Electrical Power Subsystem
Dr Andrew Ketsdever
MAE 5595
Lesson 11
Outline
• Electrical Power Subsystem
–
–
–
–
Introduction
Types of Power Sources
Design Considerations
Nuclear Power
• Nuclear Reactor
• Radioisotope Thermoelectric Generator (RTG)
– Solar Arrays
• Types
• Sample Calculation: Array sizing
– Batteries
• Types
• Sample Calculation: Battery storage
• Depth of Discharge
– Degradation of Solar Arrays
– Radiation
Introduction
Power Sources
• Chemical: Battery, Fuel Cell
– Converts chemical energy into electrical power
• Stored energy
• Chemical reaction
• Solar: Photovoltaic
– Coverts solar radiation into electrical power
• Nuclear: Fission
– Coverts nuclear fission energy into electrical power
through conversion of heat
• Dyanamic: Heat energy
– Stirling, Rankine, Brayton cycles (15-35% efficient)
• We will mainly talk about solar array and battery
systems
Power Sources
From Space
Vehicle Design,
by Griffin and
French
Design Considerations
Design Considerations
Design Considerations
Design Considerations
Nuclear Reactor
Reactor Schematic
Nuclear Reactor
• Reflector
– Reflects neutrons produced in the reaction
back into the core
– Prevents neutron leakage
– Maintains reaction balance
– Can be used to reduce the size of the reactor
– Typically made of Beryllium
Nuclear Reactor
• Moderator
– Slows down neutrons in the reactor
– Typically made of low atomic mass material
• LiH, Graphite, D2O
• H2O absorbs neutrons (light water reactor)
• Slow (or Thermal) Reactor
– Uses moderator to slow down neutrons for efficient
fissioning of low activation energy fuels
• Fast Reactor
– No moderator. Uses high kinetic energy neutrons for
fissioning of high activation energy fuels
Nuclear Reactor
• Fuel Element
– Contains the fissile fuel
– Usually Uranium or Plutonium
– Contains the propellant flow channels
• High thrust requires high contact surface area for
the propellants
• Heat exchange in the flow channels critical in
determining efficiency and performance of the
system
Nuclear Reactor
• Control Rods
– Contains material that absorbs neutrons
• Decreases and controls neutron population
• Controls reaction rate
• When fully inserted, they can shut down the reactor
– Configuration and placement is driven by the engine
power level requirements
– Typically made of Boron
– Axial Rods
• Raised and lowered into place. Depth of rods in the reactor
controls the neutron population
– Drum Rods
• Rotated into place with reflecting and absorbing sides
Fission
• Fission is a nuclear process in which a heavy
nucleus splits into two smaller nuclei
– The Fission Products (FP) can be in any combination
(with a given probability) so long as the number of
protons and neutrons in the products sum up to those
in the initial fissioning nucleus
– The free neutrons produced go on to continue the
fissioning cycle (chain reaction, criticality)
– A great amount of energy can be released in fission
because for heavy nuclei, the summed masses of the
lighter product nuclei is less than the mass of the
fissioning nucleus
Fission Reaction Energy
• The binding energy of the nucleus is directly
related to the amount of energy released in a
fission reaction
• The energy associated with the difference in mass
of the products and the fissioning atom is the
binding energy


  Z (mp  me )  ( A  Z )mn  M atom
E  c
2
Defect Mass and Energy
• Nuclear masses can change due to reactions because this "lost"
mass is converted into energy.
• For example, combining a proton (p) and a neutron (n) will produce
a deuteron (d). If we add up the masses of the proton and the
neutron, we get
– mp + mn = 1.00728u + 1.00867u = 2.01595u
– The mass of the deuteron is md = 2.01355u
– Therefore change in mass = (mp + mn) - md = (1.00728u + 1.00867u) (2.01355u) = 0.00240u
– An atomic mass unit (u) is equal to one-twelfth of the mass of a C-12
atom which is about 1.66 X 10-27 kg.
• So, using E=mc2 gives an energy/u = (1.66 X 10-27 kg)(3.00 X 108
m/s)2(1eV/1.6 X 10-19 J) which is about 931 MeV/u. So, our final
energy is 2.24 MeV.
• The quantity 2.24MeV is the binding energy of the deuteron.
Radioisotope Thermoelectric
Generator (RTG)
• Heat released by radioactive decay is converted
into electrical energy
• Half-life of the radioactive material must be long
enough to insure a relatively constant power
level
• Half-life must be short enough to insure enough
power is produced
• US uses Pu-238
– 86.8 yr half-life
– 0.55 W/g
Radioactivity
• In 1899, Ernest Rutheford discovered
Uranium produced three different kinds of
radiation.
– Separated the radiation by penetrating ability
– Called them a, b, g
• a-Radiation stopped by paper (He nucleus, 24 He )
• b-Radiation stopped by 6mm of Aluminum
(Electrons produced in the nucleus)
• g-Radiation stopped by several mm of Lead
(Photons with wavelength shortward of 124 pm or
energies greater than 10 keV)
a-Particle Decay
• The emission of an a particle, or 4He
nucleus, is a process called a decay
• Since a particles contain protons and
neutrons, they must come from the
nucleus of an atom
Ulysses RTG
• Pu-238
• Decay Branch leads
mostly to the emission of
a-particles
– Easily shielded
•
•
•
•
•
10.75 kg
4400 W or heat
PBOL = 285 W
PEOL = 250 W
Efficiency ~ 6.5 %
Solar Arrays
• A solar array is an assembly of
individual solar cells connected to
provide direct current power
– Power range: Few W to 10kW
– First array launched on Vanguard 1
in 1958
• Certain wavelengths of light are able
to ionize silicon atoms
• An internal field is produced by the
junction separates some of the
positive charges ("holes") from the
negative charges (electrons)
• The holes are swept into the positive
or p-layer and the electrons are
swept into the negative or n-layer
• Most can only recombine by passing
through an external circuit outside
the material because of the internal
potential energy barrier.
Solar Flux
• Solar Flux
– Maximum solar energy flux (normal to solar beam) variation
is quite significant at Earth orbit, between 1422 W/m2 at
perihelion to 1330 W/m2 at aphelion, a 6.7 % annual change
– Typically a value of 1358 W/m2 is used
Eclipse
• LEO
– Once per orbit typically,
except high inclinations
• GEO
– Equatorial plane is 23.5º
inclined relative to the ecliptic
plane
– Two eclipse “seasons”
centered around equinoxes
• 45 days
• Longest eclipse of about 70
minutes
shadow
Point B:
Satellite
Exits
Shadowed
Region
Point A:
Satellite
Enters
Shadowed
Region
Eclipse
--angular radius of
Earth
 (alternate interior
angles)
Satellite traverses
an angle of 2 in its
orbit from the time
it enters shadow to
the time it exits

R
h
R
 R 
  sin 

 R   h
1
2
Eclipse Time (Te ) 
(Orbital Period)
360
Configuration
Deployables
Solar Array Configurations
• Cylindrical
– Projected area of spinner is 1/ of surface
area of cylinder sides
r
PhysicalSurface Area, Ap  2rh
h
ProjectedEffective Area, Ae  2rh
 Ae 

1

Ap
Must account for orientation with respect to the
sun
Solar Array Configurations
• Omnidirectional
– Equal projected area from any direction (sphere)
– Used by many small-sats or low power S/C
(attitude doesn’t effect power generation)
– Projected area is ¼ of total surface area
P hysicalSurface Area, A p  4r 2
P rojectedEffect ive Area, Ae  r 2
1
 Ae  A p
4
Solar Array Configurations
• Inherent Degradation – loss of power from perfect case
• Shading of cells
• Temperature differential across solar array
• Real estate required for connections between cells
Solar Array Design
• What solar cell material we
choose
• Considerations:
–
–
–
–
–
Efficiency
Cost
Lifetime (radiation hardness)
Operating temperature
Ease of manufacturing (lay-up
panels)
– …
• Choice is application specific
Solar Array Design
Solar Array Design
From Spacecraft Systems
Engineering, by Fortescue
and Stark
Solar Array Characteristics
EPS—Design
Effect of Temperature on Solar Cell
Performance
From Space Vehicle Design, by Griffin and French
Solar Array Characteristics
From Space Vehicle Design, by Griffin and French
EPS—Design
Solar Array Design Process
(1&2) Calculate power output of Solar Arrays
Pd Td PeTe


Psa Td

Xd
Xe
S / A must sup ply

 

Total S / C energy
rqmt over one orbit
•
•
•
•
the
energy during daylight
portion of the orbit
Psa = power generated by solar array
Pe and Pd = S/C power loads during eclipse and daylight
Te and Td = times each orbit spent in eclipse and daylight
Xd = efficiency getting power from S/A directly to loads (typically
is 0.85)
• Xe = efficiency getting power from S/A to charge battery and
then from battery to the load (typical value is 0.65)
EPS—Design
Solar Array Design Process
(3&4) Determine size of arrays needed to generate power
W
PBOL  ( Flux )( ) ( I d ) cos   2 


m 
P from SMAD
o
• Po = power density output for cells (watts/m2)
– Flux (or Pi) = input solar power density (watts/m2)
–  (or ) = efficiency of solar cell material
• PBOL = power density S/A’s generate at beginning of
life (watts/m2)
• PEOL = power density at end of life (watts/m2)
• Id = inherent degradation
•  = sunlight incidence angle
EPS—Design
Solar Array Design Process
(5) Account for degradation due to exposure to the
space environment
PEOL
W
 PBOL Ld  ( Flux)( )(I d )(Ld ) cos  2 
m 
• PEOL = power density generated at end of life (watts/m2)
• LD = lifetime degradation
• A process will be defined later in this lecture for
determining Ld
EPS—Design
Solar Array Design Process
(6) Find size of solar array needed at end of life
 
Psa
Asa 
m2
PEOL
Substituting in previous equations:
 Pd Td PeTe 



Xe 
 Xd


Td




Asa 
m2
( Flux)( )(I d )(Ld ) cos
 
Solar Array Design Process
• Example Problem…
Energy Storage: Batteries
Primary Batteries
Secondary Batteries
EPS—Design
Battery Design Process
Equation for battery capacity:
PeTe
W  hr
Cr 
( DOD) Nn
• Cr = total S/C battery capacity
• Pe = average eclipse load (watts)
• Te = eclipse duration (hr)
• DoD = depth of discharge (0  DoD  1)
• N = number of batteries (need at least two if want some partial redundancy)
• n = transmission efficiency between battery and load (typical value is 0.9)
EPS—Design
Battery Design Process
EPS—Design
Battery Design Process
Battery Design Process
From Space Vehicle Design, by Griffin and French
Quantifying Solar Array Degradation
New values for Pmax, Vmp, Imp
Big Picture: Trying to go from
environment to performance
From Spacecraft Systems Engineering, by Fortescue and Stark and
NASA JPL Pub 96-9, GaAs Solar Cell Radiation Handbook
Effect of Charged Particles on Solar
Cells
• High energy protons & electrons collide with the crystal lattice
structure
• Collisions displace atoms from their lattice sites
• Eventually, the displaced atoms form stable defects
• Defects change the propagation of photoelectrons in the lattice
structure
Radiation Shielding


Coverglass tends to protect solar cells (from solar and
physical handling), but adds weight to design
Depending upon exact environment, more coverglass can
actually cause more damage to cells (because of high damage
caused by lower energy protons embedding in lattice)


Find optimum coverglass thickness for orbit – tedious
calculations
Assumptions/material properties:

Ratio of the solar cell coverage area to solar panel area: about 0.85
 Areal density of the solar array (before adding coverglass): about
0.3133 g/cm2
 Density of coverglass: about 2.2 g/cm3
Damage Equivalency: Electrons
• Solar cells damaged when struck by 1 MeV electrons
– Solar cells can be tested easily to characterize the effects of
radiation by using a stream of 1 MeV electrons (damage vs
number of electrons)
• Strategy: compare the damage done by a particle at a
particular energy level (E) to the damage done by a 1
MeV electron.
– Relationship is captured by damage coefficient [D(E,t)]
– Function of the energy of the particle and the thickness of the
protective shield in front of the solar cell (cover slide)
• Equivalency allows the damage done by all electrons to
be “Normalized” to equivalent 1 MeV electrons
Damage Equivalency: Electrons
# Particles
1234



n-1 n
Particle
energy
Particle energy distribution chart may be broken into ‘bins’ of energy levels
The particles from each bin cause a certain level of damage – equivalent to
some number of 1 MeV electrons
The total degradation (damage) to the arrays may be found by summing the
equivalent # 1 MeV electrons and reading experimental performance charts
Damage Equivalency: Protons
• Equivalency also allows damage done by protons to be
“Normalized” to equivalent 1 MeV electrons
– For Electrons: Table of damage coefficients converts the
damage done by one electron at an energy E to the damage
done by a number of equivalent 1 MeV electrons AND for
various solar cell cover slide thicknesses
– For Protons: Similar table converts protons to equivalent 10
MeV protons…BUT…The 10 MeV protons are then converted to
equivalent 1 MeV electrons:
Parameter
Factor
Pmax
1000
Voc
1400
Isc
400
(i.e. damage to Voc from one 10 MeV
proton equals damage from 1400 1
MeV electrons)
Solar Cell Performance: Max Power
From NASA JPL Pub 96-9,
GaAs Solar Cell Radiation
Handbook
# Electrons (cm-2 sec)
Quantifying Solar Array Degradation:
Process


# Protons (cm-2 sec)
400 450 500 550

Equivalent # 1 MeV
electrons/cm2  sec
Energy (KeV)
Equivalent # 10 MeV
protons/cm2  sec

35 40 45
Break up total particle
environment into energy bins
Energy (MeV)
Damage equivalency
Simplified Approach Process
Equivalent # 1 MeV
electrons/cm2  sec
due to electrons
(solar max & min)
Damage
equivalency
Equivalent # 1 MeV
electrons/cm2  sec
due to protons
(solar max & min)
+
Add
Total Equivalent no. of 1
MeV electrons/cm2  sec
(solar max & min)
Select worst case
(solar max or min)
Total Equivalent no. of 1
MeV electrons/cm2  sec
Power out/cm2
Integrate over
lifetime
Total # 1 MeV
electrons/cm2
Simplified Approach Example
From NASA JPL Pub 96-9, GaAs Solar Cell Radiation Handbook
Simplified Approach Example
From NASA JPL Pub 96-9, GaAs Solar Cell Radiation Handbook
Simplified Approach Example
max
same
min
From NASA JPL Pub 96-9, GaAs Solar Cell Radiation Handbook
EPS—Special Topics
Simplified Approach Example (cont’d)

For 0, 3000 nmi orbit with 30 mils coverglass, annual fluences
are:
Solar max

Solar min
Electron
fluence
(e/cm2/yr)
3.24E+12
1.85E+12
Proton fluence
(e/cm2/yr)
2.03E+15
2.03E+15
Total
(e/cm2/yr)
2.033E+15
2.031E+15
Worst case annual fluence is: 2.033E+15 (e/cm2/yr)
 Multiply by number of years for the mission
 Then use the appropriate chart in GaAs Handbook to figure
area needed for solar panel
Solar Cell Performance: Normalized Max
Power
From NASA JPL Pub 96-9,
GaAs Solar Cell Radiation
Handbook