angle of incidence of the differential ray onto the surface
of the module, β, and the distance the ray has travelled (r).
W
L'
wmod
Waz
Module
Lm
Reflector Image
Reflector
Fig. 8: Illustration showing potential partial illumination of a
module by a finite reflector length. South is down.
measured data, and the comparison of the experimental and
theoretical values is shown in Fig 7
The diffuse contribution of irradiation was evaluated using
the diffuse view factor between the reflector and PV module,
Frm , as described by [33].
1
R + 1 − (R2 + 1 − 2 × R × cos(ωincl )) 2
(15)
2
where R is the ratio of module length to reflector length, and
ωincl is the angle between the two surfaces.
Frm =
C. Azimuthal correction
The 2D model proposed above was modified to account
for the illumination effects of finite reflector lengths. It is
possible that in the morning and evening, irradaince at high
azimuth angles would not illuminate the entire module as
shown in Figure 8. This was accounted for by calculating the
non-illuminated area of the module during these periods, and
adjusting the expected energy output by the calculated area
ratio. This is a process similar to the one implemented by
Bollentin [17].
The equation proposed by Bollentin utilized was modified
to the following:
=
Lm
=
abs(L′ /Waz × W )
′
AR
= 1−
(18)
Waz
L′
′
× (L − Lm )
.5 × (L − Lm ) ×
(19)
L′ × wmod
where L′ = Lmod if L′ > Lmod. The value AR represents
the effective area ratio of the area not illuminated by the specular image of the reflection. As a first order approximation,
the total irradiance on the surface of the module is given by
Gim ∗ AR in cases where edge effects are considered.
D. Model Implementation
The BDRF model was run iteratively for the full measured
dataset of incoming irradiance and zenith angles, and the dual
integration was run at each step. The amount of irradiation
that directly impacts the module was evaluated using the
Perez irradiation translation model [34]. Once the total inplane irradiation on the face of the module was evaluated, the
predicted module output was calculated using the methodologies outlined in [35] using coefficients derived from the control
module. Note that only Isc was collected from the modules,
and therefore the validation of the model was performed using
Isc rather than power. Isc is an excellent predictor of effective
irradaince on the plane of the array [35], and is therefore well
suited for validating the model. However, when comparing
the annual outputs from the modules, the collected Isc is
utilized to calculate effective irradiance, Ee in the Sandia
Array Performance Model [36], and used with the collected
cell temperature to estimate the power production from each
module.
E. Thermal model
The Sandia cell temperature model [36] was modified to
predict the temperature of modules under low concentration.
Thus, the thermal model utilized for this study is :
TCell = GDN I × C0 + Gdif f × C1 + exp(C2 × GDN I ) + Ta
(20)
Coefficients were obtained using a least-squares optimization and were found to be C0 =0.0232,C1 =0.0276,C2 =0.00011. These coefficients gave a Normalized Root Mean
Squared Error (NRMSE) of 6% and a Mean Bias Error (MBE)
of 0.1%. A correlation plot of this fit is shown in Figure 9
Interestingly, the measured data display temperature spikes
for short periods during the day, where the cell to which
the thermocouple was attached could reach temperatures approaching 100◦ C for a short period of time, as seen in
Figure 10. One possible explanation is that these spikes are
due to inconsistent illumination from the reflector, however the
reflector is relatively uniform, and another possible explanation
is that these temperature spikes are due to the normal ”patchwork” appearance of cell temperatures for a short-circuited
module, as shown in Figure 11.
70
60
50
40
30
20
10
0
10
2020 10 0 10 20 30 40 50 60 70
Measured Temperature (C)
100
75
50
25
0
25
50
75
100
Azimuth
Waz
wref l
(16)
sin(2 × ω + ϕ − αp ) × sin(αp − ω)
−tan(γ) ∗ (L′ × cos(ω) + wref l × cos(ϕ))(17)
Modelled Temperature (C)
=
Fig. 9: Correlation plot showing the quality of the fit of the
temperature model.
90
Reflector
Simulated
80
Temperature ( ◦ C)
L′
70
Control
Ambient
60
50
40
30
20
10
04 07 10 13 16 19 22 01 04 07 10 13 16
Hour
Fig. 10: Thermal variations for May 29 and May 30, showing
the thermal spike effect, and the fit of the proposed thermal
model.
F. Model Validation
Initial validations were performed as comparisons to the
solar simulator measurements described in section II-C. It was
noted that the model accurately predicted the characteristics
of a new Mylar (m=0.03, rho=0.73) and Foylon(m=0.07,
rho=0.84) reflector as seen in Figure 12 and Figure 13. In
addition, the imaging of the reflection onto the sensor is
properly handled, as demonstrated by the matched uptake at 5o
and 15o for θincluded =100o and θincluded =90o , in Figures 12
and 13 respectively.
The model was then applied to the entire dataset, the model
predictions are in reasonable accord with the experimental
data, as shown in Figure 14. The prismatic glass module was fit
with an NRMSE of 12% and an MBE of 1%, and the flat glass
module was fit with an NRMSE of 14% and an MBE of 2%.
Figure 15 presents a time series showing a typical fit of hourly
data . It is important to note that beyond the tuning of the
temperature model, no empirical parameters are utilized. All
user inputs to the model were based on the physical properties
of the system.
16
100
75
50
25
0
25
50
75
100
12
Azimuth (o )
Modelled Isc
14
10
8
6
4
2
0
0
2
4
6
8
10
Measured Isc
12
14
16
Isc
(A)
Fig. 14: Correlation plot showing the fit of hourly data.
Fig. 11: Top:Two Infrared photographs of a module backsheet,
with reflector augmentation taken 1 minute apart. A moving
patchwork of hotspot cells is apparent. Bottom: view of multiple short-circuited modules. Only the modules highlighted
with the white circle have reflector augmentation.
14
12
10
8
6
4
2
0
00:00
Modelled
Measured
12:00
00:00
12:00
Time
00:00
12:00
00:00
Fig. 15: Three typical days from April 7th -9th demonstrating
the model fit to experimental data.
IV. E XPERIMENTAL R ESULTS
120
Foylon Exp
m=0.07 p=0.84 Model
Mylar Exp
m=0.03 p=0.73 Model
Aged Foylon Exp
Aged Mylar Exp
100
Sensor Voltage(V)
Fig 16 presents the weekly normalized increase in Pmp between
reflector and control modules. On average, the use of a
80
non-tracking planar reflector can increase system performance
∫
60
for a module at the same angle (as characterized by Pmp )
by 45% for a traditional flat glass module and by 40% for a
40
prismatic glass module.
20
It should be noted that the high module angle of 57o is
010
0
10
20
30
40
50
60
70
80 not the optimal non-augmented orientation for this latitude.
Sensor angle( )
An identical control module was mounted at 30o for the same
Fig. 12: Comparison of experimental and modelled results period of testing, which is within 0.4% of the yearly energy
for an included angle (θincluded ) of 100o . Also shown is the yield of to the regional optimal angle of 35o . A Comparison
effects of approximately 1.5 years of weathering on the optical of the energy output of the reflector augmented modules to
this optimal control module gives an the energy performance
performance of the reflectors.
increase of 18 % for both modules.
120
The effects of the reflector are also characterized in FigFoylon Exp
m=0.07 p=0.84 Model
100
ure 17, indicating the dependence of output ratio on solar
Mylar Exp
zenith angle over the year for non-cloudy days for all modules.
m=0.03 p=0.73 Model
80
Sensor Voltage (V)
o
Aged Foylon Exp
Aged Mylar Exp
60
40
20
0
0
10
20
30
40
50
Sensor angle
60
70
80
Fig. 13: Comparison of experimental and modelled results
for an included angle (θincluded ) of 90o . Also shown is the
effects of approximately 1.5 years of weathering on the optical
performance of the reflectors.
90
Fig 18 displays a probability density function for module
temperatures. It can be seen that for the majority of operation,
the module operates below or near to Normal Operating Cell
Temperature (NOCT), 48◦ C. There are some occasions where
the cell temperature rises above 90◦ C, which is beyond the
maximum design temperature of some commercial modules.
The results of this study show that it is in the best interests
of module manufacturers to ensure that segments of their
modules can withstand elevated temperature operation in order
to take advantage of the benefits of low-concentration system
integration.
Specular Reflector
Semi-Diffuse Reflector
01 02 03 04 05 06 07 08 09 10
Month
Fig. 16: Time series of daily power boost due to reflectors
as compared to control modules, averaged over a one week
period. The decrease in performance in July represents the
time when the reflectors were reduced to horizontal in order
to change the reflective material.
0.045
0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.00040
Reflector Module
Non-Reflector Module
Probability
Flat Glass
Prismatic
Power Ratio
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
20
0
20
40
60
80
Module Cell Temperature ( ◦ C)
100
Fig. 18: A probability distribution plot of cell temperatures,
showing a slight increase in cell temperatures for reflector
augmented moduels.
introduce edge effects, was chosen for this optimization, and
it is assumed that the output would not be largely affected
by changes in reflector length around this ideal. Therefore,
only panel angle (ω), reflector angle (ϕ) and the scattering
coefficient (m) were optimized for a location in Kingston,
Ontario, Canada (44◦ 14 0 N, 76◦ 30 0 W).
Combinations of ω, ϕ, and m were calculated within the
domain:
ϕ ∈ [0, 10 . . . 60]
ω ∈ [25, 35 . . . 85]
m ∈ [0.01, 0.04, 0.08, 0.15, 0.65]
ρ = 0.8
(a) Flat Glass
(b) Prismatic Glass
Fig. 17: Clear day output ratios (ratio of reflector augmented
to control module) as a function of zenith angle for one year
of data
V. M ODEL SENSITIVITY ANALYSIS
An optimization was performed to determine the best topology layout for the two typical reflector surfaces investigated
in this study. It was assumed that the length of the module
remained constant at 1m, due to manufacturing limits. The
length of the reflector was also kept constant at 2.5m, it
is assumed that this length of reflector could be reduced
through optimization, however a large reflector which will not
Note that the exact experimental apparatus is not included
in this domain (ϕ = 20◦ and 15◦ , ω = 57◦ ), however the
intention of this analysis is to sample the entire domain at
regular intervals rather than to replicate the exact experimental
apparatus, as was done in Section III-F.
The total boost, or increase in performance relative to a
non-augmented module placed at the optimal orientation for
the Kingston site (35o ) was calculated for each case, and
the results are shown in Figure 19. From this sensitivity
analysis, it can be seen that the maximum theoretical increase
in performance available is 30% over a non-augmented system.
This is true for a variety of systems with an integrated
reflectivity of 0.8, a scattering coefficient up to 0.08 and for
a reflector angles between 30o and 40o .
It can be seen that there is a relatively low sensitivity to the
overall module boost near the optimal point for each graph.
However, the daily and yearly distributions of irradiance can
vary by a large degree between different settings, which may
be useful for load matching. Figures 20- 22 show the effects
of varying ϕ, ω, and m from a base case of ϕ = 20o , ω = 55o
and m = 0.01
In order to identify if this form of system can be economically feasible, a rough economic case is presented. In
this system, the simulated reflector length was approximately
twice the length of the modules being simulated, thus 2:1
area ratio of reflector to module surface area is assumed. At
a 2:1 area ratio, the distance between rows of PV modules
would not be largely affected as compared to a non-reflector
system. Thus, it is assumed that land costs will not make a
25
35
1.3
45
55
65
75
700
85
Monthly sum of Isc
500
1.2
m=.01
1.1
400
300
1.0
1.3
Performance improvement
ω =65o
ω =55o
ω =45o
ω =35o
600
200
1.2
100
m=.04
1.1
0 Feb Mar Apr May Jun
Jan
2012
1.0
1.3
1.2
m=.08
1.1
1.0
1.3
Jul Aug Sep Oct Nov Dec Jan
2013
Month
Fig. 22: Effects on Isc when varying ω keeping ϕ = 20o and
m = 0.01.
m=.15
1.2
1.1
1.0
1.3
$0.05
m=.65
1.0
0
10
20
30
40
Reflector Angle (o )
50
60
Fig. 19: Results of evaluation of the reflector code the simulation domain. The legend indicates the module angle (ω)
in degrees, and each graph represents a different value of the
scattering coefficient, m.
Monthly sum of Isc
700
m=.01
600
m=.04
500
m=.15
400
300
200
100
0 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan
Jan
2012
2013
Month
Fig. 20: Effects on Isc when varying the scattering coefficient,
m, keeping ω = 55o and ϕ = 20o
1000
800
600
φ =10o
φ =20o
φ =30o
φ =40o
400
200
0 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan
Jan
2012
2013
Month
Fig. 21: Effects on Isc when varying ϕ, keeping ω = 55o and
m = 0.01.
Return on Investment
1.2
1.1
Monthly sum of Isc
$0.10
$0.15
$0.20
$0.30
$0.40
300%
250%
200%
150%
100%
50%
0%
‐50%
‐100%
$2.00
$3.00
$4.00
$5.00
$6.00
$7.00
$8.00
Installed cost of reflectors ($/62)
Fig. 23: Economic sensitivity analysis, showing the return on
investment of the installation of a reflector system, as the cost
of the reflector and system PPA rate are varied. This assumes
an 8% cost of capital and 20 year project lifetime.
large difference in the economics of the project, and are not
included in this analysis. The modules utilized in this system
are 1 m × 1.65 m, or 1.65m2 , thus the equivalent reflector
area is 3.3m2 . In a simple economic case, we will assume an
interest rate of 8% over 20 years for the capital expense of
the reflector system. The variables of interest are the installed
cost of the reflector system, expressed in $/f t2 , and the Power
Purchase Agreement (PPA) rate received from the PV asset.
From the results shown in Figure 23, the return on investment
of installing a reflector system is highly dependent on the
installed costs of the reflector. Further investigation is required
to determine appropriate cost models for this component.
It should be noted that these estimations do not necessarily
represent the overall economically optimal arrangement for
a practical system where a DC overrate of 20%-30% is
common. The optimal arrangement of reflectors will tend to
increase the system output around periods of the day that
already experience high levels of irradiance. Thus, much of
the additional energy available from the reflector mirrors may
not be utilized effectively by the inverters. Therefore, future
work should investigate the optimal arrangement of a reflector
system to ensure maximum inverter utilization.
VI. F UTURE W ORK
R EFERENCES
As mentioned previously, future work should investigate
the effects of DC overrate on the optimal arrangement of a
reflector system. It is conceivable that the sytem could be optimized to maximize total energy yield, or could be optimized
to produce more energy in the mornings and evenings in order
to provide passive load balancing.
Another interesting extension of this work is to perform
an optimization on the shape of the surface BRDF. Though
the model used in this research represents a symmetrical
BRDF, micro-engineered surfaces could be used to provide
other non-symmetric BRDF profiles which could increase the
effective output of planar concentrator systems. In addition
this model should be adapted for solar thermal systems and
photovoltaic solar thermal (PVT) systems, as the increased
operating temperatures would increase the exergy [37]–[39] of
both and decrease the spike annealing time of the latter [40],
[41], increasing yields further.
Finally, an extension of the presented economic analysis is
warranted to determine if the additional capital costs of the
reflector system are warranted for both existing solar farms
and retrofits.
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Humanities Research Council of Canada grant.
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