IEEE - Aerospace and Electronic Systems - December 2021 - 12

Estimation of the CubeSat's Available Energy for Free-Orientation Scenario
Table 1.
Statistical Metrics of Solar Panels Effective Area for
Various Free 2U CubeSats
Fail1 structure, one of the side panels has failed (only
for 2U and 3U sizes).
The example of the 1U CubeSat shows that the shape
of the probability distribution is quite different from the
normal one, and, in general, corresponds to both the
expected values and the physics of the process.
As may be seen from Figure 5, in the case of1U CubeSat
without attitude control (or if it fails) with panels on all
its sides (Full), we should expect 1.5 times more energy
than from one panel. In this case, mode is equal to mean
value, and mean corresponds to formula (1).
The estimates of the average power for 1U CubeSat
from the article [13] and the report [22] give slightly
underestimated (by 4%-8%) values, and therefore, they
did not lead to a discrepancy in the energy budget. The
previous calculations allow us to closely estimate the
energy margins.
The P5 and P95 values are the 5th and 95th percentiles;
the range of values between them will include 90%
of all possible illumination (or effective area). When calculating
the power system, one can rely on these values:
P5 for the worst case and P95 for the upper power estimate.
For the most likely power value, we can use statistically
calculated mode value.
If one panel fails (five-side structure), the most
in purple, the empty sides are in gray. The Shuttlecock
(3U) structure is similar to Legs, except that there are
not two, but four folding panels. The five-side structure
has no SA panel on one of the CubeSat's faces; for 2U
and 3U sizes, the panel is missing at the end face. In
Table 2.
Statistical Metrics of Solar Panels Effective Area
for Various Free 3U CubeSats
Structure Mode Mean (Std) P5-P95
Full
Fail1
Five-side
Flower
T-shirt
Legs
3.34
3.24
probable value decreases to 1.22, but the actual value
with a probability of 0.9 can be in the range from 1.02
to 1.54. The full range of the possible actual value is
from 0 (if the CubeSat is directed by the failed side to
the Sun and rotates around this direction) to 1.74 (the
maximum value is the same as that of the full structure).
It seemed that probability distribution function is
close to bimodal, with peaks at 1.22 and 1.39 and plateau
between, on which the mean lies. I assume that
this is a transition between the P
p
ffiffiffi
2
and P
p
ffiffiffi
3
cases in
Figure 1, when the empty (failed) panel is turned away
from the light.
For the Flower structure, the pdf curve ends at five
3.46 (0.31) 2.95-3.90
3.21 (0.32) 2.71-3.68
Shuttlecock 6.10
3.03/3.33 3.25 (0.36) 2.67-3.78
4.24/0.05 4.16 (2.60) 0.00-9.60
3.70 (1.33) 1.53-6.39
4.72 (0.64) 3.57-5.73
6.18 (0.76) 4.94-7.32
4.14
4.7
Foldscreen 4.74/0.05 3.67 (2.60) 0.00-8.29
12
on the axis of abscisses; this structure is designed to
work at this point, when the SA panels are pointing to
the Sun. When ACS fails, the most probable power
value shifts to the point 1.64; if the satellite completely
turns its panels away from the Sun, then the power
drops to almost zero, in the vicinity of which there is
the second peak of pdf. In this case, it may be necessary
to place a few solar cells on this side of the CubeSat,
sufficient to power the ACS.
Curves for other structures and sizes of CubeSat are
analyzed in a similar way.
The developed model does not take into account the
magnitude of the angular velocity; therefore, it is impossible
to calculate the number of revolutions of the CubeSat
for a certain time, for example, in the lighted part of the
orbit. As a consequence, the most probable value can be
used on only in orbits without shadows, or when the
IEEE A&E SYSTEMS MAGAZINE
DECEMBER 2021
IEEE - Aerospace and Electronic Systems - December 2021

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