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Satellite Torque Management Using Solar Array ThermalRadiation Control

James Wehner1, Lael von Eggers Rudd2, Christian Harris3, and Sam Foroozan4

Northrop Grumman Corporation, Los Angeles, CA, 90067

An innovative method for taking advantage of the torques produced by the thermalradiation of solar arrays is described. The method takes advantage of the difference inthermal properties between converting and un-converting portions of the solar arrays. Sincesatellites size their arrays for worst case conditions, a significant amount of the solar array istypically unused throughout most of the mission life. By proper distribution of which cellsare used to convert electricity, useful manageable torque is produced. It is shown that thismethod provides torques which are on the same order as solar disturbance torques, makingthe concept ideal for obviating the need for momentum unloading fuel for geostationarysatellites.

I. Introductionatellites in orbit about the Earth require some method for managing the environmental disturbance torquesinduced upon them. For geostationary (GEO) satellites this can be done in several ways. Propulsive unloading

(i.e. thruster firings) is the most common technique. Magnetic torque rods and gravity gradient torques areimpractical at these high altitudes. Solar-sailing momentum unloading techniques have also been used successfullyon several satellites, by clocking the solar arrays to generate “paddle” and “wind-mill” unloading torques. A similarapproach uses “solar tabs” attached to the out-most panel of each solar wing to generate the “paddle” and “wind-mill” torque effects. Finally, the use of thermal materials, such as electro-chromic materials, has been suggested.These electro-chromic materials are placed on the unpopulated sections of the solar array substrate panels.Electrical current stimulates the electro-chromic material, causing it to change optical properties, thereby generatingdifferential solar torques between the two solar arrays.

Each of these methods, while solving the torque management problem, has certain drawbacks. The propulsiveunloading requires additional fuel which increases the weight/cost of the satellite and places a definitive limit onmission lifetime. Solar-sailing techniques may require additional mechanical components and complexity. Electro-chromic approaches require complex material composites to carry current while being transparent to light, withsupporting electronic circuitry. Electro-chromic devices of this type are largely developmental and would requirespace qualification.

This paper discusses an approach which uses the difference in thermal properties of converting and non-converting solar arrays [1] to generate thermal radiation induced torques. Solar array segments are used to convertelectricity, with the current generation capability controlled through software in most modern spacecraft. Thesearrays are over-designed to account for seasonal and lifetime deterioration effects, thus substantial portions of thesearrays are often not required to generate electricity, and are unused. Due to the differential solar absorptance ofconverting and un-converting solar cells, converting and un-converting solar array segments behave very differentlyfrom a thermal perspective. Thermal gradients can result in differential thermal radiation which is realized as a

1 James Webb Space Telescope, Observatory Systems Engineering and Ground Operations Lead, R8/2789, OneSpace Park, Redondo Beach, CA, 90278, AIAA Member.2 Senior Engineering Technical Specialist, Advanced VMS and Flight Controls, One Hornet Way, W6/9V21, ElSegundo, CA, 90245, AIAA Senior Member.3 Senior Systems Engineer, Space & Optical Systems Center, M2/2311, One Space Park, Redondo Beach, CA,90278, AIAA Senior Member.4 EPS Project Manager, Power and Control Verification Department, R9/2960 G, One Space Park, Redondo Beach,CA, 90278.

S

AIAA Guidance, Navigation, and Control Conference10 - 13 August 2009, Chicago, Illinois

AIAA 2009-6111

Copyright © 2009 by Northrop Grumman Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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force, and likewise as moments about the spacecraft. By modifying software controlled power generation topreferentially utilize array segments, and take advantage of this effect, a small but substantial amount of torque, canbe generated. This torque can then be used to counteract environmentally induced disturbances, or unloadmomentum from momentum wheels. The torque generated by controlling solar array segments is comparable totypical environmental disturbances seen on orbit, obviating the need for momentum unloading fuel in many systems.Thus the prescribed method is capable of managing disturbance torques, using the existing hardware with onlymodifications to the flight software needed. Portions of this approach are the subject of pending U.S. patentapplications [1].

II. Solar Array SizingA typical spacecraft and solar array configuration is shown in Figure 1. While solar arrays vary significantly in

configuration, most modern solar array designs have array sections. Typically, but not always, the array consists oftwo identical wings, each divided into multiple sections. In modern spacecraft avionics, each section consists of agroup of parallel strings, and is electrically connected to an array regulator (AR), which regulates the voltage andpower output for that section. Figure 2 shows a block diagram of this electrical layout. Array section sizes vary, butare typically in the range of 250 to 500W maximum. Depending upon the power required, not all array sections areused, hence some sections are “converting” sunlight to electrical energy, while others are “un-converting”.

Converting Array Section

Un-Converting Array Section

Spacecraft Bus

Solar Array Sections

Solar Array Booms

Solar Array Wing

Solar Arrays Track Sun viaSolar Array Drive Assemblies (SADAs)

SunSpacecraft Bus

Solar Array Sections

Solar Array Booms

Solar Array Wing

Solar Arrays Track Sun viaSolar Array Drive Assemblies (SADAs)

Sun

Figure 1. Typical Spacecraft and Solar Array Configuration

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SOLARARRAY

SECTIONS

ARE 2

ARE 1

1 AR 1

2 AR 2

3 AR 3

4 AR 4

5 AR 5

AR 6

SPG

BATTERY

Power Control andDistribution Electronics

LOAD

Cell 1

Cell m

String 1 String n

Cell 1

Cell m

String 1 String n

» Each section consists of n diode isolated strings in parallel.» Each string includes m cells in series.» m and n are determined by required power and voltage.

Figure 2. Electrical Power Subsystem Block Diagram

Figure 3 shows a diagram of the satellite in geosynchronous orbit, and the view the solar arrays will have of thesun. In order to provide adequate energy at worst case conditions, arrays are typically oversized for nominaloperations. In GEO orbit, solar arrays are generally sized for:

1) Worst case eclipse conditions (~1.2 hrs max during 24 hr orbit)2) Two ~45 day periods for GEO orbits center around the equinoxes (Figure 4)3) End-of-Life (EOL) conditions. (Array output power degrades by several percent for the first year and

~0.5% per year subsequently.)4) ~15 to 20 hrs for battery recharge after an equinox discharge, and must include the effects of battery

charge/discharge efficiencies (~75%)As a result array power with normal sun at BOL typically generates ~1.20 times the amount of power as one at EOL.Figure 5 shows the worst case relative power output from BOL to EOL degradation in GEO. Table 1 shows thesolar array sizing and power generation for typical GEO conditions. Using the information in Table 1, the solararray generation capability compared to the required capability can be computed. Once this is known, the excesspower capability, as a fraction of the load power, can be determined. Both of these are plotted versus for BOL andEOL in Figures 6 and 7. As can be seen there is a significant amount of excess power available from the solararrays during much of the mission life, than is required from nominal operations.

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SunSun

Geosynchronous Orbit (24 hr period)

Shadow Region (Equinox)

View from Normal to the Ecliptic

Solar Array Orientation During Orbit- Solar Cells Face the Sun

Earth

N

S

View from the Ecliptic

Equinox

SummerSolstice

WinterSolstice

23.5o (solar declination)

Figure 3. Diagram of Sun Tracking by Solar Arrays

Winter Solstice Vernal Equinox Summer Solstice Autumnal Equinox

EclipseDuration

1.2 hrs

Time

45 days 45 days

Winter Solstice Vernal Equinox Summer Solstice Autumnal Equinox

EclipseDuration

1.2 hrs

Time

45 days 45 days

Figure 4. Eclipse Duration Diagram

Figure 5. Worst Case Solar Array BOL to EOL Degradation in GEO

0%

20%

40%

60%

80%

100%

120%

0 2 4 6 8 10 12 14 16

Years

Rel

ativ

eO

utp

ut

Po

wer

(W)

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Table 1. Solar Array Sizing and Power Generation for Typical Conditions� EOL Equinox: Psa, EOL, normal = 1.150 P load

� EOL Start of eclipse season: Psa, EOL, 8.9 deg = 1.257 P load

� EOL Solstice: Psa, EOL, 23.5 deg = 1.168 P load

� BOL power is substantially greater than EOL due to array degradation– BOL solar array power is ~1.2 x EOL power

� BOL Equinox: Psa, EOL, normal = 1.380 P load

� BOL Start of eclipse season: Psa, EOL, 8.9 deg = 1.508 P load

� BOL Solstice: Psa, EOL, 23.5 deg = 1.402 P load

Figure 6. Solar Array Power Generation Capability vs. Required Capability

Figure 7. Solar Array Excess Power Capability

III. Solar Array Thermal TorqueThe thermal properties between a converting and un-converting solar array are different due to the change in

solar absorptance, αsolar. An un-converting array typically has a larger absorptance value. The total energy absorbedand re-radiated is proportional to the absorptance value. Therefore, greater energy is absorbed and re-radiated from

Excess Power Capability (Fraction of Load)

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0 50 100 150 200 250 300 350

Day of Year (1 - Jan 1)

Fra

ctio

nof

Load

Pow

er

Excess Capability(P(L) fraction, EOL)

Excess Capability(P(L) fraction, BOL)

Solar Array Power Generation Capability vs. RequiredCapability (BOL and EOL)

0.00000.10000.20000.30000.40000.50000.60000.70000.80000.90001.00001.10001.20001.30001.40001.50001.6000

0 50 100 150 200 250 300 350

Day of Year (1 - Jan 1)

SA

Po

wer

/Loa

dP

ow

er P(SA)/P(L)(EOL, req)

P(SA)(EOL, cap)

P(SA)(BOL, cap)

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an un-converting array, with the infrared energy typically radiated in a Lambertian pattern. The energy conductedthrough the array is re-radiated from the back side. The temperature gradient through the panel is proportional to theenergy conducted and re-radiated. It is this differential temperature gradient which generates different net forces onconverting and un-converting array sections. Figure 8 shows a diagram of the above idea.

Un-converting Solar Array Converting Solar Array

Sun

FrontBack

αsolar/εhemispherical

= 0.92/0.82εhemispherical = 0.85

Al honeycomb coreor equivalent

Solar Cell(with cover glass)

Adhesive

High emissivity coating(white or black paint)

Front and Backfacesheets SunSun

FrontBack

αsolar/εhemispherical

= 0.92/0.82εhemispherical = 0.85

Al honeycomb coreor equivalent

Solar Cell(with cover glass)

Adhesive

High emissivity coating(white or black paint)

Front and Backfacesheets Sun

FrontBack

αsolar/εhemispherical

= 0.75/0.82εhemispherical = 0.85

Al honeycomb coreor equivalent

Solar Cell(with cover glass)

Adhesive

High emissivity coating(white or black paint)

Front and Backfacesheets SunSun

FrontBack

αsolar/εhemispherical

= 0.75/0.82εhemispherical = 0.85

Al honeycomb coreor equivalent

Solar Cell(with cover glass)

Adhesive

High emissivity coating(white or black paint)

Front and Backfacesheets

Figure 8. Solar Array Heat Absorption and Rejection

The black body radiation from the temperature produces a pressure according to:

( )c

TTP

BackBackFront Front

−

= πσεε 244

(1)

Where P is pressure, T is temperature, σ is the Stephen-Boltzmann constant, and c is the speed of light, and the 2/πis the Lambertian coefficient. As this equation shows, small temperature differences can produce significantpressures. By taking advantage of this effect and controlling which cells are converting and unconverting, the arrayscan be used as actuators to produce torque. Figure 9 shows possible configurations for converting and unconvertingarchitectures. For analysis purposes and to characterize performance, a 10 m^2 solar array with a 15 m moment armhas been assumed. This size of array was used to compare torques to spacecraft of similar power levels. Thepower generated from these arrays in this example is ~2.3 kW. This is low for many spacecraft, and typically GEOsatellites would have power usages on the order of 5 to 10 kW. Thus it would be expected that the amount of usefultorque will be even greater than what will be shown in the following example. Using Eqn. 1 to get the pressure, thetorque of each array can be calculated for one converting and one non-converting. The results of these calculationsare shown in Table 2. As seen a differential torque of 5.26E-6 ft-lb is produced. This torque is approximately equalto the solar disturbance torque for GEO satellites (discussed in the next section). The analysis has assumed a 15 oFpanel through conductance in the un-converting state. It has also assumed a linear relationship of heat flow fromfront to back. The honeycomb panels, used in most solar arrays, limit radiation between the front and backfacesheets. Therefore, conduction typically dominates and panel heat transfer from front to back is commonlymodeled as linear. Also, while temperature gradients will vary widely, 15 oF is low for many array designs. If apoorer array through conductance exists and the through gradient is increased to 30 oF the solar torque increases to1.03E-5 ft-lb (almost twice as much for the 15 oF increase).

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Spacecraft Bus

Solar Array Booms

Solar Array Wing

Converting Array Section

Un-Converting Array Section

x

y

z

x

y

z Axes Definition for Figures

No Torque Generated Torque GeneratedAbout X Axis

Torque GeneratedAbout Y Axis

Torque GeneratedAbout Z Axis

(array axes skewed –current state of the art)

Figure 9. Possible Solar Array Architectures to Generate Torque

Table 2. Thermal Torque Analysis

UnconvertingFront: 156.9 F = 342.7 KBack: 141.9 F = 334.4 K

P=1.56E-7 N/m^2T=2.33E-5 N-m

ConvertingFront: 125.2 F = 325.1 KBack: 112.9 F = 318.3 K

P=1.10E-7 N/m^2T=1.64E-5 N-m

Differential Torque = Tunconv – Tconv = 6.92E-6 N-m = 5.26E-6 ft-lb

Assumes 10 square meter solar array with 15 meter moment arm

IV. Application to Satellite Momentum ManagementUsing the results from the last two sections, the excess torque produced during the year can be calculated for

BOL and EOL. This is shown in Figure 10. The torque produced by the solar arrays is on the same order as thesolar disturbance torque for GEO satellites. Data from various flown GEO satellites is shown in Figure 11 to verifythis claim [2]. Furthermore, by controlling which parts of the arrays are chosen to convert and un-convert, thetorques about different axes are possible (as shown previously in Figure 9). This method introduces virtually noACS or EPS hardware implications. Current solid state power converter electronics (AREs) are continuallyadjusting array output power to meet load demands, and proposed usage for this approach is well within theircapability. The current concept simply changes which array sections are active. No additional magnetic moment isinduced as potential electrical current induced moments are typically eliminated at the array section level. Also,there are no additional changes to the existing attitude control system (ACS) sensors or actuators. Effectively, thearray becomes an actuator. This method reduces the fuel consumption for GEO satellites. Typical GEO launchcosts are ~$40k/lb. Table 3 shows the typical fuel consumption and potential cost savings for this concept.

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Excess Torque

0.0000E+00

2.0000E-06

4.0000E-06

6.0000E-06

8.0000E-06

1.0000E-05

1.2000E-05

1.4000E-05

0 100 200 300 400

Day of Year

To

rqu

e(N

-m)

Excess Torque (N-m)EOL capability

Excess Torque (N-m)BOL capability

Moment arm = 15 mArray area = 50 m^2

Figure 10. Excess Torque Capability

Solar Pressure•< 0.5 ft-lb-sec/day (5.8x10-6 ft-lb)Commercial Communications Satellites

Solar Pressure•0.50 ft-lb-sec/day (5.8x10-6 ft-lb)Program X

Dominant Torque Source•Solar Pressure•Thermal Pressure•Thermal Pressure•Solar Pressure

Reference 1:•0.10 ft-lb-sec/day (1.2x10-6 ft-lb)•0.54 ft-lb-sec/day (6.5x10-6 ft-lb)•0.42 ft-lb-sec/day (5.0x10-6 ft-lb)•~0.1 ft-lb-sec/day (1.2x10-6 ft-lb)

TDRS•Flight-1•Flight-3•Flight-4•Flights 5-7

CommentsRoll/Yaw Momentum Accumulation Rate (Equiv. secular torque, ft-lb)

Satellite Program

Solar Pressure•< 0.5 ft-lb-sec/day (5.8x10-6 ft-lb)Commercial Communications Satellites

Solar Pressure•0.50 ft-lb-sec/day (5.8x10-6 ft-lb)Program X

Dominant Torque Source•Solar Pressure•Thermal Pressure•Thermal Pressure•Solar Pressure

Reference 1:•0.10 ft-lb-sec/day (1.2x10-6 ft-lb)•0.54 ft-lb-sec/day (6.5x10-6 ft-lb)•0.42 ft-lb-sec/day (5.0x10-6 ft-lb)•~0.1 ft-lb-sec/day (1.2x10-6 ft-lb)

TDRS•Flight-1•Flight-3•Flight-4•Flights 5-7

CommentsRoll/Yaw Momentum Accumulation Rate (Equiv. secular torque, ft-lb)

Satellite Program

Thermal radiation induced torques due to differential emissivities on north and south solar arrays. Resultant torques were substantiallyhigher than anticipated and greater than the torque of TDRS Flight-1 which had similar array thermophysical properties.

References:1.) “Effect of Thermal Radiation Torques on the TDRS Spacecraft”, C. Harris and G. Kyroudis, TRW Space & Technology Group,Paper No. AIAA-90-3492-CP.

Torques on typical GEO spacecraft are less than, or equal to, that achieved by the approach of the current method (note value of 5.3e-6 ft-lb fromprevious analysis vs. 1.2e-6 for the balanced array design of TDRS Flight-1).This indicates that the control magnitude using the techniques of this concept can obviate the need for nearly all momentum management fuel.

Figure 11. Typical Solar Torques and Momentum Accumulation

Table 3. Fuel Consumption for Momentum Unloading

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5 Kg10HEOProgram Y

36 Kg15GEOCommercial Communications

34 Kg11L2Program Z

GEO

GEO

Mission Orbit

12 Kg5Program X

24 kg10TDRS F1-F7

Fuel Consumption for Momentum Unloading over

Mission Life(kg of Hydrazine)

Mission Life (Years)

Satellite Program

5 Kg10HEOProgram Y

36 Kg15GEOCommercial Communications

34 Kg11L2Program Z

GEO

GEO

Mission Orbit

12 Kg5Program X

24 kg10TDRS F1-F7

Fuel Consumption for Momentum Unloading over

Mission Life(kg of Hydrazine)

Mission Life (Years)

Satellite Program

Note:Launch costs for GEO are ~$80K/kg

Dollarized cost savings (~80% of momentum unloading fuelconsumption) = $2304 K for commercial comm satellites

The main modification to be made using this concept is to the ACS and electrical power system (EPS)algorithms and software. These changes are minor in nature. The concept does require additional coordinationbetween the ACS and EPS subsystem engineers to integrate the algorithms. The majority of the ACS system is thesame so the majority of algorithms stay the same. The only portion that changes is the portion which replaces oraugments the thruster based momentum control unloading algorithms. This is shown in Figures 12 and 13, whereFigure 12 corresponds to a typical thruster based system, and Figure 13 represents the proposed system being usedinstead.

Figure 12. Typical Attitude Control Block Diagram

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Figure 13. Combined Attitude Control/Power Generation Block Diagram

V. ConclusionAn innovative method has been described for momentum unloading by taking advantage of the inherent thermal

properties of the solar arrays. The converting and un-converting portions of the arrays produce varying torques dueto the difference in temperature, and thus radiative pressure. By controlling which sections of these arrays convert,the thermal radiation torque can be controlled. These torques have been shown to be on the same order as thedominating solar disturbance torque for GEO satellites. Thus, with only minor modifications to algorithms andsoftware, this concept can be used in place of thrusters for momentum control, obviating the need for substantialamounts of fuel. Dollarized mass cost savings for a GEO communications satellite can be in excess of $2M.

References[1] Wehner, J., Rudd, L., Harris, C., and Foroozan, S., Northrop Grumman Corporation., Los Angeles, CA, U.S. Patent

Application for a “Satellite Torque Control by Solar Array Thermal Radiation Management,” Docket No. 002356-804, filed Jan.2008.

[2] Harris, C., and Kyroudis, G., “Effect of Thermal Radiation Torques on the TDRS Spacecraft,” AIAA-90-3492-CP, 1990.