MECH 372 / ENGR 372
Space Systems Design and Engineering II
Assignment #4 - Power Subsystems - SOLUTIONS
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) Multi-junction 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.

  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 well-regulated 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) V-T curves are used as a part of conventional NiCad charging technicques.  What is their purpose?

The V-T 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, well-controlled 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 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."  

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 30.  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, etc.).

P=1358*A*n*cos(i)=1358*8*0.27*cos(30) = 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 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.

Capacity = energy used during eclipse / DOD = 500*(35/60) / 0.50 = 583.33 W-hrs


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 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.

rho=sin-1(6378/(6378+510))=67.8 deg

P = 2*pi*(a3/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 min-35.7 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 Watt-hours) to ensure that the DOD is not more than 70%?

Min Capacity = energy used during eclipse / DOD = 800*(35.7/60) / 0.70 = 680 W-hrs

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/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.  

Jmars = Jearth / (1.52)2 = 585 W/m2


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 = 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 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

Pbol = 1358 * n * Ipack * Ishad * Itemp * cos (theta) 

        = 1358 * .24 * 0.95 * 1 * 0.9 * 1 = 278.7 W/m2

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 array?

Peol=Pbol*(1-.02)5=251.9 W/m2

d) What is the required solar array area?

Asa=Psa/Peol=1184/251.9=4.7 m2

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 V-I curve equation for a solar cell was presented:

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.

Matlab code:

axis([0 1 0 .1]);hold on
for i=1:length(V)


b) From your plot, roughly estimate the maximum power.

Pmax ~ 0.055 * 0.55 = 30.25 mW

c) 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 (b).

Matlab code:

axis([0 .7 0 .04]);hold on
for i=1:length(V)