 Objective:
The objective of this assignment is to demonstrate an
understanding of the power subsystem theory, components and design
processes.

 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
way.
Problem 1. True or False:
T a) Solar
panel power generation is generally greater when the panel has higher
illumination.
F b) Solar
panel power generation is generally greater when the panel has a higher
temperature.
F c) Solar
panel power generation is generally greater when the panel has
experienced a higher radiation dosage.
T d) Two
solar cells connected in series will have the same current going through
them.
F e) Within
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 f) A solar
powered satellite that is always in the sun does not need batteries (or
any other power storage device). [Power
storage is used whenever load demand exceeds generation  so peak loads
may require power to be pulled from storage even when the panels are
fully illuminated]
F g) Any
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. [energy
can be absorbed as heat]
T h)
Multijunction solar cells typically have a higher efficiency than
single junction cells.
T i) The
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.
F j) A solar
cell's produces maximum power at it's point of maximum current
generation.
F k) RTGs
generate energy based on the energy released during a nuclear fission
process.
F l)
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. [power output
can't be varied for loads]
F m) Two
battery cells connected in parallel with have the same current going
through them.
T n) Primary
batteries typically have a higher energy density than secondary
batteries.
F o) As a
battery discharges, its voltage drops linearly over time.
F p) NiCad
batteries should never be discharged more than 30% due to Depth of
Discharge constraints.
T q) A Direct
Energy Transfer power regulation system is characterized by the solar
array being connected directly to the satellite's loads.
T 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?
Panel mounted arrays need to be
pointed to the sun but can reduce/eliminate pointing losses. Body
mounted arrays are simple and don't need to be pointed, but they lead
to large pointing losses.
b) Why are "protection diodes" often wired
in series with solar cells strings?
They prevent a battery from reverse
biasing the cells when they aren't illuminated.
c) What is the primary pro and con of using a peak
power tracking regulation system?
Pro: maximize power production from
solar arrays. Con: complexity.
d) What is the thermoelectric effect?
A voltage can be generated across
the junction of two materials if a temperature difference across the
materials is maintained.
e) Give a few examples of loads that need
wellregulated power and a few examples of loads that can often use
"dirty" power.
Regulated: computers, control
electronics, sensors
Dirty power: heaters, some comm
amplifiers, large actuator loads like motors
f) Why might a power designer use a larger diameter
wire for the wiring harness, even if it requires more mass?
A larger diameter reduces resistance
and therefore the power lost to resistive loading.
g) VT curves are used as a part of conventional
NiCad charging technicques. What is their purpose?
The VT curve states the max voltage
that the battery should be charged to, as a function of temperature.
h) What is the purpose of "reconditioning"
a NiCad battery?
Reconditioning is a slow,
wellcontrolled deep cycle discharge of a NiCad battery. It is used to
reverse voltage plateau drops that occur over time.
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?
The high power operating mode can be
duty cycled such that the satellite only draws that amount of power
for short periods of time. Battery power is consumed during this
time, but when the mode is not being used, another mode can be
selected to allow the batteries to fully recharge.
j) One a separate sheet of paper, sketch a
standard VI Curve for a typical solar cell. Label it "standard".
Now, on the same axes, add a sketch of the VI 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 VI 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."
The standard curve should have V
on the x axis and I on the y axis. The series curve should extend
3x in Voc but with the same Isc. The half curve should have about
the same Voc (slighly less) and half of Isc.
Problem 3. Answer the
following basic quantitative power subsystem questions:
a) What current is available at 24V for a 600W power
supply?
I=P/V=600/24= 25A
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/m^{2} 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,
etc.).
P=1358*A*n*cos(i)=1358*8*0.27*cos(30º)
= 2,540.3W
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 Whrs? 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.
Capacity = energy used during
eclipse / DOD = 500*(35/60) / 0.50 = 583.33 Whrs
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
required.
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 semimajor 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.
rho=sin^{1}(6378/(6378+510))=67.8 deg
P = 2*pi*(a^{3}/mu)^{1/2}
=5689 sec = 94.8 min
Max eclipse time = (2*rho/360)*P=35.7 min
b) What minimum average power must the solar arrays
produce when illuminated in order to support this mission?
Assume 100% charge efficiency for simplicity.
Psa =
Pave*(94.8 min/(94.8 min35.7 min))=1283 W; this assumes 100% charge
eff. If you assumed something more realistic, you should simply
have stated your assumption.
c) What is the minimum required battery capacity (in
Watthours) to ensure that the DOD is not more than 70%?
Min Capacity = energy used during
eclipse / DOD = 800*(35.7/60) / 0.70 = 680 Whrs
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?
Mars' gravitational constant and
radius.
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/m^{2}, 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/m^{2}.
Provide the mathematical equation that you would use to prove this.
Jmars = Jearth / (1.52)^{2}
= 585 W/m^{2}
^{ }
Problem 5. Using the solar array design process
from Wertz & Larson (reviewed in the lecture slides), consider a
design using GaAs cells for a nearEarth 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 =
750 W
 power required in eclipse =
500 W
 path efficiency in daylight = 0.80
 path efficiency in eclipse = 0.65
Psa = { [500*25/.65] + [750*78/.8]
}/ 78 = 1,184 W
b) What is the beginningoflife 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
Pbol = 1358 * n * Ipack * Ishad *
Itemp * cos (theta)
= 1358 * .24 * 0.95 * 1 * 0.9 * 1 = 278.7 W/m^{2}
c) For a 5year mission and
2% of panel degradation
per year, what is the endoflife power per unit area of the solar
array?
Peol=Pbol*(1.02)^{5}=251.9
W/m^{2}
d) What is the required solar array area?
Asa=Psa/Peol=1184/251.9=4.7 m^{2}
e) Assume the satellite uses a 28V array and that
Vcell=0.6V and Icell=220mA. Find the number of cells required in
the array.
N = Psa / (Vcell * Icell) =
1184 /
0.132 = 8,970 cells
f) How many strings are there and how many cells are
in series for each string?
Nseries = Vsa / Vcell = 47 cells
Nstr = N/Nseries = 191 strings
Problem 6. In lecture,
the Schottky model for the VI curve equation for a solar cell was
presented:
 where
 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:
 T=15ºC
 IL at 1358 W/m^{2} is 0.06 A
 Io=1 x 10^{12} A
Use a computational tool (e.g., Matlab or other
computerbased environment) to plot the VI curve.
Matlab code:
axis([0 1 0 .1]);hold on
Il=.06;Io=1e12;q=1.6e19;k=1.38e23;T=288;
j=1:100;V=j/100;
for i=1:length(V)
I(i)=IlIo*(exp(V(i)*q/(k*T))1);
end
plot(V,I);grid
Plot:
b) From your plot, roughly estimate the maximum
power.
Pmax ~ 0.055 * 0.55 = 30.25 mW
c) Generate an approximate PV Curve (Power output
as a function of the operating voltage; V on the
xaxis and P=IV on the yaxis) for this cell. Show your plot and
verify that the max power point is close to your estimate from part
(b).
Matlab code:
axis([0 .7 0 .04]);hold on
Il=.06;Io=1e12;q=1.6e19;k=1.38e23;T=288;
j=1:100;V=j/100;
for i=1:length(V)
I(i)=IlIo*(exp(V(i)*q/(k*T))1);
P(i)=V(i)*I(i);
end
plot(V,P);grid
