University of Leicester
PLUME
Ref: PLM-PSU-PowerProd-309-1
Date: 11/03/2009
Power Production
M. Cro
Date
Updated Reference Number
change
11/03/2009
PLM-PSU-PowerProd-309-1
first version issued
Abstract
We have calculated the maximum and minimum power we can get out of the solar cells over an
orbit, considering the efficiency of the power supply unit too. The actual power production is
expected to lie between these two extreme values. These values are Pmin=1.19W and Pmax=4.39W.
The team has also estimated the average power expected, considering the average exposed area of
the solar cells. This was found to be Pav=2.30W.
Introduction
In order to estimate the power available for the subsystems of the satellite the following need to be
considered:




The solar irradiance
The solar cell efficiency
The efficiency of the power supply unit
The effective area of the solar cells
Solar Irradiance Φ
The solar energy flux is inversely proportional to the square of the distance from the Sun. The
equation that describes the relationship between the solar luminosity L and the flux at a distance R
from the sun is

L
4R 2
[1]
We require the extraterrestrial solar irradiance distribution at a distance of 1 AU from the Sun, which
is known as the air mass zero AM0. The value recommended by the American Society of Testing and
Materials (ASTM) is 1366.1
Wm-2.
Page 1 of 5
University of Leicester
PLUME
Ref: PLM-PSU-PowerProd-309-1
Date: 11/03/2009
Solar Cell Efficiency ε
Clyde Space will supply the solar panels for the PLUME CubeSat. Clyde Space uses two types of solar
cells, EMCORE’s Advance Triple Junction cells (ATJ) with efficiency 27.5% and Spectrolab’s Triangular
Advanced Solar Cells (TASC) with efficiency 27.0%.
Efficiency of the Power Supply Unit k
The power supply unit consists of components such as the battery charge regulators and the two
power bus regulators that dissipate energy. This reduces the power available for the subsystems.
According to Clyde Space who is our power supply unit’s provider, the total efficiency of the power
supply unit is 90%.
Effective Area of the Solar Panels A
The effective area of the solar panels is the total area of the solar panels exposed to the Sun.
Obviously; the effective area will depend on the way the satellite is spinning. The team has decided
that the best way to deal with this is to consider the two extreme cases. The area is minimum when
axis of rotation of the satellite is pointing always to the Sun, thus, only one side of the satellite is
exposed. The area is maximum when the corner between 3 faces points towards the Sun. In this
case the effective area is equal to the area of a hexagon.
Figure 1. Configuration for minimum (left) and maximum (right) effective area.
Page 2 of 5
University of Leicester
PLUME
Ref: PLM-PSU-PowerProd-309-1
Date: 11/03/2009
The minimum effective area Amin is the area of one face, equal to
0.01 fraction of the face covered with solar cells
 m2
[2]
maximum effective area Amax is the area of a regular polygon,
The
3 3
 0.01 fraction of the faces covered with solar cells
2
 m2
[3]
In 
both cases we need to multiply by the fraction of the faces that is covered with solar cells since 3
out of six faces will not be completely covered with solar cells. In fact, 3 faces will have 100% of
their area covered in with solar cells, 2 faces will have 84% of their area covered in solar cells (faces
with the detector) and 1 face will have 96% of its area covered with solar cells (face with the
camera).
The PSU team has also estimated the average area exposed to the Sun by considering the area of
each face projected on a plane perpendicular to the solar rays when the satellite is at some random
orientation. These areas were then integrated between φ=0 and
the satellite to rotate by


and   0 and
to allow for
2
2

about both the y and z axis (solar flux in the was taken to be parallel to
2
the x axis). The exact expression used was



Aav 


2
0
2
0
  A cos cos  A sin  cos  A sin  dd


  dd
1
2
2
0
3
2
0
A1, A2 and
 A3 are the areas of three random faces of the satellite. In our calculations we have
substituted these areas by the average area of each face given by
A
1
6  0.102  2  0.04 2  0.022  9.4 103 m 2

6

Page 3 of 5
University of Leicester
PLUME
The final result obtained for Aav is
Calculations
8  2
2
Ref: PLM-PSU-PowerProd-309-1
Date: 11/03/2009
 9.4 103  0.0136m 2 .

The power available for the satellite is calculated using the following equation combined with the
data listed above
P   k    A
[4]
where the symbols used
 have been defined above. The following Excel Spreadsheet can be used to
calculate the power production, both when in sunlight and averaged over the orbital period for the
two extreme cases discussed above, when we have a maximum exposed area and a minimum
exposed area, and for the average exposed area.
The three tables below list the minimum, maximum and average expected power. For the minimum
power, it has been assumed that only one face will be exposed to the Sun and that face will have
only 84% of its area covered in solar cells. For the maximum power, the second geometrical
configuration was used, assuming this time that all three faces exposed to the solar radiation are
completely covered in solar cells. Both these cases are not very likely and we are expecting a more
randomised rotation of the satellite.
Maximum Exposed Area
Solar Irradiance (Wm-2)
1366.1
Solar Cell efficiency
0.275
Power Supply Unit Efficiency
0.90
Fraction of Area covered with solar cells
1.00
Effective Area (m2)
0.026
Power production when in sunlight (W)
8.78
Power production averaged over the period (W)
4.39
Minimum Exposed Area
Page 4 of 5
University of Leicester
PLUME
Ref: PLM-PSU-PowerProd-309-1
Date: 11/03/2009
Solar Irradiance (Wm-2)
1366.1
Solar Cell efficiency
0.275
Power Supply Unit Efficiency
0.90
Fraction of Area covered with solar cells
0.84
Effective Area (m2)
0.008
Power production when in sunlight (W)
2.39
Power production averaged over the period (W)
1.19
Average Exposed Area
Solar Irradiance (Wm-2)
1366.1
Solar Cell efficiency
0.275
Power Supply Unit Efficiency
0.90
Effective Area (m2)
0.0136
Power production when in sunlight (W)
4.60
Power production averaged over the period (W)
2.30
Page 5 of 5