The objective of this assignment is to demonstrate an
understanding of the power subsystem theory, components and design
- Note that the equations in the slide package
will help you, but don't apply them blindly; in some cases you may
be asked a question that will use that content but for which the
mathematical relationships may need to be applied in a different
Problem 1. True or False:
panel power generation is generally greater when the panel has higher
panel power generation is generally greater when the panel has a higher
panel power generation is generally greater when the panel has
experienced a higher radiation dosage.
solar cells connected in series will have the same current going through
the power distribution system, thicker wires lead to higher levels of
losses due to resistance. [Hint - you might consider referring to the
Electronics slides for this question]
f) A solar
powered satellite that is always in the sun does not need batteries (or
any other power storage device).
solar energy that is not converted to power within a solar cell must
pass completely through the cell or be reflected back into the
environment from the solar cell's surface.
Multi-junction solar cells typically have a higher efficiency than
single junction cells.
point at which a solar cell operates with respect to its IV curve is
largely determined by the electrical operation/properties of the load to
which it is attached.
j) A solar
cell's produces maximum power at it's point of maximum current
generate energy based on the energy released during a nuclear fission
RTGs allow precise amounts of power to be generated based on the varying
needs of the satellite's loads, and this power is generated
independently of solar illumination.
battery cells connected in parallel with have the same current going
batteries typically have a higher energy density than secondary
o) As a
battery discharges, its voltage drops linearly over time.
batteries should never be discharged more than 30% due to Depth of
q) A Direct
Energy Transfer power regulation system is characterized by the solar
array being connected directly to the satellite's loads.
r) A shunt
regulator system may be used to dissipate excess power that is produced
by either a solar array or an RTG.
Problem 2. Answer the following basic
qualitative power subsystem questions. They can all be answered
with no more than a sentence or two:
a) What are the primary pros and cons of using panel
mounted vs body mounted solar cells?
b) Why are "protection diodes" often wired
in series with solar cells strings?
c) What is the primary pro and con of using a peak
power tracking regulation system?
d) What is the thermoelectric effect?
e) Give a few examples of loads that need
well-regulated power and a few examples of loads that can often use
f) Why might a power designer use a larger diameter
wire for the wiring harness, even if it requires more mass?
g) V-T curves are used as a part of conventional
NiCad charging technicques. What is their purpose?
h) What is the purpose of "reconditioning"
a NiCad battery?
i) In putting together a power budget for your space
mission, you have one operating mode that requires 10 times more power
than the production capability of your solar arrays. In
addition, your batteries don't have nearly the capacity to run this
mode during a single eclipse. Is this an impossible situation
that requires a redesign of the satellite, or is there another option
or approach that makes that mode and the current power subsystem
design consistent with each other?
j) One a separate sheet of paper, sketch a standard
V-I Curve for a typical solar cell. Label it "standard". Now, on
the same axes, add a sketch of the V-I Curve that you would get for
3 of these cells wired in series, and label it "series." Now, on the
same axes, add a sketch of the V-I Curve that you would get for one
of the original standard cells but now operating at half of the
original illumination, and label this curve "half illumination."
Problem 3. Answer the
following basic quantitative power subsystem questions:
a) What current is available at 24V for a 600W power
b) What is the approximate power output of an ideal
2m x 4m solar panel with 27% efficient cells and inclined from
directly facing the sun at an angle of 30º. Assume that the
incident power density is 1358 W/m2 and that no other
considerations are necessary to approximate the power (e.g., the fill
factor is 100%, the cells are operating at their ideal temperature,
c) A satellite that requires 500W of continuous
total power is in an orbit with a maximum eclipse duration of 35 min.
If the maximum desired depth of discharge is 50%, what is the
required battery capacity, in W-hrs? Assume that the solar arrays are
designed to ensure that the batteries are always fully charged when
entering eclipse. Assume 100% power efficiency for simplicity.
Problem 4. You are asked to perform some
preliminary power subsystem computations for a proposed LEO (510 km
altitude circular) remote sensing mission. An initial mission
analysis has been performed already and states the need to provide the
equivalent of a continuous supply of power at a level of 800 W; the
satellite consumes this power evenly throughout the mission. Of
course, since the satellite will be going into eclipses, the solar
panels can't provide this power continuously, and batteries will be
a) What is the maximum eclipse time? Note that for
an orbit, the period of the orbit can be computed from the equation:
where T is the period (in sec), a is the semi-major axis of the orbit
(for a circular orbit, this is the same as the radius), and mu is the
standard gravitational constant for Earth, which is 398,600
(km^3s^-2). Use 6378 km as the radius of the Earth.
b) What minimum average power must the solar arrays
produce when illuminated in order to support this mission?
Assume 100% charge efficiency for simplicity.
c) What is the minimum required battery capacity (in
Watt-hours) to ensure that the DOD is not more than 70%?
d) Imagine having to perform this same preliminary
power subsystem analysis for a mission to Mars (assume same power
draws, same orbit altitude, etc.). What two parameters would
change in order to cause the maximum eclipse time to be different?
e) For the Mars mission option, the illumination of
the sun would be less due to being farther away from the sun. At
the Earth, solar illumination is 1358 W/m2, and we know
that the distance from the Sun to Mars is about 52% farther than the
distance from the Sun to the Earth. Use these numbers to show
that the average solar illumination at Mars is about 585 W/m2.
Provide the mathematical equation that you would use to prove this.
Problem 5. Using the solar array design process
from Wertz & Larson (reviewed in the lecture slides), consider a
design using GaAs cells for a near-Earth mission.
a) What is the power required from the solar array
during daylight periods given the following parameters:
- time in daylight = 78 min
- time in eclipse = 25 min
- power required in daylight =
- power required in eclipse =
- path efficiency in daylight = 0.80
- path efficiency in eclipse = 0.65
b) What is the beginning-of-life power unit area of
the solar array, assuming the following:
- 24% efficient solar cells
- 0.95 packing factor
- 0.9 temperature loss
- No shadowing losses
- Perfectly pointed arrays
c) For a 5-year mission and
2% of panel degradation
per year, what is the end-of-life power per unit area of the solar
d) What is the required solar array area?
e) Assume the satellite uses a 28V array and that
Vcell=0.6V and Icell=220mA. Find the number of cells required in
f) How many strings are there and how many cells are
in series for each string?
Problem 6. In lecture,
the Schottky model for the V-I curve equation for a solar cell was
- I=current through the cell
- IL = current generated due to illumination
- Io=cell leakage current
- n=1 for an ideal cell
- q=absolute value of an electron charge
- k=Boltzmann's constant = 1.38 x 10^-23
- T=absolute temperature
a) Assume we have a specific cell such that:
- IL at 1358 W/m2 is 0.06 A
- Io=1 x 10-12 A
Use a computational tool (e.g., Matlab or other
computer-based environment) to plot the V-I curve.
b) From your plot, roughly estimate the maximum
c) Use a computational tool to generate an approximate P-V Curve (Power
output as a function of the operating voltage; V on the
x-axis and P=IV on the y-axis) for this cell. Show your plot and
verify that the max power point is close to your estimate from part