Down-reflecting flat mirrors can be placed adjacent to a PV panel to increase the amount of radiation the panel receives. The PV panels are assumed to be on two-axis tracking platforms and pointed to the sun. Figure-1 shows how the mirrors can be placed around the PV element in the center.
Figure-1 A down-reflecting arrangement of flat mirrors
Figure-2 shows a simple application in which the four sides of a PV panel are attached to mirrors. Only one mirror is shown in the figure.
L M q
L
PV
Figure-2 A down-reflecting arrangement of flat mirrors
In this figure,
L
M
=length of mirror

L
P
= Length of PV cell
θ=Mirror tilt angle
From geometry it can be shown that
L
L
M p

Sin
Sin
(
(
2 q
90


90 q
)
)
(1)
Equation (1) indicates that as the mirror tilt angle approaches 45 degrees the length of mirror approaches zero. That means the angle of mirror must be larger than 45 degrees.
As the tilt angle approaches 90 degrees, the mirror length increases to infinity. At the angle of 60 degrees, the length of the mirror will be equal to the length of the PV panel.
We can define the mirror geometric efficiency (MGE) as the ratio of the area of reflection to the mirror area. If the area of capture by the mirror is B then
B

L
M cos( q
) (2)
Assuming the same constant width for the PV panel and the mirror
 
B
L
M

L
M
Cos (
L
M q
)

Cos ( q
) (3)
At a tilt angle of 60 degrees the MGE is 0.5 or 50%. That means a mirror only reflects half of its potential reflection area. As the tilt angle is reduced toward 45 degrees the efficiency,

, increases to its limit of 0.707 or 70.7%. But at 45 degrees the mirror size must be zero. At a tilt angle of about 53 degree the MGE becomes 60% and the mirror length becomes about 46% of the PV length. Clearly, at larger efficiencies the total capture area reduces. The choice of mirror size relative to the PV element size is a matter of optimization and economics.
By eliminating q
from Equation (1) and Equation (2) we can find a relationship that gives the capture area versus the PV area. This relationship is
B
L
P



L
M
L
P



L
M
4 L
P

1
4


L
M
L
P


2

8 (4)
When the mirror size is equal to the PV panel size, L
M
= L
P,
the capture area is 50% of the PV element area. Figure-3 shows the change in B/L
P
relative to the L
M
/L
P
ratio.

Figure-3 The change in the capture area as a function of mirror area
According to this figure, mirrors with lengths 1.4 times the length of PV panels capture and reflect about 60% of their area. The exact value from the formula is 61.4%. The ultimate decision regarding the optimal mirror size is difficult as larger size mirrors requires more costly added support areas and also affect the packaging ability of the system. Mirrors the sizes of PV panels appear to create a well-proportioned system with mirrors installed at 60 degree tilt angles. With mirror sizes the same as PV panels, each mirror boosts the radiation intensity by 50%.
Defining the system geometric intensity factor (or SGI factor) as the ratio of the system radiation capture area to the PV panel area, a PV panel with 4 PV-size mirrors placed around it at 60 degrees would have a SGI factor of 3. The actual efficiency would be lower than the SGI factor due to mirror reflection efficiency and a drop in PV panel performance due to higher temperatures.
The SGI factor can be increases by placing the mirrors at a distance from the PV panel as was previously shown in Figure-1. The mirror must also be raised to reflect on the PV panels. Figure-4 shows the new arrangement of the mirror.

L M q
L
1
L
2
L
PV
Figure-4 Placing mirrors away and above the PV element
It can be shown that for this arrangement Equation (1) can be written in a more general form as
L
M
L p


L
L
1
2

Sin (
Sin (
2 q
90


90 q
)
)
(5)
When q
= 60, the RHS of Equation (5) becomes one and
L
L
M p


L
L
1
2

1
If L
M
= L
P
, then L
1
= L
2
. Placing the mirrors away from the PV panel makes the system larger but it also provides three advantages:
1.
Four more mirrors can be placed around the larger periphery creating an 8 mirror system and boosting the SGI factor to 5. Figure-5 shows the system with one additional mirror.

Figure-5 Placing additional mirrors away and above the PV element
2.
The opening on the face of the PV panel allows the air flow and subsequent cooling of the PV panel.
3.
During periods of overcast, more diffuse light can reach the PV panel.
It is possible to determine the minimum value of L=L
1
=L
2
such that four additional mirrors can be installed next to the main mirrors.