1. Novel Solar Tracker with Tuneable Oil Prism
H. Nguyen, 2014| 1
Novel Solar Tracker with Tuneable Oil Prism
Huu D. Nguyen
Abstract
The purpose of this paper is to propose a cheap solar tracker. The tracker uses refractive index
of silicone oil and flexibility of silicone rubber to create a tuneable prism which can respond to
changing incident angle of the sun. The numerical analysis uses Snell’s Law and Fresnel’s
Equation to evaluate design’s efficiency and range of incident angle that the tracker can track.
The analysis predicts that the design capable of collect sunlight that incident within ±50° and
has average efficiency about 20%. This shows that the design’s performance is similar to the
current solar trackers’.
1. Introduction and Motivation
As the world population grows the demand for energy
increases; at the same time fossil fuel becomes scarcer. Therefore,
fossil fuel alone cannot meet with growing demand for energy. To
solve this problem, people already look at alternate energy sources
like nuclear energy, wind energy, and solar energy. Among them,
solar energy can easily harvest and its photovoltaic (PV) systems can
install and operate in urban and suburban areas. However, there are
challenges in PV systems. One of them is to have low cost tracker
that can track the sun and capture most of sunlight; currently, a
typical tracker costs about $870/kWp while the PV modulus cost
about $850/kWp1
. Therefore, the cost to install trackers into PV
system is as high as install more PV modulus; but install more PV
modulus is not a good option due to limit of space.
The purpose of this project is to design a solar tracker for
the PV system that is low cost and capable of track the sun for most
of a day while still has high efficiency.
2. Background
In solar energy harvesting, there are many photovoltaic
(PV) systems that can capture sun’s energy and convert it to
electricity. Currently, the best PV systems use solar tracker to
capture most of the sun’s radiation that incident within ±60°2, 3
. One
of the main purposes of solar trackers is to deflect sun radiation into
one single PV cell. To do that, the trackers use motors to steer
mirrors toward the sun and deflect radiation toward the PV cell; this
process requires high precision or otherwise there are significant
energy loss4
. However, the motors are costly to fabricate and
maintain; at the same time, the wind bends the trackers and creates
errors5
. To counter the wind’s effect, the trackers become bigger and
heavier but that increase the cost.
Cheng et al. are researched a new tracker that uses
electrowetting on dielectric (EWOD) as an effort to reduce the cost
of fabrication and maintain the tracker6
. The new system is
promising in reduce the cost, but its performance is poor considering
it only capable of deflect ±15° of incident light. This means that
there are significant amount of energy that the tracker cannot
capture. This limitation is mainly due to saturation of liquid-liquid
contact angle in electrowetting process and is appeared in others
devices that use electrowetting for beam steering7,8
. Due to this
limitation, EWOD is not useful for tracking the sun.
Tremblay et al. are designed another promising tracker that
uses properties of lenses and mirrors to redirect sunlight into a
waveguide and to a PV cell9
. However, the tracker only able to
capture incident sunlight within ±20°; therefore, it requires an
additional tracker to enhance its performance.
From the past designs, this design requires to make from
cheap materials and capable of deflect ±60° of incident light. At the
same time, its efficiency to collect sunlight must be high. To
maintain its function, the design needs to have long operated life and
good thermal stability.
3. Overall Design and Material Selection
Figure1 shows the tracker which consists of tuneable
prism, Fresnel lens, and optical waveguide. As shown in figure 1, the
prism is mounted on top of the Fresnel lens and the waveguide. So,
any light incidents on top of tracker will redirect toward the Fresnel
lens. The configuration for the Fresnel lens and optical waveguide is
adopted from Tremblay et al.’s design. In their design, the Fresnel
lens focus all light to a mirror underneath the optical waveguide and
reflect all light into the waveguide. The optical waveguide then
directs light toward PV cells that locate at the perimeter of
waveguide.
Figure1: The overall design of solar tracker consists of prism to
deflect sunlight, Fresnel lens to focus sunlight to optical waveguide,
and optical waveguide to direct sunlight to PV cell.
The prism (shown in figure 2) is tuneable and made from
thin glass and rubber which glue together by epoxy glue. The bottom
glass plate glues with the glass container so it cannot move. The top
glass plate hinges to the glass container so it can rotate. The top glass

2. Novel Solar Tracker with Tuneable Oil Prism
2 | H. Nguyen, 2014
plate hinges to the glass container by glue it to the rubber wall, then
the side of the rubber wall with holes for oil valves glues to the glass
container while other three sides are not. At the same time, the
rubber is flexible so it can easily fold and unfold.
Figure 2: Prism when rubber wall fully extend. The top glass plate
can rotate (as shown by the arrow) about the hinge location which in
turn tunes the prism. The size of the prism is about 22x27x40mm3
.
There are two valves for oil to flow in and out the prism.
Before the prism can be use, oil flows into one valve to flush all air
out though the other valve. After all the air flow out, one of the valve
then seal; so that by add more oil, the oil pushes against the glass
and rotates the top glass plate.
The prism is made from commercial available thin glass
(SiO2, around 1mm thick), silicone rubber (0.7 mm thick), and
silicone oil. Both the oil and glass are dielectric materials; therefore
their refractive indexes (n=1.58 and ng=1.45 respectively) are not
depend on wavelength. Thus, there is no dispersion effect when the
prism redirects sunlight toward Fresnel lens. The silicone rubber can
operate in temperature range from -40o
C to 135o
C while still
maintain over 10 years life10
. Both the silicone oil and silicone
rubber’s thermal expansion coefficients are around 10-4
m/m-C;
therefore, thermal expansion would not become a problem.
4. Theory and Experimental Design
The tracker’s performance is depending on efficiency and
the angle range that the prism can deflect. The angle range is
calculated from Snell’s law. Figure 3 shows the schematic of light
path within the prism. From Snell’s Law and figure 3, the
relationship between incident angle and exit angle is described by
eq. (1) and (2).
𝜒 = 𝑠𝑖𝑛−1 〈
𝑛
𝑛 𝑎𝑖𝑟
𝑠𝑖𝑛 {−𝛼 + 𝑠𝑖𝑛−1
[
𝑛 𝑎𝑖𝑟
𝑛
sin⁡( 𝜃 + 𝛼)]}〉 (1)
𝜀 𝜒 = 𝜀 𝛼
𝜕𝜒
𝜕𝛼
(2)
In eq. (1), n is refractive index of silicone oil, nair is
refractive index of air, θ and χ are light’s incident and exit angles
respectively, and α is angle that the top glass plate make with
horizontal plane. In eq. (2), ε is error. The eq. (2) assumes that α is
the only uncertainty parameter in the right hand side of eq. (1).
The efficiency is the ratio between power products by the
PV cells and the intensity incident on top of tracker. In theory, the
efficiency is described in eq. (3) where ηprism is the fraction of light
incident onto the prism and transmit toward the Fresnel lens, and
ηlens+waveguide+PV is the fraction of light incident onto the Fresnel lens
and convert into electricity. The ηprism is calculated in eq. (4) where
ηarea is the fraction of light that is not block by prism’s wall, and
Ttotal is fraction of light transmit through the prism.
Figure 3: Light path within the prism; θ is incident angle, α is tilt
angle, β is minimum value of α due to physical constrain, χ is exit
angle, nair is refractive index of air (~1), and n is refractive index of
silicone oil.
𝜂 = 𝜂 𝑝𝑟𝑖𝑠𝑚 ∗ 𝜂𝑙𝑒𝑛𝑠+𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒+𝑃𝑉 (3)
𝜂 𝑝𝑟𝑖𝑠𝑚 = 𝜂 𝑎𝑟𝑒𝑎 ∗ 𝑇𝑡𝑜𝑡𝑎𝑙 (4)
When light enters the prism, fraction of light gets reflect
back when it passes through an interface. There are 4 interfaces in
the prism: air and glass, glass and oil, oil and glass, and glass and
air. For each interface, the reflectance is described in Fresnel’s
Equation, eq. (5).
𝑅 = 0.5 ∗ ((−
𝑛𝑖cos⁡( 𝜑 𝑖)−𝑛 𝑡cos⁡( 𝜑 𝑡)
𝑛𝑖 cos(𝜑 𝑖)+𝑛 𝑡cos⁡( 𝜑 𝑡)
)2
+ (
𝑛 𝑡cos⁡( 𝜑 𝑖)−𝑛𝑖cos⁡( 𝜑 𝑡)
𝑛𝑖 cos(𝜑 𝑡)+𝑛 𝑡cos⁡( 𝜑 𝑖)
)2
) (5)
In eq. (5), i denotes incident, t denotes exit, n is refractive
index, and φ is the angle light makes with the normal vector of the
interface. When light is in between 2 interfaces, fraction of light
transmits thought the interface while the rest reflects back to
different interface. A fraction of the reflected light then transmits
through the interface while the rest reflects back to previous
interface. This process repeats until all light transmit outside or
absorb. To account for all this, net-radiation method calculates the
total transmittance Ttotal with eq. (6) to (10)11
.
𝑇𝑡𝑜𝑡𝑎𝑙 =
𝐷𝑡 𝐷 𝑏
1−𝐶𝑡 𝐶 𝑏
(6)
𝐶𝑡 = 𝑅1 +
𝑅2(1−𝑅1)2
1−𝑅1 𝑅2
(7)
𝐷𝑡 =
(1−𝑅1)(1−𝑅2)
1−𝑅1 𝑅2
(8)
𝐶 𝑏 = 𝑅3 +
𝑅4(1−𝑅3)2
1−𝑅3 𝑅4
(9)

3. Novel Solar Tracker with Tuneable Oil Prism
H. Nguyen, 2014| 3
𝐷 𝑏 =
(1−𝑅3)(1−𝑅4)
1−𝑅3 𝑅4
(10)
In eq. (6) to (10), R is reflectance, the subscript 1 to 4
denote air and glass, glass and oil, oil and glass, and glass and air
interface respectively. It is assumes that both glass and oil do not
absorb any light since they are dielectric.
To test the design, the experimental set up is shows in
figure 4. The set up uses a laser diode as light source and a digital
colour camera to take data. Underneath the prism is a dye chamber
contains CaCl2 and food colour to high light the exit laser. From
experimental set up and type of laser diode, the light’s incident angle
and intensity is known. By using image process program (such as
ImageJ) to process image from camera, light’s exit angle and
intensity then determine. With all data, the exit angle χ and total
transmittance Ttotal then determine.
(a) (b)
Figure 4: Experimental set up to evaluate the prism’s total
transmittance Ttotal and exit angle χ. (a) The front view of set up. (b)
The side view of set up.
5. Numerical Result
As shows in figure 1, the desire exit angle, χ, is 0o
;
therefore, by set χ equal to 0o
, figure 5 plots tilt angle, α, and α+θ as
function of incident angle, θ.
Figure 5: α and α+θ vs. θ when exit angle, χ, equals to 0o
.
Usually, the trackers require the acceptance angle to be
less than 1°; therefore the tolerance error of χ, εχ, is about 1°. Base
on this, the tolerance error for α, εα, is 1/⁡𝜕𝜒/⁡𝜕𝛼. Figure 6 plots
1/⁡𝜕𝜒/⁡𝜕𝛼 for different θ where α is chosen such that χ = 0o
.
Figure 5 shows that α change between ±40° is sufficient to
defect incident light within ±60°. Figure 6 shows that at θ=±60°, the
maximum error for α is about 1°. However, as θ approach zero, then
the tolerance for α increases toward 4°. This implies that as θ
approach zero the effect of factors that change the tracker’s
performance decreases.
In eq. (5), φ is the angle light makes with the normal
vector of the interface; therefore, the incident angle with respect to
normal vector of first interface (air and glass) is α+θ and is limited
within ±90o
. Figures 5 shows that α+θ reaches 90o
around θ =±50o
;
as a result, any light that incident within -60o
to -50o
and 50o
to 60o
would not transmit through. Figure 7 plots the total transmittance,
Ttotal, of the prism.
Figure 6: εα, vs. θ for εχ = 1o
and χ = 0o
.
Figure 7: Ttotal vs. θ when χ = 0o
.
Figure 7 shows that as θ approaches ±50o
the total
transmittance approaches 0; this implies that the efficiency
approaches 0 as well. At same time, the efficiency remains 0 for θ
within -60o
to -50o
and 50o
to 60o
.
Considering that the lens, waveguide, and PV cell
configuration is adopts from Tremblay et al.’s design, therefore the
fraction of light incident onto the Fresnel lens and convert into

4. Novel Solar Tracker with Tuneable Oil Prism
4 | H. Nguyen, 2014
electricity, ηlens+waveguide+PV, should be similar to their design’s which
is around 0.8. Figure 8 shows the top views of the prism.
Figure 8: Top view of the prism, the unit is in meter.
In figure 8, the area inside the red rectangle is the area the
prism occupies and the area inside the blue rectangle is the area that
light passes through. Base on this, the fraction of light that is not
block by prism’s wall, ηarea, is
ηarea=(0.01841*0.01841)/(0.022*0.02711)=0.56827. Since in a
single day, the sun goes from 90° to -90°, therefore, the average
efficiency in one day is
𝜂 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =
∫ 𝜂 ∗ 𝑑𝜃
𝜃=900
𝜃=−900
∫ 𝑑𝜃
𝜃=900
𝜃=−900
=
0.8 ∗ 0.56827 ∫ 𝑇𝑡𝑜𝑡𝑎𝑙 ∗ 𝑑𝜃
𝜃=500
𝜃=−500
𝜋
≈ 0.1993
So, the average efficiency of the design is about 20% and
it can deflect light that incident within ±50°. Compare to other
trackers, the performance of this design is similar. Table 1
summarizes the performance between this design, Cheng et al.’s4
,
and SunCore’s CPV system that uses motor tracker3
.
Table 1: Performance comparison between exist trackers and this
design.
Name Cheng et al.’s SunCore This design
Efficiency 37-20% 20% 20%
Incident angle ±15° ±60° ±50°
Conclusion
In theory, this design able to deflect any light incident
within ±50° and has average efficiency about 20%. The design has
similar efficiency to the EWOD tracker and the CPV tracking system
that uses motor tracker. For solar harvesting, this design is cheaper
and easier to fabricate than the motor trackers; however, it may be
not better than the EWOD tracker because few problems can occur.
One problem is that when the rubber wall fold so that the angle α
becomes negative, the rubber wall may covers the prism and blocks
out all light instead since it is not entirely glue to the glass container.
Even though there are transparent silicone rubber10
, this problem can
still significantly reduce efficiency. Thus it is needed to be
considered. Second problem is that the design relies on the rubber
continually fold and unfold. The silicone rubber has poor tear
resistance; so by continuously fold and unfold, the rubber can tear
apart.
In the analysis, the wind effect and fluid dynamic of the
silicone oil are not considered for simplicity. However, these
parameters affect how the top glass plat rotates; thus they can
contribute to the error in α. Therefore, real experimental data is
needed for evaluate these parameters.
Notes and references
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Cervantes, G. Quemere, O. Laurent, in Concentrator
Photovoltaics, A. Luque, V. Andreev, Springer, 2007, vol.
130, ch. 11, pp. 221-251.
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9 E. Tremblay, V. Zagolla, D. Loterie, C. Moser, SPIE
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10 http://www.reissmfg.com/silicone-rubber-
elastomers/technical-data.shtml, 2014
11 J. R. Howel, R. Siegel, M. P. Menguc, in Thermal
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