Lecture 8:
Power Systems and Thermal
Management
Power System Structure and Requirements
Electrical Power Subsystem
Power
Source
Energy
Storage
Power
Distribution
Regulation
& Control
Typical Requirements

Supply continuous electrical power to s/c loads during mission
 Control and distribute electrical power
 Handle average and peak electrical load
 Provide ac, dc power converters
 Protect against failures in the EPS
 Suppress transient voltages and protect against faults
Power System Design Process
Step
Info. Required
Derived
Requirements
1. Identify requirements
Top-level requirements, s/c
configuration, mission life,
payload definition
Design requirements,
average and peak power
2. Select power source
S/c configuration, average
load requirements
EOL power required,
type of solar cell, mass
and area of solar array,
solar array configuration
3. Select energy storage
Orbital parameters,
average and peak load
Battery capacity
required, battery mass,
volume and type
4 Identify power
regulation and control
Power source selection,
mission life, regulation and
thermal control
requirements
Peak power tracker or
direct energy-transfer
system, thermal control
requirements, busvoltage quality, power
control algorithms
Power Sources
Power sources
Photovoltaic
Planar
Concentrators
Static
Thermionics
Thermoelectrics
Dynamic
Brayton
Stirling
 Photovoltaic solar cells convert incident solar radiation directly
to electrical energy
 Static power sources uses a heat source, typically plutonium238 or uranium-235 for direct thermal-to-electrical conversion
 Dynamic sources also use a heat source – concentrated solar,
plutonium-238, or enriched uranium – to produce power via
Brayton, Stirling or Rankine cycles
Rankine
Comparison of Power Sources
Design
Parameters
Solar
Photovoltaic
Solar Thermal
Dynamic
Radioisotope
Nuclear
Reactor
Power range (kW)
0.2 - 25
1 - 300
0.2 - 10
25 - 100
Specific power
(W/kg)
26 - 100
9 - 15
8 - 10
15 - 22
Specific cost ($/W)
2500 - 3000
800 - 1200
16K – 18K
400 - 700
Hardness to natural
radiation
Medium
High
Very high
Very high
Low
Medium
High
High
Degradation over life
Medium
Medium
Low
Low
Storage required for
eclipse?
Yes
Yes
No
No
Sun angle sensitivity
Medium
High
None
None
Low (with
bypass diodes)
High
None
None
Unlimited
Unlimited
Very low
Very low
Stability and
maneuverability
Sensitivity to
shadowing
Fuel availability
Solar Array Design Process
Determine requirements and constraints
1.
Av. Power needed during daylight and eclipse
Eclipse durations
Design lifetime



2.
Calculate power that must be produced, Psa
Pe & Pd
Te & T d
Xe
 PeT e PdT d 



X
X
d 
Psa   e
Td
P ower requirement s during eclipse and daylight , resp.
T imes spent in eclipse and daylight , resp.
Efficiency of pat hs from t he solar arrays t hrough t he bat t eries t o t he loads
0.65, direct energy t ransfer

0.60, peak-power t racking
Xd
Efficiencies of pat hs direct ly from t he arrays t hrough t o t he loads
0.85, direct energy t ransfer

0.80, peak-power t racking
Solar Array Design Process
3. Select type of solar cell and estimate power output, P0 ,
with the sun normal to the surface of the cells
Si: P0  0.148  1, 367W m 2  202W m 2
GaAs: P0  0.185  1, 367W m 2  253W m 2
Mult ijunct ion: P0  0.22  1, 367W m 2  301W m 2
4. Determine BOL power production per unit area, taking
account of inherent degradation:
Elements of inherent degradation
Nominal
Range
Design and assembly
0.85
0.77-0.90
Temperature of array
0.85
0.80-0.98
Shadowing of cells
1.00
0.80-1.00
Inherent degradation, Id
0.72
0.49-0.88
And the cosine loss and life degradation:
PBOL  P0I d cos  ,
PEOL  PBOL Ld , Ld  1  degradat ion/ yr 
s/ c life
Energy Storage


Primary batteries have higher specific energy densities
but cannot be recharged. Thus, they typically apply to
short missions.
Characteristics of some secondary batteries:
Secondary Battery Couple
Specific Energy
Density
(W-Hr/Kg)
Status
Nickel-Cadmium
25-30
Space-qualified,
extensive database
Nickel-Hydrogen
(individual pressure vessel)
35-43
Space-qualified. Good
database
Nickel-Hydrogen
(common pressure vessel)
40-56
Space qualified for GEO
and planetary
Nickel-Hydrogen
(single pressure vessel)
43-57
Space-qualified
70-110
Space-qualified
Lithium-Ion
Sodium-Sulfur
140-210
Under development
Energy Storage
Needed bat t ery capacit y:
Cr 
PeT e
W  hr 
 DOD  Nn
40  60% for NiH 2
DOD Dept h of discharge  
10  20% for NiCd
n
Bat t ery-t o-load t ransmission efficiency  90%
N
Number of bat t eries
Black Body Radiation Model
T her m al r adiat ion or blackbody r adiat ion m odel :
 phot ons are modelled as a gas of bosons
 T he gas int eract s wit h at oms t hat randomly emit or absorb phot ons
 T he int eract ing at oms form t he walls of a cavit y cont aining t he gas
 T he most likely dist ribut ion of phot ons among energy levels is t he one t hat is
"most random" - i.e. maximizes t he st at ist ical mechanical ent ropy.
A sea of photons is
surrounded on all sides
by high temperature
atoms. These particles
randomly absorb or
emit photons,
permitting all possible
energy transitions
compatible with
conservation of overall
energy
Black Body Radiation Model
P lan ck's Law :
E 
E
2 hc 2
5

1

exp ch kT   1
spect r al ir r adian ce
 energy per unit t ime, per unit wavelengt h,

h
T
per unit surface area ( W m 2 m 1 )
wavelengt h
P lanck's const ant  6.626  10 34W s 2
Absolut e t emperat ure
c
speed of light
k
Bolt zmann's const ant  1.3807  10 23W s / K
Black Body Radiation Model
S t efan - B olt zm an n Law for t he t ot al r adian t em it t an ce, W b W / m 2  :
W b  T

4
St efan-Bolt zmann const ant  5.6705  10 8W m 2 K 4
Wavelengt h for which t he spect rum has t he maximum value = W ien 's
D isplacem en t Law :
max  m   2, 898 T  K 
Thermal Equilibrium of an Isolated Body in Space
qabsorbed  G sourceA absorb  peak 
qemit t ed   IR T 4Ar
G source  Energy flux from source
T  T emperat ure of body
qdissipated  QW
(Sun, Eart h or Moon)
  St efan-Bolt zmann const ant
Aabsorb  P roject ed area of object
 IR  Emissivit y of t he body
t hat absorbs t he radiat ion
in t he IR range of wave-
Electronics
  peak   absorbt ivit y of t he
lengt hs
mat erial at t he wavelengt h
Ar  Area of radiat ing surface
of peak source emission
qabsorbed  qdissipat ed  qemit t ed

G sourceAabsorb  peak   qdissipat ed   IR T 4Ar

 G sourceAabsorb  peak   Q W
T 

 IR  Ar

14




Spherical Spacecraft Equations
QS
Q S M
Q S E
QM
QE
QM  A FM qM  IR
QS E  A FE G S a E S K E
A  D2
qM  Moon IR emission
Q
QWW
 IR  IR emissivit y of t he sphere
FM  1  cos M

K E  0.664  0.521E  0.203 E2

2
M  Angular radius of t he Moon

A  D2
S  solar absorbt ivit y of t he sphere
a E  albedo of t he Eart h
Analogous expression for QE
QS  G S AC S
G S  Solar flux  1418 W m 2 t o 1326 W m 2
AC   D 2 4
S  solar absorbt ivit y of t he sphere

FE  viewfactor  1  cos E 2
E  Angular radius of t he Eart h
K E account s for reflect ion of sunlight from a spherical Eart h
 Analogous expression for QS M
Spherical Spacecraft Equations
QS
Q S M
Q S E
QM
QE
Q
QWW
P ower flow balance:
A IRT
4
 QS  QS M  QS E  QM  QE  QW

T  G S AC S  A FMG S a M S K M  A FEG S a E S K S  A FM qM  IR  A FE qE  IR  QW

 A IR 
14
Putting the Equations to Work:
The Preliminary Design Process
Step
Notes
Identify temperature limits – see Table 11
43, L&W
 Estimate electrical power dissipation
1. Determine requirements and constraints

2. Find the diameter of a sphere with the
same surface area as the spacecraft
Make first-order estimates assuming an
isothermal, spherical spacecraft (using the
above equations).
3. Select radiation surface property values
Initially assume white paint with S=0.6 and
IR=0.8
4. Compute worst-case hot and cold temp.s
for the spacecraft
Upper limit: Use high-side values of all power
input terms
Lower limit: Include only the IR emissions.
5. Compare worst-case hot and cold temp.s
with temp. limits found in step 1.
If worst-case hot temperature is > required
upper limit, use a deployed radiator with a
pumped-looped system. Otherwise, use bodymounted radiators
6. Estimate required area for body-mounted
radiator.
Use upper temp. limit for radiator temp., assume
no heat inputs and max. heat dissipation – see
equation 11.23, L&W
7. Estimate radiator temp. for worst-case cold
conditions
Use the area from step 6 and min. heat
dissipation
The Preliminary Design Process - Continued
Step
Notes
8. If temp. in step 7 is less than the lower
limit, determine heater power required to
maintain radiator at lower temp. limit
Assume radiator temp. is at the lower limit
9. Determine if there are special thermal
control problems
Identify components with narrow temp.
ranges, high power dissipation or low temp.
requirements. See thermal control options
in section 11.5.2, L&W.
10. Estimate subsystem weight, cost and
power.
I f no special problems, use 4.5% of
spacecraft dry weight, 4% of the total
spacecraft cost, and heater power from step
8.
Thermal Control Devices and Strategies
- If special thermal control problems are encountered in step 9




















Materials and Coatings
Optical Solar reflectors
Silver-Coated Teflon
MultiLayer Insulation
Electrical Heaters
Thermostats
Space radiators
Cold-Plates
Doublers
Phase Change Devices
Heat Pipes
Louvers
Temp. Sensors
Adhesive Tapes
Fillers
Thermal isolators
Thermoelectric Coolers
Cryogenic Systems
Active Refrigeration Systems
Expendable Cooling Systems
Thermal Control Devices and Strategies






Materials and Coatings: paints, silverized plastics, special coatings –
all with special absorptivity & emissivity values– See Table 11-44
Optical Solar Reflectors (OSRs):
– Highly reflective surface mounted on a substrate and overlaid
with a transparent coating.
– Reflects most incoming radiation back to space, IR emissivity =
0.8, solar absorptivity = 0.15
– Expensive and fragile.
Silver-Coated Teflon - Cheaper alternative to OSRs.
MultiLayer Insulation (MLI):
– The primary spacecraft insulation device.
– Alternate layers of aluminized Mylar or Kapton, separated by net
material, e.g. nylon, Dacron or Nomex
– See Fig. 11-22 for the effective emmitance of MLI
Electrical Heaters
– Used in cold-biased systems to bring selected components up to
proper temp.
– Thin electrical resister between two Kapton sheets
– Typical power densities  1 W/cm2
Thermostats
– Switches to turn heaters on/off
– Typical operating range: -50 to 1600C
Thermal Control Devices and Strategies

Space radiators
–
–
Heat exchanger on the outer surface of the spacecraft that radiates waste heat
Can be structural panels or flat plates mounted on the spacecraft
G s cos   QW AR  T
4
0
AR  radiat or area
QW  wast e heat

Cold-Plates
–

Heat dissipated by electrical equipment is conducted across the interface to the cold
plate. Fluid circulating through the cold plate Carries the heat to a space radiator.
Heat Pipes
–
Lightweight devices used to transfer heat from one location to another, e.g. from an
electrical component to a space radiator
Wicking material
Gas
Heat in - evaporation

Temp. Sensors
–
–
Liquid flow via wick
Heat out - condensation
Thermisters: Semiconductor materials that vary their resistance with temperature.
They operate around -50 to +300 0C.
Resistance Thermisters: Uses a pure platinum conductor. Very accurate and expensive